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Linear stability of a Berman flow in a channel partially filled with a porous medium Deng, Chuntao


In this thesis, the coupled flow of a Newtonian fluid both above and through a porous medium is considered. This work was motivated from a pulp and paper application, namely twin-wire forming. In the fluid-only region, the two-dimensional flow field is governed by the Navier-Stokes equation. In the porous region, the flow field is governed by the Brinkman-extended Darcy law relationship. Inertial terms are retained in both regions and the interface conditions between the two domains are those as outlined by Ochoa- Tapia and Whitaker (Int. J. Heat Mass Transfer 38, 2635 1995). The model equations were solved using two independent methods. In the first method we develop a similarity transform and reduce the governing equations to two, coupled, non-linear ordinary differential equations to form a three-point boundary value problem. This was solved numerically and validated analytically by examining asymptotic cases. Three characteristic solutions were identified and the stability of each was examined by the method of normal modes. In the second numerical approach, the governing equations were re-posed as a one-domain problem, using the procedure outlined by Basu and Khalili (Phys. Fluids 11, 1031 1999), so that the conditions at the interface need not be considered. The resulting equation was solved directly, in primitive variable form, using a finite volume formulation. Finally, an experimental device was constructed to compare to the numerical predictions. Eight test cases were performed, using two different porous media, in which the velocity profile of the fluid was measured using pulsed ultrasound doppler anemometry (PUDA). Good agreement was found between the similarity numerical predications and the experimental measurements.

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