Adjoint based compressible Euler shape optimization code for propeller driven aircraft

Abstract

High fidelity aerodynamic shape optimization using the adjoint method for gradient calculation is presented for an aircraft wing with particular emphasis on designing wings for propeller-driven aircraft with lower induced drag with lower aspect ratio. Rakshith et al. (2011) exploited the aerodynamic interaction of a wing with the slipstream of a propeller mounted in front of the wing, in order to design wings of lower drag. They got novel wing designs with lower induced drag for a propeller driven aircraft in tractor configuration using their own specially developed software PROWING, which includes the coupling of an optimizer with lifting line theory. The latter was modified for including the effect of the propeller slipstream. Inspired by this work the present work addresses a higher fidelity optimization problem by coupling the Euler equation with optimization techniques for obtaining wings with lower induced drag. Rakshith et al. (2011) optimized wings with aspect ratio of 12 which was suitable for the lifting line theory. Present work verifies the optimized shape got by Rakshith et al. (2011) and also includes optimization with small aspect ratio wing. A software package was developed for this purpose and its implementation and validation have been performed. A general Aerodynamic Shape Optimization procedure includes nonlinear constraints such as a PDE (partial differential equation, in this case Euler equation). The present work solves an optimization problem to minimize the induced drag calculated by Euler equations with other nonlinear constraints which include aerodynamic and geometric properties like lift coefficient, aspect ratio etc. Hence there was a need to have a constrained nonlinear programming algorithm for minimization of a specified cost function. A C++ software package PROP-OPT was developed for this purpose. This has been coupled to a flow solver, gradients solver, shape parametrization and domain mesh deformation, in order to automate the optimization cycle. PROP-OPT uses the open source C++ library NLOPT, which gives a choice of using various optimization techniques available on the Internet such as Sequential Quadratic Programming (SQP) which approximates the Hessian with Broyden Fletcher Goldfarb Shanno (BFGS) algorithms, to reach the optimum faster. With NLOPT library the PROP-OPT can solve the optimization problem with nonlinear constraints of PDE with aerodynamic and geometric properties of the wing-propeller system.