Multi-objective optimization of a symmetric wavy regenerative cooling channel with secondary channels based on PSO-BP and NSGA-Ⅱ

With the growing complexity of space missions and increasing demands on propulsion system performance, the thermal management of liquid rocket motor presents a severe challenge. This study proposes a novel regenerative cooling channel design for methane, featuring a symmetric wavy primary channel integrated with secondary channels. A comprehensive multi-objective optimization framework is presented to enhance the overall performance. The width (0.2≤w≤1.0mm) and inclination angle (0^°≤θ≤45^°) of the secondary channels, along with the average surface roughness (0≤Ra≤20μm) of the channel, are adopted as design variables. The channel-averaged Nusselt number (Nu) and friction factor (f) served as the objective functions. A high-quality dataset is generated from a numerically validated simulation model as the basis for surrogate training. Grey relational analysis (GRA) is employed to evaluate the sensitivity of each design variable with respect to the objective functions. Two surrogate models, a back-propagation neural network (BPNN) and a particle swarm optimization enhanced back-propagation neural network (PSO-BP) surrogate model, are established and compared. Then the PSO-BP model is combined with the Non-dominated Sorting Genetic Algorithm II (NSGA-II) algorithm to perform multi-objective optimization. The GRA results show that all three design variables exert a significant influence on the objective functions. Furthermore, the PSO-BP model provides significantly higher prediction accuracy and better generalization capability than the conventional BPNN model. Based on the Pareto front obtained from NSGA-II and the entropy-weighted Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method, the optimal configuration is identified with w=0.2 mm, θ=45°, and Ra=10.7 µm. Compared to a baseline smooth wavy cooling channel, this configuration, featuring a narrow-width, large-inclination secondary channel layout, substantially enhances heat-transfer performance while maintaining a moderate pressure loss. The final performance is Nu= 1623.77 and f=0.1155, with a performance evaluation criterion (PEC) of 2.407. The proposed regeneratively cooled channel concept and multi-objective optimization framework could provide valuable guidance for the thermal protection design of liquid rocket motor thrust chambers.