A methodology for determining aerodynamic sensitivity derivatives with respect to variation of geometric shape

Abstract

A general procedure is developed for calculating aerodynamic sensitivity coefficients using the full equations of fluid flow, where the focus of the work is the treatment of arbitrary variations of geometric shape design varibles. Using an upwind cell-centered finite volume approximation to represent the governing equations, sensitivity derivatives are determined by direct differentiation of the resulting set of coupled nonlinear algebriac equations which model the fluid flow. The technique is implemented and succesfully tested in 2D for inviscid flow (i.e., the Euler equations) through a subsonic nozzle (M, = 0.85), and also a supersonic inlet (M, = 2.0). Specifically, the method is demonstrated by calculating the sensitivity of the aerodynamic loads (forces) on the interior walls of the nozzle / inlet to variations in the geometric parameters which define their shape. The sensitivity coefficients calculated using this approach compare very well with those calculated using the method of brute force (i.e., using finite differences to approximate the sensitivity derivatives), and are computationally less expensive to obtain.