Effects of the control parameters on the stability of a laminar boundary layer on a porous flat plate

• Autorzy: Lihonou T. F. , Monwanou A. V. , Miwadinou C. H. , Chabi Orou J. B.

Identyfikatory

DOI

10.2478/ijame-2021-0053

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

permeability parameter; small Reynolds number; linear temporal stability; boundary layer; modified Orr-Sommerfeld equation; spectral collocation method

PL

przepuszczalność; liczba Reynoldsa; metoda kolokacji

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mechanics and Engineering
• Rocznik: 2021
• Tom: Vol. 26, no. 4
• Strony: 113--127
• Opis fizyczny: Bibliogr. 22 poz., tab., wykr.

Twórcy

autor

Lihonou T. F.

• 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

autor

Monwanou A. V.

• 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

autor

Miwadinou C. H.

• 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
• Ecole Normale Supérieure de Natitingou (ENS), Université Nationale des Sciences, Technologies Ingénierie et Mathématiques (UNSTIM) d'Abomey, BENIN

autor

Chabi Orou J. B.

• 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

Bibliografia

• [1] Wartemann V., Wagnerb A., Kuhn M., Eggers T. and Hannemann K. (2015): Passive hypersonic boundary layer transition control using an ultrasonically absorptive coating with random microstructure: Computational analysis based on the ultrasonic absorption properties of carbon-carbon.– Procedia IUTAM, vol.14, pp.413-422.
• [2] Wang Y., Li S. and Yang X. (2016): Numerical investigation of the passive control of cavity flow oscillations by a dimpled non-smooth surface.– Applied Acoustics, vol.111, pp.16-24.
• [3] Simonn B., Nemitz T., Rohlfing J., Fischer F., Mayer D. and Grundmann S. (2015): Active flow control of laminar boundary layers for variable flow conditions.– International Journal of Heat and Fluid Flow, vol.56, pp.344-354.
• [4] Svorcan J., Stupar S., Trivkovic S., Petrasinovic N. And Ivanov T. (2014): Active boundary layer control in linear cascades using CFD and artificial neural networks.– Aerospace Science and Technology, vol.39, pp.243-249.
• [5] Ming-Liang, Jian-Zhong L. and Fu-Tang X. (2007): On the hydrodynamic stability of a particle-laden flow in growing flat plate boundary layer.– J. Univ. Sci A: App. Ph. Eng., vol.8, No.2, pp.275-284, DOI:0.1631/jzus.2007.A0275.
• [6] Seth G.S., Raj Nandkeolyar and Ansari Md.S. (2010): Hartmann flow in a rotating system in the presence of inclined magnetic field with Hall effects.– Tamkang Journal of Science and Engineering, vol.13, No.3, pp.243-252.
• [7] HinviL.A., Monwanou V.A. and Chabi Orou J.B. (2014): Linear stability analysis of fluid flow between two parallel porous stationary plates with small suction and injection.– The African Review of Physics, vol.9, pp.115-121.
• [8] Monwanou A.V., Hinvi A.L., Miwadinou H.C. and Chabi Orou J.B. (2017): A new approach for the stability analysis in hydromagnetic Couette flow.– Journal of Applied Mathematics and Physics, vol.5, pp.1503-1514. https://doi.org/10.4236/jamp.2017.57123.
• [9] Hatziavramidisand D. and Ku H.C. (1985): An integral Chebyshev Expansion Method for boundary-value problems of O.D.E. type.– Comp. Maths. with Appls., vol.11, No.6, pp.581-586. DOI: 10.1016/0898-1221(85)90040-9.
• [10] Nasr H. and El-Hawary H.M. (1991): A Chebyshev method for the solution of boundary value problems.– International Journal of Computer Mathematics, vol.40, No.3-4, pp.251-258, DOI:10.1080/00207169108804019.
• [11] Laouer A., Mezaache E. and Laouar S. (2016): Study of the effect of parietal suction and blowing on the stability of laminar external flow.– International Journal of Heat and Technology, vol.34, No.2, pp.302-310.
• [12] Laouer A., Mezaache E. and Laouar S. (2016): Influence of surface mass transfer on the stability of forced convection flow over an horizontal flat plate. -Computational Thermal Sciences, Begell House, vol.8, No.4, pp.355-369.
• [13] Dongarra J.J., Straughan B. and Walker D.W. (1996): Chebyshev tau-QZ algorithm methods for calculating spectra of hydrodynamic stability problems.– Appl. Numer. Math., vol.22, pp.399-434.
• [14] Melenk J.M., Kirkner N.P. and Schwab V. (2000): Spectral Galerkin discretization for hydrodynamic stability problems.– Comput., vol.65, pp.97-118.
• [15] Reddy S. C., Schmid P.J. and Henningson D. (1993): Pseudospectra of Orr-Sommerfeld operator.– SIAM J. Appl. Math., vol.53, pp.15-47.
• [16] Hifdi A., Touhami M.O. and Naciri J.K. (2004): Channel entrance flow and its linear stability.– J. Stat. Mech.: Theory Exp., vol.2004, p.06003.
• [17] Peyret R. (2002): Spectral Methods for Incompressible Viscous Flow.– Applied Mathematical Sciences, Springer Verlag, New York.
• [18] Zebib A. (1984): A Chebyshev method for the solution of boundary value problems.– J. Comput. Phys., vol.53, pp.443-455.
• [19] Boyd J.P. (2001): Chebyshev and Fourier Spectral Methods.– Dover Publications, Mineola, NY.
• [20] Venkatasobbaiah K. and Sengupta T.K. (2009): Mixed convection flow past a vertical plate: Stability analysis and its direct simulation.– Int. J. Therm. Sci., vol.48, pp.461-474.
• [21] Boiko A.V., Dovgal A.V., Grek G.R. and Kozlov V.V. (2012): Physics of Transitional Shear Flows.– Instability and Laminar Turbulent Transition in Incompressible Near-Wall Shear Layers.– Springer, New York.
• [22] Motsa S.S., Marewo G.T., Sibanda P. and Shateyi S. (2011): An improved spectral homotopy analysis method for solving boundary layer problems.– Boundary Value Problems, Springer Open Journal, Article No.3.

Uwagi

PL

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023)