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Technique for the numerical analysis of the riblet effect on temporal stability of plane flows

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Abstract

Problems related to the temporal stability of laminar viscous incompressible flows in plane channels with ribbed walls are formulated, justified, and numerically solved. A new method is proposed whereby the systems of ordinary differential and algebraic equations obtained after a spatial approximation are transformed into systems of ordinary differential equations with a halved number of unknowns. New algorithms that effectively calculate stability characteristics, such as the critical Reynolds numbers, the maximum amplification of the disturbance kinetic energy density, and optimal disturbances are described and substantiated. The results of numerical experiments with riblets similar in shape to those used in practice are presented and discussed.

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Authors and Affiliations

  1. Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences, Institutskaya ul. 4/1, Novosibirsk, 630090, Russia

    A. V. Boiko

  2. Institute of Numerical Mathematics, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991, Russia

    Yu. M. Nechepurenko

Authors
  1. A. V. Boiko
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  2. Yu. M. Nechepurenko
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Correspondence to Yu. M. Nechepurenko.

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Original Russian Text © A.V. Boiko, Yu.M. Nechepurenko, 2010, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2010, Vol. 50, No. 6, pp. 1109–1125.

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Boiko, A.V., Nechepurenko, Y.M. Technique for the numerical analysis of the riblet effect on temporal stability of plane flows. Comput. Math. and Math. Phys. 50, 1055–1070 (2010). https://doi.org/10.1134/S0965542510060114

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  • DOI: https://doi.org/10.1134/S0965542510060114

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