SIMULATION OF AIRCRAFT WAKE VORTICES DURINGLANDING WITH DECAY ENHANCING OBSTACLES

A. Stephan∗ , F. Holzapfel∗ , T. Misaka∗∗∗Deutsches Zentrum fur Luft- und Raumfahrt (DLR), Institut fur Physik der

Atmosphare∗∗Tohoku University, Institute of Fluid Science

Keywords: Wake vortex, RANS-LES coupling, Plate line, Landing, Turbulence

Abstract

Wake-vortex evolution during landing of a longrange aircraft is investigated in a turbulent en-vironment. The simulations cover final ap-proach, touchdown on the tarmac, and theevolution of the wake after touchdown. Anambient turbulent crosswind and headwindfield is generated in a pre-simulation. Thewake is initialized using a RANS-LES couplingapproach. The aircraft in high-lift configu-ration with deployed flaps and slats is sweptthrough a ground fixed domain. The fuselageturbulence is modeled as white noise. The fur-ther development of the vortical wake is in-vestigated by large-eddy simulation until finaldecay. After touchdown wake vortices are sub-jected to strong three-dimensional deforma-tions and linkings with the ground. The down-wind vortex is strongly advected with the windand decays quickly. End effects, appear aftertouchdown and propagate along the wake vor-tices against the flight direction. They lead toa non-uniform circulation decay of the rolled-up wake vortices. Additionally the effect of aplate line installed in front of the runway isstudied with this method. The plates causedisturbances of the vortices propagating to ei-ther side and interacting with the end effects.The plate line further accelerates the vortexdecay.

1 Introduction

As an unavoidable consequence of lift, aircraftgenerate a pair of counter-rotating and long-lived wake vortices that pose a potential risk tofollowing aircraft, due to strong coherent flowstructures [1]. The probability of encounter-ing wake vortices increases significantly dur-ing final approach in ground proximity, sincerebounding vortices may not leave the flightcorridor vertically and the possibility of the pi-lot to counteract the imposed rolling momentis restricted [2, 3]. In the recent “Challenges ofgrowth 2013” report [4] the conceivable capac-ity problems of airports are elucidated. Sev-eral economic scenarios for the future Euro-pean airport demands are analyzed, realizingthat there will be around 1.9 million unaccom-modated flights in the most-likely case, consti-tuting approximately 12% of the demand in2035. A reduction of the established staticaircraft separation distances appears feasibleemploying advanced wake-vortex advisory sys-tems (WVAS) incorporating the state-of-the-art wake-vortex physics to accurately predictvortex strength and position [5], depending onthe environmental conditions. Therefore thephysical mechanisms of wake-vortex evolutionand decay during and after landing have to beunderstood.

Aircraft landing and the evolution of thewake in its meteorological environment is anexample of complex turbulent flows, composedof strong coherent flow structures that exhibit

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A. STEPHAN ET AL.

a range of length scales spanning several ordersof magnitude all interacting with one another.The flow around an aircraft’s main wing, fuse-lage, slat, flap, jet engine and tail plain, aswell as the interaction with the approachingground and the sudden lift reduction duringtouchdown substantially affect the generatedwake vortices. Usually Reynolds-averagedNavier-Stokes (RANS) simulations are usedfor the flow around the aircraft and the subse-quent roll-up process of the wake in the roll-upphase [6]. The dynamics of rolled-up wake vor-tices in ground proximity subjected to a turbu-lent wind have been mainly studied by large-eddy simulations (LES) [7]. This approach ne-glects the effects of different vortex generationheights above ground and of touchdown andmay not capture full three-dimensional vortexdeformations appearing during landing.

It is well known that when the vortex pairdescends it induces a vorticity layer at theground. An adverse pressure gradient buildsup in the boundary layer while the primaryvortices are diverging. The boundary layer fi-nally rolls up into secondary vortices and sepa-rates [19]. From numerical simulations, as wellas field measurement campaigns [3] we observea minimum descent height of about b0/2, (as-suming the vortices are initialized sufficientlyaloft), at the instant when secondary vorticesdetach from the ground.

The methodology of RANS-LES couplingenable an innovative methodology to fly a re-alistic aircraft through a simulation domaingenerating a realistic wake [8]. For this pur-pose, a high-fidelity steady RANS flow fieldis swept through the LES domain. So a spa-tial development of the aircraft wake is intro-duced in the LES. We use this approach tosimulate the final approach and landing andstudy the physics of the wake-vortex evolu-tion and decay. A high-lift configuration ofa long range aircraft is employed to accountfor the landing and flare phase. Note thatthis approach can be viewed as a one way cou-pling. The changing environment, i.e. the ap-proach of the ground is not reflected by theRANS field. This work continuous the investi-

gation in [9] including the effect of turbulence- ambient turbulence as well as fuselage turbu-lence. We deduce the fully three-dimensionalvortex characteristics in a turbulent environ-ment. The current study reveals that the sim-plified modeling fails to reproduce many char-acteristic flow features.

In accordance with flight practice1 we char-acterize the evolution of the aircraft’s wakeduring landing by four main phases, Final ap-proach, Flare, Touchdown and Roll-out. Com-plex vortex deformations in ground proxim-ity like vortex linking with the ground havebeen observed [7]. However, the effect of thesestructures encountered by following aircraft isnot clear. We study so called end effects, ap-pearing after touchdown, when vortex circula-tion is drastically reduced, as a reason that air-craft landings are safer than expected. Addi-tionally, the interaction of end effects and dis-turbances caused by plate lines [10] - a methodfor artificial vortex decay enhancement - isinvestigated with the present approach. Inthe meanwhile first results of flight measure-ment campaigns at Oberpfaffenhofen airportas well as Munich airport (Germany) confirm-ing plate line effects as well as landing effectshave been presented in [11], complementingthe findings in this numerical study. Resultsfrom six simulations are included in this paper,non-turbulent, crosswind and headwind simu-lations, each performed with and without theinfluence of a plate line.

2 Methods

2.1 Governing equations

The LES is performed using the incompress-ible Navier-Stokes codeMGLET, developed at Technische UniversitatMunchen, for solving the Navier-Stokes equa-

1http://www.skybrary.aero/index.php/Land

ing_Flare?utm_source=SKYbrary&utm_campaign=

47ff8e1e92-SKYbrary_Highlight_04_07_2013&

utm_medium=email&utm_term=0_e405169b04-47ff8

e1e92-264071565 date: June 30, 2014

2

SIMULATION OF AIRCRAFT WAKE VORTICES DURING LANDING

tions and the continuity equation [12]

∂ui∂t +

∂(uiu j)∂x j

=− 1ρ

∂p′∂xi

+ ∂

∂x j

((ν + νt)2Si j

)(1)

∂u j∂x j

= 0 .(2)

Here ui represents the velocity components inthree spatial directions (i = 1,2, or 3), Si j =(∂ui/∂x j + ∂u j/∂xi)/2 denotes the strain ratetensor, and p′ = p− p0 equals the pressure de-viation from the reference state p0. The kine-matic viscosity is given as the sum of molecularviscosity ν and eddy viscosity νt determined bymeans of a Lagrangian dynamic sub-grid scalemodel [13]. Equations (1) and (2) are solvedby a finite-volume approach, using a fourth-order finite-volume compact scheme [14]. Asplit-interface algorithm is used for the paral-lelization of the tri-diagonal system computingcoefficients of the compact scheme. A third-order Runge-Kutta method is used for timeintegration. The simulations are performedin parallel, using a domain decomposition ap-proach.

The concept of artificial wake vortex decayenhancement by plate lines is also pursued inthis work. A respective patent has been filedunder number DE 10 2011 010 147. Figure 1displays the arrangement of the plates in a lineperpendicular to the runway. The plate lineis characterized by the plate separation ∆y,the height h and the plate length. The plateline is modeled by introducing a drag forcesource term, −FD,i =−CD|u|ui, to Eq. (1) witha large drag coefficient at the plate. At theground surface of the LES domain we employthe Grotzbach-Schumann wall model that lo-cally computes the wall shear stress τw instan-taneously based on the logarithmic law [15].

2.2 Ambient turbulent wind field

In order to provide a realistic environment weestablish a turbulent wind in a separate sim-ulation. We simulate a turbulent half-channelflow with Reτ = 3455 applying a free-slip con-dition at the top of the domain.[16] Prescrib-ing initially a vertical wind profile following

∆yh

RUNWAY

Fig. 1 Schematic representation of a plateline. Thin plates with height h and separation∆y (from [9]).

Fig. 2 Mean velocity profile characterizingthe separately simulated turbulent wind.

the universal logarithmic law and imposing astream-wise pressure gradient of d p/dy = 1.2 ·10−4 N/m3, the wind flow is driven throughthe computational domain. We let the flowdevelop until characteristic wall streaks ap-pear and an equilibrium between the pres-sure gradient and the wall friction is estab-lished. The averaged wind profile 〈u+〉, seeFig. 2, converge to the typical half channel flowcharacteristics.[16] The time-averaged stream-wise velocity of the wind at b0 = π

4 b abovethe ground is w0 = 0.49m/s, where w0 is theinitial vortex descent speed. Let δ denotethe channel half height and consider the fol-lowing quantities as averaged in time. Forthe boundary layer approximation the Navier-Stokes equations yield the wall shear stressτw =−δ ·∂p/∂x, with constant pressure in wall-normal direction. The wall friction velocityis defined by uτ = (τw/ρ)1/2. This yields the

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A. STEPHAN ET AL.

LES

RANS

f(y,α,β)

y

Fig. 3 Schematic of a weighting function fora combination of RANS and LES flow fields(from [8]).

normalized values u+ = u/uτ, z+ = zuτ/ν andan intrinsic Reynolds number Reτ = uτδ/ν.The boundary layer of a turbulent flow hasnow three characteristic parts, the viscous sub-layer, the transition layer and the logarithmiclayer, see Fig. 2.

2.3 Wake initialization

We employ a wake initialization approachwhere a realistic aircraft wake is generated inan LES domain by sweeping a high-fidelitysteady RANS flow field through the domain,which enables the simulation of the wake-vortex evolution from generation until final de-cay [8]. The simulations are performed for along range aircraft model in high-lift configu-ration that has been used in ONERA’s cata-pult facility during the European AWIATORproject. The RANS flow field serves as a forc-ing term of the Navier-Stokes equations in theLES. This approach might be referred to as afortified solution algorithm [17]. The resultingvelocity field in the aircraft vicinity consists ofthe weighted sum

V = f (y)VLES +(1− f (y))VRANS (3)

of the LES and the RANS velocity field, seeFig 3, with a transition function

f (y,α,β) =12

[tanh

[α

(yβ− β

y

)]+ 1.0

]. (4)

Here α and β represent slope and wall-distance of the transition, chosen similar to thevalues in [8]. The mapping of the RANS flowfield from an unstructured, mesh refined grid

to the structured LES domain is performed bya linear interpolation conducted only once be-fore the wake initialization. First the steadyRANS solution is mapped to a Cartesian grid,a so-called frame, which is mapped to the LESgrid, shifted for every time step. As the framecan only be mapped at discrete grid positionsof the LES grid, a sinking glide path can notbe realized by one fixed frame. For a glidepath angle of 3.56 degree we employ 32 frames,prepared in advance. This requires additionalmemory, however, few additional computationtime is needed. This hybrid method enables tostudy the effect of an ambient turbulent cross-wind or headwind on the aircraft wake by ini-tializing the wake to a pre-simulated turbulentwind field.

2.4 Reproduction of turbulent fluctua-tions

From [18] and [10] it is evident that the trans-fer of turbulent fluctuation in the wake to theLES field is important for the simulation ofthe wake evolution. In this work we use theapproach of [8]. As the eddy viscosity is mod-eled in the RANS computation describes thesubgrid scale it cannot be reproduced by themapped velocity field. Hence, the modeledfluctuations have to be reproduced during themapping process.

In a straight forward approach the velocityfluctuations are modeled as white noise in theRANS-LES transition region, controlling themagnitude by the proportional-integral (PI)controller during the movement of the RANSfield through the LES domain.

VRANS+WN = VRANS + KVWN, (5)

K = a1(kt,LES− kt,RANS) (6)

+ a2

∫(kt,LES− kt,RANS)dt,(7)

where VWN denotes the white noise field andK controls the magnitude.The constants areset to a1 = 40 and a2 = 1.0 in the simulationsincluding turbulence.

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SIMULATION OF AIRCRAFT WAKE VORTICES DURING LANDING

2.5 Computational setting

We employ a RANS flow field obtained bythe DLR TAU-code from a steady compress-ible RANS simulation. An adaptive mesh re-finement for wing-tip and flap-tip vortices, aswell as the fuselage wake is employed. Theflow conditions of the RANS simulation arethe same as in ONERA’s catapult facility ex-periment, i.e. chord based Reynolds num-ber Re = 5.2× 105 (two orders of magnitudelower than the real aircraft flight), flight speedU∞ = 25m/s, and a lift coefficient of CL = 1.4.The 1/27 scaled model has a wingspan of2.236m. We normalize quantities with the ref-erence values for an elliptic load distribution[1], initial circulation, vortex spacing, vortexdescent velocity, characteristic time, vorticityunit,

Γ0 =2CLU∞b

πΛ, b0 =

π

4b, w0 =

Γ

2πb0, (8)

t0 =b0

w0, ω0 =

1t0, (9)

with a wing aspect ratio of Λ = 9.3. Theresulting reference values for the normaliza-tion are Γ0 = 5.36m2 /s for circulation, b0 =1.756m for length, w0 = 0.49m/s for velocity,and t0 = 3.617s for time. Normalized quanti-ties are expressed in units of the reference val-ues in Eq. (8) and are denoted by an asterisk.We set t = 0 at the instant of the touchdown.

2.6 Computational domain, approachand boundary treatment

The hybrid simulation approach and theswitch to pure LES (large arrow) is sketchedin Fig. 4. The first part of the simulationsincludes the hybrid RANS/LES wake initial-ization until touchdown, Fig. 4 (a). The sec-ond part is a pure LES of the evolution of theaircraft wake, Fig. 4 (b). We employ periodicboundary conditions in horizontal directions, ano-slip condition at the ground and a free-slipcondition at the top. The aircraft starts in theback part of the domain passes the boundaryand approaches the ground. Because of the pe-riodicity the aircraft is placed in front of the

domain in Fig. 4 (a). After touchdown the firstslice of the domain is extended into the backpart at the slope of the vortex and closed ar-tificially to a horse shoe vortex, see Fig. 4 (b).This procedure effectively avoids disturbancesgenerated at the starting point of vortex ini-tialization. Note that wake vortex linking dueto Crow instability is frequently observed incruise altitudes and may also occur in groundproximity. In the case of a crosswind the artifi-cial vortex closing is not applied, due to strongtilting of the vortices. Though the vorticesconnect after some time in the back part dis-turbances, so-called end effects appear.

When the landing gear touches the groundthe lift ceases quickly. Then the bound vor-tex, i.e. the circulation around the aircraftwings, and consequently the wake vortices arestrongly reduced. We model the touchdownjust by removing the RANS flow field forc-ing term from the simulation. In the LESwe employ uniform mesh spacing for all threespatial directions, with a resolution of dx∗ =dy∗ = dz∗ = 0.011. Different dimensions of thecomplete computational domain used for wakeinitialization and wake development, 23.3b0,5.6b0 to 11.6b0, and 2.2b0 in flight, spanwiseand vertical directions, respectively, depend-ing on the case, to capture the strong diver-gence of the vortices and the crosswind ad-vection. The back part of the domain witha length of 5b0 is used for aircraft startingand the subsequent reconnection of the vor-tex pair by a horseshoe vortex. The air-craft passes the domain boundary at a heightof 1.2b0. At touchdown the tail wing is atx∗ = 16.3 whereas the plate line is centered atx∗ = 5.1. The plates with lengths and heightsof 0.2b0× 0.1b0 are separated by 0.45b0, seeFig. 1. A maximum number of 400 millionnodes was employed in the calculations.

3 Results

3.1 General flow field

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A. STEPHAN ET AL.

(a) Wake initialization until touchdown. (b) LES, vortex decay after touchdown.

Fig. 4 Schematic of aircraft landing displaying the computational domain and the wake evolu-tion (a) before touchdown, during wake initialization, (b) after touchdown with artificial vortexreconnection (from [9]).

3.1.1 No ambient turbulence

With this novel method we simulated the com-plete landing phase of an aircraft includingfinal approach, flare, touchdown, and vortexdecay [9]. Figure 5 shows the roll-up processof the aircraft wake without the influence ofa wind. The tracer is initialized at certainvorticity levels, depicting the vortex structurebehind the aircraft. Wing-tip and flap-tip vor-tices as well as a vortex from the engine py-lon and from the wing fuselage junction re-main at the tail wing position, as strong co-herent structures. Wing-tip and flap-tip vor-tices merge in the mid-field constituting theso-called wake vortices. Figure 5 c) depictsthe instant of touchdown. Regions of high ve-locities (red color), particularly dangerous forfollowing aircraft, are around the vortex cores.After touchdown, Fig. 6, the vortices remainfreely in space for a short time. At this instantso-called end effects appear from the touch-down zone, propagating against flight direc-tion, weakening the wake vortex strength.

As vortices cannot end freely in space theytend to link with the ground. Multiple groundlinkings can be observed, Fig. 6 d). The intro-duction of a plate line at the ground surfacesubstantially accelerates vortex decay in thecritical area close to the threshold where mostvortex encounters occur, as shown in Fig. 6 c).

Fig. 7 Sketch of wake vortex flow with cross-wind.

The reddish fraction of the vortices, indicat-ing the potentially hazardous region, dissolvesquickly.

3.1.2 Crosswind effect

The crosswind situation applying a uniformvortex initialization technique is discussed in[10]. Crosswind induces vorticity at theground, which has opposite sign as the vor-ticity layer induced by the up-wind vortexand the same sign as the vorticity layer in-duced by the downwind vortex (Fig. 7). Sothe crosswind vorticity supports the formationof the downwind vorticity layer and attenu-ates the upwind vorticity layer. As a conse-quence vorticity layers generated by the wakevortices become unequally strong and the up-wind and downwind vortices behave asymmet-rically. The magnitudes of the wake-vortexinduced vorticity layers are growing leadingeventually to separation and the generation

6

SIMULATION OF AIRCRAFT WAKE VORTICES DURING LANDING

a) b)

c) d)

Fig. 5 Tracer Animation with Autodesk - 3d Studio MAX, (Gregor Hochleitner, Thomas Ruppert,DLR). Tracer initialized at high vorticity levels, velocity color coded. a) final approach, b) flare,c) touchdown, and d) vortex decay with end effects.

a) b)

c) d)

Fig. 6 Tracer Animation with Autodesk - 3d Studio MAX, (Gregor Hochleitner, Thomas Ruppert,DLR). Tracer initialized behind the aircraft, velocity color coded. a) initial wake, b) ground effectwith vortex bursting, c) plate line effect and d) ground linking.

7

A. STEPHAN ET AL.

of counter-rotating secondary vortices, first atthe downwind and then at the upwind vortex.Then the secondary vortices rebound and in-teract with the primary vortices. We observethat a tilting of the vortices may happen inthe crosswind situation, see Fig. 8 a). Whilethe downwind vortex is advected with thecrosswind, the upwind vortex remains abovethe runway for the entire simulation time, seeFig. 8 a)-d). The ambient turbulence and fa-vorable wind shear actively destroy the down-wind vortex.

3.2 Vortex topology

The RANS-LES coupling enables to investi-gate the complex three-dimensional vortex de-formations. Vortex linking after touchdown,see Fig. 8, and possible linking of other partsof the wake vortices reflect the complexity ofthe phenomenon in reality. The end effects areclearly visible, Fig. 8 (green iso-surface). Notethat LIDAR measurements use to detect thevelocity field in a plane perpendicular to theflight path. Measurement footprints showingcusps cannot be explained by classical theory.The stretching of the vortices and the influ-ence of a headwind, transporting the vorticesagainst flight direction, provide an explanationincorporating three-dimensional effects.

3.3 Vortex decay and plate line effect

As a common measure of the vortex intensityfor aircraft with sufficiently large wingspans,we consider Γ5−15 = 0.1

∫ 15m5m Γ(r)dr for the pri-

mary vortices, where Γ(r) =∮~u · d~s denotes

the circulation around a circle of radius r cen-tered in the vortex core. Figure 9 compareshead- and crosswind situation, with and with-out the influence of a plate line. All fourfigures show the end effect, starting at thepoint of touchdown and propagating againstthe flight direction. In agreement with formerresults the plate line considerably enforces thedecay. Note that the upwind vortex in thecrosswind case is tilted upwards, see Fig. 8.Therefore the interaction with the plate linestarts later. The headwind case reveals a vor-

tex ground linking, leaving a horseshoe vortexwhich is transported with the wind, similar toFig. 6 d).

4 Conclusion

A complete landing phase of a long range air-craft including final approach, flare, touch-down, in various ambient wind situations, andthe evolution of its wake was simulated, com-bining RANS and LES flow fields. A RANSsolution is used as a forcing term in the groundfixed LES domain. The effect of a plate linewas investigated in all situations. The com-plex multi-scale flow field of a landing aircraft,particularly the different vortices constitutingthe wake are visualized and analyzed. Com-plex vortex interaction with the ground, endeffects occurring after touchdown are investi-gated. They lead to rapid circulation decay.In ground proximity wake vortices are sub-jected to strong deformation and transport.The well known quasi two-dimensional vortexground interaction in crosswind and/or head-wind situation becomes much more complex.This yields a novel interpretation of vortex tra-jectory investigations in planes perpendicularto the flight path, occurring e.g. in LIDARmeasurements. Vortex decay is analyzed andplate line effectiveness established in the tur-bulent setup.

Acknowledgments

We would like to thank Stefan Melber (Insti-tut fur Aerodynamik und Stromungstechnik,DLR-Braunschweig) for providing the RANSdata of the AWIATOR long range aircraftmodel. We also acknowledge Airbus for theallowance to use it. We thank Michael Man-hart and Florian Schwertfirm for the pro-vision of the original version of the LEScode MGLET. Computer time provided byLeibniz-Rechenzentrum (LRZ) is greatly ac-knowledged.

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SIMULATION OF AIRCRAFT WAKE VORTICES DURING LANDING

a) t∗ = 0.1 b) t∗ = 1.0

c) t∗ = 1.7 d) t∗ = 2.4

Fig. 8 Vortex topology in the crosswind case without obstacles. Two pressure iso-surfaces,-1N/m2 (translucent), -5N/m2 (green).

Fig. 9 Normalized vortex circulation development for the entire upwind vortex, headwind case(up), crosswind case (down), without plate line (left), plate line (right).

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A. STEPHAN ET AL.

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