Unsteady Flow Phenomena Associated With Leading-edge Vortices

ARTICLE IN PRESS

0376-0421/$ - se

doi:10.1016/j.pa

Abbreviations

leading-edge vo�Tel.: +49 89

E-mail addr

Progress in Aerospace Sciences 44 (2008) 48–65

www.elsevier.com/locate/paerosci

Unsteady flow phenomena associated with leading-edge vortices

C. Breitsamter�

Institute of Aerodynamics, Technische Universitat Munchen, BoltzmannstraX e 15, 85748 Garching, Germany

Abstract

This paper presents selected results from extensive experimental investigations on turbulent flow fields and unsteady surface pressures

caused by leading-edge vortices, in particular, for vortex breakdown flow. Such turbulent flows may cause severe dynamic aeroelastic

problems like wing and/or fin buffeting on fighter-type aircraft. The wind tunnel models used include a generic delta wing as well as a

detailed aircraft configuration of canard-delta wing type. The turbulent flow structures are analyzed by root-mean-square and spectral

distributions of velocity and pressure fluctuations. Downstream of bursting local maxima of velocity fluctuations occur in a limited radial

range around the vortex center. The corresponding spectra exhibit significant peaks indicating that turbulent kinetic energy is channeled

into a narrow band. These quasi-periodic velocity oscillations arise from a helical mode instability of the breakdown flow. Due to vortex

bursting there is a characteristic increase in surface pressure fluctuations with increasing angle of attack, especially when the burst location

moves closer to the apex. The pressure fluctuations also show dominant frequencies corresponding to those of the velocity fluctuations.

Using the measured flow field data, scaling parameters are derived for design purposes. It is shown that a frequency parameter based on

the local semi-span and the sinus of angle of attack can be used to estimate the frequencies of dynamic loads evoked by vortex bursting.

r 2007 Elsevier Ltd. All rights reserved.

Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

2. Models and experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

2.1. Delta wing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

2.2. Delta-canard configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

2.3. Test technique and test conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

2.3.1. Wind tunnel facilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

2.3.2. Test methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

2.3.3. Test conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

3. Flow physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

3.1. Leading-edge vortex flow. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

3.2. Turbulent flow fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

3.3. Surface pressure fluctuations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

3.4. Fin buffet and buffeting characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

4. Scaling parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

4.1. Turbulence intensities and spectral densities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

4.2. Dominant frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

e front matter r 2007 Elsevier Ltd. All rights reserved.

erosci.2007.10.002

: CLV, canard leading-edge vortex; CTV, canard trailing-edge vortex; LEX, leading-edge extension; rms, root-mean-square; WLV, wing

rtex.

28916137; fax: +49 89 28916139.

ess: [email protected]

www.elsevier.com/locate/paerosci

dx.doi.org/10.1016/j.paerosci.2007.10.002

mailto:[email protected]

ARTICLE IN PRESS

Nomenclature

b span [m]CL lift coefficientCP(t) pressure coefficient [p(t)�pN]/qNCP mean (time averaged) pressure coefficientC0P fluctuation part of CP

CP amplitude spectrum of pressure coefficient,ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2SCP

DkU1=lmp

CPrmsrms value of C0P,

ffiffiffiffiffiffiffiffiC0

2P

qcr wing root chord [m]d thickness [m]f frequency [1/s]k reduced frequency, flm=U1lC characteristic length [m]lm wing mean aerodynamic chord [m]p(t), pNpressure, ambient pressure [Pa]qN free stream dynamic pressure [Pa]Relm Reynolds number, U1lm=nSCP

pressure spectral density [s]Su0

ipower spectral densities of velocity fluctuationsu0i

SNu0 power spectral density of u0 normalized with

ðDkU1Þ=ðu02lmÞ

s, sl semi-span, local semi-span [m]t time [s]UC characteristic velocity [m/s]

UN free stream velocity [m/s]u, v, w axial (stream-wise), lateral and vertical velocity

[m/s]u; v; w axial (stream-wise), lateral and vertical mean

(time averaged) velocity [m/s]u0, v0, w0fluctuation part of u, v, w; u0i [m/s]urms, vrms, wrms rms velocities of u0, v0, w0; urms ¼

ffiffiffiffiffiffiu02

p[m/s]

Y, Z non-dimensional coordinates in lateral andvertical direction, Y ¼ y/s, Z ¼ z/s

x, y, z Cartesian coordinatesa angle of attack, degL aspect ratiol taper ratiol wave length [m]n kinematic viscosity [m2/s]j leading-edge sweep [deg]r density [kg/m3]

Subscripts

B bursting, burst locationC canarddom dominantF finTE trailing-edgeW wing

C. Breitsamter / Progress in Aerospace Sciences 44 (2008) 48–65 49

1. Introduction

Modern fighter aircraft are subject to high angle ofattack maneuvers extending the flight envelope to the stalland post-stall regime [1]. Slender wing geometries, e.g.delta wing geometries, strakes, and leading-edge exten-sions (LEXs), respectively, are used to generate stronglarge-scale vortices shed at the highly swept leading-edges [2]. The leading-edge vortices improve signifi-cantly the high angle of attack performance because ofadditional lift and an increase in maximum angle ofattack. Time scales can be attributed to several unsteadyflow phenomena in comparison to time scales associ-ated with flow changes due to maneuvers [3] (Fig. 1).During maneuvers wing areas influenced by flow separa-tion or vortex bursting are shifted upstream or down-stream at larger time scales while shorter time scalescorresponding to unsteady flow phenomena, like shearlayer instabilities, instability of the breakdown flow orwake instabilities, may be of great importance for dynamicaeroelastic effects [3,4].

At high angle of attack, the phenomenon of leading-edgevortex bursting over the wing planform is of specificinterest [5,6]. The transition from stable to unstablecore flow, evident by the rapid change in the axial velo-city profiles from jet- to wake-type, leads to extremely

high turbulence intensities at the breakdown positionand to increased turbulence levels further downstream [3].Hence, the buffet excitation level increases strongly abovea certain angle of attack, and wing and fin normalforce spectra may exhibit narrow-band peaked distribu-tions (Fig. 2). Such unsteady aerodynamic loads oftenexcite the vertical tail structure or even the wing struc-ture in their natural frequencies, resulting in increasedfatigue loads, reduced service life and raised maintenancecosts [4,7].For example, the fin buffeting problem plagues twin-fin

configurations (F-15, F/A-18), but single-fin aircraft arealso affected [4,7]. Therefore, comprehensive researchprograms have been undertaken aimed at understand-ing the buffet loads and reducing the structural response.The related vortex flow features are carefully analyzedusing wind tunnel tests on small- and full-scale models[7–10], supplemented by flight tests [7,11], and detailednumerical flow simulations [12,13]. In addition, designmethods have been developed to describe the fin buffetenvironment and to predict buffet loads for use in air-craft design [14,15]. The buffet loads do not only decreasethe fatigue life of the airframe, but may, in turn, limitthe angle of attack envelope of the aircraft. To counterbuffeting problems, several methods have been suggested.They deal with alterations of the structural properties

Fig. 2. Characteristics of vortex induced fin buffeting.

Fig. 1. Unsteady flow phenomena on delta wing configurations: flow features associated with time scales of tUN/crb1 (a) and flow features associated

with time scales of tUN/crp1 (b).

C. Breitsamter / Progress in Aerospace Sciences 44 (2008) 48–6550

like stiffness and damping [16], aerodynamic modifica-tions for passive or active control of vortex trajectories toavoid a direct impact of the burst vortex flow [17] andmethods of active vibration control [18–22]. Using activecontrol, the structural dynamic loads can be reducedaimed both to increase the service live and to enhancethe maneuverability by extending the angle of attackenvelope.

To improve the knowledge on the flow physics asso-ciated with high angle of attack buffet problems caused by

unsteady vortex flows, extensive experiments have beenconducted at the Institute of Aerodynamics (AER) of theTechnische Universitat Munchen (TUM) [3,15,22,23]. Thestudies focus on the low-speed flow environment of genericdelta wing models, as well as of a modern fighter aircraftmodel. The turbulent flow structure is analyzed by thespatial and temporal characteristics of the time-dependentflow velocities supplemented by unsteady surface pressures.This paper gives an overview of the main resultscharacterizing the unsteady flow phenomena by turbulence

ARTICLE IN PRESSC. Breitsamter / Progress in Aerospace Sciences 44 (2008) 48–65 51

intensities, spectral densities and dominant reduced fre-quencies. Such data are of great importance for fighteraircraft design.

Fig. 4. Geometry and wind tunnel model of fighter aircraft configuration: geom

model mounted in test section of TUM-AER low-speed wind tunnel facility B

Fig. 3. Geometry of generic delta wing configuration.

2. Models and experiment

2.1. Delta wing

The delta wing model is a sharp-edged carbon fibermodel with a root chord of 0.670m and a span of 0.335m(Fig. 3). The leading-edge sweep is 761 corresponding to anaspect ratio of 1. Fast-response differential pressuretransducers are embedded in the right part of the uppersurface located at root chord positions of x/cr ¼ 0.3(9 transd.), x/cr ¼ 0.5 (9 transd.), x/cr ¼ 0.7 (11 transd.),and x/cr ¼ 0.8 (10 transd.). At 90% root chord 25transducers are positioned along the entire local span toprove symmetric flow conditions.

2.2. Delta-canard configuration

The delta-canard model consists of nose section, frontfuselage including rotatable canards and a single placecanopy, center fuselage with delta-wing section and athrough-flow air intake underneath, and rear fuselageincluding nozzle section and the vertical tail (fin) (Fig. 4).All model parts are made of stainless steel. The wingsweep is 501, the canard sweep 451 and the span of themodel is 0.740m. For the model tested, the leading- and

etry of delta-canard configuration (a) and views of 1/15-scale delta-canard

(b).

ARTICLE IN PRESSC. Breitsamter / Progress in Aerospace Sciences 44 (2008) 48–6552

trailing-edge flaps as well as the canard were set to 01.The fin is instrumented with 18 differential pressuretransducers at nine positions directly opposite each otheron each surface.

2.3. Test technique and test conditions

2.3.1. Wind tunnel facilities

The investigations are carried out in the Gottingen-type low-speed wind tunnel facilities A and B of theAER of the TUM. Dimensions of the open testsections (height�width� length) are 1.8m� 2.4m� 4.8m(W/T A) and 1.2m� 1.55m� 2.8m (W/T B), respectively.Maximum usable velocity is 65 and 60m/s, respectively.The test section flow was carefully inspected and cali-brated, documenting a turbulence level less than 0.4% anduncertainties in the spatial and temporal mean velocitydistributions of less than 0.067%. The blockage atmaximum angle of attack is below 6%. The models are

Fig. 5. Delta wing vortex formation: main delta wing flo

sting mounted using a computer-controlled three-axismodel support (Fig. 4b).

2.3.2. Test methods

Advanced hot-wire anemometry with miniature dual-and triple-sensor probes was used to measure the time-dependent velocity components. The sensors consist of5-mm-diameter platinum-plated tungsten wires giving alength/diameter ratio of 250. The measuring volumeformed by the wires is approximately 1mm in diameter.The wires are arranged perpendicular to each other toachieve best angular resolution [3,24]. An additionaltemperature probe is employed to correct anemometeroutput voltages if ambient flow temperature varies. Thehot-wire probes were operated by a multi-channel con-stant-temperature anemometer system. By means of itssignal conditioner modules, bridge output voltages weretypically low-pass filtered at 1000Hz before digitizationand amplified for optimal signal level. The signals were

w features (a) and vortex bursting characteristics (b).


then digitized with 16-bit precision through the sixteen-channel simultaneous-sampling A/D converter of a PChigh-speed board. The sampling rate for each channel wasset to 3000Hz. The sampling time was 6.4 s, resulting in asample block of 19,200 values for each survey point. Thesampling parameters were achieved by preliminary tests toensure that all significant flow field phenomena aredetected. Each digitized and temperature-corrected voltagetriple was converted to calculate the time-dependentvelocity components u, v, and w. The numerical methodused is based on look-up tables derived from the fullvelocity and flow angle calibration of the sensors [3,24].

Fig. 6. Typical delta wing lift polar and flow field topology as functio

Statistical accuracy of the calculated quantities wasconsidered as well. Random error calculations gaveaccuracies of 0.5%, 2%, and 3.5% for the mean andstandard deviation and spectral density estimation, respec-tively [24]. Regarding the susceptibility of vortex structuresto intrusive measurements, it was found that the presenceof the probe has no markable influence on the vortexstructures of interest [3].The fluctuating surface pressures were recorded by

transducers of active differential type giving a best signalresolution of about 2 Pa. The sensors are connected to adata acquisition system with 8 modules each fitted with 16

n of angle of attack; jW ¼ 761, UN ¼ 37m/s, Relm ¼ 1.07� 106.

ARTICLE IN PRESS

Fig. 7. Delta wing vortex flow stages as function of wing sweep jW and

angle of attack a.


differential amplifiers, low-pass filters of Butterworth type,and sample and hold units linked to a 14-bit A/Dconverter. Thus, 128 signal inputs can be treated simulta-neously. Here, the sampling rate for each channel was setto 2000Hz and the low-pass filter frequency to 256Hz. Thesampling time is 30 s, giving a sample block of 60,000values for each transducer. Statistical errors are below0.5%.

2.3.3. Test conditions

The delta wing tests were made at a free stream referencevelocity of UN ¼ 37m/s, giving a Reynolds number ofRelm ¼ 1.07� 106. The angle of attack is varied in the range01pap601. The results presented focus on symmetric freestream conditions. The velocity measurements were per-formed in planes normal to the wing surface located directlyabove the pressure transducer sections. The measurementpoints are evenly spaced in lateral and vertical direction witha relative distance of 0.045 based on the local wing semi-span.

The conditions of the delta-canard investigations corre-spond to those of the delta wing studies: UN ¼ 40m/s,Relm ¼ 0.97� 106, a ¼ 01–301. The relative spacing offlowfield survey points is 0.027 laterally and 0.042vertically, also based on the local wing semi-span.

At all tests, turbulent boundary layers were present atwing and control surfaces, proven by shear–stress sensitiveliquid crystal measurements [3].

3. Flow physics

3.1. Leading-edge vortex flow

Delta wing planforms representing lifting surfaces withhighly swept leading-edges and low aspect ratios have beeninvestigated intensively over the last 50 years [2,5,6]. Here,the interest is particularly on low-speed cases. Therefore,compressibility effects are not addressed.

The dominating flow field characteristics are given by theevolution and development of two large-scale vortices shedat the delta wing leading-edges (Fig. 5a). Vortex formationstarts already at low angles of attack developing from thewing rear part to the apex. The separating shear layersfrom the wing upper and lower surface roll up by self-induction to form a vortex, which is positioned over thewing. This primary vortex is fully developed when vorticityfeeding exists over the whole leading-edge. The vortex coreshows high axial velocities, low static pressures and highdissipation, i.e. lower total pressures, in the sub-core areadue to the steep gradient in the cross flow components. Theleading-edge vortices increase the velocities on the wingupper surface. This velocity increase leads to a high suctionlevel, with the local pressure minima indicating the track ofthe vortex axis on the wing surface. Consequently, leading-edge vortices in a fully developed, stable stage createadditional lift and an increase in maximum angle of attack,improving significantly maneuver capabilities of high-agility aircraft.

Considering a chord-wise station, the pressure increasesfrom the suction peak induced by the primary vortex to theleading-edge, resulting in a severe lateral pressure gradient.Typically, a further separation occurs, forming a second-ary, counter-rotating vortex, the evolution of whichdepends strongly on the presence of a laminar or turbulentboundary layer [25]. Further, leading-edge vortices aresubject to breakdown at high angles of attack (Fig. 5b).Vortex breakdown is caused by the stagnation of theaxial core flow due to the increase of the adversepressure gradient when raising the angle of attack[5,6,26]. Therefore, the core expands rapidly accompaniedby high velocity fluctuations [3].Delta wing research activities often focus on a sharp

leading-edge because primary separation is fixed and theleading-edge vortex development is only little influenced byReynolds number effects. A blunt leading-edge complicatesthe vortex aerodynamics as the position of the separationline is free to move, determined by the pressure gradientand the boundary layer development [25]. Thus, leading-edge radius, angle of attack and Reynolds number are themain parameters adjusting the onset of vortex evolution aswell as position and strength of the primary vortex. For thesharp leading-edge case, the angle of attack is the mainparameter only [27].


In this context, Fig. 6 shows the lift polar of theinvestigated 761 delta wing configuration supplemented bycorresponding flow fields. The vortex formation is sche-matically represented and the vector field of the cross-flowvelocities is shown at 90% wing root chord for angles ofattack of a ¼ 12.51, 251, 301 and 351. The velocity fieldclearly indicates that the vortex strength increases withincreasing angle of attack. The two primary vortices moveinboard and upward and their cross sections becomeenlarged, cp. a ¼ 12.51 and 251. Above a certain angle of

Fig. 8. Typical delta wing turbulence intensity fields for fully developed and

attack, the primary vortices move purely upward due to themutual displacement effect of the two vortices. The vortex-induced velocities create high suction on the wing, leadingto a nonlinear increase in the lift coefficient. Raising theangle of attack further changes the vortex core structure,a ¼ 301. This change reveals itself as a sudden expansion ofthe vortex core flow, known as vortex bursting or vortexbreakdown. The expansion of the vortex core flow isaccompanied by a substantial decrease of the vortex-induced velocities. Bursting starts over the wing at the

burst leading-edge vortices; jW ¼ 761, UN ¼ 37m/s, Relm ¼ 1.07� 106.

ARTICLE IN PRESSC. Breitsamter / Progress in Aerospace Sciences 44 (2008) 48–6556

trailing-edge and the breakdown position moves forwardwith increasing angle of attack, a ¼ 351. Thus, the wingupper surface is more and more affected by the breakdownflow how the suction level becomes diminished and the liftcoefficient decreases. For Reynolds numbers of Re4104

and typical swirl numbers of delta wing leading-edgevortices vortex breakdown is of the spiral type.

A correlation between wing sweep (fW ¼ 451–851) andangle of attack (a ¼ 01–401) is shown in Fig. 7, concentrat-ing on thin wings with sharp leading-edge. A first range canbe assigned to the evolution of the primary vortex startingfrom the wing rear part to the apex. Consequently, theprimary vortex is only present within the rearward range ofthe wing and is not completely rolled up yet. The dottedline indicates the vortex axis. The second range marks thatof the fully developed vortex, the axis of which movesinboard and upward with increasing angle of attack. Thetransition from range 1 to range 2 depends on the

Fig. 9. Characteristic delta wing turbulence intensity distributions and pow

jW ¼ 761, Relm ¼ 1.07� 106.

boundary layer condition, namely laminar or turbulent.For a given wing sweep, the laminar boundary layer createsthe fully developed vortex at a smaller angle of attackrelative to the turbulent case. The next range marks thecase of the span-wise fixed vortex. Here, the vortex axis isonly shifted upward with increasing angle of attack. Thetransition from range 2 to range 3 depends like before onwhether a laminar or turbulent boundary layer is present.Furthermore, it can be stated that the span-wise fixedvortex develops only for a wing sweep larger thanjWE651. The aerodynamic benefits resulting from lead-ing-edge vortices become limited when vortex burstingaffects markedly the wing flow. At moderate wing sweep,vortex bursting exists over a large incidence range until themaximum angle of attack is reached. These ranges ofleading-edge vortex conditions determine significantly theaircraft maneuverability at moderate and high angles ofattack.

er spectral densities for the leading-edge vortex breakdown flow field;


Regarding numerical simulations, great success has beenachieved in the development and application of highfidelity computational fluid dynamics (CFD) methods inthe last 10 years [28–30]. Unsteady Reynolds averagedNavier-Stokes (URANS) methods are available including avariety of turbulence models based on algebraic up toReynolds stress transport equations. Also, methods fordetached eddy simulations (DES) are formulated as acombination of a large eddy simulation (LES) to modelseparated flow dominated by large-scale structures in theouter domain and a turbulence model to calculate flowquantities in the wall-bounded domain. Even the upperwing surface pressure distribution is very sensitive to thecorrect modeling of viscous effects on the wing as well as inthe rolled-up shear layers. The calculation and analysis ofunsteady loads is even a more challenging problem, which

Fig. 10. Delta wing rms pressures as function of angle of attack considering

Relm ¼ 1.07� 106.

needs the correct representation of the turbulent and time-dependent flow field features [22].

3.2. Turbulent flow fields

The turbulent flow fields are analyzed using root-mean-square (rms) values of the velocity fluctuations referred tothe free stream velocity UN. Contours of axial rmsvelocities are shown for the 761 delta wing configuration,plotted again for the cross-flow plane located at 90% wingroot chord and angles of attack of a ¼ 12.51, 251, 301 and351 (Fig. 8, cp. Fig. 6).The fully developed vortices are indicated by regions of

moderate turbulence intensities including local maxima of5%–2%, a ¼ 12.51 and 251. These regions clearly depictthe shear layers separating from the leading-edge and

especially cases of leading-edge vortex bursting over the wing; jW ¼ 761,

ARTICLE IN PRESS

Fig. 11. Flow field characteristics of delta-canard configuration at

a ¼ 151; UN ¼ 40m/s, Relm ¼ 0.97� 106: cross-flow velocity vector fields

at 40% and 100% root chord position (a) and topology of main vortex

systems (b).


rolling up to form the rotational core of the primaryvortices. The (viscous) sub-core of the primary vortex isindicated by a circle-like region of local rms maxima ofabout 10%–12%. Also, the secondary vortices are markedby increased turbulence intensities. The areas of local rmsmaxima detected in the shear layers represent the forma-tion of coherent sub-structures associated with a shearlayer instability of the Kelvin–Helmholtz type [3] (cp.Fig. 1). Because of vortex bursting at x/cr ¼ 0.86, the flowpattern of the vortex core is significantly changed ata ¼ 301. Next to the original jet-like core, a region ofstrong flow deceleration occurs. This region of retardedaxial core flow is caused by the adverse pressure gradientarising at high angle of attack. The corresponding steepvelocity gradients and the rapid change from jet- to wake-like core flow evokes an overall maximum in turbulenceintensity at the vortex center. With increasing angle ofattack, a ¼ 351, vortex bursting occurs much more up-stream, namely at x/cr ¼ 0.49. Downstream, the region ofmaximum turbulence intensity expands rapidly, which isevident at 90% wing root chord. The associated localturbulence maxima of 5–12%, are located in a limitedradial range around the burst vortex core. This areacorresponds to the points of inflection in the radial profilesof the retarded axial core flow.

This development of rms patterns with increasing angleof attack for a fixed chordwise station can also bedetermined when fixing the angle of attack and movingdownstream from the wing apex to the trailing-edge(Fig. 9). Analyzing the spectral content of the velocityfluctuations it is shown that the breakdown flow exhibits asignificant spectral peak, indicating that turbulent kineticenergy is channeled into a narrow band. The frequencyrelated to this spectral peak is named ‘‘dominant fre-quency’’. The energy concentration in a limited frequencyrange is linked to a specific instability mechanism calledhelical mode instability of the breakdown flow [3,9]. Hence,quasi-periodic aerodynamic loads result, which maystrongly excite structural modes.

3.3. Surface pressure fluctuations

As shown before, the impingement of burst leading-edgevortices is a source of buffet excitation on an aircraftexperienced on the wing surface or on other surfaces suchas the fin. The buffet excitation is substantiated by thecorresponding pressure fluctuations measured on the deltawing surface (Fig. 10). The rms pressures are plotted as afunction of angle of attack for the symmetry location at90% wing root chord. In addition, patterns of rms surfacepressures are shown for a ¼ 351, 401, and 451. If vortexbreakdown takes place in the rear part of the wing the rmssurface pressure distribution is less affected. With thebreakdown position moving upstream the pressure fluctua-tion intensities increase strongly, especially beneath thevortex axis, where the distance to the region of maximumflow field turbulence is the smallest. A noteworthy situation

exists at a ¼ 451, when the surface pressure fluctuationsreach an absolute maximum with rms levels above 30%. Afurther increase in angle of attack shifts the breakdownposition closer to the apex and the rms pressures decrease.This decrease is due to the detachment of the vortex axisreducing the impingement of the highly fluctuating flowfield on the wing surface.

3.4. Fin buffet and buffeting characteristics

At TUM-AER comprehensive studies on the vortexflow fields associated with wing and fin buffeting havebeen conducted on generic models as well as on theEF-2000 type delta canard configuration [3,15,23,24](Fig. 4). The overall flow field development is shown inFig. 11 including a schematic representation of the mainvortex systems based on laser light sheet tests. Thedominating vortices are the wing leading-edge vortices

ARTICLE IN PRESS

Fig. 12. Lateral rms velocities vrms/UN measured in the fin region and in a plane normal to the fin for various angles of attack; UN ¼ 40m/s,

Relm ¼ 0.97� 106: rms values for different vertical fin stations Z (a) and cross-flow rms patterns and velocity vectors at a ¼ 201 (b); at a ¼ 251 (c); and

a ¼ 301 (d).


(WLVs) and the canard leading-edge vortices (CLVs) andcanard trailing-edge vortices (CTVs) influencing the flowfield in the fin region.

The impact of the flow field on the fin structure can becharacterized by the lateral rms velocities. Summarizing,the rms values for different vertical fin stations areshown as a function of angle of attack in Fig. 12a. Themagnitude of the rms values in the midsection depends onthe development of the vortex flow structure. This isdepicted by the schematics of Fig. 12a, which are basedon the rms velocity patterns in planes normal to the finsurface (Figs. 12b–d). At moderate angles of attack thearea of the center-line fin is only little affected bythe regions of highly turbulent flow attributed to theburst wing leading-edge vortices and the canard leading-and trailing-edge vortices (Fig. 12b). Above a ¼ 251, the

lateral turbulence intensities in the fin region increasesignificantly with increasing angle of attack as the burstWLV expand and approach the midsection (Fig. 12c).Also the canard leading- and trailing-edge vortices comeclose to the midsection. In particular, the fin flow isinfluenced by induction effects arising from the WLVsheets, which are the loci of maximum turbulence intensity.The interaction between the WLVs and the canard vortices(CLVs and CTVs) leads to local rms maxima near the fintip (Fig. 12d).The unsteady flow field induces pressure fluctuations on

the fin. The surface-averaged rms values of the fluctuationsin the pressure coefficient are plotted as a function of angleof attack defining the buffet situation (Fig. 13). Represent-ing the trend in the lateral turbulence intensities, the rmspressure coefficient increases significantly above a ¼ 201,

ARTICLE IN PRESS

Fig. 13. Surface-averaged fin rms pressures as function of angle of attack; UN ¼ 40m/s, Relm ¼ 0.97� 106.

Fig. 14. Amplitude pressure spectra CP taken at fin station P13 for all angles of attack tested; UN ¼ 40m/s, Relm ¼ 0.97� 106.


reaching a value of about 8% at a maximum angle ofattack of aE301. The severe increase in the rms pressureabove a certain incidence is a characteristic feature of thefin buffet phenomenon (cp. Fig. 2).

The amplitude spectra of the fluctuating pressurecoefficient, calculated from the signal taken at sensorstation P13, are shown in Fig. 14 for all angles of attacktested. Above aE221, spectral peaks can be identified in therange of reduced frequencies of k ¼ 0.8–0.6 (k ¼ f lm/UN).The helical mode instability of the burst WLVs starts toaffect the fin pressure field and the narrow-band amplitudeincreases strongly from a ¼ 241 to a ¼ 31.21. This energypeak is called ‘‘buffet peak’’. Hence, the narrow-bandconcentration of turbulent kinetic energy may result in

strong excitation of structural modes. It can be furtherdetected that the reduced frequencies associated with thebuffet peak, i.e. the dominant frequencies, are shifted tolower values at higher angle of attack. Such pressuredistributions create the buffeting or structural response tothe buffet. The resulting fin buffeting mainly consists of aresponse in the first bending and torsion mode.Thus, the fluids–structure interaction of vortex break-

down with a fin involves the following phenomena(Fig. 15): the time-averaged breakdown location dependingon the adverse pressure gradient set by the recompressionat the wing trailing-edge and/or by the blockage of the fin,the helical mode instability of the breakdown flow, quasi-periodic oscillations of the breakdown location, distortion

ARTICLE IN PRESS

Fig. 15. Phenomena related to fin buffeting: visualization of F-18 LEX

vortices bursting in front of the fins (a) and fluid–structures interaction of

leading-edge vortex bursting and (elastic) fin (b).


of the incident vortex and vortex splitting, unsteady flowseparation at the fin leading-edge, and possible couplingbetween the separated fin flow and/or fin elastic deflectionswith oscillations of the breakdown location. Among these,the dominant phenomenon causing fin buffeting is thequasi-periodic loading on the fin due to the helical modeinstability of the leading-edge vortex breakdown flow.

4. Scaling parameters

The following parameters are of main importance fordesign issues. Especially the frequency parameter asso-ciated with dominant buffet loads is of specific interest for

structural dynamic properties. As low-speed high-angle-of-attack maneuvers are of primary interest, compressibilityeffects are not taken into account.

4.1. Turbulence intensities and spectral densities

Regarding the fin buffet problem, velocity fluctuationsare measured in the fin region of the delta-canardconfiguration (midsection: Y ¼ 0.0, Z ¼ 0.21) for differentangles of attack, varying the free stream velocities in thelow-speed environment (Fig. 16). It is shown that the rmsvelocities based on the free stream velocity are constantover the considered velocity range. Hence, the rmsvelocities can be scaled by referring to the free streamvelocity UN. Similarly, rms pressures are scaled byreferring to dynamic free stream pressure qN.Further, the power spectral density values of the velocity

fluctuations can be made non-dimensional with rmsvelocities and a characteristic length lC and free streamvelocity UN as reference parameters. Thus, the non-dimensional rms valuesffiffiffiffiffiffi

u02i

q

U1(1)

and the non-dimensional spectral densities

Su0i

Dk

u02i

U1

lm(2)

can be used as appropriate scaling quantities regardingturbulence effects.

4.2. Dominant frequency

The velocity fluctuations measured in the fin region ofthe delta-canard configuration at Y ¼ 0.0, Z ¼ 0.21 arecharacterized by concentrations of turbulent kinetic energyat specific frequencies. These narrow-band concentrationsof the velocity fluctuations in the fin region are mainlyevoked by induction effects of the fluctuations associatedwith the approaching burst WLVs (see Figs. 9, 12 and 15).The corresponding dominant reduced frequencies

kdom ¼f domlC

UC, (3)

are scaled with lC=lm and UC=UN and plotted as a functionof free stream velocity UN for different angles of attack(Fig. 17). The graph substantiates that the reducedfrequency values do not change with free stream velocityUN, but decreases with angle of attack a. This shift in thedominant reduced frequency to lower values with increas-ing angle of attack was also found for the amplitudespectra of the fin surface pressure fluctuations (cp. Fig. 14).For further analysis, the dominant reduced frequency as afunction of angle of attack is plotted in Fig. 18. The quasi-periodic velocity and induced surface pressure fluctuations,respectively, result from the helical mode instability of the

ARTICLE IN PRESS

Fig. 17. Dominant reduced frequency kdom of the lateral velocity

fluctuations at fin station (xW/cr ¼ 1.13, Y ¼ 0.0, Z ¼ 0.21) of the delta-

canard configuration as function of free stream velocity UN for angles of

attack of a ¼ 25.01, 28.01, and 31.51; Relm ¼ 0.17� 106–1.22� 106.

Fig. 16. Lateral turbulence intensity (rms velocity vrms/UN) measured at fin station (xW/cr ¼ 1.13, Y ¼ 0.0, Z ¼ 0.21) of the delta-canard configuration as

a function of free stream velocity UN for angles of attack of a ¼ 20.0–31.51; Relm ¼ 0.17� 106–1.22� 106.


flow downstream of vortex breakdown. The burst vortexcore expands with increasing angle of attack and, therefore,the wavelength of the instability mode becomes larger andthe corresponding frequency smaller, fdom�1/l�1/sl.

A universal frequency parameter k�dom can be derivedusing appropriate scaling quantities (Fig. 19). Referring tovelocity, the component normal to the leading-edge (UN

sin a) has to be considered. The characteristic length scalelC must account for the vortex core expansion of the burstleading-edge vortex given approximately by the local halfspan (�sl ¼ x cotjW) and the shear layer distance(�sin2 a). Using these relations leads to a scaling with the

sinus of angle of attack and the co-tangent of the wingleading-edge sweep:

k�dom ¼f domlC

UC¼

f domx � cot jW � sin2 a

U1 � sin a

¼f domx

U1|fflffl{zfflffl}kdom

cot jW sin a ¼ 0:28� 0:025. ð4Þ

Considering especially the fin region of the delta-canardconfiguration at a downstream position of the wingtrailing-edge, Eq. (4) is written with x ¼ cr, i.e.,

k�dom ¼f domcr

U1|fflfflffl{zfflfflffl}kdom

cot jW sin a ¼ 0:28� 0:025. (5)

The application of this frequency parameter is shownin Fig. 19 for wing sweeps of jW ¼ 501 (delta-canardconfiguration, Fig. 3) and jW ¼ 761 (delta wing config-uration, Fig. 4). Measurements on different configurationssubstantiate the validity of the derived frequency para-meter [3,9,10,14,30].Fig. 18 also demonstrates that this scaling groups the

values of the dominant reduced frequencies taken in the finregion indeed within a band of k�dom ¼ 0:28� 0:025.Thus, the frequency f dom indicating a dominant energy

accumulation exciting structural modes can be derived fora certain configuration (jW) at a specific flight condition(UN, a):

f dom ¼1

cr cot jW

U1

sin að0:28� 0:025Þ. (6)

ARTICLE IN PRESS

Fig. 18. Application of the buffet load frequency parameter kdom* to the fin buffeting problem studied at the delta-canard configuration: schematic

representation of dominant fin buffeting phenomena (cf. Fig. 15) (a) and dominant reduced buffet frequency kdom as a function of angle of attack based on

amplitude pressure spectra of fin station P13 (cp. Fig. 14); UN ¼ 40m/s, Relm ¼ 0.97� 106 (b).


5. Conclusions and outlook

Detailed experimental investigations on the turbulentflow fields associated with fully developed and with burstleading-edge vortices have been conducted on a 761 sweptdelta wing and on a fighter aircraft model of canard-deltawing type with a wing sweep of 501. The measurementsinclude field distributions of velocity fluctuations based onadvanced hot-wire anemometry and distributions of sur-face pressure fluctuations obtained by unsteady pressuretransducers. Spectral quantities are analyzed as well.

Major results are as follows:

(1)
Fully developed leading-edge vortices are characterizedby moderate turbulence levels for the rolled-up shearlayers and the vortex core, ui,rmsE6%–12%. Pressurefluctuations induced on the shedding surface (wing) arelow, cprms
p3%.
(2) The turbulence intensities rise significantly when vortex
breakdown takes place. At the burst position thevelocity fluctuations show an overall maximum nearthe vortex center, whereas in the breakdown wake thevelocity fluctuations show local maxima in a limitedradial range (annular region), ui,rmsE18%–28%. Thus,the buffet excitation on an airframe componentincreases strongly when the distance between the vortex

axis and the wing or fin surface becomes smaller thanone diameter of the burst vortex core.

(3)
Quasi-periodic velocity fluctuations occur downstreamof vortex bursting corresponding to a helical modeinstability of the breakdown flow field. The amplitudesof these narrow-band fluctuations are the largest in theannual region of maximum turbulence intensities.These frequency-dependent velocity fluctuations givealso rise to coherent unsteady pressures, the frequencyof which corresponds to that of the unsteady velocities.
(4)
A universal frequency parameter can be attributed tothe dominant frequencies fdom for the velocity andpressure fluctuations of the breakdown flow field. Thisfrequency parameter is based on a length scale for thelateral expansion of the burst vortex core and acharacteristic velocity given by the wing leading-edgenormal velocity component, resulting in the relationðf domcr=U1Þ cot jW sin a ¼ 0:28� 0:025: This reducedfrequency can be used for design purposes to measurethe dominant frequencies linked to dynamic aeroelasticproblems, like vortex-induced wing and fin buffeting,when varying wing sweep and flight conditions(velocity, angle of attack).
(5)
In the presence of leading-edge vortices, the helicalmode instability of the breakdown flow at high angle ofattack is the leading mechanism for inducing severe

ARTICLE IN PRESS

Fig. 19. Buffet load frequency parameter kdom* obtained by scaling the dominant reduced buffet frequency kdom with the sinus of angle of attack a and the

cotangent of wing semi-span cot jW.


narrow-band unsteady loads (buffet) on aircraft wingand stabilizers.

The turbulence quantities reported herein serve also as adatabase for numerical investigations as performed in theEC-funded research projects FLOMANIA (Flow PhysicsModelling—An Integrated Apporach) and DESider(Detached Eddy Simulations for Industrial Aerodynamics),aimed at validating, improving and developing methods inthe field of hybrid RANS-LES methods.

References

[1] Herbst WB. Future fighter technologies. AIAA J Aircraft 1980;17(8):

561–6.

[2] Hummel D. On the vortex formation over a slender wing at large angles

of incidence. High angle of attack aerodynamics, AGARD–CP–247,

Sandefjord, Norway, October 4–6, 1978. p. 15-1–17.

[3] Breitsamter C. Turbulente Stromungsstrukturen an Flugzeugkonfi-

gurationen mit Vorderkantenwirbeln. Dissertation, Technische Uni-

versitat Munchen, Herbert Utz Verlag Wissenschaft (Aerodynamik),

1997, ISBN 3-89675-201-4.

[4] Luber W, Becker J, Sensburg O. The impact of dynamic loads on the

design of military aircraft. Loads and requirements for military

aircraft, AGARD-R-815, AGARD, Neuilly Sur Seine, France, 1996.

p. 8-1–27.

[5] Hummel D. Untersuchungen uber das Aufplatzen der Wirbel an

schlanken Deltaflugeln. Zeitschrift fur Flugwissenschaften und

Weltraumforschung, Band 13, 1965. p. 158–68.

[6] Lambourne NC, Bryer DW. The bursting of leading edge vortices.

Some observations and discussion of the phenomenon. ARC R M

3282 1962.

[7] Lee BHK, Brown D, Zgela M, Poirel D. Wind tunnel investigations

and flight tests of tail buffet on the CF-18 aircraft. Aircraft dynamic

loads due to flow separation, AGARD–CP–483, Sorrento, Italy,

April 1–6, 1990. p. 1-1–26.

[8] Canbazoglu S, Lin JC, Wolfe S, Rockwell D. Buffeting of fins:

distortion of incident vortex. AIAA J 1995;33(11):2144–50.


[9] Gursul I, Xie W. Buffeting flows over delta wings. AIAA J

1999;37(1):58–65.

[10] Meyn LA, James KD. Full-scale wind tunnel studies of F/A-18 tail

buffet. AIAA J Aircraft 1996;33(3):589–95.

[11] Del Frate JH, Zuniga FA. In-flight flow field analysis on the NASA

F-18 high alpha research vehicle with comparisons to ground facility

data. AIAA paper 90-0231, January 1990.

[12] Rizk YM, Gee K. Unsteady simulation of viscous flowfield

around F-18 aircraft at large incidence. AIAA J Aircraft 1992;29(6):

773–81.

[13] Kandil OA, Sheta EF, Liu CH. Computation and validation of

fluid/structure twin tail buffet response. In: Euromech colloquium

349, simulation of structure fluid interaction in aeronautics.

Gottingen, Germany: German Aerospace Research Center; 1996.

p. 15-1–15-10.

[14] Ferman MA, Patel SR, Zimmermann NH, Gerstenkorn G. A unified

approach to buffet response of fighter aircraft empennage. Aircraft

dynamic loads due to flow separation, AGARD–CP–483, Sorrento,

Italy, April 1–6, 1990. p. 2-1–18.

[15] Breitsamter C, Laschka B. Fin buffet pressure evaluation based

on measured flowfield velocities. AIAA J Aircraft 1998;35(5):

806–15.

[16] Ferman MA, Liguore SL, Smith CM, Colvin BJ. Composite

‘‘Exoskin’’ doubler extends F-15 vertical fatigue life. AIAA paper

93-1341, April 1993.

[17] Hebbar SK, Platzer MF, Frink WD. Effect of leading-edge extension

fences on the vortex wake of an F/A–18 Model. AIAA J Aircraft

1995;32(3):680–2.

[18] Ashley H, Rock SM, Digumarthi RV, Chaney K, Eggers Jr AJ.

Active control for fin buffet allevation. US Air Force Wright Lab.,

WL-TR-93-3099, Wright Patterson AFB, OH, January 1994.

[19] Becker J, Luber W. Comparison of Piezoelectric and aerodynamic

systems for aircraft vibration alleviation. In: SPIE 5th Annual

symposium on smart structures and materials, conference paper 3326-

04, San Diego, CA, March 1998.

[20] Galea SC, Ryall TG, Henderson DA, Moses RW, White EV, Zimcik

DG. Next generation active buffet suppression system. AIAA paper

2003-2905, July 2003.

[21] Sheta EF. Alleviation of vertical tail buffeting of F/A–18 aircraft.

AIAA J Aircraft 2004;41(2):322–30.

[22] Breitsamter C. Aerodynamic active control of fin-buffet load

alleviation. AIAA J Aircraft 2005;42(5):1252–63.

[23] Breitsamter C, Laschka B. Turbulent flow structure associated with

vortex-induced fin buffeting. AIAA J Aircraft 1994;31(4):773–81.

[24] Breitsamter C, Laschka B. Velocity measurements with hot-wires in a

vortex-dominated flow field. Wall interference, support interference

and flow field measurements, AGARD–CP–535, Brussels, Belgium,

October 4–7, 1993. p. 11-1–13.

[25] Hummel D. Effects of boundary layer formation on the vortical flow

above slender delta wings. Enhancement of NATO military flight

vehicle performance by management of interacting boundary layer

transition and separation. Prag, Czech Republic, October 4–7, 2004.

[26] Nelson RC, Visser KD. Breaking down the delta wing vortex. Vortex

flow aerodynamics, AGARD–CP–494, Scheveningen, The Nether-

lands, October 1–4, 1991. p. 21-1–15.

[27] Furman A, Breitsamter C. Investigation of flow phenomena on

generic delta wing. In: ICAS proceedings, 25th International congress

of the aeronautical sciences. Hamburg, Germany, September 13–18,

2006. p. 312-1–16.

[28] Rai P, Finley DB, Ghaffari F. An assessment of CFD effectiveness

for vortex–flow simulation to meet preliminary design needs, Vortex

flow and high angles of attack. Loen, Norway, May 7–11, 2001.

[29] Gurr A, Rieger H, Breitsamter C, Thiele F. Detached-eddy

simulation of the delta wing of a generic aircraft configuration.

Notes on numerical fluid mechanics, new results in numerical and

experimental fluid mechanics, V. Contributions to the 14th AG

STAB/DGLR symposium, Bremen, 2004 (NNFM), vol. 92. Berlin:

Springer Verlag; 2006.

[30] AVT–113/VFE–2: /http://cawap-prism.larc.nasa.gov/CAWAPI/

DELTAWING/S.

http://cawap-prism.larc.nasa.gov/CAWAPI/DELTAWING/

http://cawap-prism.larc.nasa.gov/CAWAPI/DELTAWING/

Unsteady Flow Phenomena Associated With Leading-edge Vortices

Documents