T, Praveen and Eswaran, Vinayak
(2017)
Transition to asymmetric flow in a symmetric sudden expansion: Hydrodynamics and MHD cases.
Computers and Fluids, 148.
pp. 103-120.
ISSN 0045-7930
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Abstract
Low Reynolds number planar hydrodynamic and MHD flow of an incompressible fluid through a 2-D symmetric sudden expansion is numerically studied in the present work with specific attention to the bifurcation characteristics. Hydrodynamic (non-MHD) flow is first considered. The effect of a homogeneous stream-wise magnetic field on the transition characteristics is then studied under the Quasi-static approximation of Magnetohydrodynamics, applicable, when the induced magnetic field is neglected. The Reynolds number of the flows is limited to Re ≤ 100 and selected values of the Interaction parameter (N) measuring the relative strength of the Lorentz force over the inertia in the range N ∈ [0,100] are considered. The temporal growth rate of the transverse velocity component at the location of the first (steady-state) maximum along the symmetry-line is shown to be a more informative and a more easily obtainable measure of asymmetry over other steady-state measures usually used in the literature. This growth rate is found to be independent of the symmetric initial conditions used for the computation and can be exploited in faster evaluation of the critical Reynolds number for the symmetric to asymmetric flow transition. An increase in the strength of the applied magnetic field N is found to have a stabilizing influence in general, reducing the growth rates of asymmetry. The (two equally sized) recirculation zone lengths of the steady-state symmetric solution are found to scale linearly with the Reynolds number (Re) for a fixed strength of the applied magnetic field and directly proportional to ReN and N for Re << N and Re >> N cases respectively.
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