Viscous and Inviscid Instabilities of Flow Along a Streamwise Corner |
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Authors: | SJ Parker S Balachandar |
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Institution: | (1) Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA, US;(2) Department of Theoretical and Applied Mechanics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA, US |
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Abstract: | Here we consider the stability of flow along a streamwise corner 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 corner region have been obtained
by solving the boundary layer equations for zero and nonzero streamwise pressure gradients. The stability of the mean flow
is investigated using linear stability analysis. An 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 corner layer as well, but away from the
cornerline. In a corner region of finite spanwise extent, the continuous spectrum of oblique modes degenerates to a discrete
spectrum of modes of increasing spanwise wave number. The effect of the corner on the two-dimensional viscous instability
is small and decreases 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 corner layer is
dominated by the viscous modes; however, an inviscid corner mode is also observed. The critical Reynolds number of the inviscid
mode rapidly decreases with even a small adverse streamwise pressure gradient and the inviscid mode becomes the dominant one.
Received 17 March 1998 and accepted 28 April 1999 |
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