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Effect of a Boundary Layer on Cavity Flow

Author

Listed:
  • Yuriy N. Savchenko

    (Institute of Hydromechanics of the National Academy of Sciences of Ukraine, 8/4 Zhelybova Street, 03680 Kiev, Ukraine)

  • Georgiy Y. Savchenko

    (Institute of Hydromechanics of the National Academy of Sciences of Ukraine, 8/4 Zhelybova Street, 03680 Kiev, Ukraine)

  • Yuriy A. Semenov

    (Institute of Hydromechanics of the National Academy of Sciences of Ukraine, 8/4 Zhelybova Street, 03680 Kiev, Ukraine
    Department of Mechanical Engineering University College London, Gower Street, London WC1E 6BT, UK)

Abstract

Cavity flow past an obstacle in the presence of an inflow vorticity is considered. The proposed approach to the solution of the problem is based on replacing the continuous vorticity with its discrete form in which the vorticity is concentrated along vortex lines coinciding with the streamlines. The flow between the streamlines is vortex free. The problem is to determine the shape of the streamlines and cavity boundary. The pressure on the cavity boundary is constant and equal to the vapour pressure of the liquid. The pressure is continuous across the streamlines. The theory of complex variables is used to determine the flow in the following subregions coupled via their boundary conditions: a flow in channels with curved walls, a cavity flow in a jet and an infinite flow along a curved wall. The numerical approach is based on the method of successive approximations. The numerical procedure is verified considering a body with a sharp edge, for which the point of cavity detachment is fixed. For smooth bodies, the cavity detachment is determined based on Brillouin’s criterion. It is found that the inflow vorticity delays the cavity detachment and reduces the cavity length. The results obtained are compared with experimental data.

Suggested Citation

  • Yuriy N. Savchenko & Georgiy Y. Savchenko & Yuriy A. Semenov, 2020. "Effect of a Boundary Layer on Cavity Flow," Mathematics, MDPI, vol. 8(6), pages 1-16, June.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:6:p:909-:d:366959
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    Cited by:

    1. Lidong Li & Yan Xu & Mingming Ge & Zunce Wang & Sen Li & Jinglong Zhang, 2023. "Numerical Investigation of Cavitating Jet Flow Field with Different Turbulence Models," Mathematics, MDPI, vol. 11(18), pages 1-18, September.

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