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Large Eddy Simulation of transitional flows in rotor/stator cavity

Tuliszka-Sznitko E., Zielinski A., Majchrowski W.

Archives of Mechanics

2009

Vol. 61, nr 2

95-120

An algorithm for the Large Eddy Simulation, with subgrid modelling based on the spectral Chebyshev-Fourier approximation, is developed for the investigation of 3D turbulent and transitional non-isothermal flows within a rotor/stator cavity. In LES we use a version of the dynamic Smagorinsky eddy viscosity model in which the Smagorinsky coefficient at a given position x depends on the history of the flow along the fluid particle pathline. Computations are based on the efficient pseudo-spectral Chebyshev-Fourier method (S. HUGUES, A. RANDRIAMAMPIANINA, An improved projection scheme applied to pseudospectral methods for the incompressible Navier-Stokes equations, Int. J. Numer. Methods Fluids, 28, 501, 1998). To demonstrate the effectiveness of the proposed algorithm, computations were performed for the cavity of aspect ratio L = 5 and results were compared favorably with the experimental data taken from literature.

Inviscid instability of the hyperbolic-tangent velocity profile-spectral "tau" solution

Bogusławski A.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

2001

Vol. 5, No 2

155-164

The paper presents a spectral solution of the Rayleigh equation for the case of parallel, free shear layer with the hyperbolic-tangent mean velocity profile. The expansion of the eigenfunction into the Chebyshev polynomial series allowed transformation of the differential eigenvalue problem into the general algebraic one. The standard algebraic eigenvalue problem was obtained by the use of Gary & Helgasson transformation. The results were compared with the shooting method. Although the calculations were carried out in order to validate the method, some additional study of the velocity ratio and momentum thickness influence on the temporal eigenmode growth rate was also performed.