Compact Heat Rejection System Utilizing Integral Variable  Heat Pipe Radiator for Space Application

Designing the heat rejection system for the space vehicle is a very challenging task. Due to the variation of solar position, the environmental temperature can change nearly 300 K within a few hours (Stephan, 2009). In general, the radiator panel is usually sized to meet the heat rejection requirement at a high environmental temperature. In order to reject the same amount of heat when the environmental temperature drops significantly, the surface temperature of the radiator must decrease. As a result, the coolant inside the primary loop of system may freeze and cause a serious safety issue. To avoid this problem, it is necessary to develop a heat rejection system which can maintain a nearly constant radiator surface temperature under a high system turndown ratio, defined in Equation (1) as: $T_{R} \equiv \frac{Q_{max}}{Q_{min}}$ T_{R} \equiv \frac{Q_{\max }}{Q_{\min }}

In order to meet this requirement, the variable conductance technique is introduced in the present work. The most effective way is to adjust the effective radiative area according to the heat dissipation rate. One approach is to decrease the coolant fluid flow rate that passes through the radiator, which can be achieved by controlling several on/off valves actively (Miller et al., 2011). This technique can reject heat ranges from 1000 W to 6000 W. Dividing the flow path into many small diameter pipes confers a greater degree of system control. However, long, small diameter piping introduces high-pressure losses into the system. Additionally, the surface tension of the coolant and associated capillary back-pressure makes recharging small diameter piping difficult.

Another idea is to replace the coolant pipeline loop with tubular heat pipes. Stern and Anderson combine a series of titanium/water heat pipes with a high conductivity foam saddle and fin to build the heat pipe radiator (Anderson et al., 2009). Introducing a carefully measured quantity of non-condensable gas (NCG) into the heat pipe allows precise control of the active length of the condenser. These variable conductance heat pipes (VCHPs) can handle turn-down ratios of 5:1 or more. VCHPs also have the advantage of short recovery time after being frozen since the gas-loading prevents sublimation from the evaporator when the condenser is frozen. However, between circular heat pipes and the radiator panel, heat transfer still relies on conduction, which makes the temperature distribution non-uniform, reducing the rate of heat rejection.

Therefore, the integral variable conductance planar heat pipes (VCPHP) is proposed as a solution for the heat rejection requirements for future NASA exploration and discovery missions (Lee et al., 2014). This heat rejection technology operates efficiently and reliably across a wide range of thermal environments. The VCPHP is a planar heat pipe that acquires the excess thermal energy from the thermal control system and rejects it through its condenser at its outer radiating surface. The radiator contains a NCG that varies the active radiator surface, depending on the heating and cooling conditions. This study introduces a simple mathematical model that captures the flow and thermal characteristics of the VCPHP. Two supporting experiments are conducted to validate the model. Subsequently, the feasibility of a variable conductance planar heat pipe-radiator in a space environment is investigated by the model.

METHODS

Variable Conductance Planar Heat Pipe Radiator

Figure 1 shows the schematic of the proposed VCPHP. Heat generated inside of a space vehicle is collected at heat sources and transported to the rejection system through a single fluid loop. This heat is transferred to the VCPHP evaporator. This heat injection vaporizes a portion of the working fluid, which is then transported down the heat pipe by the induced pressure differential. At the condenser, heat is rejected to the environment by radiative cooling. To form a closed loop, the capillary force generated by a wick structure returns the liquid to the evaporator. The system must maintain a constant heat rejection rate as the environmental conditions vary. This condition is achieved by the NCG reservoir attached at the condenser end.

Schematic of compact heat rejection with variable conductance planar heat pipe (VCPHP) radiator.

The heat rejection rate is controlled by two factors: the temperature difference between the radiative surface and environment, and the active area of the radiator panel. Maintaining the surface temperature of the radiator panel as the environmental temperature drops requires the active area of the heat rejection to decrease. This environmental temperature drop causes the pressure of working fluid vapor to decrease. This drop in pressure causes an increase in the volume of the NCG, covering a larger portion of the condenser. In this way, the surface temperatures of the condenser and evaporator are maintained above the working fluid freezing point.

In addition to performance, weight is a key driver for the development of electronics and aerospace cooling systems (Rosenfeld and Zarembo, 2001). Polymeric materials offer lower density than those available with metals, and are a viable approach to decreasing system mass. One such commercially available product is the CoolPoly® E2 Thermally Conductive Liquid Crystalline Polymer (LCP), a thermally conducting injection molding resin based on a liquid crystalline matrix (Cool Polymers Inc., 2007). This material has high thermal conductivity and is comparatively lightweight. The properties of CoolPoly® E2 are listed in Table 1. Brass is also listed as a reference material due to its common use in thermal applications.

Table 1.

Properties of brass and CoolPoly® E2 Liquid Crystal Polymer.

	Brass	Liquid Crystal Polymer
Density (g/cm³)	8.7	1.6
Thermal conductivity	109	20
(W/mK)
Tensile Modulus (Gpa) 100	-125	24.3
Tensile Strength (Mpa)	200	80
Flexural Modulus (Gpa)	39	32.3
Flexural Strength (Mpa)	235	139

Mathematical Modeling

To support the development of experimental and practical heat pipes, a theoretical model to predict the steady-state thermal and hydrodynamic characteristics of VCPHPs is developed. In this model, the planar heat pipe is separated into three regions: the vapor chamber, capillary grooves, and solid wall. These regions are coupled by mass and heat transfer. The NCG and working vapor are both treated as ideal gases.

Heat transfer in the solid wall

In the solid wall, the two-dimensional heat conduction equation is applied in Equation (2): $\frac{\partial^{2} T_{s}}{\partial x^{2}} + \frac{\partial^{2} T_{s}}{\partial y^{2}} = 0$ \frac{\partial^{2} T_{s}}{\partial x^{2}}+\frac{\partial^{2} T_{s}}{\partial y^{2}}=0

Heat transfer model in groove-liquid region

Heat transfer in the liquid-groove region—which involves phase change within the mini groove—had been widely studied (Stephan and Busse, 1992; Do et al., 2008). At the evaporator section—where the heat is transferred from solid to liquid—the analytical solution based on the thin-film evaporator theory derived by Wang is applied to evaluate the total heat flux across the liquid-vapor interface (Wang et al., 2008), as shown in Equation (3): $q_{l v} = \frac{1}{N w} \sqrt{\frac{2 A_{c} h_{f g} h_{l v} (T_{s} - T_{v})}{v} \ln (\frac{k_{l}}{h_{l v} δ_{0}} + 1)}$ q_{l v}=\frac{1}{N w} \sqrt{\frac{2 A_{c} h_{f g} h_{l v}\left(T_{s}-T_{v}\right)}{v} \ln \left(\frac{k_{l}}{h_{l v} \delta_{0}}+1\right)}

where $\begin{aligned} δ_{0} = {[\frac{b}{a} \frac{A_{c}}{(T_{s} - T_{v})}]}^{1 / 3} \\ h_{l v} \approx h_{f g} [a - b \times \frac{σ}{r_{c}} \frac{1}{(T_{s} - T_{v})}] \\ a = (\frac{2 c}{2 - c}) \sqrt{\frac{M}{2 π R T_{v}}} (\frac{P_{v} M h_{f g}}{R T_{v}^{2}}) \\ b = (\frac{2 c}{2 - c}) \sqrt{\frac{M}{2 π R T_{v}}} (\frac{V_{l} P_{v}}{R T_{v}}) \end{aligned}$ \begin{aligned} &\delta_{0}=\left[\frac{b}{a} \frac{A_{c}}{\left(T_{s}-T_{v}\right)}\right]^{1 / 3} \\ &h_{l v} \approx h_{f g}\left[a-b \times \frac{\sigma}{r_{c}} \frac{1}{\left(T_{s}-T_{v}\right)}\right] \\ &a=\left(\frac{2 c}{2-c}\right) \sqrt{\frac{M}{2 \pi R T_{v}}}\left(\frac{P_{v} M h_{f g}}{R T_{v}^{2}}\right) \\ &b=\left(\frac{2 c}{2-c}\right) \sqrt{\frac{M}{2 \pi R T_{v}}}\left(\frac{V_{l} P_{v}}{R T_{v}}\right) \end{aligned}

From the conservation of energy at interface, the mass flux caused by phase change can be expressed as $m_{j} = \frac{q_{l v}}{h_{f g}}$ m_{j}=\frac{q_{l v}}{h_{f g}}

For the condenser portion, the parallel conduction model introduced by Dunn and Reay (1976) is used to obtain the effective thermal conductivity, as shown in Equation (5): $k_{w} = [1 - β (1 - \frac{k_{l}}{k_{s}})]$ k_{w}=\left[1-\beta\left(1-\frac{k_{l}}{k_{s}}\right)\right]

where $β = \frac{2 w}{2 w + f}$ \beta=\frac{2 w}{2 w+f}

Due to the wall conduction in the axial direction, the evaporating region will expand beyond the heated region specified by L_e. The evaporating region needs to be calculated iteratively; the same is true for the condenser length.

Capillary flow in liquid-grooves region

The liquid-flow driven by capillary pressure in the axial grooves can be treated as one-dimensional, incompressible, low Reynolds number flow. The corresponding continuity equation (Equation (6)) and momentum conservation equation (Equation (7)) are listed below: Equation (6) $ρ_{l} \frac{d (u_{l} A_{l})}{d x} + 2 m_{j} w_{r} = 0$ \rho_{l} \frac{d\left(u_{l} A_{l}\right)}{d x}+2 m_{j} w_{r}=0 Equation (7) $\frac{d P_{l}}{d x} = - \frac{2 μ_{l} u_{l} (f Re)}{D_{h, l}^{2}}$ \frac{d P_{l}}{d x}=-\frac{2 \mu_{l} u_{l}(f \operatorname{Re})}{D_{h, l}^{2}}

By assuming the vapor phase pressure drop along the axial direction is negligible, the liquid pressure drop should be balanced by capillary pressure, described by the Young-Laplace equation: $\frac{d P_{l}}{d x} = \frac{σ}{r_{c}^{2}} \frac{d r_{c}}{d x}$ \frac{d P_{l}}{d x}=\frac{\sigma}{r_{c}^{2}} \frac{d r_{c}}{d x}

Boundary conditions

For the solid wall, the boundary conditions are:

In the evaporator region (x ≤ L_e): $- k_{s} \frac{\partial T_{s}}{\partial y} |_{y = 0} = q_{i n}$ -\left.k_{s} \frac{\partial T_{s}}{\partial y}\right|_{y=0}=q_{i n}

At the condenser/radiator panel (x > L_e): $k_{s} \frac{\partial T_{s}}{\partial y} |_{y = 0} = ε σ_{r} (T_{surface}^{4} - T_{amb}^{4})$ \left.k_{s} \frac{\partial T_{s}}{\partial y}\right|_{y=0}=\varepsilon \sigma_{r}\left(T_{\text {surface }}^{4}-T_{\text {amb }}^{4}\right)

The liquid layer thickness can be determined from the radius of meniscus curvature if the groove geometry is specified.

For the liquid within the grooves: $u_{l} (0) = 0; r_{c} (0) = r_{0}$ u_{l}(0)=0; r_{c}(0)=r_{0}

Initial radius of curvature r₀ is selected carefully to satisfy the conservation of total fluid mass.

When the system reaches steady-state, heat input should be equal to the heat that radiates out to the space, which is: $Q_{out} = W ε σ_{r} \int_{L_{c}} (T_{surface}^{4} - T_{a n b}^{4}) d x$ Q_{\text {out }}=W \varepsilon \sigma_{r} \int_{L_{c}}\left(T_{\text {surface }}^{4}-T_{a n b}^{4}\right) d x

Non-condensable gas model

As mentioned above, the surface temperature of the heat pipe can be maintained by injecting NCG. The ideal gas model is used to analyze the behavior of the NCG and its effects. For the sake of simplicity, several assumptions have been made: (1) both the vapor and NCG ideal gases are distributed uniformly inside the reservoir and heat pipe, and (2) diffusion between the NCG and vapor is neglected, i.e., a sharp interface exists between the two gases.

The governing equation for the NCG is the ideal gas law: $P_{g} = \frac{m_{g} R_{g} T_{a m b}}{(V_{r} + L_{c, i} A_{v})}$ P_{g}=\frac{m_{g} R_{g} T_{a m b}}{\left(V_{r}+L_{c, i} A_{v}\right)}

The total pressure in the inactive portion of heat pipe is the summation of the partial pressure of NCG and working fluid vapor. When the system reaches steady-state, the total pressure should balance the saturation pressure in the active portion of the heat pipe, shown in Equation (11): $P_{v} (T_{v}) = P_{g} + P_{v} (T_{a m b})$ P_{v}\left(T_{v}\right)=P_{g}+P_{v}\left(T_{a m b}\right)

Here, the vapor temperature is determined by the Clausius-Clapeyron relationship. Because the inactive length and the pressure of vapor are related, it is necessary to calculate iteratively.

The governing equations are solved by the finite element method. A 100 element long by 10 element thick formulation is used for the solid wall. At each step of iteration, the thermodynamic properties are updated according to the new saturated vapor temperature. With the additional effect of NCG, the length of cooling section is no longer constant and should be evaluated by a pressure balance between the vapor phase and the NCG. The calculation procedure for steady-state heat pipe operation is summarized in Figure 2.

Steady-state planar heat pipe operation calculation flow chart.

Supporting Ground-Based Experimental Work

Design and manufacture of brass planar heat pipe and LCP heat pipe

Two planar heat pipes are designed, fabricated, and tested to validate the model and prove the concept. Brass is chosen for the initial prototype for its easy machinability, high-durability, and compatibility with a variety of working fluids. As shown in Figure 3, the brass heat pipe (BHP) is constructed with a sandwich structure suggested in literature. The BHP consists of three main parts: two plates containing a triangular groove structure and a spacer with taps for charging and fluid injection. The three pieces are joined with machine screws and sealed with a pair of soft silicone rubber gaskets (red portion). For the other experimental heat pipe, CoolPoly® E2 LCP plate is selected as the base material. This material is chosen to test lightweight materials in this application. The design of the LCP heat pipe is very similar to the BHP. It consists of two pieces of LCP plate, acrylic, and spacer. All pieces are fastened with bolts and sealed with rubber gaskets to ensure a vacuum. The overall dimensions and geometry for these two heat pipes are given in Table 2.

(A) Brass planar heat pipe. (B) Liquid Crystal Polymer heat pipe (LCP-HP).

Table 2.

Specifications of the two planar heat pipes.

	Brass Heat Pipe (BHP)	Liquid Crystal Polymer Heat Pipe (LCP-HP)
Length (cm)	27.94	5.08
Width (cm)	13.97	5.08
Thick (cm)	1.27	0.8334
Wall thickness (mm)	3.175	3.175
Grooves type	Triangular	Rectangular
Grooves dimensions
	72 grooves per plate	32 grooves per plate

Experimental set-up

Two test systems to evaluate the thermal performance of BHP and Liquid Crystalline Polymer-Heat Pipe (LCP-HP) are designed and constructed. Heat is provided by a fluid loop heated by a resistive heating element controlled by a variable DC power supply. Because of the difficulty of maintaining a low temperature radiative environment, both heat pipes are cooled convectively. The condenser section of BHP is placed into the FLOTEK 1440 wind tunnel. By varying the wind speed and heating voltage, a wide range of thermal conditions is studied. Wall temperature profile is measured using 10 T-type thermocouples attached to the solid plate.

For the LCP-HP experiment, the heat source consists of a 0-60 V DC power supply and two 0.5″×2″ (1.27 cm×5.08 cm) Kapton film heaters attached to both polymer plates. The condenser is cooled by forced convection with a constant wind speed of 3 m/s. The wall temperature is measured by T type thermocouples. Five thermocouples are attached to each polymer plate.

Both BHP and LCP-HP are carefully cleaned, evacuated, and charged with ethanol before testing. The fluid load is slightly lower than the volume of the grooves.

RESULTS AND DISCUSSION

Validation

First, although it is assumed the pressure drop in the vapor flow is negligible so the vapor pressure is nearly uniform everywhere, it must be justified since the vapor pressure of ethanol is relatively low (8.8 kPa at 300 K). The computed pressure distributions in the vapor and liquid for both BHP and LCP heat pipes are shown in Figure 4. The figure shows the pressure drops during heat pipe operation are due primarily to the friction generated by the liquid travel through the small grooves. The maximum capillary pressure drops for BHP and PHP are 40 Pa and 44 Pa, respectively, while the vapor pressure drops are both less than 1 Pa. It can be shown that even for the larger heat pipe (to be discussed later) the vapor pressure drop is on the same order. Therefore, the uniform vapor pressure assumption is justified.

Predicted vapor and liquid pressure drops of BHP and PHP during operation.

For the BHP experiment, various loads and wind speeds are applied. The heat transfer rate at the condenser is estimated by an empirical formula for boundary layer flow over flat plate.

Typical experimental wall temperature distributions and the predicted values by the developed model are plotted in Figure 5. The dots are the measured data and the solid lines are the predictions. The evaporator is indicated as a red shaded region. The data tend to scatter. However, in terms of temperature difference between the wall and ambient temperatures, the average difference between the data and prediction is about 7%. Therefore, we can conclude the data and prediction agree reasonably well.

BHP temperature distributions with different heat inputs.

In addition, to ensure that the heat pipe is functional, the measured temperature distribution of the empty heat pipe and the prediction are shown in Figure 6. Without the working fluid, the heat transfer is by conduction only. Consequently, the wall temperature varies monotonically. The overall temperature drop is about 33°C, compared to 15°C for the same power input when the heat pipe is working. Therefore, based on the comparisons of the temperature profile and the overall temperature drop, it can be concluded the heat pipe is indeed operating.

Temperature distribution of BHP dry-run test.

Similar agreement between the experimental data and predictions is found for the polymer heat pipe, as shown in Figure 7. For the polymer heat pipe, due to its smaller dimension, its thermal performance is poor. But the main objective of this experiment is to show that this polymer material can be used as a heat pipe material, which is demonstrated in the present work.

The index of thermal performance for the planar heat pipe can be characterized by the effective thermal resistance defined as: $R_{e f f} = \frac{T_{e} - T_{c}}{Q}$ R_{e f f}=\frac{T_{e}-T_{c}}{Q}

The corresponding effective thermal resistance for BHP and LCP-HP is 0.6 K/W and 2.5 K/W, respectively.

Feasibility of VCPHP-Radiator for Space Environment

The current computational model is applied to analyze the thermal behavior of VCPHP in a radiative cooling environment, such as space. The proposed VCPHP design is similar to the ground-based heat pipe design, but with a much larger cooling area to compensate for weaker radiation cooling. The proposed size of VCPHP is 1 m by 1 m. The liquid crystal wall thickness is 0.5 cm. On each LCP plate, 600 equilateral triangular grooves (1.154 mm size) are used to generate enough capillary pressure.

The active area of the condenser is designed to maintain the working fluid temperature above its freezing point. This can be done by attaching a NCG reservoir at the end of the planar heat pipe.

In Figure 8, the heat pipe radiator is required to reject 200 W heat load from the heat source. The heat from the heat source is transported by the coolant fluid—in this case, water—to a heat exchanger attached to the evaporator section of the VCPHP. For simplicity, the black surface of the LCP plate is assumed to have an emissivity approaching unity. In the simulation, nitrogen and ethanol are used as the NCG and working fluid, respectively. The reservoir volume is 3.6×10^-4 m³. The predicted wall temperature profiles of VCPHP at different sink temperatures are shown in Figure 8. The solid lines in Figure 8 represent the wall temperature profiles without the NCG, and the dash lines are for the VCPHP, with the NCG as the ambient temperature drops from 250 K to 50 K.

Wall temperature distributions of VCPHP under different sink temperature fields (Q=200 W).

Without the NCG, when the ambient temperature drops, the planar heat pipe radiator surface temperature (solid line) decreases as well. At the evaporator (indicated as red shade region), the wall temperature for T_amb=50 K cases are lower than the freezing point of the coolant (water) inside the heat exchanger. The heat exchanger and coolant loop will be frozen and the entire thermal control system may be damaged.

To avoid this problem, 5 g of nitrogen is injected into the planar heat pipe radiator. As the dash lines show, the radiator with NCG is now being divided into two regions: active and inactive. In the inactive portion, the vapor chamber is covered by the NCG and no phase change happens inside this region. The surface temperature is approximately equal to the sink temperature. The surface temperature of the active portion can be maintained above the freezing temperature of coolant liquid (~273 K for water). This result suggests that the proposed planar heat pipe radiator with a small amount of NCG can still operate normally in a relatively cold environment.

Figure 9 is the case in which the ambient temperature is fixed at 250 K and the heat load is varied. Since the present analysis does not include the cooling loop from the heat source, we impose the condition (somewhat arbitrary) in the present analysis that the evaporator temperature cannot go above 350 K for the heat rejection system to operate. This limit is reached when Q=500 W with the NCG. As Q is reduced, the evaporator temperature decreases. Eventually, the temperature of the liquid-vapor interface in the evaporator is reduced to below the saturation temperature and the heat pipe ceases to operate. We define Q corresponding to this limit as Q_min. The lower limit is 90 W with the NCG.

Wall temperature distributions of VCPHP with different heat loads (T_amb=250 K).

The ambient temperature is reduced to 50 K in Figure 10. The maximum Q is increased to 640 W (assuming the capillary limit is greater than this). The lower limit in Q is now given by the condition that the evaporator temperature cannot go below the coolant freezing temperature. The minimum Q is equal to 90 W.

Wall temperature distributions of VCPHP with different heat loads (T_amb=50 K).

The heat rejection system is sometimes required to damp relatively large amount of Q when T_amb is high, and relatively small amount of Q when T_amb is low. In order to quantify this capability, the turndown ratio is used. Based on Figure 9 and Figure 10, when T_amb is changed from 250 K to 50 K, Q_max (at 250 K) is 500 W and Q_min (at 50 K) is 90 W, so that the turndown ratio is Q_max/Q_min=5.6.

The turndown ratio is affected, among other factors, by the amount of NCG and the heating zone size. For example, it can be shown that if the amount of NCG is increased from 5 g to 6 g in Figure 9 and Figure 10, Q_max will decrease to 490 W, but Q_min will also decrease to 60 W so that the turndown ratio will become 8.2. Also, with increased heating zone, the condenser (radiator) area is reduced, which necessitates the condenser temperature to increase in order to radiate a given amount of Q. The increased condenser temperature also increases the heating zone temperature, which helps to decrease Q_min. For example, if the heating zone is tripled in Figure 9 and Figure 10, Q_max will slightly increase to 530 W, but Q_min will be reduced to 50 W, which will make Q_max/Q_min=10.6. Clearly conditions exist under which the turndown ratio is maximized. The optimization study is currently being performed.

CONCLUSIONS

The present work deals with an alternative design of heat rejection system for space application utilizing a planar heat pipe with NCG to replace the traditional radiator panel. A two-dimensional heat transfer model combined with thin-film evaporator analytical solution is introduced. Two bench-top planar heat pipes are designed, fabricated, and tested. The experimental data are shown to agree reasonably well with the predictions without the NCG. The numerical model is used to assess the feasibility of the present heat rejection system in a space environment. The results show the idea of using NCG to adjust the cooling area and maintain the normal operation of heat rejection system is feasible.

eISSN:: 2332-7774
Sprache:: Englisch

Zeitrahmen der Veröffentlichung:: 2 Hefte pro Jahr
Fachgebiete der Zeitschrift:: Biologie, andere, Materialwissenschaft, Physik

Zeitschrift RSS Feed

Compact Heat Rejection System Utilizing Integral Variable Conductance Planar Heat Pipe Radiator for Space Application

Article Category: Research Article

Online veröffentlicht: 01. Dez. 2015

Seitenbereich: 30 - 41

DOI: https://doi.org/10.2478/gsr-2015-0009

© 2015 Kuan-Lin Lee et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Figure 1.

Figure 2.

Figure 3.

Figure 4.

Figure 5.

Figure 6.

Figure 7.

Figure 8.

Figure 9.

Figure 10.