3.3 Numerical aerodynamics
3.3.1 Numerical methods
Coupling turbulence and multigrid methods (J.-F. Boussuge)
Initially, elsA was developped for solving steady RANS equations with classical convergence acceleration methods such as local time stepping and multigrid. However, the latter method was applied to mean flow equation only which implies a convergence shift between turbulence and mean flow. This shift
To correct this behaviour, a more efficient implicit method can be used on turbulence only (work desribed in Section 3.3.1.2) or the FAS algorithm can be extended to the set of turbulence equations.
A work has been done in that direction and ends up to a significant improvement of the turbulence quantities convergence without improving the convergence of mean flow field. In fact, this technique appeared to be usefull only when the mesh presents a very high degree of anisotropy in the direction perpendicular to the flow. For such a configuration turbulent informations does not propagate easily and turbulence multigrid can overcome this problem. More over, different behaviours has been observed with respect to the turbulence model. The one equation transport model from Spalart-Allmaras being the more robust.
Gauss Seidel line (F. Lörcher, M. Montagnac, C. Gacherieu, J.-F. Boussuge)
In elsA software, the linear system coming from the time integration implicit method can be solved by different
techniques among which the Lower-Upper Symmetric Successive OverRelaxation (lussor) method. In this method, the solution
is updated point by point as in a point Gauss-Seidel method. Many other algorithms can be stated depending on the order
in which grid points are updated. On an other hand, convergence acceleration through a multigrid algorithm is only
triggered for the mean flow part of equations. Therefore, the propagation of information is slower for turbulence
equations that do not benefit from the multigrid method. On top of that, industrial configurations lead to complex
meshes that include most of the time huge anisotropic zones. In these part, stretched cells prevent a good convergence
on turbulence equations since information can not propagate easily and quickly in the direction corresponding to the
smallest cell dimension.
In this context, a line lussor method has been implemented and validated on several configurations. The principle of
this method consists in using a line relaxation in the direction of the smallest cell dimension. For each line of points
to be updated, a tridiagonal linear system has to be solved in the scalar lussor version. In the matrix lussor version,
the linear system can be block tridiagonal or pentadiagonal. In industrial applications, it is too hard to define a
unique favored direction and all directions are alternated in the process.
Fig. 3.14 shows the convergence of global coefficients for an AS28 configuration at a Reynolds
number Re=1.4 106, a Mach number M¥=0.8 and an angle of attack  =2.2. Turbulence is modeled by
Spalart-Allmaras equations. The dotted line is the convergence of the line lussor applied on turbulence equations only.
The plain line is the convergence of the reference computation.
Figure 3.14: Convergence of lift (left) and drag (right) coefficients for an AS28 wing configuration.
Preconditioning for low-speed flows (Y. Colin)
Preconditioning techniques involve the alteration of the
time-derivatives used in time-marching CFD methods with the
objective of enhancing their convergence and accuracy. The
original motivation for the development of these techniques arose
from the need to compute low speed compressible flows efficiently.
At low Mach numbers, the performances of traditional time-marching algorithms
suffer because of
the wide disparity that exists between the particle and acoustic
wave speeds.
Preconditioning methods introduce artificial time-derivatives
which alter the acoustic waves so that they travel at speeds that
are comparable in magnitude to the particle waves. Thereby good
convergence characteristics may be obtained at all speeds. One of the major
problems concerning low-Mach preconditioners is that they loose
robustness in the neighborhood of stagnation points or in boundary layers[1].
The Weiss-Smith preconditioner[2] is theoretically the most robust preconditioner
due to its eigenvector structure[3] and it has been implemented and validated
in elsA. Besides, it turns out that the low Mach number
preconditioning does not only improve the convergence of the
system, but is also responsible for maintaining accuracy at low
speeds. Thus the Roe and Jameson schemes have been modified to have a correct
conditioning of the artificial dissipation terms and to ensure reliable accuracy
at all speeds.
[1] E. Turkel, (1999), Preconditioning Techniques in Computational Fluid Dynamics, Annual Review in Fluid Mechanics, 31, 385-416.
[2] J.M. Weiss and W.A. Smith, (1995), Preconditioning Applied to Variable and Constant Density Flows, AIAA Journal, 33.
[3] D.L. Darmofal and P.J. Schmid, (1995), The importance of eigenvectors for local preconditioning of the Euler equations, AIAA paper,
AIAA-95-1655.
3.3.2 Meshing technics
Nomatch boundary conditions (M. Montagnac)
Grid generation is a crucial problem for the
computation of complex aircraft configurations using a body-fitted structured-block solver. A key point is the type of
interface between two zones or grids used during the geometry meshing. In case of one-to-one abutting or matching
interface, local refinements around the geometry and flow regions of special interest (boundary layers, stagnation
lines, wakes) tend to spread through the whole configuration domain even in zones where gradients are expected to be
weak. This can lead to very large grids, especially for complex geometries. CERFACS has developed the efficient
technique of conservative non coincident adjacent interface boundary condition or mismatched abutting interfaces to
simplify the grid generation. Two domains must have a common adjacent interface, but grid points of both interfaces do
not have to be at the same location or coincident. Grid lines through the interface may be not continuous. Therefore,
this approach prevents mesh points from spreading from a block to others. It is also possible to mesh independently two
parts of a geometry and just to abut the two resulting meshes to get the whole mesh. This meshing technique has already
been implemented and validated in the elsA software and Airbus fully exploits this numerical feature in its production
environment. Nearly all their meshes now includes non-matching interfaces. CERFACS now improves and supports this
approach to still help Airbus in decreasing simulation turn-around times.
The non coincident interface boundary condition is the core of the sliding mesh feature. This functionality could be
helpful in turbomachinery activities or in aerodynamics around advanced high-speed propellers for aeroelastic analysis.
The actuator disk boundary condition often used to model a propeller can then be replaced by the mesh of a propeller
itself.
Compatibility of wall-laws with other numerical methods (J.-Ph. Boin)
Wall laws appear to be useful for global cost reduction of high Reynolds RANS computations.
Their use is more and more current in complex CFD configuration and they are systematically
associated with other numerical methods and meshing technics. A validation work has been done
at CERFACS around the wall law implementation in the elsA code
[Boussuge, 2005].
The tested wall laws are Houdeville's
ones based on an apriori agglomeration of near-wall cells [1]. Compatibilities with low speed preconditioning,
with Adaptive Mesh Refinement and with no-match boundary conditions have been look into.
Low speed preconditioning have been already studied and validated for a 3D profile in a wind tunnel,
ONERA test-case AG29. To use wall laws, a specific mesh is built from the fine low-Reynolds meshes using
Airbus France tools damas, EDM and Quickview. The 24 first cells are concatenated for wall
adjacent blocks. Comparisons are made with and without wall laws for local quantities, pressure and friction
coefficients. Wall laws run smoothly with the preconditioning even if some differences appear for the friction
coefficient.
Compatibility of wall laws with AMR has been tested on wing-body configuration AS28G_WB. An anisotropic AMR
block is used on the extrados of the wing to capture the shock. This test-case puts forward some limitations
of the elsA solver regarding to the use of AMR in parallel. Nevertheless these problems are not related to
the wall laws and results with and without wall laws are similar. During that work, no-match boundary
conditions have been tested. Indeed that kind of boundary conditions have less limitations both for
mesh generation and for multi-processor computations.
This study has been carried on with another test-case wing-body and nacelle AS28G_NCT. Here the no match
boundary conditions are strictly around the nacelle. Figure 3.15 shows the isocontours of rE
in a slice normal to the spanwise. The no match boundary are represented with bold line. We have
checked that these boundary introduce few perturbations.
For these three approaches, the compatibility with wall laws is guaranteed. Further studies should be
done to valid wall laws with other numerical methods such as grid sequencing, ALE formulation and Chimera.
[1] E. Goncalves,(2001), Implantation et validation de lois de paroi dans un code Navier-Stokes, PhD thesis,
Ecole Nationale Supérieure de l'Aéronautique et de l'Espace.
Figure 3.15: No match BC - Wall laws, isocontours of rE
Wall functions (S. Champagneux)
It is well-known that turbulent flows computations for 3D multi-blocs configurations need an important
effort, since global quantities such as distance to the wall,... are generally needed by the turbulence
models. In the framework of DTP Modèles de Données Aérodynamiques (models for aerodynamic data)
[BenKhelil, 2004],
and in order to
decrease the numerical cost of turbulent 3D computations,
the aerodynamic team has been involved in the implementation and in the validation of a wall
function approach for Reynolds Averaged Navier-Stokes (RANS) computations in elsA. The
principle of wall functions is to decrease the numerical cost of the computations, replacing the
classical non-slip boundary condition by more sophisticated relations
between the variables and their derivatives. The wall function model is coupled with the high-Reynolds
reduction of the turbulence models, which generally does not need the distance to the wall.
Contrarily to classical implementations based on a large
cell above the wall, our implementation is based on a fictitious wall, translated from the real one.
We choose this technique because it is easy to couple with computational cost decreasing techniques,
such as multigrid schemes, and with methods to increase the precision of the
computation (Automatic Mesh Refinement -AMR- for instance). Our formulation is only sensitive to
one parameter: the distance between real and fictitious walls.
In practice, there is no difference between the real wall and the computational one. To
construct a mesh adapted for wall function computations, we need the same mesh topology as for
low-Reynolds computations (up to the wall). The formulation impact on the mesh generation appears
only in the choice of the cell height h for the first row above the wall: we typically choose
for wall-laws computations a non-dimensioned cell height h+ such that h+ ~ 50.
The mesh obtained is less refined than for low-Reynolds computation and contains about 20% cell fewer.
3.3.3 Applications
Fluid/Structure interactions (J. Delbove)
The field of aeroelasticity studies the interaction between inertial, elastic and aerodynamic forces acting on a flight vehicle. Industrial partners make significant efforts to introduce this field in an early phase of the design process in order to minimize costs and production delays. CFD simulations play a major role in this objective. This activity is often divided in two sub-domains: static and dynamic aeroelasticity.
The first area of interest is the static fluid-structure interaction. In steady flight condition, the shapes of aircraft wings are deformed by the constraint of aerodynamic loads. CERFACS
[Delbove, 2005 PhD],
in collaboration with Airbus, has developed an algorithm which, for a given flexibility matrix representing the wing structure and for a set of flight conditions, computes the deformed wing shape and the fluid flow. It implies that a robust mesh deformation algorithm must be available in elsA. An analytical deformation method coupled with a transfinite interpolation method has been successfully developed (see Fig. 3.16 for an example of mesh deformation).
Figure 3.16: Wing bending of an AS28G configuration.
The second area of interest is the dynamic aeroelasticity and direct industrial application is the flutter prediction. Flutter is a destructive fluid-structure interaction due to a transfer of energy from the fluid to the aircraft structure. It is characterized by a growing oscillation which can lead to the destruction of the aircraft. It can be predicted either with the use of unsteady aerodynamic loads provided by unsteady simulations or with a direct temporal fluid structure simulation.
CERFACS has improved numerical methods for unsteady simulations in the elsA software to get reliable loads in non linear regions. These loads are then used by the PK method [1] to predict the flutter phenomena.
Fig. 3.17 shows a good agreement between flutter results obtained with the PK method and direct aeroelastic simulations. However, the latter are too expensive to be affordable in an industrial environment.
Figure 3.17: Flutter boundary computed by the P-K method and direct aeroelastic simulations on a 2D configuration.
[1] C. A. Irwin and P. R. Guyett, (1965), The subcritical response and flutter of a swept wing model,
Royal Aircraft Establishment, August 1965, Rept 65186, Farnborough, England, U.K.
Air intake computations (Y. Colin)
Nacelles design must fulfill geometrical constraints and engine
requirements. One of the engine requirement is focused notably on
the homogeneity of the flow in front of the compressor which is quantified by
the distortion levels of the total pressure in the fan plane.
Plane on the ground with crosswind inlet flows is a critical case for the nacelle:
it occurs a subsonic or
supersonic separation in the inlet depending on the engine mass flow.
The resulting heterogeneity of the flow may account for the outbreak
of aerodynamic instabilities of the fan blades.
CERFACS, in collaboration with Snecma, is working on the numerical
simulation of such crosswind inlet flows in order to predict distortion
levels. This application is featured by the cohabitation of incompressible
and transsonic areas along with turbulent stagnation areas on the inlet lip.
The numerical issue due to low Mach number crosswind flows may be solved by preconditioning
techniques and an accurate description of the separation requires
turbulence model investigations.
Figure 3.18 shows a preconditioned RANS computation on the Lara nacelle
using the Spalart-Allmaras model.
The crosswind speed is set to 35kt (corresponding to Mach numbers of 0.05) and the
engine mass flow rate is about 750kg.s-1. It turns out that the subsonic separation
is pretty well predicted by the model and gives levels of distortion close to the experiment.
(a)
(b)
Figure 3.18: Preconditioned RANS Lara nacelle computations: (a) Mach and (b) total pressure isocontours
Dynamic derivatives of full Aircraft Configuration(J.-Ph. Boin)
The use of advanced CFD computation to determine aerodynamic features
of a full aircraft configuration has been carried on within the European program
AWIATOR(FP5)
[Margerit, 2005].
Prediction of full set of aerodynamic coefficients including
dynamic derivatives is of great interest for flight mechanics problems such as
stability, maneuverability and global behavior of an Aircraft Configuration (A/C).
elsA-RANS computations have been done on full A340 grids with finite
fuselage and engine installation (see Fig. 3.19). Results of -effect and
pitching effect have been compared to wind tunnel data from our project partner Airbus-EGAG.
In order to deal with non-symmetric configurations (b-effect), wall laws have been used on
12 million nodes grid. As a conclusion, the advanced CFD has given good results since viscosity
effects are taken into account. The next step will be to match efficient wall laws with Arbitrary
Lagrangian Eulerian (ALE) formulation and to take advantage of Full Multi-Grid Sequencing (FMG).
Figure 3.19: A340 A/C: Flight Mechanics axis definition (left) and pressure distribution, =2 (right).
VITAL project (F. Blanc)
VITAL project is an European project which began at the beginning of 2005. The goal is to reduce commercial
aircraft engines noise and emissions. Using the RANS software elsA, CERFACS is involved in the computation
of several jets on different complex configurations of bypass jet engine nozzles.
Among the challenges raised by the computations, one is mesh sizes required to precisely compute
jets (more than 11 millions of cells), see Fig. 3.20. In order to decrease the numerical cost,
we first extract coarser meshes from the original one and compute the flow on the coarser mesh using multi-grid
technique, and then, we use the solution obtained on the coarse mesh to initialize the flow on the refined one.
This is what we call the Full Multi-Grid Technique. Thanks to this technique, high convergence
levels can be achieved at a low numerical cost. VITAL project is an opportunity to use elsA on
new and realistic industrial configurations.
Figure 3.20: Mesh of a low noise exhaust nozzle
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