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High Reynolds number Navier–Stokes solutions and boundary layer separation induced by a rectilinear vortex

Authors
Journal
Computers & Fluids
0045-7930
Publisher
Elsevier
Publication Date
Volume
52
Identifiers
DOI: 10.1016/j.compfluid.2011.08.022
Keywords
  • Boundary Layer
  • Unsteady Separation
  • Navier Stokes Solutions
  • Prandtl’S Equation
  • High Reynolds Number Flows

Abstract

Abstract We compute the solutions of Prandtl’s and Navier–Stokes equations for the two dimensional flow induced by a rectilinear vortex interacting with a boundary in the half plane. For this initial datum Prandtl’s equation develops, in a finite time, a separation singularity. We investigate the different stages of unsteady separation for Navier–Stokes solution at different Reynolds numbers Re = 10 3–10 5, and we show the presence of a large-scale interaction between the viscous boundary layer and the inviscid outer flow. We also see a subsequent stage, characterized by the presence of a small-scale interaction, which is visible only for moderate-high Re numbers Re = 10 4–10 5. We also investigate the asymptotic validity of boundary layer theory by comparing Prandtl’s solution to Navier–Stokes solutions during the various stages of unsteady separation.

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