Mean and turbulence measurements of wake vortices. Wandering effects.

Transcription

1 Lisbon, Portugal, 7- July, 8 Mean and turbulence measurements of wake vortices. Wandering effects. François-Xavier Vandernoot, Philippe Barricau, Hervé Bézard, Henri-Claude Boisson : ONERA, Aerodynamics and Energetics Modelling Department, Toulouse, France, francois-xavier.vandernoot@onera.fr : IMFT, Ecoulements Monophasiques Transitionnels et Turbulents, Toulouse, France, boisson@imft.fr Abstract Experiments have been performed in a hydrodynamic tunnel behind a generic half-wing equipped with an inboard flap, up to almost 9 wingspans downstream using two-component Laser Doppler Velocimetry and three-component Particle Image Velocimetry. A half wing model of constant chord, full aspect ratio equal to 4, rounded wingtip and NACA wing section has been used. The inboard flap which allows to get two co-rotating vortices extends over 8% of the half-span and 3% of the chord. The deflection angle can be set to (clean case), 4, 6 or 8. The upstream velocity is equal to 4m.s - which corresponds to a Reynolds number based on chord of about 3.x 5. The LDV campaign has provided a characterization of the near wake in cross planes at. and.5 wingspans downstream the trailing edge. Besides, the spanwise load distribution has been estimated by measurements along closed path around the wing sections. The PIV campaign, during which the setting of the coplanarity of the laser sheet and the calibration plate was revealed of first importance, has supplied the complete velocity and turbulence fields in cross planes scattered in the extended near wake between.7 and 8.74 wingspans downstream the wing. Furthermore, the wandering phenomenon, i.e. the slow side-to-side vortex motion which strongly alters the measurements, has been considered carefully. A procedure was implemented to delete the over diffusion and the overwhelming excess of turbulence artificially induced by this phenomenon in the vortex core.. Introduction The wake vortices are generated by a wing around which the flow is three-dimensional. The initial rollup is induced by the non constant spanwise load distribution which implies the emission of the trailing wake made up of infinitesimal vortices. Interactions of these vortices cause them to curve around each other and to form the wingtip vortices. They represent a large momentum in rotation and have a slow decay, so that a following aircraft may become unpilotable because of the wake vortices of a too close preceding aircraft. That is the reason why the FAA (Federal Aviation Administration) established separation rules in order to avoid the wake vortex hazard especially during the landing and take-off phases of flight []. But these rules limit the exploitation of the congested airports. Therefore, studies about wake vortex are justified by a genuine economic stake since the final purpose is to reduce the separation minima or at least to adapt them to the plane and in particular to the flaps/slats configuration []. Many experimental studies have been carried out about wake vortices, most of them in the near wake [3]. Jacquin and al. [4] investigated the extended near wake up to 9 wingspans downstream a small scaled A3 by the means of LDV and hotwire. However, few experiments have been performed up to this distance behind a generic wing which is more easy to use for numerical simulations. Besides, the measurements carried out in a wind or a water tunnel are highly altered by a further phenomenon: the vortex wandering commonly described as long wavelength meandering of the vortex position. Devenport and al. [5] proposed a method to remove the wandering effects from hot wire measurements, in particular on the turbulence by high-pass filtering. The use of PIV which supplies the instantaneous fields allowed to develop a more objective procedure. - -

2 . Apparatus and instrumentation 4th Int Symp on Applications of Laser Techniques to Fluid Mechanics Lisbon, Portugal, 7- July, 8. Model The wing characteristics have been prescribed so that two constraints are respected: on the one hand the merging of the flap vortex and the wing tip vortex had to take place before the end of the wind tunnel test section; on the other hand the vortices circulations had to be close in order to make the measurements easier and to be more representative of a real case downstream an airliner. This needed to adapt the spanwise loads distribution which is directly linked with the vorticity distribution in the wake as explained by Betz and Donaldson [7]. A basic numerical method has been developped to get it from the geometry of a wing. It consists in coupling the -dimensional viscous code Xfoil ( with a 3-dimensional inviscid code based on the Prandtl s lifting line model. The merging distance was calculated with an empirical law [6]. The vortex circulations have been obtained thanks to the Betz and Donaldson s theories. As a result, the constraints are respected with the selected geometry for a wide range of angles of attack. The model is a generic half-wing equipped with an inboard flap (Fig. ). The wing section is a NACA with a constant chord c of 75mm and a half-span b/ of 5mm (aspect ratio of the simulated full wing equal to 4). The transition is tripped at 5% of the chord. A rounded wingtip improves the quality of the initial roll up.the flap extends over 8% of the half-span and 3% of the chord. The flap angle can be set to (clean case), 4, 6 or 8. The lift and drag behaviour of the model have been quantified in a wind tunnel equipped with an external two-component force balance. The chord Reynolds number was close to the one obtained in the hydrodynamic tunnel in which the wake has been investigated.. Test facility The velocity fields measurements have been carried out in the hydrodynamic tunnel THALES of the Aerodynamics and Energetics Modeling Department of the ONERA. This facility is running as a closed-return blower type wind tunnel. The water volume is close to m 3. The test section is.5m wide,.3m high and 3m long which allows to measure the vortices up to a relatively important distance downstream the wing (almost nine wingspans). The lateral and upper walls are made of glass windows embedded in plexiglas panels which provide a good optical access for measurements with laser techniques. The model is mounted on a lateral wall (Fig. ) in such a way that the angle of attack is set from the outside of the tunnel. The rotation axis is located.5b above the lower wall and.48b under the upper wall. The second lateral wall is.6b far from the wingtip. The leading edge is.9b donwstream the inlet section. A right-handed coordinate system (X, Y, Z) with unit vectors (e x, e y, e z ) is chosen such that e x is aligned with the upstream velocity and e z is pointing upwards. The origin is located above the trailing edge (X = ) in the root plane (Y = ) and at the height of the angle of attack rotation axis (Z = ). The main flow parameters (velocity, pressure, and temperature) are continuously monitored and possibly regulated by feedback. Indeed, the pressure inside the tunnel can be adjusted in order to avoid possible cavitation problems. However, this is not possible while using the type of walls described above. Besides, a heat exchanger located in the lower part of the circuit allows the water temperature to be controlled within C accuracy. But in the present study, we were not interested in a particular temperature. Furthermore, the recorded variations along a day do not exceed C which induce weak variations of the kinematic viscosity (%). Finally, only the upstream velocity has been regulated. It can be set from.3m.s - to 7m.s - (maximal unit Reynolds number: 7 x 6 m - ). However, the value used in the present study was U = 4m.s - to avoid cavitation around the wing, providing a chord Reynolds number equal to 3 x 5. The freestream turbulence intensity is close to.7%. - -

3 Lisbon, Portugal, 7- July, 8 The tunnel is fitted with a three dimensionnal traversing system which allows to investigate the whole test section with the measurements techniques: LDV (Laser Doppler Velocimetry) and PIV (Particle Image Velocimetry)..3 Laser Doppler Velocimetry system The THALES tunnel is equipped with a two-component LDV system from DANTEC. It works in forward-scattering mode. The transmitting-receiving optics are fixed horizontally on the traversing system and connected to a 5W Ion Argon/Krypton laser through optical fibres. At their ends, the maximum available powers are about 57mW for the green signal (λ = 54.5nm) and 36mW for the blue signal (λ = 488nm). A beam expander has been used to increase the angle between both beams of each colour and then decreases the length of the intersection zone. Here, the global measurement volume is the cross of the intersection zones corresponding to both colors. The spatial resolution is.5mm along X and Z and.8mm along Y. The seeding is made of silver-coated hollow glass spheres from DANTEC. The mean diameter of the particles is about 5µm. The signals collected by the photomultipliers are transmitted to two Broad Spectrum Analysers (one per color). For each particle, the dates of arrivals are compared by the BSA in order to select it only if it is simultaneously in both instersection zones of each color. A further post-processing allows to be even more restrictive. As the flow makes the spreading of the seeding particles non uniform, the date acquisitions rates varied between Hz and 5Hz..4 Particle Image Velocimetry system A stereoscopic PIV system from IDT has been used to measure the mean fields of the three velocity components and the six Reynolds stresses in cross planes (e y, e z ). The high-resolution cameras (8x4 pixels) allows to get mm wide and 6mm high fields with a spatial resolution inferior to mm. The pulsed laser from Quantel supplies mj at 53nm and has been used at Hz. The thickness of the laser sheet is close to mm. The cameras, the pulsed laser and the optical lenses are mounted on the traversing system which makes the investigation along the tunnel axis easier. The seeding particles are the same as the ones used for the LDV measurements. The Scheimpflug geometric configuration has been brought into play: for each camera, the image plane (CCD), the lens plane and the object plane (laser sheet) must cut each other along a single segment. This allows to record sharp images on the CCD in spite of a perspective observation and a small depth of field induced by a large numerical aperture. The cameras are on both sides of the test section to have as much as possible a symmetric configuration (Fig. 3). Moreover, water prisms have been used to see the calibration plate or the laser sheet under a 45 angle of view in the water in order to avoid the distortions effects on the PIV images. Besides, the setting of the coplanarity of the laser sheet and the calibration plate has been found to be of first importance. Even a.5mm translation of the laser sheet has an effect on the measured fields which seems surprising since this value is much less than the thickness of the laser sheet. The statistical post-processing has been run with 4 instantaneous fields. 3. Results of the LDV campaign 3. Spanwise load distribution In order to improve the knowledge of the aerodynamics of the wing, the two-component LDV system has been used to measure the axial and vertical velocities (Vx and Vz) along closed paths around the wing profiles in different sections (e x, e z ). The integral in each section yields the spanwise load distribution which is interesting in the framework of the present study since - 3 -

4 Lisbon, Portugal, 7- July, 8 it is connected to the circulation of the wake vortices. The paths follow the profiles shape but got thicker by adding e, and are vertically closed at a small distance d dowstream the trailing edge. Whatever the parameter e greater than the boundary layer thickness, the circulation should be the same because of its invariance whatever the closed path outside rotational areas. Effectively, some experiments run in the section Y/b = -. with e between 7mm and 4mm provided circulations with a discrepancy close to %. This parameter has been chosen equal to mm. Furthermore, the vertical segment downstream the trailing edge crosses the wake profile hence a rotational area. The integral along this segment does not take into account the raw measured velocities but the ones which would be got with an inviscid flow: as it is considered that the rotational area corresponds to the axial velocity deficit, the measured velocities outside this area are used to compute linear regressions which are extrapolated on each side to the point where the minimal axial velocity is reached. From an inviscid theory, this point belongs to the vortex sheet across which the tangential velocity is discontinuous. This is well retrieved with the linear regressions if d is not too small. For d larger than mm (nearly 5% of the chord), the measured velocities outside the rotational area are linearly distributed so that the procedure becomes legitimate. A value equal to 5mm has been selected. The spanwise load distribution in the clean case (δ = ) at an angle of attack α equal to 4.5 is shown in Figure 4. The transverse coordinate Y is normalised by the wingspan b. The influence of the lateral wall on which the half-wing is mounted is identifiable thanks to the circulation drop which makes felt up to % of the wingspan. Besides, the decrease towards the wing tip matches qualitatively the Prandtl s lifting line theory prediction except in the immediate vicinity of the tip (Y/b -.5) where the curve changes the sign of its concavity. This is due to the fact that the vortex roll up begins around the wingtip and gets into position above the last part of the suction side, whereas this is not expected by the Prandtl s theory since the wing is degenerated into a line. Quantitatively, the exact wingtip shape must have an influence. The lift coefficient calculated from the spanwise load distribution at δ = and α = 4.5 is equal to.53 which corresponds to the value given by the external force balance in the wind tunnel at an angle of attack.5 higher. This difference is relatively weak taking into account the fact that these results have not been obtained in the same facility. Moreover, a numerical simulation run with the ONERA elsa code (RANS approach with structured meshes) provides a lift coefficient equal to.55. For δ = 6 and α =, the influence of the flap deflection is noticeable thanks to the inflection point at the junction between the part with the flap and the one without (Y/b =.4). Indeed, this inflection point corresponds to the emission point of the flap vortex. The lift coefficient is here equal to.8 which is the value get by the force balance for α = Cross planes in the near wake The two-component LDV system has been used to get data in cross planes (e y, e z ) in the near wake at X/b =. and X/b =.5. The axial and vertical velocities (Vx and Vz) have been measured to obtain the corresponding mean velocities and turbulence fluctuations fields. This data base is useful to validate numerical simulations at small distance downstream the wing. Depending on the angle of attack α and the flap angle δ, the flow topology can be various as shown in the Figures 5 to 8 which gives the mean axial velocity fields normalized by U at X/b =.. If the flap is not deflected (δ = ), the half-wing-generated vorticity sheet rolls up into a single vortex which has a wake-like structure at low angle of attack (Fig. 5) but a jetlike structure at higher angle of attack (Fig. 6). If the inboard flap is deflected, the vorticity sheet rolls up into two corotating vortices which have both a wake-like structure at low angle of attack (Fig. 7). At higher angle of attack, for instance at α = 5.43 (Fig. 8), the scenario - 4 -

5 Lisbon, Portugal, 7- July, 8 becomes original since the flap vortex keeps a wake-like structure but the tip vortex peaks up a jet-like structure. 4. Results of the PIV campaign 4. Cross planes in the extended near wake The three-component PIV system has been used to get data in the extended near wake in cross planes (e y, e z ) scattered along the X axis between X/b =.7 and X/b = Different angles of attack α and flap deflection angles δ have been set in such a way that comparisons between the configurations are possible either at constant α or at constant C L relying on measurements given by the external two-component force balance in the wind tunnel. The laid out fields are the mean axial vorticity ω x normalized by U /b and the turbulent kinetic energy normalized by U. The coordinates are normalized by b. 4.. Measurements in the clean case Figure 9 presents the results at.7b dowstream the clean wing (δ = ) for α = 4.5. The vorticity field (Fig. 9a) shows that the roll up is almost completed: in the wake outside the vortex core, the values do not exceed 5% of the one at its center (-57.5U /b). Regarding the turbulent kinetic energy (Fig. 9b), the highest levels are found in the vortex core: the maximum is at the centre and is equal to 6.6x -3 U. In the plane wake, the values remain smaller than.x -3 U. Downstream, the single vortex is more diffused. The maximum vorticity is -37.9U /b at X/b = 5. and -3U /b at X/b = However, the decreasing of the vortex circulation estimated by integration of the vorticity fields is rather weak. The slope dγ /dx is equal to -8,. -4 m.s -. Surprinsingly, the turbulent kinetic energy in the vortex core increases with the downstream distance and keeps its maximum at the vortex centre (6.6x -3 U at X/b = 8.74) where the turbulence production is very poor. These are consequences of vortex wandering which will be tackled in the next paragraph. 4.. Measurements in a deflected flap configuration When the inboard flap is deflected, two corotating vortices are shed into the wake as it is shown in the Figure got at X/b =.7 for δ = 8 and α =. The lower vortex stems from the flap while the upper one stems from the wingtip. The vorticity values at the centres are respectively -7.4U /b and -9.4U /b (Fig. a). The strongest vortex holds the highest turbulence levels : the peak rises to.6x -3 U for the flap vortex but only to.7x -3 U for the wingtip vortex (Fig. b). Moving downstream, the co-rotating vortices rotate around each other (Fig. c and d) while both spread by diffusion. However, the weakest seems to give vorticity up to the strongest. At X/b =.87, the maximum value reaches -.8U /b for the flap vortex and -.8U /b for the wingtip vortex hence 5% lower against 3% at X/b =.7. Sufficiently far from the wing, the merging occurs. Then the resulting vortex exhibits the same behaviour as the one of the clean case (Fig. e and f). In particular, the turbulent kinetic energy is still maximum at the centre and increases downstream. These characteristics are not intrinsic to vortex dynamics but result from the wandering phenomenon. 5. Wandering phenomenon. Effects and correction 5. Description of the phenomenon Vortex wandering is a slow side-to-side erratic and broadly solid motion of the vortex centre in response to the free-stream turbulence especially in a wind or a water tunnel. As the whole vortex seems to follow the centre displacement, the measured mean vortex is the convolution product between the true mean vortex and the probability density function of the - 5 -

6 Lisbon, Portugal, 7- July, 8 instantaneous vortex centre. The wandering amplitude increases with the axial distance downstream the wing so that these effects are finally no negligible, sometimes even in the near wake. Basing on fields taken on average, the diffusion is overestimated. Indeed, the wandering motion induces artificially a growth of the core radius and a drop of the velocities and vorticies amplitudes. But the major effect concerns the turbulence which is strongly strengthened as the whole fluctuations are basically attributed to it while a great part of these fluctuations is only due to the motion of the core vortex inside which the velocity gradients are very high. In order to better understand the wandering effects, this phenomenon has been simulated numerically by shaking a q-vortex. This simplified version of the Batchelor vortex is made up of the Lamb-Oseen s gaussian vorticity profile and a gaussian axial velocity deficit. The chosen parameters are a maximum tangential velocity of.3u and a maximum axial deficit of.u where U denotes the upstream velocity. Four hundred instantaneous vortex centres are generated by a random function such that the maximum amplitudes reach.6r c where r c denotes the core radius. The standard deviation is equal to.5r c. The mesh size is.r c. All these parameters make the scenario close to the one measured in the water tunnel. The mean and fluctuations fields are computed in a fixed frame of reference as it is usually done. Figures a and b exhibit the mean axial vorticity fields of the basic and the wandered vortices and show that the wandered vortex is effectively more diffused with values 3% lower in the vortex core. But the most impressive effect concerns the turbulence created artificially by the wandering motion. High levels of turbulent kinetic energy appear with a peak of.u (Fig. a). The contours of the <v y v z > component of the Reynolds stress have the classic four-leaf clover pattern with alternatively changing sign of stress in each leaf (Fig. b). Everything looks like the wandered vortex was turbulent while the basic vortex is purely laminar yet. 5. Correction of the wandering effects Devenport [5] developped a procedure to correct a wandered vortex measured with a point to point technique (LDV or hot wire). His method is to invert the convolution product presented above. This is straightforward by assuming an axisymmetric true mean-velocity field and a Gaussian pdf of vortex position, of which the rms amplitudes and the correlation coefficient are computed on the further assumption that all the fluctuations measured at the vortex centre is due to the wandering. Besides, the Reynolds stresses are simply corrected by high pass filtering. A different method has been developped in the current study thanks to the PIV measurements which give a knowledge of the instantaneous velocity fields hence the instantaneous vortex positions. For each cross plane (e y, e z ), this consists in computing the averages and standard deviations fields not in a fixed frame of reference but in a frame which moves with the wandering. Assuming that the wandered vortex has a solid motion, this procedure allows to fix artificially the vortex position in the cross plane which corresponds to the annihilation of the wandering phenomenon. The implementation requires the accurate determination of the instantaneous vortex centres positions. First, the vortex core is detected by the negative values of the third eigen value of the tensor S²+Ω² where S and Ω respectively denote the strain and the rotation rate tensors. Then, the axial vorticity centroid which corresponds to the vortex centre position is computed by taking into account the values obtained inside the core where they are the most significant. As the vortex centre does not generally coincide with any mesh point, the velocity fields have to be interpolated on these in order to have instantaneous data on a common grid. For each mesh point, a quadric is extracted from a least square minimisation of the error estimated on the nearest neighbours

7 Lisbon, Portugal, 7- July, 8 This procedure was checked with the analytical wandered vortex described above. After applying the correction method, the wandered vortex comes back in a state very close to the basic vortex. The discrepancy on the vorticity fields is less than.3%. A slight peak of turbulent kinetic energy still remains at the vortex centre but it rises at.7x -3 U which is about three decades lower than the value inside the wandered vortex. 5.3 Results in the clean case 5.3. Focus at a fixed downstream distance for a given angle of attack The Figures 3 to 6 exhibit the results based on 4 instantaneous fields at X/b =.7 for δ = and α = 4.5. This number of samples will be discussed in the last paragraph. From now on, the term uncorrected is allocated to a result obtained from a classic post processing with a fixed frame of reference while the term corrected is allocated to a result without the wandering effects in accordance with the method described above. The instantaneous vortex centre fluctuates around a mean position with amplitudes which can reach.5mm (Fig. 3), that is about times the mesh size. The standard deviations along the transverse Y and Z axis are respectively equal to σ y =,56mm and σ z =,6mm. These values have to be compared to the core radius which is equal to.5mm at this station. Futhermore, the vortex centres distribution has a correlation coefficient of -.. The orientation of the principle axes shows that the direction along which the probability to find the centre is the highest is inclined at -67 to the Y axis. The lowest probability is along an orthogonal direction. As it was expected, the corrected vortex is less diffused : the minimum of the mean axial vorticity is % lower than the value of the uncorrected vortex (Fig. 4). The most overwhelming effect concerns the turbulence fields as it can be noticed on the turbulent kinetic energy (Fig. 5). The correction makes the levels collapse by a factor of 8 in the vortex core. On the other hand, the field is not affected outside the vortex hence the correction is active only inside. In fact, the correction effects on the turbulence is easily understood by analysing the link between the velocity profiles and the diagonal Reynolds stresses profiles for instance along the Y-axis (Fig. 6). The uncorrected axial Reynolds stress profile <v x > (Fig. 6a) is maximum at two points which correspond to the inflexion points of the axial velocity profile Vx (Fig. 6c). This is consistent with the fact that the fluctuations induced by the wandering motion are the most important where the corresponding velocity has the highest gradient. The correction cuts these peaks and <v x > becomes maximal at the vortex centre where the Vx gradient is the lowest hence where the correction has the weakest effect. Anywhere, it brings down the levels (% at the centre). The same thought process can be led with the transverse Reynolds stresses profiles <v y > and <v z >. The uncorrected profiles are maximal at the vortex centre (Fig. 6b) which corresponds to the inflection point of the tangential velocity profile Vt (Fig. 6d). The correction cancels these peaks and <v y > and <v z > become maximal near the edge of the vortex core. The levels are much lower. At the vortex centre, the values are reduced by a factor of for <v z > and 7 for <v y >. Moreover, the profiles show a slight deficit at the centre which is consistent with the very weak turbulence production at this point. Besides, the corrected stresses have close levels which remind a kind of isotropy. That was not the case before applying the correction because of the non axisymmetry of the wandering motion (σ y σ z ) Evolution with the downstream distance and the angle of attack As the wandering amplitudes and standard deviations increase with the distance downstream the wing (Fig. 7), the correction effects are even stronger. It is also noteworthy that the orientation of the principle axis change from one cross plane to another (Fig. 8). For each station, they are represented by two orthogonal segments which intersect at the vortex center. Their lengths are proportional to the square root of the corresponding eigen values. The red - 7 -

8 Lisbon, Portugal, 7- July, 8 and blue colors denote the directions along which the probabilities to find the vortex center are respectively the highest and the lowest. These directions seem to rotate at a quite steady angular velocity. As a result, none of them coincide generally with the Crow s instability plane inclined at about 45 to the Y-axis. The diffusion of the corrected vortex is weaker as shown by the reduction of the slopes of the curves which represent the evolution of the absolute mean axial vorticity at the vortex centre versus the distance downstream the wing (Fig. 9). Furthermore, the corrected turbulence levels go down slowly with X (Fig. ) which is satisfactory from a physical point of view. This is not noticed with the uncorrected results due to the growth of the wandering motion. When the angle of attack is risen from 4.5 to 9, the standard deviations become lower which seems to confirm that wandering amplitudes are linked with the ratio of kinetic energy of the vortex to the kinetic energy of the surrounding [8]. In spite of the fall of the wandering amplitudes, the correction effects go up yet because of the great increase of the velocity gradients inside the vortex core. As expected, the corrected vortex remains more turbulent for the higher angle of attack, but the turbulent kinetic energy versus X seems to level off around the same asymptote for both α = 4.5 and α = Statistical convergence Figure shows the statistical convergences of the axial vorticity and the turbulent kinetic energy at the vortex centre in the corrected and uncorrected cases. The dimensional values are normalized by the values obtained with samples. The results based on 4 samples are converged within less than % for the vorticity and about % for the turbulence. Besides, the corrected profiles seem to be less noisy probably due to the removal of the wandering which is an unsteady phenomenon. 6. Conclusion Experiments have been performed in a hydrodynamic tunnel behind a generic half-wing equipped with an inboard flap. The vortices formation and evolution have been investigated by means of Laser Doppler Velocimetry in the near wake and Particle Image Velocimetry in the extended near wake up to almost 9 wingspans downstream. Depending on the setting of flap deflection and angle of attack, various flow topologies were achieved and let foresee to rely on this data base to validate effectively numerical codes in the vortex dynamics framework. The LDV has also been used to estimate the spanwise load distribution with a good accuracy. Besides, the PIV turned out to be extremely sensitive to the setting of the coplanarity of the laser sheet and the calibration plate. The major interest of this study concerns the wandering phenomenon which distorts the measurements if a suitable post-processing is not carried out. An original method based on the translation of the PIV instantaneous fields has been implemented to cancel the wandering effects. The reliability of the procedure has been checked with an analytical wandered vortex. Hence the genuine characteristics of the turbulence have been brought out. The corrected turbulence levels collapse and go down slowly with the distance downstream the wing. On the other hand, they increase slightly while the angle of attack is risen. In addition, the transverse Reynolds stresses are no longer maximum at the vortex centre but at a radius close to the vortex core edge. The correction effects are stronger and stronger with the downstream distance and can reach two decades at the end of the test section

9 Lisbon, Portugal, 7- July, 8 Acknowledgment This study has been carried out in the frame of a doctoral thesis supported by the Délégation Générale pour l Armement. The authors thank also Guy Pailhas and Yann Touvet for their advices during the experiments. References [] SPALART P. R., Airplane Trailing vortices, Ann. Rev. of Fluid Mechanics, Vol. 3, pp 7-38, 998. [] COUSTOLS E., JACQUIN L., MOENS F., MOLTON P., Status of ONERA research on wake vortex in the framework of national activities and European collaboration, ECCOMAS 4, Jyväskylä (Finlande), 4-8 July 4 [3] CHOW J. S., ZILLIAC G. G., BRADSHAW P., Mean and Turbulence Measurements in the Near Field of a Wingtip Vortex, AIAA Journal, Vol. 35, No., October 997. [4] JACQUIN L., COUSTOLS E., GEOFFROY P., BRUNET S., PAILHAS G., Experimental study of the vortex wake behind a A3 Airbus model, Technical Report N RT 4/496 DAFE/Y, April 998 [5] DEVENPORT W. J., RIFE M. C., LIAPIS S. I. FOLLIN G. S., The structure and development of a wing-tip vortex, Journal of Fluid Mechanics, Vol. 3, pp 67-6, 996. [6] CHEN A. L., JACOB J. D. SAVAS Ö., Dynamics of corotating vortex pairs in the wakes of flapped airfoils, Journal of Fluid Mechanics, Vol. 38, pp , 999. [7] DONALDSON C. du P., SNEDEKER R. S., SULLIVAN R. D., Calculation of aircraft wake velocity profiles and comparison with experimental measurements, Journal of Aircraft, Vol., No 9, pp , 974 [8] BAILEY S. C. C., TAVOULARIS S., Measurements of the effects of free-stream turbulent kinetic energy and length scale on vortex wandering, to be published - 9 -

10 4th Int Symp on Applications of Laser Techniques to Fluid Mechanics Lisbon, Portugal, 7- July, 8.5m.35m =.6 b b/ = 5mm n a c a 75mm suction,5m = b/ cross plane side Z.45m =.48 b half wing f l a p.55m =.5 b Y 3mm.3m Y 4.7mm X Fig.. Geometry of the half wing Fig.. Schematic of the water tunnel test section optical components camera A.5 pulsed laser water prism Y 45 Γ [m.s-] X.4 45 half wing U laser sheet.3.. water prism δ= ; α=4.5 δ=6 ; α= -.5 camera B Y/b Fig. 3. PIV system arrangement Fig. 4. Spanwise load distributions Vx / U. Z/b Y/b Fig. 5. Mean axial velocity cross field for α = 4.5 and δ = (X/b =.) Vx / U Z/b Y/b Fig. 6. Mean axial velocity cross field for α = 9 and δ = (X/b =.) Vx / U.7 Z/b Y/b Fig. 7. Mean axial velocity cross field for α = and δ = 6 (X/b =.) Vx / U..7 Z/b Y/b -. Fig. 8. Mean axial velocity cross field for α = 5.43 and δ = 6 (X/b =.) - -.

11 Lisbon, Portugal, 7- July, Fig. 9a. Axial vorticity b.ω x / U Fig. 9b. Turbulent kinetic energy Fig. 9. Mean axial vorticity and turbulent kinetic energy cross fields for α = 4.5 and δ = at X/b = k / U b.ω x / U Fig. a. Axial vorticity at X/b =.7 Fig. b. Turbulent kinetic energy at X/b =.7 b.ω x / U Fig. c. Axial vorticity at X/b =.87 Fig. d. Turbulent kinetic energy at X/b =.87 b.ω x / U Fig. e. Axial vorticity at X/b = 4.3 Fig. f. Turbulent kinetic energy at X/b = 4.3 Fig.. Mean axial vorticity and turbulent kinetic energy cross fields for α = et δ = k / U k / U k / U

12 Lisbon, Portugal, 7- July, 8.3 b.ω x / U Fig. a. Analytical basic vortex b.ω x / U Fig. b. Analytical wandered vortex Fig.. Mean axial vorticity cross fields for the analytical basic and wandered vortices (fixed frame of reference) Fig. a. Apparent turbulent kinetic energy 3.k / U v y v z / U Fig. b. Apparent transverse Reynolds stress Fig.. Apparent turbulence cross fields for the analytical wandered laminar vortex (fixed frame of reference) Z c / b b.ω x / U Y c / b Fig. 3. Instantaneous centres (X/b=.7 ; α=4.5 ) -6. uncorrected non corrigé corrected corrigé Fig. 4. Axial vorticity profiles (X/b=.7 ; α=4.5 ) - -

13 Lisbon, Portugal, 7- July, Fig. 5a. Uncorrected field 3.k / U Fig. 5b. Corrected field Fig. 5. Uncorrected and corrected turbulent kinetic energy cross fields (X/b=.7 ; α=4.5 ) 3.k / U E-3.E-3.E-3 uncorrected non corrigé corrected corrigé / U 8.E-3 6.E-3 uncorrected v y non v corrigé y corrected v y corrigé v v y uncorrected z non v corrigé v z z corrigé corrected v z / U v x 8.E-4 6.E-4 et v z / U 4.E-3 4.E-4 v y.e-3.e-4.e Fig. 6a. Axial diagonal Reynolds stress.e Fig. 6b. Cross diagonal Reynolds stresses. uncorrected non corrigé corrected corrigé.. Vx / U.95 Vt / U uncorrected non corrigé corrected corrigé Fig. 6c. Axial velocity Fig. 6d. Tangential velocity Fig. 6. Uncorrected and corrected diagonal Reynolds stresses and velocity profiles (X/b=.7 ; α=4,5 ) - 3 -

14 Lisbon, Portugal, 7- July, X/b =.7 X/b =.47 X/b =.67 X/b =.87 σ / b σσ y ; y ; α=4.5 α=4,5 σ σ z ; z ; α=4.5 α=4,5 σ σ y ; y ; α=9 α=9 σ σ z ; α=9 z ; α= X / b Fig. 7. Wandering standard deviations versus downstream distance for α=4.5 and α=9 -. X/b = 4.3 X/b = 4.66 X/b = 5. X/b = Fig. 8. Evolution of the wandering principal axes with the downstream distance for α=4.5. One color per axis. 6 4 non corrigé ; α=4,5 corrigé ; α=4,5 non uncorrected corrigé ;; α=9 α=4.5 corrigé corrected ; α=9 ; α=4.5 uncorrected ; α=9 corrected ; α=9 5 4 non corrigé ; α=4,5 corrigé ; α=4,5 non uncorrected corrigé ;; α=9 α=4.5 corrigé corrected ; α=9 ; α=4.5 uncorrected ; α=9 corrected ; α=9 b. ω x c / U k c / U X / b Fig. 9. Absolute axial vorticity at the vortex centre versus downstream distance for α=4.5 and α= X / b Fig.. Turbulent kinetic energy at the vortex centre versus downstream distance for α=4.5 and α= uncorrected uncorrected.. uncorrected corrected corrected uncorrected ω c x / ωc x () k c / k c () number of samples Fig. a. axial vorticity number of samples Fig. b. turbulent kinetic energy Fig.. Statistical convergence for the uncorrected and corrected values at the vortex centre (X/b=.7 ; α=4.5 ) - 4 -