The Constrained Vapor Bubble Fin Heat Pipe in Microgravity

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The Constrained Vapor Bubble Fin Heat Pipe in Microgravity Arya Chatterjee,† Peter C. Wayner, Jr.,† Joel L. Plawsky,*,† David F. Chao,‡ Ronald J. Sicker,‡ Tibor Lorik,§ Louis Chestney,§ John Eustace,§ Raymond Margie,§ and John Zoldak§ †

Rensselaer Polytechnic Institute, Troy, New York, United States NASA Glenn Research Center, Cleveland, Ohio, United States § Zin Technologies, Cleveland, Ohio, United States ‡

ABSTRACT: The Constrained Vapor Bubble (CVB) is a wickless, grooved heat pipe and is the first, full-scale fluids experiment flown on the U.S. module of the International Space Station. The CVB promises to provide new insight into the operation of a heat pipe in space. It is a relatively simple device constructed from a spectrophotometer cuvette and uses pentane as the working fluid. The pentane flows within the corners of the cuvette due to a curvature gradient in the liquid menisci associated with the cuvette corners. The curvature of the liquid interface can be determined by viewing the meniscus through the transparent quartz walls. Extremely accurate temperature and pressure measurements were obtained in addition to the images. In the article, the results from the first two CVB modules—a dry calibration module and a wet heat pipe module—are presented. We show that the axial temperature profiles are significantly different in space. The heat pipes were seen to operate at a higher pressure and higher temperature in space primarily because radiation was the only heat loss mechanism. A fin model was developed to model the data, and Churchill’s correlations for natural convection were used to determine the external heat transfer coefficient. Inside evaporation and condensation heat transfer coefficients were regressed from the temperature data. We show that the heat transfer coefficient in microgravity was higher.

’ INTRODUCTION The influence of Stuart W. Churchill has been profound in the fields of chemical and mechanical engineering. One of the pioneers of convective heat transfer, correlations developed by Churchill and co-workers1 have found their way into all standard textbooks on transport phenomena and heat transfer. The author of more than 200 journal articles, Professor Churchill continues to publish new insights into all aspects of transport phenomena.2 His work continues to be relevant in fields as diverse as microelectronics, metal casting, and solar energy. Here, we present some recent results from a microgravity heat pipe experiment where one of his classic natural convection correlations was shown to be extremely useful in helping us analyze the system’s performance. Heat pipes are passive heat transfer devices that are commonly used to increase the effective conductivity of a material while keeping the overall weight low. They rely on phase change to transport heat and capillary pressure to transport mass. The Constrained Vapor Bubble experiment is an ideal wickless heat pipe. It consists of a quartz cuvette that is partially filled with a working fluid—pentane in this case. The pentane forms a pool at one end and flows within the four corners of the cuvette due to capillary action (see Figure 1). A thin film of liquid (of thickness ∼50 nm) adsorbs on the four flat faces of the cuvette, while the remaining volume of the cuvette is filled with pentane vapor. Thus, the central bubble volume is surrounded by liquid on all sides—the corners have a liquid meniscus while the flat faces have a thin adsorbed film. Since the bubble is effectively constrained by the walls of the cuvette, the experiment is named Constrained Vapor Bubble (CVB). r 2011 American Chemical Society

If one end of the cuvette is heated, pentane in contact with that surface evaporates. The pentane vapor is at a higher pressure than the vapor in contact with the cooler quartz surfaces at the opposite end of the system. Thus, vapor flows from the heater to the cooler section, gives up its latent heat of evaporation, and condenses. The liquid travels back to the heated end due to capillary action. Meanwhile, the menisci in the corners change shape to create the capillary pressure gradient needed to pump the liquid to the heated end. The maximum evaporation rate at any given axial location in the cuvette occurs at the contact line where liquid, vapor, and solid meet . Thus, once the liquid travels up the cuvette, it has to flow to the contact line region to evaporate. This makes the wickless heat pipe a multiscale problem where the bulk liquid flow in the corner meniscus is on a millimeter scale while the flow in the contact line is on a micrometer scale. Devices that are essentially a CVB have been studied by various researchers as micro heat pipes. Babin et al.3 performed experimental investigations of a trapezoidal microheat pipe and presented a model to determine the capillary limit of such a device. At the capillary limit, the capillary pressure gradient is no longer able to pump fluid along the entire axis of the heat pipe. When the capillary limit is reached, the region nearest the heater becomes dry. Ha and Peterson4 were able to obtain an analytical Special Issue: Churchill Issue Received: October 11, 2010 Accepted: February 2, 2011 Revised: February 1, 2011 Published: February 22, 2011 8917

dx.doi.org/10.1021/ie102072m | Ind. Eng. Chem. Res. 2011, 50, 8917–8926

Industrial & Engineering Chemistry Research expression for the prediction of this dryout point for a “V” shaped micro heat pipe groove as a function of the applied heat flux. Khrustalev and Faghri5 gave a detailed solution for the heat transfer in the evaporator and condenser and the axial fluid flow rate in the corners for a triangular micro heat pipe. Ma et al.6 and Peterson and Ma7 studied the effect of shear at the liquid-vapor interface on the flow in the corner meniscus. The CVB has been extensively investigated by Wayner and co-workers.8 Basu et al.8a examined the CVB in an evacuated chamber in the Earth’s gravity environment to isolate the effects of radiation from natural convection. Karthikeyan et al.8b,d studied the intermediate section of a horizontal CVB and calculated the effective thermal conductivity. They also modeled the fluid flow in the region and showed that the variation in radius of curvature obtained using interferometry agreed with their model. The CVB experiment represents the state of the art in heat pipe research. Highly instrumented and transparent, it allows one to determine temperatures with great accuracy while allowing

Figure 1. Constrained Vapor Bubble and liquid pool.

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one to observe the fluid flow inside. Three such heat pipes of lengths 20, 30, and 40 mm were built along with a dry unit that served as the control. These were operated on Earth and then launched into space and operated in the microgravity environment of the International Space Station. Here, we present some of the initial results from these experiments. The temperature profiles provide significant insight into the functioning of the heat pipe in space. A fin model was used to analyze the data, and an internal heat transfer coefficient was calculated for the heat pipe. Prof. Churchill’s correlations proved useful in calculating the natural convection heat transfer coefficients.

’ EXPERIMENTAL APPARATUS Space Station Hardware. The Constrained Vapor Bubble experiment is the first experiment in the Fluids Integrated Rack (FIR) on the International Space Station (ISS). The International Standard Payload Rack is a standard architecture on which the FIR is mounted, and it provides the mechanical and electrical connections to the Destiny module of the ISS. Launched on STS 128, August 28, 2009, the FIR contains the Light Microscopy Module (LMM), which is a completely automated optical microscope (Figure 2) that can be controlled from Earth. The FIR houses three main computers—the FSAP (Fluid Science Avionics Package), the IPSU (Image Processing and Storage Unit), and the IOP (Input Output Unit). They can communicate with each other, and together they can perform the experiment and collect and store the scientific data. Since crew time on the space station is very limited, a decision was made early in the planning to automate the experiment. The CVB was constructed as a module (as shown in Figure 4) that can be inserted into the LMM by the astronaut (Figure 3). Details of the experimental setup are given in ref 9 and will not be repeated here; a brief description is given for continuity. The cuvette is 5.5 5.5 mm on the outside and 3 3 mm on the inside; thus the quartz wall is 1.25-mm-thick. There are four modules—one dry and three with different sized vapor bubbles. The bubble sizes are approximately 20, 30, and 40 mm. The cuvette is closed at one end, and on this end a heater is attached. The other end is connected to an assembly that is used to fill the cuvette and also houses a pressure transducer. The connection

Figure 2. Insertion of the Constrained Vapor Bubble (CVB) experiment into the Light Microscopy Module (LMM), which in turn goes inside the Fluids Integrated Rack (FIR), which will be one of the science experiment racks in the International Space Station. 8918

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Industrial & Engineering Chemistry Research

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surface of the cuvette. Wells (0.45 mm deep) were drilled into the quartz surface, and the thermocouple junction was embedded in these using thermal paste. The locations of the thermocouples are shown in Figure 5. The thermocouples have a very high spatial resolution and, during the data acquisition phase, a very high temporal resolution as well. The high accuracy of the data allows us to determine the spatial temperature gradient. The thermocouples have a stated accuracy of (0.5 C. During the initial transient phase, readings are recorded every 1 min, while during data acquisition mode readings come at 2.40 s intervals. The pressure transducer data are collected at the same time intervals as the thermocouple data. The pressure transducer has a range of 5.4-48 psi with an accuracy of 0.1 psi. Along with this data, some additional information such as the electrical power input to the heater, the power supplied to the thermoelectric coolers, etc. are also recorded. Figure 3. NASA astronaut T. J. Creamer installing the 30 mm CVB Module into the Light Microscopy Module on the Fluids Integrated Rack of the International Space Station.

Figure 4. CVB module showing various components. It was designed for easy insertion into the LMM.

between the cuvette and the T-section is made via an invar insert that has the same thermal expansion coefficient as quartz. The insert is attached to a cooler that keeps that end at a constant temperature. The insert has small holes drilled through it to enable a continuous liquid phase to allow for the pressure measurement. As indicated above, there is a macroscopic experimental run (10) called the “Engineering Run” and a microscopic experiment (50) called the “Science Run”. In this paper, calibration data will be presented from the dry module in the Earth’s gravity and in a microgravity environment. The dry module test matrix is summarized in Table 1. This will be used to compare the effectiveness of a wickless heat pipe in the two environments using the 30 mm wet module temperature and pressure data; the details of the 30 mm module runs are given in Table 2. Image data that were also captured for determining the fluid flow characteristics in the corner meniscus will not be presented in this initial study. The 20 and 40 mm modules have also been successfully operated on Earth and in the space environment, and the results will be presented in a future publication. Temperature and Pressure Measurement. The temperature was measured using thermocouples attached to the outside

’ EXPERIMENTAL PROCEDURE The experiment proceeded in two phases. During the initial phase, the cooler and heater were turned off, and the system was allowed to come to an isothermal condition. It was assumed that equilibrium was attained, and temperature and pressure readings were collected. Next, the cooler was set to the prescribed temperature, and the heater was set to the various input heater powers. After an initial transient, the system reached the steady state. The steady state was reached when three of the temperature readings and the pressure reading were no longer fluctuating. Again, the data acquisition mode was changed from “transient mode” to “experiment mode”, and the image, temperature, and pressure data were acquired. The temperature data were averaged over the last 20 readings to remove noise. A maximum of a 0.3% standard deviation was shown by the temperature data over this period. This data was used for the calculations that follow. The experiments were repeated by going up in heater power (0 to 2 W) and then by going down (2 to 0 W). We observed that the difference between the readings at all thermocouple locations was less than 1 C, which is less than 5% of the measured temperature and close to the accuracy of the thermocouple. Similarly, the pressure reading was also found to be repeatable, and so there was no hysteresis in the operation of the heat pipe. Dry Module on Earth. The temperature profiles for the dry module at various heater inputs in the Earth’s gravity environment are shown in Figure 6a. The temperature profile was made dimensionless using θ¼

T - T¥ Tb - T¥

ð1Þ

Here, T¥ is the ambient temperature, while Tb is the temperature at the base of the CVB, attached to the heater (since the temperature at the fin heater junction is not known, the temperature of the first thermocouple has been used). The length scale, x, is normalized with the overall length of the cuvette, L, X ¼

x L

ð2Þ

The corresponding dimensionless temperature profile is plotted in Figure 6b. As apparent from the plots, most of the data collapse 8919



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Table 1. Dry CVB Module Runs type of run engineering run

details isothermal run cooler: off heater: off image data: none 1g

non-isothermal run cooler: 15 C

heater: 0 to 2 W in 0.1 W increments

image data: one μg

non-isothermal run cooler: 20.5 C

heater: 0 to 4 W in 0.1 W increments

image data: none

Table 2. Wet CVB Heat Pipe Runs type of run engineering run (10 data)

details isothermal run cooler: off heater: off image data: 3 at each axial locationa with axial locations such that the entire inside surface is captured 1g


heater: 0.2, 0.4, 0.6, 0.8, 0.2, 1.6, 2.0 W

image data: same as isothermal μg


heater: 0.2, 0.4, 0.6, 0.8, 1.2, 1.6, 2.0, 2.2, 2.4 2.6, 2.8, 3.0, 3.12 W

image data: same as isothermal science run (50 data)

isothermal run cooler: off heater: off image data: 6 at each axial locationb with the same axial locations as used in the engineering run 1g

cooler: 15 C

heater: 0.2, 0.4, 0.6, 0.8, 1.2, 1.6, 2.0 W

image data: same as isothermal μg


heater: 0.2, 0.4, 0.6, 0.8, 1.2, 1.6, 2.0 W

image data: same as isothermal a Three images required at 10 magnification with sufficient overlap between consecutive images to allow the stitching algorithm to work. b Six images required at 50 magnification with sufficient overlap between consecutive images to allow the stitching algorithm to work.

Figure 5. Thermocouple arrangement on the 30 mm module of the CVB experiment. The thermocouples are embedded into the wells drilled into the surface of the cuvette. 8920



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Figure 6. Temperature profile for the Dry Module in Earth’s gravity environment plotted for various heater powers in Celsius (a) and in dimensionless units (b). The dimensionless profiles are self-similar. The cooler was set to below ambient, such that for certain small heater power inputs, sections of the heat pipe exhibit a negative dimensionless temperature. The legend for a applies to b as well. The error in the measurements is less than the width of the line.

to self-similar profiles. The cooler was set at 15 C, and for certain low heater power inputs, the dimensionless temperatures at the cooler end were negative. This indicates that some heat was flowing into the system from the surroundings, at least for part of the fin. Dry Module in Space. The temperature profiles for the dry module in the microgravity environment are shown in Figure 7a and b. Again, self-similarity is evident in the dimensionless plot in Figure 7b. The cooler end temperature was set to ambient for this run. Thus, there are no negative dimensionless temperature locations, and θ is zero at X = 1 for all cases Wet Module on Earth. Figure 8a shows the temperature profiles of the 30 mm module in the Earth’s gravity environment as a function of heater input power. The cuvette was oriented vertically, with gravity acting along a line oriented from the heater end to the cooler end (see Figure 1). The squares in Figure 8a denote the temperature of the vapor phase as determined from the pressure measurement. The pressure transducer measures the pressure of the vapor phase pentane present in the bubble. The temperature of the vapor can be determined using the inverse form of the Antoine equation: Tv ¼

B -C A - log10 ðPv Þ

ð3Þ

Here, A, B, and C are the Antoine constants given in Table 3, and Pv is the vapor pressure of the liquid, in bars, at temperature T (in K). The location where the surface temperature coincides with Tv represents the transition between the evaporator and

Figure 7. Temperature profile for the Dry Module in a microgravity environment plotted for various heater power inputs in Celsius (a) and in dimensionless units (b). The dimensionless profiles highlight the selfsimilar behavior. The legend for a applies to b as well. The error in measurement is less than the width of the line.

condenser regions of the heat pipe. The vapor phase can be considered to be relatively homogeneous, and the vapor temperature and pressure vary only slightly along the axis of the cuvette. In the evaporator region, the surface temperature of the quartz is greater than that of the vapor, leading to evaporation of the pentane, while the quartz is cooler than the vapor phase in the condenser, where the pentane condenses from the vapor phase. The liquid pool at the cooler end forms at the location of the last three thermocouples; thus, the condenser region ends at the beginning of the liquid pool. Figure 8b shows the dimensionless temperature profile. At the lowest heater power inputs, the dimensionless temperature can become negative, similar to the dry module; at higher heater powers, self-similar profiles are obtained. Wet Module in Space. Figure 9a shows the temperature of the same 30 mm cuvette in the microgravity environment of the International Space Station. A noticeable difference is the presence of the flat region in the central portion of the heat pipe. The filled squares, as in the case of the wet module in the Earth’s gravity, denote the location of the vapor phase temperature. The location of the beginning of the condenser has shifted nearer to the heater end as compared to that on Earth. This indicates that the temperature of the vapor phase is now higher, and if the vapor temperature is assumed to be the overall operating temperature of the CVB heat pipe, the heat pipe is operating at a higher temperature. The dimensionless profiles in Figure 9b are not selfsimilar using the same scaling as in the earlier cases. In fact, for the lower heater powers, the shape is different from profiles at the higher heater powers. This is due to the relatively large variation of the inside heat transfer coefficient and will be explained in the following sections. 8921



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Figure 8. Temperature profile for the Wet Module (30 mm) in Earth’s gravity environment plotted for various heater powers in Celsius (a) and in dimensionless form (b). The filled squares denote the location of the vapor phase temperature in the cuvette. The region to the left of the filled squares is the evaporator, while the condenser region is to the right. The legend for a applies to b as well. The error in measurement is less than the width of the line.

Figure 9. Temperature profile for the Wet Module in a microgravity environment plotted for various heater powers in Celsius (a) and in dimensionless units (b). The filled squares denote the beginning of the condenser region by indicating the vapor phase temperature location in the cuvette. The legend for a applies to b as well. The error in measurement is less than the width of the line.

Table 3. Antoine Coefficients for Pentane Antoine equation coefficients

validity range

material

A

B

C

Tmin, K

Tmax, K

pentane

3.9892

1070.617

-40.454

268.7

341.37

’ RESULTS AND DISCUSSION Fin Model. The Constrained Vapor Bubble heat pipe is a fin heat exchanger and, as such, is similar in operation to a conventional fin.10 A fin or extended surface increases the surface area for heat loss to the surroundings, thus cooling the substrate onto which it is mounted. The Dry Module is thus a conventional fin and can be used to calibrate the system and to determine the external heat transfer coefficient. Figure 10 shows the schematic of the CVB. The heat transferred to the cuvette, Qin, is conducted away by the solid quartz walls. In the evaporator section, this heat is dissipated by radiation and natural convection to the outside. On the inside, the pentane evaporates, and this can be described using an inside evaporation heat transfer coefficient. In the condenser region, the pentane condenses from the vapor phase into the liquid phase, and this can be lumped into a condensation heat transfer coefficient. It is assumed that there is only conduction through the quartz. Any other internal heat transfer effects (e.g., radiation between surfaces) are neglected. Dry Module in Microgravity. The simplest case of the fin model is the dry module in microgravity. Since there is no

Figure 10. Schematic showing the fin model of the CVB heat pipe. The evaporator section temperature is above the temperature of the vapor phase in the bubble, while the temperature of the condensation region is below. The ambient temperature is preferably at the temperature of the cooler end. Heat is lost due to convection and radiation, and some heat is conducted away.

gravity, there is no natural convection, and all of the heat loss is through radiation to the surroundings. Thus, the fin equation 8922



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is given by d2 T ¼ dx2

1 1 Po σεðT 4 - T¥4 Þ Ac k

ð4Þ

Here, T is the temperature in Kelvin, T¥ is the ambient temperature, k is the thermal conductivity of the fin, Ac is the cross-sectional area of the fin, Po is the perimeter, and x is the axial location. Also, ε is the emissivity of quartz, and σ is the Stephan-Boltzmann constant. The usual boundary conditions for a fin attached to a heat source are at the heater end: dT ¼ qin ð5Þ -k dx x¼0

Figure 11. Comparison of the dimensionless temperature profiles at a heater input of 0.2 and 3.75 W for the Dry Module in microgravity with the fin model, with radiation as the sole heat loss mechanism.

at the cold end Tjx ¼ L ¼ Tc

ð6Þ

where qin is the heat flux into the cuvette and Tc is the temperature at the cooler. The heater for the CVB heat pipe is constructed from a Kanthal A-1 wire wrapped around an alumina base. The whole assembly is supported by a thin titanium holder contained in Super Firetemp insulation. Due to geometrical constraints in the microscope, the insulation is thinner than required, and considerable heat is lost from the heater surface to the surroundings. Thus, all of the heat supplied to the heater cannot be assumed to be going into the cuvette. In fact, the temperature gradient at the end attached to the heater (dT/dx|x=0) can be used to calculate the fraction of the heat entering the cuvette. This was determined to be close to 35%, indicating that 65% of the input power was lost as heat to the surroundings. When a finite element model is used for the simpler case of the dry cuvette in space, where convection is absent, this value is corroborated. These results indicate that in the boundary condition given in eq 5, qin is an unknown, and instead a temperature boundary condition is required, as given by Tjx ¼ 0 ¼ Tb

Figure 12. Natural convection Nusselt number for the Dry Module in Earth’s gravity environment calculated using the correlation obtained by Churchill as a function of the heater power input to the heater.

Nu ¼ 0:68 þ "

where hout,1g is the outside heat transfer coefficient given by the following expression for Nusselt number for natural convection near a flat plate developed by Churchill and Chu1c

ð9Þ

where Ra is the Rayleigh number

ð7Þ

where, Tb is the temperature at the base (here assumed to be the first thermocouple). Equation 4 is a second-order, nonlinear ordinary differential equation that can now be solved in a finite element method package. Since quartz is opaque to infrared radiation at the temperatures dealt with here, the emissivity is assumed to be unity. This gives very good comparison with the model, as shown in Figure 11. Dry Module in Earth’s Gravity. The dry module was also operated in the Earth’s gravity. Here, there are two heat loss mechanisms to the surroundings—convection and radiation. Thus, the fin equation for the dry module operated on Earth is d2 T 1 1 4 4 P ¼ ð8Þ o ½σεðT - T¥ Þ þ hout, 1g ðT - T¥ Þ dx2 Ac k

0:670Ra1=4 #4=9 0:492 9=16 1þ Pr

Ra ¼ GrPr ¼

gβ ðTs - T¥ ÞL3 νR

ð10Þ

Gr is the Grashof number Gr ¼

gβðTs - T¥ ÞL3 ν2

and Pr is the Prandlt number for air cp μ ν Pr ¼ ¼ R k

ð11Þ

ð12Þ

Here, R is the thermal diffusivity, β is the thermal expansion coefficient, μ and ν are the dynamic and kinematic viscosities, and k is thermal conductivity, all for air. Ts is the temperature of the substrate and, in this case, was taken as the average temperature of the quartz. The Nusselt number, Nu, calculated using this correlation for various heater power inputs is shown in Figure 12. It can then be used to obtain hout,1g, the external heat transfer coefficient. Equation 8 was solved, and Figure 13 shows the comparison between the experimental and model predicted values. Since there is very good agreement, the external heat 8923



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Figure 13. Comparison between the experiments and the predicted dimensionless temperature profiles at a heater input of 0.4 and 2.00 W for the Dry Module on Earth. The external natural convection heat transfer coefficient obtained fits the data very well.

Figure 14. Comparison between the experiments and the predicted dimensionless temperature profiles for the Wet Module on Earth. For the external heat transfer coefficient, the correlation was used while the inside heat transfer coefficients were calculated.

transfer coefficient obtained from the correlation is valid. There were no adjustable parameters in this model, so the agreement is a testament to how well Prof. Churchill’s correlation performs in practice. Wet Module in Earth’s Gravity. The wet module in Earth’s gravity is the most complicated since it has three heat loss mechanisms. There is radiation and convective heat transfer on the outside and heat loss due to evaporation on the inside, or in the condenser region, condensation. Thus, the fin equation becomes d2 T ¼ dx2

1 1 1 1 Po ½σεðT 4 - T¥4 Þ þ hout, 1g ðT - T¥ Þ þ Pi hin, 1g ðT - Tv Þ Ac k Ac k

hin, 1g ¼ hinE, 1g 0 < x < LE hin, 1g ¼ hinC, 1g LE < x < LC

ð13Þ where hin,1g is the effective inside heat transfer coefficient in 1g. The outside heat transfer coefficient is determined using the correlation given in eq 9. This fixes hout,1g, leaving hin,1g to be determined by the optimization procedure. Note that the evaporative (condensation) inside heat transfer coefficient is a constant in the evaporator (condenser) section and does not vary with axial location. Also, it is an overall heat transfer coefficient and assumed to be acting over the entire inside perimeter of the cuvette. In reality, most of the evaporation occurs at the contact line region, and no evaporation occurs from the adsorbed film region. This analysis averages the local values in the corner menisci over the entire perimeter. The dimensionless temperature profiles from the model are compared with the experimental values in Figure 14. The optimized values of the heat transfer coefficient are shown in Figure 16. Wet Module in Microgravity. In microgravity, there are distinct evaporation and condensation zones, as indicated earlier. Since the outside heat loss is entirely due to radiation, the fin equation can be rewritten as d2 T 1 1 1 1 4 4 Po σεðT - T¥ Þ þ Pi hin, μg ðT - Tv Þ ¼ dx2 Ac k Ac k hin, μg ¼ hinE, μg 0 < x < LE hin, μg ¼ hinC, μg LE < x < LC ð14Þ where Pi is the inside perimeter and Tv is the temperature of the vapor phase. hin,1g is the effective inside heat transfer coefficient,

Figure 15. Comparison between the experiments and the predicted dimensionless temperature profiles for the Wet Module in microgravity. The inside heat transfer coefficients for the evaporation and condensation regions were determined.

Figure 16. Overall inside evaporative and condensation heat transfer in the Earth’s gravity and microgravity environment for the wet module. The microgravity heat transfer coefficients are much higher. Error bars show 95% confidence intervals. They appear to be asymmetric due to the logarithmic scaling.

which is different in the evaporator section (0 < x < LE) and the condenser section (LE < x < LC). Equation 14 was solved, and an optimization procedure was used to determine the values of the inside heat transfer coefficients hinE,μg and hinC,μg. The optimization seeks to minimize the error between the measured and model predicted values in the least-squares sense. The dimensionless temperature profiles for the optimized values of the 8924



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Figure 17. The percent of heat supplied to the heater entering the heat pipe. The rest has to be dissipated from the heater by other means. The wet heat pipe in microgravity is most efficient in drawing heat from the heater, while the dry in microgravity is the worst.

inside heat transfer coefficients are compared with the experimental values in Figure 15. Heat Transfer Coefficients. The effective inside heat transfer coefficients are compared in Figure 16. Both the inside heat transfer coefficients, in the evaporator and condenser regions, are an order of magnitude higher in microgravity than on Earth. The heat pipe works by capillary action, and on Earth, gravity acts to reduce the flow of the liquid to the heater. Specifically, the Bond number Bo = ((Flgh2)/σ) on Earth is ∼0.1, while in microgravity, it is 1 10-7. Thus, an increase in performance is expected in microgravity, accounting for the higher heat transfer coefficient. Since the corner meniscus is much thicker in microgravity, the resistance to fluid flow is much lower, increasing the overall heat transfer. While this trend was expected, the details were impossible to predict without experimental data, and hence, the current data constitutes the first results from a grooved heat pipe operated in microgravity. Heat Balance. Figure 10 showed a schematic of the CVB Fin heat exchanger. Qin is the heat coming into the device from the heater, while Qout is the heat conducted out from the cooler end as a consequence of imposing the temperature boundary condition. Heat is lost from the outside surface by convection (Qconv) and radiation (Qrad). Depending on the ambient temperature, most of the heat pipe will lose heat to the surroundings. As pointed out earlier, radiation is always present, whereas convection is restricted to the Earth’s gravity environment. In the dry module, there are no other heat loss mechanisms; however, in the wet modules, heat is lost due to evaporation (Qevap) in the evaporator section. The liquid evaporated then gives up its latent heat in the condenser section. Thus, from the point of view of the quartz substrate, it loses heat in the evaporator region, while it gains heat (Qcond) from the vapor in the condenser region. The total heat lost due to radiation and natural convection can be calculated by integrating over the length of the device. Similarly, the total evaporative and condensation heat losses can also be calculated. The percentage of the heat applied to the heater going into the fin is shown in Figure 17. Less than 50% of the heat enters the fin, and the remainder is dissipated by radiation and convection (when natural convection is available as a heat loss mechanism). Since the wet fin in microgravity is able to “extract” the most amount of heat out of the heater, it can be said to be the most effective, while the dry fin in microgravity fares the worst. The importance of various heat loss mechanisms is also compared

Figure 18. The relative importance of various heat loss mechanisms for the heat entering the fin for the dry fin (a) in microgravity and (b) on earth. A huge portion of the heat is lost due to radiation.

Figure 19. Comparison of the heat loss mechanisms for the wet fin (a) in microgravity and (b) on earth. Qcond is negative since heat is entering the quartz. Radiation, again, is a dominant heat loss mechanism.

in Figure 18 for the dry fins and in Figure 19 for the wet fins. In the case of the dry fin in microgravity, Figure 18a, the dominant heat loss is through radiation, and very little is conducted away. Even in the Earth’s gravity environment, as shown in Figure 18b, radiation is comparable to natural convection as a heat loss mechanism. In the case of the wet fins, the condensation heat loss is negative, since heat enters the quartz as the pentane condenses. Interestingly, a large portion of the heat is conducted away in the case of the wet fin in microgravity, a fact borne out by the larger load put on the thermoelectric coolers (data not shown here).

’ CONCLUSION The CVB heat pipe was successfully tested on Earth and on the ISS. Two sets of data were obtained—the data from the dry 8925


Industrial & Engineering Chemistry Research module, which was used for calibration, and the data from the wet module, which was used to study the effect of the liquid. The pressure of the vapor phase was used to calculate the vapor temperature and identify the evaporator and condenser regions of a heat pipe. The temperature profile observed in the space environment varied greatly from the earth’s gravity profile. There was a flat isothermal region that is absent on Earth. A fin model was used to calculate the theoretical temperature profile of the dry module in space given radiative heat loss only. This compared well with the measured profile. Prof. Churchill’s correlation was used to calculate the heat transfer coefficient due to natural convection from the outside for the dry module operated on Earth. The experimental temperature profile compared well with the model. The effective heat transfer coefficient from the inside surface of the wet module for the evaporator and condenser regions in microgravity and on Earth were calculated using the fin model. The effective inside heat transfer coefficients in the space environment were found to be much higher than those on Earth due to higher capillary pumping. Some significant new observations were made from the space experiments. It was impossible to completely dry out the wet module in microgravity. While the image data is still being analyzed, initial results indicate that the heater end of the cuvette accumulated liquid, which could be a result of the Marangoni effect due to the presence of trace quantities of a second fluid. This may be the reason for the observed drop in evaporative heat transfer coefficient after an initial increase. It suggests that a different design, for instance a loop heat pipe, might be more suitable for space applications. Also, the effect of radiation dominated the observations. While this was anticipated, the magnitude and importance of it had been underestimated. While a much more detailed understanding is expected to come out of the image data, the current study underlines the importance of using only the temperature and pressure data to draw insightful conclusions.

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convection from gases and liquids to a circular cylinder in crossflow J. Heat Transfer 1977, 99, 300. (c) Churchill, S.; Chu, H. Correlating equations for laminar and turbulent free convection from a vertical plate. Int. J. Heat Mass Transfer 1975, 18 (11), 1323–1329. (2) Churchill, S. An analogy between reaction and heat transfer. AIChE J. 2006, 52 (11), 3645–3657. (3) Babin, B. R.; Peterson, G. P.; Wu, D. Steady-state modeling and testing of a micro heat pipe. J. Heat Transfer 1990, 112, 595–601. (4) Ha, J. M.; Peterson, G. P. Analytical prediction of the axial dryout point for evaporating liquids in triangular microgrooves. J.Heat Transfer 1994, 116 (2), 498–503. (5) Khrustalev, D.; Faghri, A. Thermal analysis of a micro heat pipe. J. Heat Transfer 1994, 116 (1), 189–198. (6) Ma, H. B.; Peterson, G. P.; Lu, X. The influence of vapor-liquid interactions on the liquid pressure drop in triangular microgrooves. Int. J. Heat Mass Transfer 1994, 37, 2211–2219. (7) Peterson, G. P.; Ma, H. B. Theoretical analysis of the maximum heat transport in triangular grooves: A study of idealized micro heat pipes. J. Heat Transfer 1996, 118 (3), 731–739. (8) (a) Basu, S.; Plawsky, J. L.; Wayner, P. C. Experimental Study of a Constrained Vapor Bubble Fin Heat Exchanger in the Absence of External Natural Convection. Ann. N.Y. Acad. Sci. 2004, 1027 (1), 317–329. (b) Karthikeyan, M.; Huang, J.; Plawsky, J.; Wayner, P., Jr. Experimental study and modeling of the intermediate section of the nonisothermal constrained vapor bubble. J. Heat Transfer 1998, 120, 166. (c) Huang, J.; Karthikeyan, M.; Plawsky, J.; Wayner, P. Constrained Vapor Bubble 1998, 155–160.(d) Karthikeyan, M.; Huang, J.; Plawsky, J.; Wayner, P. In Non-Isothermal Experimental Study of the Constrained Vapor Bubble Thermosyphon; NASA: Washington, DC, 1996. (9) Chatterjee, A.; Plawsky, J.; Wayner, P.; Chao, D.; Sicker, R.; Lorik, T.; Chestney, L.; Eustace, J.; Zoldak, J., Constrained Vapor Bubble Experiment for International Space Station: Earth’s Gravity Results. J. Thermophys. Heat Transfer 2010, 24 (2). (10) Bowman, W.; Moss, T.; Maynes, D.; Paulson, K. Efficiency of a constant-area, adiabatic tip, heat pipe fin. J. Thermophys. Heat Transfer 2000, 14 (1), 112–115.

’ AUTHOR INFORMATION Corresponding Author

*Phone: (518) 276-6049. E-mail: [email protected].

’ ACKNOWLEDGMENT The authors wish to acknowledge NASA astronaut T. J. Creamer for contributing his time voluntarily for this project. We also acknowledge the people from ZIN Technologies for their efforts in the design, construction, and operation of the experiment. NASA’s Glenn Research Center provided engineering and science support for this project through many years at NASA. We also would like to acknowledge the Lead Increment Scientist for increment 23-24, for giving us extra crew and operations time. This material is based on work supported by the National Aeronautics and Space Administration under Grant No. NNX09AL98G. Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the authors and do not necessarily reflect the view of NASA. ’ REFERENCES (1) (a) Churchill, S. A comprehensive correlating equation for laminar, assisting, forced and free convection. AIChE J. 1977, 23 (1), 10–16. (b) Churchill, S.; Bernstein, M. A correlating equation for forced 8926


The Constrained Vapor Bubble Fin Heat Pipe in Microgravity

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