Applied Energy 130 (2014) 679–684

Contents lists available at ScienceDirect

Applied Energy

journal homepage: www.elsevier .com/locate /apenergy

Experimental and numerical analysis of supersonic air ejector

http://dx.doi.org/10.1016/j.apenergy.2014.02.0230306-2619/� 2014 Elsevier Ltd. All rights reserved.

⇑ Corresponding author. Tel.: +86 29 82667753; fax: +86 29 82665359.E-mail address: chenweixiong@mail.xjtu.edu.cn (W. Chen).

Daotong Chong, Mengqi Hu, Weixiong Chen ⇑, Jinshi Wang, Jiping Liu, Junjie YanState Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, PR China

h i g h l i g h t s

� The performance and flow field inside ejectors are studied numerically and experimentally.� The pressures before the second shock position remain constant during the critical mode.� NXP has an optimal value for entrainment ratio, but no effect on the critical discharged pressure.

a r t i c l e i n f o

Article history:Received 19 November 2013Received in revised form 28 January 2014Accepted 10 February 2014Available online 28 February 2014

Keywords:Air ejectorEntrainment ratioShockStatic wall pressure

a b s t r a c t

The present paper performs experimental and numerical investigations on the global performance andinternal flow of a supersonic air ejector. The effects of operation parameters and geometrical factor onthe air ejector performance have been analyzed. The results show that: the static wall pressure andaxisymmetric line static pressure remain constant in critical mode under different discharged pressures,but they both increase in sub-critical mode with the increase of the discharged pressure. The shockposition of the mixed fluid moves upstream in critical mode. The second shock position disappears insub-critical mode. The experimental and numerical results indicate that there exists an optimal nozzleexit position (NXP) corresponding to maximum entrainment ratio, but the critical value of dischargedpressure is almost independent of NXP.

� 2014 Elsevier Ltd. All rights reserved.

1. Introduction

Supersonic ejector is a simple mechanical device where twogases are allowed to mix and recompress. The primary gas withhigh total energy can transfer part of its mechanical energy tothe secondary gas with low energy in supersonic ejector withoutany moving parts. Today, in view of pressures for protecting theenvironment, ejectors are becoming popular in industrial fieldsas an energy saving and emission reduction technique [1]. Weare using them in many engineering fields, such as heat pump inthe district-heating system [2], pressure booster in natural gasindustry [3,4]. The steam jet refrigeration is the most widely useddevice because of its relative simplicity and low capital cost com-pared to an absorption refrigerator, and the most important benefitis that the ejector refrigeration system could be powered by thelow-grade heat [5,6].

Nevertheless the low performance in present conditions is themain problem, which primarily limits the widespread use in indus-try. The ejector performance is greatly affected by the mixingprocess between primary flow and secondary flow. Therefore, it

is very necessary to investigate the mixing mechanism of ejectorin order to improve the ejector performance.

Two mixing models about ejector mixing process wereproposed by Keenan et al. [7,8]. The first mixing model is calledas constant area model, assuming that the gas obeys the law ofideal gas and the flow is isentropic. The second model named con-stant pressure model has been widely accepted and developed bymany researchers, and widely used due to its superior perfor-mance. The choking phenomenon was first proposed by Mundayand Bagster [9]. They proposed that the high and the low pressureflows reached the same pressure at some place inside the mixingchamber, which is named as an effective area. Huang et al. [10] fur-ther proposed that the effective area was located in the constantarea section, and found out that the effective area position wasaffected by operation conditions. Based on this assumption, their1D model could accurately calculate the entrainment ratio whenthe discharged pressure was less than critical discharged pressure[11]. Later, Zhu et al. [12] proposed a 2D exponential model topredict the velocity distribution in ejector, however the pressureis still assumed to be uniform in the radial direction. Zhang et al.[13] explored the behavior of direct flow induction based onpressure exchange utilizing supersonic wave structure in acrypto-steady mode, their results indicated that very high

Nomenclature

d diameter, mmL Length, mmm mass flow rate, kg/sNXP nozzle exit position, mmP pressure, MPaS generalized sourcet time, sa entrainment ratio, %U generalized diffusion coefficient

q density, kg/m3

u generalized variable

SubscriptP primary air flowS secondary air flowD discharged air flow

680 D. Chong et al. / Applied Energy 130 (2014) 679–684

compressor–expander efficiencies are possible even in the pres-ence of strong supersonic wave structure. Although these modelsare helpful to predict the ejector performance, they cannot accu-rately predict the internal flow process along the ejector becauseof the one-dimensional model.

To study the mixing mechanism of ejectors, researchers focusedon the local phenomenon of ejector by experimental study. Desev-aux et al. [14] paid their attention to investigate the flow fields in-side the ejector by experimental work. They obtained thecenterline static pressure through a slide measuring system. Then,Desevaux [15] obtained the mixing zone roughly using Rayleighscattering method. Subsequently, Desevaux et al. [16] applied lasertomography method to study the choking phenomena, and gainedthe good agreement with CFD results. Recently, the numericalmethods have been an important tool for researchers to studythe mixing process inside the ejector and predict the ejectors’ per-formance. These methods which are quiet economical l to investi-gate the internal flow phenomena and mixing mechanism ofejectors. In Hemidi et al. [17] numerical work, some local flow fea-tures were revealed and relation between overall performance andlocal flow were also investigated. Bartosiewicz et al. [18,19] inves-tigated the ejector using CFD technique. They proposed that theRNG k-epsilon model was suitable to represent the entrainmentratio of the ejector.

Though some researchers have carried out to investigate theinternal flow inside the ejector, the efforts are still needed to godeep into the mixing mechanism inside the ejector. The presentpaper focuses on the entrainment ratio and the static wall pressuredistributions along the mixing tube for air ejectors by experiment.Moreover, a 2D CFD model is developed to study the local phenom-ena and global performance of air ejector. The operation andgeometrical factors on the ejector overall and local performanceare investigated. Then the internal flow fields are analyzed exper-imentally and numerically.

2. Experimental setup

An air ejector experimental system is set up to investigate theglobal and local performance, as shown in Fig. 1. The pressurizedair then expands in the primary nozzle, and the secondary airflowis induced and accelerated due to pressure difference and flowsinto the mixing chamber. Then these two streams are mixedtogether and exchange mass, momentum and energy in the mixingtube. Finally, the discharged air will be exhausted into the atmo-sphere. The air flow rates of primary flow and secondary flow areboth controlled by ball values, and the corresponding pressure isadjusted by pressure regulator behind the ball value, and thedischarged pressure is also controlled by the pressure regulator.The air flow rates are both then measured by vortex shedding flow-meter with the accuracy of 1.5%. The experimental uncertainty

analysis was executed using the method of estimation which wasproposed by Moffat [20]. The uncertainty of the primary air flowrate is less than 2.1%, and the secondary air flow rate less than3.1%. The static wall pressure along the mixing tube is measuredby four static pressure sensors with accuracy of 0.5%, as shownin Fig. 2.

The design parameters, such as primary and secondary pres-sures, used to create the supersonic air ejector are shown in Table 1.The design of structural parameters has been essentially deter-mined by the results of research [3,4]. A simplified schematic ofthe air ejector installed in this experimental system is shown inFig. 2. The primary nozzle (A), secondary nozzle (B), mixing cham-ber (C), mixing tube (D) and diffuser (E) are the main parts of airejector, the material is stainless steel. The other parts of the ejectorare made up of carbon steel.

3. 2D model of air ejector

The commercial CFD software package, FLUENT, is adopted tosimulate the global performance and mixing processes of thesupersonic air ejector. All computational domains are taken fromthe experimental air ejector. Considering the model is in a regularpattern, mapped mesh containing only structured elements arepresented. The flow region is regular and symmetric, so the axi-symmetric space is chosen to simulate the whole flow process inthe ejector. The mesh profile with 295810 quadrilateral elementsis presented in Fig. 3, which has been proven to be sufficient to rep-resent the ejector flow field. The enhanced wall function is selectedand the pressure gradient effect is considered to ensure that the airflow adjacent to the ejector walls is realistic, when the value of Y+is about 1.

The air flows passing through the supersonic ejector are sup-posed to be compressible flow, and the controlling equations ofmass conservation, momentum conservation and energy conserva-tion are in steady-state forms. The conservation equations areimplicitly solved. The SIMPLEC algorithm is applied to get the pres-sure field. The second order upwind scheme is used to discretizethe convective terms. The RNG k-epsilon turbulence viscosity mod-el, which is proved for better simulate the ejector performancethan the other models, is chosen to simulate the turbulent flow[18,19].

The conservation equations of the supersonic air ejector are inthe general form:

@ðquÞ@t

þ divðqVuÞ ¼ divðCgraduÞ þ S

where generalized variable u, generalized diffusion coefficient Uand generalized source S denote different parameters in differentequations, and they are related with each other [21].

The working fluid used is air. The ideal gas model is used toapproximately deal with its density. Other properties are kept

Fig. 1. Schematic of the apparatus.

Fig. 2. Structure of the air ejector.

Table 1Design parameters of air ejector.

Parameters Symbols Unit Value

Primary pressure Pp MPa 1.0Primary air flow rate mp kg/s 0.075Secondary pressure Ps MPa 0.2Secondary air flow rate ms kg/s 0.015Discharged pressure PD MPa 0.52Throat diameter of primary nozzle dc mm 6.4Diameter of mixing tube dmt mm 9.4Length of mixing tube Lmt mm 47Inclination angle of diffuser h2 deg 1.43Inclination angle of mixing chamber h1 deg 14Nozzle exit position NXP mm 2.8

Fig. 3. Mesh generation of air ejector.

D. Chong et al. / Applied Energy 130 (2014) 679–684 681

constant obtained from Fluent data. The inlet types of primary flowand secondary flow are both pressure-inlet type, and the values areset to be the primary inlet pressure and secondary inlet pressure,respectively. Meanwhile, the mixed flow outlet is set as pressure-outlet type. All the wall surfaces are set to be adiabatic since theheat loss at wall surfaces has less impact on the solution.

During the simulation, two converging criteria are adopted toobtain the converged solution: (1) The mass flow difference

between the two inlet flows (primary flow and secondary flow)and the outlet flow (discharged flow) of the air ejector is no morethan 10�8 kg/s. (2) All residual results are no larger than 10�6.

4. Results and discution

4.1. Effect of operating parameter

The entrainment ratio is defined as a = mS/mP. When usingentrainment ratio as index, the ejector can be operated in three dif-ferent modes: the critical operation mode, sub-critical operationmode and back flow operation mode. When the discharged pres-sure is smaller than the critical value, the entrainment ratio isindependent of the discharged and the chocked phenomena occurwith the primary flow and secondary flow, and operation mode iscalled critical mode. With the increase of discharged pressure andlarger than the critical value, the entrainment ratio are linearly de-creased with the discharged pressure because the secondary flowis not chocked, and this is called sub-critical mode. With further in-crease of discharged pressure, the secondary flow may be reversedinto the secondary nozzle because of high discharged pressure,which deduced negative value of entrainment ratio. This is calledback flow mode.

To research the influence of discharged pressure to the ejectorperformance, the entrainment ratios and static wall pressures areall measured when PP is 1.0 MPa, PS is 0.5 MPa and PD ranges from0.4 MPa to 0.7 MPa. As it can be seen from Fig. 4, the entrainmentratio does not immediately reduce when the discharged pressureincreases. But when the discharged pressure is larger than the crit-ical pressure, the entrainment ratio starts to decrease with the in-crease of discharged pressure. The results of experiment and

Fig. 5. Experimental data of static wall pressures with different dischargedpressures.

Fig. 6. Comparison of experimental data and CFD results for different operationconditions (a) deviation of entrainment ratios and (b) deviation of static wallpressure.

Fig. 7. Numerical data of static wall pressure and axisymmetric line static pressurewith discharged pressure.

Fig. 4. Variation of entrainment ratio with discharged pressure.

682 D. Chong et al. / Applied Energy 130 (2014) 679–684

numerical simulation agree well on the trend and the value of crit-ical pressure. Fig. 5 gives the values of four static pressure mea-surements fixed along the mixing tube under differentdischarged pressure. As shown in the figure, the static wall pres-sures remain unchanged before the discharged pressure reachesthe critical value. And the static wall pressure increases remark-ably when the discharged pressure is larger than the critical value.

To investigate the accuracy of the numerical model, the erroranalysis is made. As shown in Fig. 6(a), the deviations are less than15% when the ejector operates in critical mode and less than 30% insub-critical mode. The deviations of entrainment ratio are in a rea-sonable range, so the RNG k-epsilon model can predict the globalperformance with considerable accuracy. The deviations of staticwall pressure are illustrated in Fig. 6(b). The figure shows thatthe deviation is less than 20%, so the enhanced wall function canobtain good forecasting results in static wall pressure. Based onthe above, a conclusion could be drawn that the present CFD modelcan be used to simulate the overall performance and local phenom-ena accurately for air ejectors. So the distribution of static wallpressure, axisymmetric line static pressure and Mach contour linesobtained from numerical simulation can be used to analyze theinternal flow field of air ejector.

Static wall pressure and axisymmetric line static pressure alongthe ejector is shown in Fig. 7 based on the numerical data. Thecurves markedly differ between critical mode and sub-critical

mode. As shown in Fig. 7, when the discharged pressure is less thanthe critical value (0.6 MPa), the static wall and axisymmetric linestatic pressure in the mixing tube change repeatedly because ofthe presence of consecutive shocks. The shock train can lead tostrong momentum transfer. After the shock train the velocity ofprimary flow is still higher than the secondary flow. The nonunifor-mity in velocity results in intensive momentum transfer. These two

Fig. 9. Experimental data of entrainment ratios with different NXPs.

D. Chong et al. / Applied Energy 130 (2014) 679–684 683

fluids then intermix in the mixing tube by momentum transfer.After the mixed air flows downstream to diffuser, at some section,the second shock is generated, which induces that the supersonicflow changes to subsonic flow and the pressure abruptly increases.This section is regarded as the position of second shock, which isaffected by discharged pressure in critical mode. As shown in Figs. 7and 8, the second shock’s position moves upstream as the dis-charged pressure rises from 0.4 MPa to 0.6 MPa. When the dis-charged pressure reaches to the critical value, the second shockwill move close to the exit of chamber tube. Moreover, the staticpressure along the mixing tube and the chock position remains un-changed when the discharged pressure is less than critical value. Itindicates that, the change of downstream condition can affect thesecond shock’s position in critical mode, while the information ofdownstream cannot travel back to the upstream. So the mixingbehavior of the two fluid streams will not be affected and theentrainment ratios remain constant.

As shown in Figs. 7 and 8, when the discharged pressure is lar-ger than 0.6 MPa (critical value), the static wall and axisymmetricline static pressure along the mixing tube and diffuser will changecontinuously without abruptly process. It can be concluded thatthe second shock disappears and the first and second series of ob-lique shocks combine with each other. Therefore, the informationof downstream will travel back to the mixing tube. So the staticwall pressure increases as the discharged pressure increases andthe mixing process is disturbed, which results in the decrease ofthe entrainment ratio.

Fig. 10. Experimental data of static pressures with different NXPs.

4.2. Effect of structure parameter

The structural parameters of air ejector involve the geometricparameters of the main parts of air ejector. These parameters havedifferent influences on the ejector performance. In the presentstudy, the influence of NXP on the ejector performance is per-formed. The NXP, which means of primary nozzle exit position, isone of the most important structure parameters.

The entrainment ratios and static wall pressures are all mea-sured when the NXP is 2.4 mm, 2.8 mm, 3.6 mm and 4.8 mm,respectively. Fig. 9 shows the relation between the entrainmentratio of critical mode and NXP. As shown in this figure, the entrain-ment ratio increases firstly and then decreases when the NXP

Fig. 8. Numerical data of Mach number contour lines with different dischargedpressures.

Fig. 11. Experimental data of entrainment ratios with different dischargedpressures.

increases. Moreover, the entrainment ratio reaches the maximumwhen the NXP is 2.8 mm which is the design value. The higherthe secondary pressure is, the greater the impact on entrainmentratio can be. Experimental value of pressure measuring point 1fixed in the exit of secondary nozzle with different NXP is

Fig. 12. Numerical data of static wall pressure with different NXPs.

684 D. Chong et al. / Applied Energy 130 (2014) 679–684

illustrated in Fig. 10. As shown in this figure, the static wallpressure of the exit of secondary nozzle decreases firstly and thenincreases when the NXP increases. It reaches the minimum valuewhen the NXP is 2.8 mm, which indicates that the NXP has a greatimpact on the pressure difference of secondary nozzle. The lowerthe pressure of measuring point 1, the higher the pressure differ-ence of secondary nozzle. So when the NXP is 2.8 mm, the entrain-ment ratio reaches the maximum.

The lifting-pressure performance, which is represented by thecritical discharged pressure, is another important index of ejectorperformance. The higher the critical discharged pressure is, thebetter the lifting-pressure performance obtains. As shown inFig. 11, the critical discharged pressure remains constant withdifferent NXP. It can be concluded that the lifting-pressure perfor-mance is little affected by NXP. Fig. 12 gives the static wall pres-sure distribution along the ejector. The first series of obliqueshocks are influenced by the change of NXP. So the mixing processis disturbed, the entrainment ratio will change by NXP. But theposition and the strength of second shock remains unchangedwhen the NXP changes. It indicates that the mixing flow is chokedin the same position, so the critical discharged pressure isunchanged.

5. Conclusion

In this study, the experimental and numerical methods havebeen used to research the global performance and interior flowbehaviors of air ejector. The numerical results are in good agree-ment with the experimental data. The effects of operation param-eters and geometrical parameter (NXP) on the ejector performanceare studied, and the numerical visualization is employed to analyzethe local phenomena and global performance of supersonic airejector. Based on the above work, the following results can beconcluded:

(1) The static wall pressure along the axisymmetric line remainsunchanged when the air ejector works in critical mode, butincreases remarkably in the sub-critical mode with theincrease of discharged pressure. Meanwhile, the position ofsecond shock moves upstream to the exit of mixing tubeas the discharged pressure increases. In sub-critical mode,the static wall and axisymmetric line static pressure alongthe mixing tube increase and the second shock disappearsas the discharged pressure increases. The entrainment ratiosremain constant due to the mixing process is independent ofdischarged pressure.

(2) For different NXPs, the entrainment ratio increases firstlyand then decreases, obtained through the experimental data.The flow fields analyzed by the experimental and numericalmethods prove that there exists an optimum NXP, which iscorresponding to the maximum entrainment ratio, but theNXP almost has no influence on the critical dischargedpressure.

These results shows that the CFD method, the RNG k-epsilonturbulence coupled with enhanced wall function, offers an efficienttool to study both global and local ejector performance. Also CFDvisualization represents a detained flow field and insightful studyinside the ejector flow. These results help to improve the designand application of the supersonic air ejector.

Acknowledgement

The present work is funded by the National Natural ScienceFoundation of China (Nos. 51006081 and 51125027), and NationalBasic Research program of China (973 Program) (No. 2009CB219803).

References

[1] Sun DW, Eames IW. Recent developments in the design theories andapplications of ejectors a review. J Inst Energy 1995;68:65–79.

[2] Yan JJ, Shao SF, Liu JP, Zhang Z. Experiment and analysis on performance ofsteam-driven jet injector for district-heating system. Appl Therm Eng2005;25:1153–67.

[3] Chong DT, Yan JJ, Wu GS, Liu JP. Structural optimization and experimentalinvestigation of supersonic ejectors for boosting low pressure natural gas. ApplTherm Eng 2009;29:2799–807.

[4] Chen WX, Yan JJ, Chong DT, Liu JP. Numerical optimization on the structuralparameters of natural gas ejectors. Int J Therm Sci 2011;50(8):1554–61.

[5] Chunnanond K, Aphornratana S. Ejectors: applications in refrigerationtechnology. Renew Sust Energy Rev 2004;8:129–55.

[6] Chen XJ, Worall M, Omer S, Su YH, Riffat S. Theoretical studies of a hybridejector CO2 compression cooling system for vehicles and preliminaryexperimental investigations of an ejector cycle. Appl Energy 2013;102:931–42.

[7] Keenan JH, Neumann EP. A simple air ejector. J Appl Mech Trans ASME1942;64:75–81.

[8] Keenan JH, Neumann EP, Lustwerk F. An investigation of ejector design byanalysis and experiment. J Appl Mech Trans ASME 1950;72:299–309.

[9] Munday JT, Bagster DF. A new ejector theory applied to steam jet refrigeration.Ind Eng Chem, Process Des Dev 1977;16:442–9.

[10] Huang BJ, Jiang CB, Hu FL. Ejector performance characteristics and designanalysis of jet refrigeration system. J Eng Gas Turb Power ASME1985;107:792–802.

[11] Huang BJ, Chang JM, Wang CP, Petrenko VA. A 1-D analysis of ejectorperformance. Int J Refrig 1999;22:354–64.

[12] Zhu Y, Cai W, Wen C, Li Y. Shock circle model for ejector performanceevaluation. Energy Convers Manage 2007;48:2533–41.

[13] Zhang HF, Charles A, Garris Jr. Crypto-steady supersonic pressure exchange: asimple analytical model. Appl Energy 2008;85(4):228–42.

[14] Desevaux P, Hostache G, Jacquet P. Static pressure measurement along thecenterline of an induced flow ejector. Exp Fluids 1994;16(3–4):289–91.

[15] Desevaux P. A method for visualizing the mixing zone between two co-axialflows in an ejector. Opt Lasers Eng 2001;35(5):317–23.

[16] Desevaux P, Mellal A, de Sousa A. Visualization of secondary flow chokingphenomena in a supersonic air ejector. J Visual 2004;7(3):249–56.

[17] Hemidi A, Henry F, Leclaire S, Seynhaeve J, Bartosiewicz Y. CFD analysis of asupersonic air ejector. Part II: Relation between global operation and local flowfeatures. Appl Therm Eng 2009;29:2990–8.

[18] Bartosiewicz Y, Aidoun Z, Desevaux P, Mercadier Y. Numerical andexperimental investigations on supersonic ejectors. Int J Heat Fluid Flow2005;26(1):56–70.

[19] Bartosiewicz Y, Aidoun Z, Mercadier Y. Numerical assessment of ejectoroperation for refrigeration applications based on CFD. Appl Therm Eng2006;26(4–5):604–12.

[20] Moffat RJ. Describing the uncertainties in experimental results. Exp ThermFluid Sci 1988;1(1):3–17.

[21] Tao WQ. Numerical heat transfer. 2nd ed. Xi’an Jiaotong University Press;2001.