Physics-augmented shape optimization of subsonic contraction nozzle using dual-deep neural networks

Subsonic contraction nozzles are widely adopted in aeronautical and aerospace engineering applications. Designing a proper nozzle shape profile is crucial for achieving a high-quality flow field at the nozzle outlet. A common design practice involves selecting the profile of specific algebraic formulas, such as bicubic and quintic curves. The feasibility of optimizing the nozzle profile for further enhancing the nozzle aerodynamics remains an open question. In this paper, we propose a novel physics-augmented optimization framework to efficiently optimize subsonic contraction nozzles with low contraction ratios, aiming to reduce the peak-center difference of the outlet velocity profile (OVP). To accurately capture subtle variations in peak-center differences, we construct a dual-deep neural network (dual-DNN) that outputs the nozzle OVP directly and enables fine-tuning of the OVP. We demonstrate that with only limited high-fidelity training data, the proposed NN can serve as a faithful surrogate model of computational fluid dynamics simulations for predicting the subsonic nozzles’ OVP. Moreover, based on the NN-output OVP, we designed a smoothness-regularized objective function that enforces mass conservation for the nozzle shape optimization based on the NN surrogate model. Optimization results reveal a novel nozzle shape that is insensitive to the initial nozzle shape and exhibits a significantly improved peak-center difference. We believe that the proposed Dual-DNN with an improved optimization objective function can be further extended to three-dimensional nozzle/diffuser design scenarios.