Efficient multi-objective optimization of a boot-shaped rib in a cooling channel

Multi-objective optimization of a boot-shaped rib in a cooling channel was conducted to assess the trade-off between two conflicting objectives, heat transfer performance and pressure drop. Numerical analysis using three-dimensional Reynolds-averaged Navier-Stokes equations, surrogate modelling for function approximation, and a multi-objective genetic algorithm were used for the optimization. Four geometric variables (the ratios of the tip width to rib width, rib width to rib height, rib height to channel height, and tip height to rib height) were chosen as the design variables. To characterize the heat transfer performance and pressure drop, the area-averaged Nusselt number at the rib-roughened surface and the friction factor were selected as the objective functions. For modelling turbulence, a low-Re k-ω turbulence model was used. The Latin hypercube sampling method was used to select the design points in the design space. Two different cases were considered. In the first case, the objective functions were formulated using response surface approximation models while the second case involved kriging models. The Pareto-optimal fronts obtained using the multi-objective genetic algorithm for the two cases were compared using convergence and spread performance criterion. Based on the performance analysis results, a new approach to obtain the best Pareto-optimal front is presented. Further, the flow dynamics and heat transfer characteristics of some representative Pareto-optimal solutions of the best Pareto-optimal front were used to analyze the variations of the objective functions with the design variables.