Numerical Simulation of the Separated Fluid Flows at Large Reynolds Numbers

Summary

The variety of the flow regimes (the steady separated, the periodical separated — “Karman vortex street”, the unsteady turbulent) and its characteristic peculiarities (the separation and reattachment points, the second separation, boundary layer, instability of the shear mixing layer etc.) require the construction of the effective numerical methods, which will be able to simulate adequately the considered flows.

MERANGE=SMIF — the Splitting on the physical factors Method for Incompressible Fluid [1] is used for the calculations of the steady and unsteady fluid flows past a circular cylinder in wide range of Reynolds number (10⁰ < Re < 10⁶). The finite-difference scheme of this method is of the second order of accuracy in space variables, have the minimal scheme viscosity and is monotonic. The usage of the Navier-Stokes equations with the corresponding transformation of Cartesian coordinates allows to make the calculations by one algorithm as in boundary layer as out of it. The method allows to get the calculations at Re=∞ and to simulate D’Alambert’s paradox. Some results on classical problem — flow around circular cylinder for a wide range of Reynolds numbers are discussed. The crisis of total drag coefficient and sharp rising of Strouhal number are simulated numerically (without any turbulence models) for critical Reynolds numbers (Re≈4×10⁵), which is in good agreement with experimental data.