Large-eddy simulations of tip leakage and secondary flows in an axial compressor cascade using a near-wall turbulence model

Abstract

This paper reports on the application of unsteady Reynolds averaged Navier—Stokes (U-RANS) and hybrid large-eddy simulation (LES)/Reynolds averaged Navier—Stokes (RANS) methods to predict flows in compressor cascades using an affordable computational mesh. Both approaches use the ζ—f elliptic relaxation eddy-viscosity model, which for U-RANS prevails throughout the flow, whereas for the hybrid the U-RANS is active only in the near-wall region, coupled with the dynamic LES in the rest of the flow. In this ‘seamless’ coupling the dissipation rate in the k-equation is multiplied by a grid-detection function in terms of the ratio of the RANS and LES length scales. The potential of both approaches was tested in several benchmark flows showing satisfactory agreement with the available experimental results. The flow pattern through the tip clearance in a low-speed linear cascade shows close similarity with experimental evidence, indicating that both approaches can reproduce qualitatively the tip leakage and tip separation vortices with a relatively coarse computational mesh. The hybrid method, however, showed to be superior in capturing the evolution of vortical structures and related unsteadiness in the hub and wake regions.

Keywords

hybrid large-eddy simulation/Reynolds averaged Navier—Stokes unsteady Reynolds averaged Navier—Stokes turbomachinery flows

Get full access to this article

View all access options for this article.

References

Hanjalić

Jakirlić

, Contribution towards the second moment closure modelling of separating turbulent flows. Comput. Fluids, 27(2), 1998, 137–156.

Borello

Hanjalić

Rispoli

, Computation of tip-leakage flow in a linear compressor cascade with a second-moment turbulence closure. Int. J. Heat Fluid Flows, 28(4), 2007, 587–601.

Gerolymos

G. A.

Vallet

, Robust implicit multigrid Reynolds-stress model computation of 3d turbomachinery flows. J. Fluids Eng., 129(9), 2007, 1212–1227.

Davidson

Dahlström

, Hybrid LES-RANS: An approach to make LES applicable at high Reynolds number. Int. J. Comput. Fluid Dyn., 19, 2005, 415–427.

Borello

Delibra

Hanjalić

Rispoli

, Scrutinizing a seamless hybrid LES/RANS approach for turbomachinery applications. In Proceedings of the Third Symposium on Hybrid RANS-LES methods, Gdansk, Poland, 10-12 June 2009.

Hadziabdic

, LES of flow and heat transfer in a round impinging jet. PhD Thesis, Delft University of Technology, Delft, The Netherlands, 2006.

Durbin

P. A.

, Near wall turbulence closure modelling without damping functions. Theor. Comput. Fluid Dyn., 3, 1991, 1–13.

Hanjalić

Popovac

Hadziabdic

, A robust near-wall elliptic relaxation eddy viscosity turbulence model for CFD. Int. J. Heat Fluid Flows, 25, 2004, 1047–1051.

Delibra

Borello

Hanjalić

Rispoli

, U-RANS of flow and endwall heat transfer in a pinned passage relevant to gas turbine blade cooling. Int. J. Heat Fluid Flows, 30, 2009, 549–560.

10.

Tang

, Measurements of the tip-gap turbulent flow structure in a low-speed compressor cascade. PhD Dissertation, Virgina Polytechnic Institute and State University, 2004.

11.

Ničeno

Hanjalić

, Unstructured large-eddy- and conjugate heat transfer simulations of wall-bounded flows. In Modeling and simulation of turbulent heat transfer, (Developments in Heat Transfer Series) (Eds Faghri

Sunden

), 2004, pp. 1–40 (Wessex Institute of Technology Press 2004).

12.

Muthanna

Devenport

W. J.

, Wake of a compressor cascade with tip gap, part 1: Mean flow and turbulent structure. AIAA J., 42(11), 2004, 2320–2331.