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ORIGINAL PAPER
Effects of the Control Parameters on the Stability of a Laminar Boundary Layer on a Porous Flat Plate
1
Laboratoire de Mécanique des Fluides, de la Dynamique Nonlinéaire et de la Modélisation des Systèmes, Biologiques (LMFDNMSB), Institut de Mathématiques et de Sciences Physiques(IMSP)/UAC, BP: 613 Porto-Novo, Benin
2
Ecole Normale Supérieure de Natitingou (ENS), Université Nationale des Sciences, Technologies, Ingénierie et Mathématiques (UNSTIM) d’Abomey, Benin
Online publication date: 2021-12-07
Publication date: 2021-12-01
International Journal of Applied Mechanics and Engineering 2021;26(4):113-127
KEYWORDS
permeability parametersmall Reynolds numberlinear temporal stabilityboundary layermodified Orr-Sommerfeld equationspectral collocation method
ABSTRACT
This work is devoted to the analysis of the linear temporal stability of a laminar dynamic boundary layer on a horizontal porous plane plate. The basic flow is assumed to be laminar and two-dimensional. The basic flow velocity profiles are obtained by numerically solving the Blasius equation using the Runge-Kutta method. The perturbations of these basic solutions are expressed in the form of three-dimensional Tollmien-Schlichting waves. The formulation of the stability problem leads to the Orr-Sommerfeld equation modified by the permeability parameter (Darcy number) and the small Reynolds number. This equation is given in a general form which can be applied to the Chebyshev domain and the boundary layer domain and solved numerically using the Chebyshev spectral collocation method. The marginal stability diagrams, the critical Reynolds numbers and the eigenvalue spectra are obtained for different values of the parameters which have modified the stability equation. Numerical solutions indicate the importance of the effect of these parameters on the flow stability characteristics.
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