Multi-objective aerodynamic shape optimization for unsteady viscous flows

Abstract

This paper presents an adjoint method for the multi-objective aerodynamic shape optimization of unsteady viscous flows. The goal is to introduce a Mach number variation into the Non-Linear Frequency Domain (NLFD) method and implement a novel approach to present a time-varying cost function through a multi-objective adjoint boundary condition. The paper presents the complete formulation of the time dependent optimal design problem. The approach is firstly demonstrated for the redesign of a helicopter rotor blade in two-dimensional flow and in three-dimensional viscous flow, the technique is employed to validate and redesign the NASA Rectangular Supercritical Wing (RSW).

Optimization of Airfoils for Minimum Pitching Moment and Compressibility Drag Coefficients

“…During the unsteady evolution, the airfoil surface is moving with time, and the dynamic grid technique is introduced in the grid generation to improve the computational efficiency (Ying et al, 2011). Nadarajah and Tatossian (2008) also have presented an adjoint method for the multi-objective aerodynamic shape optimization of unsteady viscous flows. Their method is beneficial when both the pitching angle and free stream Mach number are sinusoidally varied.…”

“…Their method is beneficial when both the pitching angle and free stream Mach number are sinusoidally varied. They showed that the multi-objective cost function was able to preserve both the lift and pitching moment while simultaneously decreasing the overall drag (Nadarajah and Tatossian, 2008).…”

Approximate Hessian for accelerated convergence of aerodynamic shape optimization problems in an adjoint-based framework

“…Aircraft configurations may be studied through multidisciplinary design optimization that takes into account both the flow and the structure [45,28,24]. The adjoint method has also extended to rotorcraft [29,12,30] and turbomachinery [56,34,57] design optimization.…”

Use of calculus of variations to determine the shape of hovering rotors of minimum power and its application to micro air vehicles

“…Once the shape and aerodynamic characteristics of a rotor are defined, that is, solidity, pitch angle, lift, and drag coefficients, the BEMT equation (1) yields the induced velocity radial distribution, A/(x), and using equations (3), (4), and (5) the global coefficients CT, CQ^, and CQ" are computed.…”