CFD optimization of a theoretical minimum-drag body

Abstract

This article describes a methodology behind coupling a fast, parabolized Navier-Stokes flow solver to a nonlinear constrained optimizer. The design parameters, constraints, grid refinement, behavior of the optimizer, and flow physics related to the CFD calculations are discussed. Pressure drag reduction in the supersonic regime of a theoretical minimum-drag body of revolution is performed. Careful selection of design variables allows the optimization process to improve the aerodynamic performance. A calculation including nonlinear and viscous effects produces a different minimum drag geometry than linear theory and results in a drag reduction of approximately 4%. Effect of grid density on the optimization process is also studied. In order to obtain accurate optimization results, CFD calculations must model physical phenomena that contribute to the optimization parameters. OR the past two decades, many different approaches have been developed to design aircraft with better aerodynamic performance.1 Some of these techniques fall into the general category of inverse design methods.2-3 The quality of the opti- mized shape obtained from this method depends on the distri- bution, usually pressure, it is required to match. Therefore, this approach depends on the knowledge of the designer to establish a desirable optimum. In addition, the inverse method does not lend itself to the imposition of constraints. A different approach is called shape perturbation method.4~6 In this method, an anal- ysis code is coupled with a numerical optimizer to find a shape that optimizes the objective function. This method may be com- putationally expensive because of the gradient evaluations, which require CFD calculations. Recently, intelligent methods such as the one-shot method7-8 and the control-based method9 have merged that yield rapid convergence to the design shape. Un- fortunately, these two methods make use of the governing equa- tions of the CFD code; therefore, receding is needed for dif- ferent objective functions, boundary conditions, and flow solvers. The methods cannot immediately take advantage of existing validated analysis codes that have already been developed. A shape perturbation method is chosen for optimization in the present study. An efficient CFD flow solver is coupled with an optimizer for use as a tool in aerodynamic design. Careful selection of design variables allows fast convergence in the optimization process and yields improvements in aero- dynamic performance. The present method takes advantage of a Fourier sine series that defines the original body. The Fourier coefficients are convenient, physically relevant design variables for the problem studied here. As a test case, the Haack-Adams1012 (H-A) theoretical minimum-drag body of revolution is chosen. The H-A body is selected in this study because it is a classic aerodynamics problem for which validating experimental data13 are avail- able. Because of its simple geometry, running large numbers of cases in a grid refinement study is still relatively inexpen- sive. Since the geometry ends in a finite base, it is particularly