Turbofan duct geometry optimization for low noise using remote continuous adjoint method

Abstract

In this paper, a remote continuous adjoint-based acoustic propagation (RABAP) method is proposed for low noise turbofan duct design. The goal is to develop a set of adjoint equations and their corresponding boundary conditions in order to quantify the influence of geometry modifications on the amplitude of sound pressure at a near-field location. The governing equations for the 2.5D acoustic perturbation equation solver (APE) formulation for duct acoustic propagation is first introduced. This is followed by the formulation and discretization of the remote continuous adjoint equations based on 2.5D APE. The special treatment of the adjoint boundary condition to obtain sensitivities derivatives is also discussed. The theory is applied to acoustic design of an axisymmetric fan bypass duct for two different tone noise radiations. The 2.5D APE is further validated using comparisons to an experiment data of the TURNEX nozzle geometry. The implementation of the remote continuous adjoint method is validated by comparing the sensitivity derivative with that obtained using finite difference method. The result obtained confirms the effectiveness and efficiency of the proposed RABAP framework.

A continuous adjoint-based aeroacoustic shape optimization for multi-mode duct acoustics

“…, u, v, w, p are density, velocities in axial, radial, and azimuthal directions, and pressure, respectively. It is worth noting that the velocity equation in azimuthal direction in previous paper 36,37 is cast in terms of w 0 t ¼ @w 0 =@t. Compared to that, the velocity equation for w 0 is expressed directly in MMLEE in this paper. From this formulation, we can know that it not only can account for multi-frequency contribution, but also allows a constant swirl background flow (w 0 6 ¼ 0); therefore, it has wider applications than the single-frequency formulation.…”

“…The detailed description of DRP scheme and LDDRK scheme is the same as that of the author's work. 36,37 The objective function, adjoint equation, and adjoint boundary conditions: The general formulation of the continuous adjoint-based optimization method for single mode is given in literature. 36,37 For the multi-mode problems, the adjoint equation, adjoint boundary conditions and the gradient formulations should be derivated carefully again.…”

“…In their method, the sound propagation is simulated by the time-domain linearized Euler equations (2.5-D APE) equation. Then Qiu et al 37 extend the continuous adjointbased acoustic propagation method and explores the use of the remote continuous adjoint method to minimize the amplitude of sound from a bypass duct with the acoustic objective function defined at a near field position. Only sound noise of single frequency and single mode is treated in Qiu's previous work.…”

“…Only sound noise of single frequency and single mode is treated in Qiu's previous work. 36,37 To control the more complex multi-mode fan noise and achieve noise reduction further, this paper proposes a novel continuous adjoint-based multi-mode optimization method for low-noise turbofan duct design. This paper presents a more general model to obtain optimal designs of the fan inlet shape to control the multi-mode noise propagation and radiation from a fan inlet.…”

“…This paper presents a more general model to obtain optimal designs of the fan inlet shape to control the multi-mode noise propagation and radiation from a fan inlet. The method is based on a complex form of the multi-mode LEE which is much more complex than 2.5D APE used in Qiu et al 36,37 and represents a natural extension of the work by Qiu et al 36,37 The main objective of this paper is to find an appropriate shape for the turbofan inlet duct so that the amount of the multi-mode noise radiated to the far-field from the system is minimized. And a new tool is developed to find the optimized inlet duct to deal with the multi-mode noise under the aerodynamic constraints.…”