Supersonic inverse design method for wing-fuselage design

Abstract

In this chapter, a three-dimensional supersonic wing design method that can determine both the warp and thickness at the same time is developed. The present method is extended from Takanashi's inverse design method used for the transonic wing design. Takanashi solved the inverse problem by using the integral form of the transonic small perturbation equation with ‘residual-correction’ concept. This paper will discuss the mathematical formulation of the present method, and show two design results. One is for an isolated-wing configuration and the other is for a wing‑fuselage combination that is the baseline design of the National Aerospace Laboratory's experimental scaled supersonic transport (SST). The inverse problem in the aerodynamic shape design is to find a geometry that yields a specified surface pressure distribution. The procedure of finding a corresponding geometry in the present method is described as follows. First, a target pressure distribution and an initial geometry are inputted to a design system, and then the surface pressure distribution of this initial geometry is obtained by the flow analysis. In this design system, inverse calculation stage is separated from the flow analysis stage. Thus, any type of analysis, even an experiment, can be used for the flow analysis tool. In this study, the Euler/Navier‑Stokes solver is used for the flow analysis. the pressure difference is calculate from the computed and target pressure distributions. Using this pressure difference as a boundary condition, a geometry correction is obtained by solving the linearized small perturbation (LSP) equation. By modifying the initial geometry with the geometry correction, a new geometry is produced.