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A CFD analysis of the flow structure inside a steam ejector to identify the suitable experimental operating conditions for a solar-driven refrigeration system
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A CFD analysis of the flow structure inside a steam ejector to identify the suitable experimental operating conditions for a solar-driven refrigeration system Yosr Allouche a,b,*, Chiheb Bouden a, Szabolcs Varga b a
Universite´ de Tunis El Manar, Ecole Nationale d’Inge´nieurs de Tunis, LR-11-ES16, Laboratoire de Mate´riaux, Optimisation et E´nergie pour la Durabilite´, 1002 Tunis, Tunisia b New Energy Technologies Unit, Faculty of Engineering, University of Porto, Rua Dr Roberto Frias, 4200-465 Porto, Portugal
article info
abstract
Article history:
This paper presents a numerical study of a steam ejector using CFD with the objective of
Received 3 February 2013
identifying suitable experimental conditions that allows for a reliable ejector cycle operation.
Received in revised form
The flow structure and the mixing process inside the ejector were assessed for a range of
29 July 2013
operating conditions typical for a solar driven air conditioning system. The effect of varying
Accepted 31 July 2013
the condenser pressure was studied. It was found that for relatively low condenser pressures
Available online xxx
(<2.5 kPa), two distinct shock waves occurred in the diffuser section resulting in a reduced recompression efficiency, although it did not have a direct impact on the entrainment ratio.
Keywords:
The effect of generator pressure was also studied. It was found that the entrainment ratio
Steam ejector
showed a maximum for constant condenser conditions. A near optimal condition of 70 kPa
Computational fluid dynamic
generator and 3 kPa condenser pressures were identified and tested in a preliminary
Entrainment ratio
experiment carried out with the solar driven ejector system installed in Tunis.
Experimentation
ª 2013 Elsevier Ltd and IIR. All rights reserved.
Flow structure
Une analyse en dynamique des fluides computationnelle (CFD) d’une structure d’e´coulement a` l’inte´rieur d’un e´jecteur de vapeur pour identifier les conditions de fonctionnement expe´rimentales correctes pour un syste`me frigorifique fonctionnant a` l’e´nergie solaire
* Corresponding author. Universite´ de Tunis El Manar, Ecole Nationale d’Inge´nieurs de Tunis, LR-11-ES16, Laboratoire de Mate´riaux, Optimisation et E´nergie pour la Durabilite´, 1002 Tunis, Tunisia. Tel.: þ216 28 174 403; fax: þ216 71 87 27 29. E-mail address: [email protected] (Y. Allouche). 0140-7007/$ e see front matter ª 2013 Elsevier Ltd and IIR. All rights reserved. http://dx.doi.org/10.1016/j.ijrefrig.2013.07.027
Please cite this article in press as: Allouche, Y., et al., A CFD analysis of the flow structure inside a steam ejector to identify the suitable experimental operating conditions for a solar-driven refrigeration system, International Journal of Refrigeration (2013), http://dx.doi.org/10.1016/j.ijrefrig.2013.07.027
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Nomenclature d E Er gI k M _ m P P c* T T u xd
Spindle tip position (mm) Total Energy (J) Entrainment ratio acceleration of gravity vector (m s2)identity matrix thermal conductivity (W m1 K1) Mach number Mass flow rate (kg s1) Pressure (kPa) Critical back pressure (kPa) Time (s) Temperature ( C) average velocity (m s1) Distance between two shock waves
Greek letters s Stress tensor (Pa) P Density (Kg m3) E Turbulence dissipation rate (m2 s3)
m w
Dynamic viscosity (Pa s) Kinematic viscosity (m2 s1)
Abbreviation COP Coefficient of performance CMA Constant mixing area CPM Constant pressure mixing MEPCM Micro-encapsulated phase change material NXP Nozzle exit plain Spl Spindle length (mm) Spt Spindle travel (mm) Subscripts B break down C condenser D double chocking E evaporator G generator i,j generic space coordinates (2D) Nozz nozzle
Mots cle´s : Ejecteur de vapeur ; Dynamique des fluides computationnelle ; Taux d’entraıˆnement ; Expe´rimentation ; Structure de l’e´coulement
1.
Introduction
Global warming and the increasing need for the thermal comfort has led to a rapidly increasing cooling energy, and simultaneously, electricity demand. This tendency seems to threaten the aims set by many developed and developing countries for the upcoming decades. Beside the medical services and food storage, air-conditioning in buildings is a major contributor to the increasing electricity consumption. The concept of solar cooling is of great interest, since the cooling load is directly correlated to the intensity of solar radiation. Research on solar cooling goes back as far as 1872 when Abel Pifre developed the first absorption solar refrigerator producing a small amount of ice (Abdulateef et al., 2009). Nowadays a number of technologies can be used to produce cooling by transformation of solar heat (Vidal et al., 2006). The use of ejectors to create thermal compression of a working fluid has been demonstrated to be a low electricity consumption method in comparison with the mechanical compression systems. Ejector refrigeration is a promising technology due to its relative low cost and simplicity comparing to an absorption cooling cycle, but the main disadvantage is still its moderate COP. Many researchers have been interested in solar-driven ejector refrigeration technology and its applications. Recently, Abdulateef et al. (2009) presented a valuable review on ejector based on solar cooling technologies providing a solid background of their operating principles. Generally, water has been used as the working fluid in ejectors (Sriveerakul et al., 2007b) because of its low cost, chemical
stability and safe use. However, other refrigerants have also been widely applied. For more details of these investigations, the reader is referred to Selvaraju and Mani (2004, 2006). Selvaraju and Mani (2004) studied the variation of the area ratio of the ejector and the critical entrainment ratio with generator temperature for R134a, R152a, R290, R600a and R717 refrigerants. It was observed that R134a led to a better entrainment ratio (0.3 at Tg ¼ 368 K Te ¼ 278 K and Tc ¼ 298 K) at all operating conditions in comparison with other working fluids. Beside refrigerant selection, ejector design strongly influences cycle performance since the compression ratio depends on the geometry of the nozzle throat and diffuser. A summary of experimental data available in the literature for steam ejectors discussing the influence of the throat-diffuser area ratio is given in El-Dessouky et al. (2002). It has been shown that the suction chamber geometry has an important effect on the entrainment ratio (Yadav and Patwardhan, 2008). Varga et al. (2009a,b) investigated the nozzle efficiency for different nozzle diameters and the suction efficiency for different area ratios that can be applied with simplified mathematical models e.g. the one based on the constant pressure mixing theory (CPM) (Cardemil and Colle, 2012; Zhu et al., 2008; He et al., 2009). These simplified models are excellent tools for estimating on design global ejector performances and obtaining a first ejector design. However, they are not adequate to describe the details of fluid flow inside the ejector. Varga et al. (2011) proposed to apply a movable spindle at the primary nozzle inlet to control ejector operation. Both experimental and CFD data showed that the spindle tip position affected the entrainment ratio (from 0.1 to 0.5) by
Please cite this article in press as: Allouche, Y., et al., A CFD analysis of the flow structure inside a steam ejector to identify the suitable experimental operating conditions for a solar-driven refrigeration system, International Journal of Refrigeration (2013), http://dx.doi.org/10.1016/j.ijrefrig.2013.07.027
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controlling the primary flow rate. It was also concluded that CFD results predicted experimental measurements with a good accuracy when the ejector operated in double chocking mode. The current paper aims to numerically study the flow structure inside the ejector for a better understanding of the mixing phenomenon and the location of the shock waves as a function of the operating parameters using CFD. It was assumed that the fluid flow was axi-symmetric and compressible. Turbulent behavior was treated using k-ε realizable model. These findings will lead to the identification of the optimal operating conditions in the double choking region for an existing ejector installed at the National Engineering school of Tunis (ENIT) as part of a solar energy driven air conditioner. The system is built of three sub-systems (see Fig. 1): (i) a solar loop made of 60 m2 vacuum tube collectors connected to a 3000 L storage tank, (ii) the ejector loop with 5 KW cooling capacity, and (iii) the distribution loop having a 900 L capacity cold storage tank containing 800 L micro-encapsulated phase change material (MEPCM) and 4 air-handling units. This setup has been designed to meet the thermal load of 4 offices in the solar energy laboratory at ENIT. The operation of the system has been described in previous papers (Allouche et al., 2011, 2012).
nozzle. The primary stream outs with a supersonic speed to create a very low pressure region at the Nozzle Exit plan (NXP) and consequently in the mixing chamber. This means that the “secondary fluid” can be drawn into the mixing chamber. The motive flow expands and forms a converging duct without mixing with secondary fluid. Nevertheless, the velocity of the secondary fluid increases gradually until it reaches M ¼ 1. The mixing process is considered to start at this location. By the end of the mixing chamber, the two streams are completely mixed. In an ideal case, due to the high pressure at the diffuser exit, a shock wave takes place somewhere at the end of the constant area section or at the beginning of the diffuser. This causes a major compression effect and a sudden drop in the flow speed from supersonic to subsonic. The mixed fluids leave the subsonic diffuser at a pressure defined by the condenser of the cooling cycle.
2.2. Ejector performance indicators and dependence on operating conditions Ejector performance is often measured by the entrainment ratio (Er) defined as the ratio between the secondary and the primary mass flow rates: Er ¼
2. Steam ejector design and performance indicators 2.1.
Ejector unit
A steam ejector refrigeration cycle uses heat as primary energy source in the rage of 70e150 C in order to produce cooling usually between 10 C and 20 C, depending on the ejector capacity. A typical steam ejector is composed of a primary nozzle, a mixing chamber, a throat and a diffuser as shown in Fig. 2. The primary fluid (motive) coming from the superheater enters the ejector at high temperature and high pressure (g), and then accelerates by expanding through the
3
_e m _s m
(1)
Every single ejector has its proper characteristic curve identifying its performance as a function of the operating conditions. One of the most important parameter on the curve is the critical back pressure (Pc*). Fig. 3 describes the effect of the back pressure on Er where 3 regions can be identified: choked flow, unchoked flow and reversed flow regions. Below Pc*, Er remains unchanged. This can be explained by the choking of the secondary fluid in the constant area section. Beyond Pc*, the secondary steam does not reach M ¼ 1 (only the primary stream is choked in the primary nozzle), thus Er decreases rapidly with the back pressure. Finally, the third region (Pc > Pb) indicates ejector failure, where reverse flow appears.
Fig. 1 e Configuration of the field test system installed at the National Engineering School of Tunis. Please cite this article in press as: Allouche, Y., et al., A CFD analysis of the flow structure inside a steam ejector to identify the suitable experimental operating conditions for a solar-driven refrigeration system, International Journal of Refrigeration (2013), http://dx.doi.org/10.1016/j.ijrefrig.2013.07.027
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Fig. 2 e Schematic (not scaled) view of a typical ejector.
3.
Ejector geometry and CFD model
3.1.
Ejector and spindle geometries
Depending on their geometries, generally ejectors are classified into two categories: CMA CPM ejectors. The difference between the two types is the position of the nozzle exit (Varga et al., 2009a,b). In the current study, the solar-driven refrigeration system is equipped with CPM ejector as described in Fig. 4. The Ejector is connected to the generator from the top and to the evaporator from the bottom side. In order to provide regulation for the ejector operation, a spindle was installed on the high pressure side in the primary nozzle to control the motive flow rate as shown in Fig. 5. As the spindle tip travels into the nozzle, the primary nozzle throat area decreases and thus the flow rate decreases. Several simulations showing the effect of the spindle position (SP) on the primary flow rate were carried out using CFD in a previous work (Varga et al., 2011). SP was considered to be at 50 mm in a fully open position, while 0 mm when there is no flow rate through the primary nozzle (fully closed).
3.2.
CFD model
The fluid flow inside the ejector was considered to be axisymmetric (Pianthong et al., 2007). The computational grid
was developed using the software Gambit 2.4.6. A structured mesh with quadratic control volumes have been adopted in most of the domain and triangular control volumes have been used in some specific areas of the ejector (nozzle throat, NXP) as shown in Fig. 6. Realizable version k-ε was considered as the turbulence model, since it was found that it predicts more accurately the spreading rate of jet flows (Sriveerakul et al., 2007a). This model is also suitable for flows at high Reynolds number and it takes into account the rotational effects. Zones with recirculation are more apparent than when using the standard model. It has been already found to predict well global ejector performances by several authors (Sriveerakul et al., 2007b) for details of the particular formulation of realizable k-ε turbulence model; the reader is referred to Ji et al. (2010). Flow behavior near the walls was assumed to be logarithmic. A density based solver with implicit formulation was used. Pressure boundary conditions were applied at inlets and outlet. Steam was used as a working fluid assuming the ideal gas relationship between the pressure and density. The solution was considered to be converged when the relative residual was within 106 for all unknown variables. The governing equations that describe the compressible flow in an ejector can be written in their general forms (White, 1991). Continuity: Dr þ rdiv u ¼ 0 Dt
(2)
Momentum: r
Du ¼ r g Vp þ Vsij Dt
(3)
Energy: r
Dh Dp vui ¼ þ divðkVTÞ þ sij Dt Dt vxj
(4)
where the stress tensor sij is given by:
Fig. 3 e Characteristics of a steam ejector function.
sij ¼ m
vvi vvj 2 þ I div u vxj vxi 3
(5)
Please cite this article in press as: Allouche, Y., et al., A CFD analysis of the flow structure inside a steam ejector to identify the suitable experimental operating conditions for a solar-driven refrigeration system, International Journal of Refrigeration (2013), http://dx.doi.org/10.1016/j.ijrefrig.2013.07.027
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Fig. 4 e Photo (a) and cross section drawing (b) of the tested CPM ejector.
The transport equations for the turbulent kinetic energy (k) and the turbulent kinetic energy dissipation rate (ε) can be found in Fluent 6.3 User’s Guide (2006).
4.
Results and discussion
One of the aims of this study is to determine the optimal operating conditions leading to a high ejector performance suitable for air conditioning system running on solar thermal energy. The solar loop used for vapor generation delivers hot water in the range of 90e110 C while the condenser temperatures were varied in the range of 25e40 C which is likely expected in Mediterranean climate.
4.1.
section. The results presented in Fig. 7 compare qualitatively well with the characteristics of shock (train) structure obtained by Bartosiewicz et al. (2005) and by Bouhanguel et al. (2011). Direct comparison however is difficult since in these cases air was used as working fluid. It can also be observed from Fig. 7 that for the operating conditions presented, the mixing process starts at the beginning of the constant area section and finishes just upstream the subsonic diffuser. After the mixing process is completed, the recompression of the mixed stream commence that is indicated by a monotonous increase of the pressure and decrease of the Mach number below unity. The working fluid leaves the ejector tail at a pressure determined by the condenser temperature.
4.2. Effect of condenser pressure on the flow structure and on the entrainment ratio
Study of the velocity profile inside the ejector
Fig. 7 shows the Mach number and the absolute pressure along the ejector axis. It can be seen that at the NXP, the primary fluid expands due to the gradual increase of the nozzle cross section. The velocity increases to supersonic values with a simultaneous pressure drop. In the mixing chamber, the presence of elliptical structures frequently called “diamond waves” in the literature (Pianthong et al., 2007) can be observed. These “diamond waves” are the results of complex momentum exchange between the two fluid streams, manifested by a series of oscillations of the Mach number and the static pressure along the axis of symmetry in the mixing chamber. Zhu et al. (2008) explained this phenomena by the imperfect expansion of the primary jet at the nozzle exit
Influence of the condenser pressure on the flow structure is presented in this section. Several simulations were carried out using the CFD model. Only Pc was varied, all the other boundary conditions were kept constants as summarized in Table 1. With reference to the characteristic curve shown in Fig. 8, simulation results show that one can distinguish 3 operating regimes. For condenser pressures below 3 kPa, two shock waves were located in the diffuser section corresponding to the results obtained for cases A and B. It can be seen in Fig. 9a and b where the axial velocities and Mach number contours as function of condenser pressure are respectively shown, that these shock waves in case A were stronger than in case B. Fig. 9a and b also describe the flow structure for different values of Pc shown in Table 2. These values correspond to a
Secondary inlet Nozzle throat
Primary inlet
Spindle NXP
Fig. 5 e Detail of the adjustable spindle in the primary nozzle.
Fig. 6 e Details of the computational mesh.
Please cite this article in press as: Allouche, Y., et al., A CFD analysis of the flow structure inside a steam ejector to identify the suitable experimental operating conditions for a solar-driven refrigeration system, International Journal of Refrigeration (2013), http://dx.doi.org/10.1016/j.ijrefrig.2013.07.027
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1
Double choking region
0.9 0.8 Entrainmenetratio
0.7
Double Shock wave
0.6 0.5
Single choking region Pb Single Shock wave
0.4 0.3 0.2 0.1 0
0.1 1.9
2.4
2.9
3.4
3.9
0.2
Fig. 7 e Mach number and pressure distribution along the ejector axis for d [ 21 mm, Pc [ 3 kPa, Tg [ 93 C and Te [ 10 C.
saturation temperature range from 17 C to 29 C. In case A, the shock waves are accompanied by two velocity drops: first at the diffuser inlet section and then at halfway of the diffuser length. In case B, both shock waves moved further upstream. Both cases resulted in an Er of 0.46, corresponding to operating point in the double choking region (see Fig. 1). Nevertheless, none of these conditions can be considered as optimal operating points, since in both cases a pressure drop was observed in the diffuser at supersonic velocities, while the principal function of the diffuser would be the subsonic compression of the mixed primary and secondary streams. Only one shock wave in the beginning of the diffuser was observed for cases C, D and E. Fig. 8 shows that Er remained unchanged compared to cases A and B, however, for Pc in the range of 2.85e3 kPa, the losses in the diffuser section were reduced, resulting in near optimal operation. For 3 kPa < Pc < 3.8 kPa (cases F, G and H), the position of the primary stream moves towards the mixing chamber, while the secondary flow remains unchoked. This can be seen in Fig. 9b, where the Mach number of the secondary flow in the _ e varies mixing chamber and in the throat is bellow 1, thus m with the downstream pressure. Fig. 8 also shows that for this small increase of the back pressure, the entrainment ratio which rapidly decreases from 0.47 to 0. Pc also influences the diamond wave structure as shown in Fig. 8. By increasing the back pressure, stronger diamond waves can be observed as indicated by the darker contours in the figure. Finally for Pc > 3.9 kPa (case I), the motive fluid presents very strong diamond waves downstream the nozzle exit position and it becomes subsonic in the constant area section. Reverse flow appears, Er is negative, the ejector fails to operate (Pianthong et al., 2007). Results of this step lead to the following main conclusions:
Table 1 e Boundary conditions applied at the inlets of the ejector. Pp [kPa]
Tp [ C]
Ps [kPa]
Te [ C]
70
93
1.4
10
Pc[kpa]
Fig. 8 e Effect of Pc on entrainment ratio at constant operating conditions.
The characteristic pressures describing the ejector operating are: Pc* ¼ 3 kPa and Pb ¼ 3.8 kPa. The optimal ejector operation is described by case D with the highest entrainment ratio, choked secondary flow and with single shock wave in the constant area section.
4.3.
Effect of primary flow inlet pressure
Fig. 10 shows the influence of the generator pressure on Er for different condenser conditions. It can be seen from the figure that the lower the condenser pressure, the higher the entrainment ratio. For a Pc of 2.5 kPa (Tc ¼ 20 C), a generator pressure of 40 kPa (Tg ¼ 76 C) resulted in an entrainment ratio of 0.16. By increasing slightly Pg, Er rapidly increases to a maximum of 0.61. This indicates that at Pg ¼ 40 kPa, the ejector was operating in single choking mode, the secondary fluid did not reach M ¼ 1. Beyond Pg ¼ 48 kPa, Er showed a slow decrease with generator pressure. This is due to the fact that _e the ejector was operating in double choking mode with m practically constant; however increasing Pg resulted in an _ g and thus decreased ejector performance. The increased m same Er profile was found for Pc varying from 2.85 kPa to 3.5 kPa. For a Pc of 4 kPa, the optimum value of Er ¼ 0.3 was obtained for a generator pressure going from 74 kPa to 90 kPa. It can also be seen from Fig. 10 that beyond the optimal entrainment ratio, all the curves coincide, or in other words, the ejector performance becomes independent of the back pressure. This is due to the fact that the ejector operates in double choking mode. In this sense, Fig. 10 can be used as the basis for finding optimal Pg for a given condenser condition (determined by climacteric conditions) that results in the highest entrainment ratio. In order to provide a visual interpretation of the previously mentioned, the influence of Pg on the flow structure (Mach number distribution) for a discharge pressure of 3 kPa is shown in Fig. 11. The generator pressure was varied between 30 and 90 kPa. It is clear from the figure that the generator temperature has a great impact on the flow structure. For relatively low Pg (e.g. 30 kPa), the primary stream undergoes a number of diamond shocks, the
Please cite this article in press as: Allouche, Y., et al., A CFD analysis of the flow structure inside a steam ejector to identify the suitable experimental operating conditions for a solar-driven refrigeration system, International Journal of Refrigeration (2013), http://dx.doi.org/10.1016/j.ijrefrig.2013.07.027
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Fig. 9 e a) Velocity contours for different values of condenser pressure. b) Mach number distribution for different values of condenser pressure.
secondary fluid is not entrained, the ejector fails to operate. For Pg ¼ 50 kPa, the ejector is in dingle choking mode, however still a series of strong shock waves can be observed downstream the primary nozzle exit section. For generator pressures 60 kPa and 70 kPa, the secondary fluid gets accelerated to sonic velocity, relatively weak shocks occur that
leads to near optimal ejector performance. Further increase in Pg resulted in oblique shock waves in the diffuser section, decreasing the efficiency of the recompression process. With reference to the above results, optimal generator pressure was found to be near 70 kPa.
5. Table 2 e Condenser pressures considered in the simulations. Simulation
A
B
C
D
E
F
G
H
I
Pc [kPa]
1.9
2.5
2.85
2.95
3
3.2
3.4
3.5
4
Preliminary experimental results
The solar-driven ejector refrigeration system at ENIT represented previously in Fig. 1 is shortly discussed here. A solar collector field of 60 m2 of vacuum tube collectors supplies the necessary heat to the air conditioner using water as thermal fluid. The water is circulated between the collector field and a
Please cite this article in press as: Allouche, Y., et al., A CFD analysis of the flow structure inside a steam ejector to identify the suitable experimental operating conditions for a solar-driven refrigeration system, International Journal of Refrigeration (2013), http://dx.doi.org/10.1016/j.ijrefrig.2013.07.027
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Entrainment Ratio
0.6
Pc=4 kPa Pc=3.5 kPa
0.45
Pc=3.4 kPa Pc=3.2 kPa
0.3
Pc=3 kPa Pc=2.95 kPa Pc=2.85 kPa
0.15
Pc=2.5 kPa
0
30
40
50
60
70
Pg [kPa]
80
90
100
Fig. 10 e Effect of Pg on the Entrainment Ratio for different condenser pressure values.
3000 L storage tank by a pump. The generator supplied by water from the high temperature storage tank, where the motive fluid is generated in the form of saturated steam. The super-heater acts as an additional source of energy to ensure the pressure and temperature conditions required by the ejector and to avoid condensation. At the ejector exit, the
recompressed mixed stream is discharged to a 15 kW condenser, cooled by an external chiller. The low temperature thermal energy produced in the evaporator is stored in a 900 L cold storage tank filled with PCM and distributed to the air handling units. The analyses presented in the previous sections on one hand permitted to determine the optimal operating conditions on the condenser and generator sides for this particular ejector, and on the other hand, the plausible operational pressure ranges for the ejector. As mentioned previously throughout the numerical analysis, the aim of this study was to identify the operating conditions leading to a successful ejector tests. Preliminary tests were performed for a spindle position of 21 mm under condenser (Pc ¼ 3 kPa) and generator (Pg ¼ 70 kPa) operating conditions resulting in double choking ejector operation. Before starting the ejector tests, the cycle was tested for leakage. The system was vacuumed and the pressure was monitored for 90 min. It was found that the pressure increase did not exceed a rate of 3.9 mbar h1 (Alexis and Karayiannis, 2005), which was considered to be satisfactory. The most important parameters that directly affect ejector operation were maintained constant. These were:
Fig. 11 e Mach Number contours for different generator pressures under fixed condenser conditions (Pc [ 3 kPa). Please cite this article in press as: Allouche, Y., et al., A CFD analysis of the flow structure inside a steam ejector to identify the suitable experimental operating conditions for a solar-driven refrigeration system, International Journal of Refrigeration (2013), http://dx.doi.org/10.1016/j.ijrefrig.2013.07.027
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references
Fig. 12 e Water temperature evolution inside the evaporator during the test.
Generator temperature. Pressure of the motive flow. Flow rate on the motive fluid side. Water inlet temperature in the condenser.
Fig. 12 shows the experimental evaporator water temperature evolution during a preliminary experimental runs. It can be seen from the figure that the evaporator temperature changed from 35 C to 16 C in less than 49 min, which can be considered satisfactory due to the volume of the system. The authors would like to emphasize that this experiment was a simple preliminary work to demonstrate the ejector operation without direct interpretation of the system performance. Experimental measurements will be extended in the near future to evaluate long term performance of the entire solar assisted unit within the range of operating conditions established by the numerical simulations.
6.
Conclusions
In this paper, a retrograde method has been used to identify the suitable operating conditions to make a solar-driven ejector refrigeration system functional under near optimal performances. It was found that optimal ejector operation is achieved when the ejector near critical mode. This finding was also well supported by the interpretation of the flow structures resulted from the CFD analysis. A near optimal ejector performance was obtained when weak diamond wave structure of the primary flow downstream the nozzle exit plain, and single shock wave of the mixed stream in the ejector tail were observed. Preliminary experimental results have shown good ejector operation under near optimum operating conditions. The experimental work with the test system will be expanded to confirm numerical findings and the ejector cycle performance operating under real conditions will be assessed in the near future.
Acknowledgments Authors wish to thank all AIRCOND project partners for their kind cooperation and information exchange.
Abdulateef, J.M., Sopian, K., Alghoul, M.A., Sulaiman, M.Y., 2009. Review on solar-driven ejector refrigeration technologies. Renew. Sustain. Energy Rev. 13 (6e7), 1338e1349. Alexis, G.K., Karayiannis, E.K., 2005. A solar ejector cooling system using refrigerant R134a in the Athens area. Renew. Energy 30, 1457e1469. Allouche, Y., Bouden, C., Omer, C., Riffat, S., 2011. A solar-driven ejector refrigeration system for Mediterranean climate: experience and performance. In: Proceedings of the 7th International Conference on Sustainable Energy Technologies, _ SET2011, Istanbul, Tu¨rkiye. Allouche, Y., Bouden, C., Riffat, S., 2012. A solar-driven ejector refrigeration system for Mediterranean climate: experience improvement and new results performedTerraGreen12 International Conference. Energy Procedia 18, 1115e1124. Bartosiewicz, Y., Aidoun, Z., Desevaux, P., Mercadier, Y., 2005. Numerical and experimental investigations on supersonic ejectors. Int. J. Heat Fluid Flow 26, 56e70. Bouhanguel, Y., Desevaux, P., Gavignet, E., 2011. Flow visualization in supersonic ejectors using laser tomography techniques. Int. J. Refrigeration 34, 1633e1640. Cardemil, J.M., Colle, S., 2012. A general model for evaluation of vapor ejectors performance for application in refrigeration. Energy Convers. Manag. 64, 79e86. El-Dessouky, H., Ettouney, H., Alatiqi, I., Al-Nuwaibit, G., 2002. Evaluation of steam jet ejectors. Chem. Eng. Prog. 41, 551e561. He, S., Li, Y., Wang, R.Z., 2009. Progress of mathematical modeling on ejectors. Renew. Sustain. Energy Rev. 13, 1760e1780. Ji, M., Utomo, T., Wo, J., Lee, Y., Jeong, H., Chung, H., 2010. CFD investigation on the flow structure inside thermo vapor compressor7th International Conference on Sustainable Energy Technologies. Energy 35 (6), 2674e2702. Pianthong, K., Seehanam, W., Bahnia, M., Sriveerakul, T., Aphoreratana, S., 2007. Investigation and improvement of ejector refrigeration system using computational fluid dynamics technique. Energy Convers. Manag. 48 (9), 2556e2564. Selvaraju, A., Mani, A., 2004. Analysis of an ejector with environment friendly refrigerants. Appl. Therm. Eng. 24, 827e838. Selvaraju, A., Mani, A., 2006. Experimental investigation on R134a vapour ejector refrigeration system. Int. J. Refrigeration 29, 1160e1166. Sriveerakul, T., Aphornratana, S., Chunnanond, K., 2007a. Performance prediction of steam ejector using computational fluid dynamics: part 1. Validation of the CFD results. Int. J. Therm. Sci. 46, 812e822. Sriveerakul, T., Aphoreratana, S., Chunnanond, K., 2007b. Performance of steam ejector using computational fluid dynamics: part2. Flow structure of a steam ejector influenced by operating pressures and geometries. Int. J.Therm. Sci. 46, 823e833. Varga, Sz., Oliveira, A.C., Diaconu, B., 2009a. Numerical assessment of steam ejector efficiencies using CFD. Int. J. Refrigeration 32, 1203e1211. Varga, Oliveira, Armando C., Diaconu, Bogdan, 2009b. Influence of geometrical factors on steam ejector performance e a numerical assessment. Int. J. Refrigeration 32, 1694e1701. Varga, Sz., Oliveira, A.C., Ma, X., Omer, S.A., Zhang, W., Riffat, S.B., 2011. Experimental and numerical analysis of a variable area ratio steam ejector. Int. J. Refrigeration 34, 1668e1675.
Please cite this article in press as: Allouche, Y., et al., A CFD analysis of the flow structure inside a steam ejector to identify the suitable experimental operating conditions for a solar-driven refrigeration system, International Journal of Refrigeration (2013), http://dx.doi.org/10.1016/j.ijrefrig.2013.07.027
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Vidal, H., Colle, S., dos Santos Pereira, G., 2006. Modelling and hourly simulation of a solar ejector cooling system. Appl. Therm. Eng. 26, 663e672. White, F.M., 1991. In: Viscous Fluid Flow, second ed. McGraw Hill, Boston.
Yadav, R.L., Patwardhan, A.W., 2008. Design aspects of ejectors: effects of suction chamber geometry. Chem. Eng. Sci. 63, 3886e3897. Zhu, Y., Ci, W., Wen, C., Li, Y., 2008. Simplified ejector model for control and optimization. Energy Convers. Manag. 49, 1424e1432.
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A CFD analysis of the flow structure inside a steam ejector to identify the suitable experimental operating conditions for a solar-driven refrigeration system Yosr Allouche a,b,*, Chiheb Bouden a, Szabolcs Varga b a
Universite´ de Tunis El Manar, Ecole Nationale d’Inge´nieurs de Tunis, LR-11-ES16, Laboratoire de Mate´riaux, Optimisation et E´nergie pour la Durabilite´, 1002 Tunis, Tunisia b New Energy Technologies Unit, Faculty of Engineering, University of Porto, Rua Dr Roberto Frias, 4200-465 Porto, Portugal
article info
abstract
Article history:
This paper presents a numerical study of a steam ejector using CFD with the objective of
Received 3 February 2013
identifying suitable experimental conditions that allows for a reliable ejector cycle operation.
Received in revised form
The flow structure and the mixing process inside the ejector were assessed for a range of
29 July 2013
operating conditions typical for a solar driven air conditioning system. The effect of varying
Accepted 31 July 2013
the condenser pressure was studied. It was found that for relatively low condenser pressures
Available online xxx
(<2.5 kPa), two distinct shock waves occurred in the diffuser section resulting in a reduced recompression efficiency, although it did not have a direct impact on the entrainment ratio.
Keywords:
The effect of generator pressure was also studied. It was found that the entrainment ratio
Steam ejector
showed a maximum for constant condenser conditions. A near optimal condition of 70 kPa
Computational fluid dynamic
generator and 3 kPa condenser pressures were identified and tested in a preliminary
Entrainment ratio
experiment carried out with the solar driven ejector system installed in Tunis.
Experimentation
ª 2013 Elsevier Ltd and IIR. All rights reserved.
Flow structure
Une analyse en dynamique des fluides computationnelle (CFD) d’une structure d’e´coulement a` l’inte´rieur d’un e´jecteur de vapeur pour identifier les conditions de fonctionnement expe´rimentales correctes pour un syste`me frigorifique fonctionnant a` l’e´nergie solaire
* Corresponding author. Universite´ de Tunis El Manar, Ecole Nationale d’Inge´nieurs de Tunis, LR-11-ES16, Laboratoire de Mate´riaux, Optimisation et E´nergie pour la Durabilite´, 1002 Tunis, Tunisia. Tel.: þ216 28 174 403; fax: þ216 71 87 27 29. E-mail address: [email protected] (Y. Allouche). 0140-7007/$ e see front matter ª 2013 Elsevier Ltd and IIR. All rights reserved. http://dx.doi.org/10.1016/j.ijrefrig.2013.07.027
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Nomenclature d E Er gI k M _ m P P c* T T u xd
Spindle tip position (mm) Total Energy (J) Entrainment ratio acceleration of gravity vector (m s2)identity matrix thermal conductivity (W m1 K1) Mach number Mass flow rate (kg s1) Pressure (kPa) Critical back pressure (kPa) Time (s) Temperature ( C) average velocity (m s1) Distance between two shock waves
Greek letters s Stress tensor (Pa) P Density (Kg m3) E Turbulence dissipation rate (m2 s3)
m w
Dynamic viscosity (Pa s) Kinematic viscosity (m2 s1)
Abbreviation COP Coefficient of performance CMA Constant mixing area CPM Constant pressure mixing MEPCM Micro-encapsulated phase change material NXP Nozzle exit plain Spl Spindle length (mm) Spt Spindle travel (mm) Subscripts B break down C condenser D double chocking E evaporator G generator i,j generic space coordinates (2D) Nozz nozzle
Mots cle´s : Ejecteur de vapeur ; Dynamique des fluides computationnelle ; Taux d’entraıˆnement ; Expe´rimentation ; Structure de l’e´coulement
1.
Introduction
Global warming and the increasing need for the thermal comfort has led to a rapidly increasing cooling energy, and simultaneously, electricity demand. This tendency seems to threaten the aims set by many developed and developing countries for the upcoming decades. Beside the medical services and food storage, air-conditioning in buildings is a major contributor to the increasing electricity consumption. The concept of solar cooling is of great interest, since the cooling load is directly correlated to the intensity of solar radiation. Research on solar cooling goes back as far as 1872 when Abel Pifre developed the first absorption solar refrigerator producing a small amount of ice (Abdulateef et al., 2009). Nowadays a number of technologies can be used to produce cooling by transformation of solar heat (Vidal et al., 2006). The use of ejectors to create thermal compression of a working fluid has been demonstrated to be a low electricity consumption method in comparison with the mechanical compression systems. Ejector refrigeration is a promising technology due to its relative low cost and simplicity comparing to an absorption cooling cycle, but the main disadvantage is still its moderate COP. Many researchers have been interested in solar-driven ejector refrigeration technology and its applications. Recently, Abdulateef et al. (2009) presented a valuable review on ejector based on solar cooling technologies providing a solid background of their operating principles. Generally, water has been used as the working fluid in ejectors (Sriveerakul et al., 2007b) because of its low cost, chemical
stability and safe use. However, other refrigerants have also been widely applied. For more details of these investigations, the reader is referred to Selvaraju and Mani (2004, 2006). Selvaraju and Mani (2004) studied the variation of the area ratio of the ejector and the critical entrainment ratio with generator temperature for R134a, R152a, R290, R600a and R717 refrigerants. It was observed that R134a led to a better entrainment ratio (0.3 at Tg ¼ 368 K Te ¼ 278 K and Tc ¼ 298 K) at all operating conditions in comparison with other working fluids. Beside refrigerant selection, ejector design strongly influences cycle performance since the compression ratio depends on the geometry of the nozzle throat and diffuser. A summary of experimental data available in the literature for steam ejectors discussing the influence of the throat-diffuser area ratio is given in El-Dessouky et al. (2002). It has been shown that the suction chamber geometry has an important effect on the entrainment ratio (Yadav and Patwardhan, 2008). Varga et al. (2009a,b) investigated the nozzle efficiency for different nozzle diameters and the suction efficiency for different area ratios that can be applied with simplified mathematical models e.g. the one based on the constant pressure mixing theory (CPM) (Cardemil and Colle, 2012; Zhu et al., 2008; He et al., 2009). These simplified models are excellent tools for estimating on design global ejector performances and obtaining a first ejector design. However, they are not adequate to describe the details of fluid flow inside the ejector. Varga et al. (2011) proposed to apply a movable spindle at the primary nozzle inlet to control ejector operation. Both experimental and CFD data showed that the spindle tip position affected the entrainment ratio (from 0.1 to 0.5) by
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controlling the primary flow rate. It was also concluded that CFD results predicted experimental measurements with a good accuracy when the ejector operated in double chocking mode. The current paper aims to numerically study the flow structure inside the ejector for a better understanding of the mixing phenomenon and the location of the shock waves as a function of the operating parameters using CFD. It was assumed that the fluid flow was axi-symmetric and compressible. Turbulent behavior was treated using k-ε realizable model. These findings will lead to the identification of the optimal operating conditions in the double choking region for an existing ejector installed at the National Engineering school of Tunis (ENIT) as part of a solar energy driven air conditioner. The system is built of three sub-systems (see Fig. 1): (i) a solar loop made of 60 m2 vacuum tube collectors connected to a 3000 L storage tank, (ii) the ejector loop with 5 KW cooling capacity, and (iii) the distribution loop having a 900 L capacity cold storage tank containing 800 L micro-encapsulated phase change material (MEPCM) and 4 air-handling units. This setup has been designed to meet the thermal load of 4 offices in the solar energy laboratory at ENIT. The operation of the system has been described in previous papers (Allouche et al., 2011, 2012).
nozzle. The primary stream outs with a supersonic speed to create a very low pressure region at the Nozzle Exit plan (NXP) and consequently in the mixing chamber. This means that the “secondary fluid” can be drawn into the mixing chamber. The motive flow expands and forms a converging duct without mixing with secondary fluid. Nevertheless, the velocity of the secondary fluid increases gradually until it reaches M ¼ 1. The mixing process is considered to start at this location. By the end of the mixing chamber, the two streams are completely mixed. In an ideal case, due to the high pressure at the diffuser exit, a shock wave takes place somewhere at the end of the constant area section or at the beginning of the diffuser. This causes a major compression effect and a sudden drop in the flow speed from supersonic to subsonic. The mixed fluids leave the subsonic diffuser at a pressure defined by the condenser of the cooling cycle.
2.2. Ejector performance indicators and dependence on operating conditions Ejector performance is often measured by the entrainment ratio (Er) defined as the ratio between the secondary and the primary mass flow rates: Er ¼
2. Steam ejector design and performance indicators 2.1.
Ejector unit
A steam ejector refrigeration cycle uses heat as primary energy source in the rage of 70e150 C in order to produce cooling usually between 10 C and 20 C, depending on the ejector capacity. A typical steam ejector is composed of a primary nozzle, a mixing chamber, a throat and a diffuser as shown in Fig. 2. The primary fluid (motive) coming from the superheater enters the ejector at high temperature and high pressure (g), and then accelerates by expanding through the
3
_e m _s m
(1)
Every single ejector has its proper characteristic curve identifying its performance as a function of the operating conditions. One of the most important parameter on the curve is the critical back pressure (Pc*). Fig. 3 describes the effect of the back pressure on Er where 3 regions can be identified: choked flow, unchoked flow and reversed flow regions. Below Pc*, Er remains unchanged. This can be explained by the choking of the secondary fluid in the constant area section. Beyond Pc*, the secondary steam does not reach M ¼ 1 (only the primary stream is choked in the primary nozzle), thus Er decreases rapidly with the back pressure. Finally, the third region (Pc > Pb) indicates ejector failure, where reverse flow appears.
Fig. 1 e Configuration of the field test system installed at the National Engineering School of Tunis. Please cite this article in press as: Allouche, Y., et al., A CFD analysis of the flow structure inside a steam ejector to identify the suitable experimental operating conditions for a solar-driven refrigeration system, International Journal of Refrigeration (2013), http://dx.doi.org/10.1016/j.ijrefrig.2013.07.027
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Fig. 2 e Schematic (not scaled) view of a typical ejector.
3.
Ejector geometry and CFD model
3.1.
Ejector and spindle geometries
Depending on their geometries, generally ejectors are classified into two categories: CMA CPM ejectors. The difference between the two types is the position of the nozzle exit (Varga et al., 2009a,b). In the current study, the solar-driven refrigeration system is equipped with CPM ejector as described in Fig. 4. The Ejector is connected to the generator from the top and to the evaporator from the bottom side. In order to provide regulation for the ejector operation, a spindle was installed on the high pressure side in the primary nozzle to control the motive flow rate as shown in Fig. 5. As the spindle tip travels into the nozzle, the primary nozzle throat area decreases and thus the flow rate decreases. Several simulations showing the effect of the spindle position (SP) on the primary flow rate were carried out using CFD in a previous work (Varga et al., 2011). SP was considered to be at 50 mm in a fully open position, while 0 mm when there is no flow rate through the primary nozzle (fully closed).
3.2.
CFD model
The fluid flow inside the ejector was considered to be axisymmetric (Pianthong et al., 2007). The computational grid
was developed using the software Gambit 2.4.6. A structured mesh with quadratic control volumes have been adopted in most of the domain and triangular control volumes have been used in some specific areas of the ejector (nozzle throat, NXP) as shown in Fig. 6. Realizable version k-ε was considered as the turbulence model, since it was found that it predicts more accurately the spreading rate of jet flows (Sriveerakul et al., 2007a). This model is also suitable for flows at high Reynolds number and it takes into account the rotational effects. Zones with recirculation are more apparent than when using the standard model. It has been already found to predict well global ejector performances by several authors (Sriveerakul et al., 2007b) for details of the particular formulation of realizable k-ε turbulence model; the reader is referred to Ji et al. (2010). Flow behavior near the walls was assumed to be logarithmic. A density based solver with implicit formulation was used. Pressure boundary conditions were applied at inlets and outlet. Steam was used as a working fluid assuming the ideal gas relationship between the pressure and density. The solution was considered to be converged when the relative residual was within 106 for all unknown variables. The governing equations that describe the compressible flow in an ejector can be written in their general forms (White, 1991). Continuity: Dr þ rdiv u ¼ 0 Dt
(2)
Momentum: r
Du ¼ r g Vp þ Vsij Dt
(3)
Energy: r
Dh Dp vui ¼ þ divðkVTÞ þ sij Dt Dt vxj
(4)
where the stress tensor sij is given by:
Fig. 3 e Characteristics of a steam ejector function.
sij ¼ m
vvi vvj 2 þ I div u vxj vxi 3
(5)
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Fig. 4 e Photo (a) and cross section drawing (b) of the tested CPM ejector.
The transport equations for the turbulent kinetic energy (k) and the turbulent kinetic energy dissipation rate (ε) can be found in Fluent 6.3 User’s Guide (2006).
4.
Results and discussion
One of the aims of this study is to determine the optimal operating conditions leading to a high ejector performance suitable for air conditioning system running on solar thermal energy. The solar loop used for vapor generation delivers hot water in the range of 90e110 C while the condenser temperatures were varied in the range of 25e40 C which is likely expected in Mediterranean climate.
4.1.
section. The results presented in Fig. 7 compare qualitatively well with the characteristics of shock (train) structure obtained by Bartosiewicz et al. (2005) and by Bouhanguel et al. (2011). Direct comparison however is difficult since in these cases air was used as working fluid. It can also be observed from Fig. 7 that for the operating conditions presented, the mixing process starts at the beginning of the constant area section and finishes just upstream the subsonic diffuser. After the mixing process is completed, the recompression of the mixed stream commence that is indicated by a monotonous increase of the pressure and decrease of the Mach number below unity. The working fluid leaves the ejector tail at a pressure determined by the condenser temperature.
4.2. Effect of condenser pressure on the flow structure and on the entrainment ratio
Study of the velocity profile inside the ejector
Fig. 7 shows the Mach number and the absolute pressure along the ejector axis. It can be seen that at the NXP, the primary fluid expands due to the gradual increase of the nozzle cross section. The velocity increases to supersonic values with a simultaneous pressure drop. In the mixing chamber, the presence of elliptical structures frequently called “diamond waves” in the literature (Pianthong et al., 2007) can be observed. These “diamond waves” are the results of complex momentum exchange between the two fluid streams, manifested by a series of oscillations of the Mach number and the static pressure along the axis of symmetry in the mixing chamber. Zhu et al. (2008) explained this phenomena by the imperfect expansion of the primary jet at the nozzle exit
Influence of the condenser pressure on the flow structure is presented in this section. Several simulations were carried out using the CFD model. Only Pc was varied, all the other boundary conditions were kept constants as summarized in Table 1. With reference to the characteristic curve shown in Fig. 8, simulation results show that one can distinguish 3 operating regimes. For condenser pressures below 3 kPa, two shock waves were located in the diffuser section corresponding to the results obtained for cases A and B. It can be seen in Fig. 9a and b where the axial velocities and Mach number contours as function of condenser pressure are respectively shown, that these shock waves in case A were stronger than in case B. Fig. 9a and b also describe the flow structure for different values of Pc shown in Table 2. These values correspond to a
Secondary inlet Nozzle throat
Primary inlet
Spindle NXP
Fig. 5 e Detail of the adjustable spindle in the primary nozzle.
Fig. 6 e Details of the computational mesh.
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1
Double choking region
0.9 0.8 Entrainmenetratio
0.7
Double Shock wave
0.6 0.5
Single choking region Pb Single Shock wave
0.4 0.3 0.2 0.1 0
0.1 1.9
2.4
2.9
3.4
3.9
0.2
Fig. 7 e Mach number and pressure distribution along the ejector axis for d [ 21 mm, Pc [ 3 kPa, Tg [ 93 C and Te [ 10 C.
saturation temperature range from 17 C to 29 C. In case A, the shock waves are accompanied by two velocity drops: first at the diffuser inlet section and then at halfway of the diffuser length. In case B, both shock waves moved further upstream. Both cases resulted in an Er of 0.46, corresponding to operating point in the double choking region (see Fig. 1). Nevertheless, none of these conditions can be considered as optimal operating points, since in both cases a pressure drop was observed in the diffuser at supersonic velocities, while the principal function of the diffuser would be the subsonic compression of the mixed primary and secondary streams. Only one shock wave in the beginning of the diffuser was observed for cases C, D and E. Fig. 8 shows that Er remained unchanged compared to cases A and B, however, for Pc in the range of 2.85e3 kPa, the losses in the diffuser section were reduced, resulting in near optimal operation. For 3 kPa < Pc < 3.8 kPa (cases F, G and H), the position of the primary stream moves towards the mixing chamber, while the secondary flow remains unchoked. This can be seen in Fig. 9b, where the Mach number of the secondary flow in the _ e varies mixing chamber and in the throat is bellow 1, thus m with the downstream pressure. Fig. 8 also shows that for this small increase of the back pressure, the entrainment ratio which rapidly decreases from 0.47 to 0. Pc also influences the diamond wave structure as shown in Fig. 8. By increasing the back pressure, stronger diamond waves can be observed as indicated by the darker contours in the figure. Finally for Pc > 3.9 kPa (case I), the motive fluid presents very strong diamond waves downstream the nozzle exit position and it becomes subsonic in the constant area section. Reverse flow appears, Er is negative, the ejector fails to operate (Pianthong et al., 2007). Results of this step lead to the following main conclusions:
Table 1 e Boundary conditions applied at the inlets of the ejector. Pp [kPa]
Tp [ C]
Ps [kPa]
Te [ C]
70
93
1.4
10
Pc[kpa]
Fig. 8 e Effect of Pc on entrainment ratio at constant operating conditions.
The characteristic pressures describing the ejector operating are: Pc* ¼ 3 kPa and Pb ¼ 3.8 kPa. The optimal ejector operation is described by case D with the highest entrainment ratio, choked secondary flow and with single shock wave in the constant area section.
4.3.
Effect of primary flow inlet pressure
Fig. 10 shows the influence of the generator pressure on Er for different condenser conditions. It can be seen from the figure that the lower the condenser pressure, the higher the entrainment ratio. For a Pc of 2.5 kPa (Tc ¼ 20 C), a generator pressure of 40 kPa (Tg ¼ 76 C) resulted in an entrainment ratio of 0.16. By increasing slightly Pg, Er rapidly increases to a maximum of 0.61. This indicates that at Pg ¼ 40 kPa, the ejector was operating in single choking mode, the secondary fluid did not reach M ¼ 1. Beyond Pg ¼ 48 kPa, Er showed a slow decrease with generator pressure. This is due to the fact that _e the ejector was operating in double choking mode with m practically constant; however increasing Pg resulted in an _ g and thus decreased ejector performance. The increased m same Er profile was found for Pc varying from 2.85 kPa to 3.5 kPa. For a Pc of 4 kPa, the optimum value of Er ¼ 0.3 was obtained for a generator pressure going from 74 kPa to 90 kPa. It can also be seen from Fig. 10 that beyond the optimal entrainment ratio, all the curves coincide, or in other words, the ejector performance becomes independent of the back pressure. This is due to the fact that the ejector operates in double choking mode. In this sense, Fig. 10 can be used as the basis for finding optimal Pg for a given condenser condition (determined by climacteric conditions) that results in the highest entrainment ratio. In order to provide a visual interpretation of the previously mentioned, the influence of Pg on the flow structure (Mach number distribution) for a discharge pressure of 3 kPa is shown in Fig. 11. The generator pressure was varied between 30 and 90 kPa. It is clear from the figure that the generator temperature has a great impact on the flow structure. For relatively low Pg (e.g. 30 kPa), the primary stream undergoes a number of diamond shocks, the
Please cite this article in press as: Allouche, Y., et al., A CFD analysis of the flow structure inside a steam ejector to identify the suitable experimental operating conditions for a solar-driven refrigeration system, International Journal of Refrigeration (2013), http://dx.doi.org/10.1016/j.ijrefrig.2013.07.027
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7
Fig. 9 e a) Velocity contours for different values of condenser pressure. b) Mach number distribution for different values of condenser pressure.
secondary fluid is not entrained, the ejector fails to operate. For Pg ¼ 50 kPa, the ejector is in dingle choking mode, however still a series of strong shock waves can be observed downstream the primary nozzle exit section. For generator pressures 60 kPa and 70 kPa, the secondary fluid gets accelerated to sonic velocity, relatively weak shocks occur that
leads to near optimal ejector performance. Further increase in Pg resulted in oblique shock waves in the diffuser section, decreasing the efficiency of the recompression process. With reference to the above results, optimal generator pressure was found to be near 70 kPa.
5. Table 2 e Condenser pressures considered in the simulations. Simulation
A
B
C
D
E
F
G
H
I
Pc [kPa]
1.9
2.5
2.85
2.95
3
3.2
3.4
3.5
4
Preliminary experimental results
The solar-driven ejector refrigeration system at ENIT represented previously in Fig. 1 is shortly discussed here. A solar collector field of 60 m2 of vacuum tube collectors supplies the necessary heat to the air conditioner using water as thermal fluid. The water is circulated between the collector field and a
Please cite this article in press as: Allouche, Y., et al., A CFD analysis of the flow structure inside a steam ejector to identify the suitable experimental operating conditions for a solar-driven refrigeration system, International Journal of Refrigeration (2013), http://dx.doi.org/10.1016/j.ijrefrig.2013.07.027
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Entrainment Ratio
0.6
Pc=4 kPa Pc=3.5 kPa
0.45
Pc=3.4 kPa Pc=3.2 kPa
0.3
Pc=3 kPa Pc=2.95 kPa Pc=2.85 kPa
0.15
Pc=2.5 kPa
0
30
40
50
60
70
Pg [kPa]
80
90
100
Fig. 10 e Effect of Pg on the Entrainment Ratio for different condenser pressure values.
3000 L storage tank by a pump. The generator supplied by water from the high temperature storage tank, where the motive fluid is generated in the form of saturated steam. The super-heater acts as an additional source of energy to ensure the pressure and temperature conditions required by the ejector and to avoid condensation. At the ejector exit, the
recompressed mixed stream is discharged to a 15 kW condenser, cooled by an external chiller. The low temperature thermal energy produced in the evaporator is stored in a 900 L cold storage tank filled with PCM and distributed to the air handling units. The analyses presented in the previous sections on one hand permitted to determine the optimal operating conditions on the condenser and generator sides for this particular ejector, and on the other hand, the plausible operational pressure ranges for the ejector. As mentioned previously throughout the numerical analysis, the aim of this study was to identify the operating conditions leading to a successful ejector tests. Preliminary tests were performed for a spindle position of 21 mm under condenser (Pc ¼ 3 kPa) and generator (Pg ¼ 70 kPa) operating conditions resulting in double choking ejector operation. Before starting the ejector tests, the cycle was tested for leakage. The system was vacuumed and the pressure was monitored for 90 min. It was found that the pressure increase did not exceed a rate of 3.9 mbar h1 (Alexis and Karayiannis, 2005), which was considered to be satisfactory. The most important parameters that directly affect ejector operation were maintained constant. These were:
Fig. 11 e Mach Number contours for different generator pressures under fixed condenser conditions (Pc [ 3 kPa). Please cite this article in press as: Allouche, Y., et al., A CFD analysis of the flow structure inside a steam ejector to identify the suitable experimental operating conditions for a solar-driven refrigeration system, International Journal of Refrigeration (2013), http://dx.doi.org/10.1016/j.ijrefrig.2013.07.027
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references
Fig. 12 e Water temperature evolution inside the evaporator during the test.
Generator temperature. Pressure of the motive flow. Flow rate on the motive fluid side. Water inlet temperature in the condenser.
Fig. 12 shows the experimental evaporator water temperature evolution during a preliminary experimental runs. It can be seen from the figure that the evaporator temperature changed from 35 C to 16 C in less than 49 min, which can be considered satisfactory due to the volume of the system. The authors would like to emphasize that this experiment was a simple preliminary work to demonstrate the ejector operation without direct interpretation of the system performance. Experimental measurements will be extended in the near future to evaluate long term performance of the entire solar assisted unit within the range of operating conditions established by the numerical simulations.
6.
Conclusions
In this paper, a retrograde method has been used to identify the suitable operating conditions to make a solar-driven ejector refrigeration system functional under near optimal performances. It was found that optimal ejector operation is achieved when the ejector near critical mode. This finding was also well supported by the interpretation of the flow structures resulted from the CFD analysis. A near optimal ejector performance was obtained when weak diamond wave structure of the primary flow downstream the nozzle exit plain, and single shock wave of the mixed stream in the ejector tail were observed. Preliminary experimental results have shown good ejector operation under near optimum operating conditions. The experimental work with the test system will be expanded to confirm numerical findings and the ejector cycle performance operating under real conditions will be assessed in the near future.
Acknowledgments Authors wish to thank all AIRCOND project partners for their kind cooperation and information exchange.
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Please cite this article in press as: Allouche, Y., et al., A CFD analysis of the flow structure inside a steam ejector to identify the suitable experimental operating conditions for a solar-driven refrigeration system, International Journal of Refrigeration (2013), http://dx.doi.org/10.1016/j.ijrefrig.2013.07.027