Viscous and inviscid instabilities of flow along streamwise corner

Balanchandar, S.; Parker, Scott J.

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https://hdl.handle.net/2142/112557 Copy

Description

Title

Viscous and inviscid instabilities of flow along streamwise corner

Author(s)

• Balanchandar, S.
• Parker, Scott J.

Issue Date

1997-05

Keyword(s)

• Streamwise Corner
• Stability Of Flow

Abstract

Here we consider the stability of flow along a stream wise comer formed by the intersection of two large flat plates held perpendicular to each other. Self-similar solutions for the steady laminar mean flow in the comer region have been obtained by solving the boundary layer equations for zero and non-zero stream wise pressure gradients. The stability of the mean flow is investigated using linear stability analysis. A novel eigensolver has been developed to solve the resulting linear eigenvalue problem either in a global mode to obtain an approximation to all the dominant eigenmodes or in a local mode to refine a particular eigenmode. The stability results indicate that the entire spectrum of two-dimensional and oblique viscous modes of a two-dimensional Blasius boundary layer is active in the case of a comer layer as well, but away from the comerline. In a corner region of finite spanwise extent, the continuous spectrum of oblique modes degenerates to a discrete spectrum of modes of increasing span wise wavenumber. The effect of the comer on the two-dimensional viscous instability is to superpose a spanwise standing wave pattern and decrease the growth rate. The growth rate of outgoing oblique disturbances is observed to decrease, while the growth rate of incoming oblique disturbances is enhanced by the corner. This asymmetry between the outgoing and incoming viscous modes increases with increasing obliqueness of the disturbance. The instability of a zero pressure gradient comer layer is dominated by the viscous modes; however, an inviscid corner mode is also observed. At zero pressure gradient this inviscid comer mode remains stable up to a Reynolds number of about 5 X 105, but the critical Reynolds number rapidly decreases with even a small adverse streamwise pressure gradient and the inviscid mode becomes the dominant one.

Publisher

Department of Theoretical and Applied Mechanics. College of Engineering. University of Illinois at Urbana-Champaign

Series/Report Name or Number

• TAM R 854
• 1997-6015

ISSN

0073-5264

Type of Resource

text

Language

eng

Permalink

http://hdl.handle.net/2142/112557

Sponsor(s)/Grant Number(s)

NASA Langley Research Center 97/05 NAG 1 1583 97/05

Copyright and License Information

Copyright 1997 Board of Trustees of the University of Illinois

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