Aerodynamic Shape Optimization of Hovering Rotor Blades in Transonic Flow Using Unstructured Meshes

Abstract

An aerodynamic shape optimization technique has been developed for helicopter rotor blades in hover based on a continuous adjoint method on unstructured meshes. For this purpose, the Euler flow solver and the adjoint sensitivity analysis were formulated on the rotating frame of reference. To handle the repeated evaluation of the flow solution and the sensitivity analysis efficiently, the flow and adjoint solvers were parallelized using a domain decomposition strategy. A solution-adaptive mesh refinement technique was adopted to better resolve the tip vortex. Applications were made to the aerodynamic shape optimization of the Caradonna-Tung rotor blade and the UH-60 rotor blade. The results showed that the present method is effective in determining optimum aerodynamic configurations of rotor blades in hover, which require minimum inviscid torque while maintaining the desired thrust level at transonic flight conditions. Nomenclature d = vector of design variables e o = total internal energy g = arbitrary function of flow variables h o = total enthalty I = objective function of unconstraint optimization I o = objective function of constraint optimization k = arbitrary function of design variables n = design iteration ndv = number of design variables p = static pressure Q = vector of flow variables R = residual vector of governing flow equations R = rotor radius r = radial distance along blade span s = vector of search direction U = inertial velocity component normal to domain boundary u, v, w = Cartesian velocity components in inertial frame of reference = variation operator = arbitrary small number = step size = flow density = vector of adjoint variables Subscript L = left side of control surface R = right side of control surface

Optimal Shape Design for Open Rotor Blades

“…. (12) Now, reconsider the process of finding the first variation of J when applying the surface deformation. The variation of the governing flow equations due to the change in the surface shape also appears:…”

“…Rotor design has long been pursued using various techniques, but to our knowledge, only several publications have addressed adjoint-based shape design using the non-inertial governing flow equations. Lee and Kwon [12] presented a continuous adjoint formulation for inviscid, hovering rotor flows on unstructured meshes. More recently, discrete adjoint formulations for the Reynolds-averaged Navier-Stokes (RANS) equations in a rotating frame have been shown by Nielsen et al [13] with the Spalart-Allmaras turbulence model on unstructured meshes and by Dumont et al [14] with the k !…”

Convergence studies of the time accurate and non-linear frequency domain methods for optimum shape design

“…Both the time accurate and non-linear frequency domain (NLFD) methods were applied to the redesign of two-and three-dimensional geometries in unsteady viscous flows. Lee and Kwon (2006) presented a shape optimisation technique for hovering rotor blades in an inviscid transonic flow using unstructured meshes. The approach incorporated a solution adaptive mesh refinement technique to resolve the tip vortex.…”

Aerodynamically Efficient Rotor Design for Hovering Agricultural Unmanned Helicopter

“…Unstructured meshing provides flexibility in grid generation and is widely used in helicopter rotor blade simulations in hovering flight (Lee and Kwon 2006). The surface of the rotor blade is meshed with unstructured triangular elements where the size of each triangle is defined by a base size of 0.005c and prism layers are applied to capture the boundary layer such that 5 < wall y+ < 250.…”