Acoustic receptivity and transition modeling of Tollmien-Schlichting disturbances induced by distributed surface roughness

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Title: Acoustic receptivity and transition modeling of Tollmien-Schlichting disturbances induced by distributed surface roughness
Authors: Raposo, H
Mughal, MS
Ashworth, R
Item Type: Journal Article
Abstract: Acoustic receptivity to Tollmien-Schlichting waves in the presence of surface roughness is investigated for a flat plate boundary layer using the time-harmonic incompressible linearized Navier-Stokes equations. It is shown to be an accurate and efficient means of predicting receptivity amplitudes, and therefore to be more suitable for parametric investigations than other approaches with DNS-like accuracy. Comparison with literature provides strong evidence of the correctness of the approach, including the ability to quantify non-parallel flow effects. These effects are found to be small for the efficiency function over a wide range of frequencies and local Reynolds numbers. In the presence of a two-dimensional wavy-wall, non-parallel flow effects are quite significant, producing both wavenumber detuning and an increase in maximum amplitude. However, a smaller influence is observed when considering an oblique Tollmien-Schlichting wave. This is explained by considering the non-parallel effects on receptivity and on linear growth which may, under certain conditions, cancel each other out. Ultimately, we undertake a Monte-Carlo type uncertainty quantification analysis with two-dimensional distributed random roughness. Its power spectral density (PSD) is assumed to follow a power law with an associated uncertainty following a probabilistic Gaussian distribution. The effects of the acoustic frequency over the mean amplitude of the generated two-dimensional Tollmien-Schlichting waves are studied. A strong dependence on the mean PSD shape is observed and discussed according to the basic resonance mechanisms leading to receptivity. The growth of Tollmien-Schlichting waves is predicted with non-linear parabolized stability equations computations to assess the effects of stochasticity in transition location.
Issue Date: 24-Apr-2018
Date of Acceptance: 7-Apr-2018
ISSN: 1070-6631
Publisher: AIP Publishing
Journal / Book Title: Physics of Fluids
Volume: 30
Issue: 4
Copyright Statement: © 2018 The Author(s). Published by AIP Publishing
Sponsor/Funder: Engineering and Physical Sciences Research Council
Innovate UK
Funder's Grant Number: EP/I037946/1
Keywords: 01 Mathematical Sciences
02 Physical Sciences
09 Engineering
Fluids & Plasmas
Publication Status: Published
Article Number: 044105
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences

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