Ejectors and Jet Pumps - Design For Steam Driven Flow [PDF]

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86030

EJECTORS AND JET PUMPS - DESIGN FOR STEAM DRIVEN FLOW 1.

NOTATION AND UNITS

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A coherent set of mass, length, time and temperature units must be used in all the equations in this Data Item. Two coherent sets of units - British and SI - are given below.

Note:

1 slug

= 32.174 lb mass

0°F

= 459.7°R

1 Btu/lb

= 24 990 ft lbf/slug

1 torr

= 1mm Hg abs.

SI

British

m2

ft2

m/s

ft/s

J/kg K

ft lbf/slug°R

A

cross-sectional area of component

AR

area ratio, A m ⁄ A e

A R*

area ratio, A m ⁄ A th

AT

area ratio, A e ⁄ A th

a

speed of sound in fluid

CD

primary-nozzle discharge coefficient

C1

correction factor for gases other than air (see Section 5.4.2)

C2

correction factor for air temperatures above 20ºC (see Section 5.4.2)

cp

specific heat capacity at constant pressure

C PR

ratio of specific heat capacities, c p ′ ⁄ c p ″

D

diameter of narrowest section of mixing chamber

m

ft

d

diameter of primary nozzle

m

ft

h fg

specific enthalpy of vaporisation

J/kg

ft lbf/slug

Kd

diffuser loss coefficient (steam/liquid ejectors) (Equation (B2.3))

Km

mixing chamber loss coefficient (Equation (B2.2))

Ks

secondary inlet loss coefficient (steam/liquid ejectors) (Equation (B2.1))

Issued December 1986 - 92 pages 1

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86030 L

length of parallel section of mixing chamber

m

ft

Ld

length of exit contraction or diffuser

m

ft

M

Mach number, U ⁄ a

m·

mass flow rate

kg/s

slug/s

N1

pressure ratio, ( p t5 – p t0 ) ⁄ p t1

N2

pressure ratio, ( p t5 – p t0 ) ⁄ ½ρ e ′U e ′ 2

Np

primary pressure ratio, p t1 ⁄ p t5

Ns

secondary pressure ratio, p t5 ⁄ p t0

n

number of stages in multistage ejector

p

absolute static pressure

N/m2 (Pa)

lbf/ft2

pt

absolute total pressure

N/m2 (Pa)

lbf/ft2

pv

absolute vapour pressure

N/m2 (Pa)

lbf/ft2

R

gas constant (for steam, R = 461.5 J/kg K, or 4970 ft lbf/slug°R)

J/kg K

ft lbf/slug°R

RR

ratio of gas constants, R′ ⁄ R″

rc

density ratio for steam/liquid ejectors, ρ 1 ′ ⁄ ρ″

r c1

density ratio for steam/liquid ejectors, ρ e ′ ⁄ ρ″

rm

mass flow ratio, m· ″ ⁄ m· ′

s

distance from primary-nozzle outlet to beginning of constant-area section of mixing chamber

m

ft

T

absolute static temperature

K

°R

Ts

absolute saturation temperature

K

°R

Tt

absolute total temperature

K

°R

TR

ratio of inlet total temperatures, T t1 ⁄ T t0

U

flow velocity

m/s

ft/s

W

inverse of mass flow ratio, 1 ⁄ r m

γ

ratio of specific heat capacity at constant pressure to that at constant volume saturated steam ≈ 1.1 (average) superheated steam ≈ 1.315 (average)

γR

ratio of specific heat ratios, γ′ ⁄ γ″

2

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86030 ηd

contraction or diffuser loss coefficient, p t5 ⁄ p t4 (steam/gas ejectors)

ηs

secondary inlet loss coefficient, p te ″ ⁄ p t0 (steam/gas ejectors)

ρ

fluid density

kg/m3

slug/ft3

φ1

included half-angle of convergent section of mixing chamber

degree

degree

φ2

included half-angle of diffuser

degree

degree

∆T

degree of subcooling, ( T 1 – T 0 )

K

°R

Subscripts

c

denotes conditions leading to cavitation

e

primary nozzle exit plane

f

denotes property of saturated liquid

fg

denotes change of phase at constant pressure

g

denotes property of saturated vapour

m

mixing chamber

t

denotes total value (see Section 5.3)

th

primary nozzle throat

u

denotes multistage unit

0

secondary flow entry plane

1

primary nozzle entry plane

3

entry plane of parallel section of mixing chamber

4

mixing chamber exit plane

5

contraction or diffuser exit plane

The reference planes are defined in Sketch 1.1. For constant area mixing, planes e and 3 are coincident and have been referred to by subscript e . Superscripts

′

refers to primary stream or primary nozzle

″

refers to secondary stream

3



86030

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Note that, where applicable, non-superscripted quantities are used to refer to the combined steam/secondary fluid stream.

Sketch 1.1 Steam ejector configuration and reference planes

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2.

86030 INTRODUCTION This Item is one of a series of ESDU Data Items concerned with the design and performance of ejectors and jet pumps. Such devices are characterised by the use of the kinetic energy of one fluid stream (the primary, motive or driving flow) to drive a second fluid stream (the secondary, induced or driven flow) by direct mixing. The design parameters, requirements and methods vary considerably depending on whether the working fluids are gases, liquids, vapours or mixtures of these components. Each type is therefore considered in a separate Data Item. Derivation 25 considers ejectors in which the primary and secondary fluids are both air and Derivation 26 considers ejectors in which they are both liquids. This Item considers steam driven ejectors. The terms “ejector” and “jet pump” are alternative names for the same device and the term “injector” is also used. Although common usage, it is not strictly correct to assume that the terms “ejector” and “injector” are used when the working fluids are gases and the term “jet pump” when they are liquids.

2.1

Purpose and Scope of This Item This Data Item provides information for the design and performance evaluation of ejectors, jet pumps or injectors in which the primary fluid is steam and the secondary fluid is a liquid or a gas. The terms steam/liquid and steam/gas ejector are employed according to whether the secondary fluid is a liquid or gas. Techniques for the optimum design of a steam driven ejector are presented. The method for steam/liquid ejectors is based on a theoretical analysis, that for steam/gas ejectors is based on experimental data obtained on a wide range of steam driven ejectors. A performance prediction method for steam/liquid ejectors is also presented, based on the same theoretical analysis as is used in the design method. A performance prediction method for steam/gas ejectors is discussed briefly.

2.2

Layout of This Item Section 3 of this Item discusses some applications of steam driven ejectors. Section 4 describes the principles of ejector operation and defines the different components. These may vary considerably with application and Section 4 considers some of the configurations possible. Section 5 describes design methods that can be used to determine the on-design operating conditions and optimum dimensions of a steam driven ejector. Some considerations regarding mechanical design are given in Section 5.5. Section 6 describes a method by which the performance of a steam/liquid ejector may be evaluated. Performance prediction for steam/gas ejectors is also discussed. Section 7 describes designs such as multi-stage, annular nozzle and multi-nozzle ejectors and considers their advantages in certain situations. Section 8 discusses some of the problems that may arise when an ejector is in operation. Section 9 presents worked examples that illustrate the application of the Design and Performance Prediction Methods. Section 10 lists sources of information used in the preparation of this Item together with further information.

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86030 Appendix A contains a glossary of terms used in describing ejector components, design parameters and performance.

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Appendix B presents detailed theoretical analyses of the fluid flow through ejectors. These analyses are based on one-dimensional flow representations of mass, momentum and energy conservation.

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 3.

86030 APPLICATIONS OF STEAM DRIVEN EJECTORS

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Steam driven ejectors are used extensively in the power generation, chemical processing and nuclear industries. Their main advantage is that they have no moving parts and hence require little maintenance. Almost any type of liquid, gas or vapour can be pumped, and solids-bearing fluids can be handled. Compared with mechanical pumps, steam ejectors have very low efficiencies when used in normal pumping applications but when a source of waste or low grade steam is available, a steam ejector may be cheaper to operate than a mechanical pump. Steam ejectors also have many applications, such as heating, humidifying and pumping toxic and solids-bearing fluids, where a mechanical pump may be unsuitable. In some applications, a steam driven ejector may have advantages over other types of ejector, such as air driven and liquid driven ejectors. In gas pumping applications, the primary steam flow can be separated from the secondary gas by condensation - an option which is not available for air driven ejectors. Combustible gases can be handled more safely. In liquid pumping applications, a steam driven ejector causes far less contamination of the pumped liquid than a liquid driven ejector. This is because the steam condenses within the ejector and so occupies only a small fraction of the volumetric discharge from the ejector. Offset against these advantages is the cost of the steam supply, which usually far exceeds the cost of an equivalent compressed air or liquid supply. Some typical applications of steam driven ejectors are discussed below. Although many different uses are considered, it is worth noting that most commercially supplied steam/gas ejectors are used in vacuum pumping applications and are usually sold as multistage units. The most common uses of steam/liquid ejectors are as pumps for toxic or radioactive liquids, as liquid heaters and as feed water injectors. 3.1

Applications of Steam/Liquid Ejectors Condensers When a steam driven ejector is used to pump a liquid, it is inevitable that the steam condenses. In a well designed device, the discharge flow from the ejector should not contain any uncondensed steam. The condensing characteristics of steam driven ejectors make them suitable for use as maintenance-free condensers, and they have been used in this role in the nuclear industry. Feed water injectors Steam driven ejectors are widely used to feed water to water boilers. In this role, they are often referred to as feed water injectors. The injector is driven by a steam bleed from the boiler. The driving steam performs the dual function of pressurising and heating the water before it enters the boiler. An early use of feed water injectors was in steam locomotives. Liquid heaters A steam driven ejector, when immersed in a liquid, simultaneously heats and recirculates the liquid. The ejector then acts primarily as a heater and all of the thermal energy of the steam is transferred to the liquid. Steam ejectors for use as liquid heaters are supplied in several forms. When used to heat the liquid in a tank, the ejector can be immersed in the tank as required or be attached permanently to the outside of the tank. Often an air bleed line is fitted in the secondary inlet so that the ejector performs the dual role of heating and agitating or aerating the liquid. Steam ejector heaters are also used in pipeline applications, the ejector usually being supplied as a self contained Tee-piece for insertion into the pipeline.

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86030 One particular use of steam driven ejector heaters is in reducing the viscosity of sludges and other viscous liquids.

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Pumping liquids and slurries Steam driven ejectors are widely used as pumps in the chemical processing and power generating industries. They may be installed permanently in the plant or may be portable for use in tank draining and other cleaning operations. Liquids and suspended solids can be pumped. The absence of moving parts makes steam driven ejectors particularly suitable for handling highly toxic or radioactive liquids and slurries. A possible disadvantage of steam driven ejectors in liquid pumping applications when compared with mechanical pumps is that the pumped liquid or slurry is heated and contaminated by the condensed steam. Steam desuperheaters A common requirement in the power generating and chemical processing industries is to desuperheat (i.e. cool) superheated steam. Steam ejectors are often used for this purpose. The superheated steam is used to drive the ejector. Water is fed to the secondary inlet and cools the superheated steam. A temperature controller at the outlet from the ejector adjusts the water feed rate to maintain the desired steam outlet temperature. 3.2

Applications of Steam/Gas Ejectors Gas pumps and humidifiers Steam driven ejectors can be used to pump gases or boost gas pressures in a system. The gas may be dust bearing. Compared with air driven ejectors, the main advantage of steam driven ejectors is that most of the driving steam can be removed in an aftercondenser, leaving the gas only slightly contaminated by the driving fluid. Also, steam driven ejectors can be used in applications where use of an air driven ejector would create a combustible mixture. A common use of steam driven ejectors as gas pumps is in ventilation systems. In closed loop systems, the ejector may perform the dual role of ventilating and humidifying the recirculated gases. Thermo-compressors A steam driven ejector may be used to compress a low pressure vapour to a higher pressure. The term thermo-compressor is often used to describe these devices. Thermo-compressors are widely used to compress low grade steam, although almost any vapour can be compressed. Vacuum pumps Steam driven ejectors can be used to produce or maintain a vacuum in a gas filled vessel, or simply to evacuate a gas. In this role they are used in refrigeration units, condensers, filtration units, molten metal degassers, evaporators, dryers and in many other processes requiring sub-atmospheric pressures. Multi-staged units with intercondensers can achieve vacuums well below 1 torr. More information on this widespread application of steam/gas ejectors is given in Section 7.1.

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86030

4.

THE BASIC STEAM DRIVEN EJECTOR

4.1

Principle of Operation

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An ejector is a device in which the kinetic energy of one fluid stream (the primary fluid) is used to drive another fluid stream (the secondary fluid). The primary fluid is usually supplied through a nozzle and issues as a jet into a duct (the mixing chamber) which contains the secondary fluid. Ejectors using steam as the primary fluid can be used to pump both gaseous and liquid secondary fluids. In a steam/gas ejector the gas is induced into motion by the turbulent mixing and entrainment at the edges of the steam jet. In a steam/liquid ejector, the steam jet and liquid move initially as an annular flow in the mixing chamber. Mixing may take place gradually, as the steam condenses, but usually occurs suddenly at a condensation shock. In both types of steam driven ejector, mixing may occur violently following a compression shock in the steam flow. In a well designed ejector, the primary and secondary fluids should be fully mixed by the end of the mixing chamber. Often, this mixed fluid is discharged through a diffuser, which is used to obtain some further static pressure recovery. The basic theory of the flow through a steam driven ejector, derived by considering mass, momentum and energy conservation, is described in Appendix B. Separate derivations are presented for steam/liquid and steam/gas ejectors.

Sketch 4.1 Component parts of a steam ejector with a single-central primary nozzle 4.2

Component Parts Sketch 4.1 shows a typical configuration for a steam driven ejector. The ejector consists of four main components: the primary nozzle, the mixing chamber, the diffuser and the secondary inlet. It should be noted that this terminology, although widely used, is not unique. The mixing chamber and diffuser are often considered to form one unit called the diffuser. The converging section of the mixing chamber is sometimes called the combining tube. In air pumping applications the secondary inlet is sometimes called the air chamber.

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86030 Of the component parts of an ejector, only the mixing chamber is used in all applications and hence effectively characterises the device. In most commercially supplied devices the mixing chamber consists of a converging section (the combining tube) followed by a short parallel-sided section. Other configurations are possible, however, and are discussed in Section 5.5.3. The geometry and layout of the other component parts of an ejector are dependent on the application for which the ejector is intended. The main variations that are used are described below whilst more detailed information is given in Section 5.5 (Mechanical Design Considerations) and Section 7 (Aspects of Some More Complex Designs).

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(a)Primary nozzle Most designs incorporate a primary nozzle, since it is more economical to transport steam to the ejector at high pressure, rather than at high velocity with its inherently higher pressure losses. The nozzle may be convergent but is more usually convergent-divergent (provided that there is sufficient primary pressure available to achieve supersonic flow). Detailed information on the design and optimum position of primary nozzles is given in Section 5.5.1 and 5.5.4. As an alternative the primary nozzle may be annular, producing either a discrete annular jet separate from the wall of the mixing chamber, or a wall jet located around the periphery of the mixing chamber. For a given steam flow rate, the surface area of an annular jet is greater than that from a central nozzle so that mixing is more rapid. Consequently an annular nozzle ejector requires a shorter mixing chamber than a central nozzle type. Annular nozzle ejectors are discussed in greater detail in Section 7.2. (b)Multi-nozzle ejectors Multi-nozzle units may be used in conjunction with a single mixing chamber and diffuser. They have the advantage of reducing considerably the mixing chamber length required. More information is given in Section 7.3. (c)Multi-barrel ejectors Multi-barrel units with a common secondary flow supply are sometimes used. The units are arranged in parallel and discharge into a common delivery tube. (d)Diffuser The diffuser raises the static pressure of the fluid discharged by the ejector. There need be no diffuser if the velocity of the fluid discharged from the mixing chamber is already suitable for existing pipework and the mixing chamber diameter is appropriate. A contraction may be used to connect the ejector to a duct of smaller diameter. This need not cause significant energy loss but will increase the exit velocity and decrease the discharge pressure. (e)Secondary flow inlet The secondary fluid may be supplied at various angles to the primary stream, depending on the intended application of the ejector. High angles may introduce extra losses, although these may be negligible if the inlet velocity is low. Under steady-state conditions, there need be no secondary or induced flow if the ejector is to be used solely to maintain a fixed vacuum or discharge pressure.

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86030 (f)Multi-stage ejectors

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Multi-stage units are widely used, particularly in vacuum applications. The ejectors are arranged in series, which extends the range of pressure and/or flow ratios over which the secondary fluid may be pumped. In vacuum applications, greater efficiency is achieved by condensing the steam efflux from each stage and providing a fresh supply of steam to the next stage. More information on this topic is given in Section 7.1.

11

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86030

5.

DESIGN OF STEAM DRIVEN EJECTORS

5.1

Introduction The performance of a steam driven ejector depends upon its geometry (shape, layout and dimensions), the properties of the steam and secondary fluid (density and, in the case of steam/gas ejectors, molecular weight and specific heat ratios), and the flow conditions (pressures, temperatures, mass flow rates) at the primary and secondary inlets and the diffuser outlet. The flow conditions define the performance of the device. Usually, the main aim in design is to determine the optimum geometry to obtain a given performance. Some or all of the flow conditions may be fixed by the application of the ejector; the remainder are found during the design stage. This Section describes methods for designing a steam driven ejector to achieve a given performance. Different techniques are presented for steam/liquid and steam/gas ejectors. The method for steam/liquid ejectors is based upon a theoretical analysis of the flow in the ejector. Empirical loss coefficients are used to compensate for the idealisations made in the analysis. For steam/gas ejectors, the method used is based entirely on empirical results. Although the steam driven ejector is conceptually a simple device, the physical processes of turbulent mixing, heat transfer and condensation that occur within it are extremely complex and, to date, no method has been devised that can account fully for all of these phenomena. The design methods given here are therefore necessarily approximate but should be sufficient to provide a good first estimate of the final design. Some adjustment to nozzle size and/or axial positioning will always be required before the ejector can be commissioned. The design methods assume that the optimum design, or on-design condition, corresponds to the operating condition at which the ejector uses a minimum of steam to achieve a specified pressure ratio. Different design pressure ratios are used for steam/liquid and steam/gas ejectors and these are defined in Sections 5.3 and 5.4 respectively. This definition of the on-design condition is of particular practical value since steam supply costs usually far exceed the capital cost of a steam ejector. Most commercially supplied steam driven ejectors are sold primarily on the basis of their estimated steam consumption. Steam ejectors are normally designed to operate from a supply of dry steam for reasons explained in Section 8. It is assumed in the design methods that dry steam is used. The design methods also neglect the effects of certain phenomena - vapour freezing, cavitation and vapour binding - that can reduce the performance of a steam driven ejector as discussed in Section 8. A correctly designed ejector should not be affected by these phenomena and the design methods given here assume that these problems will be eliminated by careful mechanical design. The method for steam/liquid ejectors includes checks that indicate whether cavitation or vapour binding may be a problem. The design method for steam/liquid ejectors is presented in Section 5.3 and that for steam/gas ejectors in Section 5.4. Guidelines on detailed mechanical design (i.e. the shape and layout of components) are given in Section 5.5 and these should be followed once the calculations specified in Sections 5.3 or 5.4 have been completed. It is convenient to describe the geometry, fluid properties and flow conditions in terms of non-dimensional parameters. These are defined in Section 5.2.

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 5.2

86030 Dimensionless Parameters Used in Design Geometry of the ejector The main dimensionless parameters defining the geometry of a steam driven ejector are as follows.

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(1)

The mixing chamber area ratio (minimum cross-sectional chamber/cross-sectional area of the primary nozzle exit),

area

of

the

mixing

A R = A m ⁄ A e = D 2 ⁄ d e2 . It is sometimes convenient to use an alternative area ratio A R* , which is defined by A R* = A m ⁄ A th = D 2 ⁄ d th2 . (2)

The primary nozzle area ratio (cross-sectional area of the primary nozzle exit/cross-sectional area of the n throat), 2

2

A T = A e ⁄ A th = d e ⁄ d th . Fluid Properties For steam/gas ejectors, the main dimensionless parameters defining the fluid properties are as follows. (3)

The ratio of specific heat ratios (specific heat ratio of steam/specific heat ratio of secondary gas), γ R = γ′ ⁄ γ″ .

(4)

The ratio of gas constants (gas constant of steam/gas constant of secondary gas), R R = R′ ⁄ R ″ .

For steam/liquid ejectors, a single parameter, the ratio of the steam density to the secondary fluid density may be used r c = ρ t1 ′ ⁄ ρ″ . The design methods assume that the steam flow behaves as an ideal gas with constant specific heat ratio and gas constant. This assumption is reasonable if, as is usual for steam ejectors, the steam supply is saturated or superheated. Values of γ′ = 1.315 and R′ = 461.5 J/kg K for steam are assumed throughout.

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86030 Flow Conditions The main dimensionless parameters defining the flow conditions at the ejector inlets and outlet are as follows. (5)

The primary pressure ratio (steam supply pressure/discharge pressure),

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N p = p t1 ⁄ p t5 . (6)

The secondary pressure ratio, or compression ratio (discharge pressure/secondary inlet pressure), N s = p t5 ⁄ p t0 .

(7)

For steam/liquid ejectors it is convenient to combine the pressure ratio parameters, N p and N s , into a single parameter, N 1 , defined by p5 – p0 Ns – 1 N 1 = ------------------- = ---------------- . p1 Ns Np

(8)

The mass flow ratio (secondary fluid mass flow rate/steam mass flow rate), r m = m· ″ ⁄ m· ′ .

For steam/gas ejectors, it is necessary to define an additional parameter, the ratio of the total temperatures in the primary and secondary inlet flows, T R = T t1 ⁄ T t0 . In this Data Item it is assumed throughout that flow velocities in the steam nozzle inlet, secondary inlet and diffuser outlet are small enough to be neglected so that p 1 ≈ pt1, p0 ≈ pt0, p5 ≈ p t5, T 1 ≈ Tt1, T0 ≈ T t0 . For convenience, the subscript t is omitted in the remainder of this Data Item. 5.3

Design of Steam/Liquid Ejectors The recommended design method for steam/liquid ejectors is based on the theoretical results that are presented in Section B2 of Appendix B. The theory is a development of the methods presented in Derivations 10 and 13. It has been validated against experimental results taken from Derivations 10, 12 and 13. In all cases, calculated values of mass flow ratio, r m , for given pressure ratios were within 20% of measured values. Strictly, the method is only valid for ejectors with a single central convergent-divergent nozzle and with a constant area mixing chamber. It should be used with caution for other ejector configurations. The design charts used in the design method were derived by calculating, at each pressure ratio, N 1 , and density ratio, r c , combinations of the area ratios, A R and A T , that gave the highest mass flow-ratio, r m . These calculations were performed using typical values for the loss coefficients of Ks = 0.10, Km = 0.20, K d = 0.15, C D = 1.0 . It is possible that lower values for K s, K m and K d could be obtained by careful mechanical design of the ejector. Ejector designs produced by this design method should

14



86030

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therefore be regarded as typical, rather than best possible, designs. Sketch 5.1 shows a compilation of data published by manufacturers of steam/liquid ejectors. The shaded area encompasses performance data obtained on several steam/liquid ejectors for density ratios in the range 0.002 to 0.004.

Sketch 5.1 Typical performance figures for steam/ liquid ejectors The performance of a steam/liquid ejector is limited by the phenomena of cavitation and vapour binding. These phenomena are discussed in Section 5.3.1, together with typical operating characteristics for steam/liquid ejectors. The design method is presented as a step-by-step procedure in Section 5.3.2. 5.3.1

Typical operating characteristics of steam/liquid ejectors A typical operating curve, indicating the relationship between discharge pressure and mass flow rate over the whole operating range, is shown in Sketch 5.2. The mass flow ratio delivered by the ejector increases as the steam supply pressure, p 1 , is increased or the pressure difference across the ejector is decreased. A maximum mass flow ratio is reached when the parameter, N 1 , equals zero. The maximum mass flow ratio available may be limited by the onset of cavitation. High secondary mass flow rates lead to high liquid velocities with an increased risk of cavitation. A typical cavitation-induced limit is shown in Sketch 5.2. The design method given in Section 5.3.2 indicates when cavitation may be a problem. Further discussion of cavitation can be found in Section 8.2.3.

15

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86030

Sketch 5.2 Typical operating curve for a steam/liquid ejector The mass flow ratio decreases as the parameter, N 1 , is increased. A point may be reached at which the secondary flow stops, while the steam flow continues to pass through the ejector. This point is often called the 'first shut-off', or 'breakpoint'. Further decreases in p 1 or increases in ( p 5 – p 0 ) may eventually reduce the outlet flow from the ejector to zero with the primary flow leaving via the secondary inlet so that there is effectively a negative secondary flow. This 'second shut-off' point is an important design parameter and is required so that the maximum possible pressure in the ejector due to a line blockage or valve failure can be assessed and components rated accordingly. The maximum pressure ratio that can be attained may be limited by incomplete condensation of the steam flow or by boiling of the liquid flow. Collectively, these phenomena are often called vapour binding and are discussed more fully in Section 8.3. 5.3.2

Design method : steam/liquid ejectors Stage 1 - Determine the constraints on the design The constraints may relate to the required performance of the ejector or may be dimensional, restricting the size of the ejector. For most applications the main design constraint falls into one of the following categories: (a)the secondary mass flowrate is specified (e.g. tank emptying duties), (b)the mass flow ratio is specified (e.g. liquid heating duties), (c)the pressure difference, ( p 5 – p 0 ) , across the ejector is specified (e.g. liquid pumping duties).

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86030 From these constraints it should be possible to estimate a value for the pressure ratio N 1 or the mass flow ratio, r m . If a range of values for N 1 or r m is required, then the ejector should be designed to operate at the middle of that range. It is unusual for both N 1 and r m to be constrained and that case is not considered here.

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Calculate the density ratio, r c = ρ 1 ′⁄ ρ″ , of the supply steam and the secondary flow. The density of the steam may be obtained from steam tables or, approximately, from the ideal gas relationship ρ 1 ′ = p1⁄ R′T 1 , where R′ = 461.5 J/kg K. Stage 2 - Obtain values for the area ratios AR and AT Usually, the required ejector performance can be achieved with several different combinations of A R and A T . However, only one combination leads to a design with optimum performance. This design method assumes that optimum performance corresponds to the design that achieves the highest mass flow ratio (i.e. minimum steam mass flow rate) for a given pressure ratio, N 1 . Optimum combinations of A R and A T and corresponding values of r m have been calculated using the theory in Section B2. The results are presented in Figures 1, 2 and 3 for several values of the density ratio, r c . Results for values of r c other than those in the Figures can be obtained by direct interpolation. Proceed as follows, according to the design constraints. (a)If the pressure ratio, N 1 , is defined as one of the design requirements, find the optimum values of A R and A T from Figures 1 and 2. Read off the corresponding value for the mass flow ratio, r m , from Figure 3. (b)If the mass flow ratio, r m , is defined as one of the design requirements, then read off the corresponding value for the pressure ratio, N 1 , from Figure 3. For this value of N 1 read off the optimum area ratios, A R and A T , from Figures 1 and 2. Stage 3 - Calculate the remaining unknown design parameters If either the primary or secondary mass flow rate is unknown, calculate the unknown quantity using the known or estimated value of the mass flow ratio, r m , and the value of the other mass flowrate. Find any unknown pressures from the design requirements and the design value of N 1 . Calculate the area of the primary nozzle throat, A th , from m· ′ T 1 R′ A th = ----------------------- . 0.67p 1 Calculate the primary nozzle exit area from the calculated value of A th and the known value of A T . Calculate the mixing chamber area from the calculated value of A e and the known value of A R . Calculate the nozzle throat, nozzle exit and mixing chamber diameters from the calculated areas.

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86030 Stage 4 - Determine whether cavitation or vapour binding is likely to occur If cavitation and vapour binding occur they will reduce the performance of an ejector designed by this design method. It is important to estimate whether the design is likely to be affected by either of these phenomena.

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Cavitation is likely to occur if the secondary inlet supply pressure, p 0 , is below the limit given by m· ″ 2 ( 1 + K s ) p 0 ≤ p v0 + --------------------------------------- , 2ρ″ ( A m – A e ) 2 where p v0 is the vapour pressure of the liquid at the secondary inlet temperature, T 0 , and typically K s ≈ 0.1 . Vapour binding may occur in the diffuser if the temperature T 4 approaches the value of the boiling temperature of the liquid at the pressure p 4 . An estimate of T 4 can be obtained from h fg + c p f ′T 1 + c p ″r m T 0 T 4 = ------------------------------------------------------------c pf ′ + r m c p ″ and an estimate of p 4 from ( m· ′ + m· ″ ) 2 ( 1 – K d ) p 4 = p 5 – ---------------------------------------------------- , 2ρ″A m2 where typically K d ≈ 0.15 . The criteria given above are crude, but indicate when cavitation and/or vapour binding may be a problem. Stage 5 - Assess the final design The final design should be assessed to determine whether it is acceptable in terms of the design constraints, size limitations and cavitation/vapour binding performance. Should cavitation or vapour binding be indicated the design should be reassessed: new values of A R and/or A T may be chosen, leading to poorer on-design performance, or the design constraints may be relaxed. If required the off-design performance of the ejector can be investigated by using the performance prediction procedure given in Section 6.1. The design procedure should be repeated until a satisfactory design is obtained. Stage 6 - Carry out the detailed design of the ejector The detailed design of the shape and layout of the primary nozzle, secondary inlet, mixing chamber and diffuser should be performed following the guidelines given in Section 5.5. This will define the following parameters: secondary inlet geometry, primary nozzle length and shape, mixing chamber length and shape, diffuser length and shape.

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5.4

86030 Design of Steam/Gas Ejectors The recommended design method is intended to give quick, approximate estimates of the geometry of an ejector required to achieve a given performance. The method is similar to that presented in a previous Data Item (Derivation 25) and uses data obtained on a wide range of single-stage steam/gas ejectors. In all cases, the secondary gas was air at ambient temperature (nominally 20ºC). Correction charts are presented that permit estimates of performance with other gases or with gases at higher temperatures. These charts are based on the Heat Exchange Institute Standards (Derivation 19), which in turn are based on a set of measurements made in the 1950's using two commercially available ejectors (Derivations 7 and 8). The Design Method applies only to single stage ejectors and individual units in multi-stage ejectors. Further information on the design of multi-stage units is given in Section 7.1. The data used in the Design Method were obtained mostly from Derivations 2, 4, 9, 11, 14, 17 and 35 and published manufacturers' data for steam/gas ejectors. All of the ejectors tested had the following common features: (a)a single, central, convergent-divergent primary nozzle, (b)a 'constant pressure' design of mixing chamber (see Section 5.5.3), with included half-angles, φ 1 , in the range 2° ≤ φ 1 ≤ 10° , (c)conical diffusers with included half-angles, φ 2 , in the range 4° ≤ φ 2 ≤ 8° . In most tests a saturated or slightly superheated steam supply was used with supply pressures typically in the range 5 to 20 bar abs. The design charts correspond to optimum operating conditions for these ejectors. In most cases, the optimum operating conditions were taken as the operating point at which the lowest value of secondary inlet pressure p 0 (highest vacuum) was measured for a given mass flow ratio, r m . Typically, this point was determined by first adjusting the area ratios, A R and A T , to obtain minimum p 0 for given r m then, in the resulting design, adjusting the primary nozzle position to improve further the performance of the ejector. Typical operating characteristics for steam/gas ejectors are discussed qualitatively in Section 5.4.1. The design method is presented as a step by step procedure in Section 5.4.2.

5.4.1

Typical operating characteristics for steam/gas ejectors The performance of steam/gas ejectors is usually measured in terms of the secondary pressure ratio, N s , for a fixed steam supply pressure, p 1 . A typical operating curve for a steam/gas ejector at a fixed steam supply pressure is shown in Sketch 5.3. The curve shows the relationship between the secondary pressure ratio, N s , and mass flow ratio, r m , over the whole operating range of the ejector. The mass flow ratio delivered by the ejector increases as the secondary pressure ratio is decreased. The maximum mass flow ratio that can be delivered is limited by secondary flow choking. The secondary flow is most likely to choke downstream of the primary nozzle. A typical limit on r m due to secondary flow choking is shown in Sketch 5.3. A limiting value of the compression ratio is reached when the secondary mass flow rate is zero. This point is often called the 'first shut off', or 'breakpoint'. Further increases in N s (by raising p 5 or lowering p 0 ) may eventually result in a negative mass flow ratio, with the primary flow leaving via the secondary inlet. This 'second shut off' point is an important design parameter and is required so that the maximum possible pressure in the ejector due to a line blockage or valve failure can be assessed and components rated accordingly.

19

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86030

Sketch 5.3 Typical operating curve for a steam/gas ejector 5.4.2

Design method : Steam/gas ejectors Stage 1 - Determine the constraints on the design The constraints may relate to the required performance of the ejector or may be dimensional, restricting the size of the ejector. For most applications, the main design constraint falls into one of the following categories : (a)the primary pressure ratio, N p = p 1 ⁄ p 5 , is specified, (b)the secondary pressure ratio, or compression ratio, N s = p 5 ⁄ p 0 , is specified, (c)the mass flow ratio, r m , or the secondary mass flow rate, m· ″ , is specified. To use the design method it is necessary to specify at least one of the other two design constraints. If a specific value is not available, it should normally be possible to specify a range of likely values. The design method should then be carried out for several selected values in this range. Stage 2 - Determine factors C 1 and C 2 for gases other than air and temperatures above 20°C The design method is based on data obtained for steam ejectors pumping air at 20ºC. If other gases or gases at higher temperatures are to be handled, it is necessary to convert the secondary mass flowrate to an equivalent value for air at 20ºC (the 20ºC air-equivalent mass flow rate). This conversion is made using a correction factor, C 1 , for gases other than air and a correction factor, C 2 , for gas temperatures above 20ºC.

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86030 If the secondary gas is air at 20ºC, C 1 = C 2 = 1.0 . Otherwise proceed as follows: (a)calculate the ratio between the molecular weight of the secondary gas and that of air. A value of 29 may be assumed for the molecular weight of air. Knowing this molecular weight ratio, the correction factor, C 1 , can be read directly from Figure 4,

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(b)if the secondary mass flow rate is specified, divide this specified value by the product, C 1 C 2 , to obtain the 20ºC air-equivalent value. This value is then used in the remainder of the calculations, (c)a value for the correction factor, C 2 , can be read directly from Figure 5, (d)if the secondary mass flow rate is to be calculated, multiply the value calculated in Stage 5 by the product, C 1 C 2 . Stage 3 - Estimate the unknown pressure ratio or mass flow ratio. Figures 6 show the peak values of secondary pressure ratio, N s , likely to be obtained from a well-designed ejector. These Figures are based on a compilation of more than 200 data points, together with typical operating curves published by manufacturers of steam ejectors. The data are presented in two forms. Figure 6a represents maximum achievable performance in current state of the art design whilst Figure 6b represents average performance through the data set. It is recommended that these Figures are used as follows: (a)Figure 6a can be used to estimate a target performance for an ejector, to be arrived at by fine adjustments to the geometry of the ejector while it is being commissioned, (b)Figure 6b should be used for conservative design or for a first attempt at a new design of ejector. To use Figure 6a or Figure 6b, simply read the unknown parameter, N p , N s or r m , directly from the appropriate curve. Stage 4 - Estimate the optimum geometry for the ejector. The optimum nozzle area ratio, A T , for the given primary pressure ratio, N p , can be read directly from Figure 7. This chart is theoretically based and represents the nozzle area ratio required in order that the static pressures in the steam and secondary flows are matched at the exit of the nozzle, i.e. p e ′ = p e ″ . The exit flow from the nozzle is then correctly expanded and the nozzle is operating as efficiently as possible. The curves on Figure 7 were derived as follows. Assume that p e ″ ≈ p te ″ ≈ p t0 ≈ p 0 . Assume that p te ′ ≈ p t1 ′ ≈ p e ′ ( 1 + 0.158M e ′ 2 ) 4.17 , where M e ′ is a direct function of A T . Estimate the ratio p 1 ⁄ p 0 = N p N s for fixed r m from Figure 6b. Set p e ′ = p e ″ and so estimate the optimum value for A T . The optimum area ratio, A R* , for the given mass flow ratio can be estimated from Figure 8. Read a value for the parameter, A R* ⁄ N p , and so calculate A R* . Figure 8 is based on data obtained from Derivations 4, 9, and 17; the shading indicates the range of these data. It is recommended that, for given r m , an average of the highest and lowest values of A R* ⁄ N p is taken.

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86030 Stage 5 - Calculate the remaining unknown design parameters. If either the primary or secondary mass flow rate is unknown, calculate the missing quantity using the known or estimated value of the mass flow ratio. Find any unknown pressures from the design requirements and the known values of N p and N s .

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Calculate the throat area, A th , of the primary nozzle from m· ′ T 1 R′ A th = ----------------------0.67p 1 Calculate the primary nozzle exit area using the calculated value of A th and the known value of A T . Calculate the mixing chamber area using the calculated value of A th and the known value of A R* . Calculate the nozzle throat, nozzle exit and mixing chamber diameters from the calculated areas. Stage 6 - Assess the final design. The final design should be assessed to determine whether it is acceptable in terms of the design constraints and any size limitations. It may be useful to investigate the off-design performance of the ejector using the performance prediction procedure given in Section 6.2. The design procedure should be repeated until a satisfactory design is obtained. Stage 7 - Carry out the detailed design of the ejector. The detailed design (shape, layout) of the primary nozzle, secondary inlet, mixing chamber and diffuser should be performed following the guidelines given in Section 5.5. This will define the following parameters: mixing chamber length and shape, secondary inlet geometry, primary nozzle length and shape, diffuser length and shape. 5.5

Mechanical Design Considerations Steam ejectors can be made from any material that can withstand the thermal stresses imposed by the steam flow. It is important that the shape and relationship of the component parts of the ejector do not vary during operation. The choice of material is usually a compromise between machinability, strength, cost, and resistance to wear and corrosion. Derivation 5 is a useful source of information on materials for use in steam ejectors. It is not practicable to specify precisely the optimum design of the component parts of a steam ejector. Different manufacturers favour different geometries and configurations and in some applications fabrication costs may outweigh any advantage to be gained in improved performance. The

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86030 recommendations given here are based solely on the criterion of obtaining optimum performance and production costs are not considered. Where appropriate, steam/liquid and steam/gas ejectors are considered separately. Optimum performance requires careful design and fabrication of the steam nozzle and also requires that all internal surfaces, including joints, are smooth.

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Derivations 4, 9, 10, 11 and 17 are useful sources of information on the mechanical design of steam ejectors. 5.5.1

Primary nozzle The primary nozzle in a steam ejector may be either convergent or convergent-divergent. For non-critical operation ( p 1 ⁄ p e ≤ 1.84 ) a simple convergent nozzle suffices. However, most ejector nozzles are operated under critical conditions and highest efficiency is achieved if a convergent-divergent nozzle is used. A typical design is shown in Sketch 5.4. The steam is accelerated in the short convergent section, reaching a Mach number of 1.0 just downstream of the throat of the nozzle. The steam expands and accelerates in the divergent section and leaves the nozzle as a supersonic jet. If the divergent portion of the nozzle is omitted this expansion still occurs but will be accompanied by loss-inducing compression shocks that reduce the efficiency of the ejector.

Sketch 5.4 Typical design of convergent -divergent primary nozzle for a steam ejector Optimum values for the diameter of the nozzle throat, d th , and nozzle exit, d e , should be determined from the design methods. For both convergent and convergent-divergent nozzles, it is recommended that the converging portion of the nozzle has a circular or elliptical profile with a radius or minor axis of at least 0.3d th . If a simpler but less efficient converging cone section is used, the included angle of the cone should be about 24°. A long convergent section leads to increased friction losses, and hence lower C D , without necessarily improving the smoothness of the flow at the throat. The divergent portion of the nozzle is usually conical and an included angle of about 10º is recommended. For a given area ratio, A e ⁄ A th , smaller angles lead to a longer divergent section and hence higher friction losses while larger angles lead to a danger of flow separation at low pressure ratios. The throat joining the conical and divergent portions of the nozzle should be as short as possible, and should provide a smooth transition, with no discontinuity of slope or curvature. For both convergent and convergent-divergent nozzles, the nozzle exit should have a sharp lip, as near to a feather edge as is practicable. The outer surface of the nozzle should be smooth and either parallel sided or slightly converging. These two factors together result in a narrow wake from the nozzle lip and hence increased mixing between the primary and secondary streams. All internal surfaces of the nozzle should be of high quality to reduce friction losses, particularly in the divergent portion. The steam supply line to the nozzle should be sized so as to keep friction losses within reasonable limits; it is recommended that the steam velocity in the supply line is below 50 m/s. However, the steam supply line should not be so large that it restricts the secondary flow into the ejector.

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86030 Further information on the design of steam nozzles may be found in Derivations 9, 20, 27 and 52.

5.5.2

Secondary inlet and mixing chamber entry

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In a single nozzle design, the secondary flow enters the mixing chamber via the annular gap between the primary nozzle and the body of the ejector. It is important that this flow passage is smooth, with no sharp constrictions or expansions. For steam/liquid ejectors, a bell mouth inlet to this flow passage is recommended, with the outer surface of the primary nozzle shaped to give a constantly converging inlet passage. A conical inlet is simpler to machine but entry losses are higher. An included angle between 20º and 40º is recommended for conical inlets. For more detailed recommendations, see Derivation 9. Any joints in the secondary inlet should be smoothed to reduce friction losses and minimise the risk of cavitation and the inlet should be as short as possible to minimise friction losses. Similar designs of secondary inlet can be used for steam/gas ejectors, provided the secondary flow is ducted into a plenum chamber upstream of the ejector. This configuration may not be feasible if space is limited but it has the advantage of ensuring that the supply pressure of the secondary stream is stable, which helps ensure reliable operation of the ejector. As a rough guideline, the minimum dimension of the plenum chamber should be at least ten times the diameter of the entrance to the mixing chamber. A check should be made that the velocity of the secondary stream is within reasonable limits throughout the inlet passage. Maximum velocities between 10 and 20 m/s are recommended for steam/liquid ejectors to minimise wear and friction losses. Values below 100 m/s are recommended for steam/gas ejectors to minimise friction losses and avoid losses associated with compression shocks. For steam/liquid ejectors, the cavitation performance of the inlet should be checked as described in the design method. It is recommended that the minimum clearance between the primary nozzle and the body of the ejector is at least 1 to 2 mm. 5.5.3

Mixing chamber Two designs of mixing chamber are widely used : a parallel sided circular cylinder and a converging cone combined with a short parallel section. Theoretical analyses of the flow in the mixing chamber usually assume that mixing occurs under either constant area or constant pressure conditions. This nomenclature is also used for the mixing chamber designs shown in Sketch 5.5, although the conical geometry is only a crude approximation to that required for constant pressure mixing. There is no reason to suppose that either design is more efficient. Steam/gas ejectors are usually equipped with constant pressure mixing chambers and steam/liquid ejectors with constant area chambers. The function of the mixing chamber is to mix the steam and the secondary flow. In a well designed ejector momentum and energy transfer between the steam and secondary flow should be complete before the combined flow enters the diffuser. In a steam/liquid ejector this implies that the steam is completely condensed by the end of the mixing chamber. If the mixing chamber is too short, momentum and energy exchange will continue into the diffuser, resulting in an off-design performance from the diffuser with higher friction losses and an increased risk of flow separation. Conversely, if the mixing chamber is excessively long, increased friction losses will offset any performance gains from the improved mixing between the primary and secondary streams.

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86030

Sketch 5.5 Mixing chambers for steam ejectors The optimum length for a constant area mixing chamber is typically in the range 5 to 10 D . It is more difficult to give precise recommendations for ejectors with constant pressure designs of mixing chamber since the length available for mixing depends on the axial location of the primary nozzle in the mixing chamber. A tentative recommendation is that the mixing chamber should be sized so that the distance from the nozzle exit to the start of the diffuser is in the range 5 to 10 D . More specific recommendations are given in Derivations 4, 9 and 17. For the 'constant pressure' design of mixing chamber, the included half-angle of the conical section, φ 1 , should be in the range of 2º to 10º. Some more specific recommendations are given in Derivations 4, 9, 17 and 34. It may be found advantageous to use a double taper cone in order to give a smoother transition for the flow as it enters the parallel section of the mixing chamber. For all designs, the length of the parallel section should be adjusted so that the total length for mixing is in the range recommended above. Typically, this section has a length of 2 to 4 D . These recommendations only apply to ejectors with single, central nozzles. Multi-nozzle ejectors and annular nozzle ejectors should have shorter mixing chambers, since mixing occurs over a shorter distance in these configurations and any excess length results in increased friction losses. Further information on these configurations is given in Sections 7.2 and 7.3. The optimum mixing chamber length is also related to the geometry of the diffuser. If the diffuser angle is larger than recommended, a longer mixing chamber should be used to produce a more uniform velocity profile at the diffuser inlet and hence help prevent flow separation. If the diffuser angle is smaller than recommended, a shorter mixing chamber may be used since some mixing within the diffuser may then be tolerated. The mixing chamber walls should be as smooth as economically feasible since velocities and turbulence levels in the mixing chamber are high.

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 5.5.4

86030 Primary nozzle position

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The optimum position of the primary nozzle depends on the geometry chosen for the mixing chamber and on the application of the ejector. Early designs of steam ejectors often used movable (spindle or spear) nozzles. The nozzle could be moved to assist start up and to fine tune the performance of the ejector. However, such a nozzle removes the main advantage of a steam ejector which is its lack of movable parts. Also, it is difficult to devise a mechanism to hold a movable nozzle rigidly in position and any flexure results in variable performance and an increased risk of fatigue failure. Modern steam ejectors normally use fixed primary nozzles, the optimum position being determined by experiment before the ejector is commissioned. Often, provision for slight adjustments is made by using shims or packing. Typically, movements as small as 1 mm can be sufficient to cause noticeable changes in the performance of even a large steam ejector. The nozzle should be placed centrally on the axis of the mixing chamber in the case of ejectors with a single primary nozzle. For ejectors with a constant area design of mixing chamber it is recommended, as a first attempt, that the nozzle exit is placed 0.5 to 1.0 D upstream of the start of the mixing chamber. It is difficult to give precise recommendations for the optimum nozzle position in ejectors with a constant pressure design of mixing chamber. Several correlations are given in the literature (e.g. Derivations 17 and 18), but all are of limited application since they were obtained on only one geometry. That there is an optimum nozzle position is best seen by considering what happens when the nozzle is moved from its optimum position. Retracting the nozzle increases the area available for the secondary flow and so increases the secondary mass flow rate at the expense of the discharge pressure, p 5 . The secondary flow may in some cases separate from the walls of the mixing chamber, resulting in high losses and unstable operation of the ejector. Moving the nozzle into the mixing chamber reduces the secondary mass flow rate and increases the discharge pressure, p 5 . The area available for the secondary flow may be so reduced that the secondary flow stops. For steam/gas ejectors it should be noted that the optimum position of the nozzle may depend on the composition of the gas being pumped, dense and/or viscous gases restricting the expansion of the primary jet and damping turbulence in the mixing region between the primary jet and secondary flow. 5.5.5

Contraction or diffuser This component may be required to produce a specific exit pressure or velocity, or simply to connect an ejector to a downstream duct of different diameter. The efficiency of a contraction is usually high, provided the internal wall is smooth, the contraction angle is not extreme and no turning vanes are fitted. More care must be taken in the design of a diffuser. Flow separation and hence high losses may occur if the divergence angle of the diffuser is too high or if the velocity profile at the exit of the mixing chamber is highly non-uniform. If the mixing chamber is of optimum length, it is recommended that the included half-angle of the diffuser ( φ 2 ) is in the range 3 to 4° and in no case greater than 7° (Derivations 9 and 22). For a short mixing chamber, producing highly non-uniform flow, a smaller included angle should be used. It is recommended that the area ratio of the diffuser, A 5 ⁄ A 4 , does not exceed a value of 5. Space limitations may require that a properly designed diffuser cannot be used. For steam/liquid ejectors a trumpet shaped diffuser may be a useful compromise since its efficiency is higher than that of a conical diffuser of the same length. For steam/gas ejectors boundary layer suction devices have been used successfully to permit reductions in the diffuser length (see Derivation 21). More detailed information on the design of diffusers is given in Derivation 22.

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 6.

86030 PERFORMANCE PREDICTION The aim in performance prediction is to estimate the performance of an ejector whose geometry is already known. This Section presents a performance prediction method for steam/liquid ejectors and describes a theoretical method that can be used to estimate the performance of steam/gas ejectors. Some typical uses of these methods might be:

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(a)evaluating the off-design performance of an ejector designed by the methods given in Section 5, (b)predicting the effects of structural modifications on the performance of an existing ejector, (c)predicting the effects of changes in operating conditions on the performance of an existing ejector. The performance prediction procedure for steam/liquid ejectors is closely related to the design method given in Section 5.3.2. The procedure is based on the same theoretical analysis and uses the same parameters to describe the geometry of the ejector and the flow conditions at its inlet and outlet. An outline of a performance prediction procedure for steam/gas ejectors and its theoretical basis is given in Section 6.2. 6.1

Performance Prediction for Steam/Liquid Ejectors A comprehensive set of performance curves for steam/liquid ejectors is presented in Figures 9a to 9x. The curves were calculated directly from the equations given in Appendix B2, assuming typical values for the loss coefficients, K s, K m, K d and C D . Each Figure corresponds to a specific combination of the area ratio, A R , and the density ratio, r c . The curves on each Figure show the relationship between pressure ratio, N 1 , and mass flow ratio, r m , for fixed values of the area ratio, A T . The performance prediction method gives a detailed description of how these curves may be used. The curves in Figure 9a to 9x are only valid for steam/liquid ejectors with a saturated or superheated steam supply and with a constant area design of mixing chamber. The values assumed for the loss coefficients when calculating these curves were K s = 0.10, Km = 0.20, K d = 0.15 and C D = 1.0 . If more accurate values are available, the performance of the ejector may be better estimated directly from the theoretical results given in Appendix B2. More accurate values might be available if performance data are already available for ejector designs similar to the one under study. The loss coefficients can be estimated by 'calibrating' the results of the analysis against the data.

6.1.1

Performance prediction method Stage 1 - Determine the geometry of the ejector Ascertain the diameters of the nozzle throat, nozzle exit and mixing chamber. Calculate the area ratios AR = ( D ⁄ de )2 and

A T = ( d e ⁄ d th ) 2 .

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86030 Stage 2 - Select the appropriate performance chart Begin by calculating the density ratio, rc = ρ 1 ′⁄ ρ0 ″ . From Figures 9a to 9x select the chart for which r c and A R correspond most closely to the values calculated for the ejector. The ejector performance is then defined approximately by the curve for which the area ratio, A T , is closest to the calculated value for the ejector. For more precise estimation of performance a curve can be estimated by interpolation for A T .

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Stage 3 - Check whether cavitation or vapour binding is likely to occur The methods detailed in Stage 4 of the design method (Section 5.3.2) may be used to check whether cavitation or vapour binding is likely to occur. 6.2

Performance Prediction for Steam/Gas Ejectors To date, no truly general method has been devised for predicting the performance of steam/gas ejectors. Most ejector manufacturers rely on extensive data banks to predict performance and resort to testing for special one-off designs. Data banks of this type are not freely available since they are of great commercial value. Performance prediction methods have, however, been devised for gas driven ejectors. These methods, based on a one-dimensional analysis of the flow in the ejector and assuming ideal gas behaviour, have been validated successfully against experimental data obtained on gas/gas ejectors. Derivation 25 presents a simplified version of these methods valid for air/air ejectors. These prediction methods can, in principle, be used to calculate the performance of steam/gas ejectors, provided that the following assumptions can be made: negligible condensation in the flows within the ejector, negligible heat transfer out of the ejector, ideal gas behaviour in both primary and secondary streams. These assumptions are reasonable if the steam supply is superheated and the ejector body is insulated. Appendix B3 presents theoretical results derived from a one-dimensional flow analysis of the flow in a gas/gas ejector. The analysis is valid for any combination of primary and secondary gases, including a primary supply of superheated steam. The equations can be solved to yield the performance of a steam/gas ejector by using the method outlined in Section B3.3.

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 7.

86030 ASPECTS OF SOME MORE COMPLEX DESIGNS The efficiency and compactness of an ejector can often be improved by using more complex designs than the basic single-stage device with a single, central primary nozzle. Multi-stage, annular nozzle and multi-nozzle designs are discussed here.

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7.1

Multi-stage Steam Ejectors The use of series staging of steam ejectors greatly increases their flexibility of operation. Extra stages can be added to permit higher overall pressure ratios and/or larger secondary mass flow rates. It is usually necessary to provide a fresh steam supply to each stage in order to compensate for the steam condensed by the secondary flows. Multi-staging is widely used in vacuum pumping applications. The maximum vacuum that can be achieved by a single stage is limited by the compression ratio of the stage, N s , typically around 5 to 10, limiting the maximum vacuum to around 75 to 150 torr if, as is normal, the ejector discharges at atmospheric pressure. With multi-staging, vacuums down to a few microns Hg can be achieved. Multi-stage units for vacuum applications are usually equipped with intercondensers between stages. Typical units with and without intercondensers are shown in Sketch 7.1.

a. Three stage unit with intercondensers

b. Two stage unit without intercondensers

Sketch 7.1 Multistage ejectors for use in vacuum applications The function of the intercondensers is to condense the steam from the discharge of each stage and remove it as water before feeding into the next stage. This greatly reduces the volume of gas which each stage beyond the first must handle and so reduces the overall steam consumption of the unit. Intercondensers may be of the direct contact or surface types. Direct contact units are simple and cheap to construct but have the disadvantage that the cooling water may become contaminated if the gas being pumped is toxic or radioactive. The performance of a multi-stage unit with intercondensers is affected by the performance of the intercondensers. Perfect condensation is never achieved and some steam is always carried over to the downstream stage. This carry-over increases the secondary mass flow rate through that stage and so reduces the compression ratio it can achieve. The amount of carry-over, and hence the performance of the unit, is affected by the temperature of the cooling water and the ambient temperature outside the unit. The maximum vacuum that can be achieved is limited by the temperature of the cooling water.

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86030 Careful design of a multi-stage unit can greatly reduce the total mass flow rate of steam required to maintain a given vacuum. The main parameter required is the optimum compression ratio for each stage. A first approximation is to assume that each stage has the same compression ratio. For an n stage unit maintaining a vacuum of p 0u against a discharge pressure of p 5u , the compression ratio for each stage is 1

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p5  p 5u --n----- =  ------- . p0  p 0u Better performance can be achieved by using different compression ratios for each stage. The following analysis, from Derivation 6, indicates how the optimum compression ratio for each stage may be estimated. For simplicity a two-stage unit is considered and the intercondenser is assumed to have ideal performance. The analysis can easily be extended to units with more stages and with non-ideal intercondensers. For each stage it is assumed that the operating curve, plotted in the form W = 1 ⁄ r m versus N s = p 5 ⁄ p 0 can be approximated by a straight line (see Sketch 7.2).

Sketch 7.2 Straight line approximations to operating curves for a two-stage steam/air ejector This approximation often holds over a wide range of operating conditions. Then, for a two-stage device, W 1 = a 1 N s1 + b 1 and W 2 = a 2 N s2 + b 2 , where a 1 and a 2 are the slopes and b 1 and b 2 the intercepts of the straight lines approximating the operating curves. The total steam consumption for the unit is given by m· ′ = W 1 m· ″ + W 2 m· ″ 1 T 2 = ( W 1 + W 2 )m· ″ T since m· ″ = m· ″ = the gas flow rate for the unit, m· ″ . 1

2

T

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86030 Substituting the straight line approximations, and differentiating with respect to N s1 , gives d m· ′

a 2 N sT  T ------------ =  a 1 – --------------- m· ″ , d N s1 N s12  T  where N sT is the overall compression ratio, N sT = N s1 N s2 .

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Thus for minimum steam consumption, N s1 = ( a 2 N sT ⁄ a 1 ) ½ . Knowing the optimum value of N s for each stage, the individual stages can be designed by the method given in Section 5 of this Item. More information on the design and performance of multi-stage units can be found in Derivations 14, 15, 24, 30, 31, 38 and 43. 7.2

Annular Nozzle Steam Ejectors In this configuration the steam flow enters the mixing chamber through an annular nozzle. The secondary flow is drawn into the core of the resulting steam jet. For a given steam flow rate, an annular nozzle produces a jet with a greater surface area than that produced by a single, central nozzle. The steam and secondary flows mix over a shorter distance and so a shorter mixing chamber, typically about two thirds of the length required for a central jet type, can be used. Another advantage of annular nozzle devices is that they can be made as a one piece casting if desired. Offset against these advantages is the problem that the efficiency of an annular nozzle is usually less than that of an equivalent central nozzle. This is because friction losses in the mixing chamber are higher as a result of the increased velocity shear near the walls of the mixing chamber. Also, friction losses within the nozzle are likely to be higher than those in an equivalent central nozzle. Derivation 16 gives details of operating experience with annular nozzle steam ejectors.

7.3

Multi-nozzle Steam Ejectors A multi-nozzle steam ejector requires a shorter mixing chamber than a single nozzle ejector because, for a given steam flow rate, the greater surface area of the primary jets improves mixing. For a given mass flow rate, performance is generally superior to that of a single nozzle configuration, although there are additional losses due to the extra flow, blockage caused by the nozzle assembly and the higher frictional losses resulting from using several smaller nozzles in place of one large one. The risk of blockage by frozen vapour or water droplets is greater in a multi-nozzle design because, for a given steam flow rate, each jet is smaller. Each primary nozzle may be equipped with a separate steam supply line or, alternatively, the nozzles may be fed from a single supply. A crude single supply unit can be constructed by drilling holes into the end of a pipe cap. Indeed, experiments (Derivation 4) indicate that, in some circumstances, a pipe cap nozzle with one hole can perform nearly as well as a convergent-divergent nozzle.

31



86030

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In Derivation 41, a configuration with one central hole and four outer holes is recommended. Best performance was obtained with the outer holes inclined at an angle of 9 to 10° towards the axis of the ejector so that the outer jets were directed towards this axis.

32

 8.

86030 POSSIBLE OPERATING PROBLEMS

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Operating problems with steam ejectors can usually be avoided by operating at, or close to, the design point and by careful attention to mechanical design. This Section discusses the following potential problems: (i)

problems during start-up and shut-down (Section 8.1),

(ii)

unstable behaviour (Section 8.2),

(iii)

noise and vibration (Section 8.3).

Derivation 14 gives an excellent review of the causes and methods for the avoidance of operating problems with steam/gas ejectors. 8.1

Start-up and Shut-down Problems During start-up of a steam ejector, the steam occupies a greater volume within the ejector than it does when the secondary flow is established. This is normally a problem only in steam/liquid ejectors, which are usually designed to operate with the steam fully condensed by the end of the mixing chamber. In steam/liquid ejectors, the mixing chamber is sometimes equipped with an overflow to allow the uncondensed steam to escape during start-up. The ejector may fail to start if the back pressure, p 5 , is above the design value or if the discharge pipework is too small to allow the uncondensed steam to pass. Sometimes the ejector is equipped with a spring loaded valve to prevent steam entering the discharge lines until the secondary flow is established (see Sketch 8.1).

Sketch 8.1 Steam / liquid ejector equipped with overflow and start-up valve The performance of a device like that shown in Sketch 8.1 is much poorer than that of an ejector designed by the design methods in Section 5.3 of this Data Item.

33



86030 In some applications (e.g. the nuclear industry) an overflow is not permitted so the ejector must be 'oversized' in order to be self starting. By the criteria used in this Data Item, these oversized ejectors are classed as off-design and should be designed by an iterative process, using the performance prediction methods given in Section 6.

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On shut-down the steam remaining in the ejector and pipework condenses. This creates local reductions in pressure and may result in the secondary gases or liquids entering the steam supply lines. It may be necessary to provide isolating valves to prevent this happening. 8.2

Unstable Behaviour A steam ejector is normally stable when operated at its design point. Most operating problems arise during excursions from the on-design condition, i.e: (i)

decreases in the steam supply pressure, p 1 ,

(ii)

increases in the back pressure, p 5 ,

(iii)

decreases in the suction pressure, p 0 .

Unstable operation can also occur as a result of the following phenomena: (i)

a wet steam supply,

(ii)

vapour freezing,

(iii)

cavitation in steam/liquid ejectors,

(iv)

vapour binding in steam/liquid ejectors.

The instability may take the form of fluctuations in the discharge pressure and secondary flow rate, or complete breakdown of the flow. 8.2.1

Steam supply conditions Steam ejectors are normally designed to operate from a supply of dry steam. The steam temperature is usually equal to, or slightly above, the saturation temperature of the steam, T s , at the supply pressure, p 1 . Superheating by a few degrees celsius helps ensure that the steam remains dry in the primary nozzle but entails the extra cost of providing heating equipment. Higher levels of superheat produce little or no advantage: the extra thermal energy supplied to the steam has little effect on the rate of entrainment of the secondary fluid, larger inter- and after-condensers (if used) are required and, in liquid pumping applications, vapour binding may occur (see later). If wet steam is used to drive a steam ejector, the performance of the device decreases. The extra losses occur mainly in the primary nozzle where energy is expended in accelerating droplets. The water droplets may also greatly increase the rate of wear of the primary nozzle. In small devices, water droplets may cause significant blockage of the steam supply lines and nozzle. If wet steam must be used, the number of water droplets entering the ejector can be reduced by placing strainers, separators or traps in the steam supply lines. More information on the effects of wet steam on nozzle performance can be found in Derivations 9 and 52.

34

 8.2.2

86030 Vapour freezing As the primary steam flow is accelerated through the nozzle it expands, condenses and may freeze on the internal surfaces of the nozzle. This may cause substantial reductions in performance and even a complete breakdown of the flow.

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A further related problem can arise with steam/gas ejectors when the secondary gas contains vapour. This vapour may freeze on the outer surface of the primary nozzle, causing further reductions in the performance of the ejector. Methods used to prevent vapour freezing include superheating the supply steam, equipping the ejector with a heater jacket and using different materials with higher or lower thermal conductivities in constructing the ejector. 8.2.3

Cavitation in steam/liquid ejectors Cavitation is the formation of regions of vapour in a liquid stream. It occurs in regions of the flow where the static pressure is similar to, or below, the vapour pressure of the liquid. In a steam/liquid ejector, cavitation can occur anywhere in the liquid streams within the ejector. It is most likely to occur in the vicinity of the exit from the primary nozzle since the local static pressure reaches a minimum in this region. The effect of cavitation is to restrict the secondary flows and, possibly, to damage the internal surfaces of the ejector. For liquid flows in ducts it is usual to assess the likelihood of cavitation by use of a cavitation index. This approach is used in Derivation 26 to predict the onset of cavitation in liquid/liquid ejectors. Although this approach is probably valid for steam/liquid ejectors there is, to date, no comprehensive set of measurements of cavitation indices for these devices. The design and performance prediction methods in this Data Item therefore use a simplified criterion to predict the onset of cavitation: namely that cavitation is likely if the static pressure equals, or is below, the local value of the vapour pressure. The critical minimum value for the secondary inlet pressure, p 0c , is given by p 0c = p v0 + ½ρ″U e ″ 2 ( 1 + K s ) m· ″ 2 ( 1 + K s ) = p v0 + --------------------------------------- , 2ρ″ ( A m – A e ) 2 where p v0 is the vapour pressure of the liquid at the secondary inlet temperature, T 0 . The risk of cavitation occurring can be reduced by careful mechanical design of the ejector. The internal surfaces of the ejector should be as smooth as possible, and projections and sharp changes in the flow direction should be avoided.

8.2.4

Vapour binding in steam/liquid ejectors Steam/liquid ejectors are usually designed so that the steam is completely condensed by the exit of the mixing chamber. This results in the smallest and most efficient device : the condensed steam occupies minimal volume, the flow into the diffuser is as uniform as possible and the process of complete condensation ensures maximum transfer of energy to the driven liquid.

35



86030 Vapour binding is the operating condition in which steam is not fully condensed by the entrance to the diffuser. The uncondensed vapour restricts the flow of the liquid and so reduces the performance of the ejector. Vapour binding occurs if flow conditions are such that the heat transfer between the steam and liquid is insufficient to cause complete condensation of the steam. An estimate of the liquid temperature in the diffuser can be obtained by equating the heat rejected by the steam to the heat gained by the liquid, i.e.

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m· ′c pg ′ ( T 1 – T s ) + m· ′h fg + m· ′c pf ′ ( T s – T 4 ) = m· ″c p ″ ( T 4 – T 0 ) . Here h fg is the specific enthalpy of vaporisation of the steam. Most steam ejectors operate from a supply of saturated or slightly superheated steam so that T 1 ≈ T s . It follows, writing r m = m· ″ ⁄ m· ′ , that an estimate for the temperature, T 4 , is given by h fg + c pf ′T 1 + c p ″r m T 0 T 4 ≈ T 5 ≈ ------------------------------------------------------------. c ′+r c ″ pf

m p

The design and performance prediction methods in this Item assume that vapour binding is likely if the value of T 4 exceeds the saturation temperature of the liquid, T s , at the discharge pressure, p 4 . According to this criterion, vapour binding is likely if the mass flow ratio, r m , is too low or the temperature ratio, TR = T1⁄ T0 , too high. The performance of commercially available steam/liquid ejectors is normally guaranteed only up to a specified maximum value of T 0 . Above this temperature, the mass flow ratio, r m , decreases as T 0 is increased. This maximum temperature is sometimes expressed in terms of the minimum degree of subcooling, where the degree of subcooling, ∆T , is defined by ∆T = T 1 – T 0 . 8.3

Noise and Vibration Noise is often a problem with steam/gas ejectors. Standard practice is to measure noise levels at a distance of 1 m from the ejector. Noise levels in excess of 100 dBA are not uncommon at this distance, although 85 to 95 dBA is more usual. The main source of noise is the high velocity jet discharge from the diffuser. Resonance within the ejector can also lead to high noise levels. The amount of noise emitted is greatly reduced if the ejector is equipped with an aftercondenser or, for multi-stage units, with intercondensers. These devices act as silencers. Custom made silencers may be fitted in the absence of these devices. One successful design of silencer (a re-entrant silencer) consists of a cylindrical box containing internal flow passages that reverse the direction of the flow discharged from the ejector and then reverse it again so that the flow is discharged in the original direction. The internal flow passages are constructed from acoustically resistant materials. Provision of a silencer need not greatly affect the performance of an ejector. Typically, a 45 dBA reduction in noise is achieved at a penalty of 0.5 psi (3.4 kPa) on the discharge pressure. In ejectors that are poorly designed, or operating off-design, performance may even improve, since the back pressure from the silencer helps prevent flow separation in the diffuser. One source of noise that is difficult to remove is that transmitted down the discharge line from the ejector. This noise can sometimes be reduced by fitting acoustic cladding to this line.

36



86030 Noise is generally less of a problem with steam/liquid ejectors. Derivation 13 suggests that noise levels are lower if a constant area, rather than constant pressure, mixing chamber is used. The explanation given for this observation was that, in the constant pressure configuration, extra noise is generated when the primary and secondary streams meet at an angle in the converging section of the mixing chamber.

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Vibration is a potential problem in all ejectors, sometimes causing fatigue failures at joints and causing the primary nozzle to move from its on-design position. With screw fixed primary nozzles it is not uncommon for the nozzle to unscrew and drop into the secondary inlet. These problems are difficult to anticipate and are best solved by trial and error during commissioning of the ejector.

37



86030

9.

WORKED EXAMPLES

9.1

Design Method for Steam/Liquid Ejectors

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Radioactive liquors, produced in a nuclear fuel reprocessing plant, are stored in stainless steel tanks to await further treatment. An additional storage tank is under construction and is to be fitted with a liquor sampling system. It is proposed to use a steam ejector to feed liquor to this sampling system. The sampling system is located approximately 21.0 m above the average surface level of the liquor in the tank and requires a constant liquor feed of 2.7 1/s. The liquor has a specific gravity of 1.04 and its estimated temperature in the tank is 48ºC. The physical properties of the liquor are similar to those of water. A saturated steam supply at 6.8 bar abs is available to drive the ejector. Stage 1 - Determine the constraints on the design. The pressure difference ( p 5 – p 0 ) across the ejector is equivalent to 21.0 m head of liquor, or 214.3 kPa. Note that this estimate neglects any friction losses in the supply and discharge lines connected to the ejector. The steam supply pressure is fixed at 6.8 bar abs = 688.8 kPa. The mass flow rate of liquor is fixed at 2.7 × 1.04 = 2.81 kg/s. From Steam Tables the following properties of the steam supply are determined: the steam supply temperature is 163.8°C, the density of the steam supply is 3.55 kg/m3, 3 the specific enthalpy of vaporisation of the steam is 2200 ×10 J/kg K, the vapour pressure of the liquor is 0.11 bar abs at 48°C, the specific heat capacity of the liquor is 4186 J/kg K. The pressure ratio, N 1 = ( p 5 – p 0 ) ⁄ p 1 , is equal to 214.3/688.8 = 0.31. The density ratio, r c = ρ 1 ′ ⁄ ρ 0 ″ , is equal to 3.55/1040 = 0.0034. Stage 2 - Obtain values for the area ratios A R and A T . The optimum values for the area ratios, A R and A T , can be read from Figures 1 and 2 for the fixed value of N 1 = 0.31 . The corresponding value of the mass flow ratio can be read directly from Figure 3 by direct interpolation between the curves for r c = 0.0025 and r c = 0.005 . The resulting values for these parameters are: A R = 1.98 , A T = 1.27 , r m = 19.0 .

38



86030 Stage 3 - Calculate the remaining unknown design parameters. The steam mass flow rate is given by m· ′ = m· ″ ⁄ r m

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= 2.81 ⁄ 19.0 = 0.148 kg/s. The area of the nozzle throat, A th , is given by m· ′ T 1 R′ A th = ----------------------0.67p 1

and

0.148 436.8 × 461.5 = ----------------------------------------------------- so that 0.67 × 688800 A th = 0.000144 m2 d th = 0.0135 m.

The exit area of the nozzle, A e , is given by A e = A T A th = 1.27 × 0.000144 and

= 0.00018 m2 d e = 0.0153 m.

The area of the mixing chamber, A m , is given by Am = AR Ae = 1.98 × 0.000018 and

= 0.00036 m2 D = 0.0214 m.

Stage 4 - Determine whether cavitation or vapour binding is likely to occur. Cavitation may occur if the secondary inlet pressure is below a value m· ″ 2 ( 1 + K s ) p 0c = p v0 + --------------------------------------- , 2ρ″ ( A m – A e ) 2

39



86030 where

p v0 = 11.1 kPa, m· ″ = 2.81 kg/s, ρ″ = 1040 kg/m3, A m = 0.00036 m2,

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A e = 0.00018 m2. Assuming a value of 0.10 for K s suggests that cavitation may occur if p 0 ≤ 140.0 kPa. Assuming that the pressure in the storage tank is atmospheric (nominally 100 kPa), this result indicates that the ejector would need to be submerged to a depth of a least 3.9 m below the surface level of the liquor in the tank in order to avoid cavitation. An estimate of the temperature of the liquor, T 4 , discharged from the mixing chamber is given by h fg + c p f ′T 1 + c p ″r m T 0 T 4 = ------------------------------------------------------------c pf ′ + r m c p ″ where

h fg = 2200 kJ/kg, c pf ′ ≈ c p ″ = 4186 J/kg K, r m = 19.0 , T 1 = 436.8 K, T 0 = 321.0 K,

so that

T 4 = 353.1 K = 80.1 °C.

The pressure p 4 in the liquid at this location is given by ( m· ′ + m· ″ ) 2 ( 1 + K d ) p 4 = p 5 – ----------------------------------------------------- , 2 2ρ″ A m where

p 5 = 21.0 m of liquor, equivalent to 314.3 kPa abs with zero submergence, m· ′ = 0.148 kg/s, m· ″ = 2.81 kg/s, ρ″ = 1040 kg/m3, A m = 0.00036 m2.

Assuming a value K d = 0.15 gives p 4 = 286.7 kPa. At this pressure the saturation temperature of the liquor is 132°C which is well above the value of T 4 = 80.1 °C. This result suggests that vapour binding will not be a problem with this ejector.

40



86030 Stage 6 - Carry out the detailed design of the ejector. The principal dimensions of the ejector and its cavitation/vapour binding performance have been calculated. The detailed design of the ejector should now be carried out following the guidelines given in Section 5.5.

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Sketch 9.1 shows a possible configuration for an ejector that connects to a 30.0 mm diameter steam supply line and a 40.0 mm diameter discharge line. A half-angle φ 2 = 3° was chosen for the diffuser. The exit of the steam nozzle is situated 10 mm from the start of the constant area section of the mixing chamber.

Sketch 9.1 Example 1. Principal dimensions of ejector 9.2

Design Method for Steam/Gas Ejectors A steam ejector is to be fitted to a vacuum de-aeration unit in a boiler plant. The estimated flow conditions at the secondary inlet of the ejector are: pressure = 0.5 bar abs and flow rate of water vapour and air from the de-aerator of 100 kg/h. The gas flow into the ejector consists of a 4 to 1 mixture by weight of water vapour and air. The ejector is to be driven from a dry saturated supply of steam at a pressure of 6 bar abs. The ejector will discharge to atmosphere. Stage 1 - Determine the constraints on the design. The primary pressure ratio, N p , is fixed and is given by p1 6.0 N p = ----- = ------- = 6.0 . p5 1.0 The compression ratio, N s , is fixed and is given by p5 1.0 N s = ----- = ------- = 2.0 . p0 0.5 The secondary mass flow rate is fixed at 100 kg/h (80 kg/h of water vapour, 20 kg/h of air). The molecular weights of the water vapour and air are 18 and 29 respectively. From Steam Tables the following properties are determined: the steam supply temperature is 158.8°C the pressure of the water vapour is 0.5 bar abs at 81.3°C.

41



86030 Stage 2 - Determine C 1 for gases other than air and C 2 for gas temperatures above 20°C

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The secondary gas pumped by the ejector consists of a 4:1 mixture of water vapour and air. The mass-weighted molecular weight of this mixture is equal to ( 0.8 × 18 + 0.2 × 29 ) = 20.2 . The molecular weight correction factor C 1 for this mixture is, from Figure 4, equal to 0.83. The air-equivalent secondary mass flow rate is therefore 100/0.83 = 121 kg/h. The secondary gas temperature is approximately 81.3°C. The temperature correction factor C2 is, from Figure 5, equal to 0.97. The air-equivalent secondary mass flow rate at 20°C is therefore equal to 121/0.97 = 125 kg/h. Stage 3 - Estimate the unknown pressure ratio or mass flow ratio. The pressure ratios, N p and N s , are fixed at 6.0 and 2.0 respectively. An estimate for the mass flow ratio, r m , can be obtained directly from Figures 6. Figure 6a suggests that the highest value likely to be obtained is r m ≈ 0.55 . Figure 6b suggests that a more typical value - for a good but not exceptional design - is likely to be rm ≈ 0.39 . For illustrative purposes the average value, r m = 0.39 , will be used in the remainder of this calculation. Stage 4 - Estimate the optimum geometry for the ejector. The optimum nozzle area ratio can be read directly from Figure 7. For a mass flow ratio of 0.39 and a primary pressure ratio of 6.0, the optimum value of A T is about 2.5. The optimum area ratio, A *R , can be estimated from Figure 8. For a mass flow ratio of 0.39 the optimum value for the parameter A R* ⁄ N p lies in the range 1.10 to 1.26. An average value of 1.18 will be assumed, giving a value A R* = 7.1 for a primary pressure ratio, N p , of 6.0. Stage 5 - Calculate the remaining unknown design parameters. The mass flow rate of steam is given by m· ′ = m· ″ ⁄ r m = 125 ⁄ 0.39 = 321 kg/h = 0.089 kg/s. The area of the nozzle throat corresponding to this steam mass flow rate is given by m· ′ T 1 R′ A th = ----------------------- , 0.67p 1 where

p 1 = 6 bar abs = 607.8 kPa, T 1 = 158.8 °C = 431.8 K, R′ = 461.5 J/kg K

42



86030 and

m· ′ = 0.089 kg/s,

so that

A th = 0.000098 m2

and

d th = 0.011 m.

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The exit area of the nozzle, A e , is given by A e = A T A th = 2.5 × 0.000098 = 0.00025 m2 d e = 0.018 m. The area of the narrowest portion of the mixing chamber A m = A R* A th = 7.1 × 0.000098 = 0.00070 m2, so that the diameter of this portion of the mixing chamber is D = 0.030 m. Stage 6 - Assess the final design The calculation is now complete. The required ejector has a steam consumption of 321 kg/h and dimensions D = 30 mm, d e = 18 mm and d th = 11 mm. The shape and layout of component parts of the ejector should now be designed following the guidelines given in Section 5.5. The calculation assumed a typical value of 0.39 for the mass flow ratio, r m . If the more optimistic value of 0.55 estimated at Stage 2 had been used, the ejector would have had a steam consumption of 222 kg/h and dimensions D = 25 mm, d e = 13 mm and d th = 9 mm. Stage 7 - Carry out the detailed design of the ejector A possible configuration for the ejector, assuming a 45 mm diameter steam supply line and 60 mm diameter discharge pipe is shown in Sketch 9.2.

Sketch 9.2 Example 2. Principal dimensions of ejector

43

 9.3

86030 Performance Prediction Method for Steam/Liquid Ejectors The liquor sampling ejector in Section 9.1 was designed to operate on-design when the liquor level in the storage tank was at its average value. However, in normal operation, the liquor level may vary on either side of this average value by up to 3.0 m . An estimate is required of the effect of variations in liquor level on the flow rate delivered by the ejector. The ejector will be sited 7.3 m below the minimum surface level in the storage tank.

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Stage 1 - Determine the geometry of the ejector. The area ratios, A R and A T , are respectively 1.98 and 1.27. Stage 2 - Select the appropriate performance chart. The performance prediction curves given in Figure 9a to 9x are only valid for the specified values of r c, A R and A T . The ejector in this example has area ratios A R = 1.98 and A T = 1.27 and is operating at a density ratio, r c , of 0.0034. The curves which correspond most closely to these values are those for A R = 2.0, A T = 1.1 or 2.0, r c = 0.001 and A R = 2.0, A T = 1.1 or 2.0, r c = 0.005 . Some interpolation is therefore required to find the ejector performance curve. Sketch 9.3 shows the results of an interpolation on AT and Sketch 9.4 shows the results of an interpolation on r c . An interpolation on A R was not made since A R ≈ 2.0 . The final operating curve for the ejector is shown in Sketch 9.5. The normal operating range of the ejector is between pressure head differentials of (21 - 3) and (21 + 3) metres of liquor, i.e. between 183.6 kPa and 244.5 kPa respectively. These pressure differentials correspond to values of N 1 of 0.27 and 0.35. These operating limits are indicated on Sketch 9.5. The mass flow ratios delivered by the ejector are 24.0 at N 1 = 0.27 and 12.5 at N 1 = 0.35 . Thus the secondary (liquor) mass flow rate is 1.85 kg/s at the lower liquor level and 3.55 kg/s at the upper liquor level. Stage 3 - Check whether cavitation or vapour binding is likely to occur. Cavitation is most likely to occur at high values of the mass flow ratio, i.e. when the liquor is at its upper level. At the mass flow ratio corresponding to the upper liquor level cavitation may occur if the secondary inlet pressure is below a value m· ″ 2 ( 1 + K s ) p 0c = p v0 + --------------------------------------- . 2ρ″ ( A m – A e ) 2 Using the value m· ″ = 3.55 kg/s and taking K s = 0.10 gives p 0c = 216.8 kPa. This pressure corresponds to a head of 11.4 m of liquor. The ejector is sited only 7.3 + 6.0 = 13.3 m below the upper liquor level in the tank, which implies that cavitation is unlikely to occur under these flow conditions. Vapour binding is most likely to occur at low values of the mass flow ratio, r m ; i.e. when the liquor is at its lower level. The temperature, T 4 , in the diffuser at the mass flow ratio corresponding to the lower liquor level, r m = 12.5 , is given by h fg + c pf ′T 1 + c p ″r m T 0 T 4 = ------------------------------------------------------------- . c pf ′ + r m c p ″

44



86030 Using the same values of h fg, c p ″, T 0 and T 1 as in Example 9.1 gives T 4 = 95.5 °C.

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The pressure, p 4 , in the liquor at this location is given by ( m· ′ + m· ″ ) 2 ( 1 + K d ) p 4 = p 5 – ----------------------------------------------------- . 2 2ρ″A m Taking p 5 = 419.3 kPa (equivalent to 24.0 + 7.3 = 31.3 m of liquor), m· ′ = 0.148 kg/s, m· ″ = 1.85 kg/s, K d = 0.15 , giving

p 4 = 406.7 kPa.

At this pressure, the saturation temperature of the liquor is 144°C, which is above the value of T 4 = 95.5 °C. This result suggests that vapour binding will not be a problem with this ejector, even at the lowest liquor level in the tank.

Sketch 9.3 Result of an interpolation on A T

45

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86030

Sketch 9.4 Results of an interpolation on r c

Sketch 9.5 Final performance curve for the ejector

46



86030

10.

DERIVATION AND REFERENCES

10.1

Derivation

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The derivation lists selected sources that were used in preparation of this Data Item.

1.

WATSON, F.R.B.

Production of a vacuum in an air tank by means of a steam jet. Proc. Inst. mech. Engrs, Vol.124, pp.231-300, 1931.

2.

WORK, L.T. HAEDRICH, V.W.

Performance of ejectors as a function of the molecular weights of vapours. J. ind. engng Chem., Vol.31, No.4, pp.464-476, 1939.

3.

ROYDS, R. JOHNSON, E.

The fundamental principles of the steam ejector. Proc. Inst. mech. Engrs, Vol.145, p.193, 1946 and Vol.146, pp.223-235, 1947.

4.

KROLL, A.E.

The design of jet pumps. Chem. Engng Prog., Vol.1, No.2, pp.21-24, 1947.

5.

RICHELSON, M.

Construction materials for jet pumps. Chem. Engng, pp.114-117, 248-252, Sept. 1948.

6.

ARROWSMITH, G.

The production of vacuum for industrial chemical processes. Trans. Inst. chem. Engrs, Vol.27, pp.101-112, 1949.

7.

HOLTON, W.C.

Effect of molecular weight of entrained fluid on the performance of steam jet ejectors. Trans. am. Soc. mech. Engrs, Vol.73, pp.905-910, 1951.

8.

HOLTON, W.C. SCHULZ, E.J.

Effects of temperature of entrained fluid on the performance of steam-jet ejectors. Trans. am. Soc. mech. Engrs, Vol.73, pp.911-913, 1951.

9.

JOHANNESEN, N.H. Ejector theory and experiment. Trans. danish Acad. tech. Sci., No.1, 1951.

10.

SMITH, R.A.

Theory and design of simple ejectors. Paper to Conf. at Inst. Physics, Oct. 1950. (Published as “Some Aspects of Fluid Flow,” ed. Lang, H.R. pp.229-240 Arnold, London, 1951.)

11.

MESSINA, P. BROWN, J.J. BOHNLOFINK, J.

How to check your jet utilities. Chem. Engng, Vol.61, No.1, pp.161-164, 1954.

12.

KAYE, J. RIVAS, M.A.

Experimental and analytical study of two-component two phase flows in an ejector with condensation. ASME Paper 57-HT-35, 1957.

13.

ROSE, R.P.

Steam jet pump analysis and experiment. USAEC Bettis Atomic Power Lab., R&D Report No. WAPD-TM-227, 1960.

14.

POWER, R.B.

Steam jet air ejectors: specification, evaluation and operation. ASME Paper 63-WA-143, Nov. 1963.

15.

HARRIS, L.S. FISCHER, A.S.

Characteristics of the steam jet vacuum pump. Trans. am. Soc. mech. Engrs, Series B, Vol.86, pp.358-364, 1964.

47

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10.2

86030 16.

MIGUEL, J. BROWN, G.A.

An analytical and experimental investigation of a condensing ejector with a condensable vapour. AIAA Paper 64-469, 1964.

17.

SHKLOVER, G.G. ROSINSKII, A.Z. GERASIMOV, A.V.

Dimensionless characteristics of KTZ steam-jet ejectors. Thermal Engng, Vol.13, No.3, pp.54-61, 1966.

18.

PUTILOV, M.I.

Calculating the optimal distance of the nozzle from the mixing chamber in injectors. Thermal Engng, Vol.14, No.7, pp.94-101, 1967.

19.

HEAT EXCHANGE INSTITUTE

Standards for steam-jet ejectors. Heat Exchange Institute, New York, 80 pp, 3rd edn., 1956 with revision sheets, May 1962 and November 1971.

20.

HESS, F.

The efficiency of motive nozzles in steam-jet pumps. Paper 8, 1st Symp. Jet Pumps and Ejectors, BHRA, Cranfield, UK, 1972.

21.

TAH-TEH, Y. EL-NASHER, A.M.

Jet pump performance with a short diffuser. Paper 9, 1st Symp. Jet Pumps and Ejectors, BHRA, Cranfield, UK, 1972.

22.

ESDU

Introduction to design and performance data for diffusers. Data Item No. 76027, ESDU International Ltd, London, Nov. 1976.

23.

ESDU

One dimensional compressible gas flow in ducts. Data Item No. 74028, ESDU International Ltd, London, April 1981.

24.

RYANS, J.L. CROLL, S.

Selecting vacuum systems. Chem. Engng, pp.42-48, Dec 14, 1981.

25.

ESDU

Ejectors and jet pumps: design and performance for compressible air flow. Data Item No. 84029, ESDU International Ltd, London, December 1984.

26.

ESDU

Ejectors and jet pumps: design and performance for incompressible liquid flow. Data Item No. 85032, ESDU International Ltd, London, December 1985.

References The references are recommended sources of information supplementary to this Data Item.

27.

BINNIE, A.M. WOODS, M.

The pressure distribution in a convergent-divergent steam nozzle. Proc. Inst. mech. Engrs, Vol.138, p.229, 1938.

28.

ELROD, H.G. ANNAPOLIS, M.D.

The theory of ejectors. Am. Soc. mech. Engrs, J. appl. Mech., Vol.12, No.3, pp.Al70 - A174, 1945.

29.

FLUGEL, G.

The design of jet pumps. NACA tech. Memo. 982, 2nd edn, 1951.

30.

BERKELEY, F.D.

Ejectors give any suction pressure. Chem. Engng, Vol.64, No.4, pp.255-260, 1957.

48

ESDU product release: 2006-01. For current status, contact ESDU. Observe Copyright.



86030 31.

BLATCHLEY, C.G.

Control of steam jet vacuum pumps. ASME Paper 57-F-15, Sept. 1957.

32.

MARGOLIS, S.C.

Steam jet pump operations at high pressure. USAEC Bettis Atomic Power Lab. Tech. Review WAPD-BT-14, pp.120-141, 1959.

33.

KNIGHT, G.

Five ways to automatically control pressure for ejector vacuum systems. Chem. Engng, Vol.66, No.6, pp.171-174, 1959.

34.

MOLYNEUX, F.

The design of a simple jet pump or ejector. Fluids Handling, Vol.2, pp.14-18, 1960.

35.

UEDA, T.

On the performance characteristics of steam ejectors. Bull. jap Soc. mech. Engrs, Vol.4, No.13, pp.124-130, 1961.

36.

ENGLISH ELECTRIC Steam jet ejector condensers and air ejectors. English Electric CO. Library Bibl. RC535, 1963.

37.

VIL’DER, S.I.

A simplified method of calculating steam-jet ejector vacuum pumps. Int. chem. Engng, Vol.4, No.1, pp.88-92, 1964.

38.

MAINS, W.D. RICHENBERG, R.E.

Steam jet ejectors in pilot and production plants. Chem. engng Prog., Vol.63, No.3, p.84, 1967.

39.

MEDICI, M.

The design of jet ejectors. Engrs Digest, Vol.14, No.2, pp.51-53, 1967.

40.

NEWMAN, E.F.

How to specify steam-jet ejectors. Chem. Engng, Vol.74, No.6, pp.203-209, April 1967.

41.

SHKLOVER, G.G. RODIVILIN, M.D.

Investigation of a jet steam condenser. Thermal Engng, Vol.11, No.3, pp.46-52, 1967.

42.

GROLMES, M.A.

Steam-water condensing injector performance analysis with supersonic inlet vapor and convergent condensing section. NASA, May 1968. Based on a graduate thesis, Univ. of Notre Dame. Published by Michael A. Grolmes, Argonne National Laboratory, Ill.

43.

KNIGHT, J.

How to obtain optimum performance from vacuum ejector systems. Proc. Engng, pp.35-41, Dec. 1970.

44.

ARROWSMITH, R.M. Combinations of ejectors with water ejectors and mechanical vacuum pumps for optimum performance. Paper 1, lst Symp. on Jet Pumps and Ejectors, BHRA, Cranfield, UK, 1972.

45.

BONNINGTON, S.T. KING, A.L

Jet pumps and ejectors: a state of the art review and bibliography. BHRA Fluid Engineering, Cranfield, UK, 1972.

46.

KURTZ, E.F. MOYLE, I.N.

Experimental data for steam ejectors. Proc. 4th Canadian Congress in Applied Mechanics, Montreal, pp.727-728, May 28th - June lst, 1973.

47.

KURTZ, E.F.

Theoretical model for predicting steam ejector performance. Trans. am. Soc. mech. Engrs, J. Eng. Ind., Sept. 1974.

49

ESDU product release: 2006-01. For current status, contact ESDU. Observe Copyright.



86030 48.

KURTZ, E.F.

Compound choking and compound supersonic flow in steam ejectors. Paper El, 2nd Symp. Jet Pumps and Ejectors, BHRA, Cranfield, UK, 1975.

49.

ASME

Performance test codes: code on ejectors, American Society of Mechanical Engineers, 1976.

50.

GEDDES, W.R.

The steam powered water jet pump. PhD Thesis, Univ. of Cardiff, 1980.

51.

KURMA, RAO P.S.V.

Steam jet ejectors for process condensers. Oil and Gas J., Vol. 80, No.21, pp.91-92, 1982.

52.

SARBY, T.I. KHALIFA, B.A. IBRAHIM, K.A. MAHMOUD, N.H.

Non-equilibrium wet steam flow through nozzles. 3rd Multi-phase Flow and Heat Transfer Symp., Miami, Session 3A, p.57, April 18-20, 1983.

50



86030 0.8

ESDU product release: 2006-01. For current status, contact ESDU. Observe Copyright.

0.7

0.6

0.5 N1 0.4

0.3

0.2

0.1

0.0

1

2

3

4

5

6

7

8

AR

FIGURE 1 STEAM/LIQUID EJECTORS: OPTIMUM AREA RATIO AR v PRESSURE RATIO N1 ( 0.001 < r c < 0.010 )

51

86030

 0 .8

0 .7

ESDU product release: 2006-01. For current status, contact ESDU. Observe Copyright.

0 .6

0 .5 N1

0 .4

0 .3

0 .2

0 .1

0 .0

1

2

3

4

5

6

7

8

AT

FIGURE 2 STEAM/LIQUID EJECTORS: OPTIMUM AREA RATIO AT v PRESSURE RATIO N1 ( 0.001 < r c < 0.010 )

52

ESDU product release: 2006-01. For current status, contact ESDU. Observe Copyright.



0.8

0.30 a. 0 < N1< 0.3

b. N1 > 0.3

|

0.25

0.7

0.20

0.6 N1

N1

0.5

0.15

rc

53

0.001 0.10

rc

0.4

0.0025

0.001

0.005 0.05

0.0025

0.3

0.010

0.005 0.010

0.00 0

0.2 0

100

200

300

400 rm

500

600

700

800

0

5

10

15

20

25

30

rm

86030

FIGURE 3 STEAM/LIQUID EJECTORS: OPTIMUM MASS FLOW RATIO rm v PRESSURE RATIO N1

86030

 2.0

0.0

ESDU product release: 2006-01. For current status, contact ESDU. Observe Copyright.

1.5

C1

1.0

0.5

0.0

0

20

40

60

80

100

120

140

Molecular weight of gas

FIGURE 4 STEAM / GAS EJECTORS: CORRECTION FACTOR C1 v GAS MOLECULAR WEIGHT

54

86030

 1.00

ESDU product release: 2006-01. For current status, contact ESDU. Observe Copyright.

0.95

0.90 C2

0.85

0.80

0.75

0

100

200

300

400

500

600

B

Inlet temperature of secondary airflow To ( C)

FIGURE 5 STEAM/GAS EJECTORS: CORRECTION FACTOR C2 v GAS INLET TEMPERATURE

55

86030

 rm

20

a. BEST VALUES

0.1

0 0.05

15 rm

ESDU product release: 2006-01. For current status, contact ESDU. Observe Copyright.

Ns

0.3

rm 0.2

10

0.4 0.5 0.8

5 0.7

3.0

0.6 0

0

10

20

30

40

50

60

70

Np

b. TYPICAL VALUES

rm

20

0.05 rm 0

15

0.1

Ns

0.2 10 0.3 0.4

0.5

0.75

0.6

5

3.0 0

0

10

20

30

40

50

60

70

Np

FIGURE 6 STEAM/GAS EJECTORS: EFFECT OF MASS FLOW RATIO rm ON VARIATION OF SECONDARY PRESSURE RATIO NS WITH PRIMARY PRESSURE RATIO Np

56

86030

 60

50

ESDU product release: 2006-01. For current status, contact ESDU. Observe Copyright.

40 AT 30

rm

0

0.05

0.1

0.2

0.3 0.4

20

0.75 10

0

3.0 rm 0

10

20

30

40

50

60

70

80

Np

FIGURE 7 STEAM/GAS EJECTORS: EFFECT OF MASS FLOW RATIO rm ON VARIATION OF AREA RATIO AT WITH PRIMARY PRESSURE RATIO Np

57

86030

 1.5 1.4 1.3

ESDU product release: 2006-01. For current status, contact ESDU. Observe Copyright.

1.2 AR*/Np

1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.0

0.2

0.4

0.6

0.8

1.0

1.2

rm

FIGURE 8 STEAM/GAS EJECTORS: OPTIMUM VALUES OF AREA RATIO A*R AS A FUNCTION OF MASS FLOW RATIO rm AND PRESSURE RATIO Np

58

86030

 AT

0.8

1.1

a. rc = 0.001 A R = 1.1

0.7

K s = 0.10 K m = 0.20 K d = 0.15 C D = 1.00

ESDU product release: 2006-01. For current status, contact ESDU. Observe Copyright.

0.6 2.0

0.5 N1

3.0 0.4 4.0 0.3

5.0 6.0

0.2 8.0

7.0

0.1 0.0 0 0.0

2.5

5.0

7.5

10.0

12.5

15.0

17.5

20.0

22.5

rm

FIGURE 9a STEAM/LIQUID EJECTORS: PERFORMANCE PREDICTION CURVES

59

25.0

86030

 0.45 0.40

AT 1.1 b. r c = 0.001 A R = 2.0

0.35 ESDU product release: 2006-01. For current status, contact ESDU. Observe Copyright.

K s = 0.10 K m = 0.20 K d = 0.15 C D = 1.00

2.0 0.30 N1

0.25

3.0

0.20

4.0

0.15

5.0

0.10 0.05 0.00 0 0

6.0 7.0 8.0

25

50

75

100

125

150

175

200

225

rm FIGURE 9b STEAM/LIQUID EJECTORS: PERFORMANCE PREDICTION CURVES

60

250

86030

 AT 0.24

1.1

K s = 0.10 K m = 0.20 K d = 0.15 C D = 1.00

2.0 c. rc = 0.001 A R = 3.0

ESDU product release: 2006-01. For current status, contact ESDU. Observe Copyright.

0.20

0.16

3.0

N1 4.0

0.12

5.0 6.0

0.08

7.0 8.0

0.04

0.00 0

0

50

100

150

200

250

300

350

rm

FIGURE 9c STEAM/LIQUID EJECTORS: PERFORMANCE PREDICTION CURVES

61

400

86030

 0.20

AT 1.1 2.0

ESDU product release: 2006-01. For current status, contact ESDU. Observe Copyright.

0.16

Ks = 0.10 Km = 0.20 Kd = 0.15 CD = 1.00

d. rc = 0.001 AR = 4.0

3.0

0.12 N1

4.0 0.08

5.0

0.04

0.00 0

6.0 7.0 8.0

0

50

100

150

200

250

300

350

400

450

500

550

rm FIGURE 9d STEAM/LIQUID EJECTORS: PERFORMANCE PREDICTION CURVES

62

600

86030

 AT 0.16 1.1 ESDU product release: 2006-01. For current status, contact ESDU. Observe Copyright.

Ks = 0.10 Km = 0.20 Kd = 0.15 CD = 1.00

e. rc = 0.001 AR = 5.0

2.0 0.12 3.0

N1 0.08

4.0 5.0

0.04 6.0 7.0 8.0 0.00 0

0

100

200

300

400

500

600

700

rm

FIGURE 9e STEAM/LIQUID EJECTORS: PERFORMANCE PREDICTION CURVES

63

86030

 0.12 AT

1.1

f. rc = 0.001 AR = 6.0

2.0

Ks = 0.10 Km = 0.20 Kd = 0.15 CD = 1.00

ESDU product release: 2006-01. For current status, contact ESDU. Observe Copyright.

0.10

3.0

0.08

N1

4.0 0.06 5.0 6.0 0.04

7.0 8.0

0.02

0 0.00

0

100

200

300

400

500

600

700

rm

FIGURE 9f STEAM/LIQUID EJECTORS: PERFORMANCE PREDICTION CURVES

64

86030

 0.12 AT

1.1

0.10 2.0

ESDU product release: 2006-01. For current status, contact ESDU. Observe Copyright.

Ks = 0.10 Km = 0.20 Kd = 0.15 CD = 1.00

g. rc = 0.001 AR = 7.0

0.08 3.0 N1

0.06 4.0 5.0 0.04

6.0 7.0 8.0

0.02

0.00 0

0

100

200

300

400

500

600

700

rm

FIGURE 9g STEAM/LIQUID EJECTORS: PERFORMANCE PREDICTION CURVES

65

800

86030



0.10 1.1

h. rc = 0.001 AR = 8.0

2.0

0.08

ESDU product release: 2006-01. For current status, contact ESDU. Observe Copyright.

AT Ks = 0.10 Km = 0.20 Kd = 0.15 CD = 1.00

3.0

0.06 N1

4.0 5.0

0.04

6.0

0.02 7.0

0.00 0

0

8.0

100

200

300

400

500

600

700

rm

FIGURE 9h STEAM/LIQUID EJECTORS: PERFORMANCE PREDICTION CURVES

66

800

86030

ESDU product release: 2006-01. For current status, contact ESDU. Observe Copyright.



0.8

AT 1.1

0.6

2.0

N1

i. r c = 0.005 A R = 1.1

K s = 0.10 K m = 0.20 K d = 0.15 C D = 1.00

3.0 0.4

4.0 5.0 6.0

0.2 7.0 8.0 0.0

0

2

4

6

8

rm FIGURE 9i STEAM/LIQUID EJECTORS: PERFORMANCE PREDICTION CURVES

67

10

86030

 AT 1.1

ESDU product release: 2006-01. For current status, contact ESDU. Observe Copyright.

0.4

K s = 0.10 K m = 0.20 K d = 0.15 C D = 1.00

j. r c = 0.005 A R = 2.0

2.0 0.3 3.0

N1 0.2

4.0 5.0 6.0

0.1 7.0 0.0

0

8.0

10

20

30

40

50

60

70

80

90

rm FIGURE 9j STEAM/LIQUID EJECTORS: PERFORMANCE PREDICTION CURVES

68

100

86030

 0.24 0.22

AT 1.1

k. rc = 0.005 AR = 3.0

0.20 2.0 Ks = 0.10 Km = 0.20 Kd = 0.15 CD = 1.00

ESDU product release: 2006-01. For current status, contact ESDU. Observe Copyright.

0.18 0.16

3.0

0.14 N1

4.0 0.12 0.10 0.08 0.06

5.0 6.0 7.0 8.0

0.04 0.02 0.00 0 0

20

40

60

80

100

120

140

160

180

200

rm

FIGURE 9k STEAM/LIQUID EJECTORS: PERFORMANCE PREDICTION CURVES

69

86030

 0.20

AT 1.1

l. rc = 0.005 AR = 4.0

0.18 0.16

Ks = 0.10 Km = 0.20 Kd = 0.15 CD = 1.00

2.0

ESDU product release: 2006-01. For current status, contact ESDU. Observe Copyright.

0.14 0.12 N1

0.10

3.0

4.0

0.08

5.0

0.06

6.0 7.0 8.0

0.04 0.02 0.00 0 0

20

40

60

80

100

120

140

160

180

200

220

240

260

rm

FIGURE 9l STEAM/LIQUID EJECTORS: PERFORMANCE PREDICTION CURVES

70

86030

 0.18

AT 1.1

m. rc = 0.005 AR = 5.0

0.16

Ks = 0.10 Km = 0.20 Kd = 0.15 CD = 1.00

ESDU product release: 2006-01. For current status, contact ESDU. Observe Copyright.

0.14 2.0 0.12 N1

0.10 0.08 0.06

3.0 4.0 5.0 6.0

0.04 0.02 0.00 0 0

7.0

8.0

25

50

75

100

125

150

175

200

225

250

275

rm

FIGURE 9m STEAM/LIQUID EJECTORS: PERFORMANCE PREDICTION CURVES

71

300

86030

 0.12

AT 1.1

0.11

n. rc = 0.005 AR = 6.0

2.0

Ks = 0.10 Km = 0.20 Kd = 0.15 CD = 1.00

0.10

ESDU product release: 2006-01. For current status, contact ESDU. Observe Copyright.

0.09 0.08

3.0

0.07 N1

4.0 0.06 0.05

5.0

0.04

6.0 7.0

0.03

8.0

0.02 0.01 0.00 0 0

25

50

75

100

125

150

175

200

225

250

275

300

325

350

rm

FIGURE 9n STEAM/LIQUID EJECTORS: PERFORMANCE PREDICTION CURVES

72

86030

 0.11

AT 1.1

o. rc = 0.005 AR = 7.0

0.10 0.09

Ks = 0.10 Km = 0.20 Kd = 0.15 CD = 1.00

2.0

ESDU product release: 2006-01. For current status, contact ESDU. Observe Copyright.

0.08 0.07 N1

3.0

0.06 4.0 0.05 0.04

5.0 6.0 7.0

0.03 8.0 0.02 0.01 0.00 0 0

25

50

75

100

125

150

175

200

225

250

275

300

325

rm

FIGURE 9o STEAM/LIQUID EJECTORS: PERFORMANCE PREDICTION CURVES

73

350

375

86030

 0.11 0.10

AT

p. rc = 0.005 AR = 8.0

1.1

Ks = 0.10 Km = 0.20 Kd = 0.15 CD = 1.00

0.09

ESDU product release: 2006-01. For current status, contact ESDU. Observe Copyright.

0.08

2.0

0.07 N1

0.06

3.0

0.05

4.0

0.04 0.03

5.0 6.0 7.0

0.02

8.0

0.01 0.00 0 0

25

50

75

100

125

150

175

200

225

250

275

300

325

350

375

rm

FIGURE 9p STEAM/LIQUID EJECTORS: PERFORMANCE PREDICTION CURVES

74

400

86030

 1.0

q. rc = 0.010 AR = 1.1

0.9

Ks = 0.10 Km = 0.20 Kd = 0.15 CD = 1.00

AT 0.8

1.1

ESDU product release: 2006-01. For current status, contact ESDU. Observe Copyright.

0.7 2.0

0.6 N1

0.5 3.0 0.4

4.0 5.0 6.0

0.3 0.2 0.1

7.0

0.0 0 0.0

0.5

8.0 1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

6.0

6.5

rm

FIGURE 9q STEAM/LIQUID EJECTORS: PERFORMANCE PREDICTION CURVES

75

7.0

86030

 0.45 0.40

AT 1.1

r. rc = 0.010 AR = 2.0

Ks = 0.10 Km = 0.20 Kd = 0.15 CD = 1.00

0.35 ESDU product release: 2006-01. For current status, contact ESDU. Observe Copyright.

2.0 0.30 N1

0.25

3.0

0.20

4.0 5.0

0.15

6.0

0.10 0.05 0.00 0 0

7.0

5

8.0

10

15

20

25

30

35

40

45

50

55

60

rm FIGURE 9r STEAM/LIQUID EJECTORS: PERFORMANCE PREDICTION CURVES

76

65

70

86030

 0.26

AT

1.1

s. rc = 0.010 AR = 3.0

0.24 0.22

Ks = 0.10 Km = 0.20 Kd = 0.15 CD = 1.00

2.0

ESDU product release: 2006-01. For current status, contact ESDU. Observe Copyright.

0.20 0.18 0.16

3.0

0.14 N1 0.12 0.10

4.0 5.0 6.0

0.08 0.06

7.0 8.0

0.04 0.02 0.00 0 0

10

20

30

40

50

60

70

80

90

100

110

120

130

140

rm

FIGURE 9s STEAM/LIQUID EJECTORS: PERFORMANCE PREDICTION CURVES

77

86030

 0.20 0.18

ESDU product release: 2006-01. For current status, contact ESDU. Observe Copyright.

0.16

t. rc = 0.010 AR = 4.0

AT 1.1

Ks = 0.10 Km = 0.20 Kd = 0.15 CD = 1.00

2.0

0.14 0.12

3.0

N1 0.10

4.0

0.08

5.0

0.06

6.0

0.04 0.02 0.00 00

7.0

10

8.0

20

30

40

50

60

70

80

90

100

110

120

130

140

150

rm FIGURE 9t STEAM/LIQUID EJECTORS: PERFORMANCE PREDICTION CURVES

78

160

86030

 0.18 0.16

AT

u. rc = 0.010 AR = 5.0

1.1

Ks = 0.10 Km = 0.20 Kd = 0.15 CD = 1.00

ESDU product release: 2006-01. For current status, contact ESDU. Observe Copyright.

0.14 0.12 0.10 N1 0.08 0.06 0.04

2.0

3.0 4.0 5.0 6.0 7.0

8.0 0.02 0.00 0 0

20

40

60

80

100

120

140

160

180

200

rm FIGURE 9u STEAM/LIQUID EJECTORS: PERFORMANCE PREDICTION CURVES

79

220

86030

 0.13

AT

0.12 0.11

Ks = 0.10 Km = 0.20 Kd = 0.15 CD = 1.00

v. rc = 0.010 AR = 6.0

1.1

2.0

ESDU product release: 2006-01. For current status, contact ESDU. Observe Copyright.

0.10 0.09 0.08

N1

3.0

0.07 0.06

4.0

0.05

5.0

0.04 0.03

6.0 7.0 8.0

0.02 0.01 0.00 0 0

20

40

60

80

100

120

140

160

180

200

220

240

260

rm

FIGURE 9v STEAM/LIQUID EJECTORS: PERFORMANCE PREDICTION CURVES

80

86030

 AT 0.12 0.11

w . r c = 0.010 A R = 7.0

1.1

K s = 0.10 K m = 0.20 K d = 0.15 C D = 1.00

ESDU product release: 2006-01. For current status, contact ESDU. Observe Copyright.

0.10 0.09 2.0 0.08 0.07 N1

3.0

0.06 4.0 0.05 5.0 0.04

6.0 7.0

0.03

8.0 0.02 0.01 0.00 0

0

25

50

75

100

125

150

175

200

225

250

275

rm

FIGURE 9w STEAM/LIQUID EJECTORS: PERFORMANCE PREDICTION CURVES

81

300

86030

 AT 0.10

x. rc = 0.010 A R = 8.0

1.1 0.09 2.0

0.08

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Ks = 0.10 Km = 0.20 Kd = 0.15 CD = 1.00

0.07 3.0

0.06 N1 0.05

4.0

0.04 0.03

5.0 6.0 7.0

0.02

8.0

0.01 0.00 0

0

25

50

75

100

125

150

175

200

225

250

275

rm

FIGURE 9x STEAM/LIQUID EJECTORS: PERFORMANCE PREDICTION CURVES

82

300

86030

 APPENDIX A- GLOSSARY OF TERMS

CAVITATION INDEX:

number used to predict the onset of cavitation.

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CRITICAL OR CHOKED FLOW: the operating condition for maximum mass flow rate. COMPRESSION RATIO:

the ratio of the discharge pressure to the inlet pressure of the secondary fluid.

DEGREE OF SUBCOOLING:

the difference between the temperatures of the steam supply and secondary flow.

DRIVING FLUID (OR FLOW):

see primary fluid.

DRIVING NOZZLE:

see primary nozzle.

EJECTOR:

a device in which the kinetic energy of one fluid is used to drive another fluid.

INDUCED FLUID (OR FLOW):

see secondary fluid.

INJECTOR:

an alternative name for an ejector, often used to describe steam/liquid ejectors.

JET PUMP:

an alternative name for an ejector. Often used when the secondary flow is a liquid.

MASS FLOW RATIO:

the ratio of the secondary fluid mass flow rate to the primary steam mass flow rate.

MIXING CHAMBER:

the duct, usually cylindrical or conical, in which the turbulent mixing of the primary and secondary flows takes place.

MOTIVE NOZZLE MOTIVE FLOW:

AND see primary nozzle and primary flow.

PRIMARY FLUID (OR FLOW):

the steam that is input into the ejector with high energy, generally through a nozzle.

PRIMARY NOZZLE:

the nozzle through which the primary flow enters the ejector.

SATURATED STEAM:

steam at the saturation temperature for a given pressure.

SECONDARY FLOW):

FLUID

(OR the fluid that is drawn into the ejector with low energy and is entrained by the primary fluid.

SUPERHEATED STEAM:

steam at a temperature above the saturation temperature for a specified pressure.

VAPOUR BINDING:

the operating condition in which liquid in the discharge from the mixing chamber of a steam/liquid ejector contains some uncondensed steam.

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86030

APPENDIX B- BASIC THEORY

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Theoretical results are presented separately for the primary nozzle (Section B1), for steam/liquid ejectors (Section B2) and for steam/gas ejectors (Section B3). B1.

PRIMARY NOZZLE

B1.1

Assumptions (1)

The steam supplied to the nozzle is at, or above, saturation temperature.

(2)

No condensation occurs in the nozzle.

(3)

The steam behaves as an ideal gas with constant γ′ and R′ .

(4)

The flow is one-dimensional.

(5)

The flow is adiabatic.

(6)

The flow in the nozzle is critical, i.e. the static pressure ratio across the nozzle exceeds a value of 1.84.

Departures from assumptions (1) - (5) are accounted for by a discharge coefficient C D , defined by m· ′ = C D m· ′ ideal . B1.2

Basic Theory Mass Flow Conservation The equation for conservation of mass flow through the nozzle is m· ′ = ρ th ′A th U th ′ = ρ e ′A e U e ′

(B1.1)

and, assuming adiabatic flow through the nozzle, T t1 ′ = T te ′ . Equation (B1.1) may be rearranged as shown in most textbooks on gas dynamics to give the mass flow rate through the nozzle as γ′ + 1

--------------p 1 A th γ′ 2 m· ′ = -------------- -----  --------------- γ′ – 1 .   T 1 R′ γ′ + 1

(B1.2)

The Mach number of the flow at the nozzle exit is related to the area ratio by: γ′ + 1 ----------------------Ae 1 2 γ′ – 1 2 ( γ′ – 1 ) . A T = -------- = --------- ---------------  1 + -------------- M e ′ 2   A th M e ′ γ′ + 1 2

84

(B1.3)

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86030

B2.

STEAM/LIQUID EJECTORS

B2.1

Assumptions

B2.2

(1)

The mixing chamber is a constant area duct. No significant mixing takes place between the nozzle exit and the start of the constant area section.

(2)

The steam and liquid streams form an annular flow in the mixing chamber. All of the steam has condensed by the exit from the mixing chamber, plane 4.

(3)

The secondary liquid is incompressible.

(4)

The wall thickness at the nozzle exit is zero.

(5)

The flow is one-dimensional.

(6)

The dynamic pressures in the inlet and outlet flows can be neglected.

Losses Departures from the idealisations listed in Section B2.1 are accounted for by loss coefficients which are assumed to be constant for a given ejector. Secondary inlet The loss coefficient can be expressed in terms of the pressure difference across the secondary inlet: p0 – pe ″ K s = ------------------------ – 1 . ½ρ″U e ″ 2

(B2.1)

Mixing chamber The mixing chamber loss coefficient is defined as K m = 4fL ⁄ D ,

(B2.2)

where f is the usual pipe friction factor, ∆p ⁄ 4 ( L ⁄ D )½ρU ″ 2 . e The loss coefficient is based on the liquid velocity at the primary nozzle exit, U e ″ . This velocity is representative of the liquid velocity along the length of the mixing chamber. Diffuser The loss coefficient in the diffuser is defined as p4 – p5 K d = --------------------- + 1 . 2 ½ρ″U 4

(B2.3)

85

 B2.3

86030 Basic Theory Mass Flow Conservation

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The mass flow conservation equations for the primary nozzle, secondary inlet and mixing chamber may be expressed as: m· ′ = ρ e ′A e U e ′ , m· ″ = ρ″ ( A m – A e )U e ″ and

( m· ′ + m· ″ ) = ρ″A m U 4 .

(B2.4) (B2.5) (B2.6)

It has been assumed that ρ f ′ ≈ ρ″ and that negligible error is introduced under most operating conditions. Momentum Conservation The loss coefficients for the secondary inlet and diffuser can be incorporated into the momentum conservation equations to give p 0 – p e ″ = ½ρ″U e ″ 2 ( 1 + K s ) and

p 5 – p 4 = ½ρ″U 4 ″ 2 ( 1 – K d ) .

(B2.7) (B2.8)

Momentum conservation in the mixing chamber can be expressed by [ m· ′U e ′ + m· ″U e ″ – ( m· ′ + m· ″ )U 4 – ½ρ″U e ″ 2 K m A m ] p 4 – p e ″ = ----------------------------------------------------------------------------------------------------------------------------------------- , Am

(B2.9)

assuming the primary flow is fully expanded so that p e ′ = p e ″ , as is usual in an on-design ejector. The overall pressure drop across the ejector, p 5 – p 0 , is given by p5 – p0 = ( p5 – p4 ) + ( p4 – pe ) + ( pe – p0 ) .

(B2.10)

Equations (B2.4) to (B2.9) can be substituted in Equation (B2.10) to yield the following equation for the pressure drop across the ejector:

86



86030 p5 – p0 N 2 = ------------------------½ρ e ′U e ′ 2 2

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( 1 + 2r m + r m ) = ------------------------------------------ r c1 ( 1 – K d ) 2 AR 2r m2r c1 r m2r c1 K m 2r c1 ( 1 + 2r m + r m2) 2 ----------------------------------------------------------------------------------------------------------+ – – + AR AR ( AR – 1 ) ( AR – 1 )2 A R2 r m2r c1 ( 1 + K s ) – ------------------------------------- , ( AR – 1 )2 where

(B2.11)

Am ρe ′ m· ″ r c1 = ------- , r m = ------- , and A R = ------- . ρ″ Ae m· ′

The dynamic pressure at the primary nozzle exit may be obtained from Equations (B1.1) and (B1.2), and is given by

½ρ e ′U e

′2

γ′ + 1 1 --------------p 1 M e ′γ′ 2  γ′ – 1 -------------------------------------------------- , = -------------------- --------------γ′ – 1  γ′ + 1 1 +  -------------- M e ′ 2 2A T  2 

(B2.12)

where M e ′ is given by Equation (B1.3) and A T = A e ⁄ A th . If the mass flow ratio, r m , is known, Equations (B2.11) and (B2.12) can be solved to determine the pressure rise p 5 – p 0 across the ejector. Alternatively, if this pressure rise is known, the mass flow ratio can be calculated from a rearranged form of Equation (B2.11):

r m2

r c1 ( 1 + K s + K m )A R 2 2r c1 A R ---------------------- – r c1 ( 1 + K d ) – -------------------------------------------------------- – r m [ 2r c1 ( 1 + K d ) ] ( AR – 1 ) (A – 1)2 R

2

+ [ 2A R – r c1 ( 1 + K d ) – N 2 A R ] = 0.

(B2.13) Equations (B2.11) and (B2.13) are used for both the design (Section 5.3) and performance prediction (Section 6.2) methods. The approximation, p e ′ ≈ p e ″ , is not strictly valid under off-design conditions, but introduces negligible error under typical ejector operating conditions.

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86030 Equations (B2.11) and (B2.13) can be expressed in terms of the parameters r c = ρ 1 ′ ⁄ ρ″ and N 1 = ( p 5 – p 0 ) ⁄ p 1 by means of the following relationships: γ′ + 1 2 γ′ – 1 --------------rc 2  γ′ – 1 1 +  -------------- M e ′  r c1 = ---------------- -------------- 2  M e ′A T  γ′ + 1

(B2.14)

γ′ + 1 1 --------------M e ′γ′ 2  γ′ – 1 -------------------------------------------- N 1 = N 2 -------------- --------------2 . γ′ – 1 1 +  -------------- M e ′ 2A T  γ′ + 1  2 

(B2.15)

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and

B3.

STEAM/GAS EJECTORS The subscript t , used to denote total values of pressure and temperature, is re-introduced in this section.

B3.1

B3.2

Assumptions (1)

The mixing chamber approximates to a constant area duct.

(2)

Mixing between the steam and secondary gas is complete by the end of the mixing chamber.

(3)

There is no heat exchange through the external wall of the ejector.

(4)

The wall thickness at the nozzle exit is zero.

(5)

The flow is one-dimensional.

(6)

The dynamic pressures of the secondary inlet and ejector outlet flows can be neglected.

Losses Departures from the idealisations listed in Section B3.1 are accounted for by loss coefficients. Secondary inlet A loss coefficient η s may be defined by p te ″ η s = ---------- . p t0 ′

(B3.1)

88



86030 Mixing chamber A momentum loss coefficient K m in the mixing chamber can be defined by momentum out = K m × (momentum in).

(B3.2)

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Diffuser A loss coefficient η d for the diffuser may be defined by p t5 η d = ------- . p t4 B3.3

(B3.3)

Basic Theory Secondary inlet mass flow The mass flow rate through the secondary inlet may be written: m· ″ = ρ e ″ ( A m – A e )U e ″ p te Me ″ γ″ = --------------- ( A m – A e ) ------ -------------------------------------------------------------------------- . γ″ + 1 R″ -----------------------T te ″ γ″ – 1 2 ( γ″ – 1 ) 2  1 + --------------- M e ″  2 

(B3.4)

Dividing by Equation (B1.2) for m· ′ and using the assumptions given in Section B3.1 and the loss coefficients defined in Section B3.2, yields ηs AT ( AR – 1 ) RR TR Me ″ - -------------- -------------------------------------------------------------------------, r m = ----------------------------------γ″ + 1 NP NS G2 γR -----------------------γ″ – 1 1 +  --------------- M e ″ 2 2 ( γ″ – 1 )  2  where γ′ + 1 -----------------------

2 G 2 =  --------------- 2 ( γ′ – 1 ) .  γ′ + 1 Mixing chamber: mass conservation Mass conservation across the mixing chamber may be expressed as: m· ′ + m· ″ = m· . e

e

4

89

(B3.5)



86030 Dividing by Equation (B1.2) for m· ′ , and using the assumptions given in Section B3.1 and the loss coefficients defined in Section B3.2, yields AR AT γR′T t1 M4 ( 1 + r m ) = --------------------- ----------------- ------------------------------------------------------------------- , γ″ + 1 η d N p G 2 Rγ′T t5 -----------------------( γ – 1 ) 2 2 ( γ″ – 1 ) 1 + ------------------ M 4 2

(B3.6)

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where γ′γ″ ( C PR + r m ) γ = ----------------------------------------( C PR γ″ + r m γ′ ) and ( C PR + r m ) (γ – 1) R = ------------------ c p ″ ------------------------------ . ( 1 + rm ) γ Mixing chamber: momentum conservation Momentum conservation across the mixing chamber may be expressed by K m [ p e ′A e + p e ″ ( A m – A e ) + m· ′U e ′ + m· ″U e ″ ] = p 4 A m + ( m· ′ + m· ″ )U 4 .

(B3.7)

Dividing by Equation (B1.2) for m· ′ , and using the assumptions given in Section B3.1 and the loss coefficients defined in Section B3.2, gives K m η s AT ( AR – 1 ) R′ Km A T R′ 1 1 ------------- ----- -------------------------------------------------------- + --------------------------------------- ----- ----------------------------------------------------------γ′ γ″ N G 2 γ′ N G γ′ ---------------------------------p s 2 γ′ – 1 ) γ″ – 1 )  1 + (--------------- 1 + (----------------- M e ′ 2 ( γ′ – 1 ) - M e ″ 2 ( γ″ – 1 )     2 2 Me″ Me ′ γ″R ″ + K m γ′R′ -------------------------------------------------- + K m r m ------------ ---------------------------------------------------½ ½ TR  –1 γ″ – 1  1 + γ′ 1 + --------------- M e ″ 2 -------------- M e ′ 2     2 2 AR AT T t5 M4 R′ 1 = --------------------- ----- ---------------------------------------------- + ( 1 + r m ) γR ------- ---------------------------------------------- . (B3.8) T t1  ½ ½ η d G N p γ′  γ–1 γ–1 2 1 + ------------ M 42  1 + ------------ M 42      2 2

90



86030 Mixing chamber: energy conservation Energy conservation across the mixing chamber may be expressed by m· e ′c p ′T te ′ + m· e ″c p ″T te ″ = ( m· ′ + m· ″ )c p T t4 .

(B3.9)

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Using the assumptions given in Section B3.1, this equation may be rewritten

B3.4

T t5 c p ″ ( C PR T R + r m ) ------- = ------- ------------------------------------- . T t1 cp TR ( 1 + rm ) Solution Technique

(B3.10)

Equations (B3.5), (B3.6), (B3.8) and (B3.10) together describe the performance of a steam/gas ejector. Knowing two of the three performance parameters N p, N s and r m , they can be solved for the third. Equation (B3.10) can be substituted directly into Equation (B3.6). The resulting equation together with Equations (B3.5) and (B3.8) form a set of three equations in M e ″, M 4 and the unknown performance parameter.

91



86030 THE DEVELOPMENT OF THIS DATA ITEM The work on this particular Item was monitored and guided by the following Working Party:

ESDU product release: 2006-01. For current status, contact ESDU. Observe Copyright.

Mr J.W.E. Campbell Dr D.J. Cockrell Mr R.C. Cowie Dr R.S. Sylvester Mr A.W. Wakefield

– – – – –

Babcock Power Ltd University of Leicester Graham Manufacturing Ltd British Hydromechanics Research Association Wakefield and Imberg

on behalf of the Internal Flow Panel which has the following constitution: Chairman Mr N.G. Worley

– Babcock Power Ltd

Members Dr T.W. Broyd Mr D.A. Campbell Mr J. Campbell Dr D.J. Cockrell Dr C.J. Clark Dr J.A. Eaton Prof. D.H. Freeston* Prof. J.L. Livesey Dr A. Moore

– – – – – – – – –

Atkins Research and Development Rolls-Royce Ltd, Derby Ove Arup and Partners University of Leicester BP International Ltd GEC Research Ltd, Whetstone Auckland University, New Zealand University of Salford British Hydromechanics Research Association.

The work on this Item was carried out as part of the programme for the Internal Flow Group of ESDU. The initial assessment of the available information and the subsequent development of the Item was undertaken by: Dr K.J. Sene Dr S.J. Murray

– Atkins Research and Development, Epsom, Surrey, UK – Atkins Research and Development, Epsom, Surrey, UK

and sponsored by ESDU.

*

Corresponding Member

92