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Use of natural instabilities for generation of streamwise vortices in a laminar channel flow

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Abstract

An analysis of pressure-gradient-driven flows in channels with walls modified by transverse ribs has been carried out. The ribs have been introduced intentionally in order to generate streamwise vortices through centrifugally driven instabilities. The cost of their introduction, i.e. the additional pressure losses, have been determined. Linear stability theory has been used to determine conditions required for the formation of the vortices. It has been demonstrated that there exists a finite range of rib wave numbers capable of creating vortices. Within this range, there exists an optimal wave number which results in the minimum critical Reynolds number for the specified rib amplitude. The optimal wave numbers marginally depend on the rib positions and amplitudes. As the formation of the vortices can be interfered with by viscosity-driven instabilities, the critical conditions for the onset of such instabilities have also been determined. The rib geometries which result in the vortex formation with the smallest drag penalty and without interference from the viscosity-driven instabilities have been identified.

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Authors and Affiliations

  1. Department of Mechanical and Materials Engineering, The University of Western Ontario, London, ON, N6A 5B9, Canada

    H. V. Moradi & J. M. Floryan

  2. Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1, Singapore, 117576, Singapore

    A. C. Budiman

Authors
  1. H. V. Moradi
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  2. A. C. Budiman
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  3. J. M. Floryan
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Correspondence to H. V. Moradi.

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Communicated by Sergio Pirozzoli.

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Moradi, H.V., Budiman, A.C. & Floryan, J.M. Use of natural instabilities for generation of streamwise vortices in a laminar channel flow. Theor. Comput. Fluid Dyn. 31, 233–250 (2017). https://doi.org/10.1007/s00162-016-0418-5

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  • DOI: https://doi.org/10.1007/s00162-016-0418-5

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