counter trailing vortices

Aerospace Science and Technology 13 (2009) 114–129

www.elsevier.com/locate/aescte

Experimental investigation of counter-rotating four vortex aircraft wake

Untersuchung zur Nachlaufcharakteristik von Vierwirbelsystemen

Alexander Allen ∗, Christian Breitsamter

Lehrstuhl für Aerodynamik, Technische Universität München, 85747 Garching, Germany

Received 25 July 2007; received in revised form 13 May 2008; accepted 30 May 2008

Available online 17 June 2008

Abstract

An experimental investigation on the wake vortex formation and evolution of a four vortex system of a generic model in the near field andextended near field as well as the behaviour and decay in the far field region has been conducted by means of hot-wire anemometry in a windtunnel. The results were obtained during an experimental campaign as part of the EC project “FAR-Wake”. The model used consists of a wing–tailplane configuration with the wing producing positive lift and the tail plane negative lift. The circulation ratio of tail plane to wing is −0.3 and thespan ratio is 0.3. Thus, a four vortex system with counter-rotating neighboured vortices exists. The model set-up was chosen on the condition tocreate a most promising four vortex system with respect to accelerate wake vortex decay by optimal perturbations enhancing inherent instabilitymechanisms. The flow field has been investigated for a half plane of the entire wake up to a distance of 48 span dimensions downstream of themodel. The results obtained at 1, 12, 24 and 48 span distances are shown as non-dimensional axial vorticity and vertical turbulence intensities.A significant decay in peak vorticity, swirl velocity and circulation is observable during the downward motion of the vortices. Spectral analysis ofthe unsteady velocity data reveals a peak in the power spectral density distributions indicating the presence of a dominating instability. Using twohot-wire probes cross spectral density distributions have also been evaluated, which highlight the co-operative instability leading to a rapid wakevortex decay within 30 span dimensions downstream.© 2008 Elsevier Masson SAS. All rights reserved.

Zusammenfassung

Die Nachlaufausbildung eines Vierwirbelsystems, mit gegensinnig drehenden, benachbarten Wirbeln, wird an einem generischen Modell mittelsHitzdrahtanemometrie im Windkanal untersucht. Der betrachtete Nachlaufbereich umfasst die Entwicklung im Nahfeld und erweitertem Nahfeldsowie das Verhalten und den Zerfall im Fernfeld. Die Ergebnisse wurden im Rahmen einer experimentellen Kampagne als Teil des EU Projektes“FAR-Wake” gewonnen. Das verwendete Modell besteht aus einer Flügel–Leitwerks Konfiguration, bei der der Flügel positiven und das Leitwerknegativen Auftrieb erzeugt. Das Zirkulationsverhältnis des Leitwerks zum Flügel beträgt −0.3 und das Spannweitenverhältnis 0.3. Somit entstehtein System von vier, gegensinnig drehenden, benachbarten Wirbeln. Die Versuchsparameter sind so gewählt, dass das vielversprechendste Vierwir-belsystem hinsichtlich eines beschleunigten Wirbelschleppenzerfalls entsteht, d.h. welches ein optimales Anwachsen der inhärenten Instabilitätenerwarten lässt. Das Strömungsfeld wird dabei für eine Halbebene des Nachlaufs bis zu 48 Spannweiten stromab des Modells untersucht. Die Er-gebnisse für die Querströmungsebenen beim Abstand von 1, 12, 24 und 48 Spannweiten werden anhand der dimensionslosen axialen Wirbelstärkeund der vertikalen Turbulenzintensität diskutiert. Ein bedeutender Abfall in den Spitzenwerten der Wirbelstärke, maximalen Umfangsgeschwin-digkeit und Zirkulation ist während der Abwärtsbewegung der Wirbel erkennbar. Die Spektralanalyse der instationären Geschwindigkeiten zeigteine deutliche Spitze in der spektralen Leistungsdichte, die auf das Vorhandensein einer dominierenden Instabilität hinweist. Spektrale Kreuz-leistungsdichteverteilungen, denen eine zeitgleiche Messung mit zwei Hitzdrahtsonden zugrunde liegt, belegen die Anfachung der Instabilität, diestromab zu einem beschleunigten Zerfall der Wirbelschleppe innerhalb von 30 Spannweiten führt.© 2008 Elsevier Masson SAS. All rights reserved.

Keywords: Wake vortices; Decay; Experiment; Instabilities; Correlation

* Corresponding author.E-mail address: [email protected] (A. Allen).

1270-9638/$ – see front matter © 2008 Elsevier Masson SAS. All rights reserved.doi:10.1016/j.ast.2008.05.004

A. Allen, C. Breitsamter / Aerospace Science and Technology 13 (2009) 114–129 115

Schlüsselwörter: Wirbelschleppe; Zerfall; Experiment; Instabilitäten; Korrelation

1. Introduction

Trailing vortices of Large Transport Aircraft are a poten-tial threat to succeeding aircraft encountering the wake [16,18].This is especially dangerous, when the aircraft are at take-offand landing [27]. The following aircraft may experience a sud-den decrease of climb rate or even rapid descent, a rolling mo-tion or an overload of the aircraft’s structure. In order to avoida dangerous impact of these vortices, minimum separation dis-tances for cruise, approach and take-off were established [16,18]. To increase the number of aircraft capable of landing atan airport within a given time period, the wake vortex strengthshould decay within a smaller distance than the separation dis-tance is at the moment. At the Institute of Aerodynamics (AER)of the Technische Universität München (TUM) a wind tunnelinvestigation is conducted within the framework of the Euro-pean funded specific targeted research project “FundamentalResearch on Aircraft Wake Phenomena” (“FAR-Wake”) on ageneric model generating a four vortex system aimed to obtaina quickly decaying vortex wake.

Precise prediction of wake vortex trajectories and decayunder all weather conditions is beyond the range of currenttechnology. Therefore, many research activities concentrate onalleviating the wake vortex hazard by modifications of wing ge-ometry and/or wing loading [19]. Comprehensive European re-search projects like C-Wake [6,18,19] and AWIATOR [2,17] fo-cus on a variety of means for wake vortex alleviation. Comple-mentary studies have been carried out within national researchprograms performed by DLR and ONERA [6,7,20]. Strategiesto minimise the wake vortex hazard concentrate either on aQuickly Decaying Vortex (QDV) or on a Low Vorticity Vor-tex (LVV) design [16]. An enhanced vortex decay (QDV) maybe achieved by promoting 3D instabilities by means of active orpassive devices. An active system tested by Boeing uses period-ically oscillating control surfaces to introduce the desired per-turbations leading, after sufficient amplification, to the break-upof the vortices into vortex rings [9]. Also, periodic oscillationsof Gurney flaps are investigated to perturb vortex centroids [33].Such perturbations may result in the excitation of wake in-stabilities. A further active concept to accelerate wake vortexdecay by excitation of wake instabilities has been tested on ageneric wing with oscillating winglet flaps in water tank exper-iments [22]. The LVV design reduces the wake vortex hazardby enhancing the diffusion of the vorticity field. It is aimed atgenerating wake vortices with larger core size and smaller swirlvelocities at the core radius after roll-up is completed. This maybe achieved by injecting additional turbulence into the waketo increase the dispersion of vorticity by the use of spoilers orwing fins. Specific spoilers of delta-type planform have beentested on a detailed wind tunnel model of a large transport air-craft resulting in a reduction of the axial peak vorticity of about50% at a position of six span dimensions downstream [1,2].The effect of wing fins on the maximum induced rolling mo-ment for a following aircraft has been studied for example on

a generic configuration achieving an alleviation of nearly 40%in the near field [29]. An alternative mean may be the produc-tion of multiple vortex systems by segmented trailing-edge flaps[7] or differential flap setting [1,6,29] altering the circulationdistribution of the wake generating wing. These measures in-troduce additional highly concentrated vortices in the near fieldshed at adjacent flap side edges at different deflection angles.The presence of these vortices enhances the turbulent mergingprocess of the final rolled-up vortex which may also lead toa larger core size and reduced swirl velocities, thus reducingthe induced rolling moment experienced by a follower aircraft.In addition, extensive numerical investigations are performedon all stages of wake vortex development from evolution upto decay [31,32]. Vortex filament and, much more costly, largeeddy and direct numerical simulations are used to simulate themid and far field development of the aircraft rolled-up vortexpair concentrating on instabilities and unsteadiness [20,21,24].Also, interaction mechanisms of multiple-vortex systems areanalysed as a mean of wake vortex alleviation.

With respect to 3D perturbations vortex systems are gen-erally unstable. The related mechanisms are summarised inRefs. [4,10,12,13]. Instabilities are caused by the amplifica-tion of asymmetric Kelvin waves under mutual straining ofthe vortices. If the separation between the vortices is large incomparison to their diameter, a system of stability equationscan be derived by considering parallel vortex filaments withslight sinusoidal perturbations of their respective position. Theequations of this linear system are given by Crow [10] fortwo counter-rotating vortices and by Crouch [8] and Fabre andJacquin [14] and Fabre, Jacquin and Loof [15] for multiple vor-tex pairs. The system evolves due to the superposition of threeeffects: i) the straining experienced by each filament when dis-placed by a perturbation from its mean position in the velocityfield induced by the other undisturbed filaments, ii) the selfinduced rotation of the disturbed filament and iii) the veloc-ity field induced on the filament by the other vortices whenperturbed from their mean positions [10,15]. The mechanismwhich strains the vortex due to the displacement from its meanposition in the velocity field by a perturbation induced by theother vortex filaments leads (mechanism i) to an amplificationof the asymmetric Kelvin waves in case their polarisation planesremain close to the extension planes of the straining field. Thismechanism is balanced with the self induced rotation (mecha-nism ii) which tends to shift the perturbation away from theseplanes. The frequency of this self induced oscillation is the fre-quency of the oscillation mode of the Kelvin displacement wave[14]. This mechanism introduces a dependence of the solutionwith respect to a measure of the diameter of the vortex core.Long wave co-operative instabilities are of prime importancefor applications to aircraft hazard alleviation as the dispersionof a vortex wake might be accelerated by means of this mecha-nism.

116 A. Allen, C. Breitsamter / Aerospace Science and Technology 13 (2009) 114–129

Nomenclature

AR aspect ratiob spanb0 lateral distance of main vortex pairb̃0 distance between the two adjacent vortices of a four

vortex systembM distance between two main vorticesc chord lengthCL lift coefficientf frequencyF wing reference areak reduced frequencyrc vortex core radiusRb span ratioRΓ circulation ratioRec Reynolds number based on the wing chord lengthSN

u′ non-dimensional power spectral density of u′

SNc,v′ non-dimensional cross spectral density of v′

Tux , Tuy , Tuz axial, lateral and vertical turbulence intensi-ties

u, v, w axial, lateral and vertical velocitiesu, v, w mean axial, lateral and vertical velocitiesu′, v′, w′ fluctuation part of u, v and w

U∞ free stream velocityx, y, z coordinates in x-, y- and z-directionx∗, y∗, z∗ non-dimensional coordinates in x-, y- and z-

directionα angle of attackηHTP horizontal tail plane settingΓ circulationλ wavelengthτ ∗ non-dimensional timeξ non-dimensional axial vorticity

Subscripts

dom dominantHTP horizontal tail planeW wing

Especially the stability properties of a vortex configurationcomposed of two counter-rotating vortex pairs have been con-sidered. The vortex pairs can be co-rotating (Γ1 > 0, Γ2 > 0)or counter-rotating (Γ1 > 0, Γ2 < 0) [12]. In the wake of anaircraft, the outer vortex pair is produced at the wing tips orouter flap edges and the inner one e.g. by the inner flap edgesor the horizontal tail plane. The linear stability method de-scribed above can be applied, whereby the solution dependson RΓ = Γ2/Γ1 and Rb = b2/b1. Without inner vortices theclassical Crow instability develops on the outer vortex pair.Adding the second vortex pair leads to much higher ampli-fications as shown by Fabre and Jacquin, Refs. [12,13]. Theinitially introduced small perturbation has been amplified bynearly a factor of 6000 after one revolution of the inner vor-tices around the outer vortex pair. This amplification must becompared to the value of 2.2 obtained for the Crow instabil-ity without the inner vortex pair [14,15]. Several experimentalinvestigations on co-rotating [5,11,13,23] and counter-rotating[4,13,25,26,28,30] four vortex systems have been performed inwater towing tanks. These investigations confirm that this typeof perturbation is very effective within a four vortex wake. Dueto the use of towing tanks the focus is clearly on a representa-tion of the spatial wake development by dye visualisation andmeasurements of the vorticity field by the use of Particle ImageVelocimetry (PIV). But time dependent quantities like turbu-lence data as well as spectral data are usually not available.Various models have been used including the one applied forthis investigation, resulting in a broad variety of the circulationratio RΓ and the span ratio Rb .

The focus of the present study is on wind tunnel inves-tigations of this type of vortex wake analysing in particulartime dependent quantities such as turbulence intensities andpower spectral densities for a specific circulation and span ratio.

Thus, the analysis of these data provide additional informa-tion to the existing data base on the characterisation of a fourvortex system consisting of counter-rotating neighboured vor-tices.

2. Experimental set-up

2.1. Model

The wind tunnel model used is the DLR F13 model, whichis a full model depicted in Fig. 1a [30,32]. It consists of acambered wing (bW = 0.3 m; cW = 0.05 m; FW = 0.015 m2;ARW = 6.0), which has a fixed angle of attack of α = 10◦and a horizontal tail plane (bHTP = 0.09 m; cHTP = 0.035 m;FHTP = 0.00315 m2; ARHTP = 2.57), which is inclined at −4◦.The ratio of the spans of the horizontal tail plane and the wingis Rb = 0.3. The ratio of the circulation of the two trailing vor-tex pairs emanating from the horizontal tail plane and the wingis set to RΓ = −0.3 to meet the requirements for optimal per-turbations developing on the main vortex pair based on linearstability analysis [13–15]. The flow field behind the model iscarefully investigated at a Reynolds number of Rec = 8 × 104.As the main focus is on the generation of a four vortex systemof a certain circulation ratio, the presence of a separation bub-ble of approx. 20% chord length on the wing at α = 10◦ hasbeen tolerated, Fig. 1b.

The coordinate system for the model is a right-hand systemwith x in free stream direction, y in span wise direction to theright and z in vertical direction upward with x∗ = 0 being at thewing trailing edge. The results are plotted in non-dimensionalcoordinates x∗ = x/b, y∗ = 2y/b and z∗ = 2z/b.


2.2. Wind tunnel

The wind tunnel facility C of the Institute of Aerodynamicsof the Technische Universität München has a closed test sec-tion of 21 m × 2.7 m × 1.8 m (length × width × height) asshown in Fig. 2. Maximum usable velocity is 30 m/s at a turbu-lence level less than 0.5%. The length of the tunnel test sectionallows an investigation of the wake vortex system at several

a)

b)

Fig. 1. a) The DLR F13 model in wind tunnel facility C at TUM-AER, b) oilflow visualisation for α = 10◦ indicating a laminar separation bubble.

cross-flow planes up to 48 span dimensions downstream of themodel.

2.3. Hot-wire anemometry

The time dependent velocity data gathered by hot-wireanemometry using a triple sensor probe is used to calculate themean velocity and the vorticity as well as to perform an anal-ysis of the turbulent flow field and a spectral analysis [1]. Theamplification of instability mechanisms of a four vortex sys-tem with counter-rotating outboard and inboard vortices willbe shown [13,32]. The hot wire probe operated by a multi-channel constant temperature anemometer system is positioneddownstream of the model. The tungsten wires of the probeare platinum plated and have a diameter of 5 µm and a lengthof approximately 1.25 mm. Measurements are performed at asampling rate of fM = 3000 Hz (Nyquist frequency 1500 Hz)for 6.4 s. The sampling time corresponds to 19 200 values perwire and survey point. The voltages of the hot-wire anemometerare low-pass filtered at 1000 Hz and digitised with 16 bit pre-cision. The anemometer output signals are converted into timedependent velocity components u, v and w using a look-up ta-ble previously obtained from the velocity and angle dependentcalibration of the hot-wire probe. Thus, the range of fluctuatingvelocity and flow angle is fully covered by the calibration/look-up table data. Based on statistical error evaluation, accuraciesare in the range of 1% for mean quantities, 2.5% for rms quan-tities (turbulence intensities), and 4% for spectral densities [3].

2.4. Test conditions and data reduction

The free stream velocity U∞ is 25 m/s which corresponds toa Reynolds number of approx. 8 × 104 based on the wing chordlength. The velocity data is then used to calculate the vorticityand the turbulence intensities using the equations stated below.The symbol ξ denotes the non-dimensional axial vorticity and

Fig. 2. The wind tunnel facility C at TUM-AER.


Fig. 3. Circulation ratio RΓ over HTP deflection ηHTP .

Tuz the root mean square value of the vertical velocity fluctua-tions normalised with the free stream velocity.

ξ = b/2

U∞

(∂w

∂y− ∂v

∂z

)(1)

Tuz =√

w′2U∞

(2)

Power spectral density distributions of the axial and lateralvelocity fluctuations are evaluated to detect spectral peaks asso-ciated with inherent instability mechanisms. The spectral densi-ties are calculated using a Fast Fourier Transformation (FFT) ofthe velocity fluctuation time series with a linear band averagingbased on nf = 1024 frequency bands. SN

u′ denotes the powerspectral density of u′ normalised with the free stream velocity,the variance of u′ and the wing span.

SNu′ = Su′

kU∞u′2(b/2)

; k = fM

2nf

(b/2)

U∞(3)

The cross spectral density of the lateral velocity fluctuationsis normalised in the same way.

3. Results and discussion

3.1. Force measurements

The force measurements have been conducted using a sixcomponent balance in order to determine the circulation ratio.Fig. 3 shows the curves for the circulation ratio of wing and tailplane RΓ , calculated according to Eq. (4), as function of thehorizontal tail plane setting ηHTP for three Reynolds numbers.Eq. (4) was derived using the Kutta–Joukowski equation. Theforce measurements have been conducted for the entire modeland for the wing–fuselage configuration itself, which, under theassumption that the influence of the horizontal tail plane on thewing is small, results in the needed lift coefficients given byEq. (4).

a)

b)

Fig. 4. Contour plots of non-dimensional axial vorticity ξ and turbulence inten-sity Tuz at x∗ = 1.0; Rec = 8 × 104; a) ξ ; solid lines: positive values, dashedlines: negative values; −25 � ξ � 35; ξ = 1, b) Tuz; 0.02 � Tuz � 0.1;Tuz = 0.005.

RΓ = ΓHTP

ΓW

= CL,HTP

CL,W

FHTP

FW

=(

FHTP

CL,WFW

)(CL0,HTP + dCL,HTP

dηHTPηHTP

)(4)

The required circulation ratio RΓ = −0.3 is reached forηHTP = −4.0◦ as shown in Fig. 3. The corresponding aero-dynamic coefficients for Rec = 8 × 104 are CL = 1.04 (entiremodel), CL,W = 1.48, CL0,HTP = −2.12 and dCL,HTP/dηHTP

= 0.507. The value of the circulation ratio has also beenproven by integrating the corresponding induced velocityfields.


a) b)

c) d)

Fig. 5. Contour plots of non-dimensional axial vorticity and turbulence quantities at x∗ = 12.0; Rec = 8×104; a) ξ ; solid lines: positive values, dashed lines: negativevalues; −1 � ξ � 8; ξ = 0.25, b) Tux ; 0.02 � Tux � 0.1; Tux = 0.005, c) Tuy ; 0.02 � Tuy � 0.1; Tuy = 0.005, d) Tuz; 0.02 � Tuz � 0.1; Tuz = 0.005,e) u′v′/U2∞; −0.004 � u′v′/U2∞ � 0.004; u′v′/U2∞ = 0.0004, f) u′w′/U2∞; −0.004 � u′w′/U2∞ � 0.004; u′w′/U2∞ = 0.0004, g) v′w′/U2∞; −0.004 �v′w′/U2∞ � 0.004; v′w′/U2∞ = 0.0004.

The flow field measurements have only been performed atthe lowest Reynolds number Rec = 8 × 104.

3.2. Flow field measurements

The flow fields have been investigated at discrete planes per-pendicular to the free stream flow direction at x∗ = x/b =1.0,4.0,8.0,12.0,16.0,20.0,24.0,36.0 and 48.0. Only fourof these planes (x∗ = 1.0,12.0,24.0,48.0) will be discussedin detail. The downstream stations are marked by the non-dimensional distance x∗ and the characteristic time τ ∗. The

latter number is based on an elliptical lift distribution takinginto account aspect ratio and lift coefficient as stated in Eq. (5).

τ ∗ = x∗16CL

π4AR(5)

For the cross-flow plane at station x∗ = 1.0, contour plots ofnon-dimensional axial vorticity ξ and vertical turbulence inten-sity Tuz are presented. Regarding stations x∗ = 12.0, 24.0 and48.0, contour plots of the axial and lateral turbulence intensi-ties, Tux and Tuy , and of the Reynolds shear stress componentsu′v′/U2 , u′w′/U2 and v′w′/U2 are added.
∞ ∞ ∞


e) f)

g)

Fig. 5. Continued.

Fig. 4 includes the field distributions of ξ and Tuz forx∗ = 1.0 (τ ∗ = 0.029). Note, that vorticity levels between −1and +1 are blanked in Fig. 4a. The wing (tip) vortex WTV isclearly visible at (y∗; z∗)WTV = (0.977;−0.100) being the vor-tex with the highest peak vorticity (33.5) and rotating counter-clockwise. At (y∗; z∗)HTV = (0.270;−0.035) the horizontaltail plane (tip) vortex HTV is visible rotating clockwise witha peak vorticity of (−21.1). The relatively small difference inthe peak values is due to the position of the measuring planebeing only 0.22b downstream of the HTP trailing edge, butone span downstream of the wing trailing edge. At the top leftof the HTV the vortex sheet of the HTP can still be detectedas it is not yet fully rolled up into the HTV. At the left up-per edge of the measurement plane two weaker vortices can be

seen at (y∗; z∗) = (0.066;0.200) and (y∗; z∗) = (0.014;0.021)

turning clockwise and counter-clockwise, respectively. Thesevortices are caused by the change in circulation through thefuselage interacting with the lifting surfaces, i.e. with the wingand the HTP. The drop in circulation in the fuselage area of alifting surface creates a counter-rotating vortex in comparisonto the tip vortex of the lifting surface. The position of the lowerof the two weak vortices in comparison to the remainder of theshear layer of the HTP and the direction of rotation indicate thatthis vortex is caused by the HTP, whereas the upper one is thenassigned to the wing–fuselage interaction.

Fig. 4b displays the turbulence distribution of the verticalvelocity fluctuations for this measuring plane. Note, that valuesbelow 0.02 are blanked for all turbulence intensity plots for all


a) b)

c) d)

Fig. 6. Contour plots of non-dimensional axial vorticity and turbulence quantities at x∗ = 24.0; Rec = 8 × 104; a) ξ ; solid lines: positive values, dashed lines:negative values; −0.2 � ξ � 2.5; ξ = 0.1, b) Tux ; 0.02 � Tux � 0.1; Tux = 0.005, c) Tuy ; 0.02 � Tuy � 0.1; Tuy = 0.005, d) Tuz; 0.02 � Tuz � 0.1;Tuz = 0.005, e) u′v′/U2∞; −0.001 � u′v′/U2∞ � 0.001; u′v′/U2∞ = 0.0001, f) u′w′/U2∞; −0.001 � u′w′/U2∞ � 0.001; u′w′/U2∞ = 0.0001, g) v′w′/U2∞;−0.001 � v′w′/U2∞ � 0.001; v′w′/U2∞ = 0.0001.

measuring positions. High turbulence intensities can be found atthe vortex core positions and the shear layer emanating from thewing can be seen at the lower part of the measuring plane. Theroll up of the shear layer into the WTV is almost complete asthere is only little contact between the turbulence in the vortexand the shear layer.

The next measuring plane downstream is at x∗ = 12.0 (τ ∗ =0.342), the results of which are shown in Fig. 5. For the vortic-ity distribution, values between −0.25 and +0.25 are blanked.A clear vorticity peak of 7.7 can be found at (y∗; z∗)WTV =(1.06;−0.747) for the WTV. The peak vorticity for the HTV is

only −0.5 at (y∗; z∗)HTV = (0.293;−0.520). These positionsindicate a downward and outward movement of both vortices.The peak vorticity for the HTV is difficult to attribute as thearea of vorticity of this magnitude is quite large. Both vor-tices clearly show speckles at their boundaries, indicating thatvorticity is spread over a quite large spatial area. The turbu-lence intensities show increased values for the position of theWTV indicating much higher peak values (∼17%) for the lat-eral and vertical velocity fluctuations compared to the axialones (∼10%). The high lateral and vertical fluctuations corre-spond to the radial dispersion of the vorticity field due to the


e) f)

g)

Fig. 6. Continued.

strong mutual induction of the counter-rotating WTV and HTV.The turbulent shear stress patterns u′v′ and u′w′ reflects the lat-eral and vertical straining of the vortex. The WTV is furthermarked by a quadruple structure in the v′w′-pattern revealinga double pair of local shear stress maxima of opposite sign.These pairs are characterised by an angular shift of about 90◦corresponding to the change in direction of the mean cross flowvelocities.

Fig. 6 illustrates the results obtained at x∗ = 24.0(τ ∗ = 0.683). The WTV can still be seen at (y∗; z∗)WTV =(1.17;−1.290) with a vorticity peak of 2.53. This mean po-sition indicates a continuing downward and outward motionof the WTV. The main vortex clearly shows a very large spa-tial area of vorticity spots. Due to a strong interaction between

main (outer) vortex (WTV) and secondary (inner) vortex (HTV)vorticity of the main vortex is radially spread out decreas-ing strongly the peak vorticity level. Thus, the vortex inducedvelocities are also markedly reduced which results in a signifi-cantly lower induced rolling moment on a follower aircraft. Atthis downstream measuring position the location of the HTVcould not be determined, as the mean vorticity drops so low,that a clear peak is not determinable. This is caused by theHTV starting a strong lateral sinusoidal displacement, whichis not visible as such due to time averaging of the axial vor-ticity. The higher turbulence levels are confined to the WTV,which have slightly decreased. The bending and expansion ofthe WTV is highlighted by the turbulent shear stress patterns.Especially, the WTV core area increases because the interaction


a) b)

c) d)

Fig. 7. Contour plots of non-dimensional axial vorticity and turbulence quantities at x∗ = 48.0; Rec = 8 × 104; a) ξ ; solid lines: positive values, dashed lines:negative values; −0.1 � ξ � 0.5; ξ = 0.05, b) Tux ; 0.02 � Tux � 0.1; Tux = 0.005, c) Tuy ; 0.02 � Tuy � 0.1; Tuy = 0.005, d) Tuz; 0.02 � Tuz � 0.1;Tuz = 0.005, e) u′v′/U2∞; −10−4 � u′v′/U2∞ � 10−4; u′v′/U2∞ = 10−5, f) u′w′/U2∞; −10−4 � u′w′/U2∞ � 10−4; u′w′/U2∞ = 10−5, g) v′w′/U2∞;−10−4 � v′w′/U2∞ � 10−4; v′w′/U2∞ = 10−5.

of the neighboured counter-rotating HTV stretches the WTVaccompanied by high fluctuation levels.

At x∗ = 48.0 (τ ∗ = 1.367) the position and rotational direc-tion of the WTV is also difficult to extract, Fig. 7. The HTV isnot visible in the vorticity distribution any more due to amplifi-cation of its displacement rolling around the WTV, whereas theWTV can be detected at (y∗; z∗)WTV = (1.35;−1.930) with apeak vorticity of 0.35 (values between −0.05 and +0.05 areblanked). The spatial area of distributed vorticity has nearlydoubled in comparison to x∗ = 24.0 while the peak vorticitylevel has decreased by approx. 90%. This vorticity distribu-

tion reflects the dissolution of the initially concentrated vor-tex to a region of vorticity spots with very low peak levels.The temporal–spatial development of such vorticity fields isanalysed for example by Ortega, Bristol and Savas based onPIV measurements performed in towing tank facilities for ageneric aircraft configuration [26]. For a similar problem, vor-ticity fields obtained by 3D LES computations are reported inRef. [32]. Turbulence fields have not been shown. Here, themaximum turbulence intensities have decreased to a level ofapprox. 3% in the region of the vortex core. The contour plotsof the turbulent shear stresses are adapted to local maximum


e) f)

g)

Fig. 7. Continued.

and minimum values for a better representation of the flowstructures. The corresponding turbulent flow patterns reveal thesignificant dissolution of the WTV core. Regions of local shearstress maxima surrounding the initial WTV core indicate arte-facts of the interaction between HTV and WTV. The 3D in-stability (see Section 1) developing between the neighbouredcounter-rotating vortices of unequal strength induces a sinu-soidal displacement of the HTV the amplitude of which growsrapidly when progressing downstream. A sinusoidal displace-ment of smaller amplitude develops also further downstreamon the WTV. These displacements along with the rotation of theHTV around the WTV lead finally to the stage where vorticityof opposite sign affects the WTV core region and transformsthe latter to a large spatial area of low vorticity levels.

Summarising, the vorticity distribution of the overall flowfield is illustrated in Fig. 8b depicting all measured cross flowplanes. The increase in diameter of the vortical areas and thedecay of the WTV and HTV can clearly be seen. In addition,Fig. 8a shows a smoke visualisation of the downstream devel-opment of the main vortex WTV and the effect of the HTVindicated by radial areas of smoke traces. A schematic repre-sentation further illustrates the downstream motions of WTVand HTV emphasising the instability development and indicat-ing also the wavelength of approximately 2.5π with respect tothe lateral distance of the free circulation centroid b̃0 (Eq. (6)).

Fig. 9 illustrates the development of the axial peak vorticityvalue ξmax of the WTV over the downstream distance x∗ and di-mensionless time τ ∗. Between τ ∗ = 0.05 and τ ∗ = 0.5 there isa rapid decrease in the peak vorticity level with a reduction by


a)

b) c)

Fig. 8. Flow field development at Rec = 8 × 104; a) Smoke visualisation, b) non-dimensional axial vorticity ξ , c) schematic representation.

an order of magnitude. In this time period the instability mech-anism due to the mutual induction of the neighboured counter-rotating vortices is fully developed leading to a rapid distortionof the main vortex. After τ ∗ = 0.5 there is a further reductionof peak vorticity showing again an alleviation by nearly a fac-tor of 10. A logarithmic scaling for the ξ -axis demonstrates anapproximately linear trend in the reduction of the peak vorticitylevel with a gradient of d(log ξ)/dτ ∗ = −1.48.

A significant decay in the WTV maximum vertical velocitywmax/U∞, measured at the vortex core radius rc , is shown inFig. 10. The induced vertical velocity is directly linked to theinduced rolling moment acting on a follower aircraft. Hence, adecrease in velocity w implicates a reduction in the inducedrolling moment. The vortex induced velocity is reduced byapproximately 80% between τ ∗ = 0.05 and τ ∗ = 0.5. Loga-rithmic scaling indicates two ranges of the alleviation in verti-

cal velocity; for τ ∗ � 0.5 there is a non-linear part associatedwith the strong interference between the WTV and HTV; forτ ∗ > 0.5 there is a linear part where the vertical velocity is de-creased due to the strong dispersion of the WTV vorticity field.

In addition, Fig. 11 includes the relative circulation ΓWTV/

Γ0,WTV attributed to the main vortex as function of the down-stream distance reflecting the trend of significant wake vortexdecay in presence of the developed instability mechanism.

Fig. 12 depicts the track of the mean position of the vortexcenters in the y∗–z∗-plane. As stated above the WTV movesdownward and outward continuously whereas the HTV movesinward and then outward while the downward velocity of theWTV decreases as it moves downstream. The data for the HTVis only included up to x∗ = 20.0 because further downstreamthe lateral and vertical displacement starts which is linked tothe instability mechanism.


Fig. 9. Axial peak vorticity ξmax for the Wing Tip Vortex as function of down-stream distance at Rec = 8 × 104.

Fig. 10. Maximum mean vertical velocity wmax/U∞ as function of down-stream distance at Rec = 8 × 104.

3.3. Spectral analysis

In order to judge the instabilities developing in the vortexsystem, characteristic spectral peaks are searched indicatingthat turbulent kinetic energy is channelled into a narrow banddue to quasi-periodic fluctuations. An overview is given belowhow the frequency content and related energy overshoots areevaluated with respect to the most dominant instability mecha-nisms.

3.3.1. Power spectral densitiesThe presence of instability mechanisms propagating along

the wake vortex in stream wise direction can lead to a relevantdistortion of the vortex, accelerating its dispersion and decay.Usually, long, medium and short wave instabilities occur. The

Fig. 11. Relative circulation ΓWTV/Γ0,WTV as function of downstream distanceat Rec = 8 × 104.

Fig. 12. Trajectories of mean positions of the vortices WTV and HTV in they∗–z∗-plane at Rec = 8 × 104.

most significant long wave instability for a counter-rotating vor-tex pair is the Crow instability [10]. This instability is related tothe strain effect induced by one vortex of a pair on the otherone, and appears as a sinusoidal displacement of the vortex tra-jectories. The displacement amplitude grows exponentially intime but the amplification factor is low. This kind of instabilityis ultimately responsible for the wake vortex collapse in the farfield. Regarding two vortex pairs Crouch observed an instabil-ity mechanism with both symmetric and asymmetric modes, thewavelengths of which are shorter than those of the Crow insta-bility, but large with respect to the effective vortex core size [8].


a) b)

c) d)

Fig. 13. Normalised power spectral densities of the axial velocity fluctuations at Rec = 8 × 104; a) x∗ = 1.0, b) x∗ = 12.0 c) x∗ = 24.0, d) x∗ = 48.0.

A Crouch type instability may enhance wake vortex dispersionwithin x/b ≈ 30.

Wavelengths of Crow and Crouch type instabilities areλCrow ≈ 8b0 and λCrouch ≈ 1.5b̃0–6.0b̃0, respectively.

In this case two counter-rotating vortex pairs are investi-gated. The lateral center of the free circulation is positionedaccording to Eq. (6), giving b̃0 = 1.3bM , with bM being the ini-tial distance of the main vortices, for the investigated case.

b̃0 = bM

(1 + RbRΓ

1 + RΓ

)(6)

The typical wavelength for the dominant long wave insta-bility in a counter-rotating vortex pair is given in Eq. (7) [1].Calculating the reduced frequency this leads to Eq. (8) with bM

approx. equal to the wing span bW , see Fig. 12 (fully developedWTV: y∗ ∼= 1 for x∗ ∼= 4).

λ4V S−b̃0

∼= 2.5π (7)

kdom = fdom(bW/2)

U∞= bW

2λ= 1

5π

bW

b̃0= 0.049 (8)

Fig. 13 illustrates typical power spectral density distribu-tions for the HTV and WTV at the measuring positions x∗ =1.0,12.0,24.0 and 48.0. Clearly, distinct peaks are visiblearound the calculated dominant reduced frequency of kdom =0.049 indicating the existence of such quasi-periodic fluctua-tions.


a)

b)

Fig. 14. Cross spectral density distributions with one probe at x∗1 and the other

one at x∗2 at Rec = 8 × 104; a) for the WTV, b) for the HTV.

3.3.2. Cross-spectral densitiesTwo-point measurements have been performed using two

hot-wire probes each consisting of three wires. The first probeis at a fixed position x∗

1 within the WTV or HTV, whereas thesecond probe is traversed within the same vortex at a positionfurther downstream x∗

2 . The plots shown are cross spectral den-sity distributions of the span wise velocity fluctuations (v′) andhave been evaluated using the same parameters as for the powerspectral density distributions. The plots correlate the frequencycontent of both positions.

Fig. 14a shows the cross spectral density distributions forthe WTV. The vertical line depicts the calculated value for theexpected dominant reduced frequency at which distinct peaksshould appear. For the WTV a slight shift is noticeable, show-

Fig. 15. Cross spectral density distributions with both probes at x∗ = 12.0(WTV and HTV) at Rec = 8 × 104.

ing peaks at k ≈ 0.4 in all three cases and a significant peak atk ≈ 0.6 for the case x∗

1 = 12.0 and x∗2 = 24.0. Further, energy

peaks are also visible at higher harmonics of the dominant re-duced frequency. Finding the peaks also with the first probepositioned at x∗

1 = 12.0 indicates that the frequency is con-tained downstream within the vortices.

For the HTV the cross spectral density distributions are de-picted in Fig. 14b. Note that the spectral density levels for theHTV are significantly reduced in magnitude in comparison tothe WTV. The peaks found match the predicted value very well.

Fig. 15 depicts the spectral results obtained with one probebeing within the HTV at x∗ = 12.0 and the other one being tra-versed within the WTV at x∗ = 12.0. At kdom ≈ 0.049 a clearpeak can be detected substantiating that this frequency is dom-inant at both measuring positions. Another peak is visible atk ≈ 2 · kdom, illustrating the higher harmonic.

4. Conclusions and outlook

A thorough experimental investigation using the DLR F13model creating a four-vortex system with counter-rotatingneighboured vortices has been conducted. The circulation ratioof tail plane and wing vortices was set to −0.3 proven by forcemeasurements. The span ratio of tail plane and wing is 0.3. Thiscombination of circulation and span ratio is chosen to create astrong interaction between tail plane and wing vortices resultingin an optimal amplification of the long wave instabilities devel-oping on the wing vortices. The flow fields observed by meansof hot-wire anemometry show the wake vortex developmentup to 48 span dimensions downstream. From the extended nearfield to the far field the concentrated wing vortex transforms to avortical structure with a large region of radially distributed vor-ticity. This structure becomes dominant downstream of 20 spandimensions further expanding strongly in its radial range. Con-sequently, a rapid decay in axial vorticity is observed for the


wing vortex with a gradient d(log ξ)/dτ ∗ = −1.48. Hence, thepeak vorticity level as well as the swirl velocity is reduced byone order of magnitude within 30 span dimensions. The meanmovement of the two counter-rotating vortices during this de-cay is mainly downward and outward. Spectral analysis of thetime dependent velocities obtained from the hot-wire tests hasbeen carried out. The developing instabilities are attributed tocharacteristic spectral density peaks. These peaks have beenfound at a frequency range matching the one predicted by linearstability analysis. The dominant reduced frequency is approx.kdom = (1/5π)(bW/b̃0) with bW as wing span and b̃0 as thedistance between the main vortices centroids. Correspondingfindings can be taken from the cross spectral density results ob-tained by correlation measurements using two hot-wire probes.

The wind tunnel results will be compared with data obtainedin a towing tank test planned by DLR. Thus, hot-wire results,i.e. turbulence and spectral quantities will be linked with PIVresults informing in detail about the spatial wake vortex struc-ture.

Acknowledgements

The support of this investigation within the Specific TargetedResearch Project “FAR-Wake” of the Sixth Framework Pro-gramme of the European Union under Contract No. AST4-CT-2005-012238 is gratefully acknowledged. The authors wouldlike to thank the DLR for providing the wind tunnel modelsand especially Dr. Robert Konrath, Carl F.v. Carmer and GuidoVoss (DLR-AS Göttingen/Braunschweig) for their kind assis-tance and support.

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counter trailing vortices

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