Adjoint shape optimization for enhanced heat transfer in sweeping jet impingement on concave surface

The sweeping jet has gained increasing attention in the field of impingement heat transfer due to its unique advantages. Current research primarily focuses on impinging on flat walls, with less attention given to curved wall scenarios. Recent studies have shown that the trapped vortex ring generated by a sweeping jet impinging on a curved surface can limit the effective cooling range. Therefore, modifying the structure of the fluidic oscillator offers considerable potential for enhancing the impingement heat transfer. In this paper, the shape optimization of the conventional fluidic oscillator is performed using an adjoint optimization method. Numerical simulations were first conducted with a jet Reynolds number of 10,308, an impingement distance of four times the jet hydraulic diameter, and an impingement wall radius of ten times the jet hydraulic diameter as the operating conditions. To accurately reproduce the jet dissipation characteristics and the trapped vortex ring structure, the turbulent dissipation rate was modeled with a well calibrated Generalized $k$-$\omega$ (GEKO) model. The optimized structure aimed to minimize the surface-averaged temperature. The results indicated that the improved structure reduced the jet's oscillation angle, resulting in a more concentrated jet velocity and less dissipation. This intensified the strength of the wall jet in the non-oscillation plane and pushed the trapped vortex ring farther outward, thus increasing the effective cooling range. Time- and surface-averaged results on the impingement wall revealed that the Nusselt number of the improved structure increased by 11.6%, and the temperature decreased by 2.4 K compared to the baseline structure.