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Experimental and theoretical investigation of a capillary pumped loop with a porous element in the condenser
Vol. 25, No. 8, pp. 1085-1094, 1998 Copyright © 1998 Elsevier Science Ltd Printed in the USA. All rights reserved 0735-1933/98 $19.00 + .00
Int. Comm. Heat Mass Transfer,
Pergamon
P I I S0735-1933(98)00099-2
E X P E R I M E N T A L AND T H E O R E T I C A L I N V E S T I G A T I O N O F A C A P I L L A R Y P U M P E D L O O P W I T H A P O R O U S E L E M E N T IN THE C O N D E N S E R
I. Muraoka, F.M. Ramos and V.V. Vlassov INPE - Instituto Nacional de Pesquisas Espaciais Av. dos Astronautas, 1758 12227-010 Sao Jose dos Campos-SP Brazil
(Communicated by J.P. Hartnett and W.J. Minkowycz)
ABSTRACT A new CPL design is investigated experimentally and theoretically. In order to create a fixed physical interface between the liquid and the vapor phases inside the loop, the conventional tube condenser is replaced by a condenser containing a porous wick structure. The idea is to have a simple, light, and reliable system directed to applications where a high heat-transport eapacitT over long distances is needed, but a precise temperature control of the cold plate is not required. Experimental results, under different test conditions, are presented and illustrate the overall performance of the system. A CPL mathematical model, based on the nodal method, is described and validated experimentally. © 1998 Elsevier Science Ltd
1. Introduction
Capillary. Pumped Loop (CPL) is a two-phase heat-transport system which relies on the surfacetension forces induced by a fine pore wick to displace the working fluid. Because of its efficiency - it is capable of transporting large heat loads over long distances with small temperature differences - and reliability - there are no moving parts for pumping the working fluid - CPL is emerging as the baseline design of thermal control systems for future spacecrafts. Since the first work of Stenger [1] demonstrating experimentally" the feasibilib, of this concept, extensive research has been done on CPLs, mainly over the last two decades. An excellent review of the subject can be found in [2].
Although the CPL technology, has reached a high level of development, some
issues still remain points of active research. One of them concerns the investigation of the potential failure mechanisms that may occur during the CPL start-up procedure, and has been studied in [3,4]. The 1085
1086
I. Muraoka, F.M. Ramos and V.V. Vlassov
Vol. 25, No. 8
oscillation in the pumping pressure, associated with the interaction betv,-een the fluid reservoir and the CPL loop, are another point of concern. These oscillations reported by Ku et al. [5] and O'Connell [6] have been intensely investigated [7,8] due to their adverse effects on CPL operation. Concerning the theoretical aspects of the CPL operation, there is still no established method for mathematically modeling the loop, at least not at system level. Schweickart et al. [9] describes a software package for thermal and pressure transient and steadv-state analyses, based on the nodal or lumpedparameter method. In spite of the good correlation with experimental data from a Space Shuttle experiment, this package has two major drawbacks. Firstly, some key input parameters have to be determined experimentally, such as the heat transfer coefficients associated with the vaporization and condensation processes. Secondly, a large amount of effort is spent in the determination of the liquid-vapor interface inside the condenser. Also following an empirical approach, Furukawa [10] presents a detailed CPL design procedure, constrained by functional and geometrical requirements. In the present work, a CPL with a porous element in the condenser is investigated experimentally and theoretically. The main purpose is to assess the operational characteristics of this type of CPL, including the start-up, steady-state and transient regimes.
This configuration of CPL was first proposed and
conceptually analyzed in [ 11]. The idea behind this new design concept is that the use of a wick structure in the condenser creates a stable physical interface between the liquid and the vapor phases inside the CPL, reducing or even eliminating the difficulties associated with the start-up procedure and the occurrence of pressure oscillations during operation. Also in this paper, a system-level numerical model, based on the nodal method, is presented. The model is similar to that described in [9], but with a different approach. In the present case, since the liquid-vapor interface is fixed at the condenser wick, there is no need to determine its position, and the analysis can be focused on the temperature distribution inside the evaporator and condenser. This model simulates the steady-state and transient temperature and pressure distributions inside the CPL, and is capable of predicting the occurrence of dry-out and the formation of vapor bubbles during operation. 2. CPL Proposed Design The CPL in study is schematically presented in Fig. 1. It consists of an evaporator, a condenser and two connecting pipes. In the present case. both the evaporator and the condenser have a porous wick element. The operation of this CPL is basically the same of the conventional s~'stem. The fluid evaporates on the upper surface of the evaporator wick. The vapor is transported through the vapor line and condenses on the condenser wick surface. The liquid is then subcooled as it passes through the condenser wick structure - which eliminates the need for an additional radiator for this purpose --, and returns to the evaporator
Vol. 25, No. 8
INVESTIGATION OF A CAPILLARY PUMPED LOOP
1087
through the liquid line. ,~ COLD P[~kTE
///
/
~CK
/
/
-
--~>
II/I
ill
~
VAPOR LINE
/I/
-__
ili
/
....
/
,
t COMPENSmION CAV!I~
~
klO~llO LNE
EVAPORATOR
COhDENSEFR
FIG. 1 Sketch of Prooosed CPL
3. Mathematical
Model
The CPL numerical model is based on the nodal or lumped parameter method [12]. In this method, the physical system is divided in a finite number of isothermal regions, called nodes. In this study, it is assumed that (i) the vapor is saturated in both the evaporator and the condenser, (ii) the fluid inside the liquid line is at the same temperature as the tube walls, (iii) the vapor line is adiabatic and has no thermal capacitance, and (iv) the evaporation/condensation process occurs at the evaporator/condenser wick upper surface. The thermal balance at node i is given by dT,
Micm
-~
N
,v
,,,
-~_Ci,(Tj-T,)+~.,Hj~(Tj-T,)+~_Fj,(T~-T,)+Qi j=l
j=l
i=l
...... N
(1)
j =]
The conductive, convective, and fluid conductanees are calculated respectively by
C .. - kj, Aj~ s, L ji
,
Hj~ = hji Aj,
,
and
Fie = rhj~c~.
.
(2)
Besides modeling the electrical power dissipated at the cold plate (see Fig. 1), Qi represents the latent heat released by the vapor at the condenser or absorbed at the evaporator: Q, = + th,,3. ,
i = condenser,
and
Q, = - rn.,1 ,
i = evaporator .
(3)
The vapor mass-flow rate in the vapor line is obtained from Blasius formula for turbulent flow in a smooth pipe:
1088
I. Muraoka, F.M. Ramos and V.V. Vlassov
Vol. 25, No. 8
1
f-_|/3p,,
D ,,~p,, 47s "~i7;
r h - ~.0241/L °~SL 1 )
(4)
where APv = P, ( L ) - p~ ( L ) , and p / r 0 and p/re) are the saturation pressures of the vapor at the evaporation and condensation temperatures, respectively. The mass flow rate is uniform all along the loop, that is. m, = r n . ,
(5)
in the absence of bubble formation inside the loop. 3.1 Pressure Losses in the Loop and Maximum Capillary Pumping Pressure For working properly, the total pressure loss in the CPL loop must be less than the maximum pumping pressure provided by the evaporator wick. that is.
Ap~p .... > @loop
with
~g~..p.... = 20 / r~t~:
(6)
The total pressure loss in the lo0p is given by the summation of the pressure loss in each component or process along the circuit, as follows:
@,oop - Ap.,, + Apt ' + Ap... + Ap.,c + Ape~.p + Ap~,,.a + Ap~.a,- .
(7)
The pressure loss in the liquid line. assuming laminar flow conditions, and the hydrostatic pressure are given by
Aptl -
128/ajhlLll
and
zpID~
Aph,,a,. -- P i g zZz ,
(8)
where Az is the height difference between the evaporator and the condenser. The pressure losses in the evaporator and in the condenser wick are calculated by
,ulrhtl.. .
/-lllhlL~. e
At).,~ -
and
K~.~A~,~Pr
At) ~..~ -
(9)
K~,,Aw.cPt
The pressure losses during the process of phase change are given by
m,, ~[2zl{ Ap~,w, - A~,,.p
1:,
and
At)c,,.a
tit,, ~ - A~,,,,a
"
(10)
3.2 Bubble Formation Model The appearance of bubbles at the entrance of the evaporator, in a region called the compensation cavity (see Fig. 1), strongly affects the CPL operation because it induces the formation of a liquid layer on
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INVESTIGATION OF A CAPILLARY PUMPED LOOP
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the upper surface of the condenser wick. Since the thermal conductivity of the working fluid is smaller than that of the wick material, this liquid layer represents a non-negligible thermal resistance between the heat sink and the vapor. Also, with the occurrence of bubbles, the mass-flow rate is no longer uniform inside the loop, and a correction term for Eq. (5) must be determined. The process of bubble formation depends on the temperature and the pressure of the liquid inside the compensation cavity. Assuming that half surface of the bubble is in contact with the wick and the other half is in contact with the liquid in the compensation cavity,, the variation of the vapor mass inside the bubble can be expressed as
~/] bub, v
= A 2bub
(1i)
[p.~(T,~)+p~(T~)-2pc~]
where pfI'~), p.,(Tcj are the vapor saturation pressures at the wick wall and at the compensation caviB, temperatures, respectively. Hence, the variation of fluid mass inside the compensation cavity, supposing that the vapor mass is small compared to the liquid mass , can be expressed as M ~ = -l(4b,,~, v Pt/P,, • This mass variation corresponds to the mass of liquid that is displaced by the bubble and that will eventually accumulate at the entrance of the condenser. Assuming that the vapor-flow rate is not affected by bubble formation and that the mass of liquid in all other parts of the CPL remains constant, the liquidflow rate is given by rh I = l h , +A)/c~ = rh,
Pt Ab~b , ~_/ ~ i ~
p~.
2
V Zrct¢,,l,:~ [ p , ( T ~ ) + p , ( T , . ~ ) - 2 p , ~ ] .
(12)
The pressure at the compensation c a v i l , p ~ , can be obtained from the pressure at the condenser taking into account the losses between the condenser and the compensation cavity., as follows: p ~ = p~ ( g ) -
AOco.~ - @ . , ~ - A o , - 4 0 , , ~
03)
.
Expressing Ap11and Apw.c as functions of rh~, as presented in Eqs. (8) and (9), and introducing the result into Eq. (12), the following relation for liquid-flow rate can be obtained after some rearranging:
rh, =
t h +. Abob . . .P , . ~ [ 2 p s 2 Pv
( T ~ ) - Ps (T,,.) - Ps (Tcc) - 2@co,d -- 2APhidr ]
p,~(64,u,L,,
(14)
2,u,l~.c
1
The variation A6 of the thickness of the liquid layer accumulated at the entrance of the condenser between time steps t and t + At, can now be obtained from:
1090
1. Muraoka, F.M. Ramos and V.V. Vlassov
Ad-
Vol. 25, No. 8
&'' - m l At Pt A,.c
(15)
3.3 Computing Procedure Having at hand, at time t. the conductive and convective conductances and the thermal capacitance for all nodes, the instant heat load applied at the cold plate, and the previous temperature distribution in the circuit, the procedure for computing the temperature and pressure distributions inside the CPL can be described as follows: (i) determine the saturation pressure at the condenser and evaporator and compute the vapor-mass flow rate using Eq. (4): (ii) compute the heat of vaporization and of condensation using Eq. (3); (iii) compute the liquid-mass flow rate using Eq. (14); (iv) compute the fluid conductances using Eq (2): (v) compute the thickness of the liquid layer at the condenser entrance using Eq. (15); (vi) compute the conductive conductance between vapor at the condenser entrance and the condenser wick upper surface using Eq. (2), considering the liquid layer computed on the previous step: (vii) compute the total pressure loss in the loop using Eqs. (7)-(10); (viii) check if the total pressure loss in the loop does not exceed the maximum capillar> pumping pressure using Eq (6): (ix) solve Eq. (1) for all nodes and compute the temperature distribution in the loop; (x) stop or return to (i) for the next time step t+At.
4. Experimental Investigation For the purpose of verifying the performance of the system and validating its mathematical model, the CPL shown in Fig. 1 was built and tested. Some parts of the prototype were made of transparent glass in order to allow the visualization of the phase distribution inside the CPL and to detect the formation of bubbles in the compensation cavity. Aflcr some prelimina~' tests, a sintered bronze has been chosen to manufacture both the evaporator (~bl00 x 10 ram) and the condenser (qbl00 x 7 mm) wicks. The vapor and liquid lines xxere made of stainless steel, measuring 1100 mm in length and 4.35 mm inner diameter. The prototype was charged with 138 ml of ethanol. A skin-heater, installed on the CPL cold plate, simulated the heat load dissipated at the evaporator. A cooling system, using water as the working fluid, removed this heat load at the CPL condenser. The test program was specified in order to vcri~ the operational characteristics of a CPL with a porous element in the condenser. It consisted of four distinct phases: start-up, steady-state operation, transient operation with variable heat load. and transient operation with variable heat-sink temperature. 4.1 Initial Phase Distribution and Start-up The use a wick structure at the condenser eliminates the need for an active reservoir to start-up the CPL. Unfortunately, this fact did not prevent an unsuitable initial phase distribution, after the fluid was loades into the system In particular, some liquid and vapor bubbles always remained in the cold plate
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INVESTIGATION OF A CAPILLARY PUMPED LOOP
1091
groove and in the compensation cavity, respectively, which required devising a special procedure for starting-up the loop. 4.2 Steady-State Operation Steady state was reached approximately 60 minutes after the start-up, and the operation was stable with no noticeable pressure fluctuations inside the loop. Theoretical and experimental result, for different power input and heat-sink temperature, are presented in Table 1. In all test cases, the temperature distribution along the loop computed by the mathematical model show an excellent agreement with the experimental results, with an error that never exceeds 1%. Moreover, the model correctly predicted the appearance of bubbles inside the compensation cavity and of a layer of liquid at the condenser entrance. TABLE 1 Results for Steady-State Operation Test # Power input/Heat-sink temperature experiment/thcory Cold-plate temperature (°C) Vapor temper, at evaporator (°C) Vapor temper, at condenser (°C) AT cold plate to heat sink (°C) Theoretical transported heat (W) Theor. liquid-layer thickness (ram) Total conductance (W/~C) Heat transfer coeff. (W/m2/°C)
1 2 3 4 7 3 W / 4 1 °C 120 W / 30 °C 120 W / 40 °C 120 W / 60 °C exp theo exp theo exp theo exp theo 66.3 69.7 77.5 78.8 76.7 79.2 83.5 84.5 67.5 70.3 75.2 75.6 61.8 64.3 68.1 69.8 75.2 75.2 61.7 63.9 67.8 69.2 67.4 69.7 47.5 48.8 36.7 39.2 23.5 24.5 25.3 28.7 102 61 102 102 0.69 0.65 0.29 2.4 2.2 2.8 4.4 308 274 358 555
During operation, a large temperature difference between cold plate and heat sink was observed. Conventional CPLs have a heat transfer coefficient of approximately 10,000 W/°C/m2. In the present case, since all the heat transported by the CPL passes through the condenser wick, a major temperature drop is generated at the condenser which, compounded by the accumulation of liquid at the condenser entrance, drastically reduces the total heat transfer coefficient. It is possible to improve the CPL efficiency reducing the thermal resistance at the condenser wick This requires, for example, the use of a wick with a smaller thickness and/or with a higher conductivity. 4.3 Transient Operation with Variable Heat Load The CPL dynamic response to a variable heat load was assessed by cycling the power dissipated at the cold plate between 120 and 0 W, with a period of 20 minutes. The temperature of the condenser was kept constant at 40 °C. The results are presented in Fig. 2 and include the experimental and theoretical temperature profiles of the cold plate and of the evaporator entrance. An excellent correlation between theoretical and experimental results can be observed. In spite of the geometrical complexity of the system and the range of physical phenomena involved, the relative error never exceeded 2%.
1092
1. Muraoka, F.M. Ramps and V.V. Vlassov
,~ cold plate (exper) • cold plate (model) 80 q
OW
I
During the whole cycle, the CPL
7~ evap entrance (exper) • evap entrance (model)
120W
i
OW
~!.
Vol. 25, No. 8
presented a stable operation without
120W
pressure
oscillations,
imposed o
directly
by
except the
those
heat
load
variation. The total volume occupied by the bubbles cavity
E
inside the compensation
oscillated
during
each
cycle,
decreasing or increasing as the power
I'-
input was switched, respectively, on and off Also, it was noticed that, as the 485
495
505
515
T i m e (min)
temperature of the cold plate decreased, when heat load was set to zero, the
FIG. 2 Evolution during Power Input Cycling Test
volume of the bubbles grew and pushed the
hot
liquid
accumulated
in
the
compensation cavi~ through the liquid line back to the condenser, raising the temperature at the evaporator entrance, as shown in Fig. 2. Normal operation was resumed, with the working liquid flowing in the right direction, when the power input was switched on again and the bubble started to decrease in size. 4.4 Transient Operation with Variable Heat-Sink Temperature In the last set of dynamic tests, the sink temperature was cycled between 30 and 60 °C while the power input was kept constant at 120 W. Computed and measured cold-plate tcmperature profiles are
• +
cold p l a t e ( e x p e r )
presented in Fig. 3. As in the
cold plate ( m o d e l with b u b b l e ) cold plate ( m o d e l w / o b u b b l e )
previous test, the agreement between
heat sink (exper / model)
theoretical and experimental results was found to be excellent. noticed
that
the
temperature
E
amplitude
variation
considerably I---
It was
smaller
of was
in
the
evaporator (about 6 °C) than in the 4°
heat
sink (30
°C).
Again,
this
behavior can be explained by the 20 ~- . . . . 0
i ,
1 O0
~- ~ i
~
200 300 T i m e (min)
'
400
" 500
FIG. 3 Evolution during Heat-Sink Temperature Cycling Test
formation
of
bubbles
in
the
compensation cavity. As the heat sink
is cooled,
the
volume of
Vol. 25, No. 8
INVESTIGATION OF A CAPILLARY PUMPED LOOP
1093
bubbles increases in size, displacing an equivalent volume of liquid in the direction of the condenser. This process, as mentioned earlier, eventually creates a layer of liquid at the condenser entrance, increasing locally the thermal resistance and attenuating the temperature variations at the cold plate. The opposite effect is produced when the temperature of the heat sink is raised. The impact of this phenomenon in the CPL dynamics is clearly visible if the theoretical temperature profiles (depicted in Fig. 3), computed with and without the presence of bubbles, are compared. In a sense, the process of bubble formation/collapsing inside the compensation cavity reproduces, in a smaller scale, the role performed by the active reservoir in a conventional CPL in stabilizing the temperature of the cold plate under different operating conditions. A similar behavior was reported by Maidanik et al. [ 13]. 5. Conclusions
A new CPL configuration was investigated experimentally and theoretically. In this design, the conventional tube condenser was replaced by a condenser containing a porous wick structure in order to create a fixed physical interface between the liquid and vapor phases inside the loop. The following conclusions can be drawn from the extensive experimental tests and numerical simulations: (i) the absence of an active reservoir prevented noticeable pressure oscillations, during both steady-state and transient operations; (ii) the formation of bubbles in the compensation eavity was observed in most tests; this phenomenon induces a self-regulating effect on the CPL and contributes to change its overall performance; (iii) the numerical model properly simulated the steady-state and transient temperature and pressure distributions inside the CPL and was capable of predicting the formation vapor bubbles during operation and the occurrence of dry-out. In summary, the advantages of the CPL with a porous element in the condenser configuration are its simplicity, lightness, and stability. These characteristics are very important in many space projects. However, due to the absence of an active reservoir in the loop, the use of this type of CPL is restricted to those applications that do not need a precise control of the cold plate temperature. Design modifications to increase the CPL performance and reliability are currently in study. Acknowledgment This work was supported by CNPq-Brazil, through Research Project grant Process 523859/95-3. The authors would like to acknowledge the contribution of Dr. Leonardo de-Olive Ferreira (INPE). Nomenclature
A cp
area thermal capacity
D g
diameter gravity acceleration
1094
1. Muraoka, F.M. Ramos and V.V. Vlassov
h K k L m
film coefficient permeability thermal conductivi~ length mass
A)/ th
time variation of the mass in a volume mass flow rate
p R r~ T t
pressure gas constant wick pores effective radius temperature time
Greek letters 2 latent heat p densiB" ¢t ds~amic viscosity
cr
Vol. 25, No. 8
surface tension
Subscripts bub bubble c condenser cc compensation cavity cond condensation process e evaporator evap evaporation process /' fluid i, ,I l II
node number liquid liquid line
s v vl w
saturated vapor vapor line wick
References 1. F. J. Stenger, NASA TM X-1310 (1966). 2. J. Ku. 1997 National Heat Transfer Conference, Baltimore, MD. Papcr AIAA 97-3870 (1997). 3. Y. Maidanik, Y. Fershtater, V. G. Pastukhov and M. Chernysheva, 23rd International Conference on Environmental Systems, Colorado Springs, CO. SAE Technical Paper Series 932305 (1993). 4. J. Ku, T. Hoang, T. Nguyen and S. Yun, 31st AIAA Thermophysics Conference, New Orleans, LA, Paper A1AA 96-1837 (1996). 5. J. Ku, E. I. Kroliczek. M. E. McCabe Jr., and S. M. Benner, AIAA Thermophysics, Plasmads~amics and Lasers Conference, San Antonio. TX, Papcr AIAA 88-2702 (1988). 6. T. O'Connell, T. Hoang and J. Ku, 30th AIAA Thcrmophysics Conference, San Diego, CA, Paper AIAA 95-2067 (1995). 7. J. Ku and T. Hoang, 1995 National Heat Transfcr Conference, Portland, OR, ASME HTD 307. 25 (1995). 8. K. R. Kolos and K. E. Herold. 1997 National Heat Transfer Conference, Baltimore, MD, Paper AIAA 97-3872 (1997). 9. R. B. Schweickart, L. Neiswanger and J. Ku, 22nd AIAA Thermophysics Conference, Honolulu. HI, Paper AIAA 87-1630 (1987). l 0. M. Furukawa. 31 st A1AA Thermophysics Conference, New Orleans, LA, Paper AIAA 96-1831 (1996). 11 J.M. Gottschlich and R. Richter, 1991 SAE Aerospace Atlantic, Da~on, OH, SAE Technical Paper 911188 (1991). 12. CR. Gane, A.J. Oliver, D.R. Soulsbv and P.L. Stcphenson. Numerwat Methods in Heat Tran.}'/br, 2_, p.227, John Wiley & Sons (1983). 13. Y. Maidanik, Y. Fershtater, V.G. Pastukhov, K. Goncharov, O. Zagar and Y. Golovanov, 22nd International Conference on Environmental Systems, Seattle, WA, SAE Technical Paper 921169 (1992). Received July 24, 1998
Int. Comm. Heat Mass Transfer,
Pergamon
P I I S0735-1933(98)00099-2
E X P E R I M E N T A L AND T H E O R E T I C A L I N V E S T I G A T I O N O F A C A P I L L A R Y P U M P E D L O O P W I T H A P O R O U S E L E M E N T IN THE C O N D E N S E R
I. Muraoka, F.M. Ramos and V.V. Vlassov INPE - Instituto Nacional de Pesquisas Espaciais Av. dos Astronautas, 1758 12227-010 Sao Jose dos Campos-SP Brazil
(Communicated by J.P. Hartnett and W.J. Minkowycz)
ABSTRACT A new CPL design is investigated experimentally and theoretically. In order to create a fixed physical interface between the liquid and the vapor phases inside the loop, the conventional tube condenser is replaced by a condenser containing a porous wick structure. The idea is to have a simple, light, and reliable system directed to applications where a high heat-transport eapacitT over long distances is needed, but a precise temperature control of the cold plate is not required. Experimental results, under different test conditions, are presented and illustrate the overall performance of the system. A CPL mathematical model, based on the nodal method, is described and validated experimentally. © 1998 Elsevier Science Ltd
1. Introduction
Capillary. Pumped Loop (CPL) is a two-phase heat-transport system which relies on the surfacetension forces induced by a fine pore wick to displace the working fluid. Because of its efficiency - it is capable of transporting large heat loads over long distances with small temperature differences - and reliability - there are no moving parts for pumping the working fluid - CPL is emerging as the baseline design of thermal control systems for future spacecrafts. Since the first work of Stenger [1] demonstrating experimentally" the feasibilib, of this concept, extensive research has been done on CPLs, mainly over the last two decades. An excellent review of the subject can be found in [2].
Although the CPL technology, has reached a high level of development, some
issues still remain points of active research. One of them concerns the investigation of the potential failure mechanisms that may occur during the CPL start-up procedure, and has been studied in [3,4]. The 1085
1086
I. Muraoka, F.M. Ramos and V.V. Vlassov
Vol. 25, No. 8
oscillation in the pumping pressure, associated with the interaction betv,-een the fluid reservoir and the CPL loop, are another point of concern. These oscillations reported by Ku et al. [5] and O'Connell [6] have been intensely investigated [7,8] due to their adverse effects on CPL operation. Concerning the theoretical aspects of the CPL operation, there is still no established method for mathematically modeling the loop, at least not at system level. Schweickart et al. [9] describes a software package for thermal and pressure transient and steadv-state analyses, based on the nodal or lumpedparameter method. In spite of the good correlation with experimental data from a Space Shuttle experiment, this package has two major drawbacks. Firstly, some key input parameters have to be determined experimentally, such as the heat transfer coefficients associated with the vaporization and condensation processes. Secondly, a large amount of effort is spent in the determination of the liquid-vapor interface inside the condenser. Also following an empirical approach, Furukawa [10] presents a detailed CPL design procedure, constrained by functional and geometrical requirements. In the present work, a CPL with a porous element in the condenser is investigated experimentally and theoretically. The main purpose is to assess the operational characteristics of this type of CPL, including the start-up, steady-state and transient regimes.
This configuration of CPL was first proposed and
conceptually analyzed in [ 11]. The idea behind this new design concept is that the use of a wick structure in the condenser creates a stable physical interface between the liquid and the vapor phases inside the CPL, reducing or even eliminating the difficulties associated with the start-up procedure and the occurrence of pressure oscillations during operation. Also in this paper, a system-level numerical model, based on the nodal method, is presented. The model is similar to that described in [9], but with a different approach. In the present case, since the liquid-vapor interface is fixed at the condenser wick, there is no need to determine its position, and the analysis can be focused on the temperature distribution inside the evaporator and condenser. This model simulates the steady-state and transient temperature and pressure distributions inside the CPL, and is capable of predicting the occurrence of dry-out and the formation of vapor bubbles during operation. 2. CPL Proposed Design The CPL in study is schematically presented in Fig. 1. It consists of an evaporator, a condenser and two connecting pipes. In the present case. both the evaporator and the condenser have a porous wick element. The operation of this CPL is basically the same of the conventional s~'stem. The fluid evaporates on the upper surface of the evaporator wick. The vapor is transported through the vapor line and condenses on the condenser wick surface. The liquid is then subcooled as it passes through the condenser wick structure - which eliminates the need for an additional radiator for this purpose --, and returns to the evaporator
Vol. 25, No. 8
INVESTIGATION OF A CAPILLARY PUMPED LOOP
1087
through the liquid line. ,~ COLD P[~kTE
///
/
~CK
/
/
-
--~>
II/I
ill
~
VAPOR LINE
/I/
-__
ili
/
....
/
,
t COMPENSmION CAV!I~
~
klO~llO LNE
EVAPORATOR
COhDENSEFR
FIG. 1 Sketch of Prooosed CPL
3. Mathematical
Model
The CPL numerical model is based on the nodal or lumped parameter method [12]. In this method, the physical system is divided in a finite number of isothermal regions, called nodes. In this study, it is assumed that (i) the vapor is saturated in both the evaporator and the condenser, (ii) the fluid inside the liquid line is at the same temperature as the tube walls, (iii) the vapor line is adiabatic and has no thermal capacitance, and (iv) the evaporation/condensation process occurs at the evaporator/condenser wick upper surface. The thermal balance at node i is given by dT,
Micm
-~
N
,v
,,,
-~_Ci,(Tj-T,)+~.,Hj~(Tj-T,)+~_Fj,(T~-T,)+Qi j=l
j=l
i=l
...... N
(1)
j =]
The conductive, convective, and fluid conductanees are calculated respectively by
C .. - kj, Aj~ s, L ji
,
Hj~ = hji Aj,
,
and
Fie = rhj~c~.
.
(2)
Besides modeling the electrical power dissipated at the cold plate (see Fig. 1), Qi represents the latent heat released by the vapor at the condenser or absorbed at the evaporator: Q, = + th,,3. ,
i = condenser,
and
Q, = - rn.,1 ,
i = evaporator .
(3)
The vapor mass-flow rate in the vapor line is obtained from Blasius formula for turbulent flow in a smooth pipe:
1088
I. Muraoka, F.M. Ramos and V.V. Vlassov
Vol. 25, No. 8
1
f-_|/3p,,
D ,,~p,, 47s "~i7;
r h - ~.0241/L °~SL 1 )
(4)
where APv = P, ( L ) - p~ ( L ) , and p / r 0 and p/re) are the saturation pressures of the vapor at the evaporation and condensation temperatures, respectively. The mass flow rate is uniform all along the loop, that is. m, = r n . ,
(5)
in the absence of bubble formation inside the loop. 3.1 Pressure Losses in the Loop and Maximum Capillary Pumping Pressure For working properly, the total pressure loss in the CPL loop must be less than the maximum pumping pressure provided by the evaporator wick. that is.
Ap~p .... > @loop
with
~g~..p.... = 20 / r~t~:
(6)
The total pressure loss in the lo0p is given by the summation of the pressure loss in each component or process along the circuit, as follows:
@,oop - Ap.,, + Apt ' + Ap... + Ap.,c + Ape~.p + Ap~,,.a + Ap~.a,- .
(7)
The pressure loss in the liquid line. assuming laminar flow conditions, and the hydrostatic pressure are given by
Aptl -
128/ajhlLll
and
zpID~
Aph,,a,. -- P i g zZz ,
(8)
where Az is the height difference between the evaporator and the condenser. The pressure losses in the evaporator and in the condenser wick are calculated by
,ulrhtl.. .
/-lllhlL~. e
At).,~ -
and
K~.~A~,~Pr
At) ~..~ -
(9)
K~,,Aw.cPt
The pressure losses during the process of phase change are given by
m,, ~[2zl{ Ap~,w, - A~,,.p
1:,
and
At)c,,.a
tit,, ~ - A~,,,,a
"
(10)
3.2 Bubble Formation Model The appearance of bubbles at the entrance of the evaporator, in a region called the compensation cavity (see Fig. 1), strongly affects the CPL operation because it induces the formation of a liquid layer on
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INVESTIGATION OF A CAPILLARY PUMPED LOOP
1089
the upper surface of the condenser wick. Since the thermal conductivity of the working fluid is smaller than that of the wick material, this liquid layer represents a non-negligible thermal resistance between the heat sink and the vapor. Also, with the occurrence of bubbles, the mass-flow rate is no longer uniform inside the loop, and a correction term for Eq. (5) must be determined. The process of bubble formation depends on the temperature and the pressure of the liquid inside the compensation cavity. Assuming that half surface of the bubble is in contact with the wick and the other half is in contact with the liquid in the compensation cavity,, the variation of the vapor mass inside the bubble can be expressed as
~/] bub, v
= A 2bub
(1i)
[p.~(T,~)+p~(T~)-2pc~]
where pfI'~), p.,(Tcj are the vapor saturation pressures at the wick wall and at the compensation caviB, temperatures, respectively. Hence, the variation of fluid mass inside the compensation cavity, supposing that the vapor mass is small compared to the liquid mass , can be expressed as M ~ = -l(4b,,~, v Pt/P,, • This mass variation corresponds to the mass of liquid that is displaced by the bubble and that will eventually accumulate at the entrance of the condenser. Assuming that the vapor-flow rate is not affected by bubble formation and that the mass of liquid in all other parts of the CPL remains constant, the liquidflow rate is given by rh I = l h , +A)/c~ = rh,
Pt Ab~b , ~_/ ~ i ~
p~.
2
V Zrct¢,,l,:~ [ p , ( T ~ ) + p , ( T , . ~ ) - 2 p , ~ ] .
(12)
The pressure at the compensation c a v i l , p ~ , can be obtained from the pressure at the condenser taking into account the losses between the condenser and the compensation cavity., as follows: p ~ = p~ ( g ) -
AOco.~ - @ . , ~ - A o , - 4 0 , , ~
03)
.
Expressing Ap11and Apw.c as functions of rh~, as presented in Eqs. (8) and (9), and introducing the result into Eq. (12), the following relation for liquid-flow rate can be obtained after some rearranging:
rh, =
t h +. Abob . . .P , . ~ [ 2 p s 2 Pv
( T ~ ) - Ps (T,,.) - Ps (Tcc) - 2@co,d -- 2APhidr ]
p,~(64,u,L,,
(14)
2,u,l~.c
1
The variation A6 of the thickness of the liquid layer accumulated at the entrance of the condenser between time steps t and t + At, can now be obtained from:
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1. Muraoka, F.M. Ramos and V.V. Vlassov
Ad-
Vol. 25, No. 8
&'' - m l At Pt A,.c
(15)
3.3 Computing Procedure Having at hand, at time t. the conductive and convective conductances and the thermal capacitance for all nodes, the instant heat load applied at the cold plate, and the previous temperature distribution in the circuit, the procedure for computing the temperature and pressure distributions inside the CPL can be described as follows: (i) determine the saturation pressure at the condenser and evaporator and compute the vapor-mass flow rate using Eq. (4): (ii) compute the heat of vaporization and of condensation using Eq. (3); (iii) compute the liquid-mass flow rate using Eq. (14); (iv) compute the fluid conductances using Eq (2): (v) compute the thickness of the liquid layer at the condenser entrance using Eq. (15); (vi) compute the conductive conductance between vapor at the condenser entrance and the condenser wick upper surface using Eq. (2), considering the liquid layer computed on the previous step: (vii) compute the total pressure loss in the loop using Eqs. (7)-(10); (viii) check if the total pressure loss in the loop does not exceed the maximum capillar> pumping pressure using Eq (6): (ix) solve Eq. (1) for all nodes and compute the temperature distribution in the loop; (x) stop or return to (i) for the next time step t+At.
4. Experimental Investigation For the purpose of verifying the performance of the system and validating its mathematical model, the CPL shown in Fig. 1 was built and tested. Some parts of the prototype were made of transparent glass in order to allow the visualization of the phase distribution inside the CPL and to detect the formation of bubbles in the compensation cavity. Aflcr some prelimina~' tests, a sintered bronze has been chosen to manufacture both the evaporator (~bl00 x 10 ram) and the condenser (qbl00 x 7 mm) wicks. The vapor and liquid lines xxere made of stainless steel, measuring 1100 mm in length and 4.35 mm inner diameter. The prototype was charged with 138 ml of ethanol. A skin-heater, installed on the CPL cold plate, simulated the heat load dissipated at the evaporator. A cooling system, using water as the working fluid, removed this heat load at the CPL condenser. The test program was specified in order to vcri~ the operational characteristics of a CPL with a porous element in the condenser. It consisted of four distinct phases: start-up, steady-state operation, transient operation with variable heat load. and transient operation with variable heat-sink temperature. 4.1 Initial Phase Distribution and Start-up The use a wick structure at the condenser eliminates the need for an active reservoir to start-up the CPL. Unfortunately, this fact did not prevent an unsuitable initial phase distribution, after the fluid was loades into the system In particular, some liquid and vapor bubbles always remained in the cold plate
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INVESTIGATION OF A CAPILLARY PUMPED LOOP
1091
groove and in the compensation cavity, respectively, which required devising a special procedure for starting-up the loop. 4.2 Steady-State Operation Steady state was reached approximately 60 minutes after the start-up, and the operation was stable with no noticeable pressure fluctuations inside the loop. Theoretical and experimental result, for different power input and heat-sink temperature, are presented in Table 1. In all test cases, the temperature distribution along the loop computed by the mathematical model show an excellent agreement with the experimental results, with an error that never exceeds 1%. Moreover, the model correctly predicted the appearance of bubbles inside the compensation cavity and of a layer of liquid at the condenser entrance. TABLE 1 Results for Steady-State Operation Test # Power input/Heat-sink temperature experiment/thcory Cold-plate temperature (°C) Vapor temper, at evaporator (°C) Vapor temper, at condenser (°C) AT cold plate to heat sink (°C) Theoretical transported heat (W) Theor. liquid-layer thickness (ram) Total conductance (W/~C) Heat transfer coeff. (W/m2/°C)
1 2 3 4 7 3 W / 4 1 °C 120 W / 30 °C 120 W / 40 °C 120 W / 60 °C exp theo exp theo exp theo exp theo 66.3 69.7 77.5 78.8 76.7 79.2 83.5 84.5 67.5 70.3 75.2 75.6 61.8 64.3 68.1 69.8 75.2 75.2 61.7 63.9 67.8 69.2 67.4 69.7 47.5 48.8 36.7 39.2 23.5 24.5 25.3 28.7 102 61 102 102 0.69 0.65 0.29 2.4 2.2 2.8 4.4 308 274 358 555
During operation, a large temperature difference between cold plate and heat sink was observed. Conventional CPLs have a heat transfer coefficient of approximately 10,000 W/°C/m2. In the present case, since all the heat transported by the CPL passes through the condenser wick, a major temperature drop is generated at the condenser which, compounded by the accumulation of liquid at the condenser entrance, drastically reduces the total heat transfer coefficient. It is possible to improve the CPL efficiency reducing the thermal resistance at the condenser wick This requires, for example, the use of a wick with a smaller thickness and/or with a higher conductivity. 4.3 Transient Operation with Variable Heat Load The CPL dynamic response to a variable heat load was assessed by cycling the power dissipated at the cold plate between 120 and 0 W, with a period of 20 minutes. The temperature of the condenser was kept constant at 40 °C. The results are presented in Fig. 2 and include the experimental and theoretical temperature profiles of the cold plate and of the evaporator entrance. An excellent correlation between theoretical and experimental results can be observed. In spite of the geometrical complexity of the system and the range of physical phenomena involved, the relative error never exceeded 2%.
1092
1. Muraoka, F.M. Ramps and V.V. Vlassov
,~ cold plate (exper) • cold plate (model) 80 q
OW
I
During the whole cycle, the CPL
7~ evap entrance (exper) • evap entrance (model)
120W
i
OW
~!.
Vol. 25, No. 8
presented a stable operation without
120W
pressure
oscillations,
imposed o
directly
by
except the
those
heat
load
variation. The total volume occupied by the bubbles cavity
E
inside the compensation
oscillated
during
each
cycle,
decreasing or increasing as the power
I'-
input was switched, respectively, on and off Also, it was noticed that, as the 485
495
505
515
T i m e (min)
temperature of the cold plate decreased, when heat load was set to zero, the
FIG. 2 Evolution during Power Input Cycling Test
volume of the bubbles grew and pushed the
hot
liquid
accumulated
in
the
compensation cavi~ through the liquid line back to the condenser, raising the temperature at the evaporator entrance, as shown in Fig. 2. Normal operation was resumed, with the working liquid flowing in the right direction, when the power input was switched on again and the bubble started to decrease in size. 4.4 Transient Operation with Variable Heat-Sink Temperature In the last set of dynamic tests, the sink temperature was cycled between 30 and 60 °C while the power input was kept constant at 120 W. Computed and measured cold-plate tcmperature profiles are
• +
cold p l a t e ( e x p e r )
presented in Fig. 3. As in the
cold plate ( m o d e l with b u b b l e ) cold plate ( m o d e l w / o b u b b l e )
previous test, the agreement between
heat sink (exper / model)
theoretical and experimental results was found to be excellent. noticed
that
the
temperature
E
amplitude
variation
considerably I---
It was
smaller
of was
in
the
evaporator (about 6 °C) than in the 4°
heat
sink (30
°C).
Again,
this
behavior can be explained by the 20 ~- . . . . 0
i ,
1 O0
~- ~ i
~
200 300 T i m e (min)
'
400
" 500
FIG. 3 Evolution during Heat-Sink Temperature Cycling Test
formation
of
bubbles
in
the
compensation cavity. As the heat sink
is cooled,
the
volume of
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INVESTIGATION OF A CAPILLARY PUMPED LOOP
1093
bubbles increases in size, displacing an equivalent volume of liquid in the direction of the condenser. This process, as mentioned earlier, eventually creates a layer of liquid at the condenser entrance, increasing locally the thermal resistance and attenuating the temperature variations at the cold plate. The opposite effect is produced when the temperature of the heat sink is raised. The impact of this phenomenon in the CPL dynamics is clearly visible if the theoretical temperature profiles (depicted in Fig. 3), computed with and without the presence of bubbles, are compared. In a sense, the process of bubble formation/collapsing inside the compensation cavity reproduces, in a smaller scale, the role performed by the active reservoir in a conventional CPL in stabilizing the temperature of the cold plate under different operating conditions. A similar behavior was reported by Maidanik et al. [ 13]. 5. Conclusions
A new CPL configuration was investigated experimentally and theoretically. In this design, the conventional tube condenser was replaced by a condenser containing a porous wick structure in order to create a fixed physical interface between the liquid and vapor phases inside the loop. The following conclusions can be drawn from the extensive experimental tests and numerical simulations: (i) the absence of an active reservoir prevented noticeable pressure oscillations, during both steady-state and transient operations; (ii) the formation of bubbles in the compensation eavity was observed in most tests; this phenomenon induces a self-regulating effect on the CPL and contributes to change its overall performance; (iii) the numerical model properly simulated the steady-state and transient temperature and pressure distributions inside the CPL and was capable of predicting the formation vapor bubbles during operation and the occurrence of dry-out. In summary, the advantages of the CPL with a porous element in the condenser configuration are its simplicity, lightness, and stability. These characteristics are very important in many space projects. However, due to the absence of an active reservoir in the loop, the use of this type of CPL is restricted to those applications that do not need a precise control of the cold plate temperature. Design modifications to increase the CPL performance and reliability are currently in study. Acknowledgment This work was supported by CNPq-Brazil, through Research Project grant Process 523859/95-3. The authors would like to acknowledge the contribution of Dr. Leonardo de-Olive Ferreira (INPE). Nomenclature
A cp
area thermal capacity
D g
diameter gravity acceleration
1094
1. Muraoka, F.M. Ramos and V.V. Vlassov
h K k L m
film coefficient permeability thermal conductivi~ length mass
A)/ th
time variation of the mass in a volume mass flow rate
p R r~ T t
pressure gas constant wick pores effective radius temperature time
Greek letters 2 latent heat p densiB" ¢t ds~amic viscosity
cr
Vol. 25, No. 8
surface tension
Subscripts bub bubble c condenser cc compensation cavity cond condensation process e evaporator evap evaporation process /' fluid i, ,I l II
node number liquid liquid line
s v vl w
saturated vapor vapor line wick
References 1. F. J. Stenger, NASA TM X-1310 (1966). 2. J. Ku. 1997 National Heat Transfer Conference, Baltimore, MD. Papcr AIAA 97-3870 (1997). 3. Y. Maidanik, Y. Fershtater, V. G. Pastukhov and M. Chernysheva, 23rd International Conference on Environmental Systems, Colorado Springs, CO. SAE Technical Paper Series 932305 (1993). 4. J. Ku, T. Hoang, T. Nguyen and S. Yun, 31st AIAA Thermophysics Conference, New Orleans, LA, Paper A1AA 96-1837 (1996). 5. J. Ku, E. I. Kroliczek. M. E. McCabe Jr., and S. M. Benner, AIAA Thermophysics, Plasmads~amics and Lasers Conference, San Antonio. TX, Papcr AIAA 88-2702 (1988). 6. T. O'Connell, T. Hoang and J. Ku, 30th AIAA Thcrmophysics Conference, San Diego, CA, Paper AIAA 95-2067 (1995). 7. J. Ku and T. Hoang, 1995 National Heat Transfcr Conference, Portland, OR, ASME HTD 307. 25 (1995). 8. K. R. Kolos and K. E. Herold. 1997 National Heat Transfer Conference, Baltimore, MD, Paper AIAA 97-3872 (1997). 9. R. B. Schweickart, L. Neiswanger and J. Ku, 22nd AIAA Thermophysics Conference, Honolulu. HI, Paper AIAA 87-1630 (1987). l 0. M. Furukawa. 31 st A1AA Thermophysics Conference, New Orleans, LA, Paper AIAA 96-1831 (1996). 11 J.M. Gottschlich and R. Richter, 1991 SAE Aerospace Atlantic, Da~on, OH, SAE Technical Paper 911188 (1991). 12. CR. Gane, A.J. Oliver, D.R. Soulsbv and P.L. Stcphenson. Numerwat Methods in Heat Tran.}'/br, 2_, p.227, John Wiley & Sons (1983). 13. Y. Maidanik, Y. Fershtater, V.G. Pastukhov, K. Goncharov, O. Zagar and Y. Golovanov, 22nd International Conference on Environmental Systems, Seattle, WA, SAE Technical Paper 921169 (1992). Received July 24, 1998