Robust Design Optimization of Supersonic Biplane Airfoil Using Efficient Uncertainty Analysis Method for Discontinuous Problem

Abstract

Busemann’s supersonic biplane airfoil can reduce wave drag through shock interactions at its designed freestream Mach number. However, a choking phenomenon occurs with a decrease in the freestream Mach number, and the drag coefficient increases significantly, resulting in an aerodynamic problem with a discontinuous change in the performance function. In this study, an uncertainty analysis method, the divided inexpensive Monte Carlo simulation (IMCS), is proposed to solve discontinuous problems efficiently and is applied to Busemann’s biplane airfoil. In the divided IMCS, the discontinuity point is determined using a simple sampling method. The uncertainty input space is divided at the detected discontinuity point, and a surrogate model is constructed for each space. Uncertainty analysis was performed using the constructed surrogate models, and the results of the divided IMCS showed qualitative agreement with those of the conventional Monte Carlo simulation, which is the most straightforward uncertainty analysis method. Moreover, the divided IMCS significantly reduced the computational cost of the uncertainty analysis. A robust design optimization of the supersonic biplane airfoil was performed using the divided IMCS, yielding more robust designs than Busemann’s biplane airfoil. The usefulness of the divided IMCS for uncertainty analysis of discontinuous problems was confirmed.