T-PITM: a consistent formulation for seamless RANS/TLES coupling

In the frame of inhomogeneous turbulence, a consistent formalism to seamlessly bridge LES and RANS must be based on temporal filtering. Such an approach is presented, the temporal-PITM, based on a transport equations for the subfilter-scales. In order to obtain a balance resolved/modelled energy consistent with the cutoff frequency imposed by the local mesh refinement, a dynamical subfilter-scale model is used

Modélisation de la turbulence par approches URANS et hybride RANS-LES. Prise en compte des effets de paroi par pondération elliptique.

The aim of this work is to take into account the natural large-scale unsteadiness in separated flows at a lower cost than a LES, and to model the wall effects on turbulence using second moment closures. Following Durbin's approaches, the elliptic blending model EB-RSM reproduces the non-local blocking effect of the wall, by solving a differential equation on the pressure term. The two-component limit of turbulence is well predicted in a channel flow. This model is applied to the backstep flow using URANS methodology. We have shown that the numerical errors at the step corner can be sufficient to excite the natural mode of the shear layer, leading to an unsteady solution. Actually, the solution is steady when the mesh is refined, suggesting that URANS is not reliable. Recently, Schiestel \& Dejoan have proposed the seamless hybrid model PITM. The coefficient C_{\e_2} of the dissipation equation becomes a function of the spectral cutoff, and the value C_{\e_1}=3/2 is deduced by these authors. We have given a more general formulation where the coefficient C_{\e_1} can take any value. To provide a more consistent formalism for the seamless hybrid models in near-wall flows, an approach based on temporal filtering is proposed. Finally, an elliptic blending model is developped in a hybrid framework, using PITM methodology. Results in channel flow are encouraging: the seamless transition from a RANS model near the wall, to a LES in the centre of the channel is observed. The energy transfer between modelled and resolved scales is well reproduced when the mesh is refined.L'objectif de ce travail est de prendre en compte les instationnarités naturelles à grande échelle dans les écoulements décollés et à un coût plus faible que la LES, tout en s'intéressant à la modélisation des effets de paroi par des modèles statistiques au second ordre. S'inspirant des approches de Durbin, le modèle à pondération elliptique EB-RSM reproduit l'effet non-local de blocage, en résolvant une équation différentielle sur le terme de pression. La limite à deux composantes de la turbulence est bien prédite en canal. Ce modèle est appliqué à la marche descendante, dans une approche URANS. Nous avons montré que les erreurs numériques peuvent être suffisantes pour exciter le mode le plus instable de la couche cisaillée, et aboutir à une solution instationnaire. La solution est stationnaire quand on raffine le maillage, rendant l'URANS peu fiable. Récemment, Schiestel \& Dejoan ont proposé le modèle hybride non-zonal PITM. Le coefficient C_{\e_2} de l'équation de la dissipation devient fonction de la coupure dans le spectre, et la valeur C_{\e_1}=3/2 est déduite par ces auteurs. Nous avons donné une formulation plus générale où la valeur de C_{\e_1} est quelconque. Pour offrir un formalisme plus cohérent aux modèles hybrides non-zonaux dans les écoulements de paroi, une approche basée sur un filtrage temporel est proposée. Enfin, l'adaptation du modèle EB-RSM dans un cadre hybride a été réalisée. Les résultats en canal sont encourageants : la transition continue d'un modèle RANS en proche paroi à une LES au centre du canal est mise en évidence. Le transfert d'énergie des échelles modélisées vers celles résolues est bien reproduit quand on raffine le maillage

Modélisation de la turbulence en situation instationnaire par approches URANS et hybride RANS-LES (prise en compte des effets de paroi par pondération elliptique)

L'objectif de ce travail est de prendre en compte les instationnarités à grande échelle dans les écoulements décollés et à un coût plus faible que la LES, tout en s'intéressant à la modélisation des effets de paroi par des modèles statistiques au second ordre. S'inspirant des approches de Durbin, le modèle à pondération elliptique EB-RSM reproduit l'effet non-local de blocage, en résolvant une équation différentielle sur le terme de pression. La limite à deux composantes de la turbulence est bien prédite en canal. Ce modèle est appliqué à la marche descendante, dans une approche URANS. Nous avons montré que les erreurs numériques peuvent être suffisantes pour exciter le mode le plus instable de la couche cisaillée, et aboutir à une solution instationnaire. La solution est stationnaire quand on raffine le maillage, rendant l'URANS peu fiable. Récemment, Schiestel & Dejoan ont proposé le modèle hybride non-zonal PITM. Le coefficient C 2 de l'équation de la dissipation devient fonction de la coupure spectrale. Nous avons montré que la valeur C 1=3/2, déduite par ces auteurs, découle d'une décomposition arbitraire des différents termes de l'équation de la dissipation. Une formulation plus générale est donnée où C 1 devient également fonction de la coupure. Pour offrir un formalisme plus cohérent aux modèles hybrides non-zonaux dans les écoulements de paroi, une approche basée sur un filtrage temporel est proposée. Enfin, l'adaptation du modèle EB-RSM dans un cadre hybride a été réalisée. Les résultats en canal sont très satisfaisants : la transition continue d'un modèle RANS en proche paroi à une LES au centre du canal est mise en évidence. Le transfert d'énergie des échelles modélisées vers celles résolues est bien reproduit quand on raffine le maillage.The aim of this work is to take into account the large-scale unsteadiness in separated flows at a lower cost than a LES, and to model the wall effects on turbulence using second moment closures. Following Durbin's approaches, the elliptic blending model EB-RSM reproduces the non-local blocking effect of the wall, by solving a differential equation on the pressure term. The two-component limit of turbulence is well predicted in a channel flow. This model is applied to the backstep flow using URANS methodology. We have shown that the numerical errors at the step corner can be sufficient to excite the natural mode of the shear layer, leading to an unsteady solution. Actually, the solution is steady when the mesh is refined, suggesting that URANS is not trustful. Recently, Schiestel & Dejoan have proposed the seamless hybrid model PITM. The coefficient C 2 of the dissipation equation becomes a function of the spectral cutoff. We have shown that the value C 1=3/2, given by these authors, results from an arbitrary decomposition of the different terms in the dissipation equation. A more general formulation is suggested, where C 1 also becomes a function of the cutoff. To provide a more consistent formalism for the seamless hybrid models in near-wall flows, an approach based on temporal filtering is proposed. Finally, an elliptic blending model is developped in a hybrid framework, using PITM methodology. Results in channel flow are very satisfying: the seamless transition from a RANS model near the wall, to a LES in the center of the channel is observed. The energy transfer between modelled and resolved scales is well reproduced when the mesh is refined.POITIERS-BU Sciences (861942102) / SudocSudocFranceF

A seamless hybrid RANS-LES model based on transport equations for the subgrid stresses and elliptic blending

International audienceThe aim of the present work is to develop a seamless hybrid Reynolds-averaged Navier-Stokes RANS large-eddy simulation LES model based on transport equations for the subgrid stresses, using the elliptic-blending method to account for the nonlocal kinematic blocking effect of the wall. It is shown that the elliptic relaxation strategy of Durbin is valid in a RANS steady as well as a LES context unsteady. In order to reproduce the complex production and redistribution mechanisms when the cutoff wavenumber is located in the productive zone of the turbulent energy spectrum, the model is based on transport equations for the subgrid-stress tensor. The partially integrated transport model PITM methodology offers a consistent theoretical framework for such a model, enabling to control the cutoff wavenumber c , and thus the transition from RANS to LES, by making the C 2 coefficient in the dissipation equation of a RANS model a function of c. The equivalence between the PITM and the Smagorinsky model is shown when c is in the inertial range of the energy spectrum. The extension of the underlying RANS model used in the present work, the elliptic-blending Reynolds-stress model, to the hybrid RANS-LES context, brings out some modeling issues. The different modeling possibilities are compared in a channel flow at Re = 395. Finally, a dynamic procedure is proposed in order to adjust during the computation the dissipation rate necessary to drive the model toward the expected amount of resolved energy. The final model gives very encouraging results in comparison to the direct numerical simulation data. In particular, the turbulence anisotropy in the near-wall region is satisfactorily reproduced. The contribution of the resolved and modeled fields to the Reynolds stresses behaves as expected: the modeled part is dominant in the near-wall zones RANS mode and decreases toward the center of the channel, where the relative contribution of the resolved part increases. Moreover, when the mesh is modified, the amount of resolved energy changes but the total Reynolds stresses remain nearly constant

Temporal filtering: A consistent formalism for seamless hybrid RANS–LES modeling in inhomogeneous turbulence

International audienceA consistent formalism is developed for seamless hybrid RANS-LES models in inhomogeneous, stationary flows, based on Eulerian temporal filtering. The issues of Galilean invariance of the filtering process and consistency with the Reynolds average are addressed. The similarity of the RANS and TLES equations suggests the use of the same form of model for the two limiting approaches. The inconsistency of the existing TLES models with the RANS limit leads to the choice of the opposite strategy: adapting a RANS model to the TLES limit. The method proposed to achieve this adaptation is the Temporal Partially Integrated Transport Model (TPITM), a temporal version of the spatial PITM. The applicability of the method is shown by performing channel flow simulations using transport equations for the subfilter stresses, derived from the Elliptic-Blending Reynolds-Stress RANS Model (EB-RSM). Finally, the fact that the temporal filter width can be implicitly defined by the associated spatial filter width suggests that most of the unsteady approaches used in everyday applications, such as DES, SAS, URANS, among others, can be regarded as temporally filtered approaches