Multi-objective parametric optimization of Inertance type pulse tube refrigerator using response surface methodology and non-dominated sorting genetic algorithm

The modeling and optimization of a Pulse Tube Refrigerator is a complicated task, due to its complexity of geometry and nature. The aim of the present work is to optimize the dimensions of pulse tube and regenerator for an Inertance-Type Pulse Tube Refrigerator (ITPTR) by using Response Surface Methodology (RSM) and Non-Sorted Genetic Algorithm II (NSGA II). The Box-Behnken design of the response surface methodology is used in an experimental matrix, with four factors and two levels. The diameter and length of the pulse tube and regenerator are chosen as the design variables where the rest of the dimensions and operating conditions of the ITPTR are constant. The required output responses are the cold head temperature (Tcold) and compressor input power (Wcomp). Computational fluid dynamics (CFD) have been used to model and solve the ITPTR. The CFD results agreed well with those of the previously published paper. Also using the results from the 1-D simulation, RSM is conducted to analyse the effect of the independent variables on the responses. To check the accuracy of the model, the analysis of variance (ANOVA) method has been used. Based on the proposed mathematical RSM models a multi-objective optimization study, using the Non-sorted genetic algorithm II (NSGA-II) has been performed to optimize the responses.