Wall-models for large eddy simulation based on a generic additive-filter formulation.

摘要

Based on the philosophy of only resolving the large scales of turbulent motion, Large Eddy Simulation (LES) has demonstrated potential to provide high-fidelity turbulence simulations at low computational cost. However, when the scales that control the turbulence in a particular flow are not large, LES has to increase significantly its computational cost to provide accurate predictions. This is the case in wall-bounded flows, where the grid resolution required by LES to resolve the near-wall structures is close to the requirements to resolve the smallest dissipative scales in turbulence. Therefore, to reduce this demanding requirement, it has been proposed to model the near-wall region with Reynolds-Averaged Navier-Stokes (RANS) models, in what is known as hybrid RANS/LES approach.;In this work, the mathematical implications of merging two different turbulence modeling approaches are addressed by deriving the exact hybrid RANS/LES Navier-Stokes equations. These equations are derived by introducing an additive-filter, which linearly combines the RANS and LES operators with a blending function. The equations derived with the additive-filter predict additional hybrid terms, which represent the interactions between RANS and LES formulations. Theoretically, the prediction of the hybrid terms demonstrates that the hybridization of the two approaches cannot be accomplished only by the turbulence model equations, as it is claimed in current hybrid RANS/LES models.;The importance of the exact hybrid RANS/LES equations is demonstrated by conducting numerical calculations on a turbulent flat-plate boundary layer. Results indicate that the hybrid terms help to maintain an equilibrated model transition when the hybrid formulation switches from RANS to LES. Results also indicate, that when the hybrid terms are not included, the accuracy of the calculations strongly relies on the blending function implemented in the additive-filter. On the other hand, if the exact equations are resolved, results are only weakly affected by the characteristics of the blending function. Unfortunately, for practical applications the hybrid terms cannot be exactly computed. Consequently, a reconstruction procedure is proposed to approximate these terms. Results show, that the model proposed is able to mimic the exact hybrid terms, enhancing the accuracy of current hybrid RANS/LES approaches.;In a second effort, the Two Level Simulation (TLS) approach is proposed as a nearwall model for LES simulations. Here, TLS is first extended to compressible flows by deriving the small-scale equations required by the model. The new compressible TLS formulation, is validated simulating the flow over a flat-plate turbulent boundary layer. Overall, results are found in reasonable agreement with experimental data and LES calculations. Here, issues related with the integration criteria of the TLS small-scale equations are commented. Finally, TLS is implemented in the additive-filter formulation by replacing the RANS operator with the TLS large-scale operator. The new hybrid TLS/LES approach, is evaluated on the turbulent boundary layer case, in general, results are found in good agreement with experimental data and LES calculations. Here, the dependency of hybrid TLS/LES formulation on the blending function is similar to the hybrid RANS/LES approach when the hybrid terms are neglected. However, contrary to the hybrid RANS/LES case, including the hybrid terms in the TLS/LES formulation does not seem to improve the predictions. The low impact of the hybrid terms in the accuracy of the calculations, is explained by the similarity exhibited between the large-scale TLS operator and the LES space filter. Here, both operators represent space filters, therefore, the difference between TLS and LES variables is almost negligible, reducing drastically the importance of the hybrid terms.