Unsteady aerodynamics of wings with an oscillating flap ... - Pegasus

Unsteady aerodynamics of wings with an oscillating
flap in transonic flow
Diliana Dimitrov ∗
Institute of Aerospace Engineering, Technische Universität Dresden /
Institute of Aeroelasticity, German Aerospace Center (DLR)
Within the scope of this paper the behavior of unsteady flow due to oscillating flaps
on the airfoil NLR 7301 and the AFMP wing is analysed. For the two-dimensional model,
the two flow solvers of DLR (TAU) and ONERA (elsA) are applied. Therefore, a comparison
not only with experimental data but also among both CFD-results is carried out.
Although it exists a good agreement for this two-dimensional experiment and the numerical
solutions, differences in the turbulence models of the codes are exhibited. The
three-dimensional delta wing is calculated using TAU. Surprisingly, the experimental data
is only partly reproduceable with the CFD code. Despite the existing discrepancies, the
nature of unsteady flow due to an oscillating flap can be found in the experiment as well
as in the numerical results.
Nomenclature
c f
c p
f
K
l
t
U
Skin friction coefficient
Pressure coefficient
Frequency, Hz
Turbulent kinetic energy, m2
s 2
Reference length, m
Time, s
Velocity, m s
x
Symbols
Coordinate, normalized by reference length
α Angle of attack, °
δ a Flap amplitude, °
δ m Mean flap angle, °
ω Specific rate of dissipation, 1 s
ω ∗ Reduced frequency
I. Introduction
The understanding of unsteady flow dynamics is essential in the design of an aircraft and its control
system. Even small deflections of e.g. an aileron can lead into a risky situation. Phenomena like flutter
should be avoided. Since state-of-the-art transport aircraft fly at Mach numbers in the transonic region, and
hence close to the so called ”Transonic Dip” (Tijdeman 1 ), such considerations become more important. An
accurate prediction of the unsteady aerodynamics is needed and higher-order methods as CFD have to be
applied.
One of the first measurements of unsteady pressure in a windtunnel was carried out by Erickson and
Robinson 2 in 1948. In the mid-70s the first publications occured which compared measured windtunnel
data and calculated values. The Dutch scientist Tijdeman accomplished several numerical and experimental
investigations in this field during his dissertation in 1977. 1 Until now, a lot of simulations have been carried
out in the area of unsteady control surface aerodynamics, e.g. Müller et al., 3, 4 Nitzsche et al. 5 or Yoshihara
et al. 6, 7 But most of these calculations use relatively simple aerodynamic methods and only very few include
viscous effects. That is why they are mostly limited to the linear range, i. e. subsonic flow conditions. To
avoid such limitations, the Reynolds-averaged Navier-Stokes equations will be applied during this work.
Moreover, due to a lack of computational support, most of the time only two-dimensional configurations
were in the centre of attention. This work extends the investigations to a three-dimensional model with an
∗ Research Assistant, Institute of Aeroelasticity, German Aerospace Center (DLR), Bunsenstr. 10, 37073 Göttingen, Germany
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oscillating trailing edge device. So far, only two publications, by Isogai et al. 8 and Karlsson et al., 9 are
known that deal with such a more complex model.
The motivation for the current investigations can be found in the attempt to gain more insight into the
the simulation of two- and three-dimensional unsteady aerodynamics by a more accurate way of simulation
and also to be able to judge its quality. Two CFD codes are applied for the numerical calculations: ”TAU”, 10
developed by the German Aerospace Center (DLR), and ”elsA”, 11 which is provided by the French aerospace
research center (ONERA).
II.
Numerical Modelling
All calculations carried out are based on the Reynolds-averaged Navier-Stokes (RANS) equations. The
derivation of this set of equations can be found in e.g. Ferziger 12 and Pope. 13 For the closure of this system
of equations, turbulence models are needed. In this paper, mainly K-ω-based versions like the Menter SST
(SST for ”Shear Stress Transport”) and Menter BSL (BSL for ”Baseline”) model 14 are applied. K denotes
the turbulent kinetic energy, ω the specific rate of dissipation.
TAU and elsA are based on the Finite-Volume-Method and solve the three-dimensional, time-dependent
Navier-Stokes equations. Although TAU calculates on unstructured grids and elsA uses a structured formulation,
both fluid solvers have similar numerical implementations. For the temporal discretisation a local
timestepping is applied for steady cases and a dual timestepping (Jameson 15 ) for the unsteady cases.
Figure 1 shows the meshes of both solvers for the NLR airfoil, exemplarily. The oscillation of the flap is
numerically modelled by a mesh deformation which is in TAU based on radial basis functions 16 and in elsA
based on a mixed analytical/transfinite interpolation. 17
0.2
0.2
0.1
0.1
z
0
z
0
-0.1
-0.1
-0.2
0 0.2 0.4 0.6 0.8 1
x
(a) TAU
-0.2
0 0.2 0.4 0.6 0.8 1
x
(b) elsA
Figure 1. Spatial discretisation for the NLR 7301
III.
Characteristics for an Airfoil with Oscillating Flap
Unsteady aerodynamic forces can be caused by different mechanisms. Regarding the case of an airfoil
with oscillating flap, mostly a forced motion due to e.g. a steering commando introduces the unsteadiness.
The most important geometric quantities of an airfoil with oscillating flap are displayed in Figure 2.
z
y
x
hinge line
chord length l
flap
δ a
(-) δ
δ m
δ (+)
0
a
δ
Figure 2.
Definition of the parameters on an airfoil with oscillating flap
The flap is excited harmonically over time with an amplitude δ a and a frequency f
δ(t) = δ m + Re(δ a e i2πft ). (1)
The frequency f can be expressed in a dimensionless way as reduced frequency ω ∗ with a characteristic
length l, e.g. the chordlength, and the freestream velocity U as scaling factors
ω ∗ = 2πflU −1 . (2)
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Due to the transonic and therefore non-linear flow, the response of the fluid is not expected to be harmonic,
but at least periodic. A Fourier-analysis is applied, for example to the pressure coefficent c p :
c p (x, t) = c p,m (x) +
∞∑ [
c
n
p,δ (x) δ a e in2πft] , (3)
n=1
where c p,m describes the mean pressure distribution and n the number of the harmonic oscillation. With sufficient
accuracy, and only if the amplitude δ a is small, only the first harmonic has to be taken into account, so
n = 1. For the following analysis, the absolute and the phase value of the complex number will be considered,
which are shortly denoted as |c p | and P hase(c p ). In preparation for the calculations with unsteady control
surface oscillations, analyses of the results of Tijdeman 1 and Nitzsche et al. 5 have been carried out. So far,
there is no full physical explanation which applies to all cases in the unsteady aerodynamics. Nevertheless,
Tijdeman 1 offers some explanations for at least some of the phenomena. Characteristic results for unsteady
flow around an airfoil with oscillating flap can be found in Figures 3 and 5.Typically, a singularity at the
hinge line is formed. The magnitude of the pressure has a local maximum, whereas the phase shows a root.
Tijdeman states that the flap can be regarded as pulsating pressure disturbance at the hinge line, see Figure
4. Pressure waves are spread out and amplify the signal.
10
|cp |
flap
10
|cp|
flap
30
|cp|
flap
x
x
x
(a) subsonic
(b) transonic, weak shock
(c) transonic, strong shock
Figure 3. Typical trends of the magnitude of the complex pressure coefficient, |c p|, along the chord for an oscillating
flap after analysis of the results of Tijdeman 1 and Nitzsche et al. 5 (the given numbers should be seen as general order
of magnitude and do not display any limits or the like)
8Δt 6Δt
10Δt
Ma>1
4Δt
propagating
wave
2Δt
Δt
pressure
disturbance
Figure 4.
Propagation of disturbances over time around a transonic airfoil
Phase(cp)
0°
flap
Phase(cp)
0°
flap
Phase(cp)
0°
flap
x
x
x
(a) subsonic
(b) transonic I
(c) transonic II
Figure 5. Typical trends of the phase of the complex pressure coefficient, P hase (c p), along the chord for an oscillating
flap after analysis of the results of Tijdeman 1 and Nitzsche et al. 5
Three basic types of unsteady pressure results can be observed. In subsonic flow, the magnitude shows
one additional local maximum at the suction peak. The phase proceeds almost linearly from trailing to
leading edge due to the increasing duration of the signal. The pressure magnitude for transonic flow shows
additional maxima which result from the movement of the shock during one cycle. The peak is higher with
increasing strength of the shock. The trend of the phase in transonic flow exhibits a strong rise which
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corresponds to a phase delay in the region of the shockfront. Regarding the theory of Tijdeman, the delay
can be explained due to an impounding of the waves at the shockfront when they propagate upstream. But
the sudden rise and fall of the phase curve in the flow condition called ”transonic II” is not yet explainable
by a physical background. Perhaps, the reason for this flow feature is caused by the previous period of
oscillation or the flow at the lower side of the airfoil. Further studies concerning signal propagation would
be necessary to clarify this context.
IV.A.
Test cases
IV. NLR 7301
Before unsteady calculations will be carried out on a 3D configuration, the application of both codes on a
2D configuration will be tested. The supercritical airfoil NLR 7301 is chosen due to its high thickness (max.
16.5% of the chordlength) and therefore complex flow physics. Also, as mentioned in the introduction, several
calculations and comparisons to the AGARD windtunnel-tests have been carried out, see Paraschivoiu, 18
Müller et al. 3, 4 and Tarhan et al. 19 . But none of them has applied a fluid solver based on the RANS
equations with eddy-viscosity-hypothesis. Moreover, the NLR 7301 is widely used at the DLR Institute of
Aeroelasticity. Several numerical simulations and flutter calculations have been carried out, e.g. by Schewe
et al., 20 Nitzsche 21 and Šoda.22 Calculations for the airfoil with an oscillating flap have not yet been done.
The AGARD Report 23 from the year of 1982 offers plenty of experimental test cases which provide data
that can be used to validate numerical simulations. Due to the relatively small cross-section (0.55m x 0.42m)
of the windtunnel, some interference effects were observed in the windtunnel data. Table 1 gives an overview
of the experimental test cases and proposed corrected data that should be used for numerical simulations.
Table 1. Test cases of NLR 7301 with oscillating flap, AGARD, 23 δ m = 0°, ,,CT”: ,,Computational Test”
Simulation Experiment Expected
Test Case Mach α[°] δ a [°] ω ∗ Mach α[°] δ a [°] ω ∗ Flow Physics
CT z4 0.5 0.4 1.0 0 0.503 0 0.95 0 subsonic
CT 10 0.5 0.4 1.0 0.196 0.502 0 0.97 0.196
CT z5 0.7 2.0 1.0 0 0.702 3.0 0.95 0 transonic,
CT 11 0.7 2.0 1.0 0.142 0.701 3.0 0.97 0.142 with shock
Two subsonic and transonic cases will be calculated. Transonic flow occurs already at relatively low Mach
numbers due to the high thickness of the airfoil. The flap is placed at 75% of the chord.
IV.B.
Comparison between TAU and Experiment
Starting with the steady case CT z4, the calculated and the experimental data does not match very well.
With the given angle of attack of α = −0.4° a much higher lift is predicted than it was measured. As
Figure 6 shows, an angle of attack of −0.4° seems to be more reasonable and is therefore taken for further
investigation.
-1.2
-1
-0.8
Experiment
Ma=0.5, α=0.4
Ma=0.5, α=-0.4
-0.6
-0.4
-0.2
c p
0
0.2
0.4
0 0.2 0.4
x
0.6 0.8 1
Figure 6. Variation of the angle of attack α at Mach 0.5
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Regarding the transonic test case, a variation of turbulence models is carried out in order to see, which
one captures the flow physics the best. To get a deeper insight, also the skin friction coefficient is treated.
Based on the different formulations for the eddy-viscosity in the different models, the deviations become
most obvious in this parameter.
-1.5
-1
-0.5
Experiment
SAO
Menter BSL
Menter SST
Wilcox
Wilcox SST
LEA
TNT
0.01 SAO
Menter BSL
Menter SST
Wilcox
0.008
Wilcox SST
LEA
TNT
0.006
0.004
c p
0
0.002
0.5
0 0.2 0.4 x 0.6 0.8 1
c fx
0
0 0.2 0.4 x 0.6 0.8 1
(a) Pressure distribution
(b) Skin friction distribution
Figure 7.
Influence of different turbulence models, CT z5
The turbulence models show a wide range of results, regarding the shockposition. All of them capture
the position too far aft, only the Menter SST shows reasonble agreement, also in the pressure niveau before
the shock. In this case, only SAO (Spalart-Allmaras 24 ) predicts a slight shock-induced separation, which is
displayed in c fx and contrary to all the other models. That shows one of the limitations of this one equation
model, as it is mentioned in e.g. Bardina et al.: 25 separated flow is not reasonable predictable with SAO.
Since the agreement of experimental and numerical pressure distribution especially in the region close to the
shock is best with Menter SST, this model is chosen for further calculations.
Regarding unsteady simulations, also a time independent solution has to be ensured. A convergence study
for the different parameters in dual timestepping led to 504 timesteps per period and 200 inner iterations
for at least 6 periods of simulation. These values also correspond to the parameters used by Šoda.22
The result of the unsteady subsonic test case in Figure 8 shows the pressure distribution as expected
from chapter III. The magnitude of the pressure exhibits peaks at leading edge and hinge line, the phase is
growing with increasing chord. Experimental and numerical data agree well in both diagrams.
6
Exp, up
Exp, low
TAU, up
TAU, low
180
135
|c p
|
4
2
Phase(c p
) [°]
90
45
0
0
0 0.2 0.4 0.6 0.8 1
x
(a) Magnitude
-45
0 0.2 0.4 0.6 0.8 1
x
(b) Phase
Figure 8.
Magnitude and phase of the unsteady pressure coefficient c p for a subsonic oscillating flap
Figure 9 displays also the same behavior as described in chapter III. Due to the shock motion, an
additional peak rises in the magnitude of the pressure, compared to the subsonic case. It reaches almost
10 times higher values than the one at the hinge line. The phase shows the mentioned phase lead on the
upper side, just behind the shock, and a linear phase growth on the lower side of th airfoil. Again, a good
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agreement between windtunnel and simulation data can be observed.
25
20
Exp, up
Exp, low
TAU, up
TAU, low
270
225
180
|c p
|
15
10
Phase(c p
) [°]
135
90
45
5
0
-45
0
0 0.2 0.4 0.6 0.8 1
x
-90
0 0.2 0.4 0.6 0.8 1
x
(a) Magnitude
(b) Phase
Figure 9.
Magnitude and phase of the unsteady pressure coefficient c p for a transonic oscillating flap
IV.C.
Comparison between TAU and elsA
So far, all the numerical data have been obtained using the TAU code. It has shown to produce good results
for a simulation of an airfoil with oscillating flap. Since windtunnel results are often influenced by e.g.
windtunnel wall effects or uncertainties in the measurement process, another possibility of validation is the
code to code comparison. Therefore, the following chapter deals with a comparison between TAU and elsA
in order to be able to judge their strength or weaknesses.
As in TAU, elsA offers a variety of turbulence models for the simulations. A similar scattering of the
curves as in TAU is observable. Figure 10 shows a comparison of Menter BSL and Menter SST. Contrary
to TAU, the best agreement with the experiment is achieved by the Menter BSL in elsA. That is why it is
applied for further elsA calculations.
Although the results from elsA seem to be shifted upstream in comparison to TAU, the trends for the
models with and without SST correction in both solvers are the same: SST predicts the shock further
upstream than BSL. Another tendency that can be observed is the minimum level of the skin friction
coefficient in both CFD codes: the TAU results are closer to separation than the ones calculated with elsA.
Deeper investigation would be needed to check, which differences in the implementation of the models is
causing these deviations. The default values of the according code have been used for each turbulence model.
-1.5
-1
Experiment
Menter SST, TAU
Menter BSL, TAU
Menter SST, elsA
Menter BSL, elsA
0.01
0.008
Menter SST, TAU
Menter BSL, TAU
Menter SST, elsA
Menter BSL, elsA
0.006
-0.5
0.004
c p
0
0.002
0.5
0 0.2 0.4
x
0.6 0.8 1
(a) Pressure distribution
c fx
0
0 0.2 0.4
x
0.6 0.8 1
(b) Skin friction distribution
Figure 10.
Transonic case CT z5 in comparison between TAU and elsA for Menter BSL and Menter SST
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Having a closer look at the turbulent variables K and ω, the differences of the solvers can be explained
in more detail. Figure 11 shows the contour of the specific rate of dissipation ω for Menter SST in TAU and
Menter BSL in elsA. On the upper surface up to the position of the shock, a perfect match of both curves
can be observed, which is also reflected in the skin friction coefficient for both models. Over the shock, a
sudden rise of ω is calculated in TAU which is remarkably lower according to the results of elsA. That is why,
directly behind the shock, due to a higher dissipation, the skin friction coefficient in TAU is predicted lower
than in elsA. It should be added, that this steep gradient in ω does not only apply to the Menter SST model
in TAU but also to the Menter BSL version. That leads to the assumption, that there is a basic difference
between the implementation of the models in the two codes.
0.2
0.1
ω
elsA
TAU
Z
0
-0.1
0.2 0.4 X 0.6 0.8
Figure 11.
Contur of the specific rate of dissipation ω around the airfoil in comparison between TAU and elsA
Regarding the second turbulent variable, the turbulent kinetic energy K, additional differences between
the two codes can be seen. Figure 12 displays that the flow calculated by TAU has a higher turbulent
kinetic energy in comparison to the result obtained by elsA. That supports the assumption of different
implementations of the models in the two solvers.
0.15
0.1
50 287.5 525 762.5 1000
0.15
0.1
50 287.5 525 762.5 1000
0.05
0.05
Z
0
Z
0
-0.05
-0.05
0.2 0.4 X 0.6 0.8
(a) TAU
0.2 0.4 X 0.6 0.8
(b) elsA
Figure 12.
Comparison between the turbulent kinetic energy K of the flowfield
The unsteady cases are calculated with those turbulence models that matched best the experiment in the
steady cases: Menter SST in TAU and Menter BSL in elsA. The results for the unsteady calculation show a
quite good agreement, despite some small differences in the region around the shock.
25
20
TAU, up
TAU, low
elsA, up
elsA, low
270
225
180
|c p
|
15
10
Phase(c p
) [°]
135
90
45
5
0
-45
0
0 0.2 0.4 0.6 0.8 1
x
-90
0 0.2 0.4 0.6 0.8 1
x
(a) Magnitude
(b) Phase
Figure 13. Magnitude and phase of the unsteady pressure coefficient c p for the unsteady transonic case CT 11 in
comparison between TAU and elsA
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Alltogether, both codes seem to predict the flow for an airfoil with oscillating flap in a good quality so
that the next step can be the application onto a 3D model.
V.A.
Geometry and Test cases
V. AFMP wing
The data for this 3D windtunnel model was obtained during a campaign in 2007 in the S2MA windtunnel
26 of the french ONERA. It results out of a cooperational project together with several departments of
the ONERA, Dassault Aviation, Alenia and EADS. Although the exact dimensions of the model underlie
restrictions, Figure 14 should give an impression of the used geometry. The flap is placed at 30% chord of
the wing and does not cover all the span. Pressure sensors of the depicted sections 1, 3 and 6 will be taken
for examination. Displayed is also the surface discretisation of the wing.
y
z
x
(a) Windtunnel model
(b) Surface discretisation
Section
1 3 6
(c) Pressure sensor sections
Figure 14.
Geometry of the AFMP wing
So far, two publications are known which deal with calculations for this delta wing. Both, Fleischer 27
and Cavecchia, 28 encounter difficulties in the recalculation of the experimental data. Especially transonic
flow conditions are not well captured.
In this paper, only the TAU results for the AFMP wing will be shown since the elsA results were calculated
by the ONERA department DADS. 29 The test cases are given in Table 2.
Table 2.
Test cases of the AFMP wing, 30 reference length for ω ∗ is a mean chord
Test case Ma α[°] δ a [°] ω ∗ Expected flow physics
Lot 700 0.8 2.0 0 0 subsonic
Lot 707 0.8 2.0 0.5 0.450
Lot 711 0.85 2.0 0 0 transonic,
Lot 718 0.85 2.0 0.5 0.426 with shock on lower side
V.B.
Steady Results
The result of the subsonic case is displayed in Figure 15. A systematic difference from TAU to the experiment
becomes visual. The flow in TAU is less accelerated, which results in a higher niveau of the pressure coefficient
in the region around the leading edge. A better agreement can be found around the trailing edge.
Regarding the transonic case Lot 711 (Figure 16), not only a translational deviation of the TAU results
can be observed, but also differences in the trend of the curves, e. g. it fails in predicting a shock on the
lower surface as it appears in the experiment.
After the good agreement at the NLR airfoil, a better match has been expected. Therefore, various
physical and numerical parameter studies with TAU were carried out, e.g. change of flux discretisation and
comparison of geometry. But so far, a definite source for these differences could not be found.
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-0.6
-0.6
-0.6
TAU
Experiment
-0.4
-0.4
-0.4
-0.2
-0.2
-0.2
c p
0
c p
0
c p
0
0.2
0.2
0.2
0 0.2 0.4 0.6 0.8 1
x
(a) Section 1
0 0.2 0.4 0.6 0.8 1
x
(b) Section 3
0 0.2 0.4 0.6 0.8 1
x
(c) Section 6
Figure 15. Pressure distribution of TAU and experiment on the AFMP wing, Lot 700
-0.8
-0.6
TAU
Experiment
-0.8
-0.6
-0.8
-0.6
-0.4
-0.4
-0.4
-0.2
-0.2
-0.2
c p
0
c p
0
c p
0
0.2
0.2
0.2
0 0.2 0.4 x 0.6 0.8 1
(a) Section 1
0 0.2 0.4 0.6 0.8 1
x
(b) Section 3
0 0.2 0.4 0.6 0.8 1
x
(c) Section 6
Figure 16. Pressure distribution of TAU and experiment on the AFMP wing, Lot 711
V.C.
Unsteady Results
Since no reasonable agreement could be achieved for the steady cases, it is not expected to have less deviations
in the time-dependent calculations. Especially in transonic flow, the steady solution influences the unsteady
flow. There might be different observations for the subsonic cases, because the steady and unsteady flowfields
can be regarded as independent, see Tijdeman. 1
Figure 17 shows magnitude and phase of the pressure coefficient for TAU and the experiment for Lot
707 at section 3, exemplarily. Since elsA results are only available with different forced motion kinematics
and at a slightly higher Mach number, a direct comparison does not seem reasonable for these cases. For a
better overview, the magnitude of the lower side is multiplied by -1.
Although the corresponding steady case (Lot 700) does not show a good agreement, the unsteady test
case gives a good match for TAU and the experimental data. The nature of the subsonic flow becomes
visible: steady and unsteady flowfields can be regarded as independent and do not influence each other.
Therefore, such different agreements can be obtained. Furthermore, a correct input of numerical and flow
parameters can be assumed, even if there are differences in the steady cases. Maybe, this is a hint for the
existence of interfering windtunnel effects that are not included in the numerical simulations. Alltogether,
the magnitude is matched better than the phase.
Figure 18 shows the results of the unsteady transonic test case Lot 718. As expected, the agreement
is worse than in the subsonic case. Due to the influence of the bad matching steady results, there is
also bad agreement in the unsteady data. Although the tendency for the pressure magnitude is predicted
comparably well, the phase shows a different behavior in the experiment, when compared to TAU. Moreover,
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the existence of a shock in the experiment becomes obvious: a peak in the magnitude and a phase delay are
present, whereas the simulation does not show any of those effects.
-|c p
| low
, |c p
| up
4
2
0
-2
-4
0 0.2 0.4 x 0.6 0.8 1
(a) Magnitude
Phase(c p
) [°]
360 Exp, up
Exp, low
270
TAU, up
TAU, low
180
90
0
-90
-180
0 0.2 0.4 x 0.6 0.8 1
(b) Phase
Figure 17.
Unsteady transonic test case Lot 707, Section 3: complex pressure coefficient
-|c p
| low
, |c p
| up
10 Exp, up
Exp, low
TAU, up
TAU, low
5
0
-5
0 0.2 0.4 x 0.6 0.8 1
(a) Magnitude
Phase(c p
) [°]
360
270
180
90
0
-90
-180
0 0.2 0.4 x 0.6 0.8 1
(b) Phase
Figure 18.
Unsteady transonic test case Lot 718, Section 3: complex pressure coefficient
VI.
Conclusion and Future Work
This paper presented an insight to the simulation of unsteady aerodynamics based on configurations with
an oscillating flap.
As a conclusion it can be stated that a reliable numerical simulation for two-dimensional configurations
in transonic flow can be carried out with both applied fluid solvers TAU and elsA. There are differences
between both codes which can be tracked down to a different behavior of the turbulence models, in this
particular case for the models Menter BSL and Menter SST. Nevertheless, each solver is able to capture
the characteristics in the unsteady pressure distribution that were recorded during the AGARD windtunnel
tests.
Having a look on the three-dimensional AFMP wing, bigger differences occure. Moreover, the experimental
test cases could not be recalculated successfully. That is why further investigations concerning the
experimental conditions will be needed to check the boundary conditions e.g. windtunnel interferences or unexpected
model deformation before more numerical simulations can be carried out. Despite those problems,
it can be stated that in general TAU is capable of calculating three-dimensional unsteady configurations
with control surfaces. Its quality needs still to be verified.
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Acknowledgments
The author thanks the ONERA department DADS for the hospitality during the 2-months stay in
Châtillon, Paris, and also the well-guided introduction to first calculations with elsA.
References
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