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 Daotong Chong, Mengqi Hu, Weixiong Chen ⇑, Jinshi Wang, Jiping Liu, Junjie Yan State 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 2013 Received in revised form 28 January 2014 Accepted 10 February 2014 Available online 28 February 2014 Keywords: Air ejector Entrainment ratio Shock Static wall pressure a b s t r a c t The present paper performs experimental and numerical investigations on the global performance and internal ﬂow of a supersonic air ejector. The effects of operation parameters and geometrical factor on the air ejector performance have been analyzed. The results show that: the static wall pressure and axisymmetric 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 shock position of the mixed ﬂuid moves upstream in critical mode. The second shock position disappears in sub-critical mode. The experimental and numerical results indicate that there exists an optimal nozzle exit position (NXP) corresponding to maximum entrainment ratio, but the critical value of discharged pressure is almost independent of NXP. Ó 2014 Elsevier Ltd. All rights reserved. 1. Introduction Supersonic ejector is a simple mechanical device where two gases are allowed to mix and recompress. The primary gas with high total energy can transfer part of its mechanical energy to the secondary gas with low energy in supersonic ejector without any moving parts. Today, in view of pressures for protecting the environment, ejectors are becoming popular in industrial ﬁelds as an energy saving and emission reduction technique . We are using them in many engineering ﬁelds, such as heat pump in the district-heating system , pressure booster in natural gas industry [3,4]. The steam jet refrigeration is the most widely used device because of its relative simplicity and low capital cost compared to an absorption refrigerator, and the most important beneﬁt is that the ejector refrigeration system could be powered by the low-grade heat [5,6]. Nevertheless the low performance in present conditions is the main problem, which primarily limits the widespread use in industry. The ejector performance is greatly affected by the mixing process between primary ﬂow and secondary ﬂow. Therefore, it ⇑ Corresponding author. Tel.: +86 29 82667753; fax: +86 29 82665359. E-mail address: [email protected] (W. Chen). http://dx.doi.org/10.1016/j.apenergy.2014.02.023 0306-2619/Ó 2014 Elsevier Ltd. All rights reserved. is very necessary to investigate the mixing mechanism of ejector in order to improve the ejector performance. Two mixing models about ejector mixing process were proposed by Keenan et al. [7,8]. The ﬁrst mixing model is called as constant area model, assuming that the gas obeys the law of ideal gas and the ﬂow is isentropic. The second model named constant pressure model has been widely accepted and developed by many researchers, and widely used due to its superior performance. The choking phenomenon was ﬁrst proposed by Munday and Bagster . They proposed that the high and the low pressure ﬂows reached the same pressure at some place inside the mixing chamber, which is named as an effective area. Huang et al.  further proposed that the effective area was located in the constant area section, and found out that the effective area position was affected by operation conditions. Based on this assumption, their 1D model could accurately calculate the entrainment ratio when the discharged pressure was less than critical discharged pressure . Later, Zhu et al.  proposed a 2D exponential model to predict the velocity distribution in ejector, however the pressure is still assumed to be uniform in the radial direction. Zhang et al.  explored the behavior of direct ﬂow induction based on pressure exchange utilizing supersonic wave structure in a crypto-steady mode, their results indicated that very high 680 D. Chong et al. / Applied Energy 130 (2014) 679–684 Nomenclature d L m NXP P S t a U diameter, mm Length, mm mass ﬂow rate, kg/s nozzle exit position, mm pressure, MPa generalized source time, s entrainment ratio, % generalized diffusion coefﬁcient compressor–expander efﬁciencies are possible even in the presence of strong supersonic wave structure. Although these models are helpful to predict the ejector performance, they cannot accurately predict the internal ﬂow process along the ejector because of the one-dimensional model. To study the mixing mechanism of ejectors, researchers focused on the local phenomenon of ejector by experimental study. Desevaux et al.  paid their attention to investigate the ﬂow ﬁelds inside the ejector by experimental work. They obtained the centerline static pressure through a slide measuring system. Then, Desevaux  obtained the mixing zone roughly using Rayleigh scattering method. Subsequently, Desevaux et al.  applied laser tomography method to study the choking phenomena, and gained the good agreement with CFD results. Recently, the numerical methods have been an important tool for researchers to study the mixing process inside the ejector and predict the ejectors’ performance. These methods which are quiet economical l to investigate the internal ﬂow phenomena and mixing mechanism of ejectors. In Hemidi et al.  numerical work, some local ﬂow features were revealed and relation between overall performance and local ﬂow were also investigated. Bartosiewicz et al. [18,19] investigated the ejector using CFD technique. They proposed that the RNG k-epsilon model was suitable to represent the entrainment ratio of the ejector. Though some researchers have carried out to investigate the internal ﬂow inside the ejector, the efforts are still needed to go deep into the mixing mechanism inside the ejector. The present paper focuses on the entrainment ratio and the static wall pressure distributions along the mixing tube for air ejectors by experiment. Moreover, a 2D CFD model is developed to study the local phenomena and global performance of air ejector. The operation and geometrical factors on the ejector overall and local performance are investigated. Then the internal ﬂow ﬁelds are analyzed experimentally and numerically. 2. Experimental setup An air ejector experimental system is set up to investigate the global and local performance, as shown in Fig. 1. The pressurized air then expands in the primary nozzle, and the secondary airﬂow is induced and accelerated due to pressure difference and ﬂows into the mixing chamber. Then these two streams are mixed together and exchange mass, momentum and energy in the mixing tube. Finally, the discharged air will be exhausted into the atmosphere. The air ﬂow rates of primary ﬂow and secondary ﬂow are both controlled by ball values, and the corresponding pressure is adjusted by pressure regulator behind the ball value, and the discharged pressure is also controlled by the pressure regulator. The air ﬂow rates are both then measured by vortex shedding ﬂowmeter with the accuracy of 1.5%. The experimental uncertainty q u density, kg/m3 generalized variable Subscript P primary air ﬂow S secondary air ﬂow D discharged air ﬂow analysis was executed using the method of estimation which was proposed by Moffat . The uncertainty of the primary air ﬂow rate is less than 2.1%, and the secondary air ﬂow rate less than 3.1%. The static wall pressure along the mixing tube is measured by four static pressure sensors with accuracy of 0.5%, as shown in Fig. 2. The design parameters, such as primary and secondary pressures, used to create the supersonic air ejector are shown in Table 1. The design of structural parameters has been essentially determined by the results of research [3,4]. A simpliﬁed schematic of the air ejector installed in this experimental system is shown in Fig. 2. The primary nozzle (A), secondary nozzle (B), mixing chamber (C), mixing tube (D) and diffuser (E) are the main parts of air ejector, the material is stainless steel. The other parts of the ejector are made up of carbon steel. 3. 2D model of air ejector The commercial CFD software package, FLUENT, is adopted to simulate the global performance and mixing processes of the supersonic air ejector. All computational domains are taken from the experimental air ejector. Considering the model is in a regular pattern, mapped mesh containing only structured elements are presented. The ﬂow region is regular and symmetric, so the axisymmetric space is chosen to simulate the whole ﬂow process in the ejector. The mesh proﬁle with 295810 quadrilateral elements is presented in Fig. 3, which has been proven to be sufﬁcient to represent the ejector ﬂow ﬁeld. The enhanced wall function is selected and the pressure gradient effect is considered to ensure that the air ﬂow adjacent to the ejector walls is realistic, when the value of Y+ is about 1. The air ﬂows passing through the supersonic ejector are supposed to be compressible ﬂow, and the controlling equations of mass conservation, momentum conservation and energy conservation are in steady-state forms. The conservation equations are implicitly solved. The SIMPLEC algorithm is applied to get the pressure ﬁeld. The second order upwind scheme is used to discretize the convective terms. The RNG k-epsilon turbulence viscosity model, which is proved for better simulate the ejector performance than the other models, is chosen to simulate the turbulent ﬂow [18,19]. The conservation equations of the supersonic air ejector are in the general form: @ðquÞ þ divðqV uÞ ¼ divðCgraduÞ þ S @t where generalized variable u, generalized diffusion coefﬁcient U and generalized source S denote different parameters in different equations, and they are related with each other . The working ﬂuid used is air. The ideal gas model is used to approximately deal with its density. Other properties are kept D. Chong et al. / Applied Energy 130 (2014) 679–684 681 Fig. 1. Schematic of the apparatus. Fig. 2. Structure of the air ejector. Table 1 Design parameters of air ejector. Parameters Symbols Unit Value Primary pressure Primary air ﬂow rate Secondary pressure Secondary air ﬂow rate Discharged pressure Throat diameter of primary nozzle Diameter of mixing tube Length of mixing tube Inclination angle of diffuser Inclination angle of mixing chamber Nozzle exit position Pp mp Ps ms PD dc dmt Lmt h2 h1 NXP MPa kg/s MPa kg/s MPa mm mm mm deg deg mm 1.0 0.075 0.2 0.015 0.52 6.4 9.4 47 1.43 14 2.8 Fig. 3. Mesh generation of air ejector. constant obtained from Fluent data. The inlet types of primary ﬂow and secondary ﬂow are both pressure-inlet type, and the values are set to be the primary inlet pressure and secondary inlet pressure, respectively. Meanwhile, the mixed ﬂow outlet is set as pressureoutlet type. All the wall surfaces are set to be adiabatic since the heat loss at wall surfaces has less impact on the solution. During the simulation, two converging criteria are adopted to obtain 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 more than 108 kg/s. (2) All residual results are no larger than 106. 4. Results and discution 4.1. Effect of operating parameter The entrainment ratio is deﬁned as a = mS/mP. When using entrainment ratio as index, the ejector can be operated in three different modes: the critical operation mode, sub-critical operation mode and back ﬂow operation mode. When the discharged pressure is smaller than the critical value, the entrainment ratio is independent of the discharged and the chocked phenomena occur with the primary ﬂow and secondary ﬂow, and operation mode is called critical mode. With the increase of discharged pressure and larger than the critical value, the entrainment ratio are linearly decreased with the discharged pressure because the secondary ﬂow is not chocked, and this is called sub-critical mode. With further increase of discharged pressure, the secondary ﬂow may be reversed into the secondary nozzle because of high discharged pressure, which deduced negative value of entrainment ratio. This is called back ﬂow mode. To research the inﬂuence of discharged pressure to the ejector performance, the entrainment ratios and static wall pressures are all measured when PP is 1.0 MPa, PS is 0.5 MPa and PD ranges from 0.4 MPa to 0.7 MPa. As it can be seen from Fig. 4, the entrainment ratio does not immediately reduce when the discharged pressure increases. But when the discharged pressure is larger than the critical pressure, the entrainment ratio starts to decrease with the increase of discharged pressure. The results of experiment and 682 D. Chong et al. / Applied Energy 130 (2014) 679–684 Fig. 4. Variation of entrainment ratio with discharged pressure. Fig. 6. Comparison of experimental data and CFD results for different operation conditions (a) deviation of entrainment ratios and (b) deviation of static wall pressure. Fig. 5. Experimental data of static wall pressures with different discharged pressures. numerical simulation agree well on the trend and the value of critical pressure. Fig. 5 gives the values of four static pressure measurements ﬁxed along the mixing tube under different discharged pressure. As shown in the ﬁgure, the static wall pressures remain unchanged before the discharged pressure reaches the critical value. And the static wall pressure increases remarkably when the discharged pressure is larger than the critical value. To investigate the accuracy of the numerical model, the error analysis is made. As shown in Fig. 6(a), the deviations are less than 15% when the ejector operates in critical mode and less than 30% in sub-critical mode. The deviations of entrainment ratio are in a reasonable range, so the RNG k-epsilon model can predict the global performance with considerable accuracy. The deviations of static wall pressure are illustrated in Fig. 6(b). The ﬁgure shows that the deviation is less than 20%, so the enhanced wall function can obtain good forecasting results in static wall pressure. Based on the above, a conclusion could be drawn that the present CFD model can be used to simulate the overall performance and local phenomena accurately for air ejectors. So the distribution of static wall pressure, axisymmetric line static pressure and Mach contour lines obtained from numerical simulation can be used to analyze the internal ﬂow ﬁeld of air ejector. Static wall pressure and axisymmetric line static pressure along the ejector is shown in Fig. 7 based on the numerical data. The curves markedly differ between critical mode and sub-critical Fig. 7. Numerical data of static wall pressure and axisymmetric line static pressure with discharged pressure. mode. As shown in Fig. 7, when the discharged pressure is less than the critical value (0.6 MPa), the static wall and axisymmetric line static pressure in the mixing tube change repeatedly because of the presence of consecutive shocks. The shock train can lead to strong momentum transfer. After the shock train the velocity of primary ﬂow is still higher than the secondary ﬂow. The nonuniformity in velocity results in intensive momentum transfer. These two D. Chong et al. / Applied Energy 130 (2014) 679–684 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 supersonic ﬂow changes to subsonic ﬂow and the pressure abruptly increases. This section is regarded as the position of second shock, which is affected by discharged pressure in critical mode. As shown in Figs. 7 and 8, the second shock’s position moves upstream as the discharged pressure rises from 0.4 MPa to 0.6 MPa. When the discharged pressure reaches to the critical value, the second shock will move close to the exit of chamber tube. Moreover, the static pressure along the mixing tube and the chock position remains unchanged when the discharged pressure is less than critical value. It indicates that, the change of downstream condition can affect the second shock’s position in critical mode, while the information of downstream cannot travel back to the upstream. So the mixing behavior of the two ﬂuid streams will not be affected and the entrainment ratios remain constant. As shown in Figs. 7 and 8, when the discharged pressure is larger than 0.6 MPa (critical value), the static wall and axisymmetric line static pressure along the mixing tube and diffuser will change continuously without abruptly process. It can be concluded that the second shock disappears and the ﬁrst and second series of oblique shocks combine with each other. Therefore, the information of downstream will travel back to the mixing tube. So the static wall pressure increases as the discharged pressure increases and the mixing process is disturbed, which results in the decrease of the entrainment ratio. 683 Fig. 9. Experimental data of entrainment ratios with different NXPs. 4.2. Effect of structure parameter The structural parameters of air ejector involve the geometric parameters of the main parts of air ejector. These parameters have different inﬂuences on the ejector performance. In the present study, the inﬂuence of NXP on the ejector performance is performed. The NXP, which means of primary nozzle exit position, is one of the most important structure parameters. The entrainment ratios and static wall pressures are all measured 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 entrainment ratio of critical mode and NXP. As shown in this ﬁgure, the entrainment ratio increases ﬁrstly and then decreases when the NXP Fig. 10. Experimental data of static pressures with different NXPs. Fig. 11. Experimental data of entrainment ratios with different discharged pressures. Fig. 8. Numerical data of Mach number contour lines with different discharged pressures. increases. Moreover, the entrainment ratio reaches the maximum when the NXP is 2.8 mm which is the design value. The higher the secondary pressure is, the greater the impact on entrainment ratio can be. Experimental value of pressure measuring point 1 ﬁxed in the exit of secondary nozzle with different NXP is 684 D. Chong et al. / Applied Energy 130 (2014) 679–684 (2) For different NXPs, the entrainment ratio increases ﬁrstly and then decreases, obtained through the experimental data. The ﬂow ﬁelds analyzed by the experimental and numerical methods prove that there exists an optimum NXP, which is corresponding to the maximum entrainment ratio, but the NXP almost has no inﬂuence on the critical discharged pressure. These results shows that the CFD method, the RNG k-epsilon turbulence coupled with enhanced wall function, offers an efﬁcient tool to study both global and local ejector performance. Also CFD visualization represents a detained ﬂow ﬁeld and insightful study inside the ejector ﬂow. These results help to improve the design and application of the supersonic air ejector. Acknowledgement Fig. 12. Numerical data of static wall pressure with different NXPs. illustrated in Fig. 10. As shown in this ﬁgure, the static wall pressure of the exit of secondary nozzle decreases ﬁrstly and then increases when the NXP increases. It reaches the minimum value when the NXP is 2.8 mm, which indicates that the NXP has a great impact on the pressure difference of secondary nozzle. The lower the pressure of measuring point 1, the higher the pressure difference of secondary nozzle. So when the NXP is 2.8 mm, the entrainment ratio reaches the maximum. The lifting-pressure performance, which is represented by the critical discharged pressure, is another important index of ejector performance. The higher the critical discharged pressure is, the better the lifting-pressure performance obtains. As shown in Fig. 11, the critical discharged pressure remains constant with different NXP. It can be concluded that the lifting-pressure performance is little affected by NXP. Fig. 12 gives the static wall pressure distribution along the ejector. The ﬁrst series of oblique shocks are inﬂuenced by the change of NXP. So the mixing process is disturbed, the entrainment ratio will change by NXP. But the position and the strength of second shock remains unchanged when the NXP changes. It indicates that the mixing ﬂow is choked in the same position, so the critical discharged pressure is unchanged. 5. Conclusion In this study, the experimental and numerical methods have been used to research the global performance and interior ﬂow behaviors of air ejector. The numerical results are in good agreement with the experimental data. The effects of operation parameters and geometrical parameter (NXP) on the ejector performance are studied, and the numerical visualization is employed to analyze the local phenomena and global performance of supersonic air ejector. Based on the above work, the following results can be concluded: (1) The static wall pressure along the axisymmetric line remains unchanged when the air ejector works in critical mode, but increases remarkably in the sub-critical mode with the increase of discharged pressure. Meanwhile, the position of second shock moves upstream to the exit of mixing tube as the discharged pressure increases. In sub-critical mode, the static wall and axisymmetric line static pressure along the mixing tube increase and the second shock disappears as the discharged pressure increases. The entrainment ratios remain constant due to the mixing process is independent of discharged pressure. The present work is funded by the National Natural Science Foundation of China (Nos. 51006081 and 51125027), and National Basic Research program of China (973 Program) (No. 2009CB 219803). References  Sun DW, Eames IW. Recent developments in the design theories and applications of ejectors a review. 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