Giuseppe Grazzini · Adriano Milazzo Federico Mazzelli

Ejectors for E� cient RefrigerationDesign, Applications and Computational Fluid Dynamics

Ejectors for Efficient Refrigeration

Giuseppe Grazzini • Adriano Milazzo •

Federico Mazzelli

Ejectors for EfficientRefrigerationDesign, Applications and Computational FluidDynamics

Giuseppe GrazziniDepartment of Industrial EngineeringUniversity of FlorenceFlorence, Italy

Adriano MilazzoDepartment of Industrial EngineeringUniversity of FlorenceFlorence, Italy

Federico MazzelliDepartment of Industrial EngineeringUniversity of FlorenceFlorence, Italy

ISBN 978-3-319-75243-3 ISBN 978-3-319-75244-0 (eBook)https://doi.org/10.1007/978-3-319-75244-0

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Preface: Past, Present, and Future of EjectorRefrigeration

The history of ejector refrigeration is tightly nestled in the broader history ofrefrigeration. When the steam jet chiller first appeared, many different refrigerationcycles had already been used for both refrigeration and air conditioning purposes.However, the steam jet refrigerator had the advantage that it could run using exhauststeam from any source (steam engines, industrial or chemical processes, etc.).Therefore, starting in 1910, steam jet refrigeration systems found use in breweries,chemical factories, theatres, ships, and trains.

Despite the promising start, the use of supersonic ejectors for refrigerationapplications almost ended when Thomas Midgley Jr. and his associates introducedthe first synthetic refrigerants during the 1930s. These gases could completelyovercome the problems that hampered the large-scale commercialization of vaporcompression systems. Meanwhile, steam plants became less common and electricenergy was made broadly available in developed countries. Therefore, the steam jetcycles were gradually replaced by more efficient vapor compression systems(although some east European countries such as Czechoslovakia and Russiamanufactured these systems as late as 19601).

Despite the scarce success in refrigeration applications, the research on super-sonic ejectors did not stop, given their widespread use in many other fields (as will beillustrated in Chap. 1). During the first half of the twentieth century, huge theoreticalprogresses were made in the understanding of the principles of aerodynamics appliedto supersonic flows. The developments were pioneered by scientists like Ernst Mach,Ludwig Prandtl and his dynasty of brilliant students: Theodore von Karman,Theodore Meyer, Adolf Busemann, Hermann Schlichting and many others. By theend of the 1950s, Joseph H. Keenan and his colleagues at MIT had perfected thetheory of mixing inside supersonic ejectors. Many design concepts have beendeveloped since then, and systematic experimental activities have been performedto optimize system design.

1Arora, C.P., 2003. Refrigeration and Air Conditioning, Tata-McGraw-Hill.

vii

The oil crisis that followed the YomKippur War in 1973 and the rise in awarenessof ozone depletion in 1974 laid out the groundwork for a revival of ejector systems.These two events, in conjunction with the increase in refrigeration demand andthe appearance of stringent regulations on ozone depletion and global warming(Montreal and Kyoto Protocol in 1987 and 1992, respectively), prompted researchtoward new, economical, and environmentally safe technologies. As a result, ejectorrefrigeration experienced a renewed interest, and a great number of research centersworldwide started studies in this field.

In recent years, thermodynamic optimization has been extensively pursued onejectors and ejector chillers. Meanwhile, CFD has taken a leading role in the analysisof the internal flows within supersonic ejectors. Starting from a global analysis of theejector behavior in terms of entrainment ratio and pressure lift, CFD simulationshave been specialized on the study of complex internal phenomena, such as mixingand shock trains. These numerical results are now generating increasingly accurateresults thanks to the appearance of new, sophisticated flow visualization studies.Meanwhile, a large number of configuration alternatives to the standard ejector cyclehave been proposed, which include “passive” systems, cycles with multiple parallelejectors, multiple nozzles, annular nozzles, and so forth.

Yet, vapor compression and, to a lesser extent, absorption systems stillcompletely dominate the refrigeration market. Quite surprisingly, the ejector designfrom a macroscopic point of view seems relatively unchanged in the last decades.Innovative proposals, like the above-cited unconventional configurations orimproved design procedures, didn’t impact the fundamental structure of the ejectorchiller as would have been expected. Industries rely on their consolidated experienceand proceed with understandable caution on the path of innovation, while the hugeamount of scientific literature produced seems somewhat distant from practicalapplication.

To date, the use of ejectors to enhance the efficiency of conventional refrigerationcycles seems to be the most promising development. Ejector expansion cycles areemerging as enabling technology for CO2 vapor compression cycles, as proven bythe increased interest manifested by leading global players in the refrigeration arena(e.g., Danfoss or Carel). Other refrigerants (ammonia, hydrocarbons, or HFO) allowmoderate losses in the expansion valve, and hence the insertion of additionalcomponents to increase the system efficiency could seem questionable. However,as the size increases, even a growth in efficiency below 10% may well be worth of amodest complication. In principle, the cost of a mass-produced ejector could beacceptable in comparison with other basic components of the refrigeration system.As will be shown in Sect. 1.3, the insertion of an ejector may be beneficial to thecreation of an intermediate evaporation level or may allow liquid circulation inflooded evaporators. As soon as these new possibilities are fully pursued and theejector effectively integrated with all other functions within the refrigeration system(e.g., regulation and control), we believe that the diffusion of ejectors for expansionrecovery will become widespread. Also, the integration of ejectors in absorptionsystems seem to produce significant results without requiring too heavy

viii Preface: Past, Present, and Future of Ejector Refrigeration

modifications to the cycle even if, to the author’s knowledge, there are no attempts ofcommercialization yet.

The future of supersonic ejectors in heat-powered refrigeration cycles, on theother hand, seems to be somewhat more uncertain. Research conducted over theyears at our department suggests that ejector chillers can be easily manufactured withlow-cost, off-the-shelf components (apart from the ejector itself, which must betailored to the specific application under consideration). Unfortunately, the weakpoint of this type of system is still represented by the low thermodynamic efficiency.As an order of magnitude, one could set a target COP ¼ 0.7, which is currentlyreached by commercial lithium bromide absorption chillers, but significantly higherthan the typical values reported for ejector chillers in the same working conditions.

The use of solar energy to power ejector cycles seems a logical outcome but mustbe carefully evaluated. In a recent review, Kim and Infante Ferreira (2014)2 make acomparison between solar thermal and solar electric cooling technologies, both interms of thermodynamic performances and economic feasibility. The results showthat, at present, the cheapest solution is represented by the PV panels coupled withcommercial vapor compression chiller. This result is largely due to the recentdramatic decrease in PV cost and to the large production volumes that make vaporcompression chillers very inexpensive.

However, solar thermal collectors have also seen a significant decrease of theircost, mainly due to the large amount of collectors manufactured and installed inChina. In particular, evacuated tube collectors, thanks to their reduced heat loss,perform better at relatively high temperatures and have reached a high market share.These could be profitably adopted to power heat-driven refrigerators.

Waste heat recovery may represent another field for successful application. Heatrecovery in industries, combined heating, power and cooling, or district heating andcooling may all potentially profit from the application of ejector chillers. Wheneverwaste heat is directly available in form of water vapor at moderate temperature, thesteam ejector is undoubtedly the cheapest and simplest option.

An overturn of the current supremacy of absorption chillers on the heat-poweredrefrigeration market is unlikely and undesirable, but ejector refrigeration could offeran effective alternative in all cases where simplicity, reliability, and low investmentcosts are required. From a practical point of view, the key parameter in anyrefrigeration system is the total cost per unit cooling load. If the input thermal energyhas low or zero cost (e.g., waste heat or solar power), the cost of cooling is mainlyrelated to the investment, which therefore is the main objective function to minimize.

Compared with lithium bromide/water absorption refrigerators, ejector cyclesmay avoid problems of internal corrosion and crystallization of the solution. Ammo-nia/water absorption refrigerators, on the other hand, use a toxic fluid, while ejectorchillers may use nontoxic, nonflammable, and environmentally safe refrigerants

2Kim, D.S., Infante Ferriera, C.A., 2014. Solar refrigeration options—a state-of-the-art review.International Journal of Refrigeration, 31, 3–15.

Preface: Past, Present, and Future of Ejector Refrigeration ix

(e.g., water). These advantages potentially offer significant savings in terms ofcapital and life cycle maintenance costs.

Ejector refrigeration may also have a chance of playing a role in specific marketslike developing countries, where access to electric power is limited and technicalexpertise for the maintenance and reparation of standard compression and absorptioncycles is lacking. Other opportunities may hopefully arise in the future.

This book is an attempt to review ideas, techniques, results, and open issues,combining information from the open literature and from the industry. It is intendedas a bridge between the extensive collection of scientific papers appearing on therelevant journals and the practical handbooks that have been published in the past,extending also toward the information published by the manufacturers. As such, itshould promote and stimulate the discussion between the different players in therefrigeration arena and the experts of ejectors, including those who come fromcompletely different fields.

23rd December 2017, Florence, Italy Giuseppe GrazziniAdriano MilazzoFederico Mazzelli

x Preface: Past, Present, and Future of Ejector Refrigeration

Acknowledgments

The authors wish to thank Prof. Ian Eames for all the passionate and fruitfuldiscussions about ejectors that inspired us while writing this book. Another verygood friend, Prof. Yann Bartosiewicz, has shared with us many interesting ideas.Prof. Srinivas Garimella and Adrienne B. Little have also inspired us with someoriginal proposals. Last but not least, Prof. Konstantin E. Aronson and his coworkersDmitry V. Brezgin and Ilia Murmanskii have been involved in our work andcontributed with original ideas.

Frigel S.p.A. has supported us technically and economically throughout all theseyears, and we are very grateful to Michele Livi, who has been responsible for theejector project.

Since 2016, the authors have participated in a “PRIN” research project (funded bythe Italian Ministry of University and Research for strategic national projects) named“Clean Heating and Cooling Technologies for an Energy Efficient Smart Grid” thatgroups eight Italian Universities working on refrigeration.

Special thanks also go to those people who belong or have been part of ourresearch group and involved in our research on ejectors: Andrea Rocchetti,Francesco Giacomelli, Furio Barbetti, Jafar Mahmoudian, Simone Salvadori,Dario Paganini, and Samuele Piazzini.

xi

Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Working Principle of Ejectors . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1.1 Ejectors as Components of Refrigeration Systems . . . . . . . 31.2 Historical Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.3 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.3.1 Refrigeration Applications . . . . . . . . . . . . . . . . . . . . . . . . 131.4 Closure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2 Physics of the Ejectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.1 Influence of Fluid Properties on Ejector Behavior . . . . . . . . . . . . . 212.2 Supersonic Expansion and Compression . . . . . . . . . . . . . . . . . . . . 27

2.2.1 Nozzles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272.2.2 Diffusers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

2.3 Entrainment and Mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352.4 Supersonic Condensation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

2.4.1 Phase Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402.4.2 Nucleation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 462.4.3 Droplet Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 532.4.4 Condensing Nozzle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

2.5 Flashing Ejectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60Appendix A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

Spontaneity of an Isothermal and Isobaric Process . . . . . . . . . . . . 65References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

3 Ejector Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 713.1 Zero-Dimensional Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

3.1.1 Huang et al. Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 723.1.2 ESDU Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

xiii

3.2 One- and Two-Dimensional Design . . . . . . . . . . . . . . . . . . . . . . . 833.2.1 Nozzles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 833.2.2 CRMC Diffuser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 853.2.3 Improvement of the CRMC Procedure . . . . . . . . . . . . . . . 89

3.3 Alternative Configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 903.3.1 Nozzle Modifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . 903.3.2 Multistage Configurations . . . . . . . . . . . . . . . . . . . . . . . . 913.3.3 Passive Configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

3.4 Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 943.4.1 Ejector Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 953.4.2 Ejector Irreversibilities . . . . . . . . . . . . . . . . . . . . . . . . . . . 1013.4.3 Ejector Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

3.5 Ejector Chiller Efficiency and Optimization . . . . . . . . . . . . . . . . . 109References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

4 Ejector CFD Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1174.1 Single-Phase Ejectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

4.1.1 Numerical Aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1174.1.2 Turbulence Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1234.1.3 Compressibility and 3D Effects . . . . . . . . . . . . . . . . . . . . 1264.1.4 Wall Friction and Heat Transfer . . . . . . . . . . . . . . . . . . . . 129

4.2 Condensing Ejectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1354.2.1 Numerical Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . 1354.2.2 Ejector Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1394.2.3 Modeling Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . 144

4.3 Concluding Remarks: The Need for Validation . . . . . . . . . . . . . . . 146References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147

5 Experimental Activity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1515.1 Testing of Ejectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1515.2 Flow Visualization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154

5.2.1 Shocks Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1555.2.2 Mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1585.2.3 Velocity Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163

5.3 The DIEF Ejector Chiller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172

6 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177

xiv Contents

List of Symbols: Global

Latin letters Greek lettersa Speed of sound [m s�1] or Van der Waals

constant [m5 kg�1 s�2]α Volume fraction [�]

A Cross section [m2] β Mass fraction [�]

b Van der Waals constant [m3 kg�1] γ Specific heat ratio [�]

B Second virial coefficient [m3 kg�1] (4) Γ Liquid mass generation rate[kg m�3 s�1]

cp, cv Specific heat capacity [J kg�1 K�1] δω Vorticity thickness [m]

C Third virial coefficient [m6 kg�2] δ0 Mixing layer spreading rate

Ċ Molecules condensation rate [n. molecules s�1] ε Turbulence dissipation rate[m2 s�3]

d Primary nozzle diameter [m] η Efficiency [�] or droplets perunit volume mixture [m�3]

D Mixer/diffuser diameter [m] θ Expansion ratio

e Specific internal energy [J kg�1] Θ Velocity ratio

E Internal energy [J] Λ Square root of density ratio

Ė Molecules evaporation rate [n. molecules s�1] μ Dynamic viscosity [kg m�1 s�1]

Ėx Exergy flux [W] ν Cinematic viscosity [m2 s�1]

f Darcy friction factor [�] ξ Geometric ratio or Kantrowitznon-isothermal correction

F Helmholtz free energy [J] ρ Density [kg m�3]

g Gravity acceleration [m s�2] or specific Gibbsfree energy [J kg�1]

ς Compression ratio

G Gibbs free energy [J] σ Surface tension [J m�2]

h Specific enthalpy [J kg�1] τ Shear stress [Pa]

hlv Latent heat [J kg�1] υl Liquid kinematic viscosity[m2 s�1]

İ Nucleation current [n. molecules s�1] φss Supersaturation degree

J Nucleation rate [s�1 m�3] φsc Supercooling degree

(continued)

xv

k Turbulence kinetic energy [m2 s�2] or thermalconductivity [W m�1 K�1]

ϕ Loss coefficient

kb Boltzmann constant [J K�1] Φ Generic flux

Ka Average Roughness Height [m] ω Entrainment ratio [�], specificdissipation rate [s�1]

Krms Root mean squared roughness [m] SubscriptsKsg Equivalent sand-grain roughness [m] 1 Undisturbed, isentropic flow

region

l Molecular mean free path [m] A Condenser exit

L Duct length [m] C Condenser, discharge

m Mass [kg] c Critical droplet

mm Mass of one molecule [kg] crit Fluid critical point, criticalejector pressure

_m Mass flow rate [kg s-1] CS Condenser source (externalcircuit)

_m v Mass velocity [kg m�2 s�1] d Droplet

M Mach number D Discharge

Mc Convective Mach number e Nozzle exit (ESDU procedure)

Mmol Molar mass E Entrained fluid, evaporator

n Number of droplets per unit mass of mixture[kg�1]

ES Evaporator source (externalcircuit)

nx Droplet size distribution eff Effective ¼ laminar + turbulent

P Pressure [Pa] f Refrigeration

q Specific heat power [W kg�1], heat transferrate per unit area [W m�2]

ff Flat film

qC, qE Accommodation factors g Generator

Q Heating or cooling energy [J] G Motive fluid, generator_Q Heating or cooling power [W]. GS Generator source (external

circuit)

r Radial coordinate [m], radius [m] in Input

R Specific gas constant [J kg�1 K�1] irr Irreversible

s Specific entropy [m2 s�2 K�1] l Liquid

S Entropy [J kg�1] m Mixing section, mixed flow,mixture, or molecule

Sx Surface of a liquid cluster with x molecules[m2]

p Primary flow, primary nozzle

t Time [s] rev Reversible

T Temperature [K] s Secondary flow

u Velocity [m s�1] sat Saturation

U Time-averaged velocity [m s�1] sh Superheating

v Specific volume [m3 kg�1] sub Subcooling

V Volume [m3] t Turbulent, total/stagnationcondition

w Specific shaft work [J kg�1 s�1] th Throat

W Shaft work [J] v Vapor_W Shaft power [W] y Virtual secondary choke section

(continued)

xvi List of Symbols: Global

x Axial coordinate [m] or vapor quality ‘ Primary flow (ESDU procedure)

y Transversal or radial coordinate [m] “ Secondary flow (ESDUprocedure)

z Vertical coordinate [m]

AcronymCOP Coefficient of performance

CRMC Constant rate of momentum change

EEV Electronic expansion valve

ER Entrainment ratio

FP Feed pump

Gb Gibbs parameter

GWP Global Warming Potential

HTC Heat transfer coefficient [W m�2 K�1]

N.B.P. Normal boiling point

NXP Nozzle exit plane

List of Symbols: Global xvii

Chapter 1Introduction

1.1 Working Principle of Ejectors

The basic scheme of an ejector is shown in Fig. 1.1. The shape and proportioning ofthe parts are purely indicative. The motive (or “primary”) fluid is fed through anozzle which, in most cases, is shaped as a converging/diverging duct in order toaccommodate a supersonic flow at the exit. The entrained (or “secondary”) fluid isfed through the annular space that surrounds the primary nozzle. In this way, at thenozzle exit the two streams come in touch. Their velocities are highly different, andhence a transfer of momentum accelerates the secondary and decelerates the primaryflow. We may imagine that a central core of primary flow and a lateral shell ofsecondary flow remain substantially unaffected, while the mixing takes place in anintermediate zone shaped as a cylindrical wedge, where turbulent shear stress pro-duces a velocity distribution that grows steeply toward the ejector axis. Actually, ifthe primary flow is supersonic, a sequence of oblique shocks will form along themixing zone, undergoing multiple reflections.

In modern applications, the secondary flow normally accelerates up to sonicspeed, and hence the whole mixed stream is supersonic. This mixed stream mustbe decelerated in order to convert its kinetic energy and finally reach the exitpressure, intermediate between the high value featured by the motive fluid at inletand the low value (“suction pressure”) of the entrained flow. This happens in asupersonic diffuser which follows the mixing zone and features a convergent-divergent or cylindrical-divergent shape.

It may be worth to point out that, from a functional point of view, the ejectorsubstitutes the much more complex assembly shown in Fig. 1.2. The ejector elim-inates the transmission of mechanical work from the expansion to the compressionvia the connecting shaft. Flow energy is transmitted directly from the two flows,avoiding rotating blades, bearings, lubrication, etc.

Obviously, the direct interaction between streams at different velocities intro-duces some limitations and specific losses. For example, the transition between

© Springer International Publishing AG, part of Springer Nature 2018G. Grazzini et al., Ejectors for Efficient Refrigeration,https://doi.org/10.1007/978-3-319-75244-0_1

1

super- and subsonic flow should ideally occur at the diffuser throat, and the velocityshould decrease continuously. This ideal condition happens for a single combinationof inlet/exit conditions and is hence practically unfeasible. In practice, the supersonicflow decelerates to subsonic velocity through a second shock train.

For stable operation the shock should take place downstream of the diffuserthroat. In this condition, the ejector flow rates are insensitive to any increase in thedischarge pressure. When discharge pressure increases, the shock moves toward theinlet side of the ejector, and, as it reaches the throat, the ejector experiences its mostefficient working condition.

However, any further small increase in the discharge pressure causes the flow tobecome subsonic in the throat, and hence the flow rate becomes dependent on thedischarge pressure. In this condition the ejector becomes unstable, i.e., an increase inthe discharge pressure produces a steep decrease in the ejector performance which,in most applications, is unacceptable. Many ejectors feature a cylindrical zoneupstream of the conical diffuser. They work in a stable condition as far as theshock occurs within this cylindrical zone.

A set of nondimensional parameters may be introduced:

• Entrainment ratio ω ¼ _ms= _mp, i.e., ratio between the secondary ( _ms ) and theprimary ( _mp) mass flow rates

• Compression ratio ζ ¼ PC/PE, i.e., ratio between the discharge (PC) and entrainedfluid (PE) pressures

• Expansion ratio θ ¼ PG/PE, i.e., ratio between the motive (PG) and entrained fluid(PE) pressures

Fig. 1.1 Schematic section of a supersonic ejector

Fig. 1.2 Functionallyequivalent assembly

2 1 Introduction

The aforementioned behavior may be described in terms of entrainment ratio asshown in Fig. 1.3. For a given combination of primary and secondary conditions, theline representing ω as a function of the discharge pressure PC has a first horizontalpart on the left and a second sharply decreasing part on the right. The dividing pointcorresponds to the critical discharge pressure Pcrit (or maximum discharge pressure)that is commonly taken as the limit operating condition. This critical point conju-gates the maximum entrainment ratio with the maximum compression ratio ζcrit.

When the entrained fluid pressure is lowered, e.g., from PE-3 to PE-1 at constantprimary fluid pressure PG-1, the operating curve moves left and downward, i.e., bothζcrit and ω decrease.

When the motive fluid pressure is raised, e.g., from PG-1 to PG-2 at constantentrained fluid pressure (θ increases), ω is lowered but ζcrit increases.

Another fundamental parameter is the area ratio between primary nozzle andmixer/diffuser throat flow sections. In supersonic conditions, these sections limitthe two flow rates and hence the entrainment ratio. We may hence introduce a ratioξ ¼ d/D between the nozzle throat diameter d and the diffuser throat diameter D. Asthis ratio increases, the motive flow increases and, as a rule, the compression ratiogrows. Correspondingly the entrainment ratio decreases, because the entrained flowremains constant or even decreases, as an increased portion of the diffuser throatsection is occupied by the primary flow.

1.1.1 Ejectors as Components of Refrigeration Systems

An ejector may be used as a fluid-driven compressor in a refrigeration system. Themotive fluid can be heated up in a “generator,” where it boils at constant pressure.The entrained fluid is vaporized at low pressure in an evaporator, in order to extractthe cooling load from a cold source. The mixed fluid at discharge is condensed and,once in the liquid state, is divided into two flows: the first goes to the evaporatorthrough an expansion valve, and the second is pumped back at suitable pressuretoward the generator (Fig. 1.4).

PE-3

PE-2

ω

PG-1

PG-2

PCPcrit

PE-1

Fig. 1.3 Map of theoperation for a supersonicejector

1.1 Working Principle of Ejectors 3

The ideal thermodynamic cycle, shown in Fig. 1.5 for steam on a pressure/enthalpy diagram, is actually comprised of two cycles sharing the condensationC-A: the motive cycle has a practically vertical left side (the pump absorbsvery little work in the case of water) and then has a constant pressure heating,vaporization, and superheating (if present) up to point G. From this point, the vaporexpands in the primary nozzle and mixes with the vapor exiting from the evaporatorat state E. In this simplified representation, the mixing process is assumed atconstant pressure, slightly below the evaporator exit pressure. Actually, in thereal process, the expansion of the entrained fluid before mixing is scarcely signifi-cant, and the mixing pressure is hardly distinguishable on the diagram from theevaporator pressure. The mixed fluid is then compressed in the diffuser up tothe condenser pressure and is discharged at state C. The entrained fluid exitingfrom the condenser in state A is expanded through a valve, and the process isassumed isoenthalpic.

The cycle efficiency may be calculated as a ratio between useful effect and inputpower:

COP ¼_Q f

_Qm þ _Wpump¼ ω

hE � hAhG � hA

ð1:1Þ

where _Qf is the cooling power, _Qm the motive heat power, and _Wpump the generatorfeed pump power.

The last part of Eq. 1.1 contains the entrainment ratio and a further ratio betweenthe enthalpy differences (hE � hA) and (hG � hA) that depends on the fluid andoperating conditions. Therefore, the global performance for fixed fluid and working

Fig. 1.4 Basic scheme of ejector-based refrigeration system

4 1 Introduction

conditions depend on the ejector entrainment ratio. This latter may be evaluated froman energy balance on the ejector and turns out to be

ω ¼ hG � hChC � hE

ð1:2Þ

i.e., the ratio between motive (hG � hC) and compression (hC � hE) enthalpydifferences. Ejector losses increase the enthalpy at condenser entrance hC, decreas-ing numerator and increasing denominator in Eq. 1.2.

As a heat-powered refrigeration system, the machine sketched in Fig. 1.4 may beused in addition to a heat engine for combined heating, cooling, and power gener-ation. For example, it may complement a district heating system in order to guaran-tee air conditioning in summer or produce refrigeration in civil or industrialenvironments from any form of waste heat. Alternatively, it may be used for“solar cooling” in conjunction with solar thermal panels having a suitably hightemperature or use other forms of renewable energy.

P [

MP

a]

100

75

50

25

0

125

150

1.50.5s 2.5 3.5 4.5 5.5 6.5

7.5

8.5kJ

kg K

G

CA

E

˚C

0.01

0.001

0 500 1000 1500 2000 2500 h [kJ/kg]

1

0.1

Fig. 1.5 Ideal thermodynamic cycle of refrigeration system using a steam ejector

1.1 Working Principle of Ejectors 5