NUMERICAL STUDY OF TRANSONIC BUFFET CONTROLBY MEANS OF FLUIDIC TRAILING EDGE DEVICE

Gaetan Browaeys1, Hugues Deniau2,Erwan Collin1 and Jean-Paul Bonnet1

1 Laboratoire d’Etudes Aerodynamiques (LEA)Universite de Poitiers, ENSMA, CNRS

LEA/CEAT, 43 route de l’Aerodrome 86036 Poitiers Cedex, France

2 Centre Europeen de Recherche et de Formation Avanceen Calcul Scientifique (CERFACS)

CERFACS, 42, Avenue Gaspard Coriolis, 31057 Toulouse Cedex 01, France

SummaryThe present paper deals with the numerical simulation and the control of shock wave oscillations over an OAT15A

wing profile at transonic speed. Numerical resolution of Unsteady Reynolds Average Navier-Stokes equations allowsreproducing the transonic buffet phenomenon in good agreement with the experimental investigation performed by Jacquinet al (2005). In order to control the unsteadinesses of the shock, several methods are available. The more common oneis to use actuators such as micro-jets located at the vicinity of the shock. An alternative solution has been proposed byCaruana et al (2005), in acting at the trailing edge location by a mechanical micro-flap (Trailing Edge Device, TED)located on the pressure side of the airfoil. The purpose of the present paper is to explore a fluidic version of the TED(FTED). This fluidic trailing edge acts as a deflector that allows the control of the shock oscillations and increases thewing aerodynamic performances. One major advantage of the method is its availability to produce unsteady effect, thenallowing for developing a cloosed-loop active blowing based on the shock position. The closed-loop is abble to reducethe amplitude of the shock oscillation and the time required to stop the instability.

1 IntroductionIn transonic aircraft applications, the shock wave/turbulent boundary layer interaction can lead to aerodynamic instabil-ities termed buffet, whose cause shock oscillations. These shock induced oscillations (SIO) involve structural vibrationstermed buffeting, that can lead to fatigue failure and degrade pilots and passagers confort. Thus, the upper limit envelopeof cruising speed is reduced, so that the maximum lift coefficient must be 30% lower than the buffeting entrance liftcoefficient. Consequently, the control of buffet instabilities is an outstanding problem in the aeronautic research field. Inthe present work, the control strategy consists in using a pneumatic blowing near the trailing edge on the pressure side ofthe airfoil. This control will be named fluidic trailing edge deflector (FTED) in the present discussion.

2 Turbulence Modelling and Numerical Methods

2.1 Turbulence ModellingThis study will focus on the aerodynamic buffet control over a two dimensional rigid airfoil by resolving the unsteadyReynolds average Navier Stokes (URANS) equations. This approach do not attempt to resolve any turbulent flow struc-tures but model the effect of turbulence on the mean flow by using the concept of turbulent viscosity with the Boussinesqhypothesis. To determine the turbulent viscosity, a single transport equation Spalart-Allmaras model is used, Spalart et al(1994) [6]. This model transport the quantity ν by the following :

D(ρν)Dt

= cb1(1− ft2)ρSν

+1σ

[∂

∂xj

(ρ(ν + ν)

∂ν

∂xj

)+ cb2ρ

∂ν

∂xj

∂ν

∂xj

]−

[cw1fw −

cb1κ2ft2

]ρ

[ν

d

]2(1)

with,νt = νfv1

And we also have the functions :

χ =ν

ν, fv1 =

χ3

χ3 + c3v1, fv2 = 1− χ

1 + χfv1

ft2 = ct3e−ct4χ

2, fw = g

[1 + c6w3

g6 + c6w3

] 16

g = r + cw2(r6 − r), r =ν

Sκ2d2

S = S +ν

κ2d2fv2

The constants are : cb1 = 0.1355, cb2 = 0.622, σ = 23 , κ = 0.41, cw1 = cb1

κ2 + 1+cb2σ , cw2 = 0.3, cw3 = 2, cv1 = 7.1,

ct3 = 1.1,ct4 = 2.

2.2 Numerical MethodsThe aformentioned turbulence modelling have been implemented in TGNS3D code developed at LEA/CEAT (Poitiers,France). This code solves the Navier-Stokes equations on multiblock structured grids. The Navier-Stokes equationsare discretized in space using a cell-centered finite volume method. The Euler flux at the cell interface are determinedby a Roe’s flux difference splitting scheme extended to second order with a monotonic upstream-centered scheme forconservative law (MUSCL) approach. The viscous flux are discretized using a second order centered scheme. An Hartenentropy correction is used to avoid entropy decrease (irealistic shock expansion). In order to prevent numerical instabilitiesin the shock regions, a limitation procedure using a Minmod limiter is introduced. The time integration is a first orderimplicit scheme. The inversion of the matrix system in the implicit step, is performed by a diagonally dominant alternatingdirections implicit (DDADI) methodology. The time strategy is a global time step discretization. The grid computationpresented in figure 1 is a C-H type mesh. The upper and the lower surface of the airfoil which correspond to the C-typedomain contains 400 × 80 nodes. The H-type domain contains 80 × 220, leading to 49600 nodes in the grid domain.The external condition is imposed at 10 chord length from the wing profile. A grid convergence has been performedsuccessfully. The value of y+ at the first mesh point is always below one on the upper and lower surface.

2.3 ExperimentDue to the number of experimental and numerical data to compare with, we choose to study the supercritical OAT15Awing profile design by ONERA. The profile has a chord length equal to c = 0.23m, a thickness-to-chord ratio e

c = 12.5%and a thick trailing edge of 0.5% of the chord. The transition to the turbulence is numerically forced at xc = 7% on bothsides of the airfoil.

The results are composed of four parts. The first one will compare our numerical results with the experimental workdone at the Onera S3Ch wind tunnel in 2005 with a free stream Mach number of M∞ = 0.73 and a Reynolds numberbased on the chord of Rec = 3.0e6. More details on this experiment are given by Jacquin et al (2005) [5]. The secondpart will present the role of the FTED by a description of his action at a steady regime, α = 2.5 ◦. The third part willdiscuss the buffet control achieved with an active FTED. All the present computations are done for the same Reynoldsnumber and the same free stream Mach number that in the experiment.

Figure 1: Grid mesh

3 Natural caseFigure 2.a presents the evolution of the normal lift coefficient Cn vs the angle of attack α. It shows a good coherencebetween experiment and simulation in the linearity domain. But as in previous works, Brunet (2003) [1] or Deck (2005)[3], the numerical simulation has needed to increase the angle of attack of one degree in order to obtain the establishedbuffet regime. Indeed, the buffet entrance obtained experimentally is α = 3.25 ◦ and numerically it is α = 4.25 ◦. Figure2.b presents the evolution of the pressure coefficient−Cp for three incidence of the profile. They correspond to incidencesaround the buffet entrance and to established buffet regime. With this correction in incidence, one observes a very goodagreement of the pressure coefficients. The behavior is replicated. The increase in incidence induce a rise of the super-sonic level and a flatness excursion zone because of the setting of the shock wave instability.

The figure 3.a shows the rms pressure levels. For an incidence below the buffet entrance the levels are low overall thesuction side. When the incidence increased, we observe a peak which highlight the excursion zone of the shock and theelevated levels downstream is the consequence of pressure fluctuations generated by the separated boundary layer in thispart of the flow. Between experiment and simulation, the levels of fluctuations is well restored. The amplitude of shockoscillation is however underestimated. Extracted from experimental data and from our simulation, for an establishedbuffet regime (αnum = 4.5 ◦), the shock oscillates experimentally from 34% to 51% of the chord and numerically from41.1% to 48.6% of the chord. One observes in both cases an increase in the latter with the incidence and a displacementof the average shock position (highlighted here by the maximum of rms pressure) to the leading edge.

The power spectral density (PSD) of pressure fluctuations at the wall is exposed on figure 3.b in decibels, level ofsound pressure level (SPL). The spectra are plotted on the suction side at xc = 0.3. The numerical spectrum presents apeak which is located at a frequency of 64 Hz. It is in good agreement with the experimental results which correspond toa buffet frequency of 69 Hz. After this pic, the harmonic are visible in both cases. The low frequency level (f < 50 Hz)is underestimated of approximately 20 dB and this difference decrease in the high frequencies at this station. Thisdecrease of the difference in the high frequencies is the consequence of the weak weight of the turbulent structures inthe supersonic region which are not solved by simulation. Accordingly of the present results, our simulation is consistentwith the experiment.

a) b)

Figure 2: a) Normal lift coefficient Cn vs the angle of attack α - b) Mean pressure coefficient −Cp

a) b)

Figure 3: a) Adimensional rms pressure prms

qo- b) SPL of pressure fluctuations at xc = 0.3 on the suction side for α = 4.5 ◦

4 Passive control and Influence of the FTEDIn this part, we will present the action of the FTED, for a steady regime set at an angle of attack equal to α = 2.5 ◦. Thejet presented here and later is a sonic jet. The blowing is steady along the time. We have studied to flow rate of the controljet in term of Cµ, defined by the following relation :

Cµ =ρju

2jdj

12ρ∞u

2∞c

(2)

with, ρj , uj and dj respectively the density, the velocity and the length of the jet. ρ∞, u∞ and c are respectively thedensity at the free stream, the velocity at the free stream and the chord of the profile. The variation of the flow rate Cµwill be related to the value of the jet length dj . Two cases are going to be study, with Cµ = 0.4% and Cµ = 1.5%. Dueto the littleness of dj in the Cµ = 0.4% simulation, the number of nodes in the grid has needed to be increased of 50 inthe intrados trailing edge.

Figure 4.a compares the pressure coefficient without and with blowing for different values of the Cµ. The presenceof the blowing increases the supersonic level on the extrados and the shock wave is displaced downstream. Figure 4.b

presents the schematic trailing edge deflector (TED) studied by Caruana et al (2005) [2] with a OAT15A-CA wing profile.This is an OAT15A profile with a thicker trailing edge equal to 1% of the chord. The flow conditions of the experiment areM∞ = 0.7361, Rec = 4.5e6 and α = 2.0 ◦ which correspond to a steady regime. Comparison of pressure coefficientswith an angle of the TED equal to δ = 15 ◦ and δ = 0 ◦ shows that we obtain comparable effects between the fluidic andthe mechanical deflector. The FTED mimic the behavior of the TED.

Moreover, we can also observed the downstream displacement of the shock on the isocontours of the Mach numberplotted on figure 5 without control and with control for variable flow rates. From the natural to Cµ = 0.4 % simulation,we observe a displacement of the shock wave to the trailing edge. However, when we increase the Cµ to 1.5 % theshock wave doesn’t move downstream anymore. But this increase of Cµ induces an increase of the upstream shock Machnumber respectively from 1.35 to 1.38. For the natural simulation this Mach number is equal to 1.3. Thus, the presenceof the FTED increases the upstream shock Mach number. In a shock/boundary layer interaction, Delery (1984) [4] hasshown that for an upstream shock Mach number above 1.3 the intensity of the shock is enough to detached the boundarylayer. Consequently, this supports the figure 5 which shows that the FTED creates a large recirculation zone behind theshock. Larger is the Cµ, larger is the recirculation. This shows that FTED deflector has a global effect on the flow aroundthe airfoil by modifying the flow on the pressure side but also on the suction side. To conclude from the precede, theprinciple of this control is to create an increase of circulation Γ around the wing by the presence of a fluidic “deviation”induced by the presence of the micro-jet. However, afterwards the Kutta-Jukowsky theorem, the increase in circulationinvolves an increase in lift CL. Thus, at a fixed incidence the lift is raised.

a) b)

Figure 4: a) Influence of the steady blowing on the pressure coefficient with variable Cµ and α = 2.5 ◦ - b) Action of theTED by plotting the pressure coefficient with δ = 15 ◦ and δ = 0 ◦ for M∞ = 0.7361, Rec = 4.5e6 and α = 2.0 ◦ overan OAT15A-CA profil

a) b) c)

Figure 5: Isocontour of the Mach number and steamtraces with α = 2.5 ◦, a) natural simulation - b) FTED control forCµ = 0.4% - c) FTED control for Cµ = 1.5%

A global analysis of the aerodynamic performances is presented in the next figure. By plotting the variation of themaximum and minimum lift coefficient with the angle of attack, figure 6.a shows that at iso-incidence the blowing shiftthe curve to larger lift coefficient. The improvement of the aerodynamic performances is for all the tested incidences. Wealso observed an increase of the lift with the Cµ. If we fixed for example the incidence at α = 4.5 ◦, we notice a liftincrease of +15% with Cµ = 0.4% and an increase of +27.6% with Cµ = 1.5%. This figure highlights that the blowingis abble to postpone the buffet onset up to at least α = 5.5 ◦ for both flow rates.

Figure 6.b presents the drag polar of the natural and controlled cases. The interesting point here is that for a fixedlift coefficient CL, the drag is reduced. A comparison of the pressure coefficient between natural and Cµ = 0.4%controlled flow is plotted figure 7 at iso-CL = 0.9. We observed a decrease of the supersonic level which leads to a lowerrecompression singularity and a loading of the rear part of the airfoil.

One major advantage of the method is its availability to produce unsteady effect, then allowing for developing acloosed-loop active blowing based on the shock position. Next section is going to discuss results obtain with an activecontrol instead of a steady one.

a) b)

Figure 6: a) Maximum and Minimum lift coefficient along the angle of attack - b) Drag polar of mean values

Figure 7: Iso-CL = 0.9 comparison between natural and Cµ = 0.4% controlled flow

5 Cloosed-loop active blowingTo improve the efficiency of the control we test a closed-loop blowing strategy based on the dynamic of the systemobserved in the steady regime and also on the work of Caruana et al. (2005) [2]. The jet velocity is controlled by theinstantaneous location of the shock wave with the following law :

VFTED(t) = VFTED

(1 +K

< xshock > −xshock(t− d)c

)(3)

Where VFTED is the mean FTED exit velocity, < xshock > and xshock are the average and instantaneous shockpositions respectively and c is the airfoil chord length. K is the gain and a fixed time delay d, in percent of the buffetingphenomenon period, is imposed.

The principle of this simple cloosed-loop control is to act in phase opposition with the shock motion. When theshock is moving upstream we increase the blowing and conversely when the shock is moving downstream we decreasethe blowing. A parametric study has been performed by adjusting the gain K and the time delay d to obtain optimumvalues. The best results have been obtained with K equal to one and d

T < 8%. Figure 8 presents the evolution of theshock position in time. Starting from the natural periodic shock wave oscillation, the blowing is started at t = 0.307 s.The control stops the shock motion, so the buffet is cancelled. In case of impulsive actuation, a real damping is observed,but a large increase in first observed. As expected, the cloosed-loop active blowing slightly decreases the damping timeoscillation in comparison to the steady one. Moreover, the closed-loop control reduces the control flow rate during thetransition phase, so the “shock jump” to the trailing edge is decreased.

Figure 8: Shock position along the time for the natural regime and the closed-loop with Cµ ' 1.5%, K = 1 and dT = 0%

with α = 4.5 ◦

6 ConclusionsThis study has shown the agreement of the simulation of transonic buffet phenomenon, by comparison on the mean pres-sure coefficient and the rms pressure overall the airfoil, with the experiment of Jacquin et al (2005) [5]. The controlperformed with steady jet on the lower surface of the airfoil has shown positive results on CL and it postpones the buffetto higher incidence. Indeed, after a few oscillation cycles the jet stops the motion of the shock wave, the shock wave isstabilized. A closed-loop pneumatic strategy control has allowed to slightly reduced the time required to stop the instabil-ity and the amplitude of the oscillations during the transient period.

AcknowlegementThe work had been partially funded by the EC within the FP6 AVERT project (Aerodynamic Validation of Emission

Reducing Technologies) and a grant from the French Ministry of Research.

References[1] Brunet V., (2003), Computational study of buffet phenomenon with unsteady RANS equations, 21st AIAA Applied

Aerodynamics Conference, Orlando, 23-26 June.[2] Caruana D., Mignosi A., Correge M., Le Pourhiet A., Rodde A.M., (2005), Buffet and buffeting control in transonic

flow, Aerospace Science and Technology, 9 605-616.[3] Deck S., (2005), Numerical investigation of transonic buffet over a supercritical airfoil, AIAA Journal, Vol. 43, No

7, 1556-1566.[4] Delery J., (1984), L’interaction onde de choc/couche limite turbulente et son controle, AGARD Improvement of

Aerodynamic Performance Through Boundary Layer Control and High Lift Systems, (AGARD-CP-365).[5] Jacquin L., Molton P., Deck S., Soulevant D., (2005), An experimental study of shock oscillation over a transonic

supercritical profile, AIAA Paper 2005-4902.[6] Spalart P.R., Allmaras S.R., (1994), A one-equation turbulence model for aerodynamic flows, La recherche

Aerospatiale, No 1, 5-21.