micromachines Article
Numerical Investigation of Miniature Ejector Refrigeration System Embedded with a Capillary Pump Loop Jing-Ming Dong *, He Song *, Meng-Qi Yu, Wei-Ning Wang and Xin-Xiang Pan Institute of Marine Engineering and Thermal Science, Marine Engineering College, Dalian Maritime University, Dalian 116026, China;
[email protected] (M.-Q.Y.);
[email protected] (W.-N.W.);
[email protected](X.-X.P.) * Correspondence:
[email protected] (J.-M.D.);
[email protected] (H.S.); Tel.: +86-411-8472-5295(J.-M.D. & H.S.) Received: 4 June 2017; Accepted: 25 July 2017; Published: 28 July 2017
Abstract: A miniature steam ejector refrigeration system embedded with a capillary pump loop can result in a compact design which can be used for electronics cooling. In this paper, computational fluid dynamics (CFD) is employed to investigate the effects of the area ratio of the ejector constant-area mixing section to the nozzle throat, the length of the constant-area section, and the nozzle exit position (NXP), on the performance of a miniature steam ejector. Results show that the performance of the miniature steam ejector is very sensitive to the area ratio of the constant-area mixing section to the nozzle. For the needs of practical application, the area ratio of the constant-area mixing section to the nozzle should be smaller than 16 when the temperature of the primary flow is 60 ◦ C. The NXP plays an important role in the flow phenomena inside the miniature ejector. The critical back pressure is more sensitive to length of the constant-area mixing section than the entrainment ratio. Results of this investigation provided a good solution to the miniature steam ejector embedded with a capillary pump loop for electronics cooling application. Keywords: miniature steam ejector; CFD; area ratio; NXP; electronics cooling
1. Introduction With the continuous integration of electronic components, the increasing heat flux means that heat dissipation in electronics is becoming more difficult to deal with [1]. Due to its excellent heat transfer characteristics, heat pipe is applied in electronic cooling [2]. However, it does not maintain the temperature of the electronics below the ambient temperature. Thermoelectric cooling, which consumes enormous amounts of electricity, is given great attention as an applicable method for electronic cooling [3,4]. In order to reduce power consumption, it is possible to use the heat dissipation of electronics to drive cooling plants. Riffat [5] proposed a novel concept of refrigeration, which is called the heat pipe/ejector cooling system. It is based on the combination of a heat pipe and an ejector. The schematic of the heat pipe/ejector system is shown in Figure 1. The system consists of ejector, condenser, capillary pump, generator, evaporator, and throttle valve. The capillary pump is employed to replace the electric circulation pump in the conventional ejector refrigeration system. The generator is powered by the heat dissipation of electronic devices. The vapor generated in the generator is called primary flow. The primary flow accelerates in the nozzle of the ejector and leaves the nozzle exit with supersonic speed, which creates a very low pressure in the mixing chamber. Subsequently, the secondary flow is entrained into the mixing chamber due to the pressure difference between the mixing chamber and the evaporator. In the mixing chamber and the constant-area mixing section, the primary flow and the secondary flow mix with each other. During the mixing process, shock waves appear
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and themixed velocity drops dramatically. The pressure increases mixed flows the diffuser. when fluid flows into the diffuser. After exiting thewhen ejector, the fluid mixed fluidinto enters into the After exiting the ejector, the mixed fluid enters into the condenser and is condensed into liquid. Some condenser and is condensed into liquid. Some of the liquid returns to the evaporator through the of the liquid returns to thepart evaporator through theback throttle valve. The other part of liquid comes throttle valve. The other of the liquid comes to the generator through thethe capillary pump. back toyears the generator through the[6] capillary the years since then, Smirnov [6] and Shi [7–10] In the since then, Smirnov and Shipump. [7–10] In investigated the feasibility and influence factors of investigated the feasibility and influence factors of this concept from different perspectives, such as the this concept from different perspectives, such as the wick [10], structure of the ejector [9] and wick [10], structure of the ejector [9]toand fluids [7]. According the first and second of working fluids [7]. According theworking first and second law of to thermodynamics, thelaw basic thermodynamics, of the heat system, such as entrainment characteristics of the thebasic heat characteristics pipe/ejector system, suchpipe/ejector as entrainment ratio, thermal efficiencyratio, and thermal efficiency and exergy efficiency of the system, were investigated [11]. After research exergy efficiency of the system, were investigated [11]. After that, the research onthat, this the concept has on this concept almost stalled. has almost stalled.
Figure Figure1.1.The Theschematic schematicofofthe theheat heatpipe/ejector pipe/ejector system. system.
Since Since the the development development of of CFD CFD technology, technology, itit has has been been widely widely used used in in the the study study of of ejectors. ejectors. Meanwhile, is aisuseful approach to investigate the flowthe behavior ejectors. in Yang [12] investigated Meanwhile,CFD CFD a useful approach to investigate flow in behavior ejectors. Yang [12] the flow phenomena steam ejectors numerically. simulationThe results showedresults characteristics investigated the flowinside phenomena inside steam ejectorsThe numerically. simulation showed of the mixing process clearly. process The entrainment ratio depended ratio on the mixing degree the primary characteristics of the mixing clearly. The entrainment depended on theof mixing degree and secondary the mixing area, increase the the entrainment ratio induce high of the primaryflow and in secondary flow in but the the mixing area,ofbut increase of themight entrainment ratio mechanical energy and critical back loss pressure decrease. CFD was utilized to investigate effects might induce highloss mechanical energy and critical back pressure decrease. CFD was the utilized to of operating the parameters and geometries on the performance of ejectors [13]. Moreover, the phenomena investigate effects of operating parameters and geometries on the performance of ejectors [13]. on mixing behavior, choke on flow, jet core effect choke and the shock waves have [14]. Moreover, the phenomena mixing behavior, flow, jet core effect andalso thebeen shockstudied waves have also been studied Ruangtrakoon [15] investigated the influence of the geometries on Ruangtrakoon [15][14]. investigated the influence of the nozzle geometries onnozzle the performance of the an performance ansteam ejector in the steam jet The refrigeration system. that Thethe results ejector used inof the jetused refrigeration system. results indicated CFDindicated techniquethat can the be CFD technique can be utilized efficiently predict the performance a steam ejector. Varga [16] utilized to efficiently predict thetoperformance of a steam ejector. Vargaof[16] studied performance of studiedwith performance of ejectors with variablenumerically. primary nozzle geometry numerically. research ejectors variable primary nozzle geometry The research showed that the The entrainment showed thatsensitive the entrainment ratioinisoperating very sensitive to variations in operating conditions and a ratio is very to variations conditions and a moveable spindle in the primary moveable spindle in primary nozzle can improve the employed performance of model the ejectors. Yan [17] nozzle can improve thethe performance of the ejectors. Yan [17] a CFD to estimate the employed a CFD model to estimateonthe of six geometry parameters the entrainment ratio effects of six geometry parameters theeffects entrainment ratio of an air-cooledon ejector cooling system, of an ejector cooling system, of most the most important that were most two of air-cooled the most important geometries thattwo were sensitive to the geometries performance of the ejector sensitive to the performance of the ejector weresection the area of the and constant-area section to were the area ratio of the constant-area mixing to ratio the nozzle NXP, and mixing the length of the the nozzle and NXP, and the length of the mixing section, which affected the the constant-area mixing section, which affected theconstant-area performance slightly. Varga [18] investigated performance slightly. Varga [18] investigatedmixing the influence of the the nozzle, area ratio ofand the constant-area constant-area influence of the area ratio of the constant-area section to NXP mixing section section length to the nozzle, and constant-area mixing the performance an mixing on the NXP performance of an ejector usingsection waterlength as the on working fluid. Bothofthe ejector using water as the working fluid. Both ratio of NXP the constant-area mixing to the area ratio of the constant-area mixing section tothe thearea nozzle and greatly impacted thesection entrainment nozzle and greatly the entrainment ratio and the critical pressure, while the ratio and theNXP critical back impacted pressure, while the constant-area mixing sectionback length had a little effect constant-area mixing section length had a little CFD effecttoon the entrainment [19] on the entrainment ratio. Pianthong [19] employed predict performanceratio. the ofPianthong steam ejectors employed predict performance the of ◦steam as the refrigerant (Tgcould = 120 using waterCFD as thetorefrigerant (Tg = 120 ◦ C–140 C andejectors Te = 5 ◦using C–15 ◦water C); it was found that CFD °C–140 ejector °C and characteristics Te = 5 °C–15 °C);very it was found CFD could predict ejector characteristics very well. predict well. The that investigation provided information on optimizing the The investigation provided information on optimizing the ejector performance. Varga [20] first estimated the different ejector efficiencies by means of theoretical computing and CFD analysis. The
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research also described that the entrainment ratio increased with the increase of the area ratio. Zhu ejector performance. Varga [20] first estimated the different ejector efficiencies by means of theoretical [21] investigated converging angle of mixing section and NXP by CFD. The investigation concluded computing and CFD analysis. The research also described that the entrainment ratio increased with the that the ejector performance improved as the nozzle moved away from the mixing section. It was increase of the area ratio. Zhu [21] investigated converging angle of mixing section and NXP by CFD. suggested that the converging angle of mixing section should be enlarged when the primary flow The investigation concluded that the ejector performance improved as the nozzle moved away from pressure increased. Wu [22] employed the CFD technique to study the effects of the mixing chamber the mixing section. It was suggested that the converging angle of mixing section should be enlarged geometries on the entrainment performance of steam ejectors. The study found that there is an when the primary flow pressure increased. Wu [22] employed the CFD technique to study the effects optimum range for the convergence angle and chamber length where the ejector could obtain the of the mixing chamber geometries on the entrainment performance of steam ejectors. The study found maximal entrainment ratio. that there is an optimum range for the convergence angle and chamber length where the ejector could On the basis of previous research, the miniature ejector refrigeration system embedded with a obtain the maximal entrainment ratio. capillary pump has many predictable advantages. But the investigation on the performance of the On the basis of previous research, the miniature ejector refrigeration system embedded with a miniature ejector has rarely been reported. In order to promote the application of the miniature capillary pump has many predictable advantages. But the investigation on the performance of the ejector in electronic cooling, in this paper CFD is used to investigate the effects of the area ratio of miniature ejector has rarely been reported. In order to promote the application of the miniature ejector ejector constant-area mixing section to nozzle throat, the length of constant-area section, and the in electronic cooling, in this paper CFD is used to investigate the effects of the area ratio of ejector nozzle exit position (NXP) on the performance of the miniature ejector and the flow phenomena constant-area mixing section to nozzle throat, the length of constant-area section, and the nozzle inside the miniature ejector. exit position (NXP) on the performance of the miniature ejector and the flow phenomena inside the miniature ejector. 2. CFD Modeling 2. CFD TheModeling ejector is designed based on the constant pressure mixing model, which is more flexible to operate in wider is ranges of condensing pressure [19]. Water was selected as which the working fluid in the The ejector designed based on the constant pressure mixing model, is more flexible to system. The latent heat of water is higher than most of other refrigerants. Also, water is a kind of operate in wider ranges of condensing pressure [19]. Water was selected as the working fluid in the environmentally friendly refrigerant. The model used of in other the CFD simulationAlso, comprises four parts: system. The latent heat of water is higher than most refrigerants. water is a kind of the nozzle, the mixing chamber, the constant-area mixing section and the diffuser. The effects of environmentally friendly refrigerant. The model used in the CFD simulation comprises four parts:the the area ratio ofmixing the constant-area mixing section to the nozzle (γand A), the length of constant-area mixing nozzle, the chamber, the constant-area mixing section the diffuser. The effects of the area section (L ) and the nozzle exit position (NXP) on the performance the miniature ejector are ratio of the constant-area mixing section to the nozzle (γA ), the length ofof constant-area mixing section investigated this study. The geometry theperformance ejector is shown Figure 2.ejector The diameters of the (Lm ) and thein nozzle exit position (NXP) onofthe of theinminiature are investigated constant-area mixing section are 6 mm, 7 mm and 8 mm. The length of the constant-area mixing in this study. The geometry of the ejector is shown in Figure 2. The diameters of the constant-area section from 5 mm to 45and mm8 mm. with 5The mm intervals. NXP is defined as section zero when the mixingchanges section are 6 mm, 7 mm length of theThe constant-area mixing changes nozzle the 5mixing chamberThe inlet. Theisnozzle exit changes fromexit −5 mm to 18 from 5exit mmistolocated 45 mmatwith mm intervals. NXP defined as position zero when the nozzle is located mm. The remaining parameters are fixed values. The specific geometrical parameters of the ejector at the mixing chamber inlet. The nozzle exit position changes from −5 mm to 18 mm. The remaining are listed in Table 1. values. The specific geometrical parameters of the ejector are listed in Table 1. parameters are fixed
Figure2.2.Geometry Geometryof ofthe theejector. ejector. Figure
Table 1. Geometry of the ejector. In this paper, commercial software ICEM parameters CFD 14.5 (ANSYS, Canonsburg, PA, USA) is used to generate a 2D grid. In order to accelerate the calculation and save time, Parameter Value the ejector geometry Units is set as Nozzle throat diameter Dn elements were initially created 2 in the form of a quadrangular mm axisymmetric in the ICEM CFD. The grid Nozzle exit diameter D 4 mm This was a of about 80,000 elements. Later, the grid elements were increased to about 100,000 elements. ° 17 Nozzle convergent angle θ1 to ensure that the simulated results were independent from the number of grid elements. The mesh ° 10 Nozzle divergent angle θ2 quality is higher than 0.95exit forposition each geometry. In addition, Fluent is used as the mm CFD solver. Nozzle −5, 0, 5, 14.5 8, 13, 18 5, results 10, 15, 20,[19]. 25, 30,The 35, 40, 45 mm swirl is Length ofmodel constant-area mixing sectionto Lmgive accurate The axisymmetric is good enough axis-symmetric 6, 7, 8 mm of constant-area mixing section Dm applied in Diameter this paper. Mixing chamber Convergence angle θ3 Diffuser Exit diameter Do Diffuser Divergent angle θ4
15 18 7
° mm °
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Table 1. Geometry parameters of the ejector. Parameter
Value
Units
Nozzle throat diameter Dn Nozzle exit diameter Da Nozzle convergent angle θ1 Nozzle divergent angle θ2 Nozzle exit position Length of constant-area mixing section Lm Diameter of constant-area mixing section Dm Mixing chamber Convergence angle θ3 Diffuser Exit diameter Do Diffuser Divergent angle θ4
2 4 17 10 −5, 0, 5, 8, 13, 18 5, 10, 15, 20, 25, 30, 35, 40, 45 6, 7, 8 15 18 7
mm mm ◦ ◦
mm mm mm ◦
mm ◦
For further numerical investigation, the following assumptions are made: (a) (b) (c) (d) (e) (f)
The flow inside the ejector is in steady state. The primary flow at the ejector inlet is dry saturated vapor. Vapor expansion in the nozzle is isentropic. The secondary flow at the ejector inlet is dry saturated vapor. The inner wall of the ejector is adiabatic. Water vapor is assumed as ideal gas. Based on the assumptions, the governing equations can be written as follows: The continuity equation: ∂ρ ∂ + (ρui ) = 0, ∂t ∂xi
(1)
The momentum equation: ∂τij ∂ ∂ ∂P ρui uj = − + , (ρui ) + ∂t ∂xj ∂xi ∂xj
(2)
→ → ∂ ∂ ∂T + ∇ · uj τij , (ρE) + [ui (ρE + P)] = ∇ · αeff ∂t ∂xi ∂xi
(3)
The energy equation:
ρ=
(4)
∂u k + ∂xij − 32 µeff ∂u ∂xk δij And the k − ε model equations:
with τij = µeff
p RT
∂ui ∂xj
∂ ∂ ∂ (ρk) + (ρkui ) = ∂t ∂xi ∂xj
"
µ µ+ t δk
# ∂k + Gk + Gb − ρε − YM , ∂xj
" # ∂ µt ∂ε ε2 ∂(ρε) ∂(ρεui ) ε √ + C1ε C3ε Gb , + = µ+ + ρC1 Sε − ρC2 ∂t ∂xi ∂xj δε ∂xj k k + vε h i h i p ∂uj i with C1 = max 0.43, ηµ , η = S εk S = 2Sij Sij Sij = 12 ∂u +5 ∂x + ∂x j
(5)
(6)
i
In these equations, C1 = 1.44 C3 = 0.09 C2 = 1.9 δk = 1.0 and δε = 1.3 The realizable k − ε model can both predict the spreading rate of both planar and curved jets accurately and provide superior performance for flows involving boundary layers under strong adverse pressure gradients and separation [15]. In addition, the realizable k − ε turbulence model is
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recommended to solve the high velocity flow problem [12–14,19,22–24]. Thus, the viscous model is set as realizable k − ε turbulence model in this simulation. The “standard wall functions” are selected to treat the near wall treatment. The second-order upwind scheme is employed to discretize the convective terms. The “pressure inlet” condition is adopted on both the primary and secondary inlets flow boundary conditions. Besides, the ejector outlet is set as “pressure outlet” condition. For each simulation, the solution was iterated until the scaled residual for each governing equation was5 less Micromachines 2017, 8, 235 of 10 than 10−5 . 3. Results and Discussion 3. Results and Discussion In an ejector refrigeration system, the design of the ejector has a great impact on the system’s In an ejector refrigeration system,standards the design the ejector has a great impact on theone system’s performance. There are two common to of evaluate the performance of an ejector, is the performance. There are two common standards to evaluate the performance of an ejector, one is entrainment ratio and another is known as the critical back pressure. More precisely, ω is definedthe as entrainment ratioratio: and another is known as the critical back pressure. More precisely, ω is defined as the entrainment the entrainment ratio: mass flowofofthe m thesec second fluid mass flow ond fluid me (7) ωω = = mass flow of the primary fluid = =m (7) mass flow of the primary fluid mg
Figure 33 is is the the performance performance characteristic characteristic of an an ejector. ejector. The The characteristic characteristic curve curve can can be be divided divided Figure into three modes [12]: critical mode, subcritical mode and reversed mode. The pressure at point AA is into critical mode, subcritical mode and reversed mode. The pressure at point named asas the is named thecritical criticalback backpressure pressureand andthe thepressure pressureatatpoint pointBBisis called called the the break break down down pressure. Normally, the the ejector ejector works works at at the the critical critical mode, mode, and and the the entrainment entrainment ratio ratio keeps keeps unchanged unchanged with with Normally, increasing back back pressure. pressure. After the back pressure exceeds exceeds the critical back pressure, pressure, the the entrainment entrainment increasing ratio drops drops linearly linearly with with increasing increasing back pressure. pressure. When the back pressure is higher higher than the the back back ratio down pressure, pressure, the the ejector ejector cannot cannot function functionand andbackflow backflowmay mayhappen happenin inthe thereversed reversedmode moderegion. region. down
ejector. Figure 3. Performance characteristic of an ejector.
In order to investigate the performance of the miniature steam ejector applied in electronic In order to investigate the performance of the miniature steam ejector applied in electronic cooling, cooling, a series of simulations have been conducted. The temperature of primary flow (T g) is 60 °C, a series of simulations have been conducted. The temperature of primary flow (Tg ) is 60 ◦ C, and the and the temperature of secondary flow (Te) is 10 °C. The performance of the miniature steam ejector temperature of secondary flow (Te ) is 10 ◦ C. The performance of the miniature steam ejector with a with a certain geometrical construction was investigated by changing the temperature of the certain geometrical construction was investigated by changing the temperature of the condenser (Tc ). condenser (Tc). The results are summarized and discussed as follows. The results are summarized and discussed as follows. 3.1. Effect Effect of of Area Area Ratio Ratio of of Constant-Area Constant-Area Mixing Mixing Section Section to to the the Nozzle Nozzle Throat Throat 3.1. The area area ratio ratio of of the the constant-area constant-area mixing mixing section section to to the the nozzle nozzle throat throat is is the the most most important important The parameter affecting the performance of the ejector. In this section, NXP equals 8 mm, L is fixed fixed as as parameter affecting the performance of the ejector. In this section, NXP equals 8 mm, Lm is 30 mm. mm. By By changing changing the the area area ratio ratio of of the theconstant-area constant-areamixing mixingsection sectionto tothe thenozzle nozzlethroat throat(γ (γA),), the the 30 A effects of the area ratio on the entrainment ratio and the critical back pressure of the miniature effects of the area ratio on the entrainment ratio and the critical back pressure of the miniature ejector ejector are investigated. The A is set as 9, 12.25 and 16. The results of CFD simulations are shown in are investigated. The γA is setγas 9, 12.25 and 16. The results of CFD simulations are shown in Figure 4. Figure 4. seen It canclearly be seen clearly that the entrainment ratio ω increases sharply γA increases. It is It can be that the entrainment ratio ω increases sharply when γAwhen increases. It is shown shown that the entrainment ratios are about 0.26, 0.46, 0.66 for γ A = 9, 12.25 and 16, respectively. that the entrainment ratios are about 0.26, 0.46, 0.66 for γA = 9, 12.25 and 16, respectively. They have a They haveofa about difference of aboutthe 0.2.data Besides, data of the simulation results the critical difference 0.2. Besides, of thethe simulation results reveal that thereveal criticalthat back pressure back pressure drops dramatically. Correspondingly, the critical back pressure for γA = 9, 12.25 and 16 are 2480 Pa, 2142 Pa and 1761 Pa. It can be concluded that the entrainment ratio and critical back pressure are both sensitive to γA. So the area ratio of the constant-area mixing section to the nozzle throat should be designed carefully. The velocity contours of ejectors with different γA are shown in Figure 5 for further study. It can
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drops dramatically. Correspondingly, the critical back pressure for γA = 9, 12.25 and 16 are 2480 Pa, a smaller The pressure the primary flow drops to about 1000 Pa are at the 2142 Pa and primary 1761 Pa. flow It canpressure. be concluded that the of entrainment ratio and critical back pressure both outlet of nozzle. As ratio a result, secondary flow is entrained the mixing sensitive to γthe the area of thethe constant-area mixing section to into the nozzle throatchamber should be A . So spontaneously at Te = 10 °C. designed carefully.
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a smaller primary flow pressure. The pressure of the primary flow drops to about 1000 Pa at the outlet of the nozzle. As a result, the secondary flow is entrained into the mixing chamber spontaneously at Te = 10 °C.
Figure4.4.Variation Variationof of performance performance with Figure with different differentarea arearatios. ratios.
The velocity contours of ejectors with different γA are shown in Figure 5 for further study. It can be seen that the primary flow accelerates from subsonic speed to supersonic speed in the Laval nozzle, and the velocity along the axis increases continuously after exiting the nozzle. A series of normal shock waves called the shock train can be observed downstream of the nozzle exit section. According to the law of momentum conservation, a higher primary flow velocity is corresponding to a smaller primary flow pressure. The pressure of the primary flow drops to about 1000 Pa at the outlet of the nozzle. Figure 4. Variation of performance with different area ratios. As a result, the secondary flow is entrained into the mixing chamber spontaneously at Te = 10 ◦ C.
Figure 5. Velocity contours at different area ratios.
Figure 6 is the localized velocity contours and stream trace line in mixing chamber. From Figure 6, a ‘light-colored wing-shaped’ area can be seen clearly when γA = 16. Then, the pressure in this area is lower than other places in the mixing chamber, and the ‘light-colored wing-shaped’ area becomes smaller with decreasing γA. In other words, the low pressure area in the mixing chamber becomes larger when γA increases. Therefore, the entrainment ratio increases. Focus on the detail views of the stream trace line pattern in Figure 6, therecontours is a small vortex around the outlet end of the mixing Figure 5. Velocity at different area ratios. chamber when γA = 9. However, vortex contours disappeared whenarea γA =ratios. 12.25 and 16. The reason is that Figure the 5. Velocity at different when γA is larger than 9, the primary flow expands adequately in the mixing chamber and the Figure 6 is the localized velocity contours and stream trace line in mixing chamber. From Figure 6, pressure of 6the flowvelocity can drop to lowerand level, hence the line entrainment can reach higher Figure is primary the localized contours stream trace in mixingratio chamber. Froma Figure a ‘light-colored wing-shaped’ area can be seen clearly when γA = 16. Then, the pressure in this area is value. However,wing-shaped’ increasing the improves the entrainment ratio, also induces a low 6, a ‘light-colored areaarea can ratio be seen clearly when γA = 16. Then, thebut pressure in this area is lower than other places in the mixing chamber, and the ‘light-colored wing-shaped’ area becomes smaller critical back pressure. From the point of energy loss, a larger area ratio gives more space for the lower than other places in the mixing chamber, and the ‘light-colored wing-shaped’ area becomes with decreasing words, the lowin pressure area inarea thethe mixing chamber becomes larger A . In other mixing flow toγexpand and mix, resulting the energy loss of mixing flowchamber along the radial smaller with decreasing γA. In other words, the low pressure in the mixing becomes when γ increases. Therefore, the entrainment ratio increases. Focus on the detail views of the stream Awhen direction increases correspondingly. Thisentrainment results in reduced the critical backonpressure. Inviews conclusion, larger γA increases. Therefore, the ratio increases. Focus the detail of the trace pattern Figure there is6, athere smallthe around outlet end of the chamber for line a given working condition, decreasing A resulted a worse ratio. the stream trace lineinpattern in6, Figure is vortex a γsmall vortexinthe around theentrainment outlet endmixing of the But mixing when γA = when 9. However, the vortexthe disappeared when γA = 12.25 The is that when chamber γA = 9. However, vortex disappeared when γA = and 12.2516. and 16. reason The reason is that when γA is larger than 9, the primary flow expands adequately in the mixing chamber and the pressure of the primary flow can drop to lower level, hence the entrainment ratio can reach a higher value. However, increasing the area ratio improves the entrainment ratio, but also induces a low critical back pressure. From the point of energy loss, a larger area ratio gives more space for the mixing flow to expand and mix, resulting in the energy loss of the mixing flow along the radial
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γA is larger than 9, the primary flow expands adequately in the mixing chamber and the pressure of the primary flow can drop to lower level, hence the entrainment ratio can reach a higher value. However, increasing the area ratio improves the entrainment ratio, but also induces a low critical back pressure. From the point of energy loss, a larger area ratio gives more space for the mixing flow to expand and mix, resulting in the energy loss of the mixing flow along the radial direction increases Micromachines 2017, 8,This 235 results in reduced the critical back pressure. In conclusion, for a given working 7 of 10 correspondingly. condition, decreasing the γA resulted in a worse entrainment ratio. But the ejector could operate at operate at a higher critical pressure and would therefore be changing particularly suitable aejector highercould critical back pressure and wouldback therefore be particularly suitable for condenser for changing condenser conditions in real applications. conditions in real applications.
Figure 6. Localized patterns of ejectors. Figure 6. Localized patterns of ejectors.
3.2. Effect of Range of the Length of the Constant-Area Mixing Section 3.2. Effect of Range of the Length of the Constant-Area Mixing Section The effect of the length of the constant-area mixing section, Lm , on the performance of the The effect of the length of the constant-area mixing section, Lm, on the performance of the miniature ejector is shown in Figure 7. The length of the constant-area mixing section varied in the miniature ejector is shown in Figure 7. The length of the constant-area mixing section varied in the range of 5 mm–45 mm with an increment of 5 mm. Figure 7a illustrates the variation of the entrainment range of 5 mm–45 mm with an increment of 5 mm. Figure 7a illustrates the variation of the ratio with the increase of the length of constant-area mixing section. It can be seen from the curves that entrainment ratio with the increase of the length of constant-area mixing section. It can be seen from the entrainment ratio declines with increasing Lm . To be specific, decline of the entrainment ratios for the curves that the entrainment ratio declines with increasing Lm. To be specific, decline of the γA = 9, γA = 12.25 and γA = 16 are 0.08, 0.05 and 0.03 when Lm varies from 5 mm to 45 mm, respectively. entrainment ratios for γA = 9, γA = 12.25 and γA = 16 are 0.08, 0.05 and 0.03 when Lm varies from 5 mm Also, the tendency shown in Figure 7a reveals clearly that the effect of Lm on the entrainment ratio to 45 mm, respectively. Also, the tendency shown in Figure 7a reveals clearly that the effect of L on becomes smaller when γA increases. Figure 7b indicates that the critical back pressure rises initially and the entrainment ratio becomes smaller when γA increases. Figure 7b indicates that the critical back then decreases with increasing Lm . The peak values of the critical back pressure for γA = 9, γA = 12.25 pressure rises initially and then decreases with increasing Lm. The peak values of the critical back and γA = 16 are 2480 Pa, 2142 Pa and 1761 Pa at the Lm = 30 mm, respectively. It is worth noting pressure for γA = 9, γA = 12.25 and γA = 16 are 2480 Pa, 2142 Pa and 1761 Pa at the Lm = 30 mm, that the critical mode region can’t be found when γA = 16 and Lm = 5 mm or 10 mm, which means respectively. It is worth noting that the critical mode region can’t be found when γA = 16 and Lm =5 the ejector can’t function. What’s more, the critical back pressures are all lower than the saturation mm or 10 mm, which means the ejector can’t function. What’s more, the critical back pressures are pressure of water vapor at 15 ◦ C, when γA = 12.25, Lm = 5 mm and γA = 16, Lm =5 mm–45 mm. In all lower than the saturation pressure of water vapor at 15 °C, when γA = 12.25, Lm = 5 mm and γA = other words, the structures stated above are not recommended for applying in practice. 16, Lm =5 mm–45 mm. In other words, the structures stated above are not recommended for applying To further study flow phenomena inside the ejector, velocity contours at different lengths of the in practice. constant-area mixing section of γA equals 12.25 are shown in Figure 8. It is easy to see that the profiles of the ‘wing-shaped’ area in the mixing chambers were similar to each other when Lm varied from 5mm to 45 mm, and the ‘wing-shaped’ area decreases with increasing Lm . This corresponds with the variation of the entertainment ratio shown in Figure 7a. In addition, the variation trend of the critical back pressure is in keeping with the position of the second shock shown in Figure 8. And the second shock position has been marked by dash in Figure 8. The 2nd shock position of the ejector with Lm = 30 mm is the farthest one away from the nozzle when γA = 12.25. The mixed flow has more momentum at the exit of the diffuser, which can gain a higher critical back pressure. As a result, Lm = 30 mm is the optimal length of the constant-area mixing section for primary flow and second flow to mix when γA = 12.25.
pressure for γA = 9, γA = 12.25 and γA = 16 are 2480 Pa, 2142 Pa and 1761 Pa at the Lm = 30 mm, respectively. It is worth noting that the critical mode region can’t be found when γA = 16 and Lm =5 mm or 10 mm, which means the ejector can’t function. What’s more, the critical back pressures are all lower than the saturation pressure of water vapor at 15 °C, when γA = 12.25, Lm = 5 mm and γA = Micromachines 2017, 8, 235 8 of 10 16, Lm =5 mm–45 mm. In other words, the structures stated above are not recommended for applying in practice.
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To further study flow phenomena inside the ejector, velocity contours at different lengths of the constant-area mixing section of γA equals 12.25 are shown in Figure 8. It is easy to see that the profiles of the ‘wing-shaped’ area in the mixing chambers were similar to each other when Lm varied from 5mm to 45 mm, and the ‘wing-shaped’ area decreases with increasing Lm. This corresponds with the variation of the entertainment ratio shown in Figure 7a. In addition, the variation trend of the critical back pressure is in keeping with the position of the second shock shown in Figure 8. And the second shock position has been marked by dash in Figure 8. The 2nd shock position of the ejector with Lm = 30 mm is the farthest one away from the nozzle when γA = 12.25. The mixed flow has more (a) (b) momentum at the exit of the diffuser, which can gain a higher critical back pressure. As a result, Lm = Figure 7.optimal Variation of performance with the length of constant-area mixing section; (a) Variation of to 30 Figure mm is the length of the constant-area mixing section for primary flow and flow 7. Variation of performance with the length of constant-area mixing section; (a)second Variation of entrainment ratio; (b) Variation of critical back pressure. mixentrainment when γA = ratio; 12.25. (b) Variation of critical back pressure.
Figure lengthof ofthe theconstant-area constant-areamixing mixing section. Figure8.8.Velocity Velocitycontours contours at at different length section.
3.3. EffectofofNozzle NozzleExit ExitPosition Position 3.3. Effect The nozzle position is another important parameter. the nozzle exit The nozzle exitexit position is another veryvery important parameter. The The effecteffect of theofnozzle exit position position on the performance of the ejector with different γ A is shown in Figure 9. NXP varied in on the performance of the ejector with different γA is shown in Figure 9. NXP varied in the the range of to −518 mm to The 18 mm. The variation of the entrainment ratio with different is of range −5 mm mm. variation trend of trend the entrainment ratio with different NXPs is NXPs illustrated 9a.that It is the go three upthen initially and with then increasing decline with in illustrated Figure 9a. in It Figure is found thefound threethat curves up curves initiallygoand decline NXP. increasing NXP. There is an optimal NXP for each ejector. More precisely, the optimal NXPs of the There is an optimal NXP for each ejector. More precisely, the optimal NXPs of the entrainment ratio entrainment ratio are 13 mm, 8 mm and 5 mm for γA = 9, 12.25 and 16 respectively. Correspondingly, are 13 mm, 8 mm and 5 mm for γA = 9, 12.25 and 16 respectively. Correspondingly, the peak values the peak values of the entrainment ratio are 0.27, 0.46 and 0.69. The variation trend of the critical of the entrainment ratio are 0.27, 0.46 and 0.69. The variation trend of the critical back pressure with back pressure with different NXP is shown in Figure 9b. It can be found that the three curves have different NXP is shown in Figure 9b. It can be found that the three curves have different trends. When different trends. When γA = 9, the critical back pressure increases with increasing the NXP. When γA γA = 9, the critical back pressure increases with increasing the NXP. When γA = 12.25, the critical back = 12.25, the critical back pressure increases first and then decreases with increasing the NXP. It is a pressure increases and then decreases with increasing the NXP. It is which a coincidence theasoptimal coincidence that first the optimal NXP of the critical back pressure is 8 mm, is as thethat same that of the entrainment ratio. When γA = 16, the critical back pressure has no evident changes in the range of NXP = −5 mm to 18 mm. It shows that the critical back pressure is not sensitive to NXP variations. The factors contributing to this phenomenon are complex. We thought the cause might be “entrained
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NXP of the critical back pressure is 8 mm, which is as the same as that of the entrainment ratio. When γAMicromachines = 16, the critical back pressure has no evident changes in the range of NXP = −5 mm to 189mm. 2017, 8, 235 of 10 It shows that the critical back pressure is not sensitive to NXP variations. The factors contributing to duct” formed byare thecomplex. mixing chamber and nozzle outlet has be an“entrained optimum “effective area” by at different this phenomenon We thought the cause might duct” formed the mixing NXPs. and nozzle outlet has an optimum “effective area” at different NXPs. chamber 0.8
γ A=12.25 Critical Back Pressure (Pa)
0.6
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0.5 0.4 0.3 0.2
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0
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Figure 9. Variation of the performance with different nozzle exit position (NXP); (a) Variation of Figure 9. Variation of the performance with different nozzle exit position (NXP); (a) Variation of entrainment ratio; (b) Variation of critical back pressure. entrainment ratio; (b) Variation of critical back pressure.
4. Conclusions 4. Conclusions In this study, CFD is employed to investigate the effects of the area ratio of the ejector In this study, CFD issection employed to investigate thelength effectsofofconstant-area the area ratiosection, of the ejector constant-area constant-area mixing to nozzle throat, the and the NXP, on mixing section to nozzle throat, the length of constant-area section, and the NXP,loop. on the performance the performance in a miniature steam ejector embedded with a capillary pump According to in the a miniature steam ejector withthat a capillary pump loop. According the results results presented, it canembedded be concluded the performance of the miniaturetosteam ejectorpresented, is very it can be concluded the of the miniature very to the area sensitive to the areathat ratio ofperformance the constant-area mixing sectionsteam to theejector nozzle.isFor thesensitive needs of practical ratio of the constant-area mixing section to the nozzle. the needsthe of practical the area application, the area ratio should be smaller than 16.For In addition, length ofapplication, the constant-area ratio should be smaller than 16. on In addition, length of the constant-area mixing section has more mixing section has more effect the criticalthe back pressure than the entrainment ratio. The position of the second shock that thethe total momentum of the fluid andsecond the critical effect on the critical backreflects pressure than entrainment ratio. The mixed position of the shock back reflects pressure increase when the position moves toward the diffuser. The miniature steam ejector will that the total momentum of the mixed fluid and the critical back pressure increase when the position operate at higher critical back when the ejector second will shock position diffuser. moves toward the diffuser. Thepressure miniature steam operate at moves higher toward critical the back pressure There is an optimal length of constant-area section, L m = 30 mm, where the critical back pressure has when the second shock position moves toward the diffuser. There is an optimal length of constant-area a peak value for the three ejectors with given area ratios. Furthermore, the effects of the NXP on section, Lm = 30 mm, where the critical back pressure has a peak value for the three ejectors with the given entrainment ratio and the for the three withback givenpressure area area ratios. Furthermore, thecritical effects back of thepressure NXP onare thedifferent entrainment ratio andejectors the critical The results this ejectors paper could used area to optimize the miniature areratios. different for the in three withbegiven ratios. the Thegeometry results inparameters this paperofcould be used to ejector before fabricating a real prototype. optimize the geometry parameters of the miniature ejector before fabricating a real prototype. Acknowledgments: This research work was supported by the National Natural Science Foundation of China Acknowledgments: This research work was supported by the National Natural Science Foundation of China under Award Nos. 51409034 51479020, Natural Science Foundation of Liaoning Province of China under Award Nos. 51409034 andand 51479020, thethe Natural Science Foundation of Liaoning Province of China under under Award No. 2014025013, and the Fundamental Research Funds for the Central Universities, Award No. Award No. 2014025013, and the Fundamental Research Funds for the Central Universities, Award No. 3132016337. 3132016337. Author Contributions: Jing-Ming Dong and He Song conceived the idea, performed the numerical calculations, analyzed results, and drafted the manuscript; Meng-Qi and Wei-Ning Wang performed numerical Author the Contributions: Jing-Ming Dong and He Song Yu conceived the idea, performed thethe numerical calculations and improved manuscript for the final submission. Xin-Xiang Pan impeccably revised and calculations, analyzed the the results, and drafted the manuscript; Meng-Qi Yu and Wei-Ning Wang performed improved the manuscript forand the improved final submission. the numerical calculations the manuscript for the final submission. Xin-Xiang Pan impeccably revised of and improved manuscript forno theconflict final submission. Conflicts Interest: Thethe authors declare of interest. Conflicts of Interest: The authors declare no conflict of interest.
References 1.
Kheirabadi, A.C.; Groulx, D. Cooling of server electronics: A design review of existing technology. Appl. Therm. Eng. 2016, 105, 622–638. [CrossRef]
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2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.
14.
15. 16. 17. 18. 19.
20. 21. 22. 23.
24.
10 of 10
Chougule, S.S.; Sahu, S.K. Thermal performance of nanofluid charged heat pipe with phase change material for electronics cooling. J. Electron. Packag. 2015, 137, 021004. [CrossRef] Sun, X.; Zhang, L.; Liao, S. Performance of a thermoelectric cooling system integrated with a gravity-assisted heat pipe for cooling electronics. Appl. Therm. Eng. 2017, 116, 433–444. [CrossRef] Ma, M.; Yu, J. An analysis on a two-stage cascade thermoelectric cooler for electronics cooling applications. Int. J. Refrig. 2014, 38, 352–357. [CrossRef] Riffat, S.B.; Holt, A. A novel heat pipe ejector cooler. Appl. Therm. Eng. 1998, 18, 93–101. [CrossRef] Smirnov, H.F.; Kosoy, B.V. Refrigerating heat pipes. Appl. Therm. Eng. 2001, 21, 631–641. [CrossRef] Wang, X.C.; Shi, M.H. Investigation on refrigeration system combining with heat pipe and ejector. J. Southeast Univ. 2002, 32, 634–637. Shi, M.H.; Cai, H.; Wang, X.C. Investigation on vapor ejector refrigeration system driven by capillary force. J. Eng. Thermophys. 2004, 25, 745–748. Shi, M.H.; Cai, H.; Wang, X.C. Investigation of vapor ejector in a heat pipe ejective air conditioning system. J. Eng. Thermophys. 2005, 26, 918–920. Cai, H.; Shi, M.H. The chosen of the wick for the heat pipe/ejector refrigeration system. J. Eng. Thermophys. 2006, 1, 047. Ziapour, B.M.; Abbasy, A. First and second laws analysis of the heat pipe/ejector refrigeration cycle. Energy 2010, 35, 3307–3314. [CrossRef] Yang, X.; Long, X.; Yao, X. Numerical investigation on the mixing process in a steam ejector with different nozzle structures. Int. J. Therm. Sci. 2012, 56, 95–106. [CrossRef] Sriveerakul, T.; Aphornratana, S.; Chunnanond, K. Performance prediction of steam ejector using computational fluid dynamics: Part 1. Validation of the CFD results. Int. J. Therm. Sci. 2007, 46, 812–822. [CrossRef] Sriveerakul, T.; Aphornratana, S.; Chunnanond, K. Performance prediction of steam ejector using computational fluid dynamics: Part 2. Flow structure of a steam ejector influenced by operating pressures and geometries. Int. J. Therm. Sci. 2007, 46, 823–833. [CrossRef] Ruangtrakoon, N.; Thongtip, T.; Aphornratana, S.; Sriveerakul, T. CFD simulation on the effect of primary nozzle geometries for a steam ejector in refrigeration cycle. Int. J. Therm. Sci. 2013, 63, 133–145. [CrossRef] Varga, S.; Lebre, P.M.S.; Oliveira, A.C. CFD study of a variable area ratio ejector using R600a and R152a refrigerants. Int. J. Refrig. 2013, 36, 157–165. [CrossRef] Yan, J.; Cai, W.; Li, Y. Geometry parameters effect for air-cooled ejector cooling systems with R134a refrigerant. Renew. Energy 2012, 46, 155–163. [CrossRef] Varga, S.; Oliveira, A.C.; Diaconu, B. Influence of geometrical factors on steam ejector performance—A numerical assessment. Int. J. Refrig. 2009, 32, 1694–1701. [CrossRef] Pianthong, K.; Seehanam, W.; Behnia, M.; Sriveerakul, T.; Aphornratana, S. Investigation and improvement of ejector refrigeration system using computational fluid dynamics technique. Energy Convers. Manag. 2007, 48, 2556–2564. [CrossRef] Varga, S.; Oliveira, A.C.; Diaconu, B. Numerical assessment of steam ejector efficiencies using CFD. Int. J. Refrig. 2009, 32, 1203–1211. [CrossRef] Zhu, Y.; Cai, W.; Wen, C.; Li, Y. Numerical investigation of geometry parameters for design of high performance ejectors. Appl. Therm. Eng. 2009, 29, 898–905. [CrossRef] Wu, H.; Liu, Z.; Han, B.; Li, Y. Numerical investigation of the influences of mixing chamber geometries on steam ejector performance. Desalination 2014, 353, 15–20. [CrossRef] Dong, J.; Yu, M.; Wang, W.; Song, H.; Li, C.; Pan, X. Experimental investigation on low-temperature thermal energy driven steam ejector refrigeration system for cooling application. Appl. Therm. Eng. 2017, 123, 167–176. [CrossRef] Fu, W.; Li, Y.; Liu, Z.; Wu, H.; Wu, T. Numerical study for the influences of primary nozzle on steam ejector performance. Appl. Therm. Eng. 2016, 106, 1148–1156. [CrossRef] © 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
