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Fig. 1 : Elliptic Blending Reynolds-stress model (EB-RSM). Rotating channel flow.
Fig. 2 : Elliptic Blending Reynolds-stress model (EB-RSM). Jet impinging onto a heated, rotating disk.
Fig. 3 : Explicit algebraic stress model using elliptic relaxation. Couette-Poiseuille flow.
Fig. 4 : Algebraic flux model using elliptic relaxation. Mixing convection in a vertical channel.

Statistical modelling of turbulence (RANS)

The objective is to account for complex physical phenomena in statistical turbulence models, such as those due to

  • wall blockage (Fig. 1 to 4) (Manceau, 2015 ; Oceni, Manceau, Gatski 2010 ; Oceni, Manceau, Gatski 2008 ; Fadai-Ghotbi, Manceau, Borée J 2008 ; Gatski, Rumsey, Manceau 2007) ;
  • buoyancy (Fig. 4(Dehoux, Benhamadouche, Manceau, 2017 ; Dehoux, Lecocq, Benhamadouche, Manceau, Brizzi 2012 ; Dehoux, Benhamadouche, Manceau 2011 ; Dehoux, Benhamadouche, Manceau 2010 ; Lecocq, Manceau, Bournaud, Brizzi 2008 ) ;
  • rotation (Fig. 1 and 2) (Manceau, 2015 ; Manceau, Perrin, Hadžiabdić and Benhamadouche 2014 ; de Laage de Meux, Audebert,  Manceau 2011 ; Manceau 2008).

Since the purpose of this research activity is to propose models applicable to industrial configurations, a compromise is sought between accurate representation of the physics and numerical robustness.

The main originality of this work lies in the introduction of the elliptic relaxation method to account for the kinematic wall blockage. The complete model, due to P. Durbin, is rarely used due to numerical instabilities. A crucial step
consisted in the simplification of this model by replacing the elliptic relaxation approach by the elliptic blending approach (Manceau 2015 ; Manceau, Hanjalić 2002
). The model, the so-called EB-RSM (Fig. 1 to 4), rapidly spread into the community. It has been used by at least 18 research groups, in 11 countries, for applications ranging from aeronautics to nuclear energy. It is implemented in the open-source code Saturne developed by EDF starting from version 1.3, and the commercial package STAR-CCM+ from release 10.02.
A simplified version based on the eddy-viscosity hypothesis, developed in Manchester (Billard, Laurence 2012
), is used by Airbus UK and NASA Ames.

Another step (Fig. 3) consisted in applying the theory of invariants to reduce the number of equations of the model (from 8 to 3) without loosing the representation of the most important physical phenomena (algebraic modelling) (
Oceni, Manceau, Gatski 2008 ; Oceni, Manceau, Gatski 2010).

Transport and algebraic models of the turbulent heat fluxes (Fig. 4) accounting for wall blockage are also developed in collaboration with EDF (Dehoux, Lecocq, Benhamadouche, Manceau, Brizzi 2012 ; Dehoux, Benhamadouche, Manceau 2011 ; Dehoux, Benhamadouche, Manceau 2010 ; Lecocq, Manceau, Bournaud, Brizzi 2008) .

Fig. 1 : Synthetic turbulence generated by a dynamical system (temporal view). Isocontours of vertical velocity.
Fig. 2 : Hybrid temporal LES (TPITM). Channel flow. Turbulent energy profiles.
Fig. 3 : Hybrid temporal LES. Wake of a square-sectioned cylinder.
Fig. 4: Continuous hybrid RANS-LES approach (PITM). Flow above a periodic hill. Iso-Q.

Hybrid RANS/LES modelling of turbulence

For numerous applications, statistical modelling proves insufficient, either because the flow intrinsically contains large-scale, quasi-deterministic structures, or because unsteady characteristics of the flow are explicitly required (thermal fatigue, fluid/structure interaction, ...).

Large-eddy simulation (LES) remaining very expansive for many applications, an intense research effort has been developing for a few years in the field of hybrid RANS/LES modelling, in order to make possible the treatment of some flow regions in RANS, preserving the LES description for some well-chosen regions.

A first approach, the so-called zonal approach, consists in dividing the domain into pre-determined RANS and LES zones and in compute them separately. The difficulty entirely lies in the coupling at the interfaces. In particular, the generation of realistic inlet conditions (synthetic turbulence) for LES is a very challenging issue. Several methods for the generation of turbulent inlet conditions have been developed, consisting in generating fluctuations in the inlet plane either using a dynamical system (Fig. 1) (
Perret, Delville, Manceau, Bonnet 2008 ; Perret, Delville, Manceau, Bonnet 2006), based on previous experience in the building of dynamical systems based on POD eigenmodes of the flow, or by a new anisotropic volume forcing, the ALF method (de Laage de Meux, Audebert, Manceau, Perrin 2015).

A second approach, called continuous, seamless or global, consists in building a model able to continuously migrate from a RANS to a LES model. The approaches available in the literature (DES, SAS, XLES, ...) being based on empiricism, a theoretical work has been carried out to provide a formal framework, the time filtering formalism, to this type of methods (Figs. 2 and 3) (Friess, Manceau, Gatski 2015 ; Fadai-Ghotbi, Friess, Manceau, Gatski, Borée 2010 ; Manceau, Friess, Gatski 2010).

One of the main difficulties of these approaches is the modelling of the contribution of the unresolved scales. When the cutoff between resolved and unresolved scales lies in the productive region of the turbulent spectrum, it is necessary to account for the complex phenomena due to anisotropic production and redistribution, as well as the phase shift between stress and strain, due to the non-equilibrium character of these turbulent scales.

Therefore, the modelling effort has been directed, in the framework of the German-French DFG-CNRS collaborative program (Jakirlić, Manceau, Sarić, Fadai-Ghotbi, Kniesner, Carpy, Kadavelil, Friess, Tropea, Borée 2009), towards subfilter-scale models based on transport equations (Figs. 2 to 4) (Fadai-Ghotbi, Friess, Manceau, Gatski, Borée 2010 ; Bentaleb, Manceau 2011 ; Tran, Manceau, Perrin, Borée, Nguyen 2012). 

Last update: October 15, 2016