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DEVELOPMENT OF A ROBUST ELLIPTIC-BLENDING TURBULENCE MODEL FOR NEAR-WALL, SEPARATED AND BUOYANT FLOWS
[Thesis]. Manchester, UK: The University of Manchester; 2012.
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Abstract
The thesis introduces a new version of an elliptic-blending low-Reynolds-number eddy-viscosity Reynolds-averaged Navier Stokes model. It is a model intended to be implemented in an industrial solver. It will be argued that there is still room for such a simple model, though eddy-viscosity models must rely on developments specificallymade for higher order formulations. It is the aim of the v2 − f model to integrate elements of Reynolds-stress modelling developments into a simpler formulation, but the former paradoxically suffers from numerical stiffness, which kept it out of reachof industry researchers everyday simulations. The v2 − f formulation endeavours to reproduce the near-wall asymptotic behaviour of the turbulent quantities, as sounder alternative to empirical damping functions, and the required near-wall balance of small terms represents a numerical challenge.The present work first provides a comprehensive review of v2 − f developments proposed over the past twenty years, and the different remedies for the numericalstiffness linked to the original formulation. The review focuses on ten v2 −f variants, proposed between 1991 and 2006, whose behaviour is compared in some fundamental flows: the channel flow for five different Reynolds numbers, the asymptotic case of the logarithmic layer at infinite Reynolds number and the case of a flow with homogeneous sheared turbulence.Based on the conclusions of the review, the thesis proposes new developments. Firstly, the derivation of a new model, namely the φ − α model, is introduced. It relies on the resolution of two non-dimensional variables: φ represents the wall-normal anisotropy and α is a wall-proximity sensor. It is argued that only this formulation can address the numerical problems already mentioned without altering the predictions. Secondly, additional upgrades of the φ − α model are proposed to correct the dissipation rate equation. The aim is to improve the model behaviour in some specific regions of a boundary layer, by isolating some viscous terms and by improving the representation of turbulent transport at the edge of a boundary layer. Final developments are combined in a new model, the BL-v2/k model.The φ − α and BL-v2/k models are then validated for a set of two pressure induced separated flows and two buoyant flows, and beneficial effects of the proposed developments on the predictions are demonstrated. The numerical properties of theconvergency of the BL-v2/k model are also reported at the end of this work.