3.1 Modelling
3.1.1 Wake vortex simulation (H. Moet)
CERFACS has developed a strong expertise on the topic of wake vortex dynamics,
which is now widely recognized in the scientific community. Numerous studies
have been conducted investigating the stability of different vortex systems, by
means of Direct Numerical Simulations (DNS) or Large-Eddy Simulations (LES). These
studies are both a means of characterizing the wake of an aircraft in the
near-field and a way to determine the decay in the far-field, which is important
in predicting the behaviour of the wake of a large transport aircraft. CERFACS
investigates wake vortex dynamics through a
collaboration with Airbus-Deutschland and CNRS-IRPHE and CERFACS is also
active in the framework of European programs such as AWIATOR (FP5).
CERFACS has been involved in studying the unstable behaviour of a four-vortex
system
([Moet, 2003]).
The particular four-vortex system appears to be
unstable with respect to
two- and three-dimensional perturbations. The intrinsic dynamics of the system
will lead to the development of instabilities with a range of different
wavelengths (very short wavelength/elliptic instability,
=O(rcore) or short wavelength/Crouch-type instability,
=O(b)) which amplify rapidly within the inner vortices.
The development of the instability occurring in the four-vortex system
is simulated by means of DNS simulations. The global dynamics are
illustrated by isosurfaces of vorticity magnitude in terms of the
nondimensional time, t*=t/tref with tref=b12/
 .
Figure 3.1 shows that the inner vortices (t*=10.14)
experience the amplification of the forced mode kp which corresponds to the
wavelength
of the Crouch-type instability for a
four-vortex system.
 |
 |
| t*=10.14 |
t*=13.46 |
Figure 3.1: Isosurfaces of vorticity magnitude showing the global dynamics for the simulation with e=10 -6 for time instants t/ tref=10.14 & 13.46 with tref= b12/ Gamma 1.
In the nonlinear regime, the secondary vortices experience large-scale
deformations, eventually reconnect, which leads to the formation of so
called "omega loops" (t*=13.46).
The phenomena caused by the generation and propagation of pressure waves in
vortex cores have also been investigated, by following the DNS and LES approach
([Moet, 2003 PhD]).
The propagation of pressure waves is responsible for the generation of
axial velocity, which under certain conditions lead to the development
of helical instabilities and the abrupt change of flow topology in the
vortex core. The dynamics involved may explain vortex bursting and end
effect, which are phenomena observed in smoke visualisation of real
aircraft wakes as well as in small-scale experiments that are not well
understood.
Numerous analyses have been made of the effect of external (atmospheric)
turbulence on the stability and decay of vortex systems composed of a
single vortex or a pair of counter-rotating vortices
([Holzaepfel, 2003;
Moet, 2003 PhD]).
3.1.2 Unsteady turbulence modelling
LES in elsA software (J.-C. Jouhaud, J.-F. Boussuge, X. Toussaint, P. Sagaut)
Since 2002, the Group develops LES within the elsA software using experience on AVBP, NTMIX and NSMB codes. Even if this leading-edge CFD technology can not yet be applied to complex aeronautical configurations (despite increasing computer capacities along with underlying numerical methods, grid techniques and models), it can play a major role in external aerodynamics when combined with wall functions and U-RANS models (hybridization between U-RANS and LES methods: DES, VLES ...).
In order to obtain an efficient LES tool, different Sub-Grid Models (Smagorinsly, Selective Smagorinsky, WALE, FSF), weakly dissipative schemes with skew-symmetric form that minimizes aliasing error (derivations of classical Jameson scheme) and adapted post-treatments (average quantities, RMS quantities ...) have been implemented in elsA. At the same time, QPF (Quality Programme Forms) have been elaborated to validate the developments and to ensure the integrity of LES with the production of elsA versions. Actually four test-cases are daily used: the turbulent channel flow, the free turbulence decaying in a periodic box, the temporal flat plate and the convection of a vortex in a periodic box.
Hybrid U-RANS/LES methods (X. Toussaint, J.-C. Jouhaud, P. Sagaut)
The Group is involved in a leading-edge project concerning the development of hybrid LES/U-RANS methods (application to the buffeting phenomenon
[Toussaint, 2002],
elsA software). Hybrid methods, combining precision/low cost computations, could push further away the actual limits of unsteady computations. To develop this topic, the Group recently submitted a FP'6 Research Training Network involving seven European research centers having activities in unsteady turbulence modelling: CERFACS-Toulouse, CEA-Grenoble, UPMC-Paris, EPFL-Lausanne, LSTM-Erlangen, CSIC-Zaragoza and UNINA-Naples.
Wall laws for heat exchanges (A. Devesa, J.-C. Jouhaud, F. Nicoud)
At the end of 2003, the Group started 'wall laws' activities for U-RANS/LES models. The aim of these activities is to equip the CEA Trio_U code (designed for 3D thermo hydraulics handling structured and unstructured meshes) with wall laws adapted to heat exchanges in anisothermal configurations. The target applications will concern the nuclear reactor safety.
3.1.3 Statistical turbulence models (A. Celic)
During the last quarter of 2003, implementation of a new variant of Durbin's k, e, v2, f turbulence model into elsA has been tackled. This activity is aimed at further improving elsA's predictive performance for heat transfers at walls in aerodynamic flows. Typical applications envisaged are impinging jet flows or ventilation of aircraft systems.
Compared to classical employed turbulence models like the k, w model of Wilcox [1] or the k, e model of Jones and Launder [2], the original k, e, v2, f model has proved superior predictive performance for wall heat transfers. Yet, its numerical application is non-trivial since the boundary-value problem is ill-posed. To solve this difficulty, a modified version of Durbin's model [3] was chosen to be implemented into elsA. This new variant promises higher numerical robustness while preserving all favorable predictive properties of the original model.
In addition to boundary-condition issues, the implementation of the model equations into elsA was identified as a key challenge. On the one hand, the model's equations for k, e and v2 constitute classical turbulence transport equation and are therefore straightforward to implement into the existing design of elsA. On the other hand, f represents the non-local character of redistribution terms in the transport equations of the Reynolds-stresses. To capture this non-local property, f is modeled by an elliptic equation and, hence, requires a separate treatment in elsA. This entails more elaborate implementation design and coding than a classical transport-equation model. Suggestions have been made to master this task with a minimum change in the present code structure of elsA.
[1] C. D. Wilcox, (1998), Turbulence Modeling for CFD, DWC Industries, La Cañada 2nd Ed.
[2] W. P. Jones and B. E. Launder, (1972), The Prediction of Laminarization with a Two-Equation Model of Turbulence, International Journal of Heat and Mass Transfer, 15, 301-314.
[3] P. A. Durbin, (1991), Near-Wall Turbulence Closure Modeling Without ``Damping Functions'', Theoretical and Computational Fluid Dynamics, 3, 1-13.
3.1.4 Hypersonic (G. Chevalier, M. Duloué)
The simulation of hypersonic flows with chemical unequilibrium was the last study conducted on the former Multi Bloc structured code NSMB developped in an European consortium
[Duloue, 2003]
That work was performed for the EADS Launch Vehicule division.
The task was dedicated to the simulation of hypersonic flows with chemichal desiquilibrium. The work started for inviscid flows and proceeded with laminar viscous flows. For the latter case, catalitic, and semicatalitic boundary conditions were implemented. That work gave very interesting and motivating results. In the meantime the AAM team has completely switched CFD codes from NSMB to elsA, and that development appeared as too costly to report in elsA on our own ressources. That work has been integrated and transmitted to the maintainer of NSMB, and is now stopped for the time beeing in CERFACS.
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