"HPTAM", a two-dimensional Heat Pipe Transient Analysis Model, including the startup from a frozen state (original) (raw)

1996, Thesis (Ph. D.) - University of New Mexico, Chemical and Nuclear Engineering Department, 1996.

Heat pipes are highly reliable and efficient energy transport devices, which are being considered for many terrestrial and space power thermal-management applications, such as high-performance aeronautics and space nuclear and solar dynamic power systems. In this work, a two-dimensional Heat Pipe Transient Analysis Model, "HPTAM", was developed to simulate the transient operation of fully-thawed heat pipes and the startup of heat pipes from a frozen state. The model incorporates: (a) sublimation and resolidification of working fluid; (b) melting and freezing of the working fluid in the porous wick; (c) evaporation of thawed working fluid and condensation as a thin liquid film on a frozen substrate; (d) free-molecule, transition and continuum vapor flow regimes, using the Dusty Gas Model; (e) liquid flow and heat transfer in the porous wick; and (f) thermal and hydrodynamic couplings of phases at their respective interfaces. HPTAM predicts the radius of curvature of the liquid meniscus at the liquid-vapor interface and the radial location of the working fluid level (liquid or solid) in the wick. It also includes the transverse momentum jump condition (capillary relationship of Pascal) at the liquid-vapor interface and geometrically relates the radius of curvature of the liquid meniscus to the volume fraction of vapor in the wick. The present model predicts the capillary limit and partial liquid recess (dryout) in the evaporator wick, and incorporates a liquid pooling submodel, which simulates accumulation of the excess liquid in the vapor core at the condenser end. HPTAM can handle both rectangular and cylindrical geometries. The model divides the heat pipe into three transverse regions: wall, wick, and vapor regions, and solves the complete form of governing equations in these regions. The heat pipe wick can be a wire-screened mesh, an isotropic porous medium such as a powder or a bed of spheres, or an open annulus separated from the vapor core by a thin sheet (with small holes to provide capillary forces). HPTAM incorporates several working fluids such as lithium, sodium, potassium and water, as well as various wall materials (tungsten, niobium, zirconium, stainless-steel, copper and carbon). Evaporation, condensation, sublimation and resolidification rates are calculated using the kinetic theory relationship with an accommodation coefficient of unity. To predict the flow of liquid in the porous wick of the heat pipe, HPT AM uses the Brinkman-Forchheimer-extended Darcy model. This model was successfully benchmarked against experimental data for natural convection of molten gallium in a porous bed of glass beads. Also, HPTAM handles the phase-change of working fluid in the wick using a modified fixed-grid homogeneous enthalpy method. The technique employs a mushy-cell temperature range as small as 2E-8 K (limited by machine accuracy only), without requiring under-relaxation of the temperatures and generating numerical instabilities. Instead of using the harmonic mean discretization scheme (HMDS) of Patankar, a simple method, based on the frozen volume fraction, was developed to calculate the heat fluxes at the boundaries of the mushy cell. This method improved the accuracy of the solution and reduced the oscillations in temperature time histories (usually encountered when the HMDS is used) by one-to-two orders of magnitude. Because of the physical complexity of the problem, advanced numerical methods were considered. Two segregated solution techniques, one based on the non-iterative Pressure Implicit Splitting Operator (PISO), and the other based on the SIMPLEC segregated iterative technique, were developed and tested for their stability and effectiveness in reducing the CPU time while maintaining the accuracy of results. Various linear-system solvers were also examined to determine which one was most efficient for solving the problem at hand. Based on the results of these examinations, the segregated solution technique using the SIMPLEC procedure was selected for HPTAM. To solve the fivepoint linear Poisson equations resulting from the discretization of the mass balance equations, a direct solution routine using Gaussian elimination was developed. The banded version of the solver allowed significant decreases in computation time and memory storage requirement. The iterative Strongly Implicit Solver was chosen to solve the five-point linear equations resulting from the discretization of the energy and momentum balance equations. The development of this comprehensive model was guided by continuous benchmarking of the model predictions with available experimental and numerical results. The accuracy of the physical and numerical schemes for modeling heat and mass transfers in the wick was verified using various benchmark problems, namely: (a) natural convection of liquid in a square cavity; (b) natural convection of molten gallium in a porous bed of glass beads; (c) one-dimensional pure conduction solidification problem; (d) two-dimensional pure conduction problem of freezing in a corner; and (e) the freezing of tin in a rectangular cavity in the presence of natural convection. Numerical results of the frozen startup of a radiatively-cooled water heat pipe are presented, which demonstrate the soudness of the physical model and numerical approach used in HPT AM. The results illustrate the importance of the sublimation and recondensation processes during the first period of the transient and the combined effects of phase-change and liquid hydrodynamics in the wick during the startup of the low-temperature heat pipe. The startup is characterized by partial recess of liquid in the evaporator wick after the capillary limit has been reached. After enough working fluid was melted by resolidification and condensation in the adiabatic and condenser sections of the heat pipe, resaturation of the wick was established before complete dryout of the evaporator occurred, leading to a successful startup. Also, the heat pipe model was validated using transient experimental data of a fully-thawed water heat pipe constructed at the Institute for Space and Nuclear Power Studies. The calculated steady-state vapor and wall axial temperature profiles and the transient power throughput and vapor temperature were in good agreement with measurements. Results illustrated the importance of the hydrodynamic coupling of the vapor and liquid phases and showed the appearance during the heatup transient (disappearance during cooldown) of a pool of excess liquid at the condenser end. Finally, the effects of input power and initial liquid inventory in the water heat pipe on the wet point and liquid pooling, and on the vapor and liquid pressure and temperature distributions were investigated in details.