Multi-Objective Optimization of Parameters of Channels with Staggered Frustum of a Cone Based on Response Surface Methodology

In this study, Response Surface Methodology (RSM) and multi-objective genetic algorithm were used to obtain optimum parameters of the channels with frustum of a cone with better flow and heat transfer performance. Central composite face-centered design (CCF) was applied to the experimental design of the channel parameters, and on this basis, the response surface models were constructed. The sensitivity of the channel parameters was analyzed by Sobol's method. The multi-objective optimization of the channel parameters was carried out with the goal of achieving maximum Nusselt number ratio (Nu/Nu(0)) and minimum friction coefficient ratio (f/f(0)). The results show that the root mean square errors (RSME) of the fitted response surface models are less than 0.25 and the determination coefficients (R-2) are greater than 0.93; the models have high accuracy. Sobol's method can quantitatively analyze the influence of the channel parameters on flow and heat transfer performance of the channels. When the response is Nu/Nu(0), from high to low, the total sensitivity indexes of the channel parameters are frustum of a cone angle (alpha), Reynolds number (Re), spanwise spacing ratio (Z(2)/D), and streamwise spacing ratio (Z(1)/D). When the response is f/f(0), the total sensitivity indexes of the channel parameters from high to low are Re, Z(1)/D, alpha and Z(2)/D. Four optimization channels are selected from the Pareto solution set obtained by multi-objective optimization. Compared with the reference channel, the Nu/Nu(0) of the optimized channels is increased by 21.36% on average, and the f/f(0) is reduced by 9.16% on average.