A local scattering approach for the effects of abrupt changes on boundary-layer instability and transition: a finite-Reynolds-number formulation for isolated distortions

File Description SizeFormat 
LSA-JFM-part-I-v6.pdfAccepted version704.63 kBAdobe PDFView/Open
Title: A local scattering approach for the effects of abrupt changes on boundary-layer instability and transition: a finite-Reynolds-number formulation for isolated distortions
Authors: Huang, Z
Wu, X
Item Type: Journal Article
Abstract: We investigate the influence of abrupt changes on boundary-layer instability and transition. Such changes can take different forms including a local porous wall, suction/injection and surface roughness as well as junctions between rigid and porous walls. They may modify the boundary conditions and/or the mean flow, and their effects on transition have usually been assessed by performing stability analysis for the modified base flow and/or boundary conditions. However, such a conventional local linear stability theory (LST) becomes invalid if the change occurs over a relatively short scale comparable with, or even shorter than, the characteristic wavelength of the instability. In this case, the influence on transition is through scattering with the abrupt change acting as a local scatter, that is, an instability mode propagating through the region of abrupt change is scattered by the strong streamwise inhomogeneity to acquire a different amplitude. A local scattering approach (LSA) should be formulated instead, in which a transmission coefficient, defined as the ratio of the amplitude of the instability wave after the scatter to that before, is introduced to characterize the effect on instability and transition. In the present study, we present a finite-Reynolds-number formulation of LSA for isolated changes including a rigid plate interspersed by a local porous panel and a wall suction through a narrow slot. When the weak non-parallelism of the unperturbed base flow is ignored, the local scattering problem can be cast as an eigenvalue problem, in which the transmission coefficient appears as the eigenvalue. We also improved the method to take into account the non-parallelism of the unperturbed base flow, where it is found that the weak non-parallelism has a rather minor effect. The general formulation is specialized to two-dimensional Tollmien–Schlichting (T–S) waves. The resulting eigenvalue problem is solved, and full direct numerical simulations (DNS) are performed to verify some of the predictions by LSA. A parametric study indicates that conventional LST is valid only when the change is sufficiently gradual, and becomes either inaccurate or invalid when the scale of the local distortion is short. A local porous panel enhances T–S waves, while a local suction with a moderate mass flux significantly inhibits T–S waves. In the latter case, a comprehensive comparison is made between the theoretical predictions and experimental data, and a satisfactory quantitative agreement was observed.
Issue Date: 10-Jul-2017
Date of Acceptance: 26-Apr-2017
URI: http://hdl.handle.net/10044/1/64142
DOI: https://dx.doi.org/10.1017/jfm.2017.287
ISSN: 0022-1120
Publisher: Cambridge University Press (CUP)
Start Page: 444
End Page: 483
Journal / Book Title: Journal of Fluid Mechanics
Volume: 822
Copyright Statement: © 2017 Cambridge University Press. This paper has been accepted for publication and will appear in a revised form, subsequent to peer-review and/or editorial input by Cambridge University Press.
Keywords: Science & Technology
Physical Sciences
Physics, Fluids & Plasmas
boundary layer stability
porous media
wave scattering
01 Mathematical Sciences
09 Engineering
Fluids & Plasmas
Publication Status: Published
Online Publication Date: 2017-06-06
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.

Creative Commonsx