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.