Statistical modelling of
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 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) .
Hybrid RANS/LES modelling
For numerous applications, statistical modelling
insufficient, either because the flow intrinsically
large-scale, quasi-deterministic structures, or because
characteristics of the flow are explicitly required
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
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 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
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
phenomena due to anisotropic production and
redistribution, as well as
the phase shift between stress and strain, due to the
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).