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Numerical investigation of the influences of mixing chamber geometries on steam ejector performance
Desalination 353 (2014) 15–20
Contents lists available at ScienceDirect
Desalination journal homepage: www.elsevier.com/locate/desal
Numerical investigation of the influences of mixing chamber geometries on steam ejector performance Hongqiang Wu, Zhongliang Liu ⁎, Bing Han, Yanxia Li College of Environmental and Energy Engineering, Beijing University of Technology, Pingleyuan 100, Chaoyang District, Beijing 100124, China
H I G H L I G H T S • CFD simulations were carried out to investigate the performance of the ejector. • There exists an optimum mixing chamber length range. • There is a fixed optimum mixing chamber convergence angle.
a r t i c l e
i n f o
Article history: Received 9 May 2014 Received in revised form 12 August 2014 Accepted 2 September 2014 Available online xxxx Keywords: Numerical investigation Steam ejector Chamber length Convergence angle
a b s t r a c t In this study, computational fluid dynamics (CFD) method is employed to investigate the effects of the mixing chamber geometries on the performance of steam ejectors used for multi-effect distillation systems. The internal flow characteristics of the steam ejector and the effects of the length and convergence angle of the mixing chamber were obtained. It is found that there is an optimum range of the mixing chamber length at which the ejector will acquire its largest entrainment ratio and the mixing chamber also has an optimum convergence angle at which the steam ejector performance is the best. © 2014 Elsevier B.V. All rights reserved.
1. Introduction Multi-effect distillation (MED), which can greatly reduce the energy consumption of seawater desalination systems, especially if it is combined with thermal vapor compression (TVC), is one of the most important and widely-used large-scale desalination methods. The thermal vapor compression is accomplished by steam ejector. The performance of the steam ejector is one of the limiting factors for improving the energy efficiency of MED-TVC desalination systems. The structure of steam ejectors is very simple and without any moving parts. It compresses a low-pressure vapor (entrained steam) by a high-pressure vapor (primary steam) through a series of energy and momentum exchanges into a mid pressure vapor. However, due to the fact that it involves strong irreversible mixing and other effects, its thermodynamic efficiency is usually very low. Entrainment ratio that is defined as the ratio of entrained low-pressure steam flow rate to high-pressure primary vapor flow rate is the main performance indicator of the steam ejectors. Increasing the entrainment ratio is of great importance for practical applications by optimizing the steam ejector structure and design. ⁎ Corresponding author. Tel./fax: +86 10 67392722. E-mail address: [email protected] (Z. Liu).
http://dx.doi.org/10.1016/j.desal.2014.09.002 0011-9164/© 2014 Elsevier B.V. All rights reserved.
Because of the practical importance, the wide potential applications and the complexity of the phenomena taking place inside the ejector, a lot of work has been carried out to improve the performance of the ejectors. Actually, as early as in 1950, Keenan et al. [1] developed a theory for designing and analyzing of the ejectors based on one-dimensional gas dynamic theory. However, this theory could be only used to predict the overall performance of the after-design ejectors without taking the effects of the ejector geometrical parameters into account. The flow pattern and other possible physical phenomena such as shock wave, choking and even phase transition inside the ejectors may well influence their performance. Therefore, improving the ejector performance of an ejector system needs understanding the physical phenomena that takes place inside the ejectors. Many researchers have engaged in researching the shock wave and choking of the ejectors with experimental and numerical methods. The results disclosed that the effect of the fluid parameters on the ejectors performance is important and direct [2–5]. The experimental results and theoretical predictions both proved that there exists a critical value for the ejector outlet pressure under the given primary and entrained vapor pressure conditions. Exceeding this critical pressure will result in fast degeneration of the ejector performance [2,3]. Riffat and Omer [4] used a commercial CFD package to predict the performance of a methanol driven ejector.
16
H. Wu et al. / Desalination 353 (2014) 15–20
Wang [5] simulated the flow through a steam ejector, whose results were validated against the experimental data by Sriveerakul et al. [6]. The numerical results are in good agreement with the experimental results [4,5]. There are also numerous studies of the geometrical parameters and structure because of their crucial effects on the performance of the ejectors [7–9]. Zhu et al. [7] tried to find the optimum nozzle outlet position (NXP) and the mixing chamber convergent angle by numerical simulations. From 210 testing results, it is found that the optimum NXP is not only proportional to the mixing section throat diameter, but also increases as the primary flow pressure rises. And the ejector performance is very sensitive to convergence angle θ, especially near the optimum working point. The entrainment ratio can vary as much as 26.6% by changing θ. A relatively bigger θ is required to better maximize the ejector performance when the primary flow pressure rises. Ji [8] numerically studied the influence of the convergence angle of the mixing chamber. The mixing chamber convergence angle in the study was varied as 0°, 0.5°, 1.0°, 2°, 3.5° and 4.5°. The ejector with a mixing-chamber convergence angle of 1.0° has the best performance. Natthawut et al. [9] investigated experimentally the effect of the primary nozzle geometries on the ejector entrainment. In their study, the experimental steam jet refrigerator was tested with 8 different primary nozzle's geometries. For one particular primary nozzle, operated at a fixed entrained pressure, the nozzle exit Mach number is remained unchanged with the primary pressure. And the entrainment ratio is essentially constant and independent from the area ratio of the primary nozzles. There are many structural factors that influence the ejector performance. The primary nozzle geometries are crucial to the primary steam. The mass flow rate and the nozzle exit velocity of the primary steam are decided by the primary nozzle throat diameter and diverging ratio, respectively. Ejector throat length is commonly believed to have little influences on the entrainment ratio, but the critical back pressure increased with the throat length and thus allowed to operate the ejector in double chocking mode in a wider range of operating conditions. And a proper ejector throat diameter is necessary for designing of the ejectors. Furthermore, as has been pointed out above, the ejector performance is very sensitive to the convergence angle of mixing chamber especially near its optimum value, and a slight variation in it may produce a great influence on the ejector performance. Although there are many studies on the ejector geometries, there are little investigations concerned with the mixing chamber length of the steam ejector, which is crucial to the performance of the ejectors. In this work, the effects of both the convergence angle and the length of the ejector mixing chamber on the flow characteristics and the entrainment ratio are numerically investigated.
primary nozzle in which its flow state is changed from subsonic to supersonic, creating a low pressure region at the nozzle outlet and in the mixing chamber. The entrained stream is drawn into the flow and accelerated by the pressure difference between the entrained steam and the mixing chamber that is created by the primary stream. The entrained stream is then mixed with the primary steam and recompressed in the mixing chamber and very complex interactions with the mixing layer and wave shocks in the ejector throat may take place. The mixed steam is further compressed as it flows through the diffuser. Steam ejectors are classified into two categories, the constant-area mixing ejector and the constant-pressure mixing ejector according the geometrical parameters of the mixing chamber. It is well known that the constant-pressure ejector shows a better performance than the constant-area ejector and is widely used [10]. Therefore, in this paper, only the constant-pressure mixing ejectors are studied aiming at a better understanding of the effects of the mixing chamber geometrical parameters on the ejector performance. The main geometrical parameters of the ejector used for this study are listed in Table 1. The commercial software Gambit 2.2 and FLUENT 6.3 were used as the grid generator and the CFD solver, respectively. An axisymmetric two-dimensional model is used as suggested by Pianthong et al. [11]. The mathematical model of the flow includes the Reynolds time-averaged Navier–Stokes, continuity and energy equations with the assumption of the steady and compressible flow of constant physical properties. Unsteady-state mathematical models are used to solve the problem for better convergence; the steady-state results are obtained by setting the time step to a large value after several time steps. The near wall condition was treated using the “standard wall function” and the convective terms were discretized by the second-order upwinding scheme. The realizable k–ε turbulence model was used, which was reported to predict accurately the spreading rate of jet flows and provides better performance for separation and recirculation flows [12]. Boundary conditions at the primary nozzle inlet and the entrained steam inlet of the ejector were set as “pressure inlet” condition. Meanwhile, the “pressure outlet” condition was applied on the ejector outlet of the mixing steam. Water vapor of the working fluid was assumed to be an ideal gas considering the fact that the absolute pressure inside the mixing chamber is relatively low. And the vapors that enter the ejector are all assumed to be saturated. With the above assumptions, the governing equations can be written as follows: The continuity equation: ∂ρ ∂ ðρui Þ ¼ 0 þ ∂t ∂xi
2. CFD model and validation
ð1Þ
2.1. Geometrical and mathematical models The momentum equation: A schematic view of a typical supersonic ejector is shown in Fig. 1. A steam ejector usually consists of four key parts: primary nozzle, mixing chamber, ejector throat and subsonic diffuser. The fluid with the highest total energy is referred to as the primary stream and introduced into the
∂ ∂ ∂P ∂τij ðρui Þ þ ρui u j ¼ − þ ∂t ∂x j ∂xi ∂x j
Fig. 1. Typical ejector geometry.
ð2Þ
H. Wu et al. / Desalination 353 (2014) 15–20 Table 1 Geometry parameters of the ejector.
Table 3 Grid independence test and verification results (Point 2).
Primary nozzle Throat diameter, mm Entrance diameter, mm Exit diameter, mm Convergent section length, mm Divergent section length, mm Mixing chamber entrance diameter, mm Mixing chamber length, mm Ejector throat diameter, mm Ejector throat length, mm Diffuser exit diameter, mm Diffuser length, mm Convergence angle of mixing chamber, tanθ
3.70 12.00 9.95 10.00 25.00 22.83 70.30 15.80 48.00 28.40 101.00 0.05
The energy equation: ! h i ! ∂ ∂ ∂T þ ∇ u j τ ij ½ui ðρE þ pÞ ¼ ∇ α eff ðρEÞ þ ∂t ∂xi ∂xi
ð3Þ
with τij ¼ μ eff
! ∂ui ∂u j 2 ∂u − μ eff k δij þ 3 ∂x j ∂xi ∂xk
ð4Þ
And the k − ε model equations: ∂ ∂ ∂ ðρkui Þ ¼ ðρkÞ þ ∂t ∂xi ∂x j
∂ðρε Þ ∂ðρεui Þ ∂ ¼ þ ∂t ∂xi ∂x j
" # μ t ∂k þ Gk −ρε−Y M μþ δk ∂x j
" μþ
17
ð5Þ
# μ t ∂ε ε2 pffiffiffiffiffi þ ρC 1 Sε −ρC 2 σ ε ∂x j k þ vε
ε þ C 1ε C 3ε C b k
ð6Þ
Cell number
Pressure (Pa)
Errors (%)
Velocity (m/s)
Errors (%)
32,700 53,800 107,500 209,400
14,979.82 18,250.33 16,024.77 16,023.59
– 21.83 12.19 0.01
302.49 358.72 329.63 328.74
– 18.59 8.11 0.27
computation speed. The solution is considered as converged when the two following convergent criteria were both satisfied. Firstly, it has to be shown that the mass fluxes across each face in the calculation domain are stable (in this case, the difference of mass flow rates at the inlet and at the outlet are less than 10− 7 kg/s). In the second place, the residual of the calculation should be lower than 10−6 in order to ensure that the solution from the simulation is accurate. To further confirm the reliability of the mathematical and the numerical models, the influences of the ejector back pressure (the outlet pressure) on the entrainment ratio are numerically studied. As we know, there exists a critical value (later on, we call it as the critical pressure) for the back pressure [3,6,9,13,14]. Below the critical pressure, the entrainment ratio remains its maximum value, and exceeding this value, the entrainment ratio decreases sharply with the back pressure. The simulation is carried out with the primary pressure (pp) and the secondary pressure (ps) set at 600 kPa and 15 kPa, respectively and the back pressure (pm) is changed from 20 kPa to 45.5 kPa. Fig. 2 shows the entrainment ratio as a function of the back pressure. It can be seen from this figure that the back pressure is one of the controlling factors that determine the performance of the steam ejector, as one may expect, there does exist a critical pressure. If the back pressure is lower than this critical pressure, the entrainment ratio of the steam ejector does not vary and remains a constant as the back pressure increases. However, once the back pressure is higher than the critical pressure, the entrainment ratio decreases sharply as the back pressure increases. This proves the mathematical and numerical models can predict the ejector performance correctly; this in turn verifies the reliability of the present models.
with C 1 ¼ max 0:43;
μ ; ηþ5
3. CFD results and discussion η ¼ Sk=ε:
ð7Þ In order to investigate the effects of mixing chamber geometry on the performance of the steam ejector, a series of simulations were finished based on the present geometrical and mathematical models. The results are summarized as follows.
2.2. Validation of the mathematical and numerical models The ejector geometry is modeled in an axisymmetrical 2D domain in the Gambit. The results with different grids reveal that the grid density has a strong influence on the convergence and stability characteristics, so the grid independence test and verification were carried out to guarantee the reliability and accuracy. Table 2 and Table 3 list the grid independence test and verification results. The pressure and velocity at Point 1 (the location of outlet of the primary nozzle at the axis) and Point 2 (the location of outlet of the ejector throat at the axis) as shown in Fig. 1 are used to detect the influence of the cell number. From these tables, one can see that an acceptable result is obtained with a cell number of 107,500. The denser grids are adopted for the locations with significant flow changes such as velocity boundary and shock position for faster
3.1. Optimum length of the mixing chamber The structural factors are crucial to the performance of the steam ejector, especially the mixing chamber where the mixing of the primary
Table 2 Grid independence test and verification results (Point 1). Cell number
Pressure (Pa)
Errors (%)
Velocity (m/s)
Errors (%)
32,700 53,800 107,500 209,400
10,078.81 9344.78 9881.07 9887.81
– 7.28 5.74 0.07
173.51 168.93 171.39 171.64
– 2.64 1.46 0.15
Fig. 2. The effect of pm on the entrainment ratio.
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H. Wu et al. / Desalination 353 (2014) 15–20
Fig. 3. Effect of the mixing chamber length on the entrainment ratio. Fig. 5. Effect of the mixing chamber length on the entrainment ratio (pp = 500 kPa).
and entrained steam and the violently changing of the velocity, temperature and pressure of the steam takes place. The main geometrical parameters of the mixing chamber are its length and convergence angle. In this section, the influence of the mixing chamber length is studied first by fixing its convergence angle θ at tanθ = 0.05 (θ ≈ 3.0°). In studying the influence of the mixing chamber length on the performance of the steam ejector, the primary, the secondary and the back pressure are fixed at 600 kPa, 15 kPa and 40 kPa, respectively. The mixing chamber length is changed without changing the convergence angle and the outlet diameter of the mixing chamber. The inlet diameter of the mixing chamber increases as the mixing chamber length increases. Fig. 3 shows the variation of the entrainment ratio with the mixing chamber length. It can be seen from this figure that the entrainment ratio of the steam ejector increases almost linearly with L/d (the ratio of the mixing chamber length to the primary nozzle throat diameter), if L/d b 15. And if L/d N 21 the entrainment ratio decreases sharply with L/d. However, if 15 ≤ L/d ≤ 21, the entrainment ratio almost
Fig. 4. Velocity contours at different length of the mixing chamber.
remains unchanged. It can be included that there exists an optimum mixing chamber length range for the steam ejector achieving its largest entrainment ratio. In order to explain the phenomenon, the velocity contours of the steam ejector of the various-length mixing chambers are shown in Fig. 4. It can be found that double choking occurs for the situation that L/d is 11, 13, 17 and 21, respectively. One of the choking is a diamond shock train beginning at the nozzle exit and expanding to the ejector throat. And the length of the shock train increases with L/d. Another one is a normal shock shown as A, B, C and D in the diffusion chamber. However, single choking appears for L/d being 23 and 25 which is the diamond shock train. This diamond shock train is completely inside the mixing chamber. It can be also found from Figs. 3 and 4 that the shock wave is very obvious and clear in the diffusion chamber for L/d b 15. The mixing of the steam is better distributed, which means less energy loss and this is why the entrainment ratio increases with L/d in this region. However, if L/d N 22, the double choking phenomenon disappears and there is no choking taking place within the throat section. Then, the performance of the steam ejector deteriorates dramatically as L/d increases further. Moreover, if 15 ≤ L/d ≤ 21, the normal shocks in the diffusion chamber shown as C and D in Fig. 4 weaken and the fluid in the mixing and diffusion chamber flows more gently. These are all good for improving the performance of the steam ejector. Therefore, the entrainment ratio remains the largest and unchanged in the effects of various factors in the optimum range of the mixing chamber length. In order to confirm the conclusion for the existence of the optimum range of the mixing chamber length for different primary pressures, the
Fig. 6. Effect of the mixing chamber length on the entrainment ratio (pp = 700 kPa).
H. Wu et al. / Desalination 353 (2014) 15–20
19
Figs. 5 and 6 show the effect of the mixing chamber length on the entrainment ratio, whose primary pressures are 500 kPa and 700 kPa, respectively. It can be found that the entrainment ratio is the largest if 13 ≤ L/d ≤ 17 in Fig. 5. And, the optimum range of the mixing chamber length (17 ≤ L/d ≤ 23) can be also found in Fig. 6. It is can be also seen that the changed trend of Figs. 5 and 6 is similar with Fig. 3. These calculations further confirm that, there is an optimum range of the mixing chamber length for a given ejector and this optimum range depends on the primary pressure. More careful reading of Figs. 3, 5 and 6, one may notice that the largest entrainment ratio decreases with the primary pressure. This conclusion is only true for a given ejector, i.e., for a geometry-structure fixed ejector. Since without changing the ejector structure, the flow rate of the primary steam increases more significantly with the primary pressure than that of the entrained steam. Thus, the entrainment ratio decreases with the primary pressure.
Fig. 7. Effect of the convergence angle on the entrainment ratio.
3.2. Optimum convergence angle of the mixing chamber
Fig. 8. Velocity counters at different convergence angle.
above calculation is repeated for the primary pressures of 500 kPa and 700 kPa without changing the other geometrical and operation parameters of the steam injector.
Another important geometric factor of the mixing chamber is the convergence angle. The primary flow, the secondary flow and the mixing flow pressures are set at 600 kPa, 15 kPa and 40 kPa, respectively in studying the influences of the convergence angle. The length and the outlet diameter of the mixing chamber remain unchanged in the process of changing the mixing chamber convergence angle. The inlet diameter of the mixing chamber increases as the mixing chamber convergence angle increases. Fig. 7 shows the effect of the mixing chamber convergence angle on the entrainment ratio. It is found that the variation pattern of the entrainment ratio with the convergence angle for the different-length mixing chamber is similar. The entrainment ratio increases sharply with tanθ for small convergence angles, after reaching its maximum value at tanθ = 0.04–0.05, it decreases slowly with tanθ. Therefore, there is a fixed optimum mixing chamber convergence angle for the mixing chamber of a given length. Fig. 8 shows the velocity contours inside the ejector whose L/d is 19 and Fig. 9 presents the contours and the vectors of the partially enlarged details of the vortex. The convergence angle changes from tanθ = 0.02 to tanθ = 0.10. It is obvious that the entrained inlet diameter and the volume of the mixing chamber of small convergence angles are small for keeping L/d at a given value as shown in Fig. 8. Thus, the space for entrained steam is also small. This will increase the flow friction and worsen the pumping efficiency of the ejector. The velocity of entrained steam is low and the vortexes appear at several locations near the wall of the mixing chamber if the mixing chamber convergence angle is larger than the optimum angle as shown in Fig. 8 and 9. The detailed contours and vectors of the vortex_1 are shown in Fig. 9a. Fig. 9b
a) Counters and vectors of the vortex_1 Magnification 1:30
b) The counters and vectors of the vortex_2 Magnification 1:15 Fig. 9. a. Counters and vectors of the vortex_1. b. The counters and vectors of the vortex_2.
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H. Wu et al. / Desalination 353 (2014) 15–20
shows the flow field details of the vortex_2. It can be seen from these figures that the vortexes become more apparent as the convergence angle increases. This leads to the degeneration of the steam ejector performance. From Figs. 7, 8 and 9, it can be also seen that increasing the convergence angle increases the entrainment steam inlet and the space of the mixing chamber for a given L/d. This of course decreases the energy loss and improves the flowing process of the fluid in the mixing chamber. If the mixing chamber convergent angle is larger than the optimum value, the large space of the mixing chamber may result in over expansion. This explains why vortexes appear near the wall of the mixing chamber. And after exceeding the optimum value, the larger the convergence angle is, the stronger the vortex is. The vortex formation will increase the flow friction and energy dissipation, and this at least explains partly why the entrainment ratio decreases with the mixing chamber convergence angle. 4. Conclusion In this paper, CFD simulations were carried out to investigate the influences of the mixing chamber geometry parameters including length and convergence angle on the entrainment performance of the steam ejector. The main results show that the geometry of the mixing chamber has significant effects on the ejector performance. And there exists an optimum value for both the chamber length and convergence angle at which the ejector may acquire its largest entrainment ratio. This may attribute to the fact that under the optimum geometric mixing chamber conditions, the ideal flow pattern can be obtained and the fluid energy dissipation is small.
References [1] J.H. Keenan, E.P. Neumann, F. Lustwerk, An investigation of ejector design by analysis and experiment, J. Appl. Mech. Trans. ASME 72 (1950) 299–309. [2] B.J. Huang, C.B. Jiang, F.L. Hu, Ejector performance characteristics and design analysis of jet refrigeration system, J. Eng. Gas Turbines Power 107 (1985) 792–802. [3] B.J. Huang, J.M. Chang, Empirical correlation for ejector design, Int. J. Refrig. 22 (1999) 379–388. [4] S.B. Riffat, S.A. Omer, CFD modeling and experimental investigation of an ejector refrigeration system using methanol as the working fluid, Int. J. Energy Reserv. 25 (2001) 115–128. [5] Xiao-Dong Wang, Jing-Liang Dong, Numerical study on the performances of steamjet vacuum pump at different operating conditions, Vacuum 84 (2010) 1341–1346. [6] T. Sriveerakul, S. Aphormratana, K. Chunnanond, Performance prediction of steam ejector using computational fluid dynamics: part 1. validation of the CFD results, Int. J. Therm. Sci. 46 (2007) 812–822. [7] Yinhai Zhu, Wenjian Cai, Changyun Wen, Yanzhong Li, Numerical investigation of geometry parameters for design of high performance ejectors, Appl. Therm. Eng. 29 (2009) 898–905. [8] MyoungKuk Ji, Tony Utomo, JuSik Woo, YongHun Lee, HyoMin Jeong, HanShik Chung, CFD investigation on the flow structure inside thermo vapor compressor, Energy 35 (2010) 2694–2702. [9] Natthawut Ruangtrakoon, Satha Aphornratana, Thanarath Sriveerakul, Experimental studies of a steam jet refrigeration cycle: effect of the primary nozzle geometries to system performance, Exp. Thermal Fluid Sci. 35 (2011) 676–683. [10] J.H. Keenan, E.P. Neumann, F. Lustwerk, An investigation of ejector design by analysis and experiment, J. Appl. Mech. Trans. ASME 17 (1950) 299–311. [11] K. Pianthong, W. Seehanam, M. Behnia, T. Sriveerakul, S. Aphornratana, Investigation and improvement of ejector refrigeration system using computational fluid dynamics technique, Energy Convers. Manag. 48 (2007) 2556–2564. [12] M.J. Moore, P.T. Walters, Predicting the fog drop size in wet steam turbines, Proceedings of the Wet Steam 4 Conference, 1973, pp. 37–73. [13] S. Aphornratana, Theoretical and experimental investigation of a combine ejectorabsorption refrigerator, (PhD thesis) University of Sheffield, UK, 1994. [14] K. Chunnanond, S. Aphornratana, Ejectors: applications in refrigeration technology, Renew. Sust. Energ. Rev. 8 (2004) 129–155.
Contents lists available at ScienceDirect
Desalination journal homepage: www.elsevier.com/locate/desal
Numerical investigation of the influences of mixing chamber geometries on steam ejector performance Hongqiang Wu, Zhongliang Liu ⁎, Bing Han, Yanxia Li College of Environmental and Energy Engineering, Beijing University of Technology, Pingleyuan 100, Chaoyang District, Beijing 100124, China
H I G H L I G H T S • CFD simulations were carried out to investigate the performance of the ejector. • There exists an optimum mixing chamber length range. • There is a fixed optimum mixing chamber convergence angle.
a r t i c l e
i n f o
Article history: Received 9 May 2014 Received in revised form 12 August 2014 Accepted 2 September 2014 Available online xxxx Keywords: Numerical investigation Steam ejector Chamber length Convergence angle
a b s t r a c t In this study, computational fluid dynamics (CFD) method is employed to investigate the effects of the mixing chamber geometries on the performance of steam ejectors used for multi-effect distillation systems. The internal flow characteristics of the steam ejector and the effects of the length and convergence angle of the mixing chamber were obtained. It is found that there is an optimum range of the mixing chamber length at which the ejector will acquire its largest entrainment ratio and the mixing chamber also has an optimum convergence angle at which the steam ejector performance is the best. © 2014 Elsevier B.V. All rights reserved.
1. Introduction Multi-effect distillation (MED), which can greatly reduce the energy consumption of seawater desalination systems, especially if it is combined with thermal vapor compression (TVC), is one of the most important and widely-used large-scale desalination methods. The thermal vapor compression is accomplished by steam ejector. The performance of the steam ejector is one of the limiting factors for improving the energy efficiency of MED-TVC desalination systems. The structure of steam ejectors is very simple and without any moving parts. It compresses a low-pressure vapor (entrained steam) by a high-pressure vapor (primary steam) through a series of energy and momentum exchanges into a mid pressure vapor. However, due to the fact that it involves strong irreversible mixing and other effects, its thermodynamic efficiency is usually very low. Entrainment ratio that is defined as the ratio of entrained low-pressure steam flow rate to high-pressure primary vapor flow rate is the main performance indicator of the steam ejectors. Increasing the entrainment ratio is of great importance for practical applications by optimizing the steam ejector structure and design. ⁎ Corresponding author. Tel./fax: +86 10 67392722. E-mail address: [email protected] (Z. Liu).
http://dx.doi.org/10.1016/j.desal.2014.09.002 0011-9164/© 2014 Elsevier B.V. All rights reserved.
Because of the practical importance, the wide potential applications and the complexity of the phenomena taking place inside the ejector, a lot of work has been carried out to improve the performance of the ejectors. Actually, as early as in 1950, Keenan et al. [1] developed a theory for designing and analyzing of the ejectors based on one-dimensional gas dynamic theory. However, this theory could be only used to predict the overall performance of the after-design ejectors without taking the effects of the ejector geometrical parameters into account. The flow pattern and other possible physical phenomena such as shock wave, choking and even phase transition inside the ejectors may well influence their performance. Therefore, improving the ejector performance of an ejector system needs understanding the physical phenomena that takes place inside the ejectors. Many researchers have engaged in researching the shock wave and choking of the ejectors with experimental and numerical methods. The results disclosed that the effect of the fluid parameters on the ejectors performance is important and direct [2–5]. The experimental results and theoretical predictions both proved that there exists a critical value for the ejector outlet pressure under the given primary and entrained vapor pressure conditions. Exceeding this critical pressure will result in fast degeneration of the ejector performance [2,3]. Riffat and Omer [4] used a commercial CFD package to predict the performance of a methanol driven ejector.
16
H. Wu et al. / Desalination 353 (2014) 15–20
Wang [5] simulated the flow through a steam ejector, whose results were validated against the experimental data by Sriveerakul et al. [6]. The numerical results are in good agreement with the experimental results [4,5]. There are also numerous studies of the geometrical parameters and structure because of their crucial effects on the performance of the ejectors [7–9]. Zhu et al. [7] tried to find the optimum nozzle outlet position (NXP) and the mixing chamber convergent angle by numerical simulations. From 210 testing results, it is found that the optimum NXP is not only proportional to the mixing section throat diameter, but also increases as the primary flow pressure rises. And the ejector performance is very sensitive to convergence angle θ, especially near the optimum working point. The entrainment ratio can vary as much as 26.6% by changing θ. A relatively bigger θ is required to better maximize the ejector performance when the primary flow pressure rises. Ji [8] numerically studied the influence of the convergence angle of the mixing chamber. The mixing chamber convergence angle in the study was varied as 0°, 0.5°, 1.0°, 2°, 3.5° and 4.5°. The ejector with a mixing-chamber convergence angle of 1.0° has the best performance. Natthawut et al. [9] investigated experimentally the effect of the primary nozzle geometries on the ejector entrainment. In their study, the experimental steam jet refrigerator was tested with 8 different primary nozzle's geometries. For one particular primary nozzle, operated at a fixed entrained pressure, the nozzle exit Mach number is remained unchanged with the primary pressure. And the entrainment ratio is essentially constant and independent from the area ratio of the primary nozzles. There are many structural factors that influence the ejector performance. The primary nozzle geometries are crucial to the primary steam. The mass flow rate and the nozzle exit velocity of the primary steam are decided by the primary nozzle throat diameter and diverging ratio, respectively. Ejector throat length is commonly believed to have little influences on the entrainment ratio, but the critical back pressure increased with the throat length and thus allowed to operate the ejector in double chocking mode in a wider range of operating conditions. And a proper ejector throat diameter is necessary for designing of the ejectors. Furthermore, as has been pointed out above, the ejector performance is very sensitive to the convergence angle of mixing chamber especially near its optimum value, and a slight variation in it may produce a great influence on the ejector performance. Although there are many studies on the ejector geometries, there are little investigations concerned with the mixing chamber length of the steam ejector, which is crucial to the performance of the ejectors. In this work, the effects of both the convergence angle and the length of the ejector mixing chamber on the flow characteristics and the entrainment ratio are numerically investigated.
primary nozzle in which its flow state is changed from subsonic to supersonic, creating a low pressure region at the nozzle outlet and in the mixing chamber. The entrained stream is drawn into the flow and accelerated by the pressure difference between the entrained steam and the mixing chamber that is created by the primary stream. The entrained stream is then mixed with the primary steam and recompressed in the mixing chamber and very complex interactions with the mixing layer and wave shocks in the ejector throat may take place. The mixed steam is further compressed as it flows through the diffuser. Steam ejectors are classified into two categories, the constant-area mixing ejector and the constant-pressure mixing ejector according the geometrical parameters of the mixing chamber. It is well known that the constant-pressure ejector shows a better performance than the constant-area ejector and is widely used [10]. Therefore, in this paper, only the constant-pressure mixing ejectors are studied aiming at a better understanding of the effects of the mixing chamber geometrical parameters on the ejector performance. The main geometrical parameters of the ejector used for this study are listed in Table 1. The commercial software Gambit 2.2 and FLUENT 6.3 were used as the grid generator and the CFD solver, respectively. An axisymmetric two-dimensional model is used as suggested by Pianthong et al. [11]. The mathematical model of the flow includes the Reynolds time-averaged Navier–Stokes, continuity and energy equations with the assumption of the steady and compressible flow of constant physical properties. Unsteady-state mathematical models are used to solve the problem for better convergence; the steady-state results are obtained by setting the time step to a large value after several time steps. The near wall condition was treated using the “standard wall function” and the convective terms were discretized by the second-order upwinding scheme. The realizable k–ε turbulence model was used, which was reported to predict accurately the spreading rate of jet flows and provides better performance for separation and recirculation flows [12]. Boundary conditions at the primary nozzle inlet and the entrained steam inlet of the ejector were set as “pressure inlet” condition. Meanwhile, the “pressure outlet” condition was applied on the ejector outlet of the mixing steam. Water vapor of the working fluid was assumed to be an ideal gas considering the fact that the absolute pressure inside the mixing chamber is relatively low. And the vapors that enter the ejector are all assumed to be saturated. With the above assumptions, the governing equations can be written as follows: The continuity equation: ∂ρ ∂ ðρui Þ ¼ 0 þ ∂t ∂xi
2. CFD model and validation
ð1Þ
2.1. Geometrical and mathematical models The momentum equation: A schematic view of a typical supersonic ejector is shown in Fig. 1. A steam ejector usually consists of four key parts: primary nozzle, mixing chamber, ejector throat and subsonic diffuser. The fluid with the highest total energy is referred to as the primary stream and introduced into the
∂ ∂ ∂P ∂τij ðρui Þ þ ρui u j ¼ − þ ∂t ∂x j ∂xi ∂x j
Fig. 1. Typical ejector geometry.
ð2Þ
H. Wu et al. / Desalination 353 (2014) 15–20 Table 1 Geometry parameters of the ejector.
Table 3 Grid independence test and verification results (Point 2).
Primary nozzle Throat diameter, mm Entrance diameter, mm Exit diameter, mm Convergent section length, mm Divergent section length, mm Mixing chamber entrance diameter, mm Mixing chamber length, mm Ejector throat diameter, mm Ejector throat length, mm Diffuser exit diameter, mm Diffuser length, mm Convergence angle of mixing chamber, tanθ
3.70 12.00 9.95 10.00 25.00 22.83 70.30 15.80 48.00 28.40 101.00 0.05
The energy equation: ! h i ! ∂ ∂ ∂T þ ∇ u j τ ij ½ui ðρE þ pÞ ¼ ∇ α eff ðρEÞ þ ∂t ∂xi ∂xi
ð3Þ
with τij ¼ μ eff
! ∂ui ∂u j 2 ∂u − μ eff k δij þ 3 ∂x j ∂xi ∂xk
ð4Þ
And the k − ε model equations: ∂ ∂ ∂ ðρkui Þ ¼ ðρkÞ þ ∂t ∂xi ∂x j
∂ðρε Þ ∂ðρεui Þ ∂ ¼ þ ∂t ∂xi ∂x j
" # μ t ∂k þ Gk −ρε−Y M μþ δk ∂x j
" μþ
17
ð5Þ
# μ t ∂ε ε2 pffiffiffiffiffi þ ρC 1 Sε −ρC 2 σ ε ∂x j k þ vε
ε þ C 1ε C 3ε C b k
ð6Þ
Cell number
Pressure (Pa)
Errors (%)
Velocity (m/s)
Errors (%)
32,700 53,800 107,500 209,400
14,979.82 18,250.33 16,024.77 16,023.59
– 21.83 12.19 0.01
302.49 358.72 329.63 328.74
– 18.59 8.11 0.27
computation speed. The solution is considered as converged when the two following convergent criteria were both satisfied. Firstly, it has to be shown that the mass fluxes across each face in the calculation domain are stable (in this case, the difference of mass flow rates at the inlet and at the outlet are less than 10− 7 kg/s). In the second place, the residual of the calculation should be lower than 10−6 in order to ensure that the solution from the simulation is accurate. To further confirm the reliability of the mathematical and the numerical models, the influences of the ejector back pressure (the outlet pressure) on the entrainment ratio are numerically studied. As we know, there exists a critical value (later on, we call it as the critical pressure) for the back pressure [3,6,9,13,14]. Below the critical pressure, the entrainment ratio remains its maximum value, and exceeding this value, the entrainment ratio decreases sharply with the back pressure. The simulation is carried out with the primary pressure (pp) and the secondary pressure (ps) set at 600 kPa and 15 kPa, respectively and the back pressure (pm) is changed from 20 kPa to 45.5 kPa. Fig. 2 shows the entrainment ratio as a function of the back pressure. It can be seen from this figure that the back pressure is one of the controlling factors that determine the performance of the steam ejector, as one may expect, there does exist a critical pressure. If the back pressure is lower than this critical pressure, the entrainment ratio of the steam ejector does not vary and remains a constant as the back pressure increases. However, once the back pressure is higher than the critical pressure, the entrainment ratio decreases sharply as the back pressure increases. This proves the mathematical and numerical models can predict the ejector performance correctly; this in turn verifies the reliability of the present models.
with C 1 ¼ max 0:43;
μ ; ηþ5
3. CFD results and discussion η ¼ Sk=ε:
ð7Þ In order to investigate the effects of mixing chamber geometry on the performance of the steam ejector, a series of simulations were finished based on the present geometrical and mathematical models. The results are summarized as follows.
2.2. Validation of the mathematical and numerical models The ejector geometry is modeled in an axisymmetrical 2D domain in the Gambit. The results with different grids reveal that the grid density has a strong influence on the convergence and stability characteristics, so the grid independence test and verification were carried out to guarantee the reliability and accuracy. Table 2 and Table 3 list the grid independence test and verification results. The pressure and velocity at Point 1 (the location of outlet of the primary nozzle at the axis) and Point 2 (the location of outlet of the ejector throat at the axis) as shown in Fig. 1 are used to detect the influence of the cell number. From these tables, one can see that an acceptable result is obtained with a cell number of 107,500. The denser grids are adopted for the locations with significant flow changes such as velocity boundary and shock position for faster
3.1. Optimum length of the mixing chamber The structural factors are crucial to the performance of the steam ejector, especially the mixing chamber where the mixing of the primary
Table 2 Grid independence test and verification results (Point 1). Cell number
Pressure (Pa)
Errors (%)
Velocity (m/s)
Errors (%)
32,700 53,800 107,500 209,400
10,078.81 9344.78 9881.07 9887.81
– 7.28 5.74 0.07
173.51 168.93 171.39 171.64
– 2.64 1.46 0.15
Fig. 2. The effect of pm on the entrainment ratio.
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H. Wu et al. / Desalination 353 (2014) 15–20
Fig. 3. Effect of the mixing chamber length on the entrainment ratio. Fig. 5. Effect of the mixing chamber length on the entrainment ratio (pp = 500 kPa).
and entrained steam and the violently changing of the velocity, temperature and pressure of the steam takes place. The main geometrical parameters of the mixing chamber are its length and convergence angle. In this section, the influence of the mixing chamber length is studied first by fixing its convergence angle θ at tanθ = 0.05 (θ ≈ 3.0°). In studying the influence of the mixing chamber length on the performance of the steam ejector, the primary, the secondary and the back pressure are fixed at 600 kPa, 15 kPa and 40 kPa, respectively. The mixing chamber length is changed without changing the convergence angle and the outlet diameter of the mixing chamber. The inlet diameter of the mixing chamber increases as the mixing chamber length increases. Fig. 3 shows the variation of the entrainment ratio with the mixing chamber length. It can be seen from this figure that the entrainment ratio of the steam ejector increases almost linearly with L/d (the ratio of the mixing chamber length to the primary nozzle throat diameter), if L/d b 15. And if L/d N 21 the entrainment ratio decreases sharply with L/d. However, if 15 ≤ L/d ≤ 21, the entrainment ratio almost
Fig. 4. Velocity contours at different length of the mixing chamber.
remains unchanged. It can be included that there exists an optimum mixing chamber length range for the steam ejector achieving its largest entrainment ratio. In order to explain the phenomenon, the velocity contours of the steam ejector of the various-length mixing chambers are shown in Fig. 4. It can be found that double choking occurs for the situation that L/d is 11, 13, 17 and 21, respectively. One of the choking is a diamond shock train beginning at the nozzle exit and expanding to the ejector throat. And the length of the shock train increases with L/d. Another one is a normal shock shown as A, B, C and D in the diffusion chamber. However, single choking appears for L/d being 23 and 25 which is the diamond shock train. This diamond shock train is completely inside the mixing chamber. It can be also found from Figs. 3 and 4 that the shock wave is very obvious and clear in the diffusion chamber for L/d b 15. The mixing of the steam is better distributed, which means less energy loss and this is why the entrainment ratio increases with L/d in this region. However, if L/d N 22, the double choking phenomenon disappears and there is no choking taking place within the throat section. Then, the performance of the steam ejector deteriorates dramatically as L/d increases further. Moreover, if 15 ≤ L/d ≤ 21, the normal shocks in the diffusion chamber shown as C and D in Fig. 4 weaken and the fluid in the mixing and diffusion chamber flows more gently. These are all good for improving the performance of the steam ejector. Therefore, the entrainment ratio remains the largest and unchanged in the effects of various factors in the optimum range of the mixing chamber length. In order to confirm the conclusion for the existence of the optimum range of the mixing chamber length for different primary pressures, the
Fig. 6. Effect of the mixing chamber length on the entrainment ratio (pp = 700 kPa).
H. Wu et al. / Desalination 353 (2014) 15–20
19
Figs. 5 and 6 show the effect of the mixing chamber length on the entrainment ratio, whose primary pressures are 500 kPa and 700 kPa, respectively. It can be found that the entrainment ratio is the largest if 13 ≤ L/d ≤ 17 in Fig. 5. And, the optimum range of the mixing chamber length (17 ≤ L/d ≤ 23) can be also found in Fig. 6. It is can be also seen that the changed trend of Figs. 5 and 6 is similar with Fig. 3. These calculations further confirm that, there is an optimum range of the mixing chamber length for a given ejector and this optimum range depends on the primary pressure. More careful reading of Figs. 3, 5 and 6, one may notice that the largest entrainment ratio decreases with the primary pressure. This conclusion is only true for a given ejector, i.e., for a geometry-structure fixed ejector. Since without changing the ejector structure, the flow rate of the primary steam increases more significantly with the primary pressure than that of the entrained steam. Thus, the entrainment ratio decreases with the primary pressure.
Fig. 7. Effect of the convergence angle on the entrainment ratio.
3.2. Optimum convergence angle of the mixing chamber
Fig. 8. Velocity counters at different convergence angle.
above calculation is repeated for the primary pressures of 500 kPa and 700 kPa without changing the other geometrical and operation parameters of the steam injector.
Another important geometric factor of the mixing chamber is the convergence angle. The primary flow, the secondary flow and the mixing flow pressures are set at 600 kPa, 15 kPa and 40 kPa, respectively in studying the influences of the convergence angle. The length and the outlet diameter of the mixing chamber remain unchanged in the process of changing the mixing chamber convergence angle. The inlet diameter of the mixing chamber increases as the mixing chamber convergence angle increases. Fig. 7 shows the effect of the mixing chamber convergence angle on the entrainment ratio. It is found that the variation pattern of the entrainment ratio with the convergence angle for the different-length mixing chamber is similar. The entrainment ratio increases sharply with tanθ for small convergence angles, after reaching its maximum value at tanθ = 0.04–0.05, it decreases slowly with tanθ. Therefore, there is a fixed optimum mixing chamber convergence angle for the mixing chamber of a given length. Fig. 8 shows the velocity contours inside the ejector whose L/d is 19 and Fig. 9 presents the contours and the vectors of the partially enlarged details of the vortex. The convergence angle changes from tanθ = 0.02 to tanθ = 0.10. It is obvious that the entrained inlet diameter and the volume of the mixing chamber of small convergence angles are small for keeping L/d at a given value as shown in Fig. 8. Thus, the space for entrained steam is also small. This will increase the flow friction and worsen the pumping efficiency of the ejector. The velocity of entrained steam is low and the vortexes appear at several locations near the wall of the mixing chamber if the mixing chamber convergence angle is larger than the optimum angle as shown in Fig. 8 and 9. The detailed contours and vectors of the vortex_1 are shown in Fig. 9a. Fig. 9b
a) Counters and vectors of the vortex_1 Magnification 1:30
b) The counters and vectors of the vortex_2 Magnification 1:15 Fig. 9. a. Counters and vectors of the vortex_1. b. The counters and vectors of the vortex_2.
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H. Wu et al. / Desalination 353 (2014) 15–20
shows the flow field details of the vortex_2. It can be seen from these figures that the vortexes become more apparent as the convergence angle increases. This leads to the degeneration of the steam ejector performance. From Figs. 7, 8 and 9, it can be also seen that increasing the convergence angle increases the entrainment steam inlet and the space of the mixing chamber for a given L/d. This of course decreases the energy loss and improves the flowing process of the fluid in the mixing chamber. If the mixing chamber convergent angle is larger than the optimum value, the large space of the mixing chamber may result in over expansion. This explains why vortexes appear near the wall of the mixing chamber. And after exceeding the optimum value, the larger the convergence angle is, the stronger the vortex is. The vortex formation will increase the flow friction and energy dissipation, and this at least explains partly why the entrainment ratio decreases with the mixing chamber convergence angle. 4. Conclusion In this paper, CFD simulations were carried out to investigate the influences of the mixing chamber geometry parameters including length and convergence angle on the entrainment performance of the steam ejector. The main results show that the geometry of the mixing chamber has significant effects on the ejector performance. And there exists an optimum value for both the chamber length and convergence angle at which the ejector may acquire its largest entrainment ratio. This may attribute to the fact that under the optimum geometric mixing chamber conditions, the ideal flow pattern can be obtained and the fluid energy dissipation is small.
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