Destabilisation and modification of Tollmien-Schlichting disturbances by a three dimensional surface indentation

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Title: Destabilisation and modification of Tollmien-Schlichting disturbances by a three dimensional surface indentation
Author(s): Xu, H
Mughal, SM
Gowree, E
Atkin, CJ
Sherwin, S
Item Type: Journal Article
Abstract: We consider the influence of a smooth three-dimensional (3-D) indentation on the instability of an incompressible boundary layer by linear and nonlinear analyses. The numerical work was complemented by an experimental study to investigate indentations of approximately 11δ99 and 22δ99 width at depths of 45 %, 52 % and 60 % of δ99 , where δ99 indicates 99% boundary layer thickness. For these indentations a separation bubble confined within the indentation arises. Upstream of the indentation, spanwise-uniform Tollmien–Schlichting (TS) waves are assumed to exist, with the objective to investigate how the 3-D surface indentation modifies the 2-D TS disturbance. Numerical corroboration against experimental data reveals good quantitative agreement. Comparing the structure of the 3-D separation bubble to that created by a purely 2-D indentation, there are a number of topological changes particularly in the case of the widest indentation; more rapid amplification and modification of the upstream TS waves along the symmetry plane of the indentation is observed. For the shortest indentations, beyond a certain depth there are then no distinct topological changes of the separation bubbles and hence on flow instability. The destabilising mechanism is found to be due to the confined separation bubble and is attributed to the inflectional instability of the separated shear layer. Finally for the widest width indentation investigated ( 22δ99 ), results of the linear analysis are compared with direct numerical simulations. A comparison with the traditional criteria of using N -factors to assess instability of properly 3-D disturbances reveals that a general indication of flow destabilisation and development of strongly nonlinear behaviour is indicated as N=6 values are attained. However N -factors, based on linear models, can only be used to provide indications and severity of the destabilisation, since the process of disturbance breakdown to turbulence is inherently nonlinear and dependent on the magnitude and scope of the initial forcing.
Publication Date: 27-Apr-2017
Date of Acceptance: 21-Mar-2017
URI: http://hdl.handle.net/10044/1/45705
DOI: https://dx.doi.org/10.1017/jfm.2017.193
ISSN: 1469-7645
Publisher: Cambridge University Press (CUP)
Start Page: 592
End Page: 620
Journal / Book Title: Journal of Fluid Mechanics
Volume: 819
Copyright Statement: © Cambridge University Press 2017 This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Sponsor/Funder: Engineering & Physical Science Research Council (E
Royal Academy Of Engineering
Engineering & Physical Science Research Council (E
Bombardier Aerospace
Funder's Grant Number: EP/I037946/1
AEDZ_P40009
EP/L000261/1
TSB/35896-263171-113001
Keywords: Fluids & Plasmas
01 Mathematical Sciences
09 Engineering
Publication Status: Published
Appears in Collections:Faculty of Engineering
Mathematics
Aeronautics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences



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