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The paper discusses possibilities for refinements of conventional "equilibrium" second-moment turbulence closure models, aimed at improving model performances in predicting turbulent flows of greater complexity. In focus are the invariant modelling of the low-Re-number and wall proximity effects, as well as extra strain-rates and control of the turbulence length-scale. In addition to satisfying most of the basic physical constraints, the main criterion for model validation was the quality of reproduction of flow and turbulence details, particularly, in the vicinity of a solid wall, in a broad variety of non-equilibrium flows featured by different phenomena. It is demonstrated that the new model, which includes several new modifications, but also some proposed in the past, can satisfactorily reproduce a range of attached and separating flows with strong time-or space-variations or abrupt changes of boundary conditions. Cases considered cover a wide range of Re-numbers involving in some cases also the laminar-to-turbulent or reverse transition.

Using a second moment closure, analytical solutions for homogeneous turbulence subjected to periodic compression-dilatation strains show that both the characteristic turbulence frequency and turbulence kinetic energy eventually decay, irrespective of the initial turbulence level, anisotropy of the stress field, or Reynolds number. The eddy-viscosity models give erroneous results because of the artificial positive generation of turbulence energy during both the compression and expansion phase. The first observation results from the phase lag between periodic strain rate and stresses introduced by the exact production term in the second moment closure, whereas the eddy-viscosity model synchronizes the stresses with the strain rate, resulting in an overestimation of turbulence generation. The above findings are illustrated by analytical solutions, as well as by numerical solutions of in-cylinder turbulence, using the k−ε eddy-viscosity and the second-moment closure models. The analysis and simulations support the conjecture that turbulence submitted to cyclic strains should always finally decay.

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