Investigation of the stability of a plane-channel suspension flow with account for finite particle volume fraction |
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Authors: | S. A. Boronin |
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Affiliation: | (1) Department of Aerospace Engineering, Middle East Technical University, 06531 Ankara, Turkey;(2) Department of Mechanical Engineering, Middle East Technical University, 06531 Ankara, Turkey;(3) FORD Otosan, 41670 Kocaeli, Turkey |
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Abstract: | Within the framework of the two-fluid approach, a variant of a heterogeneous-medium model which takes into account a finite volume fraction of the inclusions and a small but finite phase velocity slip is proposed. The interphase momentum exchange is described by the Stokes force with the Brinkman correction for the finite particle volume fraction. The suspension viscosity depends on the particle volume fraction in accordance with the Einstein formula. Within the framework of the model constructed, a formulation of the problem of linear stability of plane-parallel two-phase flows is proposed. As an example, the stability of a channel suspension flow is considered. The system of equations for small disturbances with the boundary conditions is reduced to an eigenvalue problem for a fourth-order ordinary differential equation. Using the orthogonalization method, the dependence of the critical Reynolds number on the governing nondimensional parameters of the problem is studied numerically. It is shown that taking a finite volume fraction of the inclusions into account significantly affects the laminar-turbulent transition limit. |
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Keywords: | suspension stability neutral curve particle volume fraction critical Reynolds number orthogonalization method |
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