Design of Adaptive Wing Sections with Natural Transition [PDF]

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Design of Adaptive Wing Sections with Natural Transition

Von der Fakult¨at f¨ur Maschinenwesen der Rheinisch–Westf¨alischen Technischen Hochschule Aachen zur Erlangung des akademischen Grades eines Doktors der Ingenieurwissenschaften genehmigte Dissertation

vorgelegt von Alexander Meijering aus Katwijk (ZH), Niederlande

Berichter: Universit¨atsprofessor Dr.-Ing. Wolfgang Schr¨oder Universit¨atsprofessor Dr.-Ing. Dieter Jacob Tag der m¨undlichen Pr¨ufung: 27.03.2003

D 82 (Diss. RWTH Aachen)

Berichte aus der Strömungstechnik

Alexander Meijering

Design of Adaptive Wing Sections with Natural Transition

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D 82 (Diss. RWTH Aachen)

Shaker Verlag Aachen 2003

Bibliographic information published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data is available in the internet at http://dnb.ddb.de. Zugl.: Aachen, Techn. Hochsch., Diss., 2003

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Copyright Shaker Verlag 2003 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the publishers. Printed in Germany. ISBN 3-8322-2265-0 ISSN 0945-2230 Shaker Verlag GmbH • P.O. BOX 101818 • D-52018 Aachen Phone: 0049/2407/9596-0 • Telefax: 0049/2407/9596-9 Internet: www.shaker.de • eMail: [email protected]

Mijn ouders

Vorwort Diese Arbeit entstand w¨ahrend meiner T¨atigkeit als wissenschaftlicher Angestellter am Aerodynamischen Institut der RWTH-Aachen und wurde im Rahmen des von der Deutschen Forschungsgemeinschaft finanzierten Sonderforschungsbereichs 401 initiiert. Herrn Professor Dr.-Ing. Wolfgang Schr¨oder gilt mein besonderer Dank f¨ ur die wissenschaftlichen Anregungen, seine stete Diskussionsbereitschaft und die wissenschaftliche Bet¨atigungs¨ freiheit. Herrn Professor Dr.-Ing. Dieter Jacob danke ich f¨ ur die Ubernahme des Koreferates und das der Arbeit entgegengebrachte Interesse. F¨ ur die F¨orderung der Arbeit danke ich Herrn Dr.rer.nat. Wolfram Limberg. Frau Dr.-Ing. Cornelia Hillenherms danke ich f¨ ur die ausgezeichnete Zusammenarbeit bei der Erweiterung der Messwerterfassungstechnik und dem Aufbau der Steuerungs- und Auswertesoftware am trisonik Windkanal sowie f¨ ur die stete Diskussionsbereitschaft. Den Herren Dr.-Ing. Guido Dietz, Stefan M¨ahlmann, Dr.-Ing. Matthias Meinke, Dr.-Ing. Andreas Henze, Dr.-Ing. Ehab Fares und Ingolf H¨orschler bin ich f¨ ur ihre wertvollen Ratschl¨age, konstruktive Kritik und Unterst¨ utzung, die Sie mir entgegenbrachten, sehr dankbar. Bei den Herren Thomas M¨ uller, Zsolt Balogh und Martin Sindermann m¨ochte ich mich stellvertretend f¨ ur alle Studienund Diplomarbeiter sowie studentischen Hilfskr¨afte bedanken. Des Weiteren bedanke ich mich stellvertretend f¨ ur die mechanische Werkstatt bei den Herren Karl-Heinz Radermacher, Hans Kreutz und Stefan Baumann, die mich bei der Entwicklung des adaptiven Tragfl¨ ugelprofilmodells unterst¨ utzt haben. Meinen Eltern bin ich besonders dankbar, da sie mich stets in meinen Entscheidungen unterst¨ utzt haben. Nicht zuletzt gilt mein Dank meiner Frau Claudia f¨ ur ihren Zuspruch und ihr Verst¨andnis.

M¨ unchen, in November 2003.

Alexander Meijering

i

Contents ¨ Abstract / Ubersicht . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

iv

Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

v

1 Introduction

1

2 Previous Research and Problem Definition

7

2.1

Laminar-Turbulent Transition . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7

2.1.1

Transition Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.1.2

Laminarization Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.2

Shock/Boundary-Layer Interference . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.3

Aerodynamic Characteristics of Airfoil Sections . . . . . . . . . . . . . . . . . . 15

2.4

Flow Control by Adaptive Shape Variation . . . . . . . . . . . . . . . . . . . . . 17

2.5

Aerodynamic Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.6

Objectives of this Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3 Aerodynamic Shape Design

23

3.1

Formulation of the Optimization Problem . . . . . . . . . . . . . . . . . . . . . 23

3.2

Evolution Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.2.1

3.3

3.4

Validation of the Optimization Algorithm . . . . . . . . . . . . . . . . . 30

Constrained Airfoil Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.3.1

Implementation of Constraints . . . . . . . . . . . . . . . . . . . . . . . . 35

3.3.2

Airfoil Shape Parameterization . . . . . . . . . . . . . . . . . . . . . . . 37

Numerical Flow Simulation Methods . . . . . . . . . . . . . . . . . . . . . . . . 40 3.4.1

Mathematical Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . 41

3.4.2

Viscous-Inviscid Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

3.4.3

Field of Application of each Flow Computation Approach . . . . . . . . . 46

ii

Contents

4 Test Facility and Models 4.1

4.2

49

Trisonic Wind Tunnel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 4.1.1

Adaptive Wall Test Section . . . . . . . . . . . . . . . . . . . . . . . . . 51

4.1.2

Flow Quality of the Test Section

. . . . . . . . . . . . . . . . . . . . . . 52

Wind Tunnel Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 4.2.1

Rigid Wing Section Model . . . . . . . . . . . . . . . . . . . . . . . . . . 57

4.2.2

Adaptive Wing Section Model . . . . . . . . . . . . . . . . . . . . . . . . 59

5 Measurement Techniques

65

5.1

Acquisition of the Aerodynamic Coefficients . . . . . . . . . . . . . . . . . . . . 65

5.2

Transition Location and Separation . . . . . . . . . . . . . . . . . . . . . . . . . 67

5.3

5.4

5.5

5.2.1

Hot-Film Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

5.2.2

Liquid-Crystal Coating Technique . . . . . . . . . . . . . . . . . . . . . . 71

Flow Visualization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 5.3.1

Oil Pattern Visualization . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

5.3.2

Optical Flow Visualization . . . . . . . . . . . . . . . . . . . . . . . . . . 73

Determination of the Mass Flux and Pressure Fluctuations . . . . . . . . . . . . 75 5.4.1

Hot-Wire Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

5.4.2

Pitot-Pressure Technique . . . . . . . . . . . . . . . . . . . . . . . . . . 78

Wind Tunnel Control and Data Acquisition . . . . . . . . . . . . . . . . . . . . 78

6 Results for the Rigid Surface Airfoil

81

6.1

Comparison of the Experimental and Numerical Methods . . . . . . . . . . . . . 81

6.2

Subsonic Laminar Separation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

6.3

Shock-Free Transition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

6.4

Shock/Boundary-Layer Interaction . . . . . . . . . . . . . . . . . . . . . . . . . 90

7 Numerical Airfoil Shape Optimization

95

7.1

Determination of the Population Size . . . . . . . . . . . . . . . . . . . . . . . . 95

7.2

Determination of the Shape Parameterization . . . . . . . . . . . . . . . . . . . 98

7.3

One-Point Airfoil Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 7.3.1

Airfoil Design at Subsonic Speeds . . . . . . . . . . . . . . . . . . . . . . 101

7.3.2

Airfoil Design at Transonic Speeds . . . . . . . . . . . . . . . . . . . . . 103

iii

7.4

Adaptive Airfoil at Transonic Speeds . . . . . . . . . . . . . . . . . . . . . . . . 104

7.5

Selection of Airfoil Shapes for Experimental Tests . . . . . . . . . . . . . . . . . 108

8 Experimental Results for the Adaptive Wing Section

111

8.1

Subsonic Airfoil Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

8.2

Transonic Airfoil Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

8.3

8.2.1

The Impact of the Airfoil Design on Local Separation . . . . . . . . . . . 114

8.2.2

Shock Strength Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . 119

Adaptive Wing Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

Summary

123

Bibliography

127

iv

Abstract To meet the requirements to enhance the airfoil performance at transonic speeds the potential of the adaptive wing technology is investigated in this work. The shock/boundary-layer interaction along with the implementation of the laminarization concept in the constrained aerodynamic design have been analyzed using numerical and experimental methods. The selection of the parameterization method of the airfoil shape and the handling of constraints are emphasized. For the investigations in the wind tunnel an adaptive wing section model has been designed and successfully tested in experiments. The aerodynamic design demonstrates the potential of the adaptive wing technology with natural transition by improving the aerodynamic characteristics of the initial LVA-1A airfoil shape at 20 transonic flight conditions. Experimental investigations with respect to the transition location and associated flow phenomena, using the hot-film technique and the liquid-crystal coating on the developed rigid surface model and the adaptive surface model validate the numerical findings. The adaptation mechanisms of the subsonic and transonic speed regime are discussed. Moreover, the reliability of the adaptive wing section model for tests with /mbox natural transition at these speeds is shown. The combination of the numerical and experimental methods demonstrates the improvement of the aerodynamic characteristics by shape adaptation at the Reynolds numbers under consideration.

¨ Ubersicht Um der Forderung einer Verbesserung der Tragfl¨ ugelprofilleistung bei schallnahen Geschwindigkeiten gerecht zu werden, wird das Leistungsverm¨ogen der adaptiven Fl¨ ugeltechnologie in der vorgelegten Arbeit untersucht. Die Stoß-Grenzschichtwechselwirkung sowie die Realisierung der Laminartechnologie im aerodynamischen Entwurf mit Nebenbedingungen werden mittels numerischer und experimenteller Methoden analysiert. Besondere Beachtung erf¨ahrt die Auswahl der Geometrieparametrisierungsmethode des Tragfl¨ ugelprofils sowie die Behandlung der Nebenbedingungen. F¨ ur die Untersuchungen im Windkanal wird ein adaptives Tragfl¨ ugelprofilmodell entworfen und erfolgreich im Experiment eingesetzt. Der aerodynamische Profilentwurf zeigt das Potential der adaptiven Tragfl¨ ugeltechnologie mit nat¨ urlicher Transition auf, indem die aerodynamischen Eigenschaften des Anfangsprofils LVA-1A bei 20 transsonischen Flugbedingungen verbessert werden. Die experimentelle Untersuchung hinsichtlich der Transitionslage und der damit verbundenen Str¨omungsph¨anomene anhand der Heissfilm- und der Fl¨ ussigkristalltechnik auf dem Modell mit starrer Kontur und dem adaptiven Konturmodell best¨atigen die numerischen Ergebnisse. Die Adaptionsmechanismen im Unterschall sowie im schallnahen Bereich werden diskutiert. Zus¨atzlich wird die Einsatzf¨ahigkeit des adaptiven Tragfl¨ ugelprofilmodels in Untersuchungen mit nat¨ urlicher Transition bei diesen Geschwindigkeiten nachgewiesen. Die Kombination der numerischen und experimentellen Methoden belegt die Verbesserung der aerodynamischen Eigenschaften durch Adaption der Profilkontur bei den betrachteten Reynolds Zahlen.

v

Nomenclature

Latin symbols A a ak
a c c¯ CL , CD d E E F¯ F f fGauß G Gr g gk ¯ H I K k km , kθ L/D Ma m N(.,.) Nt N Nu n n
n P Pr p

wave amplitude speed of sound polynomial coefficient (eqn.(3.22)) representation of an individual chord length set of strategy parameters coefficients of lift, and drag hot-wire diameter anemometer output voltage total energy flux vector curtosis objective function Gaussian normal distribution function hot-wire calibration coefficient Grasshof number constraint function base function Hessian matrix space of individuals number of base functions wave number mass flux and temperature sensitivity lift-to-drag ratio Mach number mutation operator Gaussian normal probability density function number of discrete measurement points integrated growth rates (eqn.(2.2)) Nusselt number number of objective variables hot-wire calibration coefficient wall normal vector population Prandtl number pressure

vi

Nomenclature

Latin symbols (continued)
Q Q Q q
q R Ra , Rw Re r r S s T t Tu
x x, y, z u, v, w
v

vector of conservative variables penalty function hot-wire calibration coefficient number of constraints heat transfer rate nose radius of a wing resistance of the Wheatstone bridge and the hot-wire Reynolds number recovery factor recombination operator skewness selection operator temperature time turbulence level design variables cartesian coordinate system components of the velocity vector in the cartesian coordinate system velocity vector in in the cartesian coordinate system

Greek symbols α
α α δ ∆t ∆y  χ ηk Φ ϕ φ ι λ λ λ µ µ Ψ ρ

vector of rotation angles angle of attack wavenumber boundary-layer thickness distance of a violated constraint to the feasible region vertical perturbation of the initial airfoil shape ellipticity intermediate factor amplitude of base function fitness value sweep angle normalized penalty truncation criterion wave length offspring population in evolution strategy thermal conductivity coefficient dynamic viscosity parent population in evolution strategy linear correlation coefficient density

vii

Greek symbols (continued) ν kinematic viscosity σ growth rate σ standard deviation (root mean square) σsep , σthick control parameter for the penalty operator on separation and airfoil thickness τ¯ shear stress tensor τ overheat ratio τ, τ
learning rates τr relaxation time

superscripts ()
fluctuating part of a quantity ∗ value at the global extremum τ generation counter

subscripts A crit D e i,j,k,n init ref 0 ∞ Θm ,Θr ,Θs ,Θp

θ

advective part critical value diffusive part value at the edge of the boundary layer counter initial value reference quantity total quantity or initial value freestream quantity Set of parameters monitoring the operators of mutation, recombination, selection, and penalty, respectively Based on the momentum thickness

viii

Nomenclature

Abbrieviations AD ADIF AFTI AIA ALT ATTAS CFI DLR EA EBL ELFIN EP ES EXP FWHM GA GPIB HLFC LFC LST MAW NCP NLF NS NUM PSD RMS SBI SCB TSI TSP

Automatic Differentiation Adaptronik im Fl¨ ugel Advanced Fighter Technology Integration Aerodynamisches Institut of the university of technology RWTH Aachen Attachment Line Transition Advanced Technologies Testing Aircraft System Crossflow Instability Deutsches Zentrum f¨ ur Luft- und Raumfahrt Evolutionary Algorithms Euler-Boundary-Layer method European Laminar Flow Investigation Evolutionary Programming Evolution Strategy Experimental results Full Width Half Maximum Genetic Algorithms General Purpose Interface Bus Hybrid Laminar Flow Control Laminar Flow Control Linear Stability Theory Mission Adaptive Wing Nonlinear Constrainted Optimization Problem Natural Laminar Flow Navier-Stokes method Numerical results Power Spectral Density Root-Mean-Square Shock/Boundary-layer Interaction Shock Control Bump Tollmien-Schlichting Instability Transonic Small Perturbation

Chapter 1 Introduction The increasing competition among the airlines combined with the demands for high cruise speeds of transport aircraft require the design of new wing sections to reduce the fuel consumption and hence, to lower the direct operating costs [78]. The flight performance of aircraft is governed by aerodynamics, structural mechanics, and propulsion. As demonstrated in figure 1.1 (left) the fuel reduction based on the total flight distance of an aircraft obtainable by aerodynamic means is estimated at 36% [173]. This high potential is based on an increase of the lift-to-drag ratio, which is primarily obtained through a substantial drag reduction. To improve the performance of aircraft from an aerodynamic point of view one focuses on the cruise performance, which is the dominating segment of flight for long range aircraft. To meet the demands for high cruise speeds in the transonic range the development of supercritical airfoils, that started in the 1960’s, represents a major improvement of the aerodynamic performance compared to conventional airfoil shapes. For further assessment of drag reduction technologies the drag breakdown at cruise conditions for a modern transport aircraft equipped with a modern supercritical wing is analyzed in figure 1.1 (right). Approximately 40% of the friction drag is due to the wing flow, which corresponds to 20% to 25% of the total amount of drag of an aircraft. By reducing drag the amount of thrust required by the turbine engines is also decreased, which yields a reduction of fuel as well as the environmental emission. Thus, smaller engines are required, which in turn reduce the take-off weight due to the so-called snowball effect [72]. To clarify the significant differences in aerodynamic behavior of the airfoil flow at subsonic or transonic freestream conditions the influence of an increasing Mach number on the total drag will be described for the supercritical airfoil RAE 2822 [33] (figure 1.2). At a subsonic Mach number Ma∞ =0.65 the pressure distribution remains above the critical pressure (dashed line). This means that the flow remains subsonic over the airfoil at all times. The freestream Mach number for which the flow locally accelerates to the speed of sound is identified as the critical Mach number. As the Mach number increases to Ma∞ =0.72 the flow isentropically accelerates to supersonic speed followed by isentropic recompression. For further increase of the Mach number and angle of attack above the design point a shock occurs on the suction 1

2

Chapter 1.

E n g in e 2 3 % W

8 % W e ig h t

P a r a s itic d r a g

1 0 0

W a v e In te rfe re n c e

9 0

A fte r B o d y

8 0

5 0 %

T r ip f u e l / d is t a n c e

S F C

1 0 0 %

T e c h n o lo g y s t a t u s

R e d u c t io n p o t e n t ia l m o re th a n 5 0 %

L / D A e ro 3 6 %

Introduction

% T o ta l a ir c r a ft d ra g

7 0 6 0

In d u c e d D ra g

5 0 4 0

3 0 2 0

F r ic tio n d ra g

1 0

0 %

Fig. 1.1: Left: Estimated fuel reduction potential [173]. Right: Total drag breakdown at cruise conditions [65, 165]. side (Ma∞ =0.74). The shock causes an increase of boundary-layer thickness and entropy, which results in an increase of friction drag and wave drag. Further increase of the Mach number generally shifts the shock towards the trailing edge so that an interaction between the separation region and the airfoil trailing edge flow can occur (Ma∞ =0.78). Separation of the flow over the surface arises if the wall nearest streamline detaches from the surface. A separation bubble is formed when the flow reattaches to the surface Due to unsteady effects associated with separation, this yields shock oscillations on the airfoil suction side. This unsteady phenomenon is referred to as buffeting. Airfoil shapes are not referred to as supercritical shapes because they operate at supercritical speeds. The reason is unlike conventional airfoil shapes e.g. NACA series they retain their aerodynamic efficiency at such speeds. Supercritical airfoils are designed to delay and reduce the transonic drag rise, caused by the shock and the shock-induced boundary layer separation. The described phenomena originate from the interaction between the shock and the boundary layer. The so-called shock-boundary-layer interaction (SBI) is a crucial difference between the airfoil aerodynamics in a subsonic freestream flow and at transonic conditions, that significantly determines the airfoil drag, particularly wave drag, and flight performance. The main sources of airfoil drag have been identified. The next step will determine the measures that aim at the reduction of the total drag without deteriorating other aerodynamic characteristics. From figure 1.1 the necessity to reduce the friction drag of the wings is obvious. This viscous drag depends on the state of the boundary layer. Compared to the laminar boundary layer the turbulent one is characterized by an increased energy dissipation that results in a substantially higher wall shear stress. Hence, a long extent of the laminar boundary layer is favorable for drag reduction. Initially, the boundary layer near the wing leading edge can be considered laminar. However, due to the growth of velocity, temperature and pressure fluctuations in the boundary layer transition occurs. Already in 1883 Reynolds [164] suspected that the transition phenomenon could originate from an instability mechanism of the laminar

3

0.506 1.5

1.5

Ma =0.70 ∞

1 0.5

0

0

0.504

−0.5

−0.5

−1

−1

0.4

0.6

0.8

1

−1.5

D

0.2

C

0

1.5

0.503

Ma∞=0.65

0.5

0

0.2

0.4

0.8

−1.5

1

trailing edge separation

0

0.2

0.4

0.6

0.8

1

1.5

Ma∞=0.72

Ma∞=0.76

1

0.5

0.5

−C

p

0.502

0.6

1.5 1

0.5

Ma∞=0.78

1

0.5

−1

1

∞

0.505

0 −0.5

−1.5

1.5

Ma =0.74

1

0

0

0

−0.5

−0.5

−0.5

0.501

−1 −1.5

0

0.2

0.4

0.6

x/c

0.8

−1 −1.5

1

0.5

0.66

−1 0

0.2

0.68

0.4

0.7

0.6

0.8

0.72

Ma

−1.5

1

0.74

0.76

0

0.2

0.4

0.6

0.8

1

0.78

∞

Fig. 1.2: Development of transonic drag with increasing Mach number of the RAE 2822 airfoil [33] at CL =0.50 at a chord Reynolds number of Re∞ = 2.6 · 106 . boundary layer with respect to small disturbances. This initiated experimental and numerical research to investigate the instability mechanisms to determine measures that influence the laminar/turbulent boundary-layer transition to reduce the friction drag. Some of these concepts that influence the boundary-layer flow are related to compliant walls, blowing/suction, pressure gradient, surface curvature [174] and the viscosity in the vicinity of the wall by heating/cooling the surface [29]. These technologies modify the velocity profile of the laminar boundary layer to ensure a stabilizing effect against the growth of small disturbances. The natural laminar flow technology (NLF) represents a passive measure to stabilize the laminar boundary layer by designing the shape of the airfoil to have a pressure distribution with a negative pressure gradient, which accelerates the flow over a large extent of the airfoil chord. As figure 1.3 indicates this technique can be employed for smaller passenger planes (ATTAS, F100) that do not fly at the upper boundary of the transonic speed regime (Ma∞ < 0.8), so, the leading-edge sweep angle can be reduced (ϕ < 20o ). For larger modern transport aircraft designed for high transonic speeds and Reynolds numbers the wings have a large sweep angle (ϕ ≈ 35o ). This requires alternative laminarization concepts to be pursued that actively influence the boundary layer to maintain laminar flow. The laminar flow control (LFC), in particular suction, allows the delay of transition. However, this measure requires a large amount of power to be operated. Therefore, the hybrid laminar flow control (HLFC), which represents a combination of the NLF and LFC concepts, aims at the increase of laminar flow at a minimum required power. Over the first 15-20% of the airfoil chord the flow remains laminar due to LFC measures, succeeded by a favorable pressure gradient of NLF in the mid-part of the wing surface. Numerical investigations for the application of HLFC on an A340 aircraft predict a reduction of the total drag by approximately 10% [21].

4

Chapter 1.

H L F -b o u n d a ry ?

L e a d in g - e d g e s w e e p f

[ °]

N L F - b o u n d a ry A 3 2 0 L a m in a r fin

4 0

A 3 X X

A 3 4 0 / 3 3 0

E L F IN ll * *

3 0

**

E L F IN l 2 0

Introduction

A T T A S *

A 3 2 0

A L T

F 1 0 0 N L F - F lig h t A T T A S N F L - F lig h t

A 3 1 0 -3 0 0 s h a p in g + s u c tio n

s h a p in g + s u c tio n + a c tiv e d is tu r b a n c e d a m p in g

C F I

1 0

N L F 0

1 0

2 0

H L F C

T S I 3 0

4 0

5 0 R e

x 1 0

6 0

7 0

8 0

9 0

1 0 0

-6

Fig. 1.3: Application boundaries for different laminarization concepts at transonic speeds depending on the Reynolds number and the sweep angle [72, 78]. (* : S1 wind tunnel model, ** : S1 wind tunnel model with suction) Due to the pressure increase across the shock the boundary layer is very likely to separate. Depending on the strength of the shock, the trailing-edge pressure, and the state of the boundary layer in front of the shock different shock induced separation scenarios occur [147, 194]. The higher kinetic energy of the turbulent boundary layer makes it less likely to separate compared to the laminar boundary layer, which will separate upstream of the shock. These phenomena yield a substantial change of the aerodynamic performance and cause an evident increase of drag. To reduce the wave drag generated by SBI different measures to control the boundary layer in the neighborhood of the shock, for instance, single slot suction and blowing [28, 40], passive cavity ventilation [13, 199, 204] or local shape variations (bumps) [10] have been deployed. The objective of the shock control approaches is to shift the transonic drag rise towards higher Mach numbers (figure 1.4). In the design of airfoil sections with respect to the reduction of the total drag the above mentioned phenomena have to be accounted for in the design process. Especially, the implementation of the laminar flow concepts to wings at transonic speeds, where the laminar boundary layer could extend up to the shock remains a challenge, since the laminar boundary layer can separate due to the strong positive pressure gradient across the shock. So, the advantages of the extention of the laminar boundary layer on the reduction of wall-shear stress could be reduced or even annihilated by shock/boundary-layer interaction effects. An additional characteristic of long cruise flights complicates the design of efficient airfoil sections. From the aforementioned transonic flow phenomena it is obvious that the aerodynamic characteristics change considerably depending on the flight conditions. During a typical mission the aircraft operates at different flow conditions due to the loss of fuel and the change of flight

5

0.508 0.507

initial airfoil adaptive airfoil

→ of f− de sig n

0.506 0.505

C

D

0.504 0.503

→

0.502

→

0.501 0.5

drag divergence

0.499 0.498 0.72

0.73

0.74

0.75

0.76

0.77

0.78

0.79

0.8

Ma∞

Fig. 1.4: Objective of the shock control technologies is the delay of the transonic drag rise towards higher Mach numbers. altitudes. Therefore, the aerodynamic parameters lift, drag and Mach number are permanently subject to change. Throughout the design of modern transport aircraft the altering conditions are accounted for by multiple design points instead of only one operating state. Consequently, the resulting design is a compromise between different operation points. Hence, the mission adaptive wing technology comes into play, which implies the ability to adjust the airfoil shape to changing flow and load conditions, and consequently enables the variation along the optimum flight performance at each point of the flight envelope and thus provides the full potential in the reduction of fuel consumption, weight and environmental emission [74, 195]. The main objectives of the mission adaptive wing are shown in figure 1.5. The adaptive wing concept aims at an increase of the lift-to-drag ratio of up to 9% and a shift of the buffet onset of up to 15% of the lift coefficient. Moreover, the operational range of the cruise flight will be extended to even higher lift coefficients. The major part of the research on the implementation of the adaptive wing concept, also referred to as intelligent wing, into an actual structural design is represented by the variable (rear) camber wing [79, 202]. In most implementations the variable camber method is restricted to the trailing-edge area where the adaptive part extends from approximately 85% to 100% chord. This technology can be supplemented by adding an adaptive bump device to reduce the shock strength [135]. The current study extends the variable camber concept to an adaptive wing with an adjustable upper side over the entire chord. To demonstrate the aerodynamic potential of the adaptive wing technology a wind tunnel model has been designed and manufactured, which enables the experimental investigations at transonic speeds with natural transition. The experimental investigation is supported by numerical design analyses, which efficiently optimize the initial

6

Chapter 1.

Introduction

a d a p tiv e w in g L /D rig id w in g rig id w o p e ra tio n a a d a p tiv e o p e ra tio n C L

in g l ra n g e w in g a l ra n g e

Fig. 1.5: Objectives of the mission adaptive wing technology. airfoil shape DA LVA-1A at changing freestream conditions at transonic cruise speeds. The numerical part of the investigation determines the airfoil shapes that are considered to possess improved aerodynamic performance with respect to the initial laminar-type airfoil that has been tested in the subsequent experimental investigation. This present work provides an overview of the drag reduction technologies combined with presentation of experimental and numerical research in this area and aims at reducing the total drag of transport aircraft at transonic speeds by defining an improved airfoil shape based on the adaptive wing technology. First part the numerical aerodynamic shape design of airfoils defined via optimization methods will be discussed. The experimental requirements of the test facility, wind tunnel models and the measurement techniques will be described subsequently. Finally, the numerical and experimental results of the investigation of the adaptive wing technology with natural transition will be presented and discussed.

Chapter 2 Previous Research and Problem Definition The drag breakdown at cruise conditions presented in figure 1.1 demonstrates the high potential for the reduction of the total drag by the aerodynamic design of transonic laminar-type airfoils. However, due to the complex interaction of the shock with the boundary layer additional flow phenomenon like boundary-layer separation and reattachment have to be considered to identify measures to reduce the total drag generated by the wings. Aside from the flow characteristics the numerical aerodynamic design procedures, which aim at the improvement of the aerodynamic characteristics of airfoil shapes have to be high-lighted. This chapter will describe the flow phenomena associated with transonic airfoil flow with natural transition and indicate measures to reduce drag and to improve the operational range of the airfoil shape. In this respect the adaptive wing technology is also considered.

2.1

Laminar-Turbulent Transition

It has been recognized, that the consideration of the transition location into the design of aeronautical configurations is of great significance. The transition process concerns the laminar boundary layer that is unstable with respect to small disturbances of the flow quantities, which are amplified and eventually result in a turbulent boundary layer. The boundary layer is considered stable if small disturbances are damped and unstable if the amplitudes of the fluctuations are amplified. The flow is considered to be neutrally stable if the wave is neither damped nor amplified. Stability Theory The notion of the existence of small waves traveling in the laminar boundary layer has already been postulated by Rayleigh (1880) [154] and Prandtl [152]. Years later, Tollmien [206] devised a theory for the boundary-layer instability of an incompressible flow over a flat plate, for which Schlichting [170] calculated the growth rates of the most unstable waves. Therefore, 7

8

Chapter 2. Previous Research and Problem Definition

these instability waves are referred to as Tollmien-Schlichting (TS) waves. However, the significance of this theory has only been recognized after Schubauer and Skramstad [177] provided the experimental proof of the existence of the TS-waves. The mechanism by which freestream turbulence enters the boundary layer that causes the excitation of the TS-waves is referred to as receptivity by Morkovin [136]. For a better understanding of the mechanisms leading to transition, the different stages from a laminar to a turbulent boundary layer flow will be elaborated on the basis of the incompressible flow over a flat plate depicted in the left part of figure 2.1. Starting from the leading edge of the plate a laminar boundary layer develops that is stable against small disturbance waves for all frequencies (point 1). From a certain position xcrit and the corresponding critical Reynolds number Recrit onward the waves are amplified and the two-dimensional primary (TollmienSchlichting) instability is observed (point 2). Due to the growth of the disturbance amplitude the TS-waves become unstable against three-dimensional disturbances. As a consequence of the nonlinear interaction of the two-dimensional TS-waves the three-dimensional waves, secondary instability develops. These peak-valley structures are referred to as Λ-structures of K-type (Klebanoff et al. [97]) if they are ordered and of C-type (Craik [34]) or H-type (Herbert [75]) if they form a staggered pattern (point 3). Finally, the breakdown of these structures (point 4) and the development of turbulent spots terminate the transition process (point 5) [8, 121, 141]. Downstream of this point the boundary layer is fully turbulent (point 6).



U

! "

# $

y

a d

D

U

y a

e

e

b

d d U

0

U

U

D

x

s ta b le

u n s ta b le

d (x )

la m in a r

R e c rit lin e a r

U a

b

tra n s itio n re g io n n o n lin e a r

tu rb u le n t

R e

c r it a

R e

c r it b

R e =

U ed n

Fig. 2.1: Left: Sketch of the different stages of the boundary-layer transition process of an incompressible flow over a flat plate [171]. Right: Stability diagram of the neutral stability for a velocity profile with (a) and without (b) an inflection point [8]. It has to be kept in mind, that the length of the transitional area as well as the areas of linear and nonlinear wave amplification depend on many influences e.g. pressure gradient, wall roughness or turbulence level of the outer flow. In this context the spatial extent of the growth of the primary instabilities significantly determines the transition process.

2.1. Laminar-Turbulent Transition

9

The amplification of waves of different frequencies in the linear part of the transition process from a laminar to turbulent boundary-layer state can be described by the linear stability theory (LST), based on the Orr-Sommerfeld equation [143, 190] for an incompressible shear flow under the assumption of parallel flow with small disturbance amplitudes. The solution of the eigenvalue problem stated by the Orr-Sommerfeld equation, which represents a system of ordinary differential equations of fourth order, yields the amplification rates σ for a prescribed Reynolds number and wavenumber α, which is the streamwise component of the wavenumber k = 2π/λ, where λ denotes the wavelength. The result can be shown in the stability diagram for neutral stability (figure 2.1 right) in which the dimensionless wavenumber αδ versus the Reynolds number is displayed, where δ denotes the boundary-layer thichness. In the limit of infinite Reynolds numbers, the Orr-Sommerfeld equation reduces to the Rayleigh equation. Rayleigh showed that the existence of an inflection point in the mean flow velocity profile is a necessary condition for instability. It has even been shown that it is a sufficient condition for the instability of bounded shear flow [9]. As demonstrated in figure 2.1 the neutral stability curve associated with the velocity profile with an inflection point (case a) does not close in the limit of infinite Reynolds numbers as it does for the velocity profile without an inflection point (case b). For the subsonic compressible flow over a flat plate the transition mechanism is similar to that of the incompressible flow. The normal mode analysis, that led to the Orr-Sommerfeld equation for the incompressible flow, has been applied to the equations describing the compressible flow, to obtain the linear stability equations for compressible flows. The inflection point criterion has also been extended to compressible flows. According to Lees and Lin [110] the existence of the so-called generalized inflection point in the inviscid theory is a necessary and sufficient condition for a neutral subsonic wave to exist and is, therefore, a necessary condition for instability. If the Mach number is increased such that local supersonic waves occur in the boundary layer, the stability equations have an infinite number of neutral waves (higher modes) as discovered by Mack [120]. However, for adiabatic wall conditions, the higher modes start to occur if the freestream Mach number exceeds Ma∞ ≥ 2.2 [9] and, therefore, will not be significant in the transonic regime. The demand for increasing cruise speeds for transport aircraft has led to the introduction of swept wings. Due to the sweep angle and the pressure gradient, the inviscid outer flow streamlines are deflected. However, the viscous effects cause an increase of the deflection to maintain a force equilibrium, which causes crossflow. This means an additional velocity component develops inside the boundary layer directed perpendicular to the inviscid outer flow streamline (figure 2.2). Hence, the complex structure of the boundary layer, especially in the leading edge region, influences the transition mechanisms of a swept wing substantially. Basically, three possible transition mechanisms have been recognized to occur on a swept wing as demonstrated in figure 2.2: 1. Attachment line transition (ALT) 2. Crossflow instability (CFI) 3. Tollmien-Schlichting instability (TSI)

10

Chapter 2. Previous Research and Problem Definition

a tta c h m e n t lin e tra n s itio n s tre a m lin e c lo s e to th e w a ll

sw e e p a n g le

y

u (d )

in fle x io n p o in t

y z x s tre a m lin e o f th e in v is c id flo w

v (y ) c ro s s flo w v e lo c ity c o m p o n e n t

u (y ) s tre a m w is e v e lo c ity c o m p o n e n ts

j

-z d ire c tio n o f w a ll s h e a r s tre s s x

c ro s s flo w T O L L M IE N - S C H L IC H T IN G in s ta b ility in s ta b ility

Fig. 2.2: Left: Possible instability mechanisms in a boundary layer on a swept wing. Right: Boundary-layer velocity profile (gray) and its associated streamwise and crossflow velocity components. Transition can begin on the attachment line. In the case of a swept wing, this is the streamline near the leading edge of the airfoil separating the flow over the upper and lower side of the airfoil. Due to contamination of the attachment line by the turbulent boundary layer of the fuselage, transition can occur at the leading edge resulting in a turbulent boundary layer over the entire wing. This can be prevented by the application of the so-called Gaster bump [60]. Still, transition can be initiated along the attachment line by small disturbances for Reynolds numbers based on the momentum thickness larger than Reθ ≈ 230 [148, 151]. For which Reθ can be approximated by the relation
Reθ = 0.404

u∞ R sin2 ϕ (1 + ) ν cosϕ

 12 ,

(2.1)

where R denotes the nose radius perpendicular to the leading edge, and  the ellipticity. The sweep angle is represented by ϕ at a freestream velocity u∞ . The crossflow component of the velocity profile exhibits an inflection point and is, therefore, inviscidly unstable. Fundamental research on crossflow instability at low flow speeds has been performed by Saric and Yeates [169] and in a DLR-experiment described by Deyhle and Bippes [41]. Major parameters that influence the crossflow instability are the Reynolds number, the sweep angle and the pressure distribution. When the transition is delayed further downstream of the leading edge the TS instability mechanism leads to transition from laminar to turbulent flow in the mid-chord region of the airfoil. This process is similar to the transition of the boundary layer over a flat plate.

11

2.1. Laminar-Turbulent Transition

For the transition prediction it is inevitable to capture the essential physical properties of the transition process. For the two-dimensional waves in an incompressible flow under the parallel flow assumption the Orr-Sommerfeld-equation can be applied to calculate the frequencies and amplification rates of the unstable waves. The Orr-Sommerfeld-equation can be extended to three-dimensional compressible flows [121] with or without curvature effects [174] covering the local, linear stability theory. The effect of upstream influences and nonparallelism of the boundary layer on the growth rates of the disturbance waves can be investigated using the parabolized stability equations (PSE) by Herbert and Bertolotti [19]. These equations are also capable of capturing nonlinear effects.

2.1.1

Transition Prediction

To incorporate elements of laminarization concepts in the automated numerical design process it is necessary to be able to predict the transition location. The semi-empirical eN - method based on the linear stability theory is the best known transition prediction method for engineering use. The approach that correlates the logarithmic amplification ratio N of the most amplified disturbance with the transition location has been developed independently by Smith and Gamberoni [183] and Van Ingen [208]. The so-called N factor characterizes the disturbance growth of an initial disturbance with amplitude A0 at the neutral point such that eN = A/A0 . The value of A0 is usually not known and is related to the disturbance environment by receptivity mechanisms. To compute the quantity N the linear spatial growth rates σ(x) at some frequency are integrated from the neutral point x0 where the disturbances first become unstable, to a position downstream,
  x A A = = eN with N = ln σ(x) dx. (2.2) A0 A0 x0 The eN -method assumes that the extent of the region of linear amplification of disturbances is much larger than the nonlinear breakdown to turbulence. Arnal [9] determines the linear extent of the transition process for a flow with flat plate characteristics to be an order-ofmagnitude larger than the length of the nonlinear stage. This is one reason for the good results of the eN method [162]. In order to be able to predict transition a value for the limiting N factor has to be determined. Therefore, the value of N at transition has to be correlated to the transition location obtained from wind tunnel experiments or free flight observations. The N factor distribution in the streamwise direction has to be determined for several frequencies, for which the disturbance amplitude is amplified. This amounts to an envelope curve representing the maximum amplification factor at the corresponding streamwise location x. The aspect of receptivity is only covered by the choice of the value of N . Hence, different disturbance environments yield different limiting N factors. To account for the different turbulence levels of wind tunnels and free flight that significantly influence the transition location Mack [121] proposed a relationship that correlates N to the turbulence level T u: N = −8.43 − 2.4 ln(T u).

(2.3)

12

Chapter 2. Previous Research and Problem Definition

So, in order to perform experiments on the determination of the transition location on a laminartype airfoil at transonic speeds, specific wind tunnel tests have to be conducted, to accurately determine the value of the N factor to be used in the subsequent aerodynamic design of airfoil shapes with natural transition.

2.1.2

Laminarization Concepts

The inflection point criterion is significant for the determination of measures to suppress disturbance growth in order to increase the extent of the laminar boundary layer. The development of the streamwise velocity component u in the wall normal direction y is considered using the 2-D compressible, steady laminar momentum boundary-layer equation at the wall (y = 0):
2 




 ∂ u ∂u dp ∂u ∂µ ∂T µ = ρv + . (2.4) − 2 ∂y y=0 ∂y y=0 dx ∂T ∂y y=0 ∂y y=0 The objective to delay transition is to reduce the second wall normal velocity derivative on the left hand side of eqn.(2.4) to obtain a fuller velocity profile, that is considered to be more stable against disturbance waves. The stabilizing effect is obtained if suction (v < 0) is applied and by accelerating the outer flow in chordwise direction (dp/dx < 0). Cooling also stabilizes the boundary-layer flow by increasing the wall normal viscosity gradient. The incorporation of the laminar flow concepts to transonic civil transport aircraft requires theoretical and experimental analysis. The theoretical description of the stability process enables the prediction of the transition location of various aerodynamic configurations. Additionally, experimental tests have to be performed in wind tunnels and under flight conditions, to provide an extensive and reliable data base for theoretical analysis concerning the transition prediction and also to validate the numerical methods. The experimental studies in wind tunnels offer flexibility for configuration modifications and allow many different freestream conditions. Although, wind tunnel measurements are indispensable, they have to be supplemented by flight tests to avoid disturbances with respect to the turbulence level and noise. The flight tests also allow the experiments to be performed at correct Reynolds numbers and realistic flight conditions. From eqn.(2.4) it has been demonstrated that a negative pressure gradient (accelerated flow) damps the TS-waves. This can be achieved by shaping the airfoil geometry accordingly, which is referred to as the natural laminar flow (NLF) technique. As it is shown in figure 1.3 NLF is applicable to smaller aircraft without large sweep angles. To investigate the possibilities of this method several European projects were initiated [124]. Flight tests with the DLR research aircraft VFW 614/ATTAS [88] have been accompanied by wind tunnels tests of a 1:2 model [73, 105]. On the basis of the experimental results a stability analysis has been performed i.e. in [175]. In a joint research group of five German universities flight and wind tunnel tests have been performed with the powered glider GROB G109b [48, 102, 201]. Also the Do 228 aircraft has been used in flight tests with a laminar glove [87]. Within the ELFIN I project the limits of the NLF were tested experimentally and theoretically on a FOKKER 100 with a sweep angle of 20o [46, 176]. The research activities in the US on NLF have been summarized by Wagner [214] and Joslin [95].

2.2. Shock/Boundary-Layer Interference

13

For large civil transport aircraft at the technically relevant Reynolds numbers and sweep angles the NLF technique is not sufficient to delay transition. The NLF can be combined with suction in the leading-edge area of the wing to avoid ALT and damp the CFI. This technique is referred to as the Hybrid Laminar Flow Control (HLFC). In the Airbus 320 Laminar Fin program the potential of HLFC in drag reduction has been investigated in flight tests and in wind tunnel experiments [74, 160]. The tests principally showed the possibility to implement a HLFC system in the aircraft and operate it under flight conditions. The experimental, theoretical and flight tests proved the benefits of the HLFC concept with regard to drag reduction. However, the high effort connected with the oparation of a suction system prevented their implementation in a commercial airplane. At transonic cruise speeds shock waves occur on the upper surface of the airfoil whose strength increases when the Mach number or the angle-of-attack is increased. The sudden pressure rise across the shock interacts with the boundary layer on the airfoil surface. The impact of the shock/boundary-layer interaction (SBI) depends significantly on the state of the boundary layer (laminar or turbulent) in front of the shock. Moreover, concepts have to be identified, which reduce the drag induced by the shock. The following section will provide a survey over shock control methods.

2.2

Shock/Boundary-Layer Interference

The shock/boundary-layer interaction phenomenon (SBI) has been investigated since 1941 by Regenscheit [163], Ackeret et al. [3], Liepmann [112], and Holder et al. [81]. In the case of weak interaction, where the boundary layer is attached to the airfoil, the SBI exhibits pressure drag depending on the strength of the shock. However, as the shock strength is increased with growing Mach number the pressure drag, also referred to as wave drag, is raised and the viscous drag is increased due to the thickening of the boundary layer. Further Mach number increase yields shock induced separation and the associated buffet phenomenon. Pearcey et al. [147] classified the possible shock induced separation scenarios for a turbulent boundary layer over a supercritical wing. Further research on SBI on supercritical airfoils has been performed by Finke [51], Stanewsky [194], and Franke [54]. A major factor of influence of the SBI is the state of the boundary layer upstream of the shock wave. The laminar boundary layer features a reduced amount of kinetic energy compared to the turbulent boundary layer. Therefore, the laminar boundary layer is more susceptible to separation due to the pressure rise across the shock even for weak shock strengths. This means, compared to the turbulent boundary layer, that the laminar boundary layer separates at smaller Mach numbers. Due to the transition of the separated flow at moderate Mach numbers the increase of momentum in the turbulent boundary layer causes the reattachment of the boundary layer such that a separation bubble is formed (figure 2.3). The displacement of the inviscid outer flow due to the separation bubble has an upstream effect causing the formation of compression waves upstream of the leading shock to a lambdashock pattern. Although the shock is weakened, the viscous drag and the wave drag increase combining negative effects on the buffet boundary. The turbulent boundary layer separates at

14

Chapter 2. Previous Research and Problem Definition

M a > 1 le a d in g s h o c k la m in a r b o u n d a ry la y e r

M a < 1 e x p a n s io n w a v e s s e p a ra tio n b u b b le tu rb u le n t b o u n d a ry la y e r

M a > 1 tu rb u le n t b o u n d a ry la y e r

M a < 1 b o u n d a ry -la y e r e d g e

Fig. 2.3: Sketch of the shock/boundary-layer interaction mechanism for a laminar boundary layer (left) and a turbulent boundary layer (right). higher Mach numbers or larger angles-of-attack with respect to the laminar boundary layer. Therefore, to reduce the total drag it is aimed to delay the drag-rise and buffet boundaries at transonic speeds through shock and boundary layer control. A control measure on the basis of double slots or cavities covered by perforated plates underneath the foot of the shock with and without suction has been investigated by Thiede et al. [204] on the turbulent supercritical airfoil VA-2. Due to the higher pressure aft the shock a secondary flow through the cavity towards the lower pressure ahead of the shock develops (figure 2.4). The positive effects observed were the delay of the buffet boundary to higher Mach numbers and a reduction of total drag, mainly through the reduction of wave drag. These effects have also been achieved without suction, as a passive shock control measure. Through this success the application of passive shock control for laminar-type airfoils has been initiated to reduce the strength of the shock that is already present at design conditions1 . Unfortunately, investigations with the laminar-type airfoils LVA-1A [167] and DRA-2303 [57] as well as with the channel flow [28] within the EUROSHOCK I project [197] showed a reduction of the wave drag but a substantial increase of viscous drag, which outperforms the wave drag reduction. Hence, passive control on laminar-type airfoils leads to an increase in total drag.

c o n to u r b u m p v o rte x g e n e ra to r

sh o c k w a v e

a c tiv e /p a s s iv e v e n tila tio n d is c re te s u c tio n

sh o c k w a v e d is c re te s u c tio n

Fig. 2.4: Sketch of the shock/boundary-layer control concepts for transonic airfoils [198]. Discrete suction upstream of the shock investigated at DERA on the DRA-2303 airfoil showed 1 A more detailed description of the characteristics of transonic laminar-type airfoils is presented in section 2.3

2.3. Aerodynamic Characteristics of Airfoil Sections

15

a reduction in total drag mainly due to the decrease of viscous drag caused by the reduction of the boundary-layer displacement and momentum through suction [58]. Similar to the discrete suction, the vortex generators located upstream of the shock act on the boundary layer to yield a reduced boundary-layer thickening aft the shock, as has been investigated by McCormick [126]. However, due to the obstacles in the boundary layer the flow can not be maintained laminar up to the shock. The shock control bump (SCB), shown in figure 2.4, proposed by Ashill et al. [10], is a more recent method to affect the SBI. The bump is a local modification on the suction side of the airfoil geometry in the shock region which induces isentropic compression waves to decrease the shock strength and thus reduce the wave drag. The advantage of the bump compared to the porous surface passive shock control is the independence of the displacement contour from the flow conditions so no secondary flow develops. Extensive experimental and numerical research on the benefits of the bumps for shock control has been performed on airfoils and infinitely swept wing [22, 100, 196]. Within the EUROSHOCK II-project, the SCB has been found to be the most effective shock control device for the reduction of the total drag [196]. However, most previously mentioned methods are locally confined. These shock control measures are, therefore, only effective at changing freestream conditions, if the shock position is more or less fixed, which is the case for the LVA-1A airfoil. If the shock position differs over a large extent of the upper surface at varying freestream conditions, the spatially fixed control measures do not affect the shock, anymore but are likely to impair the overall performance of the airfoil.

2.3

Aerodynamic Characteristics of Airfoil Sections

The demand for high cruise speeds of transport aircraft requires transonic freestream Mach numbers. The maximum speed is limited by the drag rise and the development of shocks accompanied by the shock induced separation. The application of swept wings delays the drag rise speed, although the drag rise onset remains well below the sonic speed. Therefore, airfoil shape modifications of the conventional subsonic airfoil shapes were required to increase the cruise speed even more. The NACA 1-digit series represents the first family of wing sections to delay the drag rise compared to the NACA4-digit series [191]. However, the aerodynamic characteristics were inferior to the successive NACA 6-digit series, which combined a significant daelay of the drag rise speed with slight reduction of the low speed characteristics compared to the NACA 4-digit series [1]. A major step towards the design of an airfoil shape with acceptable performance at transonic speeds has been made by Pearcey [146]. The airfoil shapes were characterized by a strong acceleration of the flow into the supercritical regime followed by an isentropic recompression to minimize the wave drag. The corresponding pressure distribution showed a peak shortly aft the leading edge which leads to the designation ’peaky’ profiles. The aerodynamic characteristics regarding lift and moment of this airfoil shape were improved by geometry modifications on

16

Chapter 2. Previous Research and Problem Definition

the lower side to obtain the so-called rear-loading. Unfortunately, the airfoils showed poor off-design characteristics. Further pioneering research on supercritical airfoil shapes has been conducted by Whitcomb and Clark [216]. Analytical investigation of supercritical airfoils has been performed by Nieuwland [140], Bauer, Garabedian and Korn [15, 16] and Boerstoel [25]. They applied the hodograph method to design shock-free airfoils. Although these airfoils perform well at the design conditions the drag may increase at lower off-design Mach numbers. The research led to a number of characteristics for a supercritical airfoil section. As compared with a conventional airfoil (e.g. NACA 6-series) the supercritical airfoil shows a reduced amount of camber in combination with an increased leading-edge radius. Due to the additional reduction of the surface curvature in the mid-chord section of the upper side this yields an almost constant pressure distribution on the suction side. After exceeding the critical Mach number a relatively large supersonic region develops that is terminated by a weaker shock compared with the conventional airfoil. This reduces the risk of shock induced separation and hence a shift of the buffet boundary towards higher Mach numbers. The additional concavity on the rear section of the airfoil’s pressure side results in the rear-loading that enhances the aerodynamic efficiency by increasing the lift (Fig. 2.5). Compared with the shock-free airfoils an increase in wave drag has been exchanged for an increase in lift. The supercritical airfoil technology allows the design points to be shifted far into the transonic flight regime. An extensive overview of the early research on supercritical airfoil sections and their aerodynamic characteristics is provided by Whitcomb [215]. The development of the supercritical airfoil represents a major step forward in the improvement of the aerodynamic performance at transonic cruise speeds. Under these flight conditions the laminar/turbulent boundary layer transition on supercritical airfoils is usually located near the leading edge. Since the wall shear stress of the laminar boundary layer is almost one order of magnitude less than that of the turbulent boundary layer, the laminar flow technology provides a promising means to further improve the aerodynamic performance. From the discussion on the laminarization concepts in section 2.1.2 and from eqn.(2.4) it has been demonstrated that airfoil shapes with a long laminar extent of the boundary layer can be designed through the natural laminar flow measure (NLF) due to the favorable pressure gradients. The strong acceleration on the suction and the pressure side, damps the TS-waves to postpone the transition location far downstream. The aforementioned development of the NACA 1-series not only represents the first high speed wing design but also represents the first design to meet the requirement for a large extent of the laminar boundary layer. Especially, the NACA 1-series with the pressure minimum at 60% chord, referred to as NACA 16-series is a commonly used representative of this family [1]. However, as discussed above, the aerodynamic performance of the NACA 1-series was poor. The design of a laminar-type airfoil for transonic speeds also implies the consideration of swept wings. This means that transition can occur through three transition mechanisms (ALT, CFI and TSI). Redeker et al. [161] investigated the different pressure distributions with the linear stability theory, that led to characteristics of the pressure distribution in the chordwise direction, which stabilizes the development of either of the three transition mechanisms. Near the leading edge a steep pressure drop is favorable for ALT and CFI followed by a small region of

17

2.4. Flow Control by Adaptive Shape Variation

constant pressure that stabilizes CFI. The slight acceleration over the mid-chord region of the airfoil stabilizes the TSI until the shock occurs associated with a strong recompression causing transition. The schematic pressure distributions of laminar-type transonic airfoils are shown in figure 2.5. 0.8 0.1 0.6

y/c

0.05 0

L

0.4

C

−0.05 −0.1 0

0.2 0.2

0.4

0.6

0.8

1

x/c 0

Conventional airfoil NACA 64−a212 Supercritical airfoil CAST 7 / Do A1 Transonic laminar airfoil LVA−1A

Ma

∞

−0.2 0

0.005

0.01

0.015

C

0.02

= 0.74 0.025

0.03

D

1.5

0.035 C = 0.50

Ma∞= 0.74

L

0.03

CL = 0.50 Re = 2.4 . 106 ∞

1

0.025

C

−C

D

p

0.5 0.02

0 0.015 −0.5

0.01

−1 0

0.2

0.4

0.6

x/c

0.8

1

0.005 0.65

0.7

Ma

0.75

0.8

∞

Fig. 2.5: Comparison of the aerodynamic characteristics of a conventional, a supercritical and a transonic laminar-type airfoil.

2.4

Flow Control by Adaptive Shape Variation

The objective of the transonic laminar airfoil design is to sustain the laminar flow over a large range of angles-of-attack to reduce the total drag. Typically, this laminar range is limited by a steep increase of drag due to the sudden strong upstream movement of the transition location that appears as the so-called laminar bucket in the drag polar. A drawback of the constant negative pressure gradient over the airfoil surface is the increased strength of the shock compared to supercritical airfoils. Although the reduction of the viscous drag prevails

18

Chapter 2. Previous Research and Problem Definition

over the increase of wave drag the stronger shock endangers the laminar boundary layer, which is very susceptible to steep positive pressure gradients that can cause separation. The impact of SBI on a turbulent boundary layer is not that high compared to a laminar boundary layer. Hence, the shock/boundary-layer control is considered to offer a higher potential to improve the aerodynamic performance, when applied to a transonic laminar-type airfoil than to a wing section with a turbulent boundary layer. During long distance flights of modern commercial aircraft at transonic speeds the flight conditions change substantially. Already the take-off weight varies depending on the load, the aircraft version and the mission range. Moreover, the flight weight reduces during a long distance mission by approximately 30%. So, the required lift often differs from the design-point of the airfoil and hence the airfoil operates far off the optimum flight condition for a considerable amount of time. The strong demand of the airlines to reduce the fuel consumptiom requires the total drag of transonic wings to be lowered to improve the aerodynamic performance. To accommodate the changing flight conditions in aerodynamic design of generic supercritical airfoil shapes multiple freestream flow conditions will be taken into account. This method yields an airfoil shape that poses a compromise between various conditions and thus degrades the overall achievable aerodynamic performance. To enhance the aerodynamic performance and exploit the potential of the wing at each operation point of the flight envelope the adaptive wing technology is considered. This approach implies the geometrical modification of the airfoil shape by an arbitrary technique to obtain the desired wing contour that is considered optimal for the current flow condition. As the flight conditions change subsequent modifications of the airfoil shape will maximize the aerodynamic benefits during flight. The method of variable camber represents one approach to incorporate the adaptive wing principle during flight. Research on the benefits of variable camber on the fighter aircraft performance started in the 1970’s. This resulted in a AFTI/F-111 Mission Adaptive Wing (MAW) that combined variable sweep with variable camber at the leading- and trailing edge, which demonstrated the benefits of a flexible airfoil to enhance performance for fighter configurations [184]. To investigate the potential of efficiency improvement by the variable camber concept on transport aircraft at low development costs it was proposed to use the existing high lift devices and control surfaces to provide the camber modification [79]. The effects of the variable trailing-edge camber are a significant drag reduction at higher lift coefficients and an improved lift capability combined with a shift of the buffet boundary as demonstrated in figure 2.6. Gilyard et al. [63] conducted flight tests on a L-1011 wide-body transport aircraft with modified outboard ailerons to enable the variable camber settings. Although these ailerons only cover an area of approximately 3% of the total wing area a drag reduction of 1% has been achieved. Within the ADIF program [5] various adaptive structure concepts for the variable rear camber flap have been proposed. The proposals of the horn concept, the twin-flap and the finger concept have been implemented into demonstrators that exhibit the principle without the actual aerodynamic loads [85]. Austin et al. [11] developed a demonstrator model with an adaptive upper and lower surface over the entire chord length deformed by an adaptive rib. However, neither of the aforementioned concepts have been tested under transonic freestream conditions in wind tunnel or in flight tests. Although the shock control bump has proved an effective means to reduce the wave drag

19

2.5. Aerodynamic Optimization

e n v e lo p e o f th e v a ria b le c a m b e r 2 -3 % L /D rig id w in g rig id w o p e ra tio n a v a ria b le o p e ra tio n C L

in g l ra n g e c a m b e r a l ra n g e

1 0 -1 2 %

b e g in n in g o f c ru is e C

L

= 0 .6

m id -s e c tio n o f c ru is e C

L

= 0 .5

e n d o f c ru is e C

L

= 0 .4

Fig. 2.6: Left: Comparison of lift-to-drag ratio for an airfoil with rigid shape and an airfoil with variable camber. Right: Modification of the rear camber at different stages of the mission [78]. (section 2.2) the results also indicate that the Mach number range for the performance improvement is small. At off-design conditions the drag increases. To increase the operational range the bump geometry and its location should be adapted to the prevailing flight conditions. Currently, only bump adaptation concepts that modify the bump height but not the chord wise position have been proposed [30, 70]. However, the concepts have not been tested at transonic flow conditions, yet. An approach to modify the entire airfoil upper surface at low Mach numbers has been accomplished by Guntermann [67]. An airfoil model based on the NLF(1)-0416 with an adjustable upper surface has been developed and tested in wind tunnel experiments at Ma∞ = 0.4 and Re∞ = 1.66 · 106 . The results evidenced the possibility to affect the transition location and separation bubbles with an adaptive wing shape at subsonic Mach numbers. Aside from the technological realization of the adaptive wing concept, the amount of adaptation for each flight condition has to be determined. The aerodynamic optimization represents a powerful method to obtain airfoil shapes with improved aerodynamic performance at a prescribed flight condition.

2.5

Aerodynamic Optimization

The concept to improve the shape of airfoils by prescribing desired aerodynamic characteristics has already been investigated theoretically by Mangler [122] and Lighthill [114]. On the basis of the linear potential equations for two-dimensional incompressible flows they developed a method to calculate the airfoil shape by prescribing the desired pressure (velocity) distribution

20

Chapter 2. Previous Research and Problem Definition

on the airfoil surface. If constraints are imposed on the pressure distribution, the system can be expressed in closed form [211]. This method of aerodynamic design in which a desired pressure distribution is prescribed in order to obtain the corresponding airfoil shape is referred to as inverse design. The theory of Lighthill has been extended to subcritical compressible flows by Woods [219]. Through the introduction of free parameters by Volpe and Melnik [212] the constraints imposed on the pressure distribution could be satisfied in an iterative way without a closed form expression. The inverse method offers the designer the possibility to control the process through the implementation of the desired aerodynamic characteristics into the pressure distribution. However, there is no guarantee that an airfoil shape exists for the prescribed pressure distribution. The first effort to avoid this problem was the introduction of numerical optimization methods in the field of aerodynamic design by Hicks et al. [77] and Davis [36]. This approach starts with the specification of the objective function, also referred to as cost function, which represents the mathematical characterization of the preferred aerodynamic properties of an airfoil like the improvement of the lift-to-drag ratio or a pressure distribution. The solution of the desired cost function, the ’current’ value, on an arbitrary initial airfoil shape is compared with the ’target’ value of the cost function. The airfoil shape is modified to reduce the difference between ’current’ and ’target’ value. This is done in an iterative way in which the flow field is recalculated repeatedly. This approach is referred to as the residual correction method. It is obvious that the idea of an analytical correlation between the cost function and the shape modification that was present in the Lighthill theory has been abandoned. Therefore, the new link between the cost function and the shape adjustment is represented by an optimization strategy. However, there is still no guarantee that an airfoil geometry exists for every ’target’ cost function, unless the latter satisfies some constraints. The main advantage of the numerical optimization procedure is the flexibility that is allowed in the definition of the cost function and the constraints to exercise as much control as possible over the design process. It is still possible to apply the inverse design using a prescribed pressure distribution. Furthermore, the numerical optimization approach allows the aerodynamic characteristics (drag, lift-to-drag ratio, moments) to be controlled without the necessity of extensive experience to define a pressure distribution. The significant disadvantage of the optimization method is the computational effort required to compute the flow field repeatedly. However, as the computational resources increase further, this disadvantage becomes circumstantial. An entire different approach has been pursued by Bauer, Garabedian and Korn [15, 16] and Boerstoel [25], who used the hodograph technique to design shock-free airfoils. However, the method required too many input parameters to be practical. On this basis Sobieczky et al. [188] developed the ’fictitious gas’ concept to obtain shock-free airfoil shapes. Both methods lack the control of the design through the pressure distribution. With the increase of the computational resources the aerodynamic airfoil and wing design procedure tends towards the numerical optimization, where a flow analysis method (e.g. full potential flow equations, Euler equations or Navier-Stokes equations) is coupled with an optimization algorithm in order to drive a predefined cost function subject to a number of constraints to a minimum. The major choice defining the design is the mathematical optimization method, which can be

2.6. Objectives of this Work

21

ordered in the deterministic and the stochastic methods. Due to the implementation of presumed knowledge about the objective function to be optimized, the deterministic algorithms are characterized by a fast and efficient search for the extremum. However, for highly multimodal and nonlinear design spaces, the deterministic algorithm often fails to find the optimum. Most efficient and widely applied representatives of the deterministic optimization algorithm are the gradient-based-methods such as the method of steepest descent, the quasi-Newton method or the conjugate gradient method [52, 62]. The stochastic algorithms do not make any assumption about the design space topology. Hence, they can deal with discontinuous and noisy cost functions which increases the chance to find the global extremum significantly. Their search is not as efficient as for the deterministic algorithms. Examples of the methods of stochastic search are Simulated Annealing (SA) [131, 96], Genetic Algorithms (GA) [82] or Evolution Strategy (ES) [180, 155]. In aerodynamic designs there is no analytical correlation anymore between the cost function and the design variables (defining the airfoil shape). Hence, it is difficult to provide the gradients of the cost function with respect to each design variable directly. The simplest method to obtain the gradients, or so-called sensitivities, is the finite-difference approach. The accuracy of the computed gradients depends on the step size, that is difficult to determine, especially for nonlinear cost functions. Even if accurate sensitivities can be calculated using finite-differences, the computational cost is proportional to the number of design variables. The adjoint method pioneered in fluid mechanics by Pironneau [149, 150] represents another approach to accurately determine the sensitivities. Simultaneously with the governing equations of the flow field (state equations) the adjoint equations (co-state equations) are solved. Although the determination of the additional system of adjoint equations is computationally expensive, the computational cost is independent of the number of design variables. Jameson introduced the method to the aerodynamic optimization at transonic speeds using the potential flow and Euler equations [90, 91] and later also the Navier-Stokes equations [92]. The most recent development to accurately obtain the sensitivities based on the chain rule has been proposed by Bischof et al. [23, 24]. The method of automatic differentiation (AD) poses as a preprocessor for an existing source code (e.g. a flow solver) to produce a modified source code that allows the additional computation of the sensitivity derivatives of the predefined objective function with respect to each design variable. However, the computational requirements increase with the number of design variables. Additionally, as the method operates on the source code, the flexibility in changing the cost function or the design variables is restricted, since an entirely new formulation of the modified source code is required. Moreover, as the ADapproach assumes the availability of the source code, the method prevents the implementation of commercial flow solvers into the optimization process.

2.6

Objectives of this Work

To meet the requirements to enhance the airfoil performance at transonic speeds new concepts have to be developed and tested to demonstrate their suitability to reduce the total drag. A detailed numerical and experimental investigation on the potential of the performance improvement at transonic speeds by using an adaptive wing with a rectangular top view is required

22

Chapter 2. Previous Research and Problem Definition

and will be conducted in the present work. Since the importance of laminarization and shock control for the reduction of the total drag has been recognized, the investigation will focus on the incorporation of the natural laminarization concept into the airfoil shape design. Moreover, the influence of the shock/boundary-layer interaction will be part of the study to ensure improved aerodynamic characteristics of the designed airfoil shapes. This study will use the transonic laminar-type airfoil DA LVA-1A designed by DASA Airbus as the initial airfoil shape. For the constrained aerodynamic design of airfoil shapes at transonic speeds with natural transition a robust optimization algorithm will be coupled with a method to compute the flow. The optimization approach is required to be able to find the global extremum of a highly multimodal nonlinear objective function, whereas the numerical flow simulation method is required to be fast to allow a large number of function evaluations. Special attention is required for the handling of the geometric and aerodynamic constraints imposed on the final airfoil design. An adaptive wing wind tunnel model with a rectangular top-view will be designed and manufactured for experiments at transonic speeds with natural transition, to demonstrate the benifits of the adaptive wing technology and to verify the numerical results. The test will be conducted in the trisonic wind tunnel of the Aerodynamisches Institut, which is equipped with an adaptive wall test section with a 0.4 × 0.4 m2 cross section. The dimensions of the wind tunnel and the slender airfoil shape, which is characteristic for supercritical airfoils, yield very limited space to integrate adjustment kinematics and measurement equipment. Therefore, it will be indispensable to develop a rigid surface wind tunnel model in the first stage towards the development of the adaptive wing model. To correspond to the aerodynamic design, both wind tunnel models will be based on the laminar-type airfoil DA LVA-1A. The rigid surface model will also provide the experimental reference data required for an accurate comparison with the results obtained for the adaptive wing model. The numerical flow computations will be compared with results of the detailed experimental investigation of the state of the boundary layer and the aerodynamic characteristics of the airfoil with respect to the transition location, separation and the lambda shock configuration. Essentially the multi sensor hot-film technique in combination with the liquid-crystal coating technique which are characterized by a high temporal and spatial resolution will be applied. Pressure measurements and optical flow visualization will complete the study. The comparison of the results of the tests conducted with the adaptive wing model on different airfoil shapes allow statements on the applicability of laminarization on adaptive surface wings at transonic speeds. The main objective of the present study is the combination and interaction of numerical, experimental, and structure-mechanical approaches to develop an adaptive wing equipped with sensor technology to detect the response of the flow properties to changing flight conditions. The developed technology could then be regarded as a first step towards a closed-loop adaptive wing system.

Chapter 3 Aerodynamic Shape Design The demand for the enhancement of aerodynamic properties of aerodynamic shapes requests an optimization algorithm to be coupled with an accurate and fast method for the calculation of the flow field over the airfoil or wing. The aerodynamic shape design of an airfoil at transonic speeds with natural transition and the presence of shock induced separation represents a highly nonlinear multi-modal optimization problem that is hard to tackle. This chapter will focus on the characteristics of optimization algorithms that are capable of efficiently finding the global extremum of such a direct aerodynamic design problem.

3.1

Formulation of the Optimization Problem

The parametric optimization aims to find a set of values for the design variables which describe an arbitrary system for which the features of the system are enhanced. Mathematically, the optimization minimizes the value of a scalar objective function f , also called cost function, depending on a vector of n design variables
x = (x1 , . . . , xn ) being subject to certain constraints. Without loss of generality a minimization problem can be assumed since it represents the negation of an objective function to be maximized (max(f (
x)) = min(−f (
x))). The continuous objective function f is minimized min(f ) with f : M ⊆ Rn → R , M = ∅,

(3.1)

M = {x ∈ Rn | gj (x) ≥ 0 ∀ j ∈ {1, ..., q}} .

(3.2)

subject to q constraints

The objective function and the constraints can be defined by any system of arbitrary complexity. The most general case deals with a nonlinear objective function subject to nonlinear constraints referred to as a nonlinear-constrained optimization problem (NCP) [62]. The aim is to find a set of design variables x∗ ∈ M in the global extremum f ∗ : ∀x ∈ M : f (x) ≥ f (x∗ ) = f ∗ 23

(3.3)

24

Chapter 3. Aerodynamic Shape Design

To tackle this kind of optimization problems a whole range of different methods exist. Most methods have been developed for a special range of optimization problems. If the problem at hand complies with the assumptions of the optimization method, the technique will perform well. However, the performance deteriorates if the assumed internal model and the system to be enhanced do no match. The criterion to assess the different optimization methods is the ability to find the global extremum of NCP. Additionally, the method should perform the search efficiently. This means that the optimizer has to be able to accurately determine the extremum at a minimum number of objective function evaluations. Moreover, the method should be robust in the sense that the assumptions on the internal model of the system to be optimized are met by that system. Especially, for complex objective functions characterized by the lack of an analytical correlation between the cost function and the design variables the design space topology is not known in advance. This complicates the determination if the system complies to all assumptions. As mentioned in section 2.5 the optimization techniques can be divided into the deterministic and the stochastic method. Commonly applied deterministic strategies are based on the Taylor series expansion of the objective function f (
x) about
x0 : 1 ¯ · ∆
x + . . . f (
x) = f (
x0 ) + ∇f (
x0 ) · ∆
x + ∆
xT H 2

(3.4)

The so-called gradient-based methods truncate eqn.(3.4) after the second term on the right hand side and hence assume a local linear behavior of the system. The search direction is guided by the partial derivatives of the objective function. The existence of the derivatives is assumed so the objective function has to be smooth and twice differentiable. Moreover, the partial derivatives have to be provided to determine the search direction. For complex systems these so-called sensitivities are usually provided using the numerical approximation of finite differences. However, if the source code is available, the automatic differentiation preprocessor ADIFOR or ADIC [23] or adjoint methods [92] can be used. Depending on the approach to evaluate the sensitivities the additional computation time scales with the number of design variables. The method of steepest descent is a representative of the gradient-based methods. More advanced deterministic methods truncate eqn.(3.4) after the third term. So, the local curvature information, provided by the second partial derivatives in form of the Hessian ma¯ presume a quadratic model of the system to be optimized. This means, that if the trix H, objective function is quadratic the true optimum is acquired very fast. The Newton method requires the Hessian matrix. Unfortunately, the Hessian matrix is usually not available and the numerical assessment requires too much computational time to be effective [210]. Therefore, techniques like the conjugate gradient method or the variable metric approach [52, 62], accumulate information to approximate the Hessian matrix during the successive iteration steps. The downhill simplex method due to Nelder and Mead [139] represents a deterministic method that does not require the determination of the derivative information. The method is easy to implement but is not as effective as the gradient-based techniques. An entirely different approach to obtain the extremum of a function is represented by the stochastical method. Two major classes of these methods exist. On the one hand by the

3.2. Evolution Strategy

25

Simulated Annealing (SA) approach [131, 96] based on the analogy of the cooling of liquid metals to a crystaline structure of minimum energy state. The objective function is perceived as an energy state to be minimized under slow cooling. The changes in the design variables occur stochastically. In case the parameters deteriorate the energy state the probability of the acceptance of this set is high at the beginning of the optimization (high temperature) and low towards the extremum. Since the increase of the energy state is allowed up to some point the method possesses the possibility to leave local extrema in favor of the global extremum. On the other hand the Evolutionary Algorithms (EA) based on the simplification of the Darwinian principle of the survival of the fittest [134] incorporate stochastical elements. The methods are based on the collective learning capability of a population of individuals each representing a set of design variables which is opposed to the sequential search where one point at the time is evaluated. The EA evolve due to directed stochastical modifications of the individuals by evolutionary operators. Three main implementations of the basic principle can be identified. The Evolutionary Programming (EP) by Fogel et al. [53], the Evolution Strategy (ES) initiated by Rechenberg [155] and Schwefel [180], and the Genetic Algorithms (GA) developed by Holland [82] and De Jong [39]. All the above mentioned stochastical methods have been proved to be robust algorithms capable of finding the global extremum of highly multi-modal, nonlinear, discontinuous, nondifferentiable design topologies. The EA quickly scan the design space towards the optimum due to their population based search. Their efficiency stagnates in the neighborhood of the extremum. The optimization method will be used in the aerodynamic shape design process of an airfoil at transonic speeds with natural transition subject to aerodynamic and structural constraints. This poses a highly multi-modal nonlinear design space topology to be improved. Hence, the Evolution Strategy will be applied since the method is capable of finding the global extremum in complex design spaces and no additional assumptions on the objective function are made. Moreover, the algorithm does not require the calculation of the derivatives of the objective function with respect to the design variables. The following section describes the features and the validation of the ES-method applied. Subsequently, the particular requirements of the aerodynamic shape design on the optimization method will be elaborated.

3.2

Evolution Strategy

The method of the Evolution Strategy was first proposed by Rechenberg [155] with the socalled (1+1)-ES. This algorithm evolves by a mutation-selection scheme for which one individual creates one offspring based on Gaussian normal distribution operating on real values. The scheme was even equipped with the exogenous control of the mutation step size by the 1/5 success rule. The strategies became more sophisticated by the introduction of the multimembered schemes (µ, λ)-ES and (µ + λ)-ES by Schwefel [180]. An important feature of the ES is the capability to adapt strategy parameters, which drive the algorithm, during the optimization process itself. Mainly, the mutation operator σi , which

26

Chapter 3. Aerodynamic Shape Design

can be interpreted as a mean step size, is adapted. This corresponds to large values of σi in the beginning of the search to be able to quickly scan the design space, and to small step sizes when the extremum is almost reached. Thus, the values of the step size significantly determine if the search algorithm finds the optimum, and whether it obtains this point efficiently. To describe the mathematical implementation of the biological analogy, the different operators, and their sequence in the ES algorithm the notation introduced by Schwefel and B¨ ack [12, 179] will be applied. The ES operates on a parent population of size µ ≥ 1 that creates the offspring population of size λ ≥ 1 by the evolutionary operators, recombination and mutation. In most state-ofthe-art methods the offspring size is substantially larger than the parent size, so λ > µ. Each individual is represented as a vector
a ∈ I, where I denotes the space of the individuals. One individual contains n continuous design variables, also referred to as object variables
x ∈ Rn describing the problem and a set of strategy parameters c, which adjust the parameters controlling the evolutionary operators of the algorithm to the problem. So each individual
a = (
x, c) contains object variables and strategy parameters. The population P τ at generation τ contains all individuals, P τ = {
aτ1 , . . . ,
aτµ }. The recombination operator rΘr : I µ → I λ multiplies the µ parents to the λ offspring size. The Θr denote parameter settings driving the recombination. Subsequently, the mutation operator mΘm : I λ → I λ stochastically changes the offspring monitored by Θm . The selection operator sΘs : (I λ ∪ I µ+λ ) → I µ reduces the offspring population to the parent population of the next generation. Generally, the selection operator of EA acts on the fitness function Φ : I → R defined by a mapping of the objective function f (eqn.(3.1)). However, the ES algorithm only acts on the objective function. So, the fitness function is identical to the objective function in ES, i.e. Φ(
x) = f (
x). The algorithm can be summarized in pseudo-code [12]:

τ := 0; initialize: P 0 := {
a01 , . . . ,
a0µ } ∈ I µ ; for I = Rn+w and ak = (xi , cij = cji ∀i, j ∈ 1, . . . , n); evaluate: P 0 : {Φ(
a01 ), . . . , Φ(
a0µ )}; while (ι (P τ ) = true) do
recombine : P τ := rΘr (P τ );


mutate : P τ := mΘm (P τ );

τ

τ

evaluate : P : {Φ(
a1 ), . . . , Φ(
aλ τ )};

τ (τ +1) select : P := sΘs (P ∪ Q); τ = τ + 1; done

(3.5)

The value Q ∈ {∅, P (τ )} determines whether or not the selection operator is elitist or not, whereas ι denotes the termination criterion of the optimization process. The number w denotes the size of the strategy parameters together. The details of each evolutionary operator will be described next.

27

3.2. Evolution Strategy

Mutation Operator On historical basis the mutation represents a main operator within the ES, since it was the only stochastical operator in Rechenberg’s (1+1)-ES. Mutation modifies an individual in order to explore new areas of the design space topology according to the Gaussian probability density function. Large modifications are less likely than small ones. Currently, the mutation operator represents the only solution adaptive operator in the ES algorithm accumulated in the strategy variable set c. This set can be separated into n different variances cii = σi2 (i ∈ {1, . . . , n}) and n · (n − 1)/2 co-variances cij = (i ∈ {1, . . . , n}, j ∈ {i + 1, . . . , n}) of the generalized n-dimensional normal probability density function. This amounts to w = n · (n + 1)/2 strategy variables. The co-variances can be interpreted as rotation angles αij . Usually, the standard deviation σi is used as strategy parameter. In the most general representation of an individual this is summarized to
a = (
x,
σ , α
) ∈ Rn+w where scaling and metrics are self-adaptive during the optimization [12]. This number of variables is too large, so in the current ES-scheme only the scaling is taken into account. The individual is now represented by
a = (
x,
σ ) ∈ R2n . This means, that each object variable xi , which describes the problem to be optimized, is associated with a strategy variable σi . Opposite to the GA, that use a mutation probability, the mutation operator in ES is applied to every variable of each individual of the population. For the mutation from xi to x
i the strategy parameters σi are mutated first. The mutation mτ,τ
: I → I of each variable of an individual
a = (
x,
σ ) to a

= (x

, σ

) is implemented as follows [12, 179]:


σi
= σi · e(τ ·N (0,1)+τ ·Ni (0,1))
x
=
x + N (0,
σ
)

(3.6)

where the general form of N (0, σ) denotes the Gaussian probability density function with expectation value 0 and standard deviation σ, whereas τ
and τ , the so-called learning rates, represent exogenous parameters of the method divided in a global factor τ
and an individual part τ that influence the mutation width σi . This way all mutation widths differ from each other and diversity is maintained. Numerical experiments in the present work on test functions for different values of the robust exogenous parameters yield values of τ
= τ = 0.1 to be preferable. The evolution of the mutation step sizes is based on the assumption that the suitable internal model, represented by the strategy parameters is correlated to the fitness values. The exogene control present in the 1/5 success rule has been replaced by the ability to self-adapt the parameters to the design topology [178]. Recombination Operator The recombination mechanism aims to mix the good parental information to obtain an even better offspring individual. So, recombination is only possible if the number of parents exceeds one. Schwefel [179] and Kursawe et al. [106] identified the recombination to be essential for

28

Chapter 3. Aerodynamic Shape Design

the self-adaptation mechanism to build up an internal model of the system, especially for small populations. The operator rχ
: I µ → I produces one new individual from at least two uniform randomly selected parent individuals. The recombination is applied to the object variables as well as to the strategy parameters, for which the mechanisms for each set does not have to be identical. Five different recombination mechanisms are known for ∀i ∈ {1, . . . , n} [12, 179]: ⎧ xS,i ⎪ ⎪ ⎪ ⎪ ⎨ xS,i or xT,i xS,i + χi · (xT,i − xS,i ) x
i = ⎪ ⎪ x or xTi ,i ⎪ S ,i ⎪ ⎩ i xSi ,i + χi · (xTi ,i − xSi ,i )

no recombination discrete recombination intermediate recombination global, discrete global, intermediate

(3.7)

The subscripts S and T denote two uniform randomly chosen individuals from the parent pool and the intermediate factor χi ∈ [0, 1] is a uniform random variable. The notation in eqn.(3.7) applies to object variable xi as well as to the strategy parameters σi . For the global versions a new set of parent individuals is selected for each single variable of
x. However, the global methods have not been implemented in the current version of the ES-algorithm applied in this work. Empirical results by Schwefel et al. [179] and B¨ ack et al. [12] demonstrated that the discrete recombination operator on the object variables and the intermediate recombination operator on the strategy parameters yield the best result. As proposed by Schwefel [179] the intermediate factor is set to the fixed value χ = 0.5 to avoid the over-adaptation of the strategy parameters. Selection Operator The selection determines which individuals of the current population are offered the possibility to pass their information to their descendants. Opposed to the selection operator in GA that is based on stochastical properties, the selection of the ES is entirely deterministic and only selects the µ best, according to the value of the objective function, of the pool of individuals to survive as parents for the next generation. Two different selection schemes are available for the multi-membered ES. The elitist scheme, denoted as (µ + λ)-ES, selects the parents from a pool including the parents and their offspring. The advantage of this method is a monotonically improving performance. However, individuals with excellent performance located in a local extremum act as an attractor on the other individuals of the population. Hence, the diversity of the population based search is diminished and reduces the possibility of finding the location of the global extremum, especially for small populations. Moreover, the assumption of a correlation between fitness and internal model does not hold anymore. So, the self-adaptation mechanism will be unable to adapt to new environments [12, 106, 179]. The (µ, λ)-ES variant selects the best µ individuals, according to the value of the objective function, from the λ population without keeping the best solution from the previous generation. So, all information of the previous generation is forgotten, even the best solution. This can result in negative ’convergence’ where the performance decreases during the search. However, similar to the SA-algorithm, deterioration of fitness is allowed to enhance the possibility to leave local extrema to seek for the global extremum.

3.2. Evolution Strategy

29

This extinctive selection implies that individuals that perform worse will be rejected as parents for the following population. So the ratio of parents to offspring, µ/λ, can be interpreted as selection pressure. The smaller this ratio, the tougher the selection. This offers fast convergence to a local extremum. Increased values of the ratio reduce the selection pressure and allow the search for the global extremum at a reduced ’convergence’ rate. The challenge remains to find the optimum selection pressure to reach ’convergence’ to the global optimum as fast as possible without premature convergence to a local extremum. The first calculations to determine the maximum convergence rate of a (1+1)-ES were conducted by Rechenberg [155] for two test function represented by the corridor and the sphere model and led to the 1/5 success rule. The calculations were extended to the (µ, λ)-ES and (µ + λ)-ES schemes using one standard deviation without self-adaptation or recombination by Schwefel [181]. He reached values of 1/λ ≈ 1/6.0 for the plus-scheme and 1/λ ≈ 1/4.7 for the commascheme for the different schemes. Analysis of the multi-membered ES with multi recombination has been performed by Beyer [20]. Depending on the number of object variables different combinations of µ and λ are proposed to reach maximum convergence rate. For n → ∞ the analysis confirms calculations by Rechenberg [156]. Moreover, it is shown theoretically, that the convergence rate of an ES-scheme incorporating recombination is higher than without recombination. Numerical experiments using a multi-membered ES with self-adaptation and recombination by Kursawe [106] showed that for an offspring population of 100 the number of parents should range from 12 to 20 if the scaling of the problem has to be ’learned’ by the algorithm. From the previous arguments it has been generally recognized that the selection pressure should range between 1 µ 1 ≤ ≤ . (3.8) 7 λ 5 For multimodal nonlinear objective function topologies, that use the self-adaptivity of the scheme, a moderate selection pressure of approximately 1/7 should be chosen [106, 179]. The moderate specific selection pressure also promotes the self-adaptation characteristics to determine the optimal mutation width of each variable during the optimization [106]. To summarize the previous arguments on the features of the Evolution Strategy the combination of recombination and moderate selection pressure allows the self-adaptive algorithm to learn the scaling of the mutation widths along the different dimension axes during the optimization procedure. Implementation of the Evolution Strategy on Parallel Computation Environments One critical aspect of the optimization process using the evolution strategy is the high number of function evaluations required. In aerodynamic design, the evaluation of the objective function in eqn.(3.1) means the computation of the entire flow field over the airfoil, which is a very time consuming process. Fortunately, the population based search of the ES is implicitly suitable for parallel processing since the evaluation of the objective function of each individual can be performed independently of each other and do not require any message passing between

30

Chapter 3. Aerodynamic Shape Design

processors during the cost function evaluation. The current algorithm is based on the global parallelization model that uses a master/slave scheme using the Message Passing Interface library (MPI) [66]. The master performs the ES operations and distributes the evaluations of the objective function (i.e. one flow field analysis) over the slave-nodes. To obtain an even load balancing the offspring population size represents a multiple of the number of slave-nodes available. The above described features of the Evolution Strategy according to the (µ, λ)-ES scheme with self-adapting properties of the mutation step size have been implemented in the present research using additional library functions of the PGAPack-library [111] and the LAPACK-library. The parallelization of the evaluation of the objective function is conducted on a workstation cluster. The next section describes the validation of the ES-algorithm for different test functions.

3.2.1

Validation of the Optimization Algorithm

To validate the efficiency and effectiveness of the optimization algorithm or to compare the performance with other optimization strategies various test problems have been defined. The known test cases by De Jong (F1 - F5) [39] have become standard in this sense. The tests include unimodal, discontinuous, nonlinear multi-modal and even noisy functions. M¨ uhlenbein et al. [138] extended the test suite with functions F6 to F8 by Rastrigin (F6), Schwefel (F7) and Griewangk (F8). These functions have been summarized by Whitley et al. [218]. For comparison with the results obtained by B¨ ack et al. [12] on the performance of GA and self-adapting ES the generalized version of the highly multi-modal function by Ackley [4] is proposed

⎞  n   n 1 1 2 2 fA : f (xi |i=1,n ) = −20 exp ⎝−0.2 xi ⎠ −exp xi cos(2πxi ) + 20 + e (3.9) n i=1 n i=1 ⎛

min(f (xi |i=1,n )) = f (xi |i=1,n = 0.0) = 0.0 . For n = 30 object variables in a feasible region defined by −30 ≤ xi < 30 ( ∀i ∈ {1, . . . , n}). An impression of the Ackley function in two dimensions is shown in figure 3.1. As for the following test functions, the present ES operates with self-adaptation on all variables of the problem with discrete recombination of the object variables and intermediate recombination of the strategy parameters σi . The selection pressure of approximately 1/7 remains constant for two schemes of (30, 200)-ES and (9, 60)-ES each of which have been executed 20 times to average the results. The latter scheme is additionally analyzed to investigate the number of function evaluations required to reach the optimum. With respect to the aerodynamic design for which the evaluation of the cost function is computationally expensive, the objective is to obtain an optimization algorithm that is able to effectively find the global optimum with a minimum of function evaluations. The variables have been randomly initialized by the values

31

3.2. Evolution Strategy

at the boundary of the feasible region. Both strategies always reached the minimum of the test function defined by a best objective function value smaller than fA < 10−12 . An example of the performance of the ES with respect to the number of function evaluations on the test functions is demonstrated in figure 3.1. Although the (30,200)-ES did locate the minimum, more function evaluations were required compared to the (9,60)-ES.

(9,60)−ES (30,200)−ES

0

best objective function value

25 20

fA

15 10 5 0 20 0 −20

x1

−30

−20

−10

0

10

20

10

−5

10

−10

10

30 −15

10

0

0.5

x2

1

1.5

number of evaluations

2 4

x 10

Fig. 3.1: Left: Ackley function depending on two parameters. Right: Performance of the present ES for the Ackley function. To provide an impression of the performance the results are compared with numerical experiments by B¨ ack et al. [12] for different EA in table 3.1. The scheme denoted ES1 uses the same adaptive mutation width for all variables, whereas the scheme denoted ES30 uses self-adaptation for all 30 step sizes separately. The EP scheme denotes an Evolutionary Programming scheme and GA denotes the Genetic Algorithm implementation. The present method PES performs very well. Table 3.1 also demonstrates the necessity of a self-adaptive method. The designation Avgruns denotes the mean of the best objective function values of each run over 20 runs, whereas σruns denotes the RMS value among the best objective function value of each run over 20 runs.

ES1 ES30 EP GA PES (30,200) PES ( 9,60) Table 3.1:

Avgruns 1.326 1.618 ·10−3 1.976 5.253 1.487 ·10−13 2.220 ·10−15

σruns 1.039 9.290 6.300 5.130 5.156 9.893

·10−4 ·10−1 ·10−1 ·10−14 ·10−16

Performance of different schemes on the Ackley function using 30 object variables after 1 · 105 function evaluations and averaged over 20 runs.

Although the extended test suite has become very popular for the analysis and tuning of op-

32

Chapter 3. Aerodynamic Shape Design

timization schemes, Whitley et al. [218] point out the risk of customizing the schemes to particular problems of the test suite. It is also argued that as long as the test functions are separable and symmetric the problems become significantly easier to solve. This also allows specially designed line search algorithms, that exploit separability by solving for each parameter separately. Therefore, composed test functions are proposed that are extremely nonlinear, nonseparable and scalable. The feature of scalability is necessary to allow testing of problems with increasingly higher dimensionality. One of the composed test functions uses the two parameter Rosenbrock function (F2) depending on the one-dimensional Griewangk function (F8) for an n dimensional problem [218]:

F 8F 2 : f (xi |i=1,n ) = F 8(F 2(xi |i=1,2 )) + F 8(F 2(xi |i=2,3 )) + · · · + F 8(F 2(xi |i=n−1,n )) + F 8(F 2(xi |i=n,1 )) F 2 : f (xi |i=1,2 ) = 100 (x21 + x22 )2 + (1 − x1 )2 F 8 : f (xi |i=1,n ) = 1 +

xi ∈ [−2.048, 2.047]


 n n


 x2i xi cos √ − 4000 i i=1 i=1

min(f (xi |i=1,n )) = f (xi |i=1,n = 1.0) = 0.0 .

xi ∈ [−512, 511]

(3.10)

(3.11)

(3.12) (3.13)

The performance of the PES-algorithm on the composed function is compared with the bitcoded techniques used by Whitley et al. [218] and an elitist ES with adaptive step size by De Falco et al. [37]. The methods used by Whitley et al. are generic GA incorporating elitism and tournament selection, represented by the algorithms ESGAT [64] and Genitor [217], and adaptive search technique CHC [47]. Two bit-coded hill-climbing methods have also been used, the RBC [35] and the Line search algorithm [218]. Both latter methods are specially designed to exploit separability and symmetry of the objective function. Since the purpose of the comparison is to provide an impression of the capability of the present ES and not the detailed analysis of the results among all techniques, the features of the different methods will not be presented in detail here. The ES is operated as a global optimization method, that has not been tailored for the test cases. The scheme relies on the self-adaptivity to build an internal model of the problem at hand. It has to be kept in mind, that the parameters of bit-coded methods are represented by 10 to 12 bits. Compared with ES that uses the real value representation of the parameters, the bit-coded string possesses a reduced resolution. Therefore, the optimum is easier to find, especially if the bits of the string are randomly flipped as done by RBC and the Line search algorithm. The average and the standard deviation of the best solutions after 500,000 objective function evaluations over 30 runs for four different problem dimensions are compared in table 3.2.

33

3.2. Evolution Strategy

10 CHC [47] RBC [35] ESGAT [64] Genitor [217] Line [218] ES (15,100) [37] PES (15,100) PES (30,200) Table 3.2:

Avgruns 1.344 0.139 4.077 4.365 3.029 2.117 0.313 0.279

σruns 0.921 0.422 2.742 2.741 5.153 1.417 0.273 0.270

Dimension of the test function F8F2 20 50 100 Avgruns σruns Avgruns σruns Avgruns σruns 5.630 2.862 75.100 49.644 670.223 377.59 7.243 11.289 301.651 72.745 1655.557 605.268 47.998 32.615 527.100 176.988 2991.890 596.470 21.452 19.459 398.120 220.284 2844.389 655.159 2.503 3.280 2.652 2.558 1606.400 1583.500 8.852 21.698 141.679 155.052 1579.264 631.193 0.891 0.592 4.489 1.054 14.903 2.692 0.845 0.605 3.278 0.765 9.458 1.415

Performance of different schemes on the F8F2 function of different dimensions after 5 · 105 function evaluations and averaged over 30 runs.

The good performance of the PES algorithm is obvious from the results displayed in table 3.2. For the problems of moderate dimension the bit-climber methods, RBC and Line, take advantage of their bit coding. However, as the problem dimension increases, the 5 · 105 function evaluation are not sufficient anymore to find the optimum. It is also striking, that none of the algorithms was able to confidently allocate the optimum for all runs. The runs with the best performance of the PES-algorithm with respect to their objective function value are displayed in figure 3.2. According to these results the best values of the objective functions are reached after approximately 20,000 function evaluations. So, the high number of 500,000 evaluations is in favor of the bit-climbing approaches. 6

0

10 n= 10 n= 20 n= 50 n=100

4

10

−1

mean mutation step size

best objective function value

10

2

10

0

10

−2

10

10

−2

10

−3

10

−4

10

−5

10 −4

10

−6

0

1

2

3

number of evaluations

4

5 4

x 10

10

0

100

200

300

400

500

generations

Fig. 3.2: Left: Best performance of the (30,200)-ES on the F8F2 composed test function. Right: Adaptation of two of the mutation width strategy parameters during the search. Another interesting result is the different performance of both Evolution Strategies due to

34

Chapter 3. Aerodynamic Shape Design

the (µ + λ)-ES elitist scheme used by De Falco et al. [37]. This is an excellent example of premature convergence to a local optimum since in the elitist scheme the mutation width and the fitness value are not correlated anymore which has been mentioned in section 3.2. The kink in the solid line of n = 10 in figure 3.2 demonstrates the necessity to allow the algorithm to increase the objective function value in order to improve the possibility to eventually find the global optimum. The shortcomings of the elitism scheme are apparent since the approach was not able to locate the global optimum once [37]. The investigation of the test function F8F2 with the present PES algorithm summarized in table 3.2 provides an indication of the population size required to allow the algorithm to find the global optimum at a minimum number of function evaluations. For high multi-modal nonlinear functions, with a fixed selection pressure of 1/7 the number of parents should approximately correspond to the number of object variables. This result will also be used for the subsequent aerodynamic design. The development of the mean mutation step size associated with two object variables during the optimization presented in figure 3.2 clearly evidences the adaptation of the strategy parameter as the search moves on. The parallel evolution strategy developed in this work performs very good even on extremely nonlinear, multi-modal test functions represented by F8F2. It also compares well with other evolutionary algorithms. Therefore, it is expected to perform similarly on the highly nonlinear problem of airfoil shape optimization in a transonic flow with natural transition and the presence of separation bubbles. The next section will describe the requirements for the implementation of the Evolution Strategy to aerodynamic design.

3.3

Constrained Airfoil Design

The implementation of an optimization algorithm to aerodynamic design concerns the aspects of the definition of a suitable objective function and the choice of the design variables describing the airfoil shape. Another part to be considered is the method to obtain the aerodynamic features summarized in the objective function. This is equivalent to the definition of a numerical method to compute the transonic flow over an airfoil with natural transition. The favorable aerodynamic features of an airfoil have been mentioned in chapter 2. The main objective is to improve the lift-to-drag ratio along the drag polar and to avoid the negative effects associated with the occurrence of separation. More specifically, this means the objective is to keep the boundary layer laminar over such a long distance that the friction drag is reduced and that the turbulent state is achieved just before the flow is likely to separate. However, the resulting airfoil shape has to fulfill structural requirements so therefore a constraint is imposed that does not allow the maximum airfoil thickness to fall below 12 % of the chord length. An additional constraint is imposed on the occurrence of a separation region to avoid buffeting. The mathematical implementation of the aforementioned physical considerations into the optimization procedure can be achieved by a suitable objective function containing the important

35

3.3. Constrained Airfoil Design

aerodynamic parameters describing the airfoil flow, e.g. transition location or lift-to-drag ratio. For the present investigation this yields the following objective function f to be minimized: min(f (
x)) = min(CD ).

(3.14)

Since the lift coefficient CL is kept constant and the drag coefficient CD is variable, the objective function can be regarded as a maximization of the lift-to-drag ratio. The additional requirements in the form of constraints will be accounted for by the implementation of penalty functions.

3.3.1

Implementation of Constraints

In most optimization problems constraints have to be met. The occurrence of constraints divides the design space into a feasible range, where no constraint is active and an infeasible range, for which at least one constraint is violated. The most popular approach to implement constraint-handling properties to the evolutionary algorithms is the penalty method that performs a modification of the objective function. This way, the constrained problem is transformed to an unconstrained problem. The method is easy to implement, although the design of a good penalty function is still no trivial task [134]. Other methods use decoders to assure the development of feasible individuals or repair functions that repair an infeasible individual [134]. However, both approaches are too problem dependent to be generally applicable. An evolutionary programming method proposed by Michalewicz [132] based on linear programming can not be implemented for aerodynamic design, since the direct correlation between constraints and the objective function is not available. The implementation of the penalty approach to the evolution strategy is as follows:  f (
x) if
x is feasible Φ(
x) = (3.15) f (
x) ± Q(
x) if
x is infeasible. The ±-sign distinguishes between a minimizing and a maximizing problem. The value Q represents the penalty for an infeasible individual. The approach to reject infeasible individuals, also referred to as ’death penalty’, is widely applied in evolution strategies. This individual is either assigned a predefined poor objective function value or the algorithm generates as many individuals as necessary till a feasible individual has been found. Both approaches perform reasonably well if the feasible region covers a large portion of the entire design space. The method does not exploit information from the infeasible individuals. Therefore, it has been demonstrated that the rejection approach is inferior to methods that incorporate the distance from the feasible region [134]. For the airfoil design constraints are imposed on the maximum airfoil thickness and the size of the separation bubble. Only in the case of the airfoil thickness constraint, which is directly correlated to the design variables, it would be possible to operate according to the rejection scheme. In the case of the constraint on the separation size an entire flow computation is required. It would be a waste of computational time if the information of an infeasible individual would not be used to direct the search algorithm towards feasibility. This is especially the

36

Chapter 3. Aerodynamic Shape Design

case for the aerodynamic design on a laminar-type airfoil at transonic speeds, where separation bubbles are present for some freestream conditions on the initial airfoil. The optimization process starts in the infeasible region and the primary goal is to determine feasible individuals (i.e. airfoil shapes) even if this would imply the reduction of the lift-to-drag ratio. So, information of infeasible individuals will be considered with the goal to retain feasibility for both constraints. However, the characteristic length scales of both constraints are very different. The separation bubble of 10% chord length has to be removed, whereas the maximum thickness of 12 % chord length has to be retained with an accuracy of 1 chord. Moreover, the value of the objective function differs with the freestream conditions. So, the same amount of violation of the constraints can not be allowed to have the same absolute penalty value. This would mean that the impact of a separation bubble of 10 % chord occurring at two different conditions of L/D=20 and L/D=30, which is physically equal, would be rated mathematically different. This has to be prevented. Therefore, a new penalty function has been designed in this work that allows the scaling of physically different constraints according to their impact on the objective function. Moreover, all penalties will be scaled with the objective function value. The overall penalty function value Q depends on the objective function value of the unconstrained problem and the sum of all violated constraints φiΘp monitored by some control parameters for the penalty operator Θp , Q(
x) = f (
x) ·

q 1 φi . q τr i=1 Θp

(3.16)

The values φiΘp ∈ [0, 1] represent normalized penalties, whereas q denotes the number of violated constraints. Additionally, a penalty relaxation scheme according to Michalewicz et al. [133] based on the idea of simulated annealing has been incorporated. At the beginning of the search, at high ’temperatures’ τr , the impact of violated constraints is moderate and increases as the generations evolve towards the optimum that reduces the ’temperature’. The violated constraints have been normalized according to the Gaussian-normal distribution function, fGauß (x, σ) =

1 − 12 ( σx )2 , e 2πσ

(3.17)

where the distribution is not considered as a probability density function. The advantage of the Gaussian distribution function is the control using one parameter σ, which allows the definition of the severity of the constraint violation for each constraint separately. The normalized penalty φi (∆ti ,σi ) is determined as φi

(∆ti ,σi )

=1−

fGauß (∆ti , σi ) , fGauß (0, σi )

(3.18)

where ∆ti denotes the distance of the violated constraint to the feasible region, and the standard deviation σi denotes the associated control parameter. For the application of the proposed penalty function approach to the airfoil design it is only necessary to determine the corresponding value of the control parameter for the airfoil thickness and separation constraint.

37

3.3. Constrained Airfoil Design

Regarding the maximum airfoil thickness of at least 12 % of the chord length it is essential from a structural point of view that the thickness is maintained. Therefore, a severe penalty is required if the constraint is violated. This implies a value of the penalty control parameter of σthick = 0.005. The separation penalty is not required to be as severe as the thickness penalty, which corresponds to a value of σsep = 0.030. The implications of the choice of the penalty control parameters is demonstrated in figure 3.3. 1

0.8

0.6

φ

σthick

σsep

0.4

0.2

0 −10

σ = 0.005 thick σsep = 0.030 −8

−6

−4

∆ t [%]

−2

0

Fig. 3.3: Scaling of the constraints on minimum airfoil thickness and separation with one control parameter according to the Gaussian-normal distribution function. A penalty function has been proposed for the implementation of multiple constraints of different physical background to aerodynamic optimization. During the optimization process over a wide range of freestream conditions the described values for the control parameters will not be modified, although the values of the objective function differ significantly in the prescribed range. This property is allowed due to the scaling of the penalties.

3.3.2

Airfoil Shape Parameterization

It has been recognized in many shape optimization investigations that small geometry perturbations of the initial airfoil shape can have a significant impact on the performance of the airfoil. So, the airfoil shape parameterization significantly determines the quality and effectiveness of the overall aerodynamic shape design process. Since one objective function evaluation implies the computation of the entire flow field around the airfoil a minimum number of design variables describing the airfoil geometry is required to reduce the overall computational effort. Still the number of control points has to be sufficiently large to allow a wide range of airfoil geometries to be covered by the shape describing method. Apart from the number of design variables included in the parameterization, the method has to be flexible in the sense that it is able to represent a large number of possible geometries, i.e. the initial airfoil shape LVA-1A has to be included in the parameter space of the parameterization approach. Moreover, the shape has to be very smooth since the transition of the laminar boundary layer is very sensitive

38

Chapter 3. Aerodynamic Shape Design

to small imperfections, like curvature jumps. Finally, it has to be kept in mind that the airfoil shapes resulting from the numerical aerodynamic optimization process will be tested on the wind tunnel model with the adaptive upper side. Therefore, the resulting airfoil shape has to be within the range of the adjustment kinematics described in section 4.2.2. The first well known airfoil parameterization methods are represented by the NACA-series and the Joukowski-transformation. The latter approach describes an airfoil shape by the conformal mapping of a circle to an airfoil shape using the coordinates of the center of the circle as parameters to influence the thickness and the camber. The Joukowski-transformation has been extended to increase the parameterized space [94]. The 4-digit NACA-series allows the description of an entire airfoil shape with only three parameters directly related to the airfoil geometry. However, these methods only cover a small range of airfoil shape and do not include supercritical airfoils geometries. A large number of shape parameterization methods exist. A survey of the currently applied methods in multidisciplinary shape design is provided by Samareh [168]. In the current investigation different polynomial approaches and the analytical approach using a linear combination of geometric modes have been implemented. In this work first investigations were conducted using approximated piecewise polynomials also applied by Guntermann [67] for subsonic flow. The control points have been defined by the chordwise positions of the adjustment mechanisms in the wind tunnel model. However, this parameterization approach yields too wavy airfoil shapes at transonic speeds. This has also been observed by Jameson [93]. The airfoil shape parameterization methods that proved to perform well for aerodynamic design in numerous investigations will be described in the following section.

Geometric Modes Airfoil Shape Parameterization The concept of the airfoil shape parameterization using the geometric mode formulation is the perturbation of an initial airfoil shape by a linear combination of K base functions gk according to

ynew (x) = yinit (x) +

K

ηk gk (x).

(3.19)

k=1

The design variables ηk determine the amplitude of the associated base function gk . In case all design variables are set to zero, the initial airfoil shape is computed. The base functions are predefined smooth curves that reach their maximum at a prescribed chordwise location xk . For a five parameter shape parameterization this means that five base functions are associated with five different chordwise positions. Several sets of base or shape functions have been used for airfoil modifications represented by the Hicks and Henne functions [76], the Wagner functions [153] or the aerofunctions [6]. The shape functions used in the present work have been applied by Lee et al. [109] to airfoil shape optimization. They are composed of two patched polynomials,

39

3.3. Constrained Airfoil Design

gk (x) = 1 − gk (x) = 1 −

 

xk −x xk x−xk 1−xk

2  2 

1+

A (1−xk )2

1+

B x2k



 

1−x 1−xk

for 0 ≤ x ≤ xk

x xk

(3.20)



for xk < x ≤ 1

where A = max(0, 1 − 2xk ) and B = max(0, 2xk − 1)

(3.21)

Both functions join smoothly at their definition point xk without oscillations and are continuous up to the second derivative. That is, no curvature jump in the airfoil contour will cause premature transition. An example of the definition of the geometric modes at four points on the airfoil chord xk = {0.1, 0.4, 0.5, 0.7}, ∀ k = {1, . . . , 4} is provided in figure 3.4 0.015 K

Σ η g (x)

k=1

k

k

0.01

∆ y(x)

↑ ↓

0.005

0 0

↑ ↓

↑ ↓

↑ ↓

↑ ↓

↑ ↓

↑ ↓

↑ ↓

η g (x) k

0.2

k

0.4

0.6

0.8

1

x

Fig. 3.4: Left: Example of the superposition of the geometric modes at four stations along the airfoil chord . Right: Location of each geometric mode on the airfoil upper surface. Since the base functions are added onto an initial airfoil shape, the LVA-1A initial geometry is automatically included in the parameterization space. Moreover, the shape functions show close resemblance to a simply supported beam of unit length under an intermediate load at position xk . Therefore, the definition of the shape functions is very well suited to describe the vertical deflection of the fiber composite flexible upper surface of the wind tunnel model. For the aerodynamic optimization of the airfoil shape, eight geometric modes have been distributed over the airfoil chord at the positions xk = {0.15, 0.20, 0.25, 0.30, 0.40, 0.50, 0.60, 0.70}, ∀ k = {1, . . . , 8}. These positions are visualized in figure 3.4. With respect to the definition of the design of the wind tunnel model no additional modes have been positioned nearer to the leading edge or to the trailing edge.

40

Chapter 3. Aerodynamic Shape Design

PARSEC Polynomial Representation Oyama et al. [145] conducted a comparison study on the accuracy of the reproduction of a NASA supercritical airfoil and its performance during aerodynamic design of five parameterization approaches. The PARSEC method proposed by Sobieczky [187] was shown to suite aerodynamic optimization. This method is based on a linear combination of shape functions controlled by parameters associated to characteristic features of the airfoil shape according to the polynomial

y(x) =

6

ak (x) · xk−1/2

(3.22)

k=1

The upper and lower airfoil side are modelled separately. For the entire airfoil shape definitions this yields 11 parameters demonstrated in figure 3.5 YXX UP X UP RLE

X LOW

Y UP YLOW

α TE β TE

YTE ∆ YTE

Y XX LOW

Fig. 3.5: Airfoil shape parameterization according to the 11 parameter PARSECapproach [187]: leading-edge radius (RLE ), upper and lower crest (XU P , YU P , XLOW , YLOW ) and curvature at position (YXX U P , YXX LOW ), trailing-edge thickness (∆YT E ), vertical coordinate (YT E ) and angles (αT E, βT E ). To obtain the parameters describing the initial airfoil a small optimization itself has to be conducted. Unfortunately, the transonic laminar airfoil LVA-1A is not entirely enclosed in the PARSEC-parameterization.

3.4

Numerical Flow Simulation Methods

The aerodynamic design combines an optimization algorithm with an approach to determine the value of the objective function. The optimization algorithm is represented by the Evolution Strategy, which has been described in the previous section. Its advantage is that no assumptions on the nature of the numerical method applied for the computation of the transonic flow over the airfoil have to be obeyed. Two numerical approaches have been combined with the optimization algorithm. The Navier-Stokes equations represent the most general and accurate description of flows that can be regarded as a continuum. However, the solution procedure of the Navier-Stokes equations is time consuming. A computationally less time consuming method is represented by the Euler-boundary-layer approach, that is based on assumptions on the nature of the airfoil flow to reduce the computational time required.

41

3.4. Numerical Flow Simulation Methods

3.4.1

Mathematical Formulation

Conservation Equations The conservation of mass, momentum and energy of a continuum flow is described by the Navier-Stokes equations. In the most general case of an unsteady, compressible, and viscous flow, for which external forces and heat sources can be neglegted, these equations can be written in divergence form,
∂Q + ∇ · F¯ = 0, ∂t

(3.23)


denotes the vector of conservative variables of density ρ, specific momentum ρ
v , and where Q specific energy ρE. F¯ denotes the flux through the volume surface, which can be divided into an advective part F¯ A and a diffusive part F¯ D according to ⎛

⎞ ρ
= ⎝ ρ
v ⎠ , Q ρE

⎞ ⎛ ⎞ ρ
v 0 ⎠. τ¯ F¯ = F¯ A − F¯ D = ⎝ ρ
v
v + pI¯ ⎠ − ⎝ τ¯ ·
v +
q ρE
v ⎛

(3.24)

Since the number of unknowns is larger than the number of equations additional relations have to be formulated. The equations of state for a thermally and calorically ideal gas provide a relation for the properties pressure p, density ρ, and temperature T combined with a formulation that relates the total energy E to the pressure according to γp = ρT

,



u2 p = ρ(γ − 1) E − 2

(3.25)

with the ratio of specific heats γ = cp /cv . Under the assumption of a Newtonian fluid and zero bulk viscosity, according to the Stokes hypothesis [200], the shear stress tensor τ¯ is related to the velocity gradients  2  τ¯ = µ ∇
v + (∇
v )T − I¯ ∇ ·
v 3 The dynamic viscosity is denoted by µ, whereas the superscript

(3.26) T

denotes a transposed tensor.

The rate of heat transfer, denoted by
q, is proportional to the temperature gradient according to Fourier’s law of heat conduction
q = −λ∇T,

(3.27)

where λ represents the coefficient of thermal conductivity. For the consideration of steady flow over an airfoil at transonic speeds, the following significant dimensionless quantities can be

42

Chapter 3. Aerodynamic Shape Design

defined, Ma =

u∞ a

,

Re =

u∞ l ν

,

Pr =

µ cp = 0.72. λ

(3.28)

For a constant Prandtl number and for constant specific heats the thermal conductivity coefficient λ and the dynamic viscocity µ in dimensionless form can be described by the same power law 0.72
λ µ T = = . (3.29) µref λref Tref For the study of entirely laminar flow, the system is closed by the previous relations. Under the assumption that turbulence imposes small disturbances on a mean flow and does not impose an unsteady part on the large scale mean flow each flow quantity φ(
x, t) can be split for steady flows, φ(
x, t) = φ(
x) + φ
(
x, t) (3.30) into a steady average value φ(
x), which is only position dependent, and an unsteady fluctuating part φ
(
x, t). Applied to the Navier-Stokes equations this yields the so-called Reynoldsaveraged Navier-Stokes equations (RANS), which differ from eqn.(3.24) by the additional Reynolds stress tensor τ¯t and the turbulent heat flux
qt . A widely applied closure assumption by Boussinesq [27] relates the turbulent fluctuations to the time-averaged quantities through a proportionality constant, the so-called eddy viscosity µt . Additional relations are required. The turbulence models, that apply the Prandtl mixing length hypothesis to determine of the eddy-viscosity, are referred to as algebraic eddy-viscosity models. In the present method the turbulence model according to Baldwin and Lomax [14] has been used. The turbulent heat flux
qt is accounted for through the increased thermal conductivity by the introduction of a constant turbulent Prandtl number Prt =0.9. Using the aforementioned assumptions the system of equations can be closed for the calculation of steady, high Reynolds number flows over airfoils with laminar or turbulent boundary layers. The system of equations states an initial value problem in time and a boundary value problem in space. The associated conditions will be discussed in the following section. Initial and Boundary Conditions The initial conditions at time t = 0 correspond to the cruise flight conditions at high subsonic Mach numbers
u |t=0 =
u∞ , p |t=0 = p∞ , ρ |t=0 = ρ∞ . (3.31) At the airfoil surface the boundary condition for a solid, adiabatic wall apply  ∂p 
u |y=0 =
0, = 0,
q |y=0 =
0. ∂
n y=0

(3.32)

The first term in eqn.(3.32) represents the no-slip condition. The vanishing wall normal pressure gradient is only valid within Prandtl’s first-order boundary-layer approximation for high

3.4. Numerical Flow Simulation Methods

43

Reynolds numbers. A more accurate condition results from the solution of the Euler momentum equations at the wall [43, 127]. However, for high Reynolds numbers and in the absence of strong surface curvature, the relation of a vanishing wall normal pressure gradient holds. Since the domain of integration has to be finite, artificial boundaries in the far-field are introduced. For high Reynolds number flows, for which the far-field boundary is sufficiently far away from the body, the viscous forces are small compared to the convective forces. So, in the absence of large gradients, the characteristic form of the Euler equations can be applied for the definition of the far-field conditions as described in [128]. Numerical Solution Algorithm The system of governing equations, defined by equations 3.23 and 3.24 is solved on a structured grid at each control volume. The numerical flow computation method applied here, is based on the approach developed at the Aerodynamisches Institut [69, 129]. The system of equations has been written in conservation form, to allow for discontinuities such as shocks in the flow field. The transformation of the equations into general curvilinear form enables the use of boundary-fitted grids. Although the method allows the computation of three-dimensional flows, calculations of two dimensional flows have been conducted, since the flow over an airfoil with rectangular top-view is essentially two dimensional. The spatial discretization of the advective terms in eqn.(3.24) is performed by the Advection Upwind Splitting Method (AUSM), proposed by Liou [116, 115], in the AUSMDV variant by Wada and Liou [213]. The benefit of the AUSM scheme is the separation of the advective fluxes into a convective part and a pressure gradient part, which are treated differently. The implementation in the available solver has been described in [42, 43, 127]. To achieve second order accuracy in space the Monotonic Upstream Centered Scheme for Conservation Laws (MUSCL) interpolation according to Van Leer [209] has been applied. To prevent oscillations a limiter according to Van Albada [207] locally reduces the spatial accuracy to first order in the vicinity of extrema and discontinuities. The discretization of the dissipative fluxes is performed by a central difference scheme according to a modified cell-vertex approach described by Meinke [128]. The discretization scheme is of second-order accuracy in space. The system of the governing equations state an initial value problem in time. For the integration in time an explicit 5-stage Runge-Kutta approach has been applied, for which the values of the coefficients of the method have been optimized with respect to stability [128]. Therefore, although five stages are applied, the scheme is only of second-order accuracy in time. Validation of the Numerical Method The numerical method enables the computation of general compressible, high Reynolds number flows with shocks over arbitrary configurations. For the validation of the numerical solution of the Navier-Stokes equations the numerical dissipation and the ability to accurately resolve

44

Chapter 3. Aerodynamic Shape Design

the boundary layer have to be considered. Subsequently, the computation of two-dimensional flow over the laminar-type airfoil DA LVA-1A at transonic speeds will be compared with an experimentally determined pressure distribution obtained within the EUROSHOCK I program [197]. The numerical dissipation of the scheme has been investigated by Dietz and Meijering [42, 127] for the inviscid flow over a circular cylinder and the compressible boundary-layer flow. The result of the computation of the inviscid flow over a circular cylinder has been compared with the theoretical result from the potential theory, which shows the very low numerical dissipation of the numerical approach. Analogously to the analytical, self-similar solution of the incompressible flow over a flat plate with zero pressure gradient according to Blasius the computational results of the compressible boundary-layer flow over a flat plate without pressure gradient can be compared to its selfsimilar solution [171]. The validation of the scheme has been conducted by Dietz [42] for supersonic freestream conditions and by Meijering [127] for subsonic flow, which demonstrate a very good agreement of the computed velocity and temperature profiles with the self-similar solution, even for the second derivative of these quantities with respect to the wall-normal coordinate. To validate the numerical scheme for the computation of the two-dimensional flow over the LVA-1A airfoil at transonic speeds at Ma∞ = 0.7613 and Re∞ = 4.64 · 106 with fixed transition on the upper and lower airfoil side at 45% chord the results are compared with data from the EUROSHOCK I program [197]. The grid, which defines the domain of integration, has been designed using transfinite interpolation with subsequent elliptic smoothing [205]. To reduce the influences of the far-field boundary, the domain of integration has been extended to 15 chord lengths from the leading edge of the airfoil as shown in figure 3.6. The integration domain has been divided into four blocks. 15 0.6

10

0.4

5

0.2

0

0 −0.2

−5

−0.4

−10 −15 −15

−0.6

−10

−5

0

5

10

15

−0.5

0

Fig. 3.6: Four block boundary-fitted grid over the LVA-1A airfoil.

0.5

1

1.5

45

3.4. Numerical Flow Simulation Methods

The numerically and experimentally obtained pressure distributions have been compared in figure 3.7. The figure also indicates the results of calculations by the Euler-boundary-layer method, which will be described in the next section 3.4.2. 2

ma

Navier−Stokes Euler−BL exp. Dasa

1.5

1

0.5

−Cp

1.14 1.07 0.99 0.91 0.84 0.76 0.69 0.61 0.53 0.46 0.38 0.31 0.23 0.15 0.08

0

−0.5

−1

−1.5 0

0.2

0.4

0.6

0.8

1

x/c

Fig. 3.7: Comparison of experimental and numerical data of the flow over the LVA-1A airfoil at Ma∞ = 0.7613 and Re∞ = 4.64 · 106 , and α = 1.0o with fixed transition at 48% chord on both sides. Left: Gray scale representation of the Mach numberwith isobars. Right: Comparison of the pressure distribution for two numerical schemes with the EUROSHOCK I experiment [197]. The extent of the supersonic region over the airfoil upper surface is evidenced by Mach number contours is figure 3.7. The right part of the figure indicates by juxtaposing several pressure distributions the good accuracy of both numerical methods. The flow characteristics, that are typical for transonic airfoil flows are well captured..

3.4.2

Viscous-Inviscid Method

The airfoil flow analysis method which is incorporated in the aerodynamic design process to determine the objective function value for a set of design variables has to be effective and robust. Besides the Navier-Stokes method the Euler-boundary-layer approach by Drela has been applied [44, 45, 61] for the two-dimensional airfoil shape optimization. Due to the streamline-base discretization of the steady Euler equations the method is able to compute the transonic flow over an airfoil very fast. The inviscid outer flow has been coupled with a boundary-layer method. The inviscid part of the flow field is described by the steady Euler-equations in integral form. These equations are discretized in conservation form on an H-type grid, where two neighboring horizontal grid lines correspond to a stream tube. As described by Drela the lack of convection across the streamline is exploited in the discretization of the Euler-equations. The equations of

46

Chapter 3. Aerodynamic Shape Design

continuity and energy are reduced to analytic formulations that reduce the number of variables to the normal position of each grid node and the density on the cell face, which significantly enhances the efficiency of the computation. The inviscid outer flow is coupled with the viscous boundary-layer flow through the displacement thickness. A two-equation integral boundary-layer method for the integral momentum and the kinetic energy shape parameter for laminar and/or turbulent flows has been incorporated. The approach allows the accurate analysis of a boundary-layer flow with spatially limited separation regions provided the thickness of the separation bubble remains in the order of magnitude of the boundary-layer thickness [45]. The transition from a laminar to a turbulent boundary-layer state is described by the linear stability theory in form of the Orr-Sommerfeld equation to determine the spatial amplification of Tollmien-Schlichting waves of the velocity profiles as described in section 2.1. The amplification rates of the velocity profiles at consecutive stations in chordwise direction are integrated according to eqn.(2.2) to determine the transition location based on the eN -method. The value of the N-factor has to be determined by wind tunnel experiments in the trisonic wind tunnel. The Euler-boundary-layer approach by Drela is a suitable method for the computation of shock-induced separation at transonic speeds as long as the assumption of sufficiently thin separation regions is valid. Unfortunately, the optimization scheme will inevitably propose several airfoil shapes that show massive separation due to trailing-edge separation, which violate the above assumption. Hence, the Euler-boundary-layer approach will fail to converge, so no objective function value can be returned to the optimization method to evaluate the individual under consideration. Obviously, the airfoil shape represents an infeasible result due to the massive separation that is accounted for in the penalty function as described in section 3.3.1. As mentioned above a good penalty function should exploit the information about the distance of an infeasible individual to the feasible region. However, in the specific case where convergence failed and no particular value for the objective function can be attributed to the individual, the rejection scheme has to be applied. The individual will be assigned a predefined fixed value that is even worse than the smallest possible objective function value obtained for an airfoil shape based on a flow solution that converged. Due to the extinctive selection of the Evolution Strategy this penalty method causes the rejection of the heavily penalized individual for the next generation to avoid the passing on of its information to the descendants.

3.4.3

Field of Application of each Flow Computation Approach

In the previous sections, two approaches to compute the 2-dimensional, transonic airfoil flow have been described, which both perform well. The method based on the solution of the Navier-Stokes equations represents a more general approach compared to the Eulerboundary-layer method, with respect to the number of assumptions for the airfoil flow field. The Euler-boundary-layer method, for instance, can not handle large separations. However, at cruise conditions, considered in this study, no large separation regions occur. The broader range of application of the Navier-Stokes-algorithm requires a substantial amount of additional computational resources, especially in computational time. This limits the flexibility

3.4. Numerical Flow Simulation Methods

47

of the aerodynamic design in the sense of a large population size or the maximum number of generations allowed, since every evaluation of the objective function requires the computation of the entire flow field. Moreover, the solution method for the Navier-Stokes equations does not enable the prediction of the transition location. So, although both methods have been combined with the optimization procedure, the present aerodynamic design will focus on the application of the Evolution Strategy in combination with the Euler-boundary-layer method for the design of laminar-type airfoil at transonic flow conditions with natural transition. The flow over the final airfoil shape based on the Euler-boundary-layer method will be validated afterwards by the solution of the Navier-Stokes equations, where the transition location will be fixed to the position predicted by the eN -method. To validate the results of the aerodynamic design and to demonstrate the aerodynamic potential for drag reduction by the adaptive wing technology detailed wind tunnel investigations have been conducted for a solid model and an adaptive wing model. Both wind tunnel models have been designed and manufactured in the course of this work. The test facility, the models and the measurement techniques will be presented in the following part.

48

Chapter 3. Aerodynamic Shape Design

Chapter 4 Test Facility and Models The significant flow phenomena for the transonic airfoil flow considered in the numerical simulations will be validated experimentally in the trisonic wind tunnel of the Aerodynamisches Institut. Since the flow quality of the wind tunnel is significant for the transition experiments, special attention has been payed to the determination of disturbances and uniformity of the flow in the test section. The tests have been conducted using a model with a rigid surface and an adaptive wing model.

4.1

Trisonic Wind Tunnel

The trisonic wind tunnel represents a vacuum storage type wind tunnel with a test section of 0.4 × 0.4 m2 cross section that operates according to the intermittent working principle. The wind tunnel can operate at subsonic, transonic, and supersonic Mach numbers that range from 0.2 ≤ Ma∞ ≤ 4.0. Depending on the Mach number test periods between 3 to 10 seconds can be realized. Prior to the start of the test the vacuum tanks with a total volume of 395 m3 are evacuated up to 10% of the ambient pressure by a screw-type compressor with 400 kW power (figure 4.1). The air retreated from the tanks is directed through a dryer facility filled with silica gel and pumped into the balloon with an effective volume of 165 m3 . Hence, after approximately three wind tunnel runs, condensation of the air in the test section is prevented. Inside the balloon there is ambient temperature, whereas the stagnation pressure is regulated to only a few millimeters water column above ambient pressure. That is, the stagnation conditions can be assumed constant during a wind tunnel test. Due to the operating principle of the wind tunnel the stagnation conditions are determined by the ambient conditions. For the investigation of the flow over an airfoil, this means, that at constant ambient conditions the Reynolds number is determined by the Mach number and the airfoil chord length. Figure 4.2 shows the attainable Reynolds number range based on the airfoil chord length of 200 mm at different common ambient conditions.

49

50

Chapter 4.

Test Facility and Models

Fig. 4.1: Principle sketch of the trisonic wind tunnel of the Aerodynamisches Institut.

6

3.5

x 10

3

Re∞

2.5

2

1.5 T0=298.0 K, P0=990.0 hPa T =295.5 K, P =1017.5 hPa 0 0 T =293.0 K, P =1045.0 hPa 0 0 T =290.5 K, P =1072.5 hPa 0 0 T =288.0 K, P =1100.0 hPa

1

0

0.5 0.2

0.4

0.6

0.8

1

1.2

Ma∞

0

1.4

1.6

1.8

2

Fig. 4.2: Reynolds number based on 200 mm chord length vs. Mach number in the trisonic wind tunnel for different ambient conditions p0 and T0 .

4.1. Trisonic Wind Tunnel

51

To start the test the fast acting valve that separates the vacuum tanks from the test section is opened. The air stored in the balloon flows through the intermediate section, the Laval nozzle, the test section, and the diffuser into the tanks. At subsonic and transonic conditions the speed is regulated by the continous adjustable two-plate diffuser throat, whereas the Laval nozzle determines the supersonic conditions. A detailed specification of the trisonic wind tunnel is given in [55]. Due to the closed test section the expansion of the streamlines over the airfoil is confined by the wind tunnel walls, which causes the flow to accelerate. So, the flow conditions during the wind tunnel test differ from those during free flight. To reduce the so-called wall interference the trisonic wind tunnel is equipped with an adaptive wall test section.

4.1.1

Adaptive Wall Test Section

The basic assumption for the use of adaptive floor and ceiling wall in a rectangular test section is that if the streamlines in the vicinity of the wind tunnel wall correspond to the free flight streamlines, the flow over the airfoil is free of wall interference. Therefore, the obtained forces and pressure distributions on the model correspond to those in free flight at the same conditions. The use of an adaptive wall test section also reduces the blockage effects and aims to eliminate choking at transonic speeds. For the trisonic wind tunnel the use of the adaptive wall test section, shown in figure 4.3, enables the use of airfoil models with a chord length of 200 mm to accomplish higher Reynolds numbers.

Fig. 4.3: Adaptive wall test section of the trisonic wind tunnel at the Aerodynamische Institut. The flexible top and bottom wall of the adaptive wall test section can be adjusted by means of 24 jacks on each side, distributed over a length of 1.334 m. Each jack possesses a maximum

52

Chapter 4.

Test Facility and Models

stroke of 142 mm. With respect to the location of the model with 200 mm chord length this means a streamlined section of approximately five chord lengths upstream of the leading edge followed by one chord length downstream of the trailing edge. Each of the 1.3 mm thick spring-steel flexible walls is supported by the jacks. The static pressure at the wall surfaces is measured at 25 pressure orifices aligned with the center line on either side, which are connected to the electronic pressure scanning system described in section 5.1. The PC-based control unit, described in section 5.5, acquires the wall positions of 48 jacks and the wall pressure data. The wall adaptation algorithm implemented on the host computer calculates the new wall shape which will be set. The wall shape depends on the model chord length and the flow conditions, i.e., the Mach number and the angle-of-attack. For the calculation of the wall shapes for different flow conditions two methods are available. The Euler-boundary layer method, described in section 3.4.2, calculates the entire two-dimensional flow field over an airfoil at the prescribed flow conditions. The streamlines that correspond to the wall positions are extracted from the numerical result afterwards. However, the Euler-boundary layer method fails if large separations occur. The other technique is based on the transonic small perturbation equations (TSP) [172], where the wall pressure distribution and the current wall geometry determine the boundary conditions is widely used. The TSP equations can be solved by the Cauchy-integral formula without any model representation [7]. Both methods represent two-dimensional adaptation procedures, which are sufficient for the determination of the required wall adaptation to analyze flows over an airfoil with a rectangular top-view. A detailed description of the adaptive wall test section of the trisonic wind tunnel as well as the solution algorithm of the Cauchy-integral combined with the verification of the assumptions for transonic airfoil flows is discussed by Romberg [166]. To account for the streamline displacement caused by the wall boundary layer the twoequation method for turbulent boundary layers by Head [31, 71] is applied using experimental data by Romberg as boundary conditions.

4.1.2

Flow Quality of the Test Section

As mentioned in section 2.1 the experimentally determined transition location is strongly related to the disturbance level in the wind tunnel. Systematic investigation of the transition Reynolds number on a cone conducted in different wind tunnels demonstrated a decrease of the transition Reynolds number in wind tunnels with a higher turbulence level [9]. Compared with the disturbance level of free flight conditions the transition location is associated with low disturbance wind tunnels. The dependence of the transition Reynolds number on a sharp cone at supersonic and hypersonic speeds on the wind tunnel disturbance level has also been observed by Beckwith [17]. For the prediction of the transition Reynolds number in aerodynamic design with natural transition the eN -method is used. As the numerical flow computation is accompanied by the experimental determination of the transition location, the N factor has to be correlated to the disturbance level of the trisonic wind tunnel. Equation 2.3 by Mack [121] is considered here, which can be applied with some confidence for turbulence levels between 10−3 and 10−2 as is stated by Arnal [9] on the basis of experiments. In depth investigations of the flow

4.1. Trisonic Wind Tunnel

53

quality of the trisonic wind tunnel have been performed by Jacobs [89] and Dietz [42] at supersonic Mach numbers. The work demonstrated the suitability of the trisonic wind tunnel for experiments with natural transition in the Mach number range between 1.9 ≤ M a∞ ≤ 2.5. For Mach numbers below Ma∞ < 0.5 measurements of the turbulence level have been conducted by Guntermann [67] that determined the turbulence level to be below 0.5% in the investigated Mach number range. However, no investigation of the disturbance level at transonic Mach numbers has been performed. Therefore, flow quality measurements with respect to the homogeneity of the steady core flow and the occurring disturbance in the trisonic wind tunnel for 0.7 ≤ M a∞ ≤ 0.8 have been conducted in cooperation with Hillenherms [80]. The mean total pressure distribution is obtained by a Pitot-pressure rake. The mass flow and total pressure fluctuations have been measured simultaneously with a single hot-wire sensor and a differential pressure sensor installed on a probe support with a cross section of a Rhombus profile. The probe was mounted horizontally through the side wall with the hot-wire sensor at the tunnel center line. The streamwise location of both the rake and the combined probe corresponded with the position of the airfoil models.

Fig. 4.4: Deviation of the Pitot-pressure ptot from the stagnation pressure p0 in the test section of the trisonic wind tunnel with adaptive walls at Ma∞ = 0.75. Spatial Distribution of the Flow Quantities The development of turbulent boundary layers along the wind tunnel walls reduces the cross section of the working section. The flow uniformity and the wall boundary-layer thickness of the empty test section at the model position were determined using a rake that measures the Pitot-pressure and static pressure. A detailed description of the Pitot-pressure rake is

54

Chapter 4.

Test Facility and Models

presented in section 5.1. Figure 4.4 shows the pressure loss at a freestream Mach number Ma∞ = 0.75. Inside the core section of 30 × 30 cm2 the pressure deviates from the pressure in the balloon by approximately 100 Pa, which remains within the measurement accuracy of the pressure acquisition hardware. The results are in good agreement with previous measurements of the wind tunnel boundary layer obtained by Romberg [166] Temporal Analysis of the Flow Quantities The fluctuations of mass flow and total pressure have been measured simultaneously with a single hot-wire sensor and a pressure sensor capable of resolving high frequency disturbances. A detailled description of the measurement techniques applied to acquire the unsteady freestream flow characteristics is presented in section 5.4.1. The mass flux and total temperature fluctuations have been indicated for different Mach numbers in figure 4.5. For the determination of the mass flow fluctuations obtained from eqn.(5.14) the term G · T0
/T0 has been dropped. The presented results correspond to overheat ratios τ > 0.5. Since the influence of the total temperature fluctuations is increasing with decreasing overheat ratios, the results obtained with τ < 0.5 are certainly overestimated and hence left out. Hence, the values indicated by the (•) can be interpreted as an upper boundary of the actual mass flow fluctuation level. To underline this assumption, the total temperature fluctuations determined with eqn.(5.14) by neglecting the term Q · (ρu)
/ρu, and the overheat ratios τ > 0.5 are displayed as solid triangles (∆) in figure 4.5. 1.8 1.6 1.4

(ρu)’/ρu

T0’/T0 [%]

1.2 1

0.8 0.6 0.4 0.2 0 0.45

ρu’ (τ > 0.5) T’ (τ > 0.5) 0.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

Ma

∞

Fig. 4.5: Nondimensionalized mass flux and total temperature fluctuations of the freestream flow in the trisonic wind tunnel vs. the Mach number. The fact that the total temperature fluctuations are substantially lower than the mass flow fluctuations, reveals that their influence on the fluctuating component of the hot-wire signal is also significantly smaller than that of the mass flow fluctuations. Thus, the shown mass flow

55

4.1. Trisonic Wind Tunnel

fluctuation level can be treated as a worst case scenario. At the transonic Mach number range above Ma∞ = 0.70 the disturbance level decreases well below 1% of the freestream level. So, it is valid to apply the eN -method to predict the transition location. However, the values of the N -factor will not be larger than N ≤ 7. A more detailed analysis on the nature of the disturbances has been conducted in the frequency domain. Power spectral densities (PSD) of the hot-wire AC signal were determined with the discrete Fourier transformation and integrated over a frequency band of f1 = 10 Hz to f2 = 1000 Hz. This offers an excellent opportunity to compare the noise level of the tunnel flow for different Mach numbers and to identify dominant frequencies inherent to the flow. Figure 4.6 shows the obtained power spectra of the hot-wire output voltage at Mach numbers Ma∞ = 0.72 and Ma∞ = 0.75, which correspond to the velocities under investigation in this study. −4

−4

10

10

−5

−5

10

10 F = 239.26 Hz

−6

−6

10

F = 240.48 Hz

10

F = 478.52 Hz

−7

−7

10 [Amp2/Hz]

[Amp2/Hz]

10

−8

10

−9

−8

10

−9

10

10

−10

−10

10

10

−11

−11

10

10

−12

10

F = 245.97 Hz F = 247.19 Hz

F = 20.75 Hz

−12

100

200

300

400 500 600 Frequency [Hz]

700

800

900

1000

10

100

200

300

400 500 600 Frequency [Hz]

700

800

900

1000

Fig. 4.6: Power spectrum density of the hot-wire signal to identify dominant frequencies in the freestream flow at Ma∞ = 0.72 (left) and at Ma∞ = 0.75 (right).

The most dominant frequency peaks have been marked. The power of the identified peaks is clearly higher for smaller Mach number, which corroborates the observation concerning the mass flow fluctuations in the Mach number range 0.65 ≤ Ma∞ ≤ 0.8. The acquired total pressure fluctuations are shown in figure 4.7 as root mean square values related to the mean total pressure versus the Mach number. Qualitatively, the distribution is similar to that of the mass flow fluctuations, i.e. maximum fluctuations occur at Mach numbers between 0.60 and 0.70 and the minimum levels at Ma = 0.50 and Ma ≥ 0.80. However, with respect to the mass flow disturbances the fluctuation level of the pressure is more than one order of magnitude lower.

56

Chapter 4.

Test Facility and Models

0.07

0.06

0.04

P0’/P0

[%]

0.05

0.03

0.02

0.01

0 0.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

Ma∞

Fig. 4.7: Pitot pressure fluctuations of the freestream flow in the trisonic wind tunnel depending on the Mach number.

4.2

Wind Tunnel Models

Generic supercritical airfoil shapes are characterized as slender bodies with a relative maximum thickness of approximately 12% of the chord length. Considering the scale of the model this leaves little space for the integration of adjustment kinematics and measurement equipment. Although the measurement techniques used in the present investigation have been applied in previous experiments at the Aerodynamische Institut [67, 89, 102], the simultaneous acquisition of the transition location by flush-mounted hot-film sensors and liquid-crystal coating has not been conducted on a laminar-type transonic airfoil. So, in the first stage towards the design of an adaptive wing model, it is inevitable to manufacture a reference wind tunnel model with a rigid surface to obtain knowledge in the integration of kinematics and test equipment within limited space, while maintaining structural stiffness. The model will also be used to perform reference measurements of the aerodynamic characteristics. The laminar-type airfoil DA LVA-1A has been selected as basic airfoil shape. The geometry has been designed by DASA Airbus to maintain a laminar boundary layer up to 50% chord on both the upper and the lower side at a transonic Mach number Ma∞ =0.73 and a lift coefficient of CL = 0.4 at a Reynolds number based on the airfoil chord length of Re∞ =20 million. The rear-loaded airfoil has a maximum thickness of 12% chord with a leading-edge radius of 1.4% chord [203]. The pressure distribution and the transition location at the design-point is shown in figure 4.8. Satisfying the guidelines for the design of natural laminar airfoils (section 2.3) the pressure distribution shows a strong acceleration near the leading edge to avoid premature transition due to attachment line and crossflow instability followed by a moderate acceleration due to a favorable pressure gradient to damp the TS waves. Due to the required long extent of the accelerated flow even at the design point a weak shock occurs on the airfoils upper side. Based

57

4.2. Wind Tunnel Models

1.5

1

−Cp

0.5

0

transition location

−0.5

↓

−1 ↑

−1.5 0

0.2

0.4

0.6

0.8

1

x/c

Fig. 4.8: Pressure distribution and the transition location of the transonic laminar-type airfoil DA LVA-1A at the design point Ma∞ =0.73, CL = 0.4 and Re∞ =20·106 . on these aerodynamic characteristics the airfoil shape is well suited for the investigation of the shock/boundary-layer interaction with a laminar boundary layer. The next sections describe the design of the reference airfoil wind tunnel model followed by the adaptive airfoil model design.

4.2.1

Rigid Wing Section Model

With respect to blockage in the trisonic wind tunnel with an adaptive wall test section the maximum allowable chord length of the model is 200 mm. So, the model possesses a top-view of 400 × 200 mm2 (figure 4.9). closing mechanism

upper O b e part r s e ite

U n t e part r s e ite lower

Fig. 4.9: Principle sketch of the rigid LVA-1A wind tunnel model. To conduct measurements with natural transition the surface has to be hydraulically smooth. Therefore, it is a must that the measuring equipment like the pressure tubing is mounted from the inside of the model to ensure a perfectly smooth outer surface. Moreover, to easily gain

58

Chapter 4.

Test Facility and Models

access to the interior of the airfoil model either to integrate additional measuring equipment or to repair the system, the model has been split in an upper and a lower part, as shown in figure 4.9. To prevent premature transition due to edges between the upper and the lower part, the upper surface extends towards the lower side, which consequently possesses a smaller length than the chord of the airfoil. A special closing mechanism integrated inside the model near the leading edge ensures a smooth surface at the joining interface on the lower side without the use of screws which would damage the surface. Figure 4.10 demonstrates the inside of the two parts of the rigid wind tunnel model. The model is manufactured from an aluminum alloy Fortal with a wall thickness of 3 mm. For the experimental investigation under the high aerodynamic loads during transonic flight the model should not only possess sufficient strength, it should also feature a smooth bending line, which is significant for a two-dimensional flow field. Therefore, the structure mechanical strength and the local deflection have been computed using the finite element software package I-DEAS. At stagnation conditions corresponding to ambient conditions the maximum deflection at Ma∞ =0.74 and α=4o remains with 0.7 mm well below 5 chord.

Fig. 4.10: View inside the lower (left) and the upper (right) side of the rigid surface wind tunnel model with LVA-1A geometry.

4.2. Wind Tunnel Models

59

The airfoil model is equipped with 60 pressure taps with 0.5 mm diameter orifices, which are distributed at an angle of 15o to the flow direction to avoid disturbances from upstream pressure taps. The tubes inside the model are connected to the orifices and directed outside the wind tunnel through the mounting device on either side of the model. The mounting device has been developed such that undisturbed visual access to the model upper side is ensured.

4.2.2

Adaptive Wing Section Model

This section elaborates the development of a wind tunnel model with an adaptive geometry over the entire upper side of the airfoil chord. The model is equipped with different measuring technologies to experimentally demonstrate the potential of the adaptive wing technology. The adaptive wing wind tunnel model has the same dimensions as the rigid airfoil model and possesses the LVA-1A geometry on the lower side. The two major requirements on an adaptive structure used for aerodynamic purposes are contradictory. On the one hand, the shape has to be flexible to allow adaptation of the entire upper side of the airfoil. On the other hand, the structure has to possess sufficient stiffness to support the shape under the aerodynamic loads, which are very high at transonic speeds. Moreover, for a wind tunnel model of 200 mm chord there is little space (max. 24 mm) to integrate kinematics to adjust the upper surface and still incorporate the measurement equipment in the model. The most recent concepts for adaptive geometries of wings concentrated on the variable trailingedge camber technology. Different proposals for variable camber systems like the horn concept, the twin-flap or the finger concept [70, 85, 125] can not be extrapolated to adjust the entire upper surface. The concept of Austin et al. [11], which modifies the upper and lower side by active trusses in a rib structure, has been integrated in a model of 4 ft width and 10 in. height. These dimensions are too large for the implementation in the trisonic wind tunnel and the concept can not be scaled down to the size of the trisonic wind tunnel. Guntermann [67] performed experiments on a windtunnel model with an adjustable upper side geometry at the subsonic Mach number Ma∞ = 0.4. The flexible upper surface is vacuumed on to nine shape determining drive mechanisms by creating a pressure difference between the inside and the outside of the model. As the flexible steal surface has not been attached to the drives, sufficient force is achieved only if the Mach number remains subsonic. At transonic Mach numbers it is the static pressure outside the model, which prevents the necessary pressure difference over the surface to be achieved. Thus, the adaptation concept can not be applied to models used for investigations in the transonic Mach number range. The investigation of laminar-turbulent transition imposes heavy constraints on the roughness and waviness of the airfoil surface and hence, on the manufacturing and adjustment accuracy of the wing contour [95]. To prevent premature transition the surface must possess a smooth finish without curvature discontinuities at the position of the actuators, where the fixating forces are introduced to the flexible surface. Besides the adjustment kinematics the measurement equipment like the pressure acquisition and the hot-film technique have to be integrated in the limited space of the wind tunnel model.

.. ..

..

lo w e r s id e m o d u le

a d ju s tm e n t k in e m a tic s

m a in m o d u le

Chapter 4.

p re s s u re tu b e s

T -s lo t

p re s s u re tu b e s

h in g e c o n n e c tio n

p re s s u re o rific e s

fle x ib le u p p e r s u rfa c e

60 Test Facility and Models

Fig. 4.11: Principle sketch of the modular architecture of the laminar-type adaptive wing section wind tunnel model for tests at transonic speeds with natural transition.

4.2. Wind Tunnel Models

61

The present adaptive wing model consists of three modules as demonstrated in figure 4.11. The main module manufactured out of C45 steal absorbs the aerodynamic loads and introduces them to the windtunnel supports, which correspond to the supports used for the rigid model. The steal module is equipped with nine drive mechanisms, which have been distributed equidistantly from 12.5% to 72.5% of the chord length to support and adjust the flexible upper surface shell. Each drive mechanism consists of five grub screws integrated in five modified cog wheels. So, the adjustment kinematics transform a rotating movement into a vertical translation. This mechanism allows a continuous adjustment over 2.5 mm, which corresponds to more than 10% of the chord length. Results of the numerical aerodynamic design showed 2 mm adjustment range to be sufficient, since even small shape modification can cause large changes in aerodynamic performance. The five cog wheels of one drive mechanism are synchronized by a tooth belt tightened at the end of each drive mechanism. By rotating the cog wheels, the grub screws, which are jointly connected to the flexible upper surface, will translate in the vertical direction and hence locally modify the airfoil geometry at the position of the drive mechanism. Adjusting all nine drives yields the desired airfoil shape. As for the rigid model the maximum deflection and strains of the steal core module combined with the nine drive mechanisms have been verified using I-DEAS. The analysis evidenced, that for the highest aerodynamic loads to be expected, the maximum deflection of 0.8 mm remains below 5 chord. The flexible upper surface shell represents the second module and extends over the leading edge towards 7% chord on the lower side to avoid premature transition due to edges at the joint. At this position the shell is connected with skrews to the main module. The basic configuration of the surface shell corresponds to the LVA-1A geometry of the rigid wing model. To ensure simultaneous flexibility in the chordwise direction and structural strength in the spanwise direction the shell is manufactured of four layers of unidirectional 90 gram carbon fiber reinforced laminate. For the spanwise stiffness the shell is equipped with nine steal pipes, which are embedded between the carbon fiber laminate at positions corresponding to the drive mechanisms. By the high-grade steel rods inserted in the embedded pipes the carbon fiber reinforced shell is hinge connected to the drive kinematics by the five grub screws. This allows the vertical translation of the upper surface shell without imposing a rotating moment on it and thus prevents curvature discontinuities. The carbon fiber surface shell and adaptation mechanism are visualized in figure 4.12. At the trailing edge the shell is adhered to the steal module with a flexible adhesive that absorbs the changes of the surface arc length due to the shape adjustments. The third module is the lower side of the wind tunnel model. Through a T-slot mechanism this module can be removed laterally from the main module without the use of bolts, which would damage the surface. This enables the model assembly and provides access to the drive adjustment kinematics. The module consists of a brass plate containing three tongues on the model’s outside and pressure tubes on the other side. The casting compound Araldit shapes the brass plate’s outer side according to the LVA-1A contour and covers the pressure tubes. The adaptive shape kinematics allows an adjustment accuracy of 30 µm at the positions of the drive mechanics, as shown in figure 4.13. The form accuracy is verified prior to the measurement campaign and afterwards by a mill machine equipped with a distance measuring facility with a spherical probe with an accuracy of 5 µm.

62

Chapter 4.

Test Facility and Models

Fig. 4.12: Adaptive wing model mounted in the wind tunnel. The insert demonstrates four out of nine drive mechanisms. 0.1 0.08

∆y

adjust

[mm]

0.06 0.04 0.02 0 −0.02 −0.04 −0.06 −0.08 −0.1 0

50

100

150

200

x [mm]

Fig. 4.13: Difference between the target and the current position of the adjustment kinematics at the locations of the drive mechanics of the adaptive wing model.

4.2. Wind Tunnel Models

63

To determine the aerodynamic forces the model is equipped with 50 pressure orifices of 0.5 mm diameter. The corresponding tubes leave the model laterally. As for the rigid model the pressure orifices are arranged at an angle of 15o to the flow. One of the advantages of this shape adjustment system is that energy is required only to modify the airfoil shape, not to maintain the position of the flexible surface. A smooth surface is achieved without curvature discontinuities and thus the model allows the investigation of flow characteristics at natural transition. The adaptive wing wind tunnel model presented here allows a high resolution global modification of the upper surface. Hence the airfoil’s shape can be highly accurately adjusted to changing flow conditions, which enables the experimental investigation of the adaptive wing technology. Moreover, the model provides a system that allows an economical and fast experimental parametric study of different airfoil shapes without the need to build new models with integrated measuring equipment. Currently, the basic geometry corresponds to the LVA-1A airfoil shape. However, the modular architecture of the adaptive wing system with predefined interfaces allows the adjustment to any airfoil contour by replacing the lower side module or the carbon fiber reinforced laminate upper surface shell.

64

Chapter 4.

Test Facility and Models

Chapter 5 Measurement Techniques The accurate determination of the flow field over the adaptive wing model with respect to the transition location and the related flow phenomena of separation and lambda-shock configuration in the trisonic wind tunnel requires the application of local and zonal measurement techniques. In the following section a detailed description of the pressure acquisition system is presented that allows the determination of the static airfoil surface pressure distribution and the stagnation and static pressure distribution in the wake of the airfoil to acquire the aerodynamic coefficients of lift and drag. In the subsequent section the methods to determine the transition location and the location and extent of the separation bubble will be presented. The local unsteady hot-film data will be supplemented by the global shear sensitive liquid-crystal coating technique. The combination of the different measurement techniques is indispensable for a detailed analysis of the state of the boundary layer and the overall flow field over the airfoil. Then, the flow visualization methods are described. The oil pattern method is used to assess the two-dimensionality of the flow whereas the optical flow visualization techniques are used to capture the shock configuration on the airfoil upper surface. Finally, the hot-wire anemometry and Pitot pressure measurement technique are described to determine the mass flux and total temperature and stagnation pressure fluctuations.

5.1

Acquisition of the Aerodynamic Coefficients

The aerodynamic coefficients of lift and drag have been determined by pressure measurements. The lift is acquired by integrating the wall pressure on the airfoil surface described in section 4.2.2. The total drag of the airfoil is determined by integrating the stagnation pressure loss in the wake. A pressure acquisition rake has been applied that is equipped with 60 Pitot pressure tubes for the acquisition of the stagnation pressure and four tubes for the static pressure. The wake rake has been built by Guntermann [67] according to the design by Somers [189]. The Pitot pressure tubes with an inner diameter of 1 mm cover a range of 200 mm with a minimum distance between neighboring tubes of 2.5 mm near the center of the rake. The static pressure tubes are equipped with 0.5 mm orifices and cover a 200 mm range. The wake rake has been positioned off the center line of the wind tunnel at one chord length behind the trailing edge of the model, to avoid perturbations generated by the pressure orifices on the 65

66

Chapter 5.

Measurement Techniques

airfoil’s surface, as indicated in figure 5.1. This guarantees that the outer Pitot tubes cover the almost undisturbed flow in which the gradients of the pressure loss can be neglected. The rake is mounted on a continuously traversable mechanism positioned behind the model outside the core flow of the wind tunnel.

flo w d ire c tio n

6 0 P

IT O T

p re ssu re p ro b e s

4 s ta tic p re s s u re p ro b e s m o u n tin g

d e v ic e

Fig. 5.1: Left: Detail of the pressure rake. Right: Arrangement of the pressure rake with respect to the airfoil.

The pressure tubes of the model and rake are connected to an electronic pressure scanning system Hyscan 2000 manufactured by Scanivalve. The system consists of six electronic pressure scanning modules with a maximum of 192 pneumatic inputs and one 16 channel A/D converter module. The system scans the channels with a resolution of 16 bit at a maximum sample rate of 100 kHz. The accuracy of the system can be maintained between 5 - 20 Pa by frequent calibration. Four temperature compensated scanning modules with a total of 64 channels have been connected to the wake rake. The two remaining pressure scanning modules, the so-called satellite modules, allow the pressure acquisition near the wind tunnel wall, which reduces the tube length and hence, increases the frequency resolution of the system. The satellite module operates in duplex mode, which enables the connection of 64 pneumatic inputs from which only 32 channels are scanned simultaneously. So, the scanning system allows the simultaneous scanning of 128 of 192 connected inputs during one wind tunnel run. The pressure orifices of the airfoil models and those of the adaptive wind tunnel walls are connected to the satellite modules. The acquired pressure signals are transmitted by the IEEE-488-2 interface to the data acquisition host computer system described in section 5.5.

5.2. Transition Location and Separation

5.2

67

Detection of the Separation and Transition Location

To determine the transition location and the position of separation the multi-sensor hot-film method with a high temporal and a moderate spatial resolution is combined with the liquidcrystal coating technique characterized by a high spatial and a moderate temporal resolution. This combination of transition location detection methods is applied to avoid the misinterpretation of either measurement technique. A similar concept has been followed in [67, 68, 83]

5.2.1

Hot-Film Technique

Within the experimental aerodynamic research the hot-film technique represents a standard method for analysing the wall shear stress. The method has been used at subsonic speeds in wind tunnel and free flight experiments [48, 101] and also at transonic speeds during flight tests [88]. A hot-film sensor is an electrically heated thin metal wire deposited onto a non-conducting substrate that is used to determine the local wall shear stress. The principle is based on the analogy between convective heat transfer and the local wall shear stress for forced convection (Gr 1.2, as demonstrated by Morkovin [137]), for overheat ratios τ greater than 0.5 and wire Reynolds number greater than 20. During the tests the Reynolds number based on the wire thickness was 49 < Red < 71.

77

5.4. Determination of the Mass Flux and Pressure Fluctuations

Based on the introduced relationships for the wire heat transfer the sensitivity coefficients can be obtained by   n−1 nM E 2 − L n , (5.10) 2E M     E L
(E 2 − L)
r τ +r (E 2 − L) f + g − 0.768 = · n . (5.11) 0.768 − − 2T0 τ E2 f (τ ) g(τ ) E2

km = kΘ

For a detailed derivation of relations (5.10) and (5.11) refer to [80]. With the dimensionless sensitivity coefficients Q and G [103]
 n L km ρu = 1− 2 , Q = (5.12) E 2 E k Θ T0 G = . (5.13) E Eqn.(5.9) can be rewritten to T
(ρu)
E
+G 0 . = Q ρu E T0

(5.14)

To determine the mass flux and total temperature fluctuations in the freestream of the trisonic wind tunnel, the calibration coefficients Q and G have to be determined. Therefore, tests with at least three overheat ratios τ for each Mach number have to be conducted. Relations E 2 = f (ρu)n are shown in figure 5.7 at four different overheat ratios. 0.4

2.2

L = −0.695 + 1.533 ⋅ τ N = 0.127 + 0.326 ⋅ τ

2.1

0.3

τ

2

0.532 0.415 0.394 0.342

1.9

0.2

1.8 1.7

L, N

E2

0.1

1.6

0

1.5 1.4

−0.1 1.3 1.2

6

6.1

6.2

6.3

6.4 (ρ u) 0.35

6.5

6.6

6.7

6.8

−0.2 0.34

0.36

0.38

0.4

0.42

0.44

τ

0.46

0.48

0.5

0.52

0.54

Fig. 5.7: Left: Dependence of the hot-wire anemometer output voltage E 2 of the mass flow (ρu)n , with n = 0.35 at four different overheat ratios τ . Right: Calculated calibration coefficients L and N vs. the overheat ratio τ . The exponent n in eqn.(5.8) was determined experimentally to a value of n = 0.35 to yield linearity. The coefficients L(τ ) and N (τ ) in eqn.(5.8) serve to calibrate the mean hot-wire

78

Chapter 5.

Measurement Techniques

signal and provide the basis for the evaluation of the fluctuating component. The results for L(τ ), N (τ ), f (τ ) and g(τ ) are used to determine the hot-wire calibration for the mass flow fluctuations (ρu)
based on eqn.(5.9). A set of three equations for each Mach number can be set up by squaring eqn.(5.9) and can be solved for (ρu)
, (ρu)
2 , T0
, and T0
2 , as proposed by Smits et al. [186]. However, problems occur if the variation of the sensitivities with the overheat ratio is small and thus, the resulting matrix is nearly singular. Even though it was not possible to adjust the overheat ratios as high as required to be able to entirely neglegt the total temperature fluctuations, this was assumed as a first approximation in order to prevent nearly singular matrices during the solution process.

5.4.2

Pitot-Pressure Technique

Unlike to the system to acquire almost steady pressure data, presented in section 5.1, a miniature piezo-resistive pressure sensor is required to determine the fluctuations of the Pitotpressure with sufficient temporal resolution. The sensor is positioned directly behind the pressure orifice to prevent damping and a low frequency response of the oscillatory pressure signals due to long tubing. R The miniaturized design of the cylindrical pressure sensor, Kulite  XCQ-107-093-5 D, allows the integration in the mounting device, described in the previous section. Hence, the intrusion of the flow field is kept as small as possible. The pressure probe is located at a distance of 25 mm from the hot-wire sensor, to allow the simultaneous acquisition of the mass flux and Pitot-pressure fluctuations.

5.5

Wind Tunnel Control and Data Acquisition

Operating the wind tunnel facility is entirely computer controlled by the data acquisition host computer using the graphical programming package Labview that additionally allows the online analysis and storage of all acquired data of the pressure measurements of the airfoil surface pressure, the stagnation pressure loss in the wake, the unsteady hot-film signals and the wall pressure distribution of the adaptive wall test section [182]. These values are used to determine and set the new wall shape. The wind tunnel control and data acquisition is shown in figure 5.8 The ambient pressure is acquired by the absolute pressure device of the pressure scanning system. The ambient temperature and the humidity inside the balloon are electronically obtained by a calibrated humidity measuring device. The control of the humidity is significant to guarantee that the air is sufficiently dry to make sure that no condensation occurs during a wind tunnel run. The freestream conditions during the wind tunnel run are acquired by a side wall pressure orifice connected to the pressure scanning system. The 20 hot-film sensor signals have been acquired by a 96 channel transient recorder TRC-6810 manufactured by Krenz Electronics with a resolution of 12 bit. The system is equipped with 9 Mb onboard memory and allows a maximum sample rate of 50 kHz per channel. The

79

5.5. Wind Tunnel Control and Data Acquisition

apparatus is entirely computer controlled, i.e., data transfer and the unit instructions are controlled over the IEEE-488 interface, also known as GPIB-interface, by the host computer. The transient recorder is operated at a sample frequency of 10 kHz for each sensor. Since the critical frequency of a hot-film sensor amounts to 5 kHz the sample rate is sufficient. The use of a low pass filter is not required to avoid aliasing due to the high amplitude damping of the sensors [56]. To reduce the measured data to a minimum the data acquisition hard-ware like the pressure system and the transient recorder have been connected to a trigger device. This device is connected to an electronic wall pressure device that determines the begin of the steady flow phase of the wind tunnel run and then triggers the data acquisition [42]. After a run the host computer transfers the data from the data acquisition hard-ware and automatically displays significant information like the surface pressure distribution on the airfoil and the RMS and skewness values of the hot-film signals that allow a first analysis of the acquired data. The collected data of a measurement campaign is transferred from the data acquisition host computer to a local area network (LAN) for further analysis and permanent storage.

L O C A L

a n a lo g d a ta a c q u is itio n

m a ss sto r a g e L A N

D E C E N T R A L

d ig ita l d a ta a c q u is itio n

p h o to

A /D

- p re ssu re (1 ) IT O T

P

h o t-w ire (1 )

(2 0 )

H o st P C

C D -w r ite

A /D

h o t-film

w a k e p re ssu re (6 4 )

p r e s s u r e a c q u is itio n sy ste m H y sc a n 2 0 0 0

A /D

p re ssu re (1 ) fre e s tre a m

s ta g n a tio n p re s s u re (1 )

w a ll s u rfa c e p re s s u re (5 0 )

w a ll c o n tro l (4 8 )

w a ll d e fle c tio n (4 8 )

h u m id ity (1 )

s ta g n a tio n te m p e ra tu tre (1 )

A /D

a irfo il s u rfa c e p re s s u re (6 0 )

se n so r s (a e r o d y n a m ic c h a r a c te r is tic s )

w in d tu n n e l c o n tr o l a d a p tiv e w a ll c o n tr o l

Fig. 5.8: Principle sketch of the wind tunnel control and data acquisition.

80

Chapter 5.

Measurement Techniques

Chapter 6 Results for the Rigid Surface Airfoil The experimental results will be compared with the numerical data to validate the computational method with respect to the determination of the aerodynamic characteristics such as the transition location and surface pressure distribution. This validation is indispensable, since the numerical method to compute the transonic airfoil flow will be used to optimize the airfoil shape of the transonic laminar-type airfoil during the subsequent step of the investigation. Moreover, the turbulence level of the trisonic wind tunnel has to be correlated with the value of the N -factor to allow an accurate numerical prediction of the transition location, which is crucial for numerical drag reduction studies for the present investigation. The studies to improve the aerodynamic characteristics numerically and experimentally represent the second part of the investigation. After it has been demonstrated that the measurement techniques enable the accurate determination of the state of the boundary layer and the associated aerodynamic characteristics, the experimental investigation of the adaptive wing model will focus on the description of the phenomena that lead to an increase of the aerodynamic performance for different Mach numbers and angles-of-attack. The objective of the optimization is to enhance the aerodynamic performance by reducing the drag at a prescribed lift coefficient through the design of the shape of the airfoil. The improvements will become especially evident in the high speed regime. Therefore, the experiments have been performed at Mach numbers ranging from subsonic to transonic flow speeds of 0.65 ≤ M a∞ ≤ 0.76 at moderate angles-of-attack in the range of 0o ≤ α ≤ 4o on a laminartype airfoil LVA-1A. The following section provides a description of the airfoil characteristics obtained by the different measurement techniques, which will also evidence the possibilities for the subsequent improvement concepts.

6.1

Comparison of the Experimental and Numerical Methods

The rigid surface wing wind tunnel model is equipped with various different measurement techniques, each of them covers a separate part of the model surface. The flow over the model with a rectangular top-view without sweep angle is of two-dimensional nature except for the flow 81

82

Chapter 6. Results for the Rigid Surface Airfoil

in the neighborhood of the wind tunnel walls. The determination of the thickness of the wall boundary layer of an empty test section has been described in section 4.1.2. The investigation showed a homogeneous core flow of approximately 30×30 cm2 . To verify the two-dimensionality of the flow with the model in the test section the oil pattern method is applied (figure 6.1). c e n te r lin e T ra ilin g E d g e

L e a d in g E d g e

Fig. 6.1: Oil pattern image of the upper side of the LVA-1A airfoil at Ma∞ = 0.72, Re∞ = 2.4 × 106 , and α = 2.0o . The figure evidences the three-dimensional effects confined to the near wall area. The flow of the remaining part of the airfoil surface can be considered as two-dimensional. The experimentally determined surface pressure distributions at a fixed Mach number of Ma∞ =0.74 and Re∞ = 2.6 · 106 at different moderate angles-of-attack is shown in figure 6.2. The transition location has been fixed neither on the upper surface nor on the lower surface. The aerodynamic properties regarding the pressure distribution of the LVA-1A airfoil shape mentioned in section 4.2 also correspond to the desired features of a laminar-type airfoil. At the transonic Mach number the pressure distributions exhibit at all depicted angles-of-attack and all lift coefficients, the pronounced accelerated region over the airfoil surface up to 50 % of the chord length to damp the growth of the disturbance amplitudes of the TS-waves. Hence, the laminar boundary layer is retained up to the recompression point. Another striking feature of the LVA-1A airfoil is, that although the shock strength increases for increasing angles of incidence, the shock position remains almost unchanged. This is one of the airfoil characteristics, that is exploited by local shock control measures [197] mentioned in section 2.2. The lines in figure 6.2 denote the numerical results obtained at the same freestream conditions by the Navier-Stokes method in combination with the eN -method to predict the transition location. The good agreement between experimental and computational data is obvious. The good performance of the Euler-boundary-layer method will be shown in separate figures. At a lower Mach number of Ma∞ =0.71 and Re∞ = 2.6 · 106 the sudden acceleration at the leading edge is followed by a decelaration zone terminated by a shock, which moves upstream for higher angles-of-attack, as is demonstrated in figure 6.3. At these lift coefficients the method to passively maintain laminarity fails on a rigid surface airfoil. Also the local shock control approaches would fail due to the shock movement.

83

6.1. Comparison of the Experimental and Numerical Methods

EXP: C =0.34 L NUM NS:C =0.34 L EXP: C =0.41 L NUM NS:C =0.41 L EXP: C =0.68 L NUM NS:C =0.68 L EXP: C =0.81 L NUM NS:C =0.81 L

2 1.5 1

−Cp

0.5 0

−0.5 −1 −1.5 0

0.2

0.4

0.6

0.8

1

x/c Fig. 6.2: Experimentally and numerically determined surface pressure distributions over the LVA-1A airfoil with natural transition at Ma∞ =0.74 and Re∞ = 2.6 · 106 at different lift coefficients. EXP: CL=0.35 NUM NS:C =0.35 L EXP: C =0.52 L NUM NS:C =0.52 L EXP: C =0.65 L NUM NS:C =0.65 L EXP: C =0.81 L NUM NS:C =0.81

2 1.5 1

L

−C

p

0.5 0

−0.5 −1 −1.5 0

0.2

0.4

0.6

0.8

1

x/c Fig. 6.3: Experimentally and numerically determined surface pressure distributions over the LVA-1A airfoil with natural transition at Ma∞ =0.71 and Re∞ = 2.6 · 106 at different lift coefficients.

84

Chapter 6. Results for the Rigid Surface Airfoil

For the determination of the transition location and for a detailed analysis of the shock/boundary-layer interaction only the information provided by the pressure distribution is not sufficient. From the pressure distribution it is not apparent whether or not a separation bubble is present or at what position the transition occurs. Therefore, the additional measurement techniques will be applied. To detect the transition location and the position and extent of a separation bubble the liquid-crystal technique is supplemented by the multi-sensor hot-film method. The combination of both methods is indispensable to avoid a misinterpretation of the obtained data from either method. To make sure that a phase reversal is not misinterpreted as an indication to detect shocks and to avoid that unsteady shock fluctuations influence the detection of transition and/or separation regions the first validation of the methods is performed at flow conditions that do not possess any supersonic flow and do not yield shocks.

6.2

Subsonic Laminar Separation

The pressure distribution of the subsonic flow at Ma∞ =0.65, Re∞ = 2.4 × 106 over the LVA-1A airfoil and CL = 0.21 is shown in figure 6.4, which obviously shows no supersonic regions. The transition location and separated area can not be uniquely identified from the pressure distribution. 2 EXP NUM−NS NUM−EBL

1.5

1

−C

p

0.5

0

−0.5

↓

−1

−1.5 0

0.2

0.4

0.6

0.8

1

x/c

Fig. 6.4: Experimentally and numerically obtained surface pressure distribution of the LVA-1A airfoil with natural transition at Ma∞ = 0.65, Re∞ = 2.4 × 106 , and CL = 0.21. The corresponding liquid-crystal image is depicted in figure 6.5. The rusty red color from the leading edge onward indicates a laminar boundary layer. Downstream of the laminar part,

85

6.2. Subsonic Laminar Separation

the liquid-crystal colors turn to a spatially limited bright red area, which indicates a region of reduced local skin friction associated with the presence of a separation bubble. It can definitely be identified as a laminar separation since no blue color occurs upstream of the separation line, which indicates areas of high local skin friction. Due to the separation, transition occurs causing the turbulent boundary layer to reattach, which is visualized by the color change from bright red to green/blue.

la m in a r b o u n d a ry la y e r

s e p a ra tio n b u b b le

tu rb u le n t b o u n d a ry la y e r

tu rb u le n t w e d g e 0 .6 2 < x re d

se p

/c < 0 .7 2

b rig h t re d

b lu e

Fig. 6.5: Skin friction measurements using the liquid crystal technique on the LVA-1A airfoil at Ma∞ = 0.65, Re∞ = 2.4 × 106 , and CL = 0.21. Moreover, the liquid-crystal image shows the two-dimensional character of the airfoil flow, so a global impression of the skin friction is available at high spatial resolution. Only few turbulent cones occur on the surface due to dust particles or the pressure orifices. The laminar separation of the boundary layer also can be detected by the hot-film sensor array with high temporal resolution. The 20 sensors are positioned betweeen 49 % and 77 % of the chord length. As mentioned in section 5.2.1 two approaches for the detection of laminar separation are available. The well-known phase reversal phenomenon according to Stack et al. [192] and the approach on the basis of the linear correlation coefficient of the hot film signals of neigboring sensors [2, 56]. For the subsonic airfoil flow both methods have been used. According to the phase reversal phenomenon the separation of the boundary layer can be detected by a phase shift of 180o of the low frequency signals located on either side of the separation.

86

Chapter 6. Results for the Rigid Surface Airfoil

It is apparent from figure 6.6 (left) that a phase shift of 180o occurs between the time traces of sensor 5 located upstream of the separation and sensor 9, which is located inside the separated region. Separation Area 1.0

200 150 100

0.5 Corr.coef.

∆ Θ [o]

50 0 −50

0.0

−100 −150 −200 0

50

100

f [Hz]

150

200

−0.5 0.45

0.55 0.65 Sensor position X/C

0.75

Fig. 6.6: Separation detection methods based on hot-film sensor signals on the LVA-1A airfoil at Ma∞ = 0.65, Re∞ = 2.4 × 106 , and CL = 0.21. Left: Phase reversal phenomenon, sensor 5 at x/c=0.55 (dashed), sensor 9 at x/c=0.61 (solid line), and sensor 18 at x/c=0.75 (dashed-dotted line). Right: Linear correlation coefficient of neighboring sensor signals. Another phase shift of the sensor signals is apparent between sensor 9 and sensor 18 located downstream of the reattachment point of the boundary layer. Hence, the phase reversal phenomenon has been shown to be applicable for separation detection on laminar-type airfoils. The method to determine the phase reversal between two sensor signals, however, is timeconsuming, especially when the time traces do not clearly evidence the phase shift in the low frequency range as it is usually the case in transonic flows. Therefore, an approach that is based on the distribution of the linear correlation coefficient as proposed by Abstiens et al. [2] and F¨ uhling [56] is used. The method is easier to use and possesses a wider universality, since it also yields reliable results in turbulent boundary layers. Figure 6.6 (right) evidences the pronounced minima that determine the location and the size of the separation bubble. The extent of the separation bubble of 10% chord obtained by the liquid-crystal coating technique has been indicated in figure 6.6 to compare the result with the hot-film data. For the subsonic airfoil flow both separation detection criteria based on the unsteady hot-film sensor signals proved to yield the same result. Moreover, the location and extent of the laminar separation bubble obtained from the hot-film data and from the liquid-crystal image compare very well. Since the approach based on the linear correlation coefficient is more universal and easier to apply, this method will be used to identify separated areas for further analysis of hot-film data.

87

6.3. Shock-Free Transition

6.3

Shock-Free Transition

At a freestream Mach number of Ma∞ =0.72 and a lift coefficient of CL = 0.35 the flow isentropically accelerates over a long extent of the chord length as is shown by the surface pressure distribution in figure 6.7. 2 EXP NUM−NS NUM−EBL

1.5

1

−C

p

0.5

0

−0.5

↓

−1

−1.5 0

0.2

0.4

0.6

0.8

1

x/c

Fig. 6.7: Experimentally and numerically obtained surface pressure distributions over the LVA-1A airfoil with natural transition at Ma∞ = 0.72, Re∞ = 2.57 × 106 , and CL = 0.35. The transition location predicted by the Euler-boundary-layer method has also been indicated, which shows the long extent of the laminar boundary layer. Again, it is impossible to determine the transition location and to determine whether or not a separation bubble occurs. Therefore, the liquid-crystal image and the hot-film data will be analyzed for a detailed description of the state of the boundary layer. The liquid crystal image in figure 6.8 indicates a long extent of the laminar boundary layer up to 69% chord by the red color. This part is directly followed by the blue color denoting high skin friction associated with the turbulent boundary-layer flow. At these freestream conditions, the red color is not followed by the bright red color, so there is no indication for a separation bubble. The transition location according to the liquid-crystal coating image is determined at 69% of the chord length. This corresponds to the prediction of the transition location by the Euler-boundary-layer method in combination with the eN -method for an N -factor of N =7. To identify the transition location on the basis of the hot-film sensor signals the statistical analysis, using a combination of the RMS values according to Owen [144] and the skewness, is used to avoid a misinterpretation of the unsteady sensor signals. Hence, the hot-film technique can show the capability to determine the transition location for an airfoil flow without the occurrence of a shock.

88

Chapter 6. Results for the Rigid Surface Airfoil

la m in a r b o u n d a ry la y e r

tra n s itio n

tu rb u le n t b o u n d a ry la y e r

x tr/ c = 0 . 6 9 re d

b lu e

Fig. 6.8: Skin friction measurements with the liquid-crystal technique on the LVA-1A airfoil at Ma∞ = 0.72, Re∞ = 2.57 × 106 , and CL = 0.35. The time traces of the hot-film sensors at different positions of the chord are displayed in figure 6.9. It is obvious that, although the hot-film technique only detects local flow phenomena, an array of 20 sensors distributed over the presumed transition region allows the detection of separation and transition if a high spatial resolution is ensured. To locate the transition location from the time traces the sensor array has to cover the entire transition region from laminar over transitional to the turbulent boundary-layer state. The low amplitude level of the disturbances at the first sensors indicates a fixed boundary-layer state under the existing experimental conditions, i.e. the laminar state, followed by an increase of the amplitudes of the fluctuations that starts at sensor 7 and reaches a maximum at sensor 11 to end at sensor 13, which denotes the transitional region. Further downstream the disturbance amplitude decreases to the amplitude values of the laminar boundary layer indicating a turbulent boundary layer. The observations on the basis of the time traces of the hot-film sensor signals are confirmed by the statistical analysis of the unsteady hot-film data shown in figure 6.10. The maximum of the RMS-values corresponds to a transition stage in which the turbulent matches the laminar portion of the boundary-layer flow, evidencing an intermittency factor γ=0.5. At this stage the skewness, which is a measure of the deviation of a signal from the Gaussian normal distribution, changes its sign from positive to negative values. This location is determined as the transition ’point’ located at 65 % chord.

89

6.3. Shock-Free Transition

2 1.95 1.9 1.85

t [s]

1.8 1.75 1.7 1.65 1.6 1.55 1.5

0.5

0.55

0.6

0.65

0.7

0.75

sensors position x/c

Fig. 6.9: Time traces of the hot-film sensor signals on the LVA-1A airfoil with natural transition at Ma∞ = 0.72, Re∞ = 2.57 × 106 , and CL = 0.35.

1 RMS skewness

RMS

0.3

0.71

0.25

0.43

0.2

0.14

0.15

−0.14

0.1

−0.43

0.05

−0.71

0 0.5

0.55

0.6

0.65

0.7

0.75

−1 0.8

x/c Fig. 6.10: Identification of the transition position by means of the RMS-values and the skewness of the hot-film sensor time traces on the LVA-1A airfoil at Ma∞ = 0.72, Re∞ = 2.57 × 106 , and CL = 0.35.

skewness

0.35

90

Chapter 6. Results for the Rigid Surface Airfoil

Both previous examples demonstrated the capability of the liquid-crystal coating method and the multi-sensor hot-film technique to determine the transition location and the position and size of the separation bubble in a flow without a shock. The same methology can be applied to a transonic airfoil flow in which the shock interacts with the laminar boundary layer.

6.4

Shock/Boundary-Layer Interaction

If the Mach number increases from Ma∞ =0.72 to Ma∞ =0.74 the supercritical region on the airfoil expands and is terminated by a shock. The corresponding pressure distribution of the flow over the LVA-1A airfoil at freestream conditions Ma∞ =0.74, Re∞ = 2.7 × 106 , and CL = 0.42 is displayed in figure 6.11 and shows the good agreement between experimental and computational data.

1.5 EXP NUM−NS NUM−EBL

1

−C

p

0.5

0

−0.5

↓

−1

−1.5 0

0.2

0.4

0.6

0.8

1

x/c

Fig. 6.11: Experimentally and numerically obtained surface pressure distributions over the LVA-1A airfoil with natural transition at Ma∞ = 0.74, Re∞ = 2.7 × 106 , and CL = 0.42. As indicated in section 2.2 the presence of the pressure rise across the shock has a tremendous impact on the state of the boundary layer, since it can cause the boundary layer to separate. The turbulent boundary layer with a larger amount of kinetic energy is capable to resist shocks of higher strength than a laminar boundary layer. So, the turbulent boundary layer remains attached at higher Mach numbers and angles-of-attack compared to the laminar boundary layer. Already at moderate shock strength the laminar boundary layer separates upstream of the shock forming a separation bubble underneath the shock. This causes expansion waves above the separated region to form a so-called lambda-shock pattern.

91

6.4. Shock/Boundary-Layer Interaction

The detailed analysis of the state of the boundary layer flow, which contains separation, transition, and reattachment in the shock region, requires the application of several measurement techniques. Therefore, the methods validated in the previous sections will be applied to characterize the state of the boundary layer at any position on the airfoil surface. The liquid-crystal image associated to the pressure distribution is displayed in figure 6.12.

la m in a r b o u n d a ry la y e r

s e p a ra tio n b u b b le

tu rb u le n t b o u n d a ry la y e r

tu rb u le n t w e d g e 0 .5 5 < x re d

se p

/c < 0 .7 0

b rig h t re d

b lu e

Fig. 6.12: Skin friction measurements with the liquid-crystal technique on the LVA-1A airfoil at Ma∞ = 0.74, Re∞ = 2.7 × 106 , and CL = 0.42. The qualitative features of the liquid-crystal visualization of the transonic flow, which includes shocks, correspond to those of the subsonic flow at Ma∞ =0.65 presented in figure 6.5. The rusty red color that evolves from the leading edge visualizes a region of moderate skin friction associated with a laminar boundary layer. The subsequent bright red area indicates a separated region with reduced skin friction, followed by the blue color associated with the turbulent boundary layer. The location and extent of the underlying separation bubble obtained by the liquid-crystal technique reaches from 55% chord to 70% chord. From the liquid-crystal image it is obvious that the transition location inside the separation bubble can not be determined by the shear-sensitive liquid-crystal coating technique since no color change inside the separated area is apparent. Using the surface mounted hot-film arrays it is possible to identify the transition position even for transition in a laminar separated flow. The statistical analysis of the unsteady hot-film sensor signals, with the same statistical moments of the RMS and skewness distribution as used for the attached flow, enable the identification of the transition location. The characteristics of the RMS and skewness values are shown in figure 6.13.

92

Chapter 6. Results for the Rigid Surface Airfoil

0.25

1

0.2

0.6

0.15

0.2

0.1

−0.2

0.05

−0.6

0 0.5

0.55

0.6

0.65

0.7

0.75

skewness

RMS

RMS skewness

−1 0.8

x/c Fig. 6.13: Identification of the transition position by means of the RMS-values and the skewness of the hot-film sensor time traces on the LVA-1A airfoil at Ma∞ = 0.74, Re∞ = 2.7 × 106 , and CL = 0.42. The previous examples demonstrated the necessity to combine the liquid-crystal method with the multi-sensor hot-film technique to enable a detailed description of the state of the boundary layer, which is indispensable to investigate to drag reduction methods within the adaptive wing technology. The experimental data on the transition location over the transonic speed range have been summarized in figure 6.14 for different Mach numbers 0.70 ≤ Ma∞ ≤ 0.74 at a lift coefficient CL ≈ 0.55. The transition location has been determined by the hot-film sensor technique, supported by the liquid-crystal technique. The transition location moves slightly upstream at increasing Mach numbers. At higher Mach numbers shock induced separation occurs that can lead to the negative characteristics of the unsteady buffet phenomenon. The figure evidences the good agreement between the experimental results and the location predicted by the Euler-boundary-layer method. The comparison of the experimentally with the numerically obtained pressure distributions presented in figures 6.2, 6.3, 6.4, 6.7, 6.11 demonstrates the ability of the computational method to accurately determine the pressure distribution of a transonic flow for natural transition in combination with the associated shock-boundary-layer interaction phenomena. Moreover, from figure 6.14 the good agreement of the numerically predicted transition location based on the eN method for an N -factor N =7 with the experiments is obvious. Therefore, it is justified to apply the numerical algorithm, based on the Euler-boundary-layer equations in conjunction with the eN -criterion, to the design of the shape of the airfoil with natural transition at transonic speeds.

93

6.4. Shock/Boundary-Layer Interaction

0.75 EXP NUM EBL

0.745 0.74 0.735

Ma∞

0.73 0.725 0.72 0.715 0.71 0.705 0.7 0

0.2

0.4

Xtr/C

0.6

0.8

1

Fig. 6.14: Transition location obtained by hot-film gauges and by the eN transition prediction method with N =7 on the LVA-1A airfoil at CL ≈ 0.55 for different Mach numbers. The following chapters will focus on the improvement of the aerodynamic performance by the use of a wing section with an adaptive upper side geometry. The potential increase of the airfoil performance along with the associated airfoil geometry will be determined by the numerical aerodynamic design. The airfoil shapes that are considered best with respect to their performance at the design point and at off-design conditions will be selected for the subsequent experimental investigation of the aerodynamic characteristics in the trisonic wind tunnel at transonic speeds with natural transition.

94

Chapter 6. Results for the Rigid Surface Airfoil

Chapter 7 Numerical Airfoil Shape Optimization The numerical optimization of the airfoil shape of the initial LVA-1A airfoil pursues two objectives. On the one hand, the potential for the improvement of the aerodynamic airfoil performance at transonic speeds considering the NLF concept of a mission adaptive wing with an adjustable upper surface shape and the shape of the LVA-1A airfoil on the pressure side is investigated. On the other hand, the numerical optimization has to provide a moderate number of airfoil shapes for the experimental investigation that not only show enhanced performance at the design-point, but also perform well over a wide range of flight conditions compared to the initial airfoil shape. This is why the freestream conditions of the trisonic wind tunnel will be prescribed for the computational flow analysis. The Reynolds number can not be varied separately and is determined by the ambient conditions and the Mach number. At transonic speeds investigated in this study, ranging from 0.65 ≤ Ma∞ ≤ 0.76, the chord Reynolds number, which is approximately Re∞ = 2.4 · 106 (figure 4.2), has been prescribed for all computations of the flow field over the airfoil. In the wind tunnel tests models with a rectangular top-view without sweep angle are considered. Since the flow field is two-dimensional, this implies that from the three possible transition mechanisms (ALT, CFI, and TSI) only the Tollmien-Schlichting instability will be significant for the determination of the transition location. Since the evaluation of an individual of the population requires the computation of the flow field, the number of function evaluations has to be minimized. Therefore, the minimum number of the population size has to be determined that still enables a significant improvement of the liftto-drag ratio considering the constraints on airfoil thickness and separation region (section 3.3). The other issue to be considered is the choice of the suitable shape parameterization. Both issues will be discussed in the next two sections.

7.1

Determination of the Population Size

The choice of the size of the population is closely linked to the computational equipment available and the number of designs to be performed. Most aerodynamic designs presented in this 95

96

Chapter 7. Numerical Airfoil Shape Optimization

work have been performed on a workstation cluster using 10 to 20 processors, simultaneously. Hence, the population size has to be a multiple of 10. For the study on the most suitable population size three different ES-schemes have been investigated using the geometric mode parameterization with eight object variables. The (3,10)-ES aims at fast convergence due to the increased selection pressure combined with a small number of individuals in the population. The second (6,40)-ES corresponds to the conclusions based on the performance of the ES on the F8F2-test function in the sense that the number of parents should be approximately the same size as the number of object variables. For the geometric mode parameterization eight design variables have been defined, whereas the upper side of the airfoil requires six variables within the PARSEC parameterization. Therefore, the number of parents is set to six, which yields a population size of approximately 40 considering the 1/7 selection pressure. The (15,100)-ES represents the third scheme which uses the 1/7 selection pressure and is associated with the scheme frequently applied in the literature. Except for the parent and population settings all parameters were the same for all versions. The LVA-1A airfoil has been enhanced in one-point designs at a Mach number Ma∞ =0.74 and Re∞ =2.4·106 at four different lift coefficients ranging from 0.40 ≤ cL ≤ 0.70. At these freestream conditions the transition position on the initial airfoil is located far downstream of the leading edge and a separation bubble occurs due to the shock-boundary-layer interaction, as has been shown by the experimental results in figure 6.2. Hence, the entire scope of flow phenomena discussed in chapter 2 is enclosed at this freestream Mach number. A typical result of the airfoil design by the different schemes is indicated in figure 7.1 at the freestream conditions Ma∞ =0.74 and Re∞ =2.4·106 and CL = 0.60. At these flight conditions the transition position on the upper side of the LVA-1A airfoil is located at xtr upper /c=0.63 (indicated by the last arrow in the figure) associated with a separation bubble with the length of lsep =7.6% of the chord length (indicated by the horizontal bar in the figure). Due to the penalty on the occurrence of a separation bubble this implies that the optimization procedure starts in the infeasible domain. Hence, the major effort of the optimization algorithm is to search for the feasible domain inside the airfoil shape parameter space, for which no separation occurs, even if this means a decrease of the lift-to-drag ratio. Subsequently, the optimizer aims to increase the lift-to-drag ratio within the feasible domain. This could mean that, although the flow over the resulting airfoil shape shows no separation an overall decrease of the lift-to-drag ratio is achieved. Physically, the price for an increased buffet boundary is paid by an increase of drag. Fortunately, all ES-schemes were able to develop airfoil shapes without separation at the indicated flow conditions. Moreover, for all 12 resulting airfoil shapes at the four different freestream conditions the separation bubble vanished combined with an improvement of the lift-to-drag ratio. From figure 7.1 it is apparent that the optimization algorithm aims at the reduction of the shock strength by additional acceleration of the flow near the leading edge to enhance the lift in this region to be able to reduce the lift and hence, the shock strength in the shock region. Therefore, the wave drag is reduced. Combined with the upstream movement of the transition location the occurrence of separation is suppressed, which additionally reduces the wave drag.

97

7.1. Determination of the Population Size

2 LVA−1A (3,10)−ES (6,40)−ES (15,100)−ES

1.5

1

−Cp

0.5

0 l

sep

−0.5

LVA−1A ↓↓ ↓ ↓ xtr LVA−1A

−1

−1.5 0

0.2

0.4

0.6

0.8

1

x/c

Fig. 7.1: Comparison of the pressure distribution of the designed airfoil shapes using different ES-schemes and the initial airfoil LVA-1A at the design point Ma∞ =0.74, cL =0.60 and Re∞ =2.4·106 . The airfoil thickness remains constant at 12% of the chord length. So, all objectives of the airfoil design have been reached, simultaneously. Although the (3,10)-ES scheme performs very well in the sense that the leading-edge acceleration is combined with the vanishing separation bubble, the scheme gets stuck in a local extremum. According to the pressure distributions in figure 7.1 only a small difference between the airfoil designed by the (6,40)-ES scheme and the (15,100)-ES scheme is apparent. However, to achieve the result of the latter scheme a substantial amount of additional function evaluations is required. Another significant result from the pressure distributions is that the ES-schemes, provided the population size is large enough, converge towards the same airfoil shape, although the random initialization by the mutation operator yields different airfoil shapes in the beginning of the design process. Thus, the airfoil design is independent of the initialization of the airfoils shapes. The integral results based on the improvement of the lift-to-drag ratio of the designed airfoil shapes at four different freestream conditions by three ES-schemes have been summarized in figure 7.2. The figure demonstrates the power of the ES-algorithm, since even with a (3,10)-ES scheme a substantial improvement of the lift-to-drag ratio can be obtained at a reduced amount of computational time compared with both other schemes. However, it is also evident that the high selection pressure drives the (3,10)-ES scheme towards a local extremum. At smaller Mach numbers the (6,40)-ES scheme yields approximately the same results as the (15,100)-ES scheme, whereas the difference increases towards higher Mach numbers. The minor additional

98

Chapter 7. Numerical Airfoil Shape Optimization

140

120

increase L/D [%]

100

80

60

40

20

0 0.4

(3,10)−ES (6,40)−ES (15,100)−ES 0.45

0.5

0.55

CL

0.6

0.65

0.7

0.75

Fig. 7.2: Improvement of the lift-to-drag ratio of the designed airfoil shapes using three different ES-schemes with respect to the LVA-1A airfoil at Ma∞ =0.74 and Re∞ =2.4·106 . improvements, however, require a substantial amount of computational time for each one-point design. In view of the large number of one-point designs at a wide range of Mach numbers and lift coefficients required to demonstrate the potential of the adaptive wing technology, the (6,40)-ES scheme represents the algorithm that obtains the best results possible for a moderate amount of computational resources. All following airfoil designs will be conducted with the (6,40)-ES scheme. Apart from the suitable ES-scheme the choice of the airfoil shape parameterization plays a significant role with respect to the possible improvements that can be achieved. Moreover, the suitability of the parameterization method with respect to the subsequent experimental verification of the aerodynamic design will be discussed in the following section.

7.2

Determination of the Shape Parameterization

The main objective of the present work is to demonstrate the potential of the enhancement of the aerodynamic characteristics by employing the adaptive wing technology through a combination of a numerical airfoil design and an experimental verification. Therefore, the parameter space spanned by the airfoil shape parameterization approach has to correspond to the parameter space of the adaptive wing model. Otherwise, the designed airfoil shapes can not be tested in the wind tunnel experiments, since the adjustment kinematics can not modify the airfoil shape according to the airfoil geometry prescribed by the aerodynamic design. In section 3.3.2 the implementation of the shape parameterization method based on the geometric modes and the

99

7.2. Determination of the Shape Parameterization

approach based on the PARSEC polynomial has been presented. Their applicability to provide airfoil geometries, which conform with the adaptive model parameter space, is tested next. Since the adaptive wing model possesses a flexible upper surface the parameterization methods are required to focus on this side. Therefore, the number of object variables of the PARSECapproach reduces to six. The aerodynamic design starts with the initial airfoil shape LVA-1A, which is perturbed during the initialization stage by the mutation operator. This means, it is required to determine the PARSEC coefficients that describe the LVA-1A airfoil to obtain the same starting point for both parameterization methods. This actually poses a minimization procedure, itself. Although the initial airfoil shape LVA-1A does not entirely lie within the PARSEC parameter space, the parameter setting associated with the nearest geometry represents the initial shape. The mutation widths at each of the eight stations in chordwise direction, which can be interpreted as the average airfoil’s thickness perturbation, have been initialized by reducing the corresponding object variable by one order of magnitude. The airfoil has been designed at the freestream conditions Ma∞ = 0.74, CL = 0.40, and Re∞ =2.4·106 . Similar to the flow field at the same transonic Mach number and a higher lift coefficient in figure 7.1, a separation bubble is present on the upper surface of the initial airfoil. The pressure distribution of the LVA-1A airfoil and the final design by the PARSEC-method have been displayed in figure 7.3. −3

0x 10 16

2 LVA−1A design

0.2

0.4

0.6

0.8

1

13.75

1.5

11.5 1

∆ y/c

−Cp

y/c

9.25 0.5

7

0

4.75 LVA−1A ↓

−0.5

↓ design

2.5

−1

−1.5 0

∆ y/c LVA−1A design

0.25

0.2

0.4

0.6

x/c

0.8

1

−2 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

x/c

Fig. 7.3: Left: Pressure distributions of the LVA-1A airfoil and the designed airfoil shape with the PARSEC parameterization using the (6,40)-ES. (Ma∞ = 0.74, CL = 0.40 and Re∞ =2.4·106 ) Right: Modification of the initial airfoil (∆ y) to obtain the designed shape. (Increased display of the y-ordinate) The optimization algorithm reduces the strength of the shock by extensive additional rear loading, which yields a shock-free airfoil shape at the design point. The reduction of the positive pressure gradient causes the separation bubble to vanish and allows the downstream movement of the transition location. The additional gain in the lift-to-drag ratio corresponds to 13.05%. The right part of figure 7.3 displays both airfoil geometries and the difference between

100

Chapter 7. Numerical Airfoil Shape Optimization

both airfoil shapes. The significant increase of the local airfoil thickness over the last 30% of chord of the airfoil indicates the rear loading. The positions of the eight geometric modes cover almost the same range as the drive mechanics of the model from 15% to 70% of the chord length. Since the geometric modes are superimposed on the base geometry, the LVA-1A airfoil is part of the parameterization. All mutation widths have been initialized by 1 of the chord length. The pressure distribution of the initial shape and the result of the (6,40)-ES based on the geometric modes parameterization has been displayed in figure 7.4. −3

0x 10 6

2 LVA−1A design Euler−BL design NS

1.5

0.2

0.4

0.6

0.8

1

5.125 4.25

1

∆ y/c

p

−C

y/c

3.375 0.5

2.5

0

1.625 LVA−1A ↓

−0.5

↓ design

0.75

−1

−1.5 0

∆ y/c LVA−1A design

−0.125

0.2

0.4

0.6

x/c

0.8

1

−1 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

x/c

Fig. 7.4: Left: Pressure distributions of the LVA-1A airfoil and the designed airfoil shape with the geometric mode parameterization using the (6,40)-ES. (Ma∞ = 0.74, CL = 0.40 and Re∞ =2.4·106 ). Right: Modification of the initial airfoil (∆ y) to obtain the designed shape. (Increased display of the y-ordinate)

Similar to the result obtained by the PARSEC-approach, the rear loading is increased associated with a downstream movement of the transition location with a vanishing separation bubble. However, since the last geometric mode is located at 70% chord, a maximum modification at 85% chord corresponding to the PARSEC method can not be reached, which is also demonstrated in the right part of figure 7.4. The gain in lift-to-drag ratio obtained of 12.68% is, therefore, slightly reduced compared to the gain of 13.05% achieved by the PARSEC design. Still, the PARSEC parameterization is not suited for further airfoil design since the resulting airfoil shapes are outside the bounds of the adaptive wing model. Extensive additional restriction penalties of the parameter space of the PARSEC method to reduce its parameter space, such that it corresponds to the adaptive wing possibilities, would not yield a method that outperforms the geometric mode parameterization. Therefore, all subsequent one-point designs will apply the geometric mode airfoil shape parameterization using eight geometric modes.

101

7.3. One-Point Airfoil Designs

7.3

One-Point Airfoil Designs

The previous sections determined the final algorithm, which enables the aerodynamic design of airfoil shapes. From the experimental results presented in chapter 6 the freestream conditions where the LVA-1A airfoil shape exhibits aerodynamic characteristics that can be improved, have been identified. At subsonic Mach numbers the occurrence of transition near the leading edge, as indicated in figure 6.14, increases the friction drag, whereas at higher transonic Mach numbers the extended laminar boundary layer is accompanied by separation with the corresponding negative effects with respect to the buffet phenomenon, displayed in figure 6.12. However, figure 6.8 demonstrates the good performance of the LVA-1A at Ma∞ = 0.72, Re∞ = 2.57 × 106 , so little improvement potential is expected at this Mach number. Nonetheless, the discussion in chapter 6 implies the requirement for aerodynamic designs of the initial airfoil over a wide range of Mach numbers and lift coefficients. The flow computations with natural transition have been performed by the Euler-boundarylayer method that has been validated in chapter 6. During the optimization process the prescribed lift coefficient is required constant. This yields the description of the one-point designs for 20 different transonic freestream conditions. The Ma-∞ CL -combinations and their corresponding identifier are shown in table 7.1. cL Ma∞ 0.65 0.70 0.72 0.74 0.76 Table 7.1:

0.40

0.50

0.60

0.70

CS25NT CS20NT CS16NT CS05NT CS07NT

CS24NT CS19NT CS15NT CS03NT CS02NT

CS22NT CS18NT CS14NT CS01NT CS08NT

CS23NT CS17NT CS13NT CS04NT CS09NT

Flow conditions of the one-point designs of the upper airfoil surface with natural transition with LVA-1A initial airfoil shape.

Preliminary investigation at smaller lift coefficients 0.10 ≤ CL < 0.40 proved the good aerodynamic characteristics of the LVA-1A airfoil, so no additional adaptation is required in this range. Similar to the discussion of the experimental results in chapter 6 the results of the one-point designs will be separated according to their freestream velocity in the subsonic and transonic range.

7.3.1

Airfoil Design at Subsonic Speeds

At the freestream conditions Ma∞ =0.65, CL = 0.60, and Re∞ =2.4·106 a suction peak near the leading edge occurs on the LVA-1A airfoil, which even extends into the supercritical range. The suction peak causes premature transition at 7.6% of the chord length indicated by the left arrow and a weak shock, which means an increase of friction drag and wave drag, shown in figure 7.5.

102

Chapter 7. Numerical Airfoil Shape Optimization

2 LVA−1A design Euler−BL design NS

1.5

1

−Cp

0.5

0

−0.5

LVA−1A ↓

↓ design

−1

−1.5 0

0.2

0.4

0.6

0.8

1

x/c

Fig. 7.5: Comparison of the pressure distributions of the LVA-1A airfoil and the designed airfoil shape CS22NT with the geometric mode parameterization using the (6,40)-ES at Ma∞ =0.65, CL = 0.60 and Re∞ =2.4·106 .

The optimization algorithm reduces the acceleration near the leading edge combined with a constant pressure level well below the supercritical value that extends over a longer portion of the chord length to delay the transition location to 72% of the chord length as indicated by the arrow. Figure 7.5 also shows the good agreement of the computational pressure distribution over the designed airfoil obtained by the Euler-boundary-layer method and the Navier-Stokes approach. The effect of the increase of the extent of the laminar boundary layer has also been visualized in figure 7.6. The left part indicates the drag polar of the initial airfoil and of all one-point designs at Ma∞ =0.65. This means that the latter does not represent one airfoil shape, but a combination of airfoil shapes, which have been designed with respect to their aerodynamic characteristics for each particular Ma∞ -CL -combination. The right part of the figure indicates the predicted transition location associated with both drag polars. The ES algorithm automatically initiates the downstream movement of the transition location to over x/c=0.70 without the occurrence of separation, which yields a significant enhancement of the flight performance at the Mach number investigated. It is interesting to realize that, although the physical property of the transition location is not present in the objective function, the optimization algorithm autonomously determines its own laminarization concept.

103

0.8

0.8

0.7

0.7

0.6

0.6

0.5

0.5

0.4

0.4

0.3

0.3

0.2

0.2

0.1

0.1

LVA−1A Adaptive wing 0 4

LVA−1A Adaptive wing

CL

CL

7.3. One-Point Airfoil Designs

5

6

7

C

D

8

9

10

0 0

−3

x 10

0.2

0.4

x /c

0.6

0.8

1

tr

Fig. 7.6: Correlation of the airfoil performance and the transition location for the family of designed airfoil shapes and for the initial LVA-1A airfoil at Ma∞ =0.65 and Re∞ =2.4·106 . Left: Drag polars. Right: Predicted transition location.

7.3.2

Airfoil Design at Transonic Speeds

Some of the flow properties over the LVA-1A airfoil have been discussed in section 7.1. The main problem at transonic speeds is the occurrence of separation due to the interaction of the shock with the laminar boundary layer. In figure 7.1 the enhanced airfoil geometries have been discussed. They demonstrated the ability of the ES-algorithm to remove the separation bubble and reduce the shock strength to increase the lift-to-drag ratio. Similar to the previously shown subsonic airfoil design at Ma∞ = 0.65, the summary of the airfoil designs at Ma∞ = 0.74 is shown in figure 7.7. From the right part of the figure, it can be deduced that at the higher Mach numbers an upstream movement of the transition is favorable to reduce the influence of the shock-boundarylayer interaction and to remove the separation bubble to decrease the total drag. It is evident, that at transonic speeds with separation the optimization algorithm reduces the extent of the laminar boundary layer to enhance the overall aerodynamic properties. This is in contrast to the handling of the transition at subsonic speeds. The power of the optimization algorithm with respect to the improvement of the aerodynamic characteristics at varying freestream conditions has been demonstrated. The next section will discuss the first objective of the numerical design in the sense that the results of the onepoint designs can be summarized to demonstrate the aerodynamic improvement potential of an adaptive wing, which is able to adjust to changing flight conditions.

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Chapter 7. Numerical Airfoil Shape Optimization

0.8

0.7

0.7

0.6

0.6

0.5

0.5

LVA−1A Adaptive wing

L

0.4

C

C

L

0.8

0.4

0.3

0.3

0.2

0.2 0.1

0.1 LVA−1A Adaptive wing 0 4

5

6

7

C

D

8

9

10

11

0 0

0.2

0.4

−3

x 10

x /c

0.6

0.8

1

tr

Fig. 7.7: Correlation of the airfoil performance and the transition location for the family of designed airfoil shapes and for the initial LVA-1A airfoil at Ma∞ =0.74 and Re∞ =2.4·106 . Left: Drag polars. Right: Predicted transition location.

7.4

Adaptive Airfoil at Transonic Speeds

Instead of searching for one airfoil shape, which performs reasonably well at all relevant flight conditions of a drag polar using a multi-point optimization, the present investigation focuses on the optimization based on an airfoil with an adaptive upper surface. An adaptive surface shape represents the boundary of best possible aerodynamic performance available employing all possibilities within the parameter space of the geometric mode shape parameterization. The first objective of the airfoil design was the delay of the drag divergence towards higher Mach numbers (figure 1.4). This allows the increase of the flight speed without an overproportional increase of drag. The development of the transonic drag rise of the LVA-1A airfoil is displayed in the left part of figure 7.8. For a lift coefficient CL = 0.40 the drag divergence starts at Ma∞ = 0.746 and decreases towards a Mach number of Ma∞ = 0.723 at CL = 0.70. From the dependence of the total drag coefficient on the Mach number it is evident, that the design-point of the LVA-1A airfoil is located between 0.72 ≤ Ma∞ ≤ 0.73, since a significant reduction of drag is visible at the corresponding Mach numbers. As discussed in section 7.3.1, the reduced amount of laminar flow at smaller speeds has a negative effect on the drag, whereas at speeds higher than Ma∞ = 0.73 the shock development causes the transonic drag rise, as discussed in section 7.3.2. The distribution of the drag depending on the Mach number for the family of designed airfoil shapes is indicated in the right part of figure 7.8. In this figure not the drag rise of one airfoil shape is investigated, but of all 20 airfoils designed for a specific flight condition in the Ma∞ -CL table 7.1. For comparison with the performance of the LVA-1A airfoil shape, the scaling of the vertical ordinate remained the same. The figure 7.8 evidences the effort of the

105

7.4. Adaptive Airfoil at Transonic Speeds

0.022 0.02 0.018

0.022

CL=0.40 CL=0.50 CL=0.60 C =0.70

0.02 0.018

L

0.014

0.014

L

C

CD

0.016

D

0.016

CL=0.40 CL=0.50 CL=0.60 C =0.70

0.012

0.012

0.01

0.01

0.008

0.008

0.006

0.006

0.004

0.66

0.68

0.7

Ma∞

0.72

0.74

0.76

0.004

0.66

0.68

0.7

Ma∞

0.72

0.74

0.76

Fig. 7.8: Comparison of the drag divergence for the designed airfoils and the LVA-1A airfoil. Left: LVA-1A airfoil. Right: Family of designed airfoils at the corresponding Ma∞ -CL -combination. optimization algorithm to develop shock-free airfoil shapes to avoid wave drag accompanied with the movement of the transition location far downstream to reduce the friction drag. Although the total drag increases from Ma∞ = 0.74 to Ma∞ = 0.76 the point for drag divergence has not been reached, according to the definition by Ganzer [59]. This increase of drag is due to the wave drag induced by the occurring shock wave, which becomes inevitable, since all possibilities within the geometry parameterization have been exhausted. The impact of the drag reduction strategy developed by the optimization algorithm on the aerodynamic performance with respect to the lift-to-drag ratio is demonstrated in figures 7.9 and 7.10 The latter consists of the envelope of lift-to-drag ratios of the family of designed airfoil shapes at different Ma∞ -CL -combinations. They can be interpreted as the settings of an adaptive wing airfoil. This means that it will not be possible to reach a point with reduced drag compared to the adaptive airfoil polar by modifying the airfoil geometry or by varying the angle of attack. The ordinates of both lift-to-drag surfaces have been normalized with the maximum lift-to-drag value achieved by the LVA-1A airfoil to indicate the potential for the performance improvements, which can be achieved by the adaptive wing technology. The small Mach number influence of the adaptive airfoil section on the lift-to-drag ratio is an indication that the envelope surface is located in the neighborhood of the optimum airfoil shape family at each flight condition. Figuratively, one could imagine that the adaptive airfoil unwraps the lift-to-drag ratio sheet formerly folded over the Ma∞ = 0.72 drag polar of the rigid LVA-1A airfoil. Figures 7.9 and 7.10 evidence that the second objective of the aerodynamic airfoil design with respect to the improvement of the operational range of the wing has been reached (also see figure 1.5). For all Mach numbers the LVA-1A airfoil has reached the maximum liftto-drag ratio in this Ma∞ -CL -regime, whereas the adaptive airfoil shape represented by the envelope surface of the lift-to-drag ratio is still on the ascending branch and has not reached the maximum lift-to-drag ratio, yet. However, since the numerical findings will be validated in

106

Chapter 7. Numerical Airfoil Shape Optimization

140

(L/D)/(L/Dmax LVA−1A) [%]

120 100 80 60 40 20 0 0.6 0.4 0.2

0.66

0.68

CL

0.7

0.72

0.74

0.76

Ma

∞

Fig. 7.9: Envelope surface of the lift-to-drag ratio at 20 different Ma∞ -CL -combinations showing the performance of the LVA-1A airfoil.

140

100

max LVA−1A

) [%]

120

(L/D)/(L/D

80

60

40

20

0 0.6

0.5

0.4

C

L

0.3

0.2

0.1

0.66

0.68

0.7

0.72

0.74

0.76

Ma∞

Fig. 7.10: Envelope surface of the lift-to-drag ratio of all designed airfoils at 20 different Ma∞ -CL -combinations.

107

7.4. Adaptive Airfoil at Transonic Speeds

wind tunnel tests that prevent that high angle-of-attack due to blockage, no additional airfoil designs have been conducted to attain the maximum lift-to-drag ratio for all Mach numbers of the adaptive airfoil. The overall potential of the adaptive wing technology with respect to an improvement of the operation range at each transonic Mach number is demonstrated in figure 7.11 according to the relation (L/Ddesign − L/DLV A−1A ) . (7.1) L/Dincrease = L/DLV A−1A L/D

increase

0.7

[%] 180

0.65

160

140

0.6

CL

120

100

0.55

80

0.5

60

40

0.45 20

0.4

0.66

0.68

0.7

0.72

0.74

0.76

Ma∞

Fig. 7.11: Improvement of the lift-to-drag ratio of the adaptive airfoil represented by all 20 designed airfoils with respect to the LVA-1A airfoil at different freestream conditions The figure indicates the additional potential to enhance the lift-to-drag ratio in percent by an adaptive airfoil shape compared with the rigid wing represented by the LVA-1A airfoil. The good aerodynamic properties of the LVA-1A airfoil at Ma∞ = 0.72 become apparent, since only small improvements can be achieved at this Mach number. The operational area is extended significantly by the adaptive airfoil towards both lower and higher flight Mach numbers to fully exploit the aerodynamic potential at each point of the mission at cruise speed. The evolution strategy in combination with the Euler-boundary-layer method and the eN transition location prediction approach proved a valuable technique for the aerodynamic design of transonic laminar-type airfoil shapes. In the next section, a selection from the 20 designed airfoils for the subsequent tests with the adaptive wing wind tunnel model will be discussed.

108

7.5

Chapter 7. Numerical Airfoil Shape Optimization

Selection of Airfoil Shapes for Experimental Tests

The requirements imposed on the airfoil shapes selected from the data base of 20 designs for wind tunnel tests are higher than those for each single one-point design. Since the detailed experimental investigation of the state of the boundary layer and the shock configuration will not only focus on the airfoil design-point, but cover the entire Mach number and angle-ofattack range required during cruise flight, the selected airfoil shapes have to show enhanced performance at the design-point, combined with better performance at off-design flow conditions compared to the initial airfoil shape. Hence, the aerodynamic performance of the optimized one-point design airfoil shapes is analyzed numerically over a wide Mach number- and lift range, to identify wing geometries that also perform well regarding aerodynamic characteristics over a wide range of flight conditions. For the experimental investigation of the aerodynamic performance of the adaptive wing three airfoil shapes have been selected from the available 20 geometries. The CS18NT airfoil has been designed for Ma∞ = 0.70 and CL = 0.60. The corresponding increase of performance with respect to the LVA-1A airfoil is displayed in figure 7.12.

L/D

increase

0.7

[%] 30

20

0.6

10

CL

0.65

0

0.55

0.5

−10

0.45

−20

0.4

−30

0.66

0.68

0.7

0.72

0.74

0.76

Ma

∞

Fig. 7.12: Improvement of the lift-to-drag ratio of the CS18NT airfoil (designed for Ma∞ = 0.70 and CL = 0.60) compared to the LVA-1A airfoil. The figure clearly demonstrates the strength of the CS18NT airfoil in the lower Mach number range. The CS05NT airfoil, designed for Ma∞ = 0.74 and CL = 0.40, has been selected for the transonic Mach number range . Figure 7.13 visualizes the performance in the speed and lift range under consideration.

109

7.5. Selection of Airfoil Shapes for Experimental Tests

L/Dincrease [%]

0.7

60

0.65

50

40

0.6

CL

30

20

0.55

10

0.5

0

−10

0.45 −20

0.4

−30

0.66

0.68

0.7

0.72

0.74

0.76

Ma ∞ Fig. 7.13: Improvement of the lift-to-drag ratio of the CS05NT-airfoil (designed for Ma∞ = 0.74 and CL = 0.40) compared to the LVA-1A airfoil.

L/Dincrease [%]

0.7

120

0.65 100

80

CL

0.6

60

0.55 40

0.5

20

0

0.45 −20

0.4

0.66

0.68

0.7

0.72

0.74

0.76

Ma∞ Fig. 7.14: Improvement of the lift-to-drag ratio of the CS20NT-airfoil (designed for Ma∞ = 0.70 and CL = 0.40) compared to the LVA-1A airfoil.

110

Chapter 7. Numerical Airfoil Shape Optimization

The figure indicates a significant increase of the CS05NT airfoil performance compared to the LVA-1A airfoil and only a moderate reduction of the aerodynamic efficiency around the design-point of the LVA-1A shape at Ma∞ = 0.72. Finally, the CS20NT airfoil designed for Ma∞ = 0.70 and CL = 0.40 has been selected to improve the performance at higher lift coefficients, as shown in figure 7.14. From the figures 7.12, 7.13, 7.14 describing the improvement of the aerodynamic performance it is obvious that the strength of each single selected airfoil shape focuses on a particular area of the total Mach number and lift range. This means, that it is possible to enhance the performance over a wide range of flight conditions using only a limited number of airfoil geometries and still remain in the neighborhood of optimal performance. A detailed experimental analysis of the flow phenomena for these three selected airfoil shapes will be conducted in the trisonic wind tunnel of the Aerodynamische Institut and will be compared with the results of the flow over the LVA-1A airfoil in the following chapter.

Chapter 8 Experimental Results for the Adaptive Wing Section The experimental investigation aims at the validation of the aerodynamic design by determining important flow phenonema that consequently will exhibit the potential of the adaptive wing concept for a wind tunnel demonstrator model. Already in chapter 6 the necessity to apply the variety of measurment techniques supplementing each other has been proved. Therefore, the same techniques will be applied on the adaptive wing model to determine the flow characteristics with respect to the transition location and the shock-boundary-layer interaction, which are responsible for the differences of the total drag on the adaptive wing compared with the rigid surface LVA-1A airfoil. Similar to the experimental tests on the rigid surface LVA-1A airfoil, discussed in chapter 6, the investigations on the adaptive wing model focus on cruise flight conditions of modern transportation aircraft at transonic speeds ranging from 0.70 ≤ Ma∞ ≤ 0.75 and an angle-ofattack range of 1.0o ≤ α ≤ 4.0o , since this regime represents the part of a typical long range mission for which the adaptive wing technology is recognized to be most appropriate. A main feature of the adaptive wing wind tunnel model is the smooth airfoil surface without any curvature jumps, which allows the experiments to be conducted with natural transition on the upper airfoil surface. However, due to the integration of the drive mechanics near the leading edge of the airfoil, the model design prevented the installation of a sufficient number of pressure orifices near the leading edge on the model lower surface. Therefore, it is not possible to acquire the pressure distribution in this area, which prohibits statements on the possible premature transition of the boundary layer. Hence, the transition position of the lower side had to be fixed near the leading edge at 7 % of the chord length using a transition strip in an open triangle form. The initial shape of the adaptive wing wind tunnel model corresponds to the LVA-1A geometry, which will be set to the three airfoil shapes selected from the database of 20 one-point designs discussed in chapter 7. The design of the model allows the influence on the adapted airfoil geometry in a range from 12.5% to 72.5% of the chord length with a high accuracy of 30 µm. However, it is impossible to actively influence the first 12.5% chord near the leading edge or the last 27.5% chord near the trailing edge of the model. Hence, the airfoil shape tested 111

112

Chapter 8. Experimental Results for the Adaptive Wing Section

in the wind tunnel will not entirely correspond to the selected airfoil shapes, and, therefore, experimental results will not be expected to entirely conform with the numerical prediction of the aerodynamic improvement. The next sections will discuss typical flow phenomena on the adaptive wing model with different geometries, which have also been observed in the discussion on the results of the aerodynamic design. This implies the aerodynamic behavior at subsonic speeds and the performance at transonic speeds with respect to the transition location, separation and shock strength.

8.1

Subsonic Airfoil Characteristics

From section 7.3.1 the effort of the optimization algorithm to reduce the total drag by the downstream movement of the transition location has been demonstrated. In figure 8.1 the pressure distribution on the airfoil surface for the initial LVA-1A and the CS05NT airfoil shape at Ma∞ = 0.72 and CL = 0.35 are shown. The markers indicate the measured pressure distributions, whereas the lines correspond to the flow computations by the Euler-boundarylayer method, which compare very well for both airfoil shapes. The arrows in the figure indicate the numerically predicted transition location.

2 EXP LVA−1A NUM LVA−1A EXP CS05NT NUM CS05NT

1.5

1

−C

p

0.5

0 LVA1A

−0.5

↓ ↓

CS05NT

−1

−1.5 0

0.2

0.4

0.6

0.8

1

x/c

Fig. 8.1: Experimentally and numerically obtained pressure distributions over the LVA-1A and CS05NT airfoils with natural transition at Ma∞ = 0.72, Re∞ = 2.7 × 106 , and CL = 0.35. The slight increase of the acceleration near the leading edge of the CS05NT airfoil, followed by a constant pressure distribution over a long extent of the chord length becomes visible. Compared to the LVA-1A airfoil, this yields additional rear-loading. Numerical calculations

113

8.1. Subsonic Airfoil Characteristics

determined the reduction of the total drag by 5%, which has been supported by observations from the experiment. From the pressure distribution it can not be definitely deduced that the boundary layer stays laminar up to the recompression point. For a detailed analysis of the state of the boundary layer, the delay of the laminar/turbulent transition has been identified by the hot-film sensors. The objective of the optimization algorithm was to delay the transition location between 70% and 80% of the chord length, which is why the sensor array has also been positioned further downstream compared to the hot-film array on the rigid surface model, now covering a range between 50% and 80% chord. The distribution of the RMS values and the skewness of the hot-film sensor signals over the chord of the CS05NT airfoil are displayed in figure 8.2. The transition location on the LVA-1A airfoil at the corresponding flow conditions has been determined to 65% of the chord length in figure 6.10. −3

x 10

0.5

1.56

0

1.32

−0.5

transition

1.08 0.84 0.6 0.6

−1

skewness

RMS

1.8

−1.5

0.64

0.68

0.72

0.76

−2 0.8

x/c Fig. 8.2: Determination of the transition location by means of the RMS values (solid line) and the skewness (dashed-dotted line) of the hot-film sensor signals on the LVA-1A and CS05NT airfoil at Ma∞ = 0.72, Re∞ = 2.7 × 106 , and CL = 0.35. Figure 8.2 illustrates that the transition location has been shifted from 65% chord on the LVA-1A airfoil to 73% chord on the CS05NT airfoil, which is associated with a reduction of the friction drag, and at subsonic speeds with a reduction of the total drag. Consequently, the implementation of the NLF concept for laminarization at these freestream conditions is successful. The description of the transition phenomenon in section 2.1 and the numerical results of the aerodynamic design in chapter 7 have demonstrated that the transition location is very susceptible to small changes in the surface contour of the wing section. Therefore, the requirements on an adaptive wing wind tunnel model with respect to the smoothness of the surface are extremely high, since small imperfections can trigger transition. The results of the delay of transition on the adaptive wing model at the subsonic Mach number, not only evidence the

114

Chapter 8. Experimental Results for the Adaptive Wing Section

potential of the downstream movement of the transition location, but also demonstrate the quality of the surface smoothness of the adaptive wing, which avoids curvature jumps. Thus, the model enables the investigation of the influence of the airfoil shape on the transition location on the total drag. The following section will elaborate the potential of the adaptive wing as far as drag reduction at transonic speeds is concerned.

8.2

Transonic Airfoil Characteristics

The introduction of the shock/boundary-layer interaction associated with the possibility of the occurrence of a separation bubble underneath the shock foot at transonic flow speeds changes the control measures to reduce the total drag. From the aerodynamic design in chapter 7 the objective of the optimization algorithm to remove the separation bubble by an upstream movement of the transition location along with a reduction of the shock strength has been indicated. At flow conditions, where no separation is present on the initial airfoil LVA-1A the reduction of the shock strength is the measure to reduce the total drag. The subsequent sections will demonstrate the experimental verification of the previously mentioned drag reduction approaches.

8.2.1

The Impact of the Airfoil Design on Local Separation

The negative aerodynamic effects of separated regions at transonic flight conditions are represented by the unsteady shock movement and an increase of the wave drag. Therefore, it is indispensible to modify the airfoil shape to remove the separated regions. Figure 8.3 displays the pressure distribution on the airfoil of the CS05NT compared with the LVA-1A airfoil at Ma∞ = 0.74 and CL = 0.67. From the surface pressure distribution a reduction of the negative pressure gradient is indicated. Moreover, the shock is moved upstream and the shock strength is somewhat reduced by a slight smearing of the shock over the CS05NT airfoil compared with the LVA-1A airfoil. Similar to the subsonic flow case, the rear-loading is increased for the modified wing section CS05NT. Again, the effect of the modified pressure distribution on the transition location and separated regions can not be deduced from figure 8.3. Therefore, the liquid-crystal skin friction visualizations will be analyzed in figures 8.5 and 8.6. The reddish color of the liquid-crystal coating on the LVA-1A airfoil surface in figure 8.5 characterizes a long extent of the laminar boundary layer. This region coincides with the region of the negative pressure gradient shown in figure 8.3. The subsequent area of bright red color depicts a region of low shear stress, which is typical for a separated region. Thus, the laminar boundary layer separates upstream of the shock, whereas the blue color indicates the reattachment of the turbulent boundary layer. The difference of the flow characteristics of the CS05NT airfoil are demonstrated by the liquid-crystal visualization in figure 8.6. The reddish color starting from the leading edge to the point on the airfoil surface, which corresponds to the pressure minimum, evidences a laminar boundary layer.

115

8.2. Transonic Airfoil Characteristics 2 EXP LVA−1A NUM LVA−1A EXP CS05NT NUM CS05NT

1.5

1

−C

p

0.5

0 CS05NT ↓ ↓ LVA1A

−0.5

−1

−1.5 0

0.2

0.4

0.6

0.8

1

x/c

Fig. 8.3: Experimentally and numerically obtained pressure distributions over the LVA-1A and CS05NT airfoils with natural transition at Ma∞ = 0.74, Re∞ = 2.7 × 106 , and CL = 0.67. However, in the case of the CS05NT airfoil the reddish color is not followed by a bright red region, but it is terminated at 62% chord directly by the blue color, which is characteristic for a laminar-turbulent boundary layer transition without separation. The upstream movement of the shock also reduces the extent of the laminar boundary layer. Thus, the liquid-crystal images show that the separation bubble, which was present on the LVA-1A airfoil, has been removed on the CS05NT airfoil at the same transonic flow conditions. This observation of the removed separation on the CS05NT airfoil is verified by the linear correlation coefficient of neighboring hot-film sensors in figure 8.4.

1

Corr. coeff.

Corr. coeff.

1 0.5 0 −0.5 −1 0.5

0.55

0.6

0.65

0.7

Sensor position x/c

0.75

0.8

0.5 0 −0.5 −1 0.5

0.55

0.6

0.65

0.7

0.75

0.8

Sensor position x/c

LVA-1A CS05NT Fig. 8.4: Comparison of the linear correlation coefficient indicating separation for the LVA-1A and attached flow for the CS05NT airfoil at Ma∞ = 0.74, Re∞ = 2.7 × 106 , and CL = 0.67. As discussed in section 5.2.1 and demonstrated in section 6.1 the linear correlation coefficient is recognized to be more effective to indicate separation in the vicinity of shocks and turbulent

116

Chapter 8. Experimental Results for the Adaptive Wing Section

la m in a r b o u n d a ry la y e r

re d

s e p a ra tio n b u b b le

0 .5 5 < x

tu rb u le n t b o u n d a ry la y e r

se p / c < 0 . 7 0 b rig h t re d

b lu e

Fig. 8.5: Liquid-crystal visualization of the transition location and the separated areas on the LVA-1A airfoil at Ma∞ = 0.74, Re∞ = 2.7 × 106 , and CL = 0.67.

la m in a r b o u n d a ry la y e r

tra n s itio n

tu rb u le n t b o u n d a ry la y e r

x tr/ c = 0 . 6 2 re d

b lu e

Fig. 8.6: Liquid-crystal visualization of the transition location on the CS05NT airfoil at Ma∞ = 0.74, Re∞ = 2.7 × 106 , and CL = 0.67.

8.2. Transonic Airfoil Characteristics

117

boundary layers than the 180o phase shift criterion. The two distinct peaks of strong negative values of this coefficient deduced from the hot-film sensor signals on the LVA-1A airfoil indicate the location and extent of a laminar separation bubble from 57% - 70% chord in the shock region, which corresponds with the observations of the liquid-crystal coating image. Unlike these results, the linear correlation coefficient distribution associated with the CS05NT airfoil does not show any pronounced minima, which indicates an attached boundary layer over the entire airfoil surface. These findings verify the results from the liquid-crystal measurements. So, with respect to the LVA-1A airfoil the CS05NT airfoil shape smoothes the shock, and hence reduces the shock strength. This effect, combined with the upstream movement of the transition location yields a boundary layer, which remains attached to the surface and hence reduces the total drag by 19% and additionally improves the aerodynamic characteristics by avoiding the buffet phenomenon. The quantification of the reduction results from numerical and experimental observations. The influence of the modified wing section shape on the separation characteristics of the airfoil flow can also be visualized by the shadowgraph method. As discussed in section 2.2, a laminar boundary layer separates upstream of the shock, which causes the shock to form a lambda-shock pattern. A shadowgraph image of the transonic flow over the LVA-1A airfoil at Ma∞ = 0.74 and CL = 0.8 is visualized in figure 8.7. The figure definitely indicates the thickening of the boundary layer downstream of the trailing shock and the turbulent structures inside the boundary layer and wake flow. These features can only be captured, due to the illumination with a spark light source with a short spark duration. The increase of the displacement of the outer flow due to the separated region has clearly been visualized. The outer flow, which is still supersonic in this area, experiences the sudden displacement increase as a ramp, and hence an oblique leading shock is formed. The flow downstream of the leading shock is still supersonic till the supersonic region is terminated by the trailing shock, forming a lambda-shock configuration. The separated region is located beneath the lambda-shock pattern. The shadowgraph visualization of the flow over the CS05NT airfoil at Ma∞ = 0.74 and CL = 0.8 is shown in figure 8.8. At this airfoil shape the supersonic region is terminated by an almost normal shock instead of a lambda-shock pattern. This is an indication that no sudden increase of the boundary layer is present, and as such no separation occurs in the vicinity of the shock. Moreover, the thickness of the turbulent boundary layer downstream of the shock is substantially smaller compared with the boundary layer of the LVA-1A airfoil in figure 8.7. The numerical investigations supported by the experimental ones determine the overall reduction of the total drag due to the modified airfoil shape amounts to 22% at these flow conditions.

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Chapter 8. Experimental Results for the Adaptive Wing Section

Fig. 8.7: Shadowgraph image on the LVA-1A airfoil at Ma∞ = 0.74, Re∞ = 2.7 × 106 , and CL = 0.8.

Fig. 8.8: Shadowgraph image on the CS05NT airfoil at Ma∞ = 0.74, Re∞ = 2.7 × 106 , and CL = 0.8.

119

8.2. Transonic Airfoil Characteristics

8.2.2

Shock Strength Reduction

From the previous examples it has been shown, that it is possible to reduce the drag by removing the separation. However, the total drag can also be lowered by reducing the wave drag induced by the shock. For the freestream conditions Ma∞ = 0.72 and CL = 0.8 the pressure distributions on the airfoil are shown in figure 8.9. In this case the aerodynamic characteristics of the LVA-1A airfoil have been compared to the CS18NT airfoil, which has been designed to perform well at the smaller cruise flight Mach numbers. 2 EXP LVA−1A NUM LVA−1A EXP CS18NT NUM CS18NT

1.5

1

−C

p

0.5

0 CS18NT ↓ −0.5

↓ LVA1A

−1

−1.5 0

0.2

0.4

0.6

0.8

1

x/c

Fig. 8.9: Experimentally and numerically obtained pressure distributions over the LVA-1A and CS18NT airfoils at Ma∞ = 0.72, Re∞ = 2.7 × 106 , and CL = 0.8. Due to a smoothed shock with a reduced shock strength and additional rear-loading almost the same lift as for the initial airfoil is achieved. The presence of separation in the vicinity of the shock can not be deduced from the surface pressure distribution. Therefore, the shadowgraph image in figure 8.10 will be analyzed. The shadowgraph image shows a strong shock on the airfoil’s upper side of the LVA-1A airfoil. The configuration of the shock is similar to the one shown in figure 8.8 for the transonic flow over the CS05NT airfoil. The presence of an almost normal shock indicates the attached boundary layer. At the foot of the shock the boundary-layer thickness increases. However, this increase is small compared to the flow over the LVA-1A airfoil at the higher Mach number Ma∞ = 0.74 and CL = 0.8. The reduced strength of the shock has also been visualized by the shadowgraph image of the flow over the CS18NT airfoil at Ma∞ = 0.72 and CL = 0.8 in figure 8.11. The shock pattern on the CS18NT airfoil is similar to the shock occurring on the LVA-1A airfoil, which indicates the absence of a separation bubble. The attached boundary layer has also

120

Chapter 8. Experimental Results for the Adaptive Wing Section

Fig. 8.10: Shadowgraph image on the LVA-1A airfoil at Ma∞ = 0.72, Re∞ = 2.7 × 106 , and CL = 0.8.

Fig. 8.11: Shadowgraph image on the CS05NT airfoil at Ma∞ = 0.72, Re∞ = 2.7 × 106 , and CL = 0.8.

8.3. Adaptive Wing Section

121

been visualized. Moreover, the shadowgraph images clearly demonstrate the reduced intensity of the shock wave, which appears more smeared over the airfoil surface and hence reduces the wave drag increase compared to the LVA-1A airfoil. The total drag reduction obtained by the CS18NT wing section shape amounts to 9% at the flight condition under investigation. The observations provided in the previous sections demonstrate that it is indispensable to combine a wide range of measurement techniques to accurately determine the flow phenomena, which yield the reduction of the total drag, and to improve the lift-to-drag ratio. Moreover, the feasibility has been proved to develop airfoil shapes, which possess the concepts of natural laminarization at the investigated Reynolds numbers in association with the reduction of the shock strength.

8.3

Adaptive Wing Section

Only the adaptive wing technology is able to account for the changing flight conditions during a long range mission, and to exploit the aerodynamic potential at each point of the flight polar. Thus, in the most extreme case, off-design conditions do not exist anymore, since the airfoil shape can be adjusted to the optimum geometry for each part of the mission. The benefits achieved with the adaptive shape modification can be compared with the efficiency of the local shape modification represented by the bump. These devices only act as a shock control measure, which merely adapt to changing flight conditions in the supercritical range by modifications of the bump height. In this respect the necessity of a bump with an adaptive height has been recognized [100]. However, if the shock position changes at different flow conditions, the bump fails as a shock control measure. Moreover, if the chordwise location of the bump does not correspond to the location of the shock, the existence of the bump even has a reverse effect of the flow characteristics and hence deteriorates the aerodynamic performance. Hence, the bump device is only benificial if the shock is located above the bump, but reduces the performance outside this regime. This is in contrast to the performance enhancement of an adaptive wing with a flexible upper surface over the entire chord length, which is effective over a wide Mach number and lift range. At low Mach number flows, which are below the supercritical regime over the airfoil surface, the approach of flow control differs from the method required to remain close to the optimum flight polar at high Mach numbers. As has been demonstrated in chapter 7, the optimization algorithm aims to move the transition location as far downstream as possible at subsonic flight conditions. This concept has been realized by the adaptive wing model (section 8.1). At transonic flows, where shocks occur, the objective of the optimization algorithm has been twofold. If a separation bubble occurred due to the shock/boundary-layer interaction the transition location has been moved upstream in combination with the reduction of the shock strength to eliminate the separation and enhance the airfoil performance. In the case of no separation at transonic speeds only the shock strength is reduced. For both flight regimes, the adaptive wing technology achieves significant improvements of the lift-to-drag ratio, associated with an enhancement of the aerodynamic characteristics, since the separated regions have been avoided by the appropriate airfoil shape.

122

Chapter 8. Experimental Results for the Adaptive Wing Section

The combination of the design of the adaptive wing section model, the numerical aerodynamic design, and the experimental verification proved essential for the implementation of the adaptive wing technology. The adaptive wing section wind tunnel model is equipped with different sensor technology to determine the current freestream conditions and the associated state of the boundary layer. The surface pressure measurement devices determine the pressure distribution, whereas the hot-film sensors acquire the location of the laminar/turbulent transition and the position and size of a possibly occurring separated region. From the data-base of airfoil designs the shape, which is considered best for the current flight conditions can be selected. Subsequently, the airfoil shape is modified to comply with the new geometry. The adaptive wing wind tunnel model designed and used in this work, does not require any power to maintain the flexible surface in a fixed position. Extra power is only needed to modify the airfoil contour, from one shape to another. The adaptive wing section model can, therefore, be considered as an initiation towards a closed-loop adaptive wing system.

Summary To demonstrate the suitability of the adaptive wing technology to increase the aerodynamic performance at transonic speeds, numerical and experimental investigations have been conducted in the present work. To improve the aerodynamic characteristics and reduce the total drag induced by the airfoil shape in the transonic speed regime, this work focuses on the implementation of the methods of laminarization and shock control in the adaptive wing section design. For the aerodynamic airfoil shape design an optimization algorithm has been coupled with a method to compute the flow field over the airfoil. This numerical investigation of 20 one-point designs demonstrated the benefits of an adaptive airfoil shape at high subsonic, and transonic speeds at moderate angles-of-attack. The aerodynamic design also supported the experimental investigation by providing three airfoil shapes, which not only improved the lift-to-drag ratio at the design point, but also demonstrated good off-design characteristics. The developed optimization algorithm is based on the Evolution Strategy, which represents a stochastical method capable of finding the global extremum of highly nonlinear multi-modal objective functions. Moreover, to reduce the overall time required by the optimization process, the implicit parallel character of the population based search has been exploited by a parallel implementation of the objective function evaluation of the individuals of the population, each of which represents one flow field computation. The performance of the algorithm has been validated on the Ackley test function and on the composed testfunction F8F2. For the implementation of the optimization algorithm to the constrained aerodynamic design, a new penalty function, based on one parameter, has been developed in this work. Penalties are imposed on the occurrence of separation and on the maximum airfoil thickness, which should be at least 12% chord. The overall objective of the aerodynamic design is to enhance the lift-to-drag ratio. For the parameterization of the airfoil shape, the method based on the geometric modes and the polynomial approach PARSEC have been implemented. Subsequent aerodynamic design, however, showed the incompatibility of the design space of the PARSEC parameterization with that of the designed adaptive wing wind tunnel model. Therefore, the method of the geometric modes with eight design variables has been selected for the one-point airfoil shape designs over a wide transonic Mach number-range corresponding to cruise flight conditions of transport aircraft. The optimization algorithm has been coupled with two methods to compute the flow field over the airfoil. The first method solves the two-dimensional Reynolds averaged NavierStokes equations using the Baldwin-Lomax turbulence model on structured grids, whereas 123

124

Summary

the second approach is represented by the well-known Euler boundary-layer method, MSES. Both approaches have been successfully validated against existing experimental data on the LVA-1A airfoil. Although the Navier-Stokes approach represents a more general method for flow computations, the Euler boundary-layer method has been selected for the final onepoint designs, since it incorporates a transition prediction method, based on the eN -method, and requires less computational time to compute the flow field. To demonstrate the improvement potential of the adaptive wing technology and to validate the results of the aerodynamic design, a wind tunnel model with an adaptable upper surface over the entire chord length has been developed and manufactured for tests in the trisonic wind tunnel of the Aerodynamisches Institut at transonic speeds with natural transition. The wind tunnel is equipped with an adaptive wall test section with a 0.4 × 0.4 m2 cross section. Since only a limited space for the integration of adjustment kinematics and measuring equipment is available in the slender supercritical airfoil shapes, it was inevitable to additionally design a rigid surface model as a first stage towards the adaptive surface model. Both models are based on the shape of the laminar-type airfoil DA LVA-1A, designed by DASA Airbus. The adaptive wing model has the same rectangular top-view as the rigid model of 200×400 mm2 and is equipped with a carbon-fiber reinforced flexible upper surface over the entire chord length. This shell is connected to nine drive mechanisms, which are distributed equidistantly between 12.5% and 72.5% chord in streamwise direction. Each drive mechanism enables a continuous vertical deflection of 2.5 mm. Hence a high spatial adjustment resolution combined with a high adjustment accuracy is provided by the model. Since both wind tunnel models possess a rectangular top-view without sweep, from the three transition mechanisms, only the Tollmien-Schlichting instability mechanism is significant for transition in the present investigation. To numerically predict the transition location with the semi-empirical eN -method, the disturbance level of the trisonic wind tunnel has been determined, for transonic Mach numbers with the hot-wire technique and Pitot-pressure measurements, to correlate the so-called N -factor to the disturbance level. The state of the boundary layer and the shock/boundary-layer interaction have been investigated with respect to the transition location and the associated flow phenomena like separation and the shock configuration. The use of the multi-sensor hot-film technique supplemented by the liquid-crystal coating technique allow a detailled analysis of the flow phenomena near the surface with a high temporal and spatial resolution. Pressure measurements on the surface and in the wake of the airfoil enable the determination of the aerodynamic force coefficients, whereas the flow visualization monitors the configuration of the shock. For the subsequent aerodynamic design, the numerically predicted transition location for N =7 has successfully been validated with the transition location on the rigid surface model, determined by the hot-film technique in combination with the liquid-crystal coating. The experimental investigation also demonstrated, that it is indispensable to combine both methods for an accurate analysis. The liquid-crystal coating determined the transition location if it occurred upstream of the first sensor, whereas the hot-film technique has been able to acquire the transition location inside a separated region. Hence, the flow computational method has been validated by the experiments, and has, therefore, been applied for the aerodynamic design of airfoil shapes at transonic speeds with natural transition.

125

Within the aerodynamic design 20 one-point designs in the Mach number range 0.65 ≤ Ma∞ ≤ 0.76 and for lift coefficients between 0.40 ≤ CL ≤ 0.70 for a Reynolds number of 2.4 million have been performed. The Reynolds number is correlated to the ones attainable in the trisonic wind tunnel. The main focus of the current investigation is the demonstration that the combination of aerodynamic design algorithms with the adaptive shape wind tunnel model yield the improvement of aerodynamic characteristics. Subsequent investigations on wings with sweep at higher Reynolds numbers will have to be conducted. Due to the high Reynolds number and to the additional transition mechanisms ALT and CFI only HLFC is able to delay the transition. The concept of the adjustment of the upper airfoil surface can be implemented on a wing model. Also, the optimization algorithm can deal with 3D-flow fields. However, the computational time for such an aerodynamic design will be huge. At subsonic speeds, a significant downstream movement of the transition location compared to the initial airfoil, yields the enhancement of the flight performance. However, at transonic Mach numbers, where the shock interacts with the laminar boundary layer, the optimization algorithm initiates an upstream movement of the transition location to avoid separation. Even if separation is present on the initial airfoil, the algorithm develops a shape for which the separation has been removed, and lift-to-drag ratio has been improved. Additionally, from the data-base of 20 one-point design, three airfoil shapes have been selected, which also demonstrate good off-design performance, for the subsequent experimental investigation with the adaptive wing section model. The objective of the experimental investigation on the adaptive wing wind tunnel model has been to validate the trends, that have been indicated by the aerodynamic design. Although, the model enables adjustment over 60% of the chord length, the leading-edge and trailing-edge area can not be controlled directly. Still, the delay of the transition location at subsonic speeds on the adaptive wing model validated the numerical calculation and demonstrated the suitability of the model for tests with natural transition. Moreover, also the upstream movement of the transition location associated with the removal of separated areas have been documented, based on data provided by the hot-film technique, the liquid-crystal coating and the optical flow visualization technique. Additionally, the reduction of the shock strength has been demonstrated to enhance the aerodynamic characteristics of the adaptive wing section model. The aerodynamic benefits of the adaptive wing technology incorporating laminarization concepts have been demonstrated in the aerodynamic design and in experiments. Since the adaptive wing section model is equipped with a wide range of sensor technology to acquire the flow conditions (Ma∞ , Re∞ , . . . ) and the state of the boundary layer (laminar, turbulent, separated), the combination of numerical, experimental and structure enhancing techniques presented in this work, provide the first step towards a closed-loop adaptive wing system.

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[218] D. Whitley, K. Mathias, S. Rana, and J. Dzubera. Evaluating Evolutionary Algorithms. Artificial Intelligence, 85:245 – 276, 1996. [219] L. C. Woods. Aerofoil Design in Two-Dimensional Subsonic Compressible Flow. Aeronautical Research Council, R & M 2845, 1952.

Lebenslauf

Name:

Alexander Meijering

Geburtsdatum: 28. Februar 1971 Geburtsort:

Katwijk (ZH), Niederlande

Familienstand:

verheiratet

1977 - 1983

Besuch der Grundschule in Eindhoven, Niederlande

1983 - 1989

Besuch des ’Eindhovens Protestants Lyceum’ in Eindhoven, Niederlande. Abschluss: Atheneum B (Allgemeine Hochschulreife)

1989 - 1993

Studium des Maschinenbaus an der Fachhochschule ’Hogeschool Eindhoven’ in Eindhoven, Niederlande. Abschluss: Diplom

1993 - 1996

Studium des Maschinenbaus an der ’Technische Universiteit Eindhoven’ in Eindhoven, Niederlande. Abschluss: Diplom

Aug. ’96 – Nov. ’96

Wissenschaftliche Hilfskraft an der Deutschen Forschungsanstalt f¨ ur Luft- und Raumfahrt e.V.

Dez. ’96 – Mai ’97

Wissenschaftliche Hilfskraft am Aerodynamischen Institut der RWTH Aachen

Juni ’97 – M¨arz ’03

Wissenschaftlicher Angestellter am Aerodynamischen Institut der RWTH Aachen