A Numerical and Optimization Study of Compressible Phase-Change Heat Transfer in a Part-Unit-Cell Model of a Pulsating Heat Pipe (PHP)

The heat transfer capacity of a PHP is tremendously high and is finding many applications such as in electronic cooling. In order to maximize its heat transfer potential, the working parameters of a PHP have to be set to the right values. The present work deals with the optimization study of a part-unit-cell model of a Pulsating Heat Pipe (PHP) comprising of a single meniscus oscillating between evaporator and adiabatic sections. The parameters considered for this study are the effective length of the evaporator section, the evaporator temperature and the fluid fill ratio. All the numerical studies on PHP till date make the approximation of incompressibility of working fluid. However, recent experimental studies by M.Rao et al. [1] have shown the importance of compressibility effects on the working of a PHP. The present work involves a compressible phase change heat transfer model, based on the Volume-of-Fluid solver. The compressible model is incorporated into open source CFD solver OpenFOAM. This solver is validated in stages by Ghanta and Pattamatta [2] and the part-unit cell of the PHP is validated against the existing experimental results of M. Rao et al [1] and contrast is made with an incompressible solver, to emphasise the importance of considering the compressibility effects. Following validation of the compressible phase change solver, a parametric study explaining the effects of the above mentioned parameters on the objective functions and working of the PHP is performed, which forms the basis for the optimization presented in this work. Accordingly, the ratio of evaporator to the adiabatic length (L_e/L_a) is varied between 2 and 10, the evaporator superheat between 5 and 20 and the fluid filling ratio is varied between 35–80 %. A multi-objective optimization problem is set-up taking the maximum vapour pressure attained and working time (the time for which the working fluid is in contact with the part unit cell of the PHP) as the objective functions. Models are created using two different methods — Kriging and Response Surface Approximation (RSA). The models are optimized using multi-objective Genetic Algorithm, coded in MATLAB. Both the models used predicted the same optimum values, with a variation of 0.01%. The optimum values point at a fluid fill ratio of 79.5%, evaporator excess temperature of 7.89 and an evaporator section of length seven times that of the adiabatic section. The same is also validated with results of numerical simulation at the optimal point. In majority of the works presented so far, the maximum vapour pressure alone is taken as a benchmark for the performance of the PHP. To elucidate the importance of considering working time as an objective function, a single objective optimization study was also performed, with only the maximum pressure as the objective function. The results of single objective optimization showed a deviated optimal point, with similar optimal pressure value as that of multi-objective optimization, but working time reduced by half. Hence by not considering the working time of PHP as an objective function, the optimal point generated results in only half the maximum heat transfer that can otherwise be attained with different parameters.