Aeroacoustic and Aerodynamic Adjoint-Based Shape Optimization of an Axisymmetric Aero-Engine Intake

Abstract

A continuous adjoint-based aeroacoustic optimization, based on a hybrid model including the Ffowcs Williams–Hawkings (FW–H) acoustic analogy, to account for the multidisciplinary design of aero-engine intakes with an axisymmetric geometry, is presented. To optimize such an intake, the generatrix of its lips is parameterized using B-Splines, and the energy contained in the sound pressure spectrum, at the blade passing frequency at receivers located axisymmetrically around the axis of the engine, is minimized. The engine is not included in the optimization and manifests its presence through an independently computed time-series of static pressure over the annular boundary of the simulation domain that corresponds to the inlet to the fan. Taking advantage of the case axisymmetry, the steady 3D RANS equations are solved in the rotating frame of reference and post-processed to compute the flow quantities’ time-series required by the FW–H analogy. The numerical solution of the unsteady flow equations and the otherwise excessive overall cost of the optimization are, thus, avoided. The objective function gradient is computed using the continuous adjoint method, coupled with the analytical differentiation of the FW–H analogy. The adjoint equations are also solved in the rotating frame via steady solver.

Interactive Airfoil Optimization Using Parsec Parametrization and Adjoint Method

“…After solving for w and λ, it is easy to obtain the gradient of ϕ with respect to F. It can be proven that this gradient is identically equal to the gradient of I, as the constraints R must always be satisfied (5). Then, the simple algorithm of the steepest descent is applied to obtain the new approximation of the optimal parameters (11).…”

“…However, its complexity in both the mathematical apparatus and the programming implementation made initial progress after its proposal rather slow-paced [4]. Since its proposal, it has been successfully used in a variety of optimization problems in the field of fluid mechanics (both external and internal), such as those in [2][3][4][5][6][7]. The adjoint method comes from the theory of optimal control, as stated in [3,8], and was first proposed by Olivier Pironneau (*1945) and Anthony Jameson (*1934) [7].…”