Abstract

In order to predict unsteady flow fields one can use the Reynolds Averaged Navier-Stokes Equations (RANS) with a statistical turbulence model or Large Eddy Simulation (LES) in conjunction with a subgrid-scale model. Since the flow field in rotating machinery, internal combustion engines etc., is often strongly three-dimensional and unsteady, the calculation with LES and RANS are similar in terms of cpu-time providing the grid resolutions are similar. The turbulence models used with RANS have been designed in order to capture all the turbulence effects since a steady state calculation cannot resolve any fluctuation. If one wants to perform an unsteady calculation, then a fraction of the turbulent fluctuations is already resolved by the numerical scheme, depending on the temporal and spatial resolution, and therefore the turbulence model must only model the unresolved part of the turbulence. The standard turbulence models used today cannot be used for such simulations, since they model always the whole turbulence spectrum. On the other hand, the subgrid-scale models for LES model only a fraction of the turbulent spectrum, but they fail to model the turbulence in the limit of high cell Reynolds numbers (Speziale, 1998). A new adaptive turbulence model based on the popular two-equation models will be proposed which can be used for all cell Reynolds numbers in the unsteady case. It has the property that it reduces to a Direct Numerical Simulation (DNS) if the temporal and spatial resolution of the flow field is in the order of the Kolmogorov micro scale. If one does not resolve fluctuations (steady state) then the model reduces to a standard two-equation model. In between these two extremes it automatically adapts itself to the resolved turbulent fluctuations.

Highlights

  • Turbulentows are characterized by a wide range of length- and time-scales for Reynolds numbers of practical interest

  • In order to achieve this, we propose to split the total turbulent kinetic energy k and the total dissipation rate of

  • Twoow ®elds have been investigated in order to study the new turbulence model and compared with the standard turbulence models

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Summary

Introduction

Turbulentows are characterized by a wide range of length- and time-scales for Reynolds numbers of practical interest. The statistical approach uses the idea of a decomposition in mean values anductuations. Inserting this decomposition into the Navier ± Stokes equations yields the averaged equations plus the unknown Reynolds stresses which have to be modeled. For a DNS one needs to resolve all length- and time-scales, this means performing a time-dependent and three-dimensional calculation with very high temporal and spatial resolution (Piomelli, 1997). In between the statistical approach and the direct approach stands LES which is still threedimensional and time-dependent. The instantaneousow ®eld is decomposed, but into a resolved and an unresolved part with an characteristic space and time ®lter. LES still requires fairly ®ne meshes, but with the help

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