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Acoustic receptivity of compressible Tollmien-Schlichting waves with an efficient time-harmonic linearized Navier-Stokes method

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Title: Acoustic receptivity of compressible Tollmien-Schlichting waves with an efficient time-harmonic linearized Navier-Stokes method
Authors: Raposo, H
Mughal, MS
Ashworth, R
Item Type: Conference Paper
Abstract: The compressible formulation of the time-harmonic linearized Navier-Stokes (LNS) method for acoustic receptivity prediction is described. The efficiency of the proposed approach is rooted in the assumption that the problems of interest only require the time-asymptotic solution of a few select frequencies. We explore the parabolic nature of the basic flow and of the Stokes layer, and we implement an efficient LU decomposition method to obtain the roughness- induced steady perturbation and Tollmien-Schlichting wave. Before attempting to predict receptivity amplitudes, the compressible Stokes layer solution based on the linearized unsteady boundary layer equations is validated in the subsonic regime against an Orr-Sommerfeld-type equation. Further testing of the model is conducted by reproducing the experiments of King & Breuer in near incompressible conditions. The results are consistent with the analogue incompressible receptivity model, and reveal excellent agreement with finite-Reynolds number theory for two-dimensional instabilities. Qualitative agreement with the experimental results for oblique waves is observed. Differences can be partially explained by the choice of physical model used to determine the N-factors, which in turn are used to extrapolate amplitudes to the first-branch of stability. Ultimately, a comprehensive comparison with direct-numerical- simulation-based subsonic receptivity amplitudes is conducted, demonstrating the correctness of the mathematical model and numerical implementation described herein.
Issue Date: 25-Jun-2018
Date of Acceptance: 1-Jun-2018
URI: http://hdl.handle.net/10044/1/62211
DOI: https://dx.doi.org/10.2514/6.2018-3379
Publisher: AIAA
Journal / Book Title: 2018 Fluid Dynamics Conference, AIAA AVIATION Forum
Copyright Statement: © 2018 by Airbus Group Ltd.. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.
Sponsor/Funder: Engineering and Physical Sciences Research Council
Innovate UK
Funder's Grant Number: EP/I037946/1
Conference Name: 2018 Fluid Dynamics Conference
Publication Status: Published
Start Date: 2018-06-25
Finish Date: 2018-06-29
Conference Place: Atlanta, Georgia
Online Publication Date: 2018-06-27
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences

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