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Heat transfer of a capillary evaporator in a loop heat pipe was analyzed through 3D numerical simulations to study the effects of the thermal conductivity of the wick, the contact area between the casing and the wick, and the subcooling in the compensation chamber (CC) on the thermal performance of the evaporator. A pore network model with a distribution of pore radii was used to simulate liquid flow in the porous structure of the wick. To obtain high accuracy, fine meshes were used at the boundaries among the casing, the wick, and the grooves. Distributions of temperature, pressure, and mass flow rate were compared for polytetra-fluoroethylene (PTFE) and stainless steel wicks. The thermal conductivity of the wick and the contact area between the casing and the wick significantly impacted thermal performance of the evaporator heat-transfer coefficient and the heat leak to the CC. The 3D analysis provided highly accurate values for the heat leak; in some cases, the heat leaks of PTFE and stainless steel wicks showed little differences. In general, the heat flux is concentrated at the boundaries between the casing, the wick, and the grooves; therefore, thermal performance can be optimized by increasing the length of the boundary.

Loop heat pipes (LHPs) and capillary pumped loops (CPLs) have attracted attention as advanced thermal control devices of spacecrafts, electronic devices, etc. The LHP and CPL require no external power to drive working fluids because of the capillary pressure generated in a porous structure in the evaporator, and they have high heat-transfer capabilities because heat transport is associated with phase changes between liquid and vapor (

The thermal performance of these devises is significantly affected by the design of the evaporator, and several studies of heat and mass transfer in capillary evaporators have been reported [

A high-performance evaporator requires high-efficiency heat exchange between the casing of the heating surface and the vapor transferred to the condenser. In addition, heat leaks to the CC must be small because the saturated state in the CC controls the state of the LHP. Therefore, evaporator designs for thermal performance can be discussed in terms of the trade-off between the heat-transfer coefficient and heat leaks to the CC. This approach has been addressed in [

In this study, a 3D numerical model of an LHP evaporator with the wick fully saturated with liquid is developed. The purpose was to find a guide for a design that attains geometric optimization in terms of the capillary evaporator’s thermal performance. Focus has been provided on how the thermal performance of the evaporator is affected by the wick’s thermal conductivity, the contact area between the casing and the wick, and the subcooling in the CC. Note that, in this study, situations wherein the wick contains fluid in two-phase vapor-liquid states are not considered; those situations have been addressed elsewhere [

This section presents our numerical model for heat and mass transfer in the evaporator.

permeability. Using this simple model, the PNM can include more pores and calculate over a larger porous media than the lattice Boltzmann method. Energy conservation in other components of the LHP was excluded, allowing us to easily determine heat-transfer only in the evaporator.

The main assumptions used in the model were as follows: 1) grooves were filled with saturated vapor at constant temperature and pressure; 2) the bulk solid and fluid in the wick were in local thermal equilibrium; 3) the fluid was incompressible; 4) fluid properties were temperature dependent; 5) the liquid-vapor interface had no thickness; 6) the process was at steady state; and 7) the effects of gravity and thermal radiation were negligible.

In the PNM, mass flow rate

where,

where,

Energy conservation in the wick, including conduction and convection, can be written as

and heat conduction by the evaporator casing is given by

In Equations (4) and (5),

Liquid evaporate at the interface between the wick and the grooves, which is defined as

where

where ^{2}∙K used in [^{2}∙K used in a previous study [

In the PNM, characteristics of the porous structure can be established by setting dimensions for voids―the radius of each pore^{−14} m^{2}, respectively, is modeled. The mode and maximum pore radius were 1.2 and 2.1 μm, respectively. The throat radius was determined by using a log-normal probability density function to fit the pore radius distribution, which was measured by mercury porosimetry [

The method used to solve the above equations is shown by the flow chart in

An energy balance over the entire system can be written as

where,

The energy balance (Equation (10)) was satisfied with a maximum relative error of less than 1%.

Generally, a mesh size of

Calculations were performed for the eight conditions shown in

Calculation number | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
---|---|---|---|---|---|---|---|---|

Material of a wick | PTFE^{a} | PTFE | PTFE | SUS^{b} | SUS | SUS | PTFE | SUS |

Area of contact surface (%) | 75 | 50 | 25 | 75 | 50 | 25 | 50 | 50 |

Subcooling of the CC (˚C) | 0 | 0 | 0 | 0 | 0 | 0 | 5 | 5 |

^{a}Thermal conductivity is 0.25 W/m∙K. ^{b}SUS is stainless steel and the thermal conductivity is 16 W/m∙K.

gate how the thermal performance of the evaporator was affected by the thermal conductivity of wicks, contact area between wick and casing, and the subcooling of liquid in the CC. The effective thermal conductivities of the PTFE and stainless steel wicks completely filled with liquid were 0.22 and 10.6 W/m∙K, respectively. The contact area between the casing and the wick depends on the width of the grooves^{2}, the saturation temperature in the CC was 29.4˚C, and the thermal conductivity of the stainless steel casing was 16 W/m∙K. The working fluid was ethanol.

In

In

The evaporator heat-transfer coefficient

where

heat flux concentrates at the boundaries between the casing, the wick, and the grooves. Therefore, the evaporator heat-transfer coefficient is higher when the region of the boundary is larger. Therefore, the thermal performance of the evaporator can be optimized by changing the length of the boundary per unit area of contact surface. In this calculation, the lengths were 0.67, 1.0, and 2.0 mm on contact areas of 75%, 50%, and 25%, respectively. In [

Evaporator heat-transfer coefficients calculated with 5˚ of subcooling (calculations 7 and 8 in

The thermal performance of the evaporator in a loop heat pipe using 3D numerical simulations with a pore network model for situations wherein the wick was fully filled with liquid, has been investigated. In particular, how the evaporator’s performance responded to changes in the thermal conductivity of the wick, the contact area

Calculation number | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
---|---|---|---|---|---|---|---|---|

^{2}∙K) | 497 | 714 | 1300 | 5680 | 7400 | 10900 | 678 | 6810 |

91.2 | 92.9 | 93.8 | 93.5 | 93.8 | 93.8 | 87.8 | 85.0 | |

5.64 | 3.91 | 2.86 | 5.59 | 5.27 | 5.05 | 7.99 | 12.7 |

between the casing and the wick, and the subcooling of the CC has been studied. Three-dimensional color renderings of pressure and temperature distributions were presented as well as 2D distributions of mass flow rates. Mass flow rates in the PTFE wick were more sensitive to the temperature distribution than those in the stainless steel wick. The evaporator heat-transfer coefficient for the stainless steel wick was approximately 10 times higher than that for the PTFE wick. On both wicks, heat fluxes concentrated at the boundary among the casing, the wick, and the grooves, and the result of the PTFE wick has larger distribution. The computational results showed that the length of the boundary per unit contact area is an important parameter in geometric optimization of the evaporator with respect to thermal performance. In our 3D analyses, the heat leak to the CC was estimated with high accuracy, and some cases showed small differences in the heat leaks between the PTFE and stainless steel wicks. In addition, the calculated results showed a heat-pipe effect in which evaporation and condensation occurred at the groove-wick interface. This effect was larger for the PTFE wick, which had a larger temperature distribution.

This research was partially supported by a Grant-in-Aid for JSPS Fellows (No. 25148) and by JST, PRESTO. A super computer system in the Information Technology center of Nagoya University was used for the calculations. LM and MP gratefully thank CNES and Airbus Defence and Space for their financial support.