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Development of Tollmien-Schlichting disturbances in the presence of laminar separation bubbles on an unswept infinite wavy wing

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Title: Development of Tollmien-Schlichting disturbances in the presence of laminar separation bubbles on an unswept infinite wavy wing
Authors: Thomas, C
Mughal, M
Ashworth, R
Item Type: Journal Article
Abstract: The effect of long-wavelength sinusoidal surface waviness on the development of Tollmien-Schlichting (TS) wave instabilities is investigated. The analysis is based on the compressible flow that forms over an unswept infinite wavy wing with surface variations of variable amplitude, wavelength, and phase. Boundary layer profiles are extracted directly from solutions of a Navier-Stokes solver, which allows a thorough parametric analysis to be undertaken. Many wavy surface configurations are examined that can be sufficient to establish localized pockets of separated flow. Linear stability analysis is undertaken using parabolized stability equations (PSE) and linearized Navier-Stokes (LNS) methods, and surface waviness is generally found to enhance unstable behavior. Results of the two schemes are compared and criteria for PSE to establish accurate solutions in separated flows are determined, which are based on the number of TS waves per wavelength of the surface deformation. Relationships are formulated, relating the instability variations to the surface parameters, which are consistent with previous observations regarding the growth of TS waves on a flat plate. Additionally, some long-wavelength surface deformations are found to stabilize TS disturbances.
Issue Date: 26-Apr-2017
Date of Acceptance: 31-Mar-2017
URI: http://hdl.handle.net/10044/1/46178
DOI: https://dx.doi.org/10.1103/PhysRevFluids.2.043903
ISSN: 2469-990X
Publisher: American Physical Society
Journal / Book Title: Physical Review Fluids
Volume: 2
Issue: 4
Copyright Statement: © 2017 American Physical Society
Sponsor/Funder: Engineering and Physical Sciences Research Council
Innovate UK
Funder's Grant Number: EP/I037946/1
113022
Keywords: Science & Technology
Physical Sciences
Physics, Fluids & Plasmas
Physics
PARABOLIZED STABILITY EQUATIONS
BOUNDARY-LAYER
NONLINEAR STABILITY
SURFACE WAVINESS
TRANSITION
INSTABILITY
PREDICTION
FLOWS
SWEPT
HUMP
Publication Status: Published
Article Number: 043903
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences



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