Comparison of Numerical Simulation of the Flow
around an Airfoil in High Lift Configuration with
PIV Experimental Results
D. Tran
DASSAULT AVIATION, 78 quai Marcel Dassault, 92552 Saint Cloud, France
Abstract
Airplane high lift systems allow to obtain aerodynamic characteristics required for
take-off and landing stages. In order to optimize such systems, it is necessary to
improve the understanding of the complex flow phenomena in high lift conditions
and to develop numerical methods capable to predict this flow with high accuracy.
In the framework of the Europiv2 project, velocity fields provided by PIV for the
ONERA RA16SC1 three component airfoil in high lift configuration offer an opportunity to acquire flow characteristics, to assess and validate numerical tools. In
this paper, 2D steady k-ε Navier-Stokes results are presented for 2 angles of attack
and compared to averaged PIV data.
For the slat, a good prediction of the stagnation point and the separated zone on
the windward side is observed.
Concerning the main body, computations as well as experiments show an increase of the boundary layer thickness and a delayed merging of the boundary
layer and the wake if the angle of attack becomes higher; but as expected for one
point turbulence closures, this mixing is slower in the case of computations.
Over the flap, a separated region although more limited in comparison with experiment, is observed in the numerical simulation for the lowest angle of attack
considered.
1 Introduction
Airplane high lift systems provide aerodynamic characteristics required during
take-off and landing stages (Fig. 1). An improved efficiency of such systems allows to increase airplane performance in terms of approach speed, landing and
take off lengths and loads, safety, noise. But, the analysis of the flow field around
a high lift configuration reveals a complexity with the coincidence of a variety of
flow phenomena such as separation, transition, interaction between wakes and
boundary layer (Fig. 2). In order to optimize such systems, it is necessary to well
understand the flow physics in high lift conditions and to develop numerical tools
capable to predict this flow with high accuracy.
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Fig. 1. Airplane in high lift configuration.
Fig. 2. Flow around an airfoil in high lift conditions.
Within Europiv1 and Europiv2, flowfield velocity data obtained by means of
the PIV technique offer opportunities on the one hand to study flow characteristics
and on the other hand to assess and validate numerical tools for high lift configurations. In Europiv1, the success of DLR PIV measurements in the AIRBUS Bremen wind tunnel (LSWT) for the ONERA RA16SC1 two element airfoil, has
demonstrated the applicability of this technique in industrial conditions and has
allowed to get a data base which was used for the validation of numerical simulation [1]. In Europiv2, the considered geometry is the RA16SC1 airfoil in landing
configuration with slat and flap deployed respectively at the positions of 30° and
40°. In addition to the main phenomena observed with a two component airfoil
(slat lower side separation and interaction between the slat wake and the main
body boundary layer), the presence of the flap generates other interesting phenomena such as :
- interaction between the wakes coming from the slat and the main body
with the flap boundary layer
Aeronautics 45
- for low and medium angles of attack, separation on the flap.
For this configuration, steady and unsteady velocity data fields provided by
PIV measurements allow to analyze the complex flow around a representative
high lift configuration and complement the Navier-Stokes code validation of Dassault Aviation.
In this paper, 2D steady k-ε Navier-Stokes results are presented and compared
to Europiv2 PIV data.
2 Steady Navier-Stokes Aether code
The main features of Dassault Aviation's steady Navier-Stokes Aether code are
Grids
The code can handle the unstructured mixture of numerous types of elements (triangles and quadrilaterals in 2D; tetrahedral, bricks and prisms in 3D).
Mean Flow transport Equations
Dassault Aviation's Navier-Stodes code solves the 2D, axisymmetric and 3-D
compressible Navier-Stokes equations.
Space discretisation
A finite element approach, based on a symmetric form of the equations is written
in terms of entropy variables. The advantages of this change of variables are numerous : in addition to the strong mathematical and numerical coherence they
provide (dimensionally correct dot product, symmetric operators with positivity
properties, efficient preconditioning), entropy variables yield further improvements over the usual conservation variables, in particular in the context of chemically reacting flows [2], [3].
Integration
The Galerkin/least squares (GLS) formulation introduced by Hughes and Johnson,
is a full space-time finite element technique, employing the discontinuous
Galerkin method in time [4]. The least square operator ensures good stability
characteristics while retaining a high level of accuracy. The local control of the
solution in the vicinity of sharp gradients is further enhanced by use of a nonlinear discontinuity capturing operator [4].
Acceleration
Convergence to steady state of the compressible Navier-Stokes equations is
achieved through a fully-implicit iterative time-marching procedure based on
GMRES algorithm with nodal block-diagonal preconditioning [5]. A low-storage
extension based solely on residual evaluations was also introduced [6]. It is particularly well adapted to parallel processing, where the linear solver often constitutes a painful bottleneck. This algorithm has proven extremely efficient on many
scalar or vector architectures [7, 8].
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Turbulence Models
Due to lack of universality of any turbulence model, several models are implemented in the Navier-Stokes code to cover the whole envelope of numerical
simulations. The models available today are the one equation Spalart-Almaras and
two-equations models such as k-ε SST wall functions, k-ε SST two layer, k-l, k-ω
SST, EARSM. In the k-ε SST two-layer formulation [9] used in this work, the turbulence kinetic energy equation and the mean flow equations are solved in the vicinity of the wall. The eddy viscosity and the turbulence dissipation are evaluated
using algebraic length scales. This option requires the distance to the wall to be
evaluated before the computation.
Turbulence model Implementation
In the Navier-Stokes code, all the turbulence models use the "eddy viscosity "
concept. The turbulent stresses and fluxes are modeled by analogy to molecular
stresses and fluxes. In this approach, generally referred to as the Boussinesq approximation, the effect of turbulence on the mean flow can be expressed in terms
of an eddy viscosity function µt and a turbulent Prandtl number assumed to be
constant (Pn= 0.9 for turbulent boundary layers). The eddy viscosity function µt is
computed with a turbulence model.
Coupling with the Navier-Stokes Equations
The discretized mean flow equations and the turbulence equations are integrated
using a splitting method. At a current time step, we solve the Navier-Stokes equations using turbulence data evaluated at the previous time while the turbulence
equations are solved using the flow variables computed at the current time step.
3 Geometry and wind tunnel tests in EUROPIV2
The studied geometry is the supercritical ONERA RA16SC1 airfoil in landing
configuration (Fig. 3); it is characterized by a slat and a flap having deflection angles of 30° and 40°.
RA16
flap 40 degrees; slat 30 degrees
Fig. 3. RA16SC1 Airfoil.
The wind tunnel model with a span equal to 2 m and a chord equal to 0.5 m,
was designed and manufactured by ONERA-IMFL with aerodynamic loads pro-
Aeronautics 47
vided by Dassault Aviation's computations. Experiments were carried out in the
LSWT wind tunnel by AIRBUS BREMEN and PIV measurements were performed by DLR. During this test campaign, pressure distributions were obtained
along the line of pressure taps located near the center line of the model for 20 angles of attack in the range between 0° and 19.5°. Because of a wind tunnel wall
separation which increased with angle of attack and which contaminated completely the wing for angles higher than 20°, the investigation was limited to 19.5°.
Concerning PIV measurements, they were performed for 3 angles of attack : 12°,
17.5° and 19°. In order to support these wind tunnel tests, Dassault Aviation had
provided two kinds of computational results :
- The first one was obtained with a pre-design level code based on an inviscid
panel method coupled with a viscous integral method; in the multi-component
airfoil case, this code also takes into account the mixing boundary layer and
wakes. As output, it provides in a very short time the global aerodynamic coefficients (Lift coefficient, Drag coefficient and Pitching moment) as a function
of the angle of attack. This code is a very useful and efficient tool during the
design loop of a project. Results obtained for the studied geometry have been
sent to ONERA for a strength analysis in order to prepare the model for wind
tunnel tests.
- The second part of the results was provided by 2D steady turbulent NavierStokes computations for the support of the test matrix definition and more precisely for the definition of 3 angles of attack of interest : 12°, 17.5° and 22°
(one in the linear part of the polar, one near maximum lift and one beyond the
maximum).
Perhaps, due to a more important blockage effect with the presence of the flap,
a strong separation not visible in Europiv1 experiments, appeared this time at the
wind tunnel walls which hold the model, leading to more 3D flow. Hence, during
the tests, it was observed that an important correction of the angle of attack was
necessary for the comparison between computed pressure distributions and experimental results. This correction can be obtained by using a strategy which will
be presented in the next chapter.
4 Computations
The upstream conditions are as follows :
V = 54 m/s Reynolds number = 1.8 106 based on the chord length C = 0.5 m.
The flow is supposed to be fully turbulent and free stream conditions were used
(no confinement). In these conditions, 2D k-ε SST steady Navier-Stokes computations have been performed for several angles of attack. The mesh used is unstructured; it contains 47,000 nodes. Fig. 4 shows an important concentration of
nodes near the wall.
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RA16SC1 slat 30 deg. flap 40 deg.
Fig. 4. Mesh.
4.1 Pressure coefficient
As mentioned above, because of a separation on the wind tunnel walls where there
was no boundary layer suction device, the flow became three dimensional for this
2D geometry. Hence, a correction of the angle of attack is necessary for comparison between 2D computation and 3D experiment.
This correction can be based on the same slat lift coefficient for both 2D computation and 3D experiment.
Fig. 5 shows that the correction is -2° for αexp equal to 6° and for αexp equal to
12°, 17.5° and 19° for which PIV measurements were performed, this correction is
equal to -4°.
Fig. 5. Slat lift coefficient.
Aeronautics 49
The equivalence between 3D experiment angles of attack and 2D numerical
simulation ones are given in table 1:
Table 1. Difference in angle of attack between experiments and computations
3D experiment
2D computation
6°
4°
12°
8°
17.5°
13°.5
19°
15°
Fig. 6 presents the comparison between computed pressure coefficient and experimental results with the consideration of the angle of attack correction. For the
slat, a good agreement is observed. On the lower side of this element, a region
without pressure gradient is visible; it is due to a separation which will be put in
light clearly with the velocity field analysis in the next chapter. Concerning the
main body, a very good prediction of pressure is obtained. Also, the decrease of
the pressure at the suction peak is observed if α increases. Regarding the flap,
numerical simulation gives results very comparable to the experiments, except for
αexp = 17.5° and 19° where computations overestimate slightly the pressure at the
peak suction.
Fig. 6. Pressure coefficient. Comparison between computations and measurements.
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In the light of this comparison, the strategy which consists in using an angle of
attack correction based on the same slat lift coefficient for both computation and
experiment, seems to be adequate.
4.2 Comparison between Computations and PIV Data
PIV measurements were performed for the angles of attack equal to 12°, 17.5° and
19°.
The analysis of pressure distributions in Fig. 6 shows that the results corresponding to the angles of attack equal to 17.5° and 19° are close to each other.
Hence, for comparison between 2D steady Navier-Stokes results and PIV data,
only the experimental angles of attack equal to 12° and 19° were considered.
Fig. 7 shows windows corresponding to different set-ups where instantaneous
and averaged velocity fields were measured by PIV [10]. For comparison between
steady Navier-Stokes results and PIV data, averaged experimental velocities given
in these windows were used.
Fig. 7. PIV windows for different set-ups.
4.2.1 Velocity field
Fig. 8 gives the comparison between computation (continuous lines) and PIV
results (dashed lines) for αexp equal to 12°. Several flow phenomena mentioned
above for a 3 component airfoil in high lift configuration can be seen (separation
on the slat lower side, slat wake and main body boundary layer interaction, main
body cove separation, slat wake-main body wake and flap boundary layer interaction,..).
Aeronautics 51
Fig. 8. Mean velocity modulus. Comparison between computation and PIV data for α =
12°.
In Fig. 9, velocity modulus is shown for the slat with PIV data represented by
dashed lines and computed velocities by solid lines. A good prediction of the stagnation point on the slat can be observed; with increasing angle of attack, this point
moves towards the slat edge. Under this element of the geometry, a separation
bubble is visible; its shape and its reverse flow are also correctly reproduced by
numerical simulations. As expected, the bubble size decreases if the angle of attack increases. In the gap between the slat and the main body, the flow is correctly
predicted and no blockage effect is observed.
(a)
(b)
Fig. 9. Mean velocity modulus under the slat for α = 12° (a) and 19° (b). Comparison between computations and PIV data.
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Over the forward part (Fig. 10) and the rear part (Fig. 11) of the main body, a
decelerated flow also visible with pressure analysis in Fig. 6, is disturbed by the
slat wake. Comparison between numerical prediction and experiment shows a
pretty good agreement for the flow above the wake for 2 angles of attack. Concerning the boundary layer and the slat wake, an analysis in detail will be performed with the study of extracted velocity profiles in Fig. 15. Also, one can see
the PIV data dispersion in the overlapping region of the windows D and E where
the data in window D are a little bit different from those in window E. For the
window G (Fig. 11) where experimental results are obtained from 3 set-ups, a
small dispersion is also observed.
(a)
(b)
Fig. 10. Mean velocity modulus over the forward part of the main body for α = 12° (a) and
19° (b). Comparison between computations and PIV data.
(a)
(b)
Fig. 11. Mean velocity modulus over the rear part of the main body for α = 12° (a) and 19°
(b). Comparison between computations and PIV data.
In Fig. 12 corresponding to window K, the flow given by computations in the
separated region of the main body cove, is close to experiments. On the flap, the
stagnation point is correctly predicted. In the gap between the main body and the
flap, no blockage effect is observed.
Aeronautics 53
(a)
(b)
Fig. 12. Mean velocity modulus under the rear part of the main body for α = 12° (a) and
19° (b). Comparison between computations and PIV data.
Fig. 13 presents results over the flap. We can observe the disturbances generated
by the slat wake and the main body wake in the decelerated flow. If the angle of
attack increases, the slat and main body wakes become more pronounced for both
computed and experimental results.
Regarding the main body wake region, the flow is decelerated up to a region
where the velocity value is very low. This area observed over the flap trailing
edge, is located farther downstream in the case of experiments.
(a)
(b)
Fig. 13. Mean velocity modulus over the flap for α = 12° (a) and 19° (b). Comparison between computations and PIV data.
4.2.2 Velocity profiles
Fig. 14 presents the locations where velocity profiles are extracted: 3 profiles over
the main body and 2 profiles over the flap.
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Fig. 14. Locations of extracted velocity profiles.
In Fig. 15, the velocity profiles at stations 1, 2 and 3 located over the main body
are displayed. We can see that the prediction is close to experiment in the boundary layer at stations 2 and 3 and for the flow above the slat wake.
As it was observed in Europiv1 [1], the mixing between the slat wake and the
main body boundary layer is slow in the case of computations. This discrepancy
with experiment can be explained by the hypothesis used for one point turbulence
closures that kinetic turbulent energy spectrum is in equilibrium; which is not the
case for this wake fed by a large separated zone under the slat.
If α increases, both experiments and computations show the effects such as:
- an increase of the boundary layer thickness
- a more pronounced wake
- a delayed merging of the boundary layer and the slat wake.
(a)
(b)
Fig. 15. Velocity profiles for α = 12° (a) and 19° (b). Comparison between computations
and PIV data.
Fig. 16 displays the velocity profiles at station 4 located at mid-chord of the
flap. We can observe a correct prediction of the boundary layer for α = 19° and
the minimal value of the main body wake velocity for 2 angles of attack. If α in-
Aeronautics 55
creases, the wakes become more pronounced for both computations and experiments.
(a)
(b)
Fig. 16. Velocity profiles for α = 12° (a) and 19° (b). Comparison between computations
and PIV data (station 4).
Concerning the velocity profile at station 5 located over the flap trailing edge,
computed results are very different from PIV data for α = 12° (Fig. 17). The discrepancy is due to the presence of a separation bubble which is important with experiment but very thin in the case of computation as we can observe with streamline analysis (Fig. 18, Fig. 19 and Fig. 20).
For the case of α = 19°, the minimal value of the main body wake velocity is
predicted correctly.
(a)
(b)
Fig. 17. Velocity profiles for α = 12° (a) and 19° (b). Comparison between computations
and PIV data (station 5).
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4.2.3 Streamlines
Fig. 18 displays over the flap streamlines obtained with experimental velocity
fields. At α = 12°, the flow is separated on the last third part of the flap but remains attached for the case of α = 19°.
(a)
(b)
Fig. 18. PIV streamlines for α = 12° (a) and 19° (b).
In Fig. 19, no separation can be seen with computed streamlines for 2 angles of attack. But a close-view near the flap trailing edge wall shows a
separation for α = 12° but more limited in comparison with the experiment
(Fig. 20). These results are confirmed by the analysis of the skin friction
which is negative at the flap trailing edge for this angle of attack (
Fig. 21). It would be interesting to know whether the difference between computation and experiment, concerning the separated area size, is due to the turbulence model or to the three-dimensionality of experimental flow.
(a)
(b)
Fig. 19. Computed streamlines for α (experiment) = 12° (a) and 19° (b).
In Fig. 19, another result can be observed : at α = 19°, the steady computation
displays a strong deformation of streamlines over the flap trailing edge. This phe-
Aeronautics 57
nomenon which is also shown by several PIV snapshots based on instantaneous
velocity fields (Fig. 22), is not visible with averaged experimental results (Fig. 18).
(a)
(b)
Fig. 20. Computed streamlines near the flap wall for α (experiment) = 12° (left) and 19°
(right).
Fig. 21. Computed skin friction coefficient.
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5 Conclusions
2D Steady Navier-Stokes computations using the k-ε SST turbulence model for
the RA16SC1 airfoil in landing configuration have been carried out with the unstructured Aether code.
Due to a wind tunnel wall separation leading to a 3D flow for this 2D geometry, an angle of attack correction was necessary for comparison of 2D numerical
simulation with PIV data. This correction obtained by considering the same slat
lift coefficient for both computation and experiment, has allowed to observe a
good agreement in wall pressure distribution between 2D computation and 3D experiment.
(a)
(b)
Fig. 22. Streamlines obtained with instantaneous PIV results (run 537 images n°16 (a) and
n°34 (b)).
Within the flow field, the comparison of computations with PIV data has shown
in the slat region a good prediction of the stagnation point location, the lower side
separation and the flow in the gap between the slat and the main body.
Concerning the main body, the comparison with experiment is correct for the
flow in the boundary layer and above the wake. With increasing angle of attack,
computations as well as experiments show an increase of the boundary layer
thickness and a delayed merging of the boundary layer and the wake. But, as expected for one point turbulence closures, this mixing is slower in the case of computations.
On the flap, the change from a separated flow to an attached one if the angle of
attack increases, is predicted by CFD. But, the separated area observed at low angle of attack is more limited in the case of numerical simulation.
Note that the quality of the previous comparison is submitted to several sources
of uncertainties such as :
- transition locations which were not measured during tests and which
should be taken into account in computations instead of fully turbulent calculations
- three-dimensionality of experimental flow due to wind tunnel wall separation.
Aeronautics 59
In conclusion, owing to velocity fields provided by PIV, a detailed study of
flow characteristics has been possible. This analysis allows to improve the understanding of physics of the complex flow surrounding typical high lift configurations and therefore contributes to enhance our capability to predict this kind of
flow.
As far as code validation is concerned, a pretty good agreement is observed
between averaged PIV data and 2D steady computations (RANS), using the k-ε
SST turbulence model. Such results are achieved despite the weakness of one
point turbulence closure and the sources of uncertainties mentioned above (threedimensionality of experimental flow and transition locations).
Currently, unsteady computations are under way and comparison with instantaneous velocity fields provided by PIV, will be performed.
In the long term, the experimental data base obtained within EUROPIV2 will
be used for additional numerical investigations in order to improve turbulence
models and validate LES and DES codes.
Acknowledgement
This work has been performed under the EUROPIV 2 project: EUROPIV 2 (A
Joint Program to Improve PIV Performance for Industry and Research) is a collaboration between LML URA CNRS 1441, Dassault Aviation, DASA, ITAP,
CIRA, DLR, ISL, NLR, ONERA, DNW and the universities of Delft, Madrid,
Oldenburg, Rome, Rouen (CORIA URA CNRS 230), St Etienne (TSI URA
CNRS 842) and Zaragoza. The project is managed by LML URA CNRS 1441
and is funded by the CEC under the IMT initiative (contract no: GRD1-199910835).
We would like to acknowledge the good cooperation with all the partners involved in Task 3.1 and Task 3.2. We also wish to thank Mr. J.C. Courty and F.
Chalot of Dassault Aviation for their fruitful discussions.
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