Performance of heat pipes as capillary pumps: modelling and comparison with experimental results

Transcription

1 Performance of heat pipes as capiary pumps: modeing and comparison with experimenta resuts Prof. Dionissios P. Margaris 1, Zisis G. Diamantis, Dionysios I. Photeinos, Prof. Demos T. Tsahais (corresponding author) 1 Fuid Mechanics Laboratory (FML/UoP), Department of Mechanica Engineering and Aeronautics, Uniersity of Patras, 6500 Patras, Greece E-mai: margaris@mech.upatras.gr, web page: Laboratory of Fuid Mechanics and Energy (LFME), Department of Chemica Engineering, Uniersity of Patras, P.O. BOX 1400, 6500 Patras, Greece E-mai: tsahais@fme.chemeng.upatras.gr, web page: Abstract The objectie of this paper is to present a theoretica inestigation of the operationa characteristics on a sma-scae Capiary Pump Loop (CPL), focused on the CPL capacity to create fow in addition to its heat transfer capacity. A typica design of a CPL is composed of a capiary eaporator, a condenser, a two-phase reseroir, iquid and apour ines. The capiary eaporator generates the required pressure pumping for moing the working fuid from the condenser to the eaporator section. The fundamenta principes of the proposed modeing are: The oera pressure drop in the oop must be ess than the maximum capiary pressure in order to ensure that the system wi operate continuousy. The major components of the CPL pressure drop are reated to the fow in the wick structure, condenser, apour and iquid ines. The wick structure present in the eaporator causes a fow restriction that affects the CPL performance, which is dependent on the wick permeabiity, a property of the porous materia that describes its abiity to transport the iquid under an appied pressure gradient. An experimenta ab-scae instaation is used for the aidation of the theoretica anaysis. The resuts showed that the proposed CPL modeing is abe to describe the CPL performance ery we. Keywords Capiary pump; CPL; heat pipes; pressure head rise Nomencature A w porous media surface [m ] C constant [ ] d pipe diameter [m] f friction factor [ ] g graitationa acceeration [m /s] g c graitationa conersion constant [ ] G mass eocity [kg/s m ] h reatie height [m] h, enthapy [kj/kg] K w porous media permeabiity [m ] L pipe ength [m] ṁ mass fow rate [kg/s] P e appied heat oad of eaporator [W] Q fow rate [m 3 /s] Internationa Journa of Low Carbon Technoogies / Downoaded from on 8 Apri 018

2 150 D. P. Margaris et a. Re Reynods number [ ] r c porous media radius [m] T temperature [ C] u eocity [m/s] m iscosity [kg/m s] r density [kg/m 3 ] s L surface tension [N/m] pressure drop [Pa] Subscripts b buoyancy head c capiary force, condenser e eaporator eff effectie g graity head h hydrauic iquid phase max maximum o reference point apour phase w wick Introduction Capiary pumping two-phase oops hae been continuousy inestigated for eectronic cooing systems, sateite therma contro and other space appications. Most tests were performed in capiary eaporators using pastic or metaic porous wick as the capiary structure and anhydrous ammonia as the working fuid. A Capiary Pump Loop (CPL) is designed for operation as a two-phase heat transfer deice in passie mode, without the need of any mechanica pump for driing the working fuid from a ow temperature sink to a high temperature source. Athough earth-based appications of the CPL hae been proposed, it is especiay we suited for therma management in spacecraft, where graity and hence its potentiay deeterious effects on the CPL s operation are absent. The CPL uses capiary action for fuid transport and contains no moing parts. Mutipe eaporators and condensers can be added at different ocations in a CPL, aowing the use of a singe oop to reject heat from mutipe sources to mutipe sinks, possiby at different temperatures. In contrast to the heat pipe, wicks are absent in most of the transport section of the CPL. Instead, iquid and apour fow through smooth waed tubing, thereby reducing the frictiona pressure osses and increasing the maximum potentia fuid fow and heat transfer rates. A typica design of a CPL (Figure 1) is composed of a capiary eaporator (responsibe for generating the capiary forces that drie the working fuid), a condenser, a two-phase reseroir (to contro the oop saturation pressure), iquid and apour ines. The capiary forces are generated by the capiary eaporator, which Internationa Journa of Low Carbon Technoogies / Downoaded from on 8 Apri 018

3 Performance of heat pipes as capiary pumps 151 Figure 1. The schematic diagram of the capiary pumped oop. acquires heat and transfers it to the working fuid. Formation of apour is responsibe for the dispacement of the iquid in the ines towards the condenser during the start up. The two-phase reseroir is used to set the operation temperature at which the entire oop wi operate. The CPL works without moing parts and with ery itte power consumption. The fuid must be used in its pure state without contaminants, which enabes its use in micrograity. It passiey promotes the therma contro, aowing fine contro on the operating temperature of components. CPL deeopment began in the 1960s but receied specia attention in the ate 1970s. At this time, CPL began to be intensiey inestigated, proing to be operationay reiabe for therma contro and abe to transport heat oer ong distances with minor temperature difference. Exceent reiews of the deeopment history and theory of operation are aaiabe in the iterature [1, ]. In recent years, numerous CPLs hae been fabricated and ground-tested, seera hae been tested in fight experiments and designs hae been seected for use on a few spacecraft missions [3]. Neertheess, issues reating to the CPL s reiabiity and robustness hae imited its acceptance and impementation, and hae been the primary focus in recent years [4 7]. One probem which has pagued CPLs in both ground and fight tests is the difficuty in starting the eaporators. Typicay, after a CPL successfuy starts and enters into a steady operation mode it performs quite we and the operation is fairy predictabe. Howeer, before steady state operation can occur, a series of transient eents, coectiey referred to as the start-up, must take pace where the thermophysica state of fuid through much of the oop changes quite dramaticay. During the start-up, the ocations occupied by iquid and apour transienty shift to those corresponding to steady state operation. This repositioning of iquid and apour occurs through the combined processes of aporization, condensation, and mutiphase fuid fow through arious portions of the oop. Internationa Journa of Low Carbon Technoogies / Downoaded from on 8 Apri 018

4 15 D. P. Margaris et a. In theory, apour shoud form ony in the apour grooes of an eaporator. Howeer, if sufficient superheat deeops in the grooes before nuceation occurs, the wick and possiby the iquid core can aso heat up to a temperature that is greater than the saturation temperature, and nuceation coud potentiay occur there as we. Additionay, apour may be forced through the wick and injected into the iquid core during the initia pressure spike or pressure surge of the start-up. If the temperature of the iquid core is at a temperature near or at saturation, then apour may remain there without condensing and in some cases may actuay grow. Vapour presence in the iquid core has been found to fuy or partiay bock iquid fow to the wick, which may ead eentuay to deprime the oss of capiary pumping action of an eaporator [8, 9]. Aso, apour presence in the eaporator core has been to infuence pressure osciations in the CPL [10]. The two-phase reseroir has to be heated, prior to the start-up of a CPL, so that the operation temperature can be set. The entire oop wi then operate at this temperature with sight ariations owing to some superheat or subcooing. Upon setting an operating temperature in the reseroir, the interna pressure wi raise which wi fi the entire oop with iquid, causing the so-caed pressure priming. When the oop is fied with iquid, the CPL is ready to start operating. Then, heat is appied to the capiary eaporator and as its temperature rises, ony sensibe heat is transferred to the working fuid. When the eaporator temperature reaches the same temperature as the reseroir, atent heat is transferred to the working fuid starting the eaporation process. A meniscus is formed at the iquid-apour interface, which is responsibe for deeoping the capiary pressure that wi drie the working fuid. Vapour is dispaced from the eaporator, which causes the dispacement of the iquid in the channes aowing the apour to reach the condenser. In the condenser, heat is remoed and iquid wi aso present some subcooing. At the start-up, the excess of iquid present in the channes is dispaced by the apour back to the reseroir, which equaizes the right amount of working fuid for a gien heat oad. With such particuarities, the CPL has been used to transfer heat oer ong distances with sma pressure drops oer the entire oop aowing its use in arge systems. CPLs hae been tested oer different configurations, and it is known to transport up to 5000 W when capiary eaporators are used [11]. Without moing parts and because a CPL acts as a therma diode, the working fuid cannot fow from the condenser to the eaporator by the apour ine. Reated, mainy to the porous structures (caed wick) present in the capiary eaporator, great deeopments were achieed on CPLs. Different materias hae been used as porous wick such as sintered nicke, stainess stee, titanium and utrahigh moecuar weight poyethyene [1 14]. As the generation of capiary forces is dependent on the working fuid surface tension and wick pore size, CPLs hae been inestigated using methano, acetone and anhydrous ammonia as working fuids. Seera inestigations hae been performed towards the achieement of sintered nicke components with fine pore sizes [15, 16]. The working fuid must operate without impurities as an important condition to aoid the presence of non-condensabe gases (NCG) in the oop. The presence of NCG in a CPL can cause a genera faiure of the capiary eaporator, but in genera, Internationa Journa of Low Carbon Technoogies / Downoaded from on 8 Apri 018

5 Performance of heat pipes as capiary pumps 153 it is ess ikey to occur than in heat pipes. The presence of NCG can be minimized using compatibe materias with the seected working fuid. Ensuring that a good acuum condition is erified in the oop as we as using fuid with minimum contaminants aso minimizes the presence of NCGs. Nowadays, there are efforts to extend the appication of capiary pump oops to commercia and industria systems. The use of such deices offers many adantages regarding the fexibiity in operation and appication, as they are ery efficient in transporting heat, een under a sma temperature difference. Very few inestigations hae been conducted towards the use of sma size capiary eaporators in order to manufacture a more compact CPL. Inestigators [17] hae reported that sma eaporators hae a tendency of depriming more easiy, probaby due to an insufficient subcooed iquid suppy to the porous wick. More information regarding this matter is important especiay when more compact CPLs need to be deeoped for specific appications. The objectie of this paper is to present a theoretica inestigation of the operationa characteristics on a sma-scae CPL, focused on the CPL capacity to create fow in addition to its heat transfer capacity. An experimenta ab-scae instaation, described anayticay in [18] and the modified configuration in [19, 0], is used for the aidation of the theoretica anaysis. The resuts showed that the proposed CPL modeing is abe to describe the CPL performance ery we. Modeing of a CPL The CPL design is reated to the maximum capiary pressure that can be deeoped by the wick structure and working fuid. The oera pressure drop in the oop must be ess than the maximum capiary pressure in order to ensure that the system wi operate continuousy. Thus the driing pressure difference eff is gien by: eff = c,max + b tota (1) where c,max is the pressure drop due to maximum capiary force, b is the pressure drop due to buoyancy force effect, and tota is the tota pressure drop in the oera oop. The pressure drop due to maximum capiary force is gien by: L c,max = s () rc with s L the surface tension and r c the radius of the porous media. The pressure drop due to buoyancy force effect is gien by: b = ( r r) gh (3) with r the density of iquid and apour respectiey and h the reatie height. The major components of the CPL pressure drop are reated to the fow in the eaporator (wick structure), condenser, apour and the iquid ines. Thus the tota pressure drop in the oera oop is gien by: Internationa Journa of Low Carbon Technoogies / Downoaded from on 8 Apri 018

6 154 D. P. Margaris et a. = tota w c g The pressure drop in the eaporator due to iquid fowing through the porous media (based on the Darcy s aw) may be written as: LWm w = m (5) rkwaw where L w the ength, A w the surface, and K w the permeabiity of the porous media (wick) and ṁ the mass fow rate. The pressure drop in the condenser is reated to the mass eocity G of the iquid, the eocity of the iquid u and the eocity of the apour u through the equation: (4) G c = ( u u ) gc where g c is the graitationa conersion constant. The mass eocity G and the iquid eocity u are gien by the equations: (6) G 4rQ 4Q = and u = pd pd c,h c,h and the fow rate of the iquid Q and the apour Q are reated with the equation: (7) Q = r Q r (8) where r is the density of the iquid and r is the density of the apour. Substituting equations (7) and (8) into equation (6) it is obtained that: c = 16 r 4 g d 1 rq p r c c,h (9) The pressure drop due to iquid fowing through the iquid head ine is gien by: = f L d,h ru (10) where L the ength and d,h the hydrauic diameter of the iquid head ine. The pressure drop due to apour fowing through the apour head ine is gien by: = f L d,h ru (11) where L the ength and d,h the hydrauic diameter of the apour head ine. And finay the pressure drop due to graitationa head effect is gien simpy by the equation: g = r gh (1) Internationa Journa of Low Carbon Technoogies / Downoaded from on 8 Apri 018

7 Performance of heat pipes as capiary pumps 155 In the aboe equations f is the friction factor dependent on the Reynods number of each phase, f(re). The friction factor can be determined as foows: fre ( )= 64 Re for Re < fre ( )= 05 Re. for 300 Re 0000 f( Re)= Re. for Re > 0000 (13a) (13b) (13c) Usuay the fow is in the aminar region, Re < 300, and by substitution of equation (13a) into equations (10) and (11) we get: 18mL 18mL r = Q and = Q 4 4 pd pd r, h, (14) By combining equations (5), (9), (1) and (14) it is obtained: tota mlwm 16 r 18mL = rq + Q 4 rkwaw gcp dc,h r pd, h 18mL r + Q+ rgh 4 pd r, Equation (15) gies the tota pressure drop tota in the oop from parameters which are either directy measurabe (pipe ength and diameter, fow rate) or materia properties which can be found in the bibiography (iscosity of the fuids). (15) Couping fuid dynamics with heat transfer By means of the reation between fuid eocity, mass fow rate, appied heat oad of the eaporator, P e, and enthapy, h,, it is possibe to coupe fuid dynamics with thermodynamics magnitudes. The fuid eocity may be expressed as: u= 4m 4Pe = rpd rpdh (16) and by substituting into the aboe deried reations for pressure drops, we get: mlwm mpl e w w = = r K A r K A h (17) c 16 r QPe = 4 4 g d = 16 r g d h 1 r 1 Q p r p r c h w c,h w f L r u = = C d h, w w, m PL e r d h 1 4, h, h, c c,h, (18) (19) Internationa Journa of Low Carbon Technoogies / Downoaded from on 8 Apri 018

8 156 D. P. Margaris et a. f L r = = C d m PL r d h u e 4 h,, h, (0) The pressure drop due to buoyancy force effect may be expressed as: b = ( r r) gh (1) Under natura circuation conditions, when the reatie ertica distance between the eaporator and condenser is arge enough, the oop operates without a pump, and the fow is drien dominanty by the buoyancy-generated pressure head. The maximum power that can be remoed by the natura conection for a gien oop configuration is gien by substituting the equations (), (1), (17) (1) into equation (1). By rearranging terms, the foowing equation can be deried: s L rgh + ( r r )gh rc Pe = () mlw 16Q r ml m L + C C r K A h g p d h r r d h r d h w w, c c,h,, h,, h, From the aboe equation the maximum remoa power of the capiary oop can be obtained. Resuts and discussion The experimenta ab-scae instaation, presented in [19], is used for the aidation of the theoretica anaysis. The wick thickness is m, the transersa area is m, the pore radius is m and its permeabiity is m, as gien by the manufacturer. The ength of the iquid ine is 3.67 m, the ength of the apour ine is 3.05 m and the diameter of the oop is 1 inches (0.017 m). The properties of the iquid are those for 0 C (density r = 998.kg/m 3, iscosity m = kg/ms, and surface tension s = N/m) and of the apour are those for 100 C (density r = 0.595kg/m 3 and iscosity m = kg/ms). The resuts show that the aboe proposed CPL modeing is abe to describe we the CPL performance. A sampe of the comparison diagram between theoretica and experimenta resuts for the pressure head rise s. fow rate is gien in Fig.. It is obious that for higher fow rates there is a ery good agreement between theoretica and experimenta resuts. For fow rates ower than 1.5 t/h there is a disagreement due to the unsteady character of the fow at the start-up period. As the time passes the temperatures are stabiized and the capiary pump oop operates steadiy. Figure 3 shows the maximum power that can be remoed from the capiary pump oop as a function of the iquid fow rate. For the experimenta instaation and the conditions mentioned aboe, deries from Fig. 3 that the maximum power for iquid fow rate 1 t/h is equa to 598 W, for t/h is 589 W, and for 3 t/h is 56 W. The pressure head rise ersus input heat fux of the eaporator is shown in Figure 4 for different fow rates. Input heat fux of the eaporator affects ery much the Internationa Journa of Low Carbon Technoogies / Downoaded from on 8 Apri 018

9 Performance of heat pipes as capiary pumps 157 Figure. Comparison between theoretica and experimenta resuts for the pressure head rise s. fow rate. Figure 3. The maximum remoa power from the capiary pump oop as a function of the iquid fow rate. Internationa Journa of Low Carbon Technoogies / Downoaded from on 8 Apri 018

10 158 D. P. Margaris et a. Figure 4. Pressure head rise as a function of the appied heat oad of the eaporator for different iquid fow rate. pressure head rise (or effectie pressure drop). The function is inear and the iquid fow rate does not pay a significant roe. Another resut from this figure is that the maximum input heat fux of the eaporator or the maximum power is between 560 and 590 W which is the same resut deried from Figure 3. The concusion is that the iquid fow rate does not affect the maximum power that can be remoed from the capiary pump oop ery much and as a resut we may use a round aue of 600 W independent of the iquid fow rate. Appying the deeoped modeing to any instaation with known geometry and fow conditions, it is possibe to estimate the maximum power that can be remoed by the capiary pump oop. Pressure head rise as a function of the porous media surface can be cacuated using equation (15). These resuts are gien in Figure 5 for three different iquid fow rates. The main resut is that for any iquid fow rate there is a minimum aue of the porous media surface necessary to start the fow. As it is cear, the higher the fow rates, the arger the surface necessary for the oop operation. Another resut is that as the porous media (or wick) surface increases, for a specific fow rate, the pressure head rise increases firsty quite steepy and then tends asymptoticay to a constant aue. The same behaiour may be seen for the pressure head rise as a function of the permeabiity of the wick, which means that these parameters affect ery much the operation of a capiary pump oop. Concusions A mathematica mode was deeoped for the theoretica inestigation of the operationa characteristics on a sma-scae Capiary Pump Loop (CPL). An Internationa Journa of Low Carbon Technoogies / Downoaded from on 8 Apri 018

11 Performance of heat pipes as capiary pumps 159 Figure 5. Pressure head rise as a function of the porous media surface for different iquid fow rate. experimenta ab-scae instaation was used for the aidation of the theoretica anaysis. Usuay, in the CPL research area information such as temperature is gien to show the performance of a CPL. Such information is gien in the first part of the present research work [0] concerning the experimenta inestigation of a CPL instaation. On the contrary, there is a ack of information in the iterature concerning pressure drop and especiay fow rates of a CPL. Since the target of the present research work is to use a CPL, instead of a centrifuga pump, in instaations where fow rates are critica, the presented theoretica mode is focused on the prediction of the pressure head rise and the fow rates of a CPL. From the comparison diagram between theoretica and experimenta resuts for the pressure head rise s. fow rate, it is obious that for higher fow rates there is a ery good agreement between theoretica and experimenta resuts. For ower fow rates there is a disagreement due to the unsteady character of the fow at the startup period. During the start-up period, the temperature of the iquid inet increases up to a maximum aue and then drops down to a steady state temperature eading to a steady state operation of the capiary pump oop. The iquid fow rate does not affect the maximum power that can be remoed from the capiary pump oop ery much and thus, for any instaation with known geometry and fow conditions, it is possibe to estimate a round aue of the maximum power independent of the iquid fow rate. The major components of the CPL pressure drop are reated to the fow in the wick structure, apour and the iquid ines. The wick structure present in the eaporator causes fow restriction that affects the CPL performance, which is dependent Internationa Journa of Low Carbon Technoogies / Downoaded from on 8 Apri 018

12 160 D. P. Margaris et a. on the wick transersa area and permeabiity, a property of the porous materia that describes its abiity to transport the iquid under an appied pressure gradient. The resuts showed that the proposed CPL modeing is abe to describe ery we the CPL performance. Acknowedgements The work presented in this paper was supported by the European Commission and was performed under the framework of the FP5 project entited A Noe Tri-Generation Eectrogasdynamic Conerter System (TRI-GEN EGD), Contract Number ENK6-CT The foowing partners were inoed in the project: Uniersity of Porto, Department of Mechanica Engineering & Industria Management (Coordinator) Uniersity of Nottingham, Institute of Buiding Technoogy, Te Ai Uniersity, Department of Fuid Mechanics and Heat Transfer Venturi Jet Pumps (VJP) Ltd. Uniersity of Patras, Laboratory of Fuid Mechanics and Energy (LFME) Thermacore Europe Ltd. References [1] B. A. Cuimore, Capiary pumped oop appication guide, SAE Paper (1993). [] J. Ku, Oeriew of capiary pumped oop technoogy, in HTD-Vo. 36, Proceedings of the 9 th Nationa Heat Transfer Conference, Atanta, GA, USA, (1993), [3] J. Ku, Recent adances in capiary pumped oop technoogy, AIAA Paper (1997). [4] T. T. Hoang, J. Ku, Theory of hydrodynamic stabiity for capiary pumped oops, in HTD-Vo. 307, Proceedings of the 1995 Nationa Heat Transfer Conference, Portand, OR, USA, 5 (1995), [5] T. Hoang, J. Ku, Hydrodynamic aspects of capiary pumped oops, SAE Paper (1996). [6] T. Hoang, Deeopment of an adanced capiary pumped oop, SAE Paper 9735 (1997). [7] J. H. Kim, K. Cheung, D. Buter, J. Ku, E. Haught, E. J. Kroiczek, B. Cuimore and J. Baumann, The capiary pumped oop III (CAPL III) fight demonstration description and status, Proceedings of the Space Technoogy and Appications Internationa Forum, Abuquerque, NM, USA, 1997, [8] B. A. Cuimore, Start-up transients in capiary pumped oops, AIAA Paper (1991). [9] J. Ku, Start-up issues of capiary pumped oops, Adances in Heat Pipe Science and Technoogy, in Proceedings of the 9 th Internationa Heat Pipe Conference, Abuquerque, NM, USA, 1995, [10] J. Ku, T. Hoang, T. Nguyen, S. Yun, Performance tests of CAPL starter pump cod pates, AIAA Paper (1996). [11] H. Grenier, M. Feuiatre, T. Maciaszek and H. Hustaix, Deeopment and test resuts of a 5 kw ammonia capiary pumped oop, Proceedings of the 5 th Internationa Conference on Enironmenta Systems, San Diego, CA, USA, 1995, paper [1] C. Gerhart, D. Guck, Summary of operating characteristics of a dua compensation chamber oop heat pipe in graity, 11 th Internationa Heat Pipe Conference, Tokyo, Japan, [13] G. Muhoand, C. Gerhart, D. Guck and S. Staney, Comparison between anaytica predictions and experimenta data for oop heat pipes, Space Technoogy and Appications Internationa Forum, Abuquerque, NM, USA, 1999, Internationa Journa of Low Carbon Technoogies / Downoaded from on 8 Apri 018

13 Performance of heat pipes as capiary pumps 161 [14] J. Ku, L. Ottenstein, K. Cheung, T. Hoang and S. Yun, Ground tests of a capiary pumped oop (CALP 3) fight experiment, Proceedings of the 8 th Internationa Conference on Enironmenta Systems, Daners, MS, USA, 1998, paper [15] E. G. Reimbrecht, M. C. Frede, E. Bazzo and F. M. Pereira, Manufacturing and micro-structura characterization of sintered nicke wicks for capiary pumps, Mater. Res. (3) (1999), 5 9. [16] E. G. Reimbrecht, P. C. Phiippi and E. Bazzo, Wick characterization by image anaysis, Proceedings of the 30 th ICES-Internationa Conference on Enironmenta Systems, 001, paper 38. [17] A. A. M. Dei, M. DuBois and W. Supper, The European two-phase experiments TPX I & II, 10 th Internationa Heat Pipe Conference, Stuttgart, Germany, [18] Z. G. Diamantis, D. I. Photeinos and D. T. Tsahais, Inestigation of the performance of heat pipes used as capiary pumps, Internationa Journa of Low Carbon Technoogies, 1(1) (006), [19] Z. G. Diamantis, D. I. Photeinos, D. P. Margaris and D. T. Tsahais, Deeopment of an experimenta setup to inestigate the performance of heat pipes as capiary pumps, 1 st Int. Conf. on Experiments/ Process/System Modeing/Simuation/Optimization, 1 st IC-EpsMsO, Athens, Greece, 6 9 Juy, 005. [0] Zisis G. Diamantis, Dionysios I. Photeinos, Professor Dionissios P. Margaris and Professor Demos T. Tsahais, Performance of Heat Pipes as Capiary Pumps: Experiments, currenty in print to be pubished in the Journa of Low Carbon Technoogies, January 007. Internationa Journa of Low Carbon Technoogies / Downoaded from on 8 Apri 018