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Specified discharge velocity models for numerical simulations of laminar vortex rings

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Abstract

We numerically and theoretically investigate the flow generated at the exit section of a piston/cylinder arrangement that is generally used in experiments to produce vortex rings. Accurate models for the velocity profile in this section (also called specified discharge velocity, SDV models) are necessary in (i) numerical simulations of laminar vortex rings that do not compute the flow inside the cylinder and (ii) in slug-models that provide a formula for the total circulation of the flow. Based on the theoretical and numerical analysis of the flow evolution in the entrance region of a pipe, we derive two new and easy to implement SDV models. A first model takes into account the unsteady evolution of the centerline velocity, while the second model also includes the time variation of the characteristics of the boundary layer at the exit plane of the vortex generator. The models are tested in axisymmetric direct numerical simulations of vortex rings. As distinguished from classical SDV model, the new models allow to accurately reproduce the characteristics of the flow. In particular, the time evolution of the total circulation is in good agreement with experimental results and previous numerical simulations including the vortex generator. The second model also provides a more realistic time evolution of the vortex ring circulation. Using the classical slug-model and the new correction for the centerline velocity, we finally derive a new and accurate analytical expression for the total circulation of the flow.

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Authors and Affiliations

  1. Laboratoire Jacques-Louis Lions, UPMC Univ Paris 06, UMR 7598, 75005, Paris, France

    Ionut Danaila

  2. Laboratoire Jacques-Louis Lions, CNRS, UMR 7598, 75005, Paris, France

    Ionut Danaila

  3. Faculty of Aerospace Engineering, Politehnica University, Calea Grivitei 132, Bucharest, Romania

    Claudiu Vadean & Sterian Danaila

Authors
  1. Ionut Danaila
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  2. Claudiu Vadean
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  3. Sterian Danaila
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Correspondence to Ionut Danaila.

Additional information

Communicated by M. Y. Hussaini

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Danaila, I., Vadean, C. & Danaila, S. Specified discharge velocity models for numerical simulations of laminar vortex rings. Theor. Comput. Fluid Dyn. 23, 317–332 (2009). https://doi.org/10.1007/s00162-009-0142-5

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  • DOI: https://doi.org/10.1007/s00162-009-0142-5

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