Wall functions
When the tangential pressure gradient is low, the turbulent boundary
layer above the wall can be represented in 1D and the variables are
essentially varying in the direction normal to the wall. Building and
implementing wall functions need to use mathematical assumption from
physical considerations based on directional analysis. In practice,
wall functions replace the classical no-slip boundary condition by more
sophisticated relations between the variables and their derivatives:
the question to answer is how the kinetic energy is transformed in heat
transfer. In the literature, most of the wall functions are defined
for an incompressible flow or for a compressible transonic flow. For
such flows, the heat transfer modelling has not a so strong impact.
During my PhD and when I worked at CEA, I was interested in the
development of a new formulation dedicated to heat transfer at
supersonic (or hypersonic) inflow conditions. Finally, two kinds of
laws have been proposed and validated: a version for perfect gas and a
version including thermal effects (assumption: the turbulent Prandtl
number is not constant!).During reentry, ablation of the thermal shield occurs and for composite material, ablation is not homogeneous: roughness appears. It is very complicated to account locally for wall roughness in classical turbulence models (valid up to the wall). A new way to treat the problem has been adopted. Instead of modelling locally the roughness effects, a better way to proceed is to model globally the effect of the presence of rough elements. Remember that the classical roughness size is about 100 microns, about 10 times greater than the classical size of mesh elements in the tangential direction. The new version of wall functions corrects the predicted heat transfer and friction for a smooth wall and the correction is built upon data assimilation.
Cooperation with B. Mohammadi (U. of Montpellier II - CERFACS), S. Galera, L. Hallo (CELIA / U. of Bordeaux I).
RANS turbulence models, thermal turbulence and wall functions.
In most of turbulence models, temperature is supposed to be a passive scalar and therefore thermal turbulence is supposed to be a consequence of kinetic turbulence. However, DNS with thermal gradient or experiments in recirculation areas have shown that the hypothesis is false. For supersonic / hypersonic flows, heat transfer is one of the most important parameters and a more precise contribution from turbulence must be accounted for. We have analyzed the thermal turbulence models published in the literature and dedicated to liquid metals (incompressible flows). We have extended to compressible flows one of them based on 4 transport equations (classical k-epsilon + 2 equations for thermal turbulent energy and its dissipation). We have also built a two-layer coupled kinetic / thermal turbulence model from which new wall functions have been proposed.Cooperation with B. Mohammadi (U. of Montpellier II - CERFACS), S. Galera, L. Hallo (CELIA / U. of Bordeaux I).
Transient regime in periodic flows
A large number of unsteady industrial flows are in fact periodic. With classical time integration approaches, monitoring the convergence of unsteady simulations is not an easy task and generally, a strong experience of the kind of simulation and of the considered solver are necessary. In all configurations, a transient regime not periodic must be by-passed and this transient regime can have a strong impact on the total numerical cost: in some cases (not necessary anticipated!), about 40 periods must be computed before the flow is periodic. We have implemented and validated in elsA a harmonic balance technique issued from literature. The basis of the technique is very simple: if a flow is periodic, then the conservative variables are periodic and the right hand side of the Navier Stokes equations is also periodic. Limiting the analysis of the first harmonics, one can transform the problem in Fourier space back to the time domain and the solution is to compute snapshots of the flow at some time instants located over the period. The unsteady computation is finally transformed in several steady simulations coupled by a source term. The convergence of steady flows can be enhanced with a multigrid technique and an implicit time integration. The implicit treatment is very complex and has been published in AIAA J.Cooperation with F. Sicot, G. Dufour, A. Dugeai (ONERA/DADS), C. Liauzun (ONERA/DADS), T. Guédeney (CIFRE Snecma / Cerfacs).
Hybrid Structured / Unstructured solver
The CFD community is mainly divided into two parts, following the kind of mesh considered.On one hand, structured meshes account for flow anisotropy with mesh lines aligned with the flow feature. This structured anisotropic approach enables an easy mesh refinement inside the boundary layer in the direction normal to the wall. The multibloc structure of the mesh is very useful for parallel computations, even if a good load balancing is not achieved easily on complex configurations with advanced meshing techniques (chimera, non abutting mesh interfaces...). The CPU efficiency is very high for structured codes since all data can be accessed directly.
On the other hand, unstructured tetrahedral meshes have become widespread for use in low and medium Reynolds number flows since complex geometries can be meshed very easily with little effort. The automatic generation process can not account easily the anisotropy of the flow and the community (mesh tools and CFD codes) have extended the treatment to "hybrid" meshes composed of several elements shapes (tetrahedra, prisms, pyramids and hexahedra). The numerical cost is higher for unstructured grids since some connectivity tables must be read to access the data. Finally, recent analysis of CFD solutions on structured and unstructured meshes have shown a larger sensibility on the mesh for unstructured computations (see AIAA High Lift Prediction Workshop or AIAA Drag Prediction Workshop).
A way to take advantage of both techniques seems to handle structured zones and multielements unstructured zones at the same time ina single mesh. Therefore, we have implemented inside elsA unstructured capabilities. We have chosen a cell centred framework for compatibility with the structured approach and the Object-Oriented data structure of elsA has clearly been an advantage for incorporating the unstructured capabilities: our approach is not code coupling and we have proceeded such that most of the computing routines may be used for structured and unstructured zones, avoiding most code duplication with the associated maintenance nightmare.
Cooperation with M. Gazaix (ONERA/DSNA), M. Montagnac, V. Couaillier (ONERA/DSNA).
Exemple of a hybrid Structured / Unstructured grid around DPW4 configuration. Colored lines represent the structured block limits. View of the unstructured grid in the symmetry plane.
Cell-centred schemes for LES on unstructured grids
Cerfacs has a strong expertise in
numerical schemes dedicated to LES for the AVBP code. However, AVBP is
based on a cell-vertex formalism with data stored at mesh nodes.
This approach is generally adopted by CFD codes built upon Finite
Element technique (also called Continuous Galerkin in the litterature).
This approach cannot be directly extended to cell-centred CFD codes
like elsA. We are currently developing new
schemes based on a non-MUSCL approach.
Cooperation with P. Cayot (CIFRE Snecma / Cerfacs), P. Sagaut (UPMC)
Cooperation with P. Cayot (CIFRE Snecma / Cerfacs), P. Sagaut (UPMC)