Computation of Unsteady and Non-equilibrium Turbulent Flows Using Reynolds Stress Transport Models

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Abstract

In this work the predictive capability of a number of Reynolds stress transport(RST) models was first tested in a range of non-equilibrium homogeneous flows,comparisons being drawn with existing direct numerical simulation (DNS) resultsand physical measurements. The cases considered include both shear and nor-mally strained flows, in some cases with a constant applied strain rate, and inothers where this varied with time. Models were generally found to perform well in homogeneous shear at lowshear rates, but their performance increasingly deteriorated at higher shear rates.This was attributed mainly to weaknesses in the pressure–strain rate models,leading to over–prediction of the shear stress component of the stress anisotropytensor at high shear rates. Performance in irrotational homogeneous strains was generally good, and wasmore consistent over a much wider range of strain rates. In the experimentalplane strain and axisymmetric contraction cases, with time-varying strain rates,there was evidence of an accelerated dissipation rate generation. Significant im-provement was achieved through the use of an alternative dissipation rate gen-eration term, Pε , in these cases, suggesting a possible route for future modellinginvestigation. Subsequently, the models were also tested in the inhomogeneous case of pul-sating channel flow over a wide range of frequencies, the reference for these casesbeing the LES of Scotti and Piomelli (2001). A particularly challenging featurein this problem set was the partial laminarisation and re-transition that occurredcyclically at low and, to a lesser extent, intermediate frequencies. None of themodels tested were able to reproduce correctly all of the observed flow features,and none returned consistently superior results in all the cases examined. Finally, models were tested in the case of a plane jet interacting with a rect-angular dead-end enclosure. Two geometric configurations are examined, corre-sponding a steady regime, and an intrinsically unsteady regime in which periodicflow oscillations are experimentally observed (Mataoui et al., 2003). In the steadycase generally similar flow patterns were returned by the models tested, with somedifferences arising in the degree of downward deflection of the impinging jet, whichin turn affected the level of turbulence energy developing in the lower part of thecavity. In the unsteady case, only two of the models tested, a two-equation k−εmodel and an advanced RST model, correctly returned purely periodic solutions.The other two RST models, based on linear pressure–strain rate terms, returnedunsteady flow patterns that exhibited complex oscillations with significant cycle-to-cycle variations. Unfortunately, the limited availability of reliable experimentaldata did not allow a detailed quantitative examination of model performance.

Keyword(s)

Non-equilibrium Turbulent Flows; Reynolds Stress Transport; Second Moment Closure; Turbulence Modelling; URANS

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