3.1 Modelling
3.1.1 Wake vortex simulation (L. Nybelen)
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 mean 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 for large transport aircraft. A PhD student at CERFACS investigates
wake vortex dynamics through a collaboration with Airbus -Deustchland and IMFT (Institute of Fluids Mechanic of Toulouse).
CERFACS is also active in the framework of European programs such as AWIATOR (FP5) and FAR-Wake (FP6).
CERFACS has been involved in studying the merging process of two co-rotating vortex, which governed principally the wake
vortex dynamic in the near- extended field (1<x/B<10). These co-rotating vortices correspond to the vortices shed by
the flap and the wing tip. In certain cases depending on the Reynolds number and the position of the vortices, the system
may be subject to the development of a very short wavelength/elliptic instability (li = 0(rcore)) which
amplifies rapidly within the inner vortices. Thus, the merging process becomes unstable. The development of elliptic
instability is characterized by an oscillation of the vortex core position. The vortices finally exchange
their vorticity and lose their structure coherence, leading to the merging by a reorganization of turbulent structures.
The unstable merging process is faster than the stable merging
[Nybelen, 2005].
Unstable and stable merging
mechanisms have been analyzed using two analytical vortex models, namely the Lamb-Oseen and the Jacquin VM2 model
which describes better a realistic vortex in the extended near-field.
Figure 3.1: Isocontours of vorticity magnitude || w|| : the dynamic flow of the unstable merging with Lamb-Oseen vortex model as initial condition. Left to right : t*= t/(2  2 b2/  ) ~1.95,2.45,3.25.
The phenomena caused by the generation and propagation of pressure waves in vortex cores have also been investigated
with DNS and LES approaches
[Moet, 2005].
The propagation of pressure waves is responsible for the generation
of axial velocity, which under certain conditions leads to the development of helical instabilities and to an abrupt
change of flow topology in the vortex core. Involved dynamics may explain vortex bursting and end-effects, which are
phenomena observed in smoke visualization of real aircraft wakes as well as in small-sacle experiments that are
not well understood.
Numerous analyzes have been made of the interaction between an exhaust jet and trailing vortex in two phases, the
jet regime then the entrainment case.
3.1.2 Aerothermal Simulations
Improvement of k- v2-f turbulence model simulations (A. Celic)
Durbin's k- v2-f turbulence model theoretical basis [1] consists in a construction
of the turbulent eddy viscosity in order to reproduce more accurately the behavior of µt in
the boundary layer. The model contains three transport equations coupled with an elliptic one
(for f). At CERFACS, the activity began with comparisons of turbulence models behaviors
for several applications (including Durbin original turbulence model) and lead to the implementation
of a new variant of Durbin's k- v2-f turbulence model in elsA. This model
contains
[Celic, 2005]:
-
a new version of the realizability condition which is adapted from Durbin's one,
- an extra source term on f equation for a better conditionning of f wall boundary condition,
- a dissipation term for v2 constructed from Sveningsson one.
This new version of Durbin's turbulence model was first validated over a flat plate [2]
(Fig. 3.2) and lead to interesting results for the computation
of cold jets impinging on a hot wall [3], as shown on Fig. 3.3.
This work has been done in the framework of MAEVA project
('Aerothermal Modelling of Fluids for Ventilation of Planes').
Figure 3.2: Flat plate : non dimension velocity as function of the non dimension distance to the wall. The experimental data and the test case are proposed in [2].
Figure 3.3: Jet impinging on a plate: comparison of turbulent kinetic energy distribution for Durbin's modified and Jones Launder turbulence models; Nusselt coefficient computed on the flat plate and experimental data.
[1] P. A. Durbin, (1991), Near-Wall Turbulence Closure Modeling Without ``Damping Functions'', Theoretical and Computational Fluid Dynamics, 3, 1-13.
[2] D.B. DeGraaff and J.K. Eaton, (2000), Reynolds-Number Scaling of the Flat-Plate Turbulent Boundary Layer, Journal of Fluid Mechanics, 422, 319-346.
[3] J. Baughn, A. Hechanova and X. Yan, (1991), An experimental Study of Entrainment Effects on the Heat Transfer from a Flat Surface to a Heated Circular Impinging Jet, Journal of Heat Transfer, 113, 1023-1025.
Jet in cross flow (J.C. Jouhaud)
The 'Jet in Cross Flow' topic represents for CERFACS an initiative to strengthen the fundamental scientific aspect
in the field of turbulence modelling for aerothermal applications
[Priere, 2005].
More precisely, this topic
concerns here the development of a reliable simulation tool for the computation of industrial configurations
which involves warm jets exhausting in cold cross-flows, i.e. turbojet anti-ice exhaust flows. This type of
aerothermal flow is a major stake for AIRBUS France.
Figure 3.4: Square Jet in Cross-Flow Produced by a Scoop - Instantly Temperature Field (Y=0 plane).
In the MAEVA framework ('Aerothermal Modelling of Fluids for Ventilation of Planes'), our recent LES computations with
AVBP solver (see Fig. 3.4) have shown that LES appears like an efficient tool for aerothermal predictions
[Jouhaud, 2005].
In fact, only these types of computations are able today to predict very
precisely the right thermal profiles (see Fig. 3.5) compared to U-RANS methods, without an excessive CPU
cost (good turnover). In the future our objective could be to develop hybrid LES/U-RANS methods in a production
code dedicated to AIRBUS aerothermal computations.
Figure 3.5: Comparisons between LES, U-RANS and MAEVA Experiment - Average Temperature Curves.
Wall modeling for unsteady dilatable flows (A. Devesa, F. Nicoud)
This research topic corresponds to A. Devesa's on-going PhD thesis that started at the end of 2003. It is the
result of a collaboration between three entities: CEA, the French Agency for Nuclear Energy based at Grenoble (France),
University Montpellier II hosting F. Nicoud (PhD advisor) and CERFACS. The objective is to model accurately and reliably
the fluid / solid interaction in energetical industrial applications, e.g. nuclear reactor safety, where strong
temperature gradients exist. For those flows, the correct prediction of thermal fluxes at the wall is a crucial problem,
because materials can be subject to contraction, to dilatation and to ablation phenomena, leading to a possible destruction.
In this study, the CEA in-house Trio_U CFD code is used, as well as Matlab. Crossed comparisons were systematically undertaken
between the two numerical approaches.
First, the study was limited to a steady state approach. Under the classical law-of-the-wall assumptions,
density changes in the boundary layer, virtually due to strong temperature gradients were taken into account
in a new non-isothermal wall law. The analytic derivation of this new wall function was deduced from
Van Driest's transform [1]. Implementation in Trio_U code was carried out and results
showed significant improvement compared to the standard law-of-the-wall
(logarithmic law for the velocity and Kader's formula for the temperature)
[Devesa, 2005].
The following step was to adopt an unsteady approach in the wall modeling, using a two-layer model, namely the TBLE
(Thin Boundary Layer Equation) model [2]. The concept of this model lies on solving a set of simplified
equations in a one dimensional fine mesh embedded between the first off-wall point and the wall. The work consisted in
adapting this model, previously validated in incompressible cases, to dilatable fluid cases and in implementing it into
Trio_U software. At the end of 2005, the validation process was still under progress, but showed (Fig. 3.6)
that, for steady state quasi-isothermal flow, the ``dilatable version'' of the TBLE model recovered the standard law-of-the-wall,
while in non-isothermal case, it behaved like the non-isothermal wall function previously described
[Devesa, 2005].
Figure 3.6: Velocity profiles from TBLE model. Left: isothermal case, right: non-isothermal.
Finally, the problem of unsteady effects in wall modeling was adressed. Even if two-layer models
are developed for unsteady turbulent flows, there must exist a critical frequency beyond which the model can not be used in
an accurate way. To answer this question, a Direst Numerical Simulation (DNS) of turbulent channel flow with 6 passive scalars
submitted to a temporal varying forcing term was set up.
[1] E.R. Van Driest, 1951, Turbulent boundary layers in compressible fluids, Journal of Aeronautical Sciences, 18(3).
[2] E. Balaras, C. Benocci and U. Piomelli, (1996), Two-layer approximate boundary conditions for Large-Eddy Simulations, AIAA Journal, 34(6), 1111-1119.
3.1.3 Detached eddy simulation
Detached Eddy Simulation with k-w turbulence model (J.-C. Jouhaud, X. Toussaint, P. Sagaut)
Since 2004, the aerodynamic team is involved in the development of hybrid U-RANS/LES techniques for complex aeronautical
configurations. In fact, these techniques when combined with wall functions and grid strategies (automatic mesh
refinement, non-coincident interface boundary conditions ...) could push further away the actual limits of
unsteady computations by optimizing the 'precision/cost computations' ratio.
Figure 3.7: Buffet phenomenon over the OAT15A airfoil - View of the mesh around the airfoil and zoom on the non-coincident part.
Figure 3.8: Buffet phenomenon over the OAT15A airfoil ( M=0.15 and  =3.4 deg) - Rising and descendant phases of the pressure coefficient.
Our first subject of investigation has concerned the development of a turbulence model that exploits the
concept of Detached Eddy Simulation (DES) [1]. More precisely, the formulation proposed by
H. Bush and M. Mani [2] with a primary inspiration from Strelets [3] has been considered. In this formulation, the near wall boundary layer
predictive capabilities of the Wilcox k-w turbulence model is combined with LES behaviour for large scale
separated regions of the flow. This is done by comparing the length scales of the turbulence with the
resolved scales of the grid.
To evaluate this DES with k-w turbulence model, we have focused on aerodynamics buffet on the rigid OAT15A
airfoil that is characterised by a periodic motion of the shock over the airfoil (see Fig. 3.7 and
Fig. 3.8). In order to decrease the computational costs, two strategies were considered: wall functions
and conservative non-coincident interface boundary conditions [4]. This computation is still under investigations.
[1] P.R. Spalart, W.H. Jou, M. Strelets and S.R. Allmaras, (1997), Comments on the Feasability of LES for Wings,
and on a Hybrid RANS/LES Approach, 1st AFOSR International Conference on DNS/LES, Aug. 4-8, Ruston, LA.
[2] R.H. Bush and M. Mani, (2001), A Two-Equation Large Eddy Stress Model for High Sub-Grid Shear, 15th AIAA
Computational Fluid Dynamics Conference, 11-14 June, AIAA paper 2001-2561, Anaheim, CA.
[3] M. Strelets, (2001), Detached Eddy Simulation of Massively Separated Flows. 39th AIAA Aerospace Sciences Meeting and Exhibit, 8-11 January, AIAA paper 2001-0879,
Reno, Nevada.
[4] A. Benkenida and J. Bohbot and J.-C. Jouhaud, (2002), Patched grid and adaptive mesh refinement strategies for Vorticies transport calculation, International Journal Numerical Methods in Fluids Dynamics, 40, 855-873.
Zonal Detached Eddy Simulation (J.-F. Boussuge, V. Brunet, S. Deck)
In addition to the work done in section 3.1.3.1, the buffet phenomenon has been studied with a zonal Detached Eddy Simulation approach based on the Spalart-Allmaras model [1]. The zonal approach decouples the determination of LES zone from the mesh characteristics. The user can define the RANS and LES zones, so the attached boundary layer regions are explicitly treated in RANS mode regardless of the grid resolution which avoids grid induced separation.This method has been implemented in elsA in collaboration with the Applied Aerodynamics Department from ONERA.
Moreover, in order to optimize the computational cost, a study has been done on time integration schemes. The Dual Time Stepping technique and the GEAR scheme were evaluated in term of CPU cost on a 2,5D supercritical airfoil. Both schemes were able to capture the buffet phenomenon with the right frequency and at the right experimental angle. In term of CPU cost, the GEAR scheme appeared to be more efficient than the DTS.
[1] S. Deck, (2005), Numerical simulation of transonic buffet over a supercritical airfoil,AIAA Journal, Vol 43, No 7
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