Gradient-based shape optimization for unsteady turbulent simulations using field inversion and machine learning

Abstract

This paper presents a method for gradient-based shape optimization using unsteady models of turbulent flowfields, for which forward simulations are already expensive and adjoint calculations diverge or require costly regularization. The proposed method targets an objective and constraints computed from the time-averaged flowfield and does not use either an unsteady adjoint nor an input-to-output surrogate. The method relies on the field-inversion, machine-learning (FIML) approach, in which a correction field modifies the production term in a Reynolds-averaged Navier-Stokes (RANS) model of the flow. Steady, adjoint-based, field inversion yields this correction field, and a neural-network model is trained, only from readily-available unsteady primal data, to reproduce the field from local flow quantities. Gradient-based shape optimization is then performed using the corrected RANS model, which must include a linearization of the correction field calculation for accurate gradients. The complete design optimization loop consists of iterations of unsteady simulation, FIML, and steady adjoint-based optimization. Low and moderate Reynolds number airfoil optimization problems demonstrate the performance of the proposed method, and comparisons to RANS-alone designs illustrate the importance of accounting for the unsteady flow effects in the optimization.