Adjoint-Based Aeroacoustic Design-Optimization of Flexible Rotors in Forward Flight

Abstract

This paper presents the development and application of a time-dependent adjoint-based method for aeroacoustic design optimization of flexible helicopter rotors in forward flight. The rotor noise signature at a farfield observer is computed with the hybrid aeroacoustic approach in which a near-body coupled computational fluid dynamics/computational structural dynamics solver provides flow and geometry data to an FW-H acoustic module that propagates the acoustic waves to a farfield observer. Forward and adjoint sensitivity formulations are derived that correspond to analogues of the multidisciplinary flexible aeroacoustic analysis problem. The newly implemented aeroacoustic capability is first verified to effectively perform forward flight noise prediction by comparison with the PSU-WOPWOP acoustic tool. Upon successful validation, a gradient based optimization method is used to minimize the required torque of the flexible HART-II rotor in trimmed forward flight while reducing the acoustic signature at a farfield observer by changing the shape of the blades. The adjoint formulation developed in this work is used to efficiently compute the sensitivity required by the optimization algorithm.

Toward Adjoint-Based Aeroacoustic Optimization for Propeller and Rotorcraft Applications

“…In the present development, the authors follow the impermeable surface approach again with the time domain implementation as shown in Eqs. (5) - (7). Moreover, the present code is capable of computing moving sources using the full F1A formulation in addition to the previous implementation in Ref.…”

“…The computational cost of evaluating the adjoint-based sensitivities is independent of the number of design variables [1][2][3]. Significant progress has been achieved in adjoint-based aerodynamic shape optimization in both steady and unsteady settings [3][4][5][6][7][8][9][10][11]. Herein, a computational framework is developed and presented to analyze a complex flowfield and acoustic wave propagation generated by propellers and rotary wing aircraft.…”

Flutter Boundary Identification from Time-Domain Simulations Using the Matrix Pencil Method

“…Since the derivative of the damping estimate depends on the samples obtained from time history of an aeroelastic simulation, the proposed technique requires a fully coupled aeroelastic sensitivity method. Several research groups have developed high-fidelity aeroelastic tools that employ adjoint-based gradient evaluation techniques for both steady and unsteady aeroelastic problems [6,7,8,9,10,11,12,13,14,15] that meet this requirement. The proposed matrix pencil method is demonstrated on a pitch-plunge airfoil model modeled using FUN3D within the recently developed FUNtoFEM framework for aeroelastic simulations [11,16,17].…”

“…For the structural model, the plunge is initially held fixed and the pitch motion is forced at 100 rad/s with an amplitude of 1 • for one period of forcing. After this initial forced motion, the structural degrees of freedom are released and driven by the governing equations(14). To estimate the aeroelastic damping, the matrix pencil method is applied to the final 1000 steps of the time history of the pitch angle.…”

Sensitivity Analysis of Multidisciplinary Rotorcraft Simulations

“…15 In contrast with the finite-difference methods employing real-valued perturbations, the complex-variable approach does not suffer from subtractive error cancellation and is capable of producing the true sensitivity of the discrete solution with respect to a chosen design parameter. Recently, adjoint-based sensitivity analyses of model rotorcraft simulations 11,16,17 have been demonstrated to guide design and optimization.…”