Wall boundary conditions for high-order finite difference schemes in computational aeroacoustics

Starting from the 3D linearized Euler equations and decomposing the 3D perturbation quantities into a Fourier series in the azimuthal direction, a set of 2.5D linearized disturbance equations is derived which are valid for each azimuthal mode of fluctuation. The derivation is based on an axisymmetric mean flow and axisymmetric acoustic boundary conditions. A Computational Aeroacoustics (CAA) approach is applied to solve the 2.5D equation system. A fourth-order Dispersion-Relation-Preserving finite difference scheme is implemented for spatial discretization, whereas a 2N storage form Low Dissipation and Low Dispersion Runge-Kutta scheme is applied for time integration. Appropriate boundary conditions are prescribed at different boundary regions. The numerical procedure is firstly validated by a straight circular pipe and a straight annular duct subjected on subsonic uniform mean flows. Numerical results show very good agreement with the analytical solutions. Further numerical example is presented for an axisymmetric duct inlet with an aero-engine like geometry including a spinner inside. The aeroacoustic computation is based on an inviscid mean flow calculated by a 2nd order CFD solver. The CAA solutions agree rather well with the finite element results of Eversman as well as the semi-analytical multiple-scales solutions of Rienstra. In particular, a cut-on cut-off transition case has been simulated. This reveals the feasibility of the proposed theory and solution procedure.

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“…Hence along the curvilinear solid walls, a slip boundary condition with ghost points inside the wall is imposed. 15 …”

Section: Solid Wall Boundarymentioning

confidence: 99%

On the Azimuthal Mode Propagation in Axisymmetric Duct FLows

Li¹,

Schemel²,

Michel³

et al. 2002

8th AIAA/CEAS Aeroacoustics Conference &Amp;amp; Exhibit

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“…The implementation of slip-wall boundary conditions (zero normal velocity) for aeroacoustic computations has received attention, most notably the ghost cell method of Tam and Dong 4 and Kurbatski and Tam. 5 But, implementation of transpiration type boundary conditions for inviscid compressible flows has received relatively less attention.…”

Section: Wall Boundary Conditionsmentioning

confidence: 99%

Optimal Transpiration Boundary Control for Aeroacoustics

2003

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We consider the optimal boundary control of aeroacoustic noise governed by the two-dimensional unsteady compressible Euler equations. The control is the time and space varying wall-normal velocity on a subset of an otherwise solid wall. The objective functional to be minimized is a measure of acoustic amplitude. Optimal transpiration boundary control of aeroacoustic noise introduces challenges beyond those encountered in direct aeroacoustic simulations or in many other optimization problems governed by compressible Euler equations. One nontrivial issue that arises in our optimal control problem is the formulation and implementation of transpiration boundary conditions. Since we allow suction and blowing on the boundary, portions of the boundary may change from inflow to outflow, or vice versa, and different numbers of boundary conditions must be imposed at inflow versus outflow boundaries. Another important issue is the derivation of adjoint equations which are required to compute the gradient of the objective function with respect to the control. Among other things, this is influenced by the choice of boundary conditions for the compressible Euler equations. This paper describes our approaches to meet these challenges and presents results for three model problems. These problems are designed to validate our transpiration boundary conditions and their implementation, study the accuracy of gradient computations, and assess the performance of the computed controls.

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Section: Wall Boundary Conditionsmentioning

confidence: 99%

Optimal Control of Aeroacoustic Flows: Transpiration Boundary Control

Collis

Ghayour

Heinkenschloss

2002

3rd Theoretical Fluid Mechanics Meeting

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We consider the optimal boundary control of aeroacoustic noise governed by the two-dimensional unsteady compressible Euler equations. The control is the time and space varying wall-normal velocity (transpiration velocity) on a subset of a solid wall. The objective functional to be minimized is a measure of acoustic amplitude. Optimal transpiration boundary control of aeroacoustic noise introduces challenges beyond those encountered in direct aeroacoustic simulations or in many other optimization problems governed by compressible Euler equations. One nontrivial issue that arises in our optimal control problem is the formulation and implementation of transpiration boundary conditions. Since we allow suction and blowing on the boundary, portions of the boundary may change from inflow to outflow, or vice versa, and different numbers of boundary conditions must be imposed depending on whether a boundary portion is an inflow or an outflow boundary. Another important issue is the derivation of adjoint equations, which are needed for the computation of the gradient of the objective function with respect to the control. Among other things, this is influenced by the choice of boundary conditions for the compressible Euler equations. This paper describes our approaches to meet these challenges and presents first results for two model problems. These problems are designed to validate our transpiration boundary conditions and their implementation, study the accuracy of gradient computations, and assess the performance of the computed controls.

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Wall boundary conditions for high-order finite difference schemes in computational aeroacoustics

Cited by 24 publications

References 7 publications

On the Azimuthal Mode Propagation in Axisymmetric Duct FLows

On the Azimuthal Mode Propagation in Axisymmetric Duct FLows

Optimal Transpiration Boundary Control for Aeroacoustics

Optimal Control of Aeroacoustic Flows: Transpiration Boundary Control

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