Effects of streamwise elongated and spanwise periodic surface roughness elements on boundary-layer instability
File(s)
Accepted version
Author(s)
Katai, Csaba
Wu, Xuesong
Type
Journal Article
Abstract
We investigate the impact on the boundary-layer stability of spanwise periodic, stream-wise elongated surface roughness elements. Our interest is in their effects on the so-called lower-branch Tollmien–Schlichting modes, and so the spanwise spacing of the elements is taken to be comparable with the spanwise wavelength of the latter, which is ofO(R−3/8L), whereLis the dimensional length from the leading edge of the flat plate to the surface roughness, and R is the Reynolds number based onL. The streamwise length is much longer, consistent with experimental setup. The roughness height is chosen such that the wall shear is altered byO(1). From the generic triple-deck theory for three-dimensional roughness elements with both the streamwise and spanwise length scales being ofO(R−3/8L), we derived the relevant governing equations by appropriate rescaling. The resulting equations are nonlinear but parabolic because the pressure gradient in the streamwise direction is negligible while in the spanwise direction is completely determined by the roughness shape. Appropriate upstream, boundary and13matching conditions are derived for the problem. Due to the parabolicity, the equations are solved efficiently using a marching method to obtain the streaky flow. The instability of the streaky flow is shown to be controlled by the spanwise dependent (periodic) wall shear. Two- and weakly three-dimensional lower-frequency modes are found to be stabilised by the streaks, confirming previous experimental findings, while stronger three-dimensional and higher-frequency modes are destabilised. Among the three roughness shapes considered, the roughness elements in the form of hemispherical cap is found to be most effective for a given height. A resonant subharmonic interaction was found to occur for modes with spanwise wavelength twice that of the roughness elements.
Date Issued
2020-07-27
Date Acceptance
2020-06-04
Citation
Journal of Fluid Mechanics, 2020, 899, pp.1-47
ISSN
0022-1120
Publisher
Cambridge University Press (CUP)
Start Page
1
End Page
47
Journal / Book Title
Journal of Fluid Mechanics
Volume
899
Copyright Statement
© The Author(s), 2020. Published by 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.
Identifier
https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/effects-of-streamwiseelongated-and-spanwiseperiodic-surface-roughness-elements-on-boundarylayer-instability/F9C119880B2B616D4F482A7E0D6AA1EE
Subjects
Science & Technology
Technology
Physical Sciences
Mechanics
Physics, Fluids & Plasmas
Physics
boundary layer stability
instability control
transition to turbulence
TOLLMIEN-SCHLICHTING WAVES
SECONDARY INSTABILITY
FLOW-THROUGH
STABILITY
STREAKS
GROWTH
STABILIZATION
DISTURBANCES
TRANSITION
ROW
01 Mathematical Sciences
09 Engineering
Fluids & Plasmas
Publication Status
Published
Date Publish Online
2020-07-27