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Statistical modelling of turbulence (RANS)
The objective is to account for complex physical phenomena in statistical turbulence models, such as those due to
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 socalled EBRSM (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 opensource code Saturne developed by EDF starting from version 1.3, and the commercial package STARCCM+ from release 10.02. A simplified version based on the eddyviscosity 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) . 

Hybrid RANS/LES modelling of turbulence
For numerous applications, statistical modelling proves
insufficient, either because the flow intrinsically contains
largescale, quasideterministic structures, or because unsteady
characteristics of the flow are explicitly required (thermal fatigue,
fluid/structure interaction, ...).
Largeeddy 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 wellchosen regions.
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 ; FadaiGhotbi, 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 nonequilibrium
character of these turbulent scales. Therefore, the modelling effort has been directed, in the framework of the GermanFrench DFGCNRS collaborative program (Jakirlić, Manceau, Sarić, FadaiGhotbi, Kniesner, Carpy, Kadavelil, Friess, Tropea, Borée 2009), towards subfilterscale models based on transport equations (Figs. 2 to 4) (FadaiGhotbi, Friess, Manceau, Gatski, Borée 2010 ; Bentaleb, Manceau 2011 ; Tran, Manceau, Perrin, Borée, Nguyen 2012).
