Aerodynamic Shape Optimization of Hovering Rotors Using a Discrete Adjoint of the Reynolds-Averaged Navier–Stokes Equations

Abstract

A gradient-based method using a discrete adjoint of the Reynolds-averaged Navier-Stokes (RANS) equations is applied to the problem of helicopter blade shape optimization in hover. First, the RANS equations expressed in a specific coordinate system, adapted to the problem of a hovering rotor, are introduced. Then the numerical scheme used to solve the flow equations and the discrete adjoint equation is presented. They are then used within a gradient-based optimizer to perform rotor shape optimizations. The method is applied to the planform optimization of two different rotor blades: a classical rectangular blade and an innovative double swept blade planform. Design variables define the twist, chord, anhedral, and sweep distributions over the blade span, and the objective of the optimization is to improve the rotor figure of merit. The method demonstrated its efficiency in terms of central processing unit time and memory requirement and succeeded in providing interesting rotor blade shapes. The main interest of the present method is its ability to perform local optimization of isolated rotor in hover using an accurate computational fluid dynamics model and accounting for a large number of shape parameters. T turbulent heat flux vector ϕ rotation of a blade section generated by twist (deg) rotor rotational speed (rad·s −1 )

Comparison of Local and Global Constrained Aerodynamic Shape Optimization

“…[1][2][3] Compressible CFD has been used in numerous optimizations of two-dimensional aerofoil sections, 4, 5 threedimensional aircraft, [6][7][8] and three-dimensional aeroelastic aircraft, 9,10 and there has been a recent increase in activity in the rotor area. [11][12][13][14][15] The authors have also presented work in the optimization area, having developed a modularised, generic optimization tool that is applicable to any aerodynamic problem. [16][17][18][19] Aerodynamic shape optimization often uses volume-based CFD methods to analyse the flow physics to obtain values for the objective function, constraints and sensitivities such that an optimization algorithm can construct a search process.…”

Aerodynamic rotor blade optimization at Eurocopter - a new way of industrial rotor blade design

“…A recent step in automatic optimization of rotor blades at hover conditions using CFD was the integration of adjoint methods to directly include the gradients of all parameters in the optimization loop. 6 The direct inclusion of gradient information for all parameters allowed for finding the local optimum within a small number of simulations.…”

Metric-Based Mathematical Derivation of Aerofoil Design Variables

“…Computational fluid dynamics (CFD) is at the forefront of aerodynamic analysis capabilities, and application of numerical optimization algorithms with compressible CFD has been used in numerous optimizations of two-dimensional aerofoil sections, 1, 2 three-dimensional aircraft, [3][4][5] and three-dimensional aeroelastic aircraft, 6 and there has been a recent increase in activity in the rotor area. [7][8][9][10][11] The authors have also presented work in this area, having developed a modularised, generic optimization tool, that is flow-solver and mesh type independent, and applicable to any aerodynamic problem. [12][13][14] The key aspect of a flexible optimization and design process is an effective geometry parameterization and surface control technique.…”