Dynamical characteristics of wave-excited channel flow

Abstract

This paper is part of a study on the receptivity characteristics of the shear flow in a channel whose walls are subjected to a wave-like excitation. The small amplitude forced wavy wall motion is characterised by a wave number vector 21, 22 and a frequency o~g. The basic flow in the problem is a superposition of the PoiseuiUe flow and a periodic component that corresponds to the wave excitation of the wall. The aim of the study is to examine the susceptibility of this flow to transition. The problem is approached through studying the stability characteristics of the basic flow with respect to small disturbances. The theoretical framework for this purpose is Floquet theory. The solution procedure for solving the eigenvalue problem is the spectral collocation method. Preliminary results showing the influence of the amplitude and the wave number of the wall excitation on the stability boundary of the flow are presented.

A numerical study of flow through wavy-walled channels

“…the streamfunction method of Sobey [4] Tsangaris and Leiter [2], is that the pressure and the phase information are obtained directly. For further details see Reference [20]. Both the finite difference method and the collocation method produced the same results for calculation of flow through a wavy channel at a Reynolds number of 150.…”

“…The underlying principle of the algorithm is then to piece together the intermediate (orthoganalized) solutions, defined on the various subintervals, to obtain the desired solution. The details are given in Reference [20]. Sengupta [21] has also applied a similar procedure in the study of boundary layer flow over rigid and moving wavy surfaces using a wave-following co-ordinate system.…”

“…Numerical experiments [20] indicated that as the Reynolds number is increased, the amplitude functions vary rapidly close to the boundaries. While using the finite difference method, sufficient points are needed for discretization of the domain closer to the wall.…”

“…Both the finite difference method and the collocation method produced the same results for calculation of flow through a wavy channel at a Reynolds number of 150. Numerical experiments [20] indicated that as the Reynolds number is increased, the amplitude functions vary rapidly close to the boundaries. While using the finite difference method, sufficient points are needed for discretization of the domain closer to the wall.…”