synthesis of eu far-wake project results · project synthesis task. results and conclusions...

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Executive summary

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Nationaal Lucht- en Ruimtevaartlaboratorium

National Aerospace Laboratory NLR

Report no. NLR-CR-2008-023 Author(s) A.C. de Bruin Report classification UNCLASSIFIED Date July 2008 Knowledge area(s) Aeroacoustic & Experimental Aerodynamics Descriptor(s) Aircraft wakes wake instabilities wake safety AIRPORT CAPACITY Vortex alleviation

Synthesis of EU FAR-Wake project results Final Synthesis Report Description of work Within the EU co-funded project FAR-Wake fundamental aspects of airplane wake vortex formation and decay are studied. The project considers wake instability and decay, vortex interactions with jets and wakes and wake evolution near the ground. Within the FAR-Wake project NLR and Airbus are responsible for the synthesis of the project results. Technical and scientific assessment of the results is made in the various Tasks and Subtasks. The applicability to real aircraft and the implications for wake vortex safety issues and airport capacity are addressed in the project Synthesis Task. Results and conclusions Improved understanding of vortex core mode disturbances and traveling waves has been obtained. Important progress has been made with the simulation of vortex instabilities in multiple vortex wake systems, including a comparison of 2D, 3D temporal and 3D spatial evolution of a developing wake. A potentially interesting method for Crow mode forcing at the wake symmetry plane was discovered. Experiments and numerical simulations show that a jet

interacting with a nearby vortex leads to a significantly larger vortex core, creating a more benign vortex. Numerical simulations of wake vortices in crosswind, reveal asymmetric rebound and increased decay as a result of the viscous interaction with the ground. These effects are also observed in LIDAR data. This let to improved modeling of wake vortex behavior during crosswind dependent reduced separation distances, as currently considered for airport operations in e.g. the CREDOS project. Advanced numerical simulations with LES have been very valuable to improve the understanding of the complex physics of wake vortices and led to improved prediction of wake transport and decay of vortices near the ground, in cross or head wind and on vortex interaction with jets and wakes. Applicability The present document considers the final synthesis of the results. It provides a summary of exploitable results that might be used to obtain more benign wakes by aircraft design and/ or to allow smaller separation distances between aircraft in certain weather conditions.

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UNCLASSIFIED

Synthesis of EU FAR-Wake project results Final Synthesis Report

Nationaal Lucht- en Ruimtevaartlaboratorium, National Aerospace Laboratory NLR Anthony Fokkerweg 2, 1059 CM Amsterdam, P.O. Box 90502, 1006 BM Amsterdam, The Netherlands Telephone +31 20 511 31 13, Fax +31 20 511 32 10, Web site: www.nlr.nl

Nationaal Lucht- en Ruimtevaartlaboratorium

National Aerospace Laboratory NLR

NLR-CR-2008-023

Synthesis of EU FAR-Wake project results Final Synthesis Report

A.C. de Bruin

No part of this report may be reproduced and/or disclosed, in any form or by any means without the prior written permission of the owner.

Customer European Commission Contract number Owner National Aerospace Laboratory NLR + partner(s) Division NLR Aerospace Vehicles Distribution Limited Classification of title Unclassified Approved by:

Author

Reviewer Managing department

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AST4-CT-2005-012238

FAR-Wake Fundamental Research on Aircraft Wake Phenomena

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Specific Targeted Research Project Start: 01 February 2005 Duration: 40 months

Synthesis of EU FAR-Wake project results

Final Synthesis Report

Prepared by: A. C. de Bruin (NLR)

Document control data

Deliverable No.: D 4.2 - 3 Due date: May 2008 (m40)

Version: 1.0 Task manager: A. C. de Bruin

Date delivered: 23 July 2008 Project manager: T. Leweke EC Officer: S. Stoltz-Douchet

Project co-funded by the European Commission within the Sixth Framework Programme (2002-2006)

Dissemination Level PU Public × PP Restricted to other programme participants (including the Commission Services) RE Restricted to a group specified by the consortium (including the Commission Services) CO Confidential, only for members of the consortium (including the Commission Services)

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Summary

Within the FAR-Wake project fundamental research is focussed on the precise role of wake vortex instabilities on wake development and decay (WP1), the effects of engine jets and fuselage wakes on wake formation and roll-up (WP2), and the influence of ground proximity on wake evolution (WP3). The first two work packages deal with an increased physical understanding on the evolution of the wake, depending on aircraft dependent parameters. Conditions are sought that could lead to a more benign wake for following aircraft. WP 3 is especially relevant to the question of safe separation distances in the airport environment. Experimental and numerical investigations as well as theoretical/analytical studies are made and, where appropriate, this is complemented with existing knowledge and exploitation of data from previous projects. The work in the technical work packages is oriented to fundamental aspects of the wake generation and its evolution downstream. The research aims to assist with practical solutions for reducing the potential hazard for following aircraft and to enable reduced aircraft separation distances to be applied. Wake alleviation, airport capacity and safety of aircraft operations are research priorities in the FP6 EC Work programme, synthesis and therefore assessment of these aspects are made in Work Package 4 of the FAR-Wake project. The present report considers the final Synthesis Report (deliverable D4.2-3 of Task 4.2). It is based on the Technical Reports and Deliverables, presentations during technical meetings, partner publications and Annual Progress reports.

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Contents

1 Introduction 9

2 Vortex instabilities and decay 10 2.1 Task 1.1: Waves on vortices 10 2.1.1 Task 1.1.1: Vortex meandering 10 2.1.2 Task 1.1.2: End effects and vortex-bursting 13 2.2 Task 1.2: Instabilities of vortex systems 16 2.2.1 Task 1.2.1: Short wavelength instabilities 16 2.2.2 Task 1.2.2: Medium and long wavelength instabilities 19

3 WP 2: Vortex interactions with jets and wakes 23 3.1 Task 2.1: Vortex interactions with jets 23 3.1.1 Task 2.1.1: Cold engine jets 23 3.1.2 Task 2.1.2: Hot engine jets 27 3.2 Task 2.2: Vortex interactions with wakes 29 3.2.1 Task 2.2.1: Effect of fuselage on vortex wake 29 3.2.2 Task 2.2.2: Wakes generated by wing elements 30

4 WP 3: Wake evolution near the ground 32 4.1 Task 3.1: Dynamics and decay in idealized conditions 32 4.1.1 Subtask 3.1.1: Longitudinal uniform wakes 32 4.1.2 Subtask 3.1.2: Spatially evolving wakes 35 4.2 Task 3.2: Dynamics and decay in real conditions 37 4.3 Task 3.3: Assessment and real-time modelling 39

5 Conclusions and recommendations 40 5.1 Synthesis of main WP1 results 40 5.2 Synthesis of main WP2 results 41 5.3 Synthesis of main WP3 results 43

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Abbreviations

a, rc core radius b0 initial spacing of vorticity centroids b wingspan b1, b2 distance between primary vortices (b1) or secondary vortices (b2) c wing chord h distance between jet and vortex core (WP2) distance to ground (WP3) m mode number of azimuthal vortex disturbance r distance to vortex core t0 reference time: t0=b0/w0 t*, τ non-dimensional wake vortex life-time t*=t/t0 x downstream position in wake y lateral position of vortex core z vertical position of vortex core CL lift coefficient Dj jet diameter Rj parameter defining the relative strength of the jet and vortex (see Eq. 2-34 in Ref. 8) Vθ velocity around the vortex core

greek symbols α angle of attack ω vorticity Γ circulation strength

sub-fixes j jet 0 initial value

Abbreviations ATC-Wake EC project under Information Society Technologies (IST) program AWIATOR Aircraft WIng Advanced Technology OpeRation CFD Computational Fluid Dynamics CREDOS EU project on Crosswind Reduced Separations for Departure Operations C-Wake Wake Vortex Control, former EU research project

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DES Detached Eddy Simulation DNS Direct Numerical Simulation Eurowake Wake Vortex Formation of Transport Aircraft HSVA Hamburgische Schiffbau-Versuchsanstalt IGE In Ground Effect LIDAR LIght Detection And Ranging LES Large Eddy Simulation NGE Near Ground Effect PIV Particle Image Velocimetry POD Proper Orthogonal Decomposition PSE Parabolic Stability Equations RANS Reynolds Averaged Navier Stokes SVA Schiffbau-Versuchsanstalt (Potsdam) S-Wake Assessment of Wake Vortex Safety, former EU research project SWIM Simple Wall Interference Model VIC-PFM Vortex In Cell Parallel Fast Multi-pole method WAVENC Wake Vortex Evolution and WAke Vortex ENCounter WSG Wasserschleppkanal Göttingen WP Work Package

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1 Introduction

The aim of the FAR-Wake project (Ref. 1) is to gain new knowledge on aircraft wake vortex phenomena, critical in the context of wake turbulence behind civil aircraft, but not sufficiently addressed or understood in previous studies. The research in FAR-Wake is focussed on the effect of vortex instabilities on wake decay (WP1), the effects of engine jets and fuselage wakes (WP2), and the influence of ground proximity on wake evolution (WP3). The latter is especially relevant for the airport environment. Experimental as well as theoretical/analytical studies are made. Where appropriate this is complemented with existing knowledge from previous projects. At the beginning of the project a status summary for each of the WP topics was presented in Refs. 2-4. In-depth analysis of the results was made in the different technical work packages (see Refs. 5-7), but a separate assessment of the practical implications is made in WP4: Synthesis and Assessment. This is to provide a solid knowledge base for future wake vortex prediction and reduction strategies, relevant for increasing airport capacity and safety of air transport, one of the priorities of the EC work programme. Within the FAR-Wake project 17 partners participate (see Table 1 for an overview), having different background and expertise. Some already participated in previous European research projects on aircraft wakes, but some are new in this field. The document ‘Framework definition and wake characterisation’ (Ref. 8) provides a recommended approach for analysing the results of experimental, numerical and theoretical work in order to enable a comparison of results and to facilitate the assessment of their practical implications. Intermediate synthesis reports have been issued by NLR, in collaboration with Airbus and the WP and task managers, after each annual review (see Ref. 9 and 10). The present report provides the final synthesis of the project results, based on the project deliverables and partner publications. The purpose of the final synthesis and assessment Task 4.2 is two-fold:

• To synthesize and summarise the technical and scientific results of all tasks • To evaluate the potential benefits and applicability to real aircraft wakes

Additional information is also available from the Annual Progress Reports Ref. 11-12.

A detailed synthesis of the results of WP1 (effect of vortex instabilities on wake decay) is given in section 2, for WP2 (effects of engine jets and fuselage wakes) in section 3 and for WP3 (the influence of ground proximity on wake evolution) in section 4. The main conclusions are summarised in section 5.

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2 Vortex instabilities and decay

2.1 Task 1.1: Waves on vortices 2.1.1 Task 1.1.1: Vortex meandering A large Reynolds number asymptotic analysis of viscous centre modes on an arbitrary axi-symmetrical vortex with an axial jet has been made by IRPHE and UPS-IMFT, using a temporal stability analysis method (Ref. 14). Three different viscous centre modes can be distinguished (modes A, B and C). Results have been published in JFM (Ref. 22). General formulas for growth rate and radial structure of the viscous centre modes are obtained for any vortex with axial jet. Results have been compared and validated with numerical results obtained for the “q” vortex and the Batchelor vortex (incorporating non-parallel effects). Both are Lamb-Oseen type vortices with axial flow. Figure 1 gives some examples for the temporal spectra for the Batchelor vortex as obtained by the theory (circles) and by a spectral calculation method (stars). A good comparison is found. It is shown that any vortex where simultaneously the axial vorticity ω and the second radial derivative of the axial (jet) velocity in the vortex centre d2U/dr2 are non-zero, becomes unstable if the Reynolds number is sufficiently large. This work has been continued by a study in the vicinity of the neutral curves (a paper has been submitted to JFM, see Ref. 23). UPS-IMFT analysed the dynamics of the Lamb-Oseen vortex when continuously forced by white noise random excitation (Ref. 15). A stochastic forcing method was applied to mimic the effect of external perturbations in realistic conditions. The long-time statistical response of the vortex and the coherent structures participating to the vortex excitation were analysed. Compared to optimal perturbation analysis the growth rates are larger, since it corresponds to energy growth resulting from a continuous noise input and not from a single initial condition. Classical optimum perturbation analysis focuses on the most amplified disturbance and can sometimes miss transient scenarios, while the stochastic method includes the effect of sub-optimal disturbances. For helical perturbations, the stochastic forcing shows that the emerging Kelvin mode depends on the axial wave number. At large wavelengths the displacement mode corresponds to the critical layer modes as described by Fabre (Ref. 28). Though these modes are normally damped, the stochastic forcing method shows that transient growth may occur. This mechanism might play a role in vortex meandering. Analysis for m=0 modes gave a theoretical explanation of the recurrent development of vortex rings as observed at the periphery of vortices when submerged in ambient turbulence. For this case the optimal perturbations, as mentioned in Ref. 24, do naturally develop from the background noise. A spatial stability analysis of convective/absolute instabilities of viscous centre modes for the

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Batchelor vortex was made by UMA (Ref. 16). An example, showing the structure of a viscous centre mode is given in Figure 2. An article on this work has published in JFM (Ref. 19). The study started with the assumption of parallel flow and for high Reynolds numbers the results were in excellent agreement with those of Ref. 14. A fairly complete mapping of instabilities was obtained up to the 3rd azimuthal instability mode (m= -3). In the next step a Parabolic Stability Equations (PSE) approach was followed to study the linear instability of the non-parallel Batchelor vortex case, where the vortex is allowed to have a slow variation in axial direction. It was found that, if the swirling number (defined as the ratio between maximum azimuthal velocity and axial flow velocity in vortex core) is large enough, the stability properties of the non-parallel Batchelor vortex become quite different from the parallel “q” vortex. However, in practice the differences become only noticeable if the travelled distance in the wake is in the order of 100 to 1000 core radii. However, the PSE method predicts that the viscous modes in the non-parallel case become sooner stable than in the parallel case (typically 4 times shorter distance in the wake). Limited experimental evidence shows about one order of magnitude difference between observed frequencies and the most unstable mode (m=-1), so that a direct link between viscous instabilities and vortex meandering, seems unlikely. Considering the sensitivity of vortex viscous instability to actual vortex velocity profile and the limited experimental data on frequencies and wavelengths available, no definite conclusion could be made on the role that viscous instabilities play in vortex meandering. IRPHE analysed the dynamics of a single vortex generated by a generic low aspect ratio (c=10 and b/2= 15 cm) half-wing in a water channel (Ref. 17). Dye was injected from the wing-tip and the flow was visualised with a laser sheet at a fixed position x/c=11.2 from the trailing edge. Stereo PIV measurements for characterising the flow parameters were taken at the same position. Measurements were taken at three different tunnel velocities (U=46, 67 and 91 cm/s) and three different model angle of attack (6, 9 and 12 deg). The flow turbulence in the water tunnel is about 1.5% (streamwise) and about 0.6% (lateral). For each flow condition 400 PIV images ware taken. Vortex centre position was determined by fitting to a Gaussian vortex model and average vortex position was determined. All vortex positions were shifted to mean vortex position in order to evaluate mean axial vorticity and velocity profiles. At higher tunnel velocity and/or angle of attack the low pressure in the vortex cores attracted small air bubbles, leading to a distortion of the PIV results along a horizontal line through the vortex core. When this occurred the velocity and vorticity profile was determined from a vertical cross-section through the vortex core only. In all other cases the whole velocity field was used to characterise the mean profiles. The axial velocity defect could be well fitted with a Gaussian and the azimuthal velocity with the two-length scale VM2 model from Fabre and Jacquin. An example for α=9 deg and U=67 cm/s is shown in Figure 3. High speed dye visualisation (16000 frames, taken at 300 Hz over a period of 54 seconds) allowed to follow the position of the vortex centre

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(characterised as the centre of light intensity) in time. The variation in vortex centre position was further characterised by computing the eigenvalues of the co-variance matrix of xc and yc. This gives the ellipse of dispersion radii aM and am aligned along principle directions vM and vm, as illustrated in Figure 4. The mean dispersion radii remain well within the vortex core radius. If tunnel velocity and/or model angle of attack increase, the principle axis of the ellipse becomes more normal to the wing (wing trailing edge is vertical in the figure). The nature of the vortex perturbations was further investigated with Proper Orthogonal Decomposition (POD) of the measured vorticity fields from 2D high speed (2000Hz during 8 sec) PIV measurements with a single camera. The POD results into an ordered set of modes. An example for the first six most energetic modes for the α= 6 deg and U= 46 cm/s case is shown in Figure 5.The first mode is the axi-symmetric mean flow field, the 2nd and 3rd mode are associated to a Kelvin mode with azimuthal wave number m=1. The associated energy of both the latter modes is similar, so they form a high-energy doublet. The 4th mode is related to a combination of m=0 and m=2 Kelvin waves and represents an elliptic compression mode. The 5th and 6th mode are similar to a m=2 Kelvin mode, but disturbed by a m=0 mode. Pure m=0 and m=2 Kelvin modes can be recovered by linear combination of modes 4, 5 and 6. Due to hardware limitations it was not possible to record PIV images over sufficiently long times to allow determination of meandering frequency from a spectral analysis. An alternative POD analysis was therefore applied to the dye visualisation results obtained over a period of 54 sec. This yielded basically the same modes as for the PIV vorticity fields. Subsequent perturbation mode decomposition and spectral analysis showed that for all cases the power spectral density of the 2nd mode peaks roughly at a frequency of 1 Hz and the corresponding wave length is about 120a1 (a1 is the inner core radius according to the VM2 model), so a very long wavelength. The corresponding non-dimensional wave number is about ka1=0.05. At the x-position investigated the non-dimensional time is given by τ=(Γ/2πa1

2).(z/U)= 150. Antkowiak & Brancher (Ref. 24) showed that for a Lamb-Oseen vortex transient energy growth of long wavelength perturbations may result from random fluctuations. Antkowiak and Brancher computed the optimal time (for maximum vortex perturbation) in relation to the wave number ka. As shown in Figure 6 the present results fit their results quite well, despite the differences in vortex structure. The mode structure (shown in Figure 5b) also agrees with the most amplified mode (vortex displacement mode) in the low wave number range of Ref. 24, this strongly suggests that the meandering phenomenon observed in the water tunnel is due the transient growth of vortex perturbations. In conclusion (see also Ref. 13) vortex meandering seems most likely connected to the transient growth of critical layer modes subject to random excitation by the external flow turbulence and not to viscous modes.

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2.1.2 Task 1.1.2: End effects and vortex-bursting This work has been performed in close co-operation between IRPHE, ONERA, CERFACS, UCL and UPS-IMFT. IRPHE made experiments in a water tank (Ref. 26). Vortices were created with an impulsively rotated flat plate (see Figure 7), for which the created vorticity depends on the rotation speed ( θω &= ). The temporal evolution of single rectilinear laminar vortices was observed, subject to different types of perturbations:

• A 90° bend at one “end” of the vortex, inducing a propagation of deformation and pressure waves and wave fronts along the vortex. An example of flow visualisation results is given in Figure 8.

• A sinusoidal deformation of short axial extent of the vortex (see Figure 7c). The 90° bend perturbation tests revealed two kinds of travelling perturbation. The first one creates some axial flow in the vortex and is related to the m=0 Kelvin mode. The second one introduces an undulation of the vortex centreline and is related to the m=1 Kelvin mode. The experiments also gave a first evidence of the critical layer modes predicted by Ref. 28. For both cases, the vortex parameters, as well as the properties of the different waves propagating on the vortex, were determined from dye visualisations and PIV measurements. The frequencies and transport velocities of the waves have been compared with the theoretical dispersion relations of the Kelvin waves (as given by Ref. 28 and Ref. 32). For the sinusoidal deformation tests the agreement with theory is excellent (see Figure 9). CERFACS studied the propagation of pressure waves along a Lamb-Oseen vortex, using three-dimensional DNS (Ref. 27). Prescribing a sinusoidal changing core radius in the vortex axial direction, creates a pressure gradient along the vortex core and a perturbation similar to the m=0 Kelvin mode. In a previous study by CERFACS (Ref. 33) a similar simulation strategy was made for core radius ratio rc2/rc1=2, E (length of the changing core radius region) =5 and ReΓ=104. This reference case was again computed but in addition a more complete parametric study was made for a range of core radius ratios (from 1.0625 to 2), core radius changing length E (from 3 to 13) and ReΓ (from 103 to 104). The results show that the pressure wave propagates at an approximately constant speed in close agreement with linear theory for m=0 Kelvin waves (Ref. 32) and in reasonable agreement with the experimental results from CNRS-IRPHE (Ref. 26). The pressure wave creates an axial velocity in the vortex core which can destabilize the vortex through the development of helical disturbances. For the reference case, small initial perturbations were added, creating the growth of helical instabilities, depending on Reynolds number (see Figure 10).

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CERFACS also performed a parametric study with DNS to investigate vortex bursting by collision of pressure waves propagating in opposite directions (Ref. 30). Such waves are assumed to be related to vortex bursting phenomena that have been observed during flight tests (e.g. in the AWIATOR project). The strength of the simulated pressure waves is again influenced by changing the ratio of core radii. If core radius variation is larger than 40 % the collision leads to a drastic and sudden change of the vortex structure. A computed result for two colliding pressure waves is shown in Figure 12 and the effects on the circulation profile at different times and for two core radius ratios is shown in Figure 13. A numerical stability analysis of Kelvin waves has been made by UPS-IMT and ONERA for a Lamb-Oseen vortex (Ref. 28). This is much more realistic than the highly idealized Rankine vortex, for which such modes were mainly studied so-far. An exhaustive presentation of the normal instability modes of the Lamb-Oseen vortex is given. The complete mapping of all normal modes turned out to be a numerical challenge and (contrary to the Rankine vortex case) also highly damped singular viscous modes are found. Several groups of modes could be identified, some are specific for the Lamb-Oseen model, others are also found for the Rankine model. One class of modes is responsible for the propagation of axi-symmetric, helical or flattening waves and the associated disturbances and kinetic energy along a vortex tube. A second similar group of modes is formed by so-called C (core) modes, which are generally more damped and entirely located in the vortex core and have not yet been observed in real practice. The third group of modes are the so-called critical layer waves. These waves have no counter-part in the Rankine vortex case and the effect of viscosity is highly non-trivial. These waves seem to play a role in the “communication” between the vortex core and regions outside and are therefore of practical relevance, e.g. in the interaction between a vortex with its turbulent surroundings. ONERA made numerical simulations of wave propagation along vortices with its DNS code FLUDILES and also analyzed existing PIV data from the B-20 catapult facility (Ref. 29). 2C-PIV data from B-20 catapult facility were analysed in detail, using various post-processing algorithms. This clearly showed a sudden widening of the vortex core and the perturbation of the vortex core structure as a result of so-called travelling waves. If 3C-PIV data would have been available this could have been studied in better detail. Subsequent DNS simulations were made. The numerical procedure was validated in the small perturbation linear regime by comparison with existing numerical results (Ref. 28) for a linearized situation of a Lamb-Oseen vortex submitted to m=0, m=1 and m=2 modes. A spatial filtering procedure was developed to remove numerical oscillations at high Reynolds numbers. Also a special counter-diffusion technique and improved meshing techniques were developed to improve the numerical results. At ReΓ=202 and 103 the numerical results agreed well with the linearized theory. Some small

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deviation developed at high vortex Reynolds number (ReΓ=204). For m=0, 1 and 2 modes simulations in the non-linear regime were performed by increasing the initial amplitude of the perturbations and the simulation results suggest a different behaviour in the non-linear regime. In a subsequent simulation for a sufficiently strong m=1 mode perturbation , the non-linear effects clearly cause a transfer of energy between azimuthal modes. As a result also m=0 modes are generated, which have a relatively large propagation speed. Some results on perturbation energy decay, depending on initial amplitude, are shown in Figure 14. UCL developed its VIC-PFM code and post-processing algorithms to handle temporally and spatially developing flows. The propagation of instabilities within a vortex pair due to the acceleration/deceleration of a wake generating wing has been simulated (Ref. 31). A snap-shot of the time-developing simulation for a stopped wing is shown in Figure 16. Due to the sudden stop, disturbances start to travel along the vortices. The propagation speed of the disturbances is about 0.85 times the maximum tangential velocity within the undisturbed vortex. Contrary to experimental results from IRPHE (Ref. 26), no difference is observed between the “pressure wave propagation” and “instability propagation” speeds. A time-developing simulation with a wing accelerated over a distance of 0.5b0, then flying over a distance of 20 b and then again decelerated over a distance of 0.5 b0 (needed because of the periodic boundary conditions) was made. A snap-shot is shown in Figure 17. Three snap-shots of the same case, but now with a spatial simulation, are shown in Figure 18. Both simulations required about 65.106 grid points. Inspection of the space developing circulation profile (before it is disturbed), shows that this is best fitted with the regularized Kaden-Winckelmans or the Jacquin model. In the time- and space-developing simulations the same dynamics were observed and the wave propagation speed along the vortex cores was about the same. Detailed examination shows that first an axial perturbation develops, corresponding to a pressure wave. If the resulting axial velocity is large enough, as in the computed examples, this wave destabilizes the vortex and a helical instability develops. It should be noted that axial velocity defect in the initial wake (as would occur in real wake flows) was not taken into account in the simulations. This effect is taken into account in Task 2.2.2 (see Ref. 92). Results from Ref. 28 have important implications for Task 1.1.1. The so-called critical layer class of waves have a structure that is particularly receptive to external perturbations. Analysis in Task1.1.1 showed that the critical layer modes play a role in vortex meandering. The observed differences in group velocity of the various families of waves are interesting. The fastest are the axi-symmetric ones, with a non-dimensional group velocity of 0.63 (non-dimensionalized with Γ/(2πa), where a is the vortex core radius), so close to the maximum azimuthal velocity of the vortex. The next one is the helical translation wave with a group

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velocity of 0.29. The helical "C" waves are equally fast but are not expected to play an important role, because these are damped. All other families of waves have much slower group velocities. Vortex bursting and other end effects are most likely related to the fastest waves, and the description of their structure (as done in the numerical simulations by CERFACS and UCL) is useful. The main outcomes of the subtask were synthesized in Ref. 25. 2.2 Task 1.2: Instabilities of vortex systems 2.2.1 Task 1.2.1: Short wavelength instabilities Vortices generated by aircraft wings are known to interact with each other. Each vortex is subjected to the strain field induced by nearby other vortices and this causes a so-called elliptic instability. For a vortex without axial flow it causes a short wavelength (proportional to the wake vortex core diameter) sinuous deformation of the vortex line. The main results of the sub-task are reported in Ref. 34. UPM studied the linear temporal stability of a counter rotating two-vortex system (Ref. 35) using a finite-element based three-dimensional BiGlobal eigenvalue method. The basic flow is first computed with a 2D spectral collocation DNS method, initialised by a Lamb-Oseen vortex and an axial flow model. The computed flow at certain times has subsequently been used for the stability analysis. A 2nd order Taylor-Hood FEM method (see Ref. 45) was first validated for the Batchelor vortex. The method monitors the modal response of vortical systems to small-amplitude perturbations, periodic along the homogeneous axial direction, without the need to invoke an assumption of azimuthal homogeneity. The effects of Reynolds number and of non-zero axial flow magnitude were investigated for different stages of vortex diffusion. A full range of unstable axial wave number parameters has been identified and a consistent picture of the instability of the dipole vortex emerged. The Reynolds number and initial peak axial velocity were found to have a minor effect on the peak amplification rates, although they do affect in a systematic manner the leading eigenmodes at off-peak conditions. The viscous decay of the vortex dipole, results in a flow which is increasingly more stable against all three-dimensional perturbations. An example of computed amplitude functions for velocity components for the leading eigenmode (wave number α=3) at ReΓ=3180 and initial axial flow U0=0.25 is shown in Figure 19. For the first and second mode, the dependence of amplification rate and frequency on the initial axial flow magnitude U0 is shown in Figure 20. The 2nd-order FEM method could only provide reliable results on a high resolution computational mesh. The resolution demands are prohibitive for serial solutions of the eigenvalue problem, such that the method quickly loses

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its competitive advantage of geometric flexibility. This fact has been recognised and a new high-order FEM method has been developed (see Ref. 46). In a study by IRPHE the effect of axial flow on the elliptical linear instability was investigated for a single Batchelor type vortex with relatively small axial flow and different levels ε of added strain (Ref. 36). The added strain resembles the practical situation of a rolled-up aircraft wake with two parallel vortices. Depending on external strain rate ε and Reynolds number the stability diagram of the Batchelor vortex has been mapped. Figure 21 shows an example of the instability area of the principal azimuthal (m) coupling modes in the axial flow-wave number plane (W0, k) for the Re=Γ/(2πν)=20000, ε=0.01 case. Without axial flow, the elliptic instability mode is formed by the resonance of two stationary Kelvin modes m=1 and m=-1 (the (-1, 1, i) modes shown in Figure 22). Axial flow breaks the symmetry between the m=-1 and m=1 Kelvin modes. For larger axial flow the resonance between these modes disappears because the two modes becomes strongly damped due to a critical layer singularity. However, then a new resonance between m=-2 and m=0 becomes possible, and next a resonance between the m=-3 and m=-1 mode, and so on. In the far-wake, where axial flow in the vortex cores is expected to be more than 0.1 times the maximum azimuthal velocity, the new instability modes (-2,0,i) could well be present and perhaps play a role in the development of the Crow instability. This work has been continued with temporal DNS simulations of short-wave instabilities of co-rotating Batchelor vortices at several initial distances and different levels of axial flow (Ref. 37). Figure 23 shows computed average velocity and vorticity profiles after merging of the vortices, for different levels of axial flow. Basically similar modes are observed as with the linear stability analysis (shown in Figure 21). However, for large Reynoldsnumbers also other instability modes become amplified. Though these are less unstable than the principle modes, they make the vortex pair unstable in a large wave number band, whatever the axial flow. Without axial flow, weakly non-linear limit-cycle behaviour is observed close to stability margins. Strongly non-linear behaviour is observed elsewhere and is characterised by the following steps:

• Concentration of vorticity in thin layers around the vortex periphery • Expulsion of vortex loops • Breakdown of whole vortex structure • Re-laminarisation process leading to a weaker and larger vortex

The elliptic instability leads to an earlier merging of co-rotating vortices. With axial flow the elliptic instability becomes less violent and merging occurs later than without axial flow, especially if the initial distance between the vortices is relatively large. Systematic comparison between wake merging evolution in 2D flow, 3D without axial flow and 3D with axial flow have been made, showing the differences in vortex merging. Some results for the Re=12500,

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(a/b)0 =0.20 case are shown in Figure 24. Several publications on these results have been made or are in preparation (Ref. 41-44). Finally, IRPHE also performed fundamental flow experiments on co-rotating and counter-rotating vortex configurations with axial flow in a wind tunnel and in a water channel (Ref. 38). Flow visualisation results confirm the existence of short wavelength instabilities in reasonable agreement with theoretical predictions (see Figure 25) and of vortex meandering during the vortex merging of the co-rotating vortices. TUE-FDL performed dedicated experiments on the effect of flow turbulence on the development of an isolated vortex and of counter-rotating vortex pairs having different initial spacing (Ref. 39). Initial results have been presented (Ref. 48). The test setup is schematically shown in Figure 26. The length of the test section is 8 m and the cross section is 1.05 m high end 0.70 m wide. Tests were made with and without different turbulence grids placed at the test section entrance. An impression of the 0.1 m grid cells (with flow agitators mounted on rotatable bars) is shown in Figure 27. Measurements with turbulence grid were made for different grid transparencies: 1 (maximum open), 0.94, 0.85 and 0.71. Compact vortices were created with (a) special lightly twisted Clark Y type profile(s) with a chord length of 0.075 m, set at different angles of attack, creating vortices of different strengths. Vortex pairs are created with two profiles protruding from the opposite vertical tunnel walls and set at equal angle of attack. Three different wing tip separation distances (d0= 0.03, 0.05 and 0.10 m) were used, with the profiles placed at 3.465 m behind the different turbulence grids. Measurements were made with 2C-PIV. Tunnel flow was seeded with an aerosol generator. Supplemental smoke was injected from the wing tips in order to seed the vortex cores. Measurements were made for two different delay times between images in order to get optimum particle displacement either in the vortex core (large velocities, small delay times) or the far-field (small velocities, large delay times). Procedures for obtaining vortex core position and for computing circulation strength as function of radial distance were carefully tested. Prior to the tests the development of the flow turbulence downstream of the grid (urms and eddy dissipation rate ε) was measured, using a hot-wire probe. For the isolated vortex the vortex core radius increases with downstream distance (or time) as shown in Figure 28a. And the vortex meandering is well described by the correlation shown in Figure 28b. For a vortex pair without grid turbulence, Crow type oscillations are only observed for the smallest vortex spacing case (with distance between wing tips d0=0.03 m, see Figure 29). Presence of grid turbulence promotes the onset of the Crow instability, but in too strong turbulence conditions vortex linking can no longer be observed (see left figure of Figure 30). Also the final oscillation angle with respect to horizon (about 33 deg, see right figure of Figure 30) is less than the optimum oscillation angle (48 deg) and the amplification rate is about half that predicted by inviscid theory. Analysis of the results shows

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that there is also a significant decay of circulation strength due to the cross-diffusion of vorticity over the symmetry plane. The development of Crow modes in the presence of significant cross-diffusion leads to a complex decay mechanism. The merging of co-rotating vortices can either take place under stable conditions or through the development of short-wavelength elliptic instabilities, called unstable merging. As shown by IRPHE (Ref. 36) the unstable merging involves 3D flow. CERFACS (Ref. 40, 49 and 50) made spatial DNS simulations of co-rotating vortex pairs with various levels of axial flow and with small amplitude random perturbation of the vortex core position at the inflow boundary. The code was adapted with suitable boundary conditions and filtering techniques in order to minimize reflections from the boundaries and have proper inflow and outflow conditions. Figure 31 shows the spatial evolution of co-rotating vortices and their merging through the development of short wavelength instabilities for one of the three computed cases (ratio between maximum azimuthal velocity V0 and free-stream velocity W is V0/W=1.5 and in the vortex cores it is V0/W=0.54). As shown in Ref. 36 the axial flow causes the normal elliptic m= (+1,-1) Kelvin resonance mode to become damped and a new mode (m=-2, 0) to become amplified. The vortical structures evolving during the vortex merging phase ultimately lead to a disturbed vortex. 2.2.2 Task 1.2.2: Medium and long wavelength instabilities DLR work on temporal numerical simulation studies of 4-vortex systems, related to the DLR F13 model tested in the towing tank at Potsdam, is in progress (Ref. 52). Parameter settings and grids for near-wake unsteady simulations with the TAU code have been established and the unsteady calculations are running. Chimera grids are used in order to simulate an oscillating flap. Preparation of the LES code in order to extend the unsteady simulations in the extended near-field and the far wake region is in progress. Figure 32 shows numerical results from DLR of an optimum disturbed 4-vortex system, showing enhanced Crow-mode amplitude after the vortex merging. The optimal perturbation for the Crow instability of a vortex dipole (Ref. 55) has been computed with an adjoint based gradient method (as in Ref. 58) and has been published by ONERA (see Ref. 62). It is found that long-wavelength forcing with the adjoint mode of the most unstable direct Crow mode causes a strong and fast transient growth of the Crow instability. At larger times, after the transient phase, the amplification is 36 times greater than that of the modal disturbance of the most amplified Crow mode. It is shown that the characteristic time of the Crow instability can thus be reduced significantly (see Figure 36). The study revealed the role of spirals of vorticity around the vortex core (which for the case of a single Lamb-Oseen vortex have already been reported to give optimal forcing, see Ref. 24) and the hyperbolic stagnation points of the vortex dipole for the optimum amplification of the Crow

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mode. Since forcing with the adjoint Crow mode is not really practical (requires forcing over a large physical domain), ONERA also investigated a slightly less optimal perturbation. It is argued that the optimum vorticity perturbation (as shown in left hand of Figure 36) can be closely matched with perturbations near wake symmetry plane only. Since any vorticity perturbation can be initiated by a local force a particular local (vertical) force distribution was assumed. It is defined by: fy=(1-cos(x/ax))(1+cos((y-y0)/ay), with y0=-0.8, ax=0.05 and ay=0.7 defining the location and the form of the distributed force. The resulting vorticity distribution is shown in Figure 37 (left). A comparison of disturbance energy growth of the Crow mode is shown in Figure 37 (right). The thin long-dash line represents the energy growth of the normal of Crow mode, the thick line shows the growth of the Crow mode with optimum adjoint forcing and the thin line the result with not optimum forcing using the vertical distributed force distribution given in Figure 37 (left). Clearly the non-optimal perturbation is still close to the optimum perturbation mode and still gives a much more amplified Crow mode. With optimum forcing predominantly localized near the symmetry plane, it seems very attractive for practical applications. Further work is needed to investigate if the proposed method (giving an alternative to 4-vortex solutions) is really practical.

UCL investigated the sensitivity of counter-rotating four-vortex systems to the relative strength of the primary and secondary vortices using an inviscid 3D vortex filament method (Ref. 53). Five cases were analysed: Γ2/Γ1= [-0.1, -0.15, -0.2, -0.25, -0.3], the initial relative vortex spacing being fixed to b2/b1=0.3. All cases were compared to a reference two vortex system such that they all produce the same lift and that the initial spacing of the primary vortices, b1, is also constant. The vortex trajectories, the modal growth rate of the perturbation amplitude and it's spectrum were analyzed for each case up to reconnection. The growth rate of the most unstable mode decreases only slightly, when the relative strength of primary and secondary vortices is decreased (σ*= 7.9, 7.5 and 6.7 for Γ2/Γ1= -0.3, -0.2 and -0.1 respectively). The wave number of the most unstable mode increases more significantly: kb1=4.53 for Γ2/Γ1= -0.3 and kb1=8.2 for Γ2/Γ1= -0.1. For small circulation ratios, the range of unstable modes becomes broader. These observations would lead to the conclusion that small circulation ratios are as effective as larger ratios to enhance instabilities. It was however also shown that the level of perturbations on the primary vortex just before reconnection decreases for smaller circulation ratios. Γ2/Γ1=-0.2 therefore seems a good trade-off between realizability and effectiveness. Both the Γ2/Γ1=-0.2 and Γ2/Γ1= -0.3 case have then been studied with a spectral LES approach (Ref. 53). At non-dimensional time τ*=2.9, results are shown in Figure 33. The temporal evolution of the Γ2/Γ1= -0.3 case is shown in Figure 34. The simulations were run over a long domain (i.e., one Crow length). The growth of instabilities, energy decay, circulation decay, spectra and the longitudinally averaged flow fields were analyzed. The energy decay of the -0.2 case is only

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slightly slower than the -0.3 case, but it is still very effective. As the -0.2 case also has a slightly lower initial energy level, it is certainly an interesting case. This finding is of large importance for the practical application of counter-rotating vortices on real aircraft, which hitherto was believed to be only effective for rather large and unpractical Γ2/Γ1 ratios. A space-developing LES of Γ2/Γ1= -0.3 case was also performed (Ref. 53). The wing lift coefficient was artificially set to a high value (6 instead of 1.5) in order to reduce the computational domain to 20 b1 (which is still very large: the VIC-PFM method required ~111 million grid points!). The simulation was carried on for sufficiently long times in order to reach the final state and then to obtain statistically converged time-averaged quantities. Related publications are given in reference 59-61 and a graphical representation of the results is given in Figure 35. UPM attempted a temporal stability analysis of 2 and 4 (co-rotating) vortex systems by a Floquet method (Ref. 54). It was found that the computing costs of serial Floquet analysis is prohibitively high if parametric studies are to be performed. Converged results for the Floquet multipliers have been obtained for two cases with a pair of equal strength co-rotating vortices, with ratio between vortex core radius and distance between vortices being either a/b0=0.2 or 0.1. The first case results in a stable and the second case in an unstable perturbation. Axial periodicity has been imposed artificially, and it remains to be investigated what the effect of this assumption is. The extremely slow convergence of the Floquet analysis prevented to obtain fully converged results for the 4-vortex system case yet. This situation is exclusively due to the long periods of rotation at the relatively high Reynolds numbers monitored and is unlike previously experienced low-Reynolds applications. TUM-AER measured a promising four-vortex configuration for instability amplification with the DLR F13/F13X model in their wind tunnel (Ref. 57 and Ref. 63) in preparation of tests by DLR with the F13 model in a towing tank. The model is shown in Figure 38. Six component balance measurements were made to check for lift coefficient and tail loads with respect to the defined four-vortex configuration. Reynolds number influence was also addressed. The tail circulation / wing circulation ratio was adjusted to attain the “optimum” Γt/Γw = -0.3, with tail / wing span ratio bt/b=0.3. The wing span of the F13 model is 0.3 m and of the F13X model it is 1.2 m. Smoke visualisations of the global wake evolution (see Figure 38) show the deformation of the main wing tip vortex due to the presence of the tail plane vortex. Advanced hot-wire measurements were made at stations x/b = 1, 2, 4, 8, 12, 16, 20, 24, 36 and 48 for the small F13 model (at Rec=80000) and at stations x/b = 1, 4, 8 and 12 for the large F13X model (at Rec=80000 and 320000). Additional 3C-PIV measurements were made at x/b= 1.5 (0.5) 10.0 for the small F13 model (at Rec=80000). Results from hot-wire and 3C-PIV were compared in detail and showed some differences, especially for the axial flow component. The peak vorticity of the tail plane vortex decays rapidly for both low Reynolds number tests, but much slower for

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the high Reynolds number test. Figure 39 shows a comparison of vortex trajectories and peak vorticity decay for the two Reynolds numbers tested with the large model. The focus was on the analysis of the time dependent quantities from the hot-wire measurements, enabling to analyze the interaction of the wing and tail vortices and the presence of dominant frequencies, indicating the development of co-operative instabilities. DLR performed a validation experiment with the DLR F13 model in the large SVA water tank in Potsdam (Ref. 56). The main wingspan of the model is b1=0.3 m and the chord length is 0.05 m, the towing speed was taken U=1.71 m/s, leading to the same Reynolds number (Rec=80100) as for the wind tunnel tests by TUM-AER. Lift coefficient (CL=1.15) is also taken the same as in that experiment. When creating a 4-vortex system, the model was equipped with a horizontal tail wing having a span of b2/b1= 0.3. Two-vortex systems (with only main wing) were tested at two different towing speeds (U=1.71 and 1.2 m/s). Tests at U=1.71 m/s, were made with two settings of the horizontal tail, leading to circulation strengths Γ2/Γ1 =-0.3 and -0.38. Mainly a qualitative analysis has been made so far and final data analysis is not yet completed. The model was towed at a depth of 0.3 m. Contrary to most previous experiments on wakes, the complete wake flow field (both sides) was measured. In addition stereo PIV was used (both camera’s looking under about 45 deg to the wake observation area; one from the front and one from the back), resulting in 3-component velocity vectors. The towing tank is 4.5 m deep, 9 m wide and 280 m long (see Figure 40 for an impression of the test facility) and therefore there are no problems due to end-effects and/or ground effects. The laser light sheet and cameras are translated, so that the wake development can be followed up to a considerable time (non-dimensional times up to about τ= 9). The effective distance in the wake Ut/b= x/b becomes 288 (2-vortex system) or more than 600 (4-vortex system). The two-vortex system starts to develop large scale asymmetries at about x/b=169 (τ=5.3). For the Γ2/Γ1 =-0.3 case a strong interaction between inner and outer vortices occurs at about x/b=30 (τ=0.39) and a new 2-vortex system (with decreased circulation strength and increased vortex spacing) develops thereafter. However, due to the larger vortex spacing, the decay of the new vortex system progresses much slower than for the 2-vortex system. A fairly complete data-base up to long wake evolution times has been obtained, but further analysis of the data is needed to quantify the decay of circulation strength an the evolution of the vortex core radii. Some PIV data are shown in Figure 41 and Figure 42.

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3 WP 2: Vortex interactions with jets and wakes

3.1 Task 2.1: Vortex interactions with jets 3.1.1 Task 2.1.1: Cold engine jets In order to choose realistic vortex core sizes, jet velocities and temperatures for experiments and numerical simulation studies, an engineering assessment was made by NLR at the start of the project (Ref. 64). An overview of main sub-Task results is given in Refs. 66-67. The main finding of the work is that a jet can have a significant effect on the vorticity distribution in a vortex core, provided that during the vortex jet interaction the jet velocity is still sufficiently strong. Since the peak jet excess velocity decays quite rapidly (about as 1/x), the initial jet velocity needs to be sufficiently large and/or the initial distance between the jet and the developing vortex needs to be sufficiently small. If this is the case this can effectively reduce the maximum cross-flow velocity around the vortex. Detailed results are discussed below. Flow field measurement data from the C-Wake project has been released by Airbus under a non-disclosure agreement between Airbus and NLR. Wake data at two position (x/b=0.3 and x/b=1.3) behind the wing tip of a realistic Airbus type half model were analysed (Ref. 65). The data include four high-lift flap arrangements tested at four different thrust levels (simulated with Turbo-Power Simulators), ranging from zero thrust to thrust for level flight. At high thrust levels the jet has a significant effect on the nearby flap edge vortex. Peak vorticity is significantly reduced and vortex core size is increased as a result of the interaction (see Figure 43). This means that, especially during take-off conditions where the thrust levels are even significantly larger than in the experiment, cross-flow velocities in the flap tip vortex are reduced. The wind tunnel data are restricted to the very near wake, so it can not be concluded that this effect will definitely lead to a more benign wake. As will be shown in Ref. 72 this conclusion can also not be generalised, because with some jet locations the jet interference effect may lead to cross-flow velocity profiles with smaller vortex core and larger velocities. It critically depends on jet vortex distance and jet orientation. U-Bath performed flow visualization work on single jet- vortex interaction in a water tunnel and extensive PIV measurements, both in a wind and a water tunnel (Ref. 68). Parametric effects of jet-to-vortex distance (h/Dj between 1.4 and 6.7), ratio of jet strength to vortex strength (Rj between 0 and 4.5), jet inclination (between -15 and +15 deg) and Reynolds number (Γ/ν= 5500 or 33000) have been investigated. The jet was placed at a certain distance h below the wing-tip. Just as in Ref. 65, the maximum vorticity and maximum cross-flow velocity decay with increasing Rj and or decreasing h/Dj. Figure 44 gives an example from flow visualisation tests in the water tunnel, showing the merging process between jet and vortex. Figure 45 shows that,

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just as from the NLR analysis of Airbus data, the vorticity is strongly reduced when the jet intensity increases. In a few experiments jet inclination angle was changed, while keeping (initial) distance between jet exit and wingtip constant. When the jet was pointed towards the vortex core this led to an earlier and therefore more intense jet-vortex interaction. U-Bath performed further experiments in order to understand the effect of an axial jet on the merging process of a flap-edge and wing-tip co-rotating vortex pair in the near wake (Ref. 71 and Ref. 75). Cross-flow velocity measurements and flow visualisation were performed for three realistic jet positions on both equal and unequal strength co-rotating vortices for a range of jet momentum coefficients. For a given jet strength, Figure 46 shows flow visualisation results for two jet positions with respect to the equal strength co-rotating flap and wing-tip vortex. Figure 47 shows the very different effect of jet strength on vortex merging for the two different jet locations. The effect on the vortex merging process critically depends on the initial jet position. If the jet turbulence interacts rapidly with only one of the vortices, severe diffusion of that vortex occurs which ultimately wraps around and becomes consumed by the unaffected vortex structure. The jet causes a reduction in the vortex spacing and an increase in the rotation angle, hence merging is promoted. If the jet turbulence does not interact directly with either vortex, but instead interferes with the mechanism in the outer-recirculation region that advects vorticity to a larger radius, then vortex merging can be retarded: an increase in vortex spacing and reduction in rotation angle then occurred. Increasing the jet momentum, hence introducing more turbulence into the flow, has a large effect on the merging process. The findings of this study, in particular the sensitive effect of jet position (depending on particular aircraft) and the large effect of jet momentum (depending on flight phase), have implications for the practical usage of the effect, e.g. during take-off condition.

Finally, U-Bath performed dedicated experiments on the effect of vortex / pulsed jet interaction. These experiments had to be made at a lower flow velocity than the previous experiments reported in Ref. 71. Results presented in Ref. 74 show that pulsation with realistic small amplitudes (in majority of the tests the rms in jet velocity at optimum jet disturbance frequency was less than 7%) has a negligible effect on single jet/ vortex interaction. Separate testing of isolated pulsed or non-pulsed jets revealed that, at jet-vortex distances representative for normal engine jet-vortex interaction, there no visible effect on jet flow turbulence. For jet pulsation to be effective the jet has to interact rapidly with the vortex, so initial spacing has to be rather close. Similar tests with equal strength co-rotating vortices and with the pulsed jet either placed inboard or below the simulated flap vortex showed no appreciable effect on vortex merging. Only a very minor effect was observed when the jet was placed below the flap vortex. At this position the jet interacts earlier with the flap vortex, so some added turbulence effect from the pulsation is still active. In a next set of experiments pulsating and non pulsating jets were tested

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at the symmetry plane between two counter rotating vortices. Again no appreciable effects of pulsation were found. Recognizing that jet pulsation for jet positions representative for normal engine jet locations did not show appreciable effects, in a final set of experiments a small pulsating jet (a so called control jet) was tested at difference distances above a single vortex. Non-pulsating jets had the largest effect when placed in the region outside (but close to) the vortex core. Pulsation did not show any appreciable effect (see Figure 48). ONERA made time-developing LES simulations (with periodic boundary conditions in axial direction) for cold jet vortex interaction (Ref. 69). Initial jet and vortex conditions at x/b=0.1 were approximately matched to experimental conditions of the ONERA experiment described in Ref. 82. The initial distance between the jet and the vortex was taken 0.1b horizontally and 0.05b vertically. The computations were split in two phases: the jet phase and the interaction phase. The jet simulation stopped when the maximum velocity in the jet had decreased to that of the experimentally observed peak velocity at x/b=0.1. In the next step a Lamb-Oseen vortex was added, with circulation strength and core radius approximately matched to the experimental conditions. The simulations reveal a complex interaction between the vortex and the turbulent jet. When the jet is deflected around the vortex, vortical structures become twisted around the vortex core and turbulent kinetic energy increases rapidly around the core. At later times the kinetic energy in the flow diminishes and core size is growing due to the enhanced diffusion (which is characteristic for interaction of vortical structures of different orientation). Figure 49 shows results for the different phases of the vortex jet interaction. CERFACS performed temporal LES simulations for an isolated cold turbulent jet interacting with a vortex. Results are reported in Ref. 70. Different parametric conditions representing cruise, take-off and approach conditions and two different distances between vortex and jet were simulated. The cruise condition was simulated for two characteristic distances between wing tip vortex and jet (Δy/b=0.145 and 0.290, Δz=-0.058b) and, as ONERA, a two-phase simulation strategy was used. When the distance becomes smaller, the interaction is more intense and the decay of peak vorticity and increase in core size growth is more effective. For the approach and take-off condition the spanwise distance between vortex and jet was taken equal to zero (assuming jet engine close to a flap edge position) and simulations had to be started from a laminar jet-vortex interaction. In the take-off condition the jet has a considerable effect on the coherence of the vortex, leading to a large increase of the vortex core. Figure 50 shows iso-vorticity contours for the cruise conditions showing the jet vortex interaction at different distances downstream. Figure 51 shows the downstream development of the circulation profile for the different conditions investigated. The overshoot on the circulation profile is a strong

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indication for enhanced diffusion. Indeed there is a very large effect during high trust conditions, leading to a large vortex core. However total circulation strength (at larger distance from the core) is not affected. TU-Delft performed stereo-PIV measurements behind a generic wing model with a 2/3 span flap with jet simulators (SWIM-J model, Ref. 72) placed at three different positions with respect to flap edge. An extensive data set has been obtained in a towing tank, representing the complete development of the vortex wake encompassing the roll-up, vortex merging and mid to far field phase (x/b ≈ 100). To obtain accurate vortex related parameters like vortex core radius, velocity distribution, etc. a Double-Gaussian (DG) vortex model was proposed. It fitted the experimental data exceptionally well. The jet effect on the total circulation strength is limited, but significant effects are seen in the velocity distributions and related parameters like the vortex core radius. Figure 52 shows for two different model angles of attack (α=0 and 6 deg) a comparison of fitted profiles at non-dimensional time τ=0.73 (corresponding to x/b=36 at α=0 and x/b= 22 at α=6 deg: well after the merging of both vortices) and with- and without operating jet. For the cases shown, the jet has been placed directly below the flap tip. The shape of the vortex velocity profile after merging changes both with model angle of attack (jets rotate with the model) as well as with jet velocity. The results have been used in a approximate wake encounter rolling moment analysis. Two generic leader (A380 and B747) and follower aircraft (F50 and B737) were taken and it was found that the jet effect on the induced rolling moment can be larger than the difference in induced rolling moment caused by both leader aircraft. Hence it was concluded that the application of a well tuned jet effect (optimized position and jet velocity), may lead to a reduced rolling moment upset for follower aircraft. UCL (Ref. 73) performed time developing LES simulations of the effect of two jets on the wake development of a propelled wing in cruise configuration using its VIC-PFM method (a combination of Lagrangian and finite difference methods). The length of the computational box is 0.5b, so only short and medium wavelength disturbances can develop in the simulation. The initial conditions correspond to an elliptically loaded wing wake with velocity deficit (as investigated in detail in Ref. 92), but with two turbulent cold jets added at 60% of the wingspan and 0.058b below the wake. This position of the jets is characteristic for a 2-engined aircraft. The strength of the jets is about taken equal to the drag of the wing, so realistic for the cruise condition. The wake of the propelled wing is compared to that of the isolated wing investigated in Ref. 92. Since the simulation of the jets required a higher numerical resolution (h/b= 1/400 instead of 1/200), the case without jet has also been re-computed with the higher grid resolution, enabling a comparison with Ref. 92 results. Figure 53shows the initial conditions. Figure 54 compares the computed average axial vorticity and velocity distributions at approximately x/b= 2.4 for the propelled and non-propelled wake. Figure 55 compares the three-dimensional iso-vorticity structures (coloured by the magnitude of the axial velocity: red indicates jet related

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parts) at x/b=2.4. The main conclusion is that the global wake physics is hardly influenced by the jets, but it should be noted that this result applies for a case where the initial distance between the jet and the wing-tip vortex is rather large (more than 0.2b). Later, numerical simulations were also made for a 4-engined aircraft configuration in high lift condition, starting from wind tunnel data at x/b= 0.3 as supplied by Airbus (see Ref. 67 and Ref. 65). Both time-developing and space developing LES simulations were made with the VIC-PFM method for a thrust for level flight condition (highest thrust tested by Airbus). The time-developing simulation is made within a L/b=1 long computational box until non-dimensional time τ= 1.1 (corresponding to x/b= 35). The space developing simulation is made up to x/b= 5. Based on comparison with experimental data (available at last experimental station x/b=1.3), it is concluded that the space time simulations give better results for the axial velocity, because the spatio-temporal development of the jet can be correctly simulated. Figure 56 shows a comparison between the calculated results and the experimental data at x/b= 1.3. Over the full computed length of the wake both methods give comparable results in terms of vortex positions, vorticity distribution, vortex core radii and averaged circulation profiles. Figure 57 shows the circulation distribution after complete roll-up, as predicted with the temporal approach at x/b= 19.3, showing the two-layer nature of the vortex core. Such information is important for predicting the effects on follower aircraft. For the same high-thrust configuration temporal LES simulations were also performed by CERFACS and showed good comparison with the results from UCL (Ref. 67). CERFACS also simulated a zero thrust case, showing a significant delay in vortex merging and a substantially smaller vortex core after merging of wing tip and flap tip vortex (see Figure 58). The main outcome of this work of UCL and CERFACS is that LES simulations can be initiated from experimental data. This enables a realistic prediction of wake development much farther downstream than possible in the wind tunnel tests. 3.1.2 Task 2.1.2: Hot engine jets CUT performed LES analysis of the influence of axial and helical disturbances at the jet inlet boundary for isothermal and non-isothermal conditions (Ref. 78). Initially, important differences with the experimental data from CUT were observed. Additionally work concentrated on the generation of correct inflow boundary conditions. The “real” turbulence imposed at the inlet boundary has an important effect on the flow field evolution both for the excited, as well as for the natural jet. For the investigated inlet turbulence levels 0.5% and 2%, the influence of the shear layer thickness appears very significant. For a thick boundary layer, the length of the potential core is increased significantly, compared to the case with a thin shear

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layer. The configuration with ratio between inlet momentum thickness with respect to jet diameter equal to 1/40 was computed with different forcing frequencies, results are shown in Figure 59. A theoretical and computational study on hot and cold vortex cores was made by ONERA. Results are presented in two publications (Refs. 83-84). ONERA first performed a stability analysis of a vortex with temperature variations in its core (Ref. 79). Both centrifugal and Rayleigh-Taylor instabilities were investigated. The centrifugal instability (CTI) mainly influences axi-symmetric, short axial wavelength eigen-modes. The Rayleigh-Taylor instability (RTI) mainly influences non axi-symmetric, two-dimensional eigen-modes. For a family of model flows with a Gaussian vortex and a density variation represented by a Gaussian distribution, a full characterization of amplification rates and the structure of the most amplified eigen-modes was given. Necessary conditions for those instabilities to occur are presented. An overview of CTI and RTI instabilities is given in Figure 60. The velocity and temperature profile family is defined by parameters b (ratio between hot jet and vortex core radius) and C (density ratio of the hot jet), see top of Figure 60. ONERA also performed 2D Direct Numerical Simulation (DNS) of a two-dimensional Lamb-Oseen vortex with a heavy internal core (Ref. 79). The DNS first exhibits wavy azimuthal perturbations which are non-linearly distorted into bubble-like patterns, characteristic for Rayleigh-Taylor type instabilities. However, in the later stage of development of the instability, contrary to the standard case, the bubbles are then stretched in the azimuthal direction leading to a strong radial filamentation of the flow. From these results, shown in Figure 61, the practical applicability of density effects for enhanced vortex decay is estimated to be rather poor. However, the observed mechanism is very powerful for mixing and could be used in the field of mixing and combustion. In a different study (Ref. 80) ONERA performed LES simulations of turbulent hot jet/vortex interaction using the same code as for the simulation of cold jets (Ref. 69). The jet temperature was taken two times the ambient temperature (similar as in cruise conditions). Three different distances between jet and vortex core were simulated, one of which is with the jet in the vortex core. With jet and vortex position being separated, basically the same jet/vortex interaction mechanisms are observed as for the cold jet (Ref. 69). The passive scalar (jet temperature) decreases rapidly and does not enter the vortex core. When the jet is injected in the vortex core, the passive scalar (temperature) remains concentrated in it and seems not to be able to escape from the core region. This behaviour is consistent with the “dispersion buffer” region, introduced by Jacquin and Pantano (Ref. 85).

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ONERA also performed experiments on hot and cold jet/vortex interaction (Ref. 82). A straight NACA 0012 airfoil wing of 0.5 m span was combined with two 10 mm diameter jets. Previous tests had been made with the same model, but other jet positions, as part of the Eurowake project. Pitot tube measurements were made at x/b= 0.002, 0.007, 0.020, 0.070, 0.100 and 0.200. LDA measurements were made at x/b=1 and 3 and with the jets at 0.05b and 0.1b from the wing-tips. The combined results of hot and cold jet interactions have been distributed on a CD-Rom. The main conclusion is that the hot jet behaves almost as a passive scalar. Figure 62 shows the test set-up and a comparison of axial flow distributions close behind the trailing edge of the wing. In most of the cases the jet plume is just wrapped around the vortices without penetrating significantly in the vortex cores. Only when the jet-vortex spacing became very small one observes that the jets are trapped into the vortices, where they remain confined afterwards (see Figure 63). CERFACS performed temporal LES simulations on the interaction of a “hot” jet with a vortex for take-off, approach and cruise conditions. The same configurations, with the same specific thrust setting, as in subtask 2.1.1 were simulated (Ref. 81). The results indicate that the jet temperature has some direct effect on the development of the jet (e.g. the jet rises due to buoyancy effects), but it has no major effect on the jet vortex interaction mechanisms. A summary of sub-Task results is given in Ref 77. 3.2 Task 2.2: Vortex interactions with wakes 3.2.1 Task 2.2.1: Effect of fuselage on vortex wake The lateral distance between vorticity centroids (the vortex spacing) plays an important role in wake decay and transport. Airbus performed an analysis (Ref. 87) on possible fuselage effects, using existing wind tunnel data from the Awiator project. The analysis focussed on the lift carry-over from wing to fuselage and its possible effect on vorticity centroid position. It was concluded that even minor details of the lift-carry over can have a considerable effect on the vorticity centroid position in the wake. Figure 64 shows a typical example for a fictitious load distribution as derived from 5-hole rake measurements and the derived vorticity centroid positions for the original (blue) and modified (red) load-distribution. The effect of the fuselage on the structure of the wake vortex system has been studied experimentally by TUM-AER and RANS simulations were made by DLR (TAU code) and CENAERO (Argo code). The results have been reported in Ref. 86 and in Ref. 88. CENAERO first generated the CAD description and afterwards DLR generated initial coarse meshes for the TAK wind-tunnel model geometries that were tested in the TUM-AER wind tunnel (body alone,

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body plus horizontal tail, body plus wing and complete body plus wing plus horizontal tail geometry). DLR made RANS calculations at wind tunnel and full scale Reynolds number. In an extra simulation the effect of the wind tunnel walls and model peniche was also simulated to enable a direct comparison with the experiments. DLR used k-ω SST and Reynolds Stress Model (RSM) and computations were made at low (wind tunnel) and high (full scale) Reynolds number. Some grid refinement studies were made by DLR. CENAERO also performed simulations for the fuselage alone case using medium and fine grids. Iso-vorticity contour results at x*=0.37 (just aft of fuselage tail) for low-Reynolds fuselage alone, using different turbulence model and grid adaptation, are shown in Figure 65. On the coarse grids vortical structures in the wake, although qualitatively similar, appear too weak and too much diffused compared to the experimental data. The use of a RSM model gives some improvement over the k-ω model, but a larger improvement is obtained after grid adaptation (DLR results, shown in Figure 65d). A clear improvement is also observed for the CENAERO result on the fine mesh. For the present case of stable separated flow from the aft fuselage, the usage of RANS/DES does not improve this result anymore. Half-model testing in wind tunnels is a topic of high practical interest. Usually it is attempted to eliminate the effect of the tunnel wall boundary layers by placing the model on a so-called peniche. On the initial coarse computational mesh DLR made a systematic investigation on the effect of peniche height and also a comparison of free-flight model against wind tunnel, showing differences in wake flow topology. In the wind tunnel the inboard vortices appear more inboard and the outboard vortices more outboard, compared to the free flight condition. Finally DLR also performed a Reynolds number effect investigation showing that the prime effect is an overall lift increase, with only little effect on the span-wise lift distribution. The complex vortical flow around an isolated landing gear was also calculated and reported in Ref. 86 (though strictly belonging to Task 2.2.2). The computed vortex topology is shown in Figure 67. 3.2.2 Task 2.2.2: Wakes generated by wing elements TUM-AER designed and manufactured a landing gear for the TAK model and performed a wind tunnel test campaign during which time dependent flow velocities were measured at several planes downstream, using a triple hot-wire probe. The landing gear wake is only visible as a weak distributed stream-wise vorticity region with minor effect on the surrounding flow. It produces a large region with increased turbulence intensities. The levels of this turbulence are in the same range as of the turbulent wing vortex sheet (see Figure 66a). Results until x/b= 1 have been reported in Ref. 89 (see Figure 66b), more downstream wake results with landing gear have been reported in Ref. 90. Spectral analysis of the hot-wire signals shows broadband turbulence without preferred frequency peaks. Apart from a region with increased turbulence level and a small effect on vortex position of the horizontal tail plane, the landing gear does not

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seem to have an influence on the overall wake development, even at the most downstream station x/b=4.7 (see Figure 66c). TUM-AER also performed extensive wind tunnel surveys for various TAK model configurations (see Ref. 90 and Ref 91).

• Baseline • Baseline without through flow nacelles • Baseline without winglet • Baseline without winglet and without horizontal tail

All configurations were tested at α=7 deg and mean and turbulent flow measurements were made at x/b=0.37, 1, 2, 3, 4 and 4.7. The corresponding lift was measured with a force balance. Inspection of the flow field for the configuration without nacelles against the flow field with nacelles allows discrimination between wing and flap edge vortices and vortices created by the nacelles. Configurations without winglet lead to a wing-tip vortex with a smaller core radius and a larger peak vorticity and also create a significantly larger rotation velocity for the wing-tip and flap-tip vortex. The created data-base, providing detailed information on wake evolution for different geometries, might be very useful for CFD validation. UCL performed a rather fundamental temporal LES simulation of the wake roll-up behind an elliptically loaded wing with a finite vortex sheet thickness (Ref. 92). In a next step a wake velocity defect model was added and wake roll-up simulations were performed at two different Reynolds numbers (ReΓ= 104 and 106). Figure 68 compares computed axial vorticity distributions with and without simulated axial velocity defect. Without simulated velocity defect the wake roll-up behaves laminar-like. With simulated velocity defect, the wake develops instabilities due to the stretching of spanwise and vertical vorticity components (induced by the axial velocity deficit). Results shown in Figure 69 display vortex like structures near the wake symmetry plane and the wrapping of these structures around the vortex core. Already at relatively early times, this induces deformations of the primary vortex, which are likely related to the vortex meandering effect that is often observed in experiments. However, as shown in Figure 70, there is only a relatively minor effect on the shape of the average cross-flow and circulation profile. Only a mildly faster decay of peak cross-flow velocity is observed for the case with simulated velocity defect. Later the same wake was also computed with a simulated jet (see Ref. 73).

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4 WP 3: Wake evolution near the ground

4.1 Task 3.1: Dynamics and decay in idealized conditions 4.1.1 Subtask 3.1.1: Longitudinal uniform wakes UCL investigated the effect on wing span-loading due to the presence of the ground (Ref. 93). Using a panel method it was found that the lift coefficient of a 2D airfoil near ground is only modified when height/chord ratio h/c<1 (see Figure 71), so this is negligible for normal aircraft wings. Using a modified lifting line theory, different wing plan forms (elliptic, rectangular and double-elliptic) were analysed in the presence of the ground. The double-elliptic wing case simulates a part span flap configuration. It was found that significant changes in span-loading only occur when h/b becomes less then 0.5. Span-loading results were used to initiate time developing vortex-roll-up IGE simulations, including viscous ground effect. Simulations for an elliptic loaded wing were made for initial vortex heights h/b=1.0, 0.5, 0.25 and 0.125 at ReΓ= 10000 and for h/b=0.25 at different Reynolds numbers (ReΓ= 5000, 10000, 20000 and 100000). Wake roll-up is only effected by ground when h/b<0.25. Reynolds number effects are seen to be moderate, even in ground effect (see Figure 72). These results are important for the definition of test cases with more advanced numerical methods. UCL also performed 3D vortex filament simulations (inviscid) of vortex instabilities NGE/IGE (Ref. 98). Since viscous interaction with the ground is known to be important, the application with an inviscid method has been restricted to the analysis of long-wave (Crow-type) instabilities for wake vortices IGE. Two cases have been considered:

• A configuration close to the one studied by CNRS-IRPHE (a thick vortex pair with forced long wave instability). These results were very close to the experiment (see Figure 73).

• Aircraft like vortices IGE with different perturbation levels of forced Crow instabilities. For low initial perturbation level, the vortices enter IGE before reconnection and interact (and eventually reconnect) with their respective ground image. When initial perturbation is high enough, the vortex filaments reconnect before entering IGE, else when the vortices come close enough to the ground, the Crow mode of the vortices changes to an interaction with the image vortices (below the ground). In the transient phase this causes a tilting of the perturbation plane angle and a reduced amplification rate, but at later stages the interaction with the image vortices dominates and growth rate continues as for the original vortex pair. Examples are shown in Figure 74.

CENAERO performed LES simulations of a two-vortex system in ground effect in close co-operation with UCL. Simulations were made at Re=2x104 (Ref. 99 and Ref. 95). Two different

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sub-grid scale models were used; classical Smagorinsky and a multi-scale version of the same model (both with a Piomelli wall-damping). Laminar initial conditions, with vortices at one vortex spacing above the ground, are perturbed with small random 3D perturbations. The vortex evolution in relation to the specific type of modelling was analysed (see Figure 75). In a further test at a lower Reynolds number Re=5x103, a comparison was made with a DNS simulation by UCL. This showed clearly the superior performance of the multi-scale version of the Smagorinsky model. The simulations show the growth of instabilities while the secondary vorticity created at the ground is wrapping around the primary vortex. When the Reynolds number is increased the growth rate of these disturbances increases. The simulations clearly show the effect of ground interaction on rapid vortex decay of vortices IGE, irrespective of the atmospheric turbulence level. For vortices released at h/b0=1 the rapid decay sets in at non-dimensional time τ*=2.8. UPS-IMFT did also perform a LES simulation (Ref. 100) of a counter-rotating 4-vortex pair (Γ2/Γ1 = -0.3 with vortex spacing ratio b2/b1=0.3) at Reynolds number 2x104 (based on total circulation Γ0). These simulations were made without wind. The weaker vortex comes rapidly in interaction with the ground and develops short wavelength instabilities. The rapid decay phase sets in much earlier (τ*≈0.3, see Figure 76), than in the corresponding 2-vortex simulation made by CENAERO (τ*≈1.7). Also the circulation is decaying to half its original value already at τ*≈1.7, compared to τ*≈ 6 for the 2-vortex system. This clearly shows the benefits that such 4-vortex systems might have in ground proximity. Detailed diagnostics of the model energy and enstrophy reveals that the weaker vortices combine with the equal signed vorticity created at the wall, the combined weak vorticity wraps and loops around the main vortex and produces small scale unsteadiness faster than in the case of a 2-vortex system IGE. IRPHE performed an experimental study of the dynamics of uniform laminar counter-rotating vortex pairs approaching a solid wall (Ref. 101 and publication Ref. 102). The vortices were generated in a water tank at the edges of two impulsively rotated flat plates, and visualised using fluorescent dye. Measurements were performed using image analysis and PIV. Vortices were created at 2 vortex spacing’s above ground at ReΓ = 1900, 3500 and 5200 and at six vortex spacing’s above the ground at ReΓ = 3000 and 4000. The shape of the created vortex profile matches Lamb-Oseen quite well. The ratio between core radius and vortex spacing was around 0.2 (quite large with respect to normal aircraft vortices). For vortices created at 2 vortex spacing’s above the wall, short wavelength instabilities develop before wall effects become important, as can be clearly observed in Figure 77 and in more detail in Figure 78 and Figure 79. As detailed in Ref. 101, the very short wave-length instabilities, visible at higher Reynolds numbers, seem to be related to a centrifugal instability, originating from the way the vortices are created. The other short wavelength instabilities are elliptic instabilities, as are also observed in

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other studies (e.g. the numerical simulations by UCL, Ref. 99). As the Reynolds number increases, the primary vortices are more deformed by interaction with the secondary vortices and the bursting into small scale turbulence is enhanced. During successive rebounds the primary vortices remain at a distance between 0.6b0 and 1.3b0 form the ground. At reaching maximum altitude after rebound, the secondary vortices develop short-wavelength instabilities, affecting subsequently the primary ones. The observations and measurements show similar mechanisms than observed in full scale testing, despite the three orders of magnitude difference in Reynolds number and the relatively large a/b0 ratio in the sub-scale experiments. The precise influence of both aspects needs to be further investigated, e.g. using numerical simulations. Dedicated 2D and 3D numerical simulations for the ReΓ = 3500 case were reported by UCL (Ref. 103). Results shown in Figure 81 show a good comparison. Vortices created at 6 vortex spacing’s above the wall developed Crow instability, especially when the wake generator is adapted with a sinusoidal perturbation of wavelength 4.8b0 and amplitude 0.04b0 (with b0=0.025 m). The non-dimensional growth rate of the Crow mode, inferred from Figure 80, closely resembles the theoretical growth rate (0.83 versus 0.8). Very interesting results were observed for the Crow modes linking with the ground, but these are not of real practical value and therefore are not discussed here. A summary of sub-task 3.1.1 results is given in Ref. 94 (giving a compilation of Ref. 98 to 101). CENAERO (again with support from UCL) also performed very interesting LES simulations of vortex pairs IGE in the presence of turbulent cross wind or turbulent head wind. Simulations were made at ReΓ=2*104. Fully resolved turbulence for head and cross-wind was first computed after which the vortex pair was released in the turbulent wind field at height h/b0=1. The strength of the head or crosswind at initial height h=b0 was taken equal to the initial sink speed of the vortex pair. Compared to the no-wind case the rapid decay of the vortices sets in earlier (τ*=2.0 instead of 2.8, see Figure 82). Head and cross-wind have a similar effect. In cross-wind conditions the downwind vortex displays rapid decay a little earlier than the upwind vortex. Similarly UPS-IMFT also made simulations of a vortex pair, but now for two levels of the crosswind: V(h)/V0= 1 and V(h)/V0= 2 (with V0 being the initial sink velocity of the vortex pair). Iso-vorticity distributions for both cases are shown in Figure 83 for non-dimensional times τ*= 1 and 2. As for the UCL simulations, the downwind vortex enters the rapid decay phase earlier than the upwind vortex. A more direct comparison of results (Ref. 95) is shown in Figure 84. For the V(h)=V0 case the comparison between both computational methods is quite good. The main conclusion from this work is that the crosswind leads to an asymmetric decay and rebound behaviour of the vortices: the downwind vortex decays faster than the upwind

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vortex, especially in stronger crosswinds. Especially for the low crosswind case the downwind vortex rebounds to a higher altitude than the upwind vortex. In general the predicted vortex behaviour is in good qualitative agreement with measurements (such as reported in Refs. 108 and 109). The LES simulations are very useful to understand the physical phenomena playing a role in the interaction with the ground. IST performed stochastic 2D NS calculations for vortices IGE and cross-wind (Refs. 96 and 97). A Polynomial Chaos Expansion method for the solution of differential equations containing random/stochastic inputs of variables is used. This leads to a coupled system of Navier Stokes equations. In the study subsequently three uncertainty sources with 10% random input and uniform uncertainty distribution have been considered for a 2-vortex system released at one vortex spacing above the ground and at Re=5x103:

• Initial circulation of one of the vortices (see Figure 85) • Initial position of one of the vortices • Magnitude of crosswind

The solution of the coupled system is shown to be at least 103 times faster than a classical Monte-Carlo simulation. The results, amongst other, show the effect on variation in vortex trajectories and variability of the circulation decay depending on the particular effect investigated. 4.1.2 Subtask 3.1.2: Spatially evolving wakes A summary of results of this sub-task is given in Ref. 104. Airbus provided wake vortex data for a set of B747 aircraft wakes, measured at Frankfurt airport with lidar. These results have been analysed by NLR in Task 3.2. DLR made stereo PIV measurements in the WSG towing-tank facility at Göttingen using the F13 model to generate 2- and 4-vortex systems in ground effect (Ref. 105). The ground effect was created with a ground-plate (of finite streamwise extend), placed at different heights. Figure 86 shows the test set-up and the development of the separating vorticity layer for the 2-vortex configuration case with vortices released at 0.25b above the ground. Figure 87 and Figure 88 show vortex trajectories and circulation decay as evaluated for the co-rotating Γ2/Γ1=0.3 and counter-rotating Γ2/Γ1=-0.3 vortex pairs, created at h/b=0.5, 0.25 or 0.125 above the ground. UCL performed interesting flow visualisation studies of 2-vortex systems IGE. Construction of the model (based on Wortmann FX137B-PT profile), optimization of the dye injection procedure, preliminary visualizations to determine the best way to generate laminar trailing vortices and the testing of some devices to alleviate end-effects was made in the preparatory

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phase. The results of the flow visualisations were reported in Ref. 106. Cross-section (laser sheet) and volume (black light illumination LIF) visualisations of the primary vortices (green), the ground generated boundary layer (red), and the orbiting secondary vorticity (red) were performed for three altitudes of the wing model above the ground (h0/b0 = 0.5, 0.25, 0.125) at a model chord Reynolds number Rec= 4x104 (ReΓ=3.2x104). If vortices are created at low altitude, the interaction with the ground sets in quicker. Figure 89 shows the entrainment of ground turbulence around the vortices (h/b0=0.25 case). Vortex trajectories were obtained from image analysis of cross-section visualisations. The results were qualitatively compared, when possible, to available investigations of wake vortices IGE. For h0 = 0.25b0 and below, the roll-up process is significantly influenced by the ground (in agreement with Ref. 93). The visualisations show that in the beginning the flow is still well organised, but than quickly develops large disturbances, like if an ‘end-effect’ is propagating along the vortex. However, this ‘end-effect’ appears to travel with the speed of the wing model and therefore qualitatively resembles the numerical simulation of a spatial developing wake (Ref. 107), where a rapid distortion of the flow occurs at a certain distance behind the wing. These visualisations support the numerical simulations of vortices IGE, as reported in Ref. 95, Ref. 99, Ref. 104 and Ref. 107. UCL performed very challenging (70 million grid points!) LES calculations of a spatially evolving vortex wake of an elliptically loaded wing IGE (Ref. 107). The simulation was made possible by assuming a high lift coefficient (CL=6 instead of the usual 1.5, allowing for a shorter computational box) and by considering a relatively low initial vortex position (h/b0=0.25) such that all time evolutions perform quicker, allowing to confine the stream-wise extend of the computational domain to 12.5b. The space-developing simulation was carried out on 32 processors for sufficiently long times (~104 time steps) in order to reach the regime state and then to obtain statistically converged time-averaged quantities. Results of the well developed wake are shown in Figure 90. The same configuration was also investigated in a time-developing and in a 2D LES computation. The three simulation results have been compared. Figure 91 shows a comparison of the averaged vorticity fields. The main results are:

• During the (essentially two-dimensional) initial phase, the results match well with the 2D reference configuration.

• The space-developing case transitions earlier to turbulence than the time developing one. This is partly due to the larger initial perturbation (induced by the inflow condition) in the space-developing case.

• The main difference is the significant axial velocity defect obtained in the space developing case due to the helical vortex rollup of the vortex sheet emanating from the wing, and leading to additional instabilities. However, this phenomenon is here also artificially increased due to the use of a larger lift coefficient.

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• Longitudinal uniform wake simulations (time-developing) are certainly a valid tool although some specific features of rapidly space developing flows can not be ignored.

4.2 Task 3.2: Dynamics and decay in real conditions DLR performed an analysis of pulsed LIDAR measurements taken at Frankfurt airport from August to December 2004 (Ref. 108). A total of 282 wake vortex pairs generated in ground proximity by aircraft in approach landing phase to the closely spaced parallel runways 25L and 25R were collected and analysed in detail. Results have been presented in an article for the Journal of Aircraft (Ref. 112) and at an AIAA Conference (Ref. 113). The nominal height of the aircraft passing the LIDAR measurement plane was 55 (runway 25L) and 61 m (runway 25R). The data-set is quite unique since it also combines very nearby measurements of a wind-line and a SODAR/RASS wind/temperature profiler. Together with runway-log information this provides a high quality data-set for statistic wake vortex transport and decay analysis as well as for improved modelling of WV rebound in ground effect in the presence of relative mild cross-winds (up to 5 m/s). The test site and the position of the LIDAR and SODAR/RASS are shown in Figure 92a. The scatter plot of all measured lateral wake vortex positions (Figure 92b, with y measured with respect to LIDAR position and normal to the runways) shows that winds are predominantly from the south. This leads to vortex transport in positive y direction. Also, vortices created in weak crosswind condition tend to live longer (up to about 200 seconds). Figure 92c shows a scatter plot of average lateral transport velocity of luff and lee side vortices as function of the crosswind measured at z*=0.6b0. Assuming maximum 15 m lateral deviation of the aircraft from the runway centre, plus a minimum required distance of 30 m between vortex core and aircraft fuselage, the luff vortex has to travel up to 0.5b0+ 2*15 m+ 30 m ≈ 84 m. Then, a 5NM separation distance corresponds to about 125s separation time, requiring at least 0.67 m/s average wake vortex transport velocity for runway clearance. Similarly a 2NM separation requires at least 1.7 m/s lateral transport velocity. These values have been used for the safety corridors displayed in Figure 92c. The rightmost symbol in the dark shaded area corresponds to a crosswind magnitude of 2.6 m/s (2.5 m/s at 10 m height). The rightmost symbol in the light shaded area corresponds to a crosswind magnitude of 3.6 m/s (3.3 m/s at 10 m height). Though these values are approximate, and only apply for the investigated position along flight track, this indicates a potential for safe reduction of minimum aircraft separation distances under cross-wind conditions. Figure 92d shows a scatter plot of normalized circulation strength Γ* against non-dimensional time t* for a subset of 127 approaches to runway 25R. The line corresponds to the median value determined within a running window of width Δt*= 1. The broken line is a fit to these median data using the D2P model. At larger times the model does not seem to fit the data. However, subsequent analysis showed that this is due to a bias in the lidar data, which increasingly fails to track the vortices once they have decayed, especially when decayed below Γ*= 0.3. Figure 93 shows a comparison of rebound behaviour in minor and mild

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crosswind conditions, showing the clear asymmetric rebound effect in (mild) crosswind. The main conclusions from this work are:

• Crosswind in ground effect condition leads to a substantial difference in rebound characteristics for the luff and leeside vortex, because cross-wind shear attenuates/ intensifies the formation of counter rotating vorticity around the luff/lee-side vortex.

• A relative small cross-wind (e.g. about 1.5 to 2m/s at 10m altitude) is already sufficient to trigger pronounced asymmetric rebound behaviour.

• Crosswind causes only a weak asymmetric decay rate for the luff and lee-side vortices. • A clear correlation between ambient turbulence and vortex decay is found. However

this turns out to be not significant to wake prediction skill. • Good vortex prediction IGE is achieved based on simply crosswind and aircraft data. • For single runway applications, a relatively mild crosswind of 2.5 m/s (a conservative

value, based on 10-minute averaged crosswind at 10m height) is sufficient to blow the vortices out of the flight corridor when aircraft separation is 5Nm. For 2.5 Nm separations (minimum radar distance) the required cross-wind would be 3.3 m/s.

• These results show the potential for applying cross-wind dependent wake vortex separation standards for enhanced airport landing capacity during rush hours (tactical usage).

• Some data have been recorded in the presence of jet-like shear layers (aloft of the wake generation height) and a clear influence due to the interaction between the rebounded vortices and the shear layer can be observed. These data segments should be used for improved wake vortex modelling in cross-wind shear conditions.

• Analysis of the experimental data led to an improvement of the P2P modelling of wake vortices in ground effect.

In an accompanying study, using a sub-set (B747 wakes only) of the same dataset as used by DLR, NLR investigated the vortex transport and decay in relation to crosswind, atmospheric turbulence and thermal stratification of the atmosphere. NLR entirely focussed on the data as such, without referring to correlation with a specific vortex prediction model. Results are given in Ref. 109. Figure 94 shows the circulation strength at the initial and final observation time for the B747 data, giving some impression on the mean wake decay. It can also be noted that sometimes the vortices can no longer be tracked (and circulation strength no longer determined) by the lidar, even though the last measured circulation strength is still rather strong. Figure 95 shows the final observed lateral wake position as function of the crosswind magnitude (at 40m altitude), indicating that some of the vortices created at runway 25L do almost travel to runway 25R. The right hand side of the same figure shows the lateral position and altitude at the moment of reaching the maximum altitude, indicating that some vortices rise to high altitude due to the presence of a cross-wind shear. Figure 96 shows as an example the vortex trajectories

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and the atmospheric (wind and temperature) profiles for one of the cases. Even though the quality of the measured data (vortex strengths and positions) is high, the lidar observation time is often not conclusive for the actual wake vortex life-time. As shown in Figure 97 the results on asymmetric rebound in crosswind do support the DLR conclusions. In addition an inventory was made with the much poorer quality selected data from Memphis database (only vortex pairs that show clear rebound IGE). This confirmed the asymmetric rebound behaviour in crosswind, as observed in the Frankfurt data. 4.3 Task 3.3: Assessment and real-time modelling Based on the Method of Discrete Vortices (MDV), a new wake vortex predictor (DVM) was developed by UCL. The new model is based on the numerical methodology and physical models of the Vortex Forecast System (VFS, see Ref. 111), but UCL developed an improved model to determine the circulation and position of the secondary vortex particles. In addition also a new IGE decay model was developed, based on the exchange between primary and secondary vorticity. An improved evaluation of meteorological profile input was obtained by fitting the profiles with B-splines instead of the formerly used cubic-splines. This let to smoother profiles and a less subjective evaluation of derivatives needed in the wind shear and stratification models. The new DVM model has been calibrated against LES results from CENAERO/UCL with- and without crosswind and against data from the WakeFra test campaign (110 cases for B747 aircraft landing at Frankfurt, see Task 3.2). Figure 98 shows a comparison of previous VFS and new MDV model performance against LES simulation results for wake vortex rebound in crosswind conditions. Clearly the new model performs better than the old version. The new MDV model has been integrated in a probabilistic method (PVM) based on Monte-Carlo simulations, allowing for a realistic range of variability in model input parameters. Results are reported in Ref. 110. Work of DLR in this sub-Task has partly been reported in Ref. 110, Ref. 108 and in Ref. 113. The P2P model has been adapted by taking into account the results of Task 3.1 and 3.2. The rapid decay model has been adapted to take account of the rapid decay observed in ground proximity shortly after vortex rebound (see Figure 99). The P2P model was also adapted (see Figure 100) in order to mimic asymmetric rebound in crosswind as observed in lidar measurements (see e.g. Figure 93). The model has also been modified in case vortices are created at an altitude below one vortex spacing. In that case the location of the secondary vortices created near the ground has been adapted and the effective viscosity in the rapid decay model is modified in order to simulate a more rapid decay. Comparison to the original model performance reported in Ref. 112, the deterministic skill of the model is improved by 58%, 69% and 29% for lateral position, vertical position and circulation, respectively (see Ref. 113).

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5 Conclusions and recommendations

An overview of the main exploitable and scientific results, with a classification for the difficulty to exploit, the practical implication and their scientific importance, is given in Table 2. A large number of publications resulted from the work and many more have been submitted. In this respect the FAR-Wake project is already highly successful. 5.1 Synthesis of main WP1 results Much progress has been made in the mapping and the physical understanding of the role of vortex instabilities. In particular from the combined experimental and theoretical work it became clear that vortex meandering is due to the transient growth of a vortex displacement mode due to background turbulence. A quite complete mapping of viscous core modes has been made as well and resulted in a number of publications. Numerical simulation of end-effects induced by local vortex core perturbations (using different simulation strategies: either local core size variation or acceleration/deceleration), combined with dedicated experiments improved the understanding of the end-effects, as experienced in sub-scale testing in water tanks and ONERA catapult facility. Numerical simulations, experiments and analytical stability analysis improved the physical understanding of short wave-length elliptic instabilities and the role of axial core flow during the merging of co- and counter rotating vortices. Linear temporal stability of co- and counter-rotating vortices with axial flow has been obtained for a large range of parameters. The instability can be described as a resonance phenomenon of Kelvin waves. This work permitted to understand why, when axial flow increases, the sinuous mode (the most unstable mode without axial flow) stabilizes and new instability modes involving combinations of Kelvin modes of different azimuthal wavenumber arise, depending on axial flow parameter. At small vortex separation distance a wide range of instability modes was observed. It was shown that, after a linear growth of instabilities, a strongly non-linear phase occurs, leading to vortex breakdown and the re-formation of a weaker vortex with a larger core. The non-linear dynamics and the vortex core size were found to depend on the linear modes involved in the elliptic instability. Direct numerical simulation of the spatial development of the instability has been performed for co-rotating vortices with axial flow. Results qualitatively agree with the temporal evolution. Experiments made for counter-rotating vortices showed an m=2 azimuthal mode structure and the measured wavelength and growth rate were in reasonable good agreement with the theoretical/numerical results.

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For long-wavelength instabilities the effect of flow turbulence has been investigated experimentally for a pair of counter rotating vortices. Flow turbulence increased vortex meandering and favoured Crow instability. LES simulations of various four vortex systems showed that with b2/b1=0.3 a significant enhanced vortex decay is already obtained for a circulation strength ratio of about Γ2/Γ1 = -0.2, a much more practical value than the optimum case Γ2/Γ1 = -0.3. From linear stability theory and numerical simulations interesting results were obtained for the optimum forcing of Crow modes for 4-vortex wakes with counter-rotating vortices. The optimum forcing location appears to be close to the wake symmetry plane and this offers some benefits. Practical implications and exploitation of this result should be further investigated. Experiments in the Potsdam towing tank showed a strong interaction of main and counter rotating vortex at about x/b=30, with a substantial decay of circulation strength and an increase in core radius. However, the newly developed 2-vortex system has a larger lateral spacing and sinks and decays slower than a corresponding (same lift) 2 vortex configuration. 5.2 Synthesis of main WP2 results Experiments and numerical simulations on jet-vortex interaction both revealed that the jet-vortex interaction can be divided in three stages:

• the jet is entrained around the vortex core; • due to the rotational velocity field, significant azimuthal vorticity structures are formed

around the jet and do interact with the jet; • finally, these structures decay and only the vortex remains.

A sufficiently strong jet, when placed sufficiently close to a vortex, can have a large effect on the peak vorticity and the core size of the final vortex. The favorable effect can only be exploited by dedicated design of the engine position in relation to the flap tip. A generic wing and jet test set-up has been employed for tests on jet and single or two-vortex interactions. A large parametric experimental data base (flow visualization and PIV measurements) has been obtained by U-Bath on the effects of jet position, jet strength, jet pulsation and Reynolds number. Additional experiments by TUD for an aircraft model with part span flaps and two jets in a towing tank showed that the effects of jet-vortex interaction far downstream, after wake rollup, can be either favourable (reduced cross-flow velocities in the vortex) or adverse (increased cross flow), depending on jet position with respect to the vortex core(s).

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Measured wake data for a realistic high lift 4-engined aircraft configuration with Turbo-Powered-Simulators (TPS) (half-model test set-up) at different thrust settings have been provided by Airbus and were evaluated by NLR. In agreement with observations from the generic model tests an important effect of the inner jet on the nearby flap edge vortex was observed. These data have also been used to initiate time-developing LES (CERFACS and UCL) and spatial developing LES (UCL), allowing a prediction of the flow further downstream until merging of tip and flap vortex. With a strong jet (thrust for level flight) the predicted vortex core after vortex merging at x/b=5 becomes rc/b= 0.036, whereas with zero thrust vortex merging occurs only at x/b=15 and the core size is much smaller rc/b= 0.02. The parametric data set from ONERA on hot and cold jet vortex interaction for a straight wing, with two jets positioned at different positions along the span, shows that the temperature of the jet plays no dominant factor in jet vortex interaction: the temperature mainly behaves as a passive scalar. This was also confirmed by LES simulations for hot and cold jet-vortex interaction by ONERA and CERFACS. Analysis of wake experiments by DLR and Airbus showed an important effect of wing body lift carry over effect on the lateral position of the vorticity centroid. The lateral spacing of the vorticity centroid is an important parameter for the wake decay and vortex sink speed. It appears to depend quite sensitively on the details of the flow in the wing-body junction and the wake of the fuselage. Dedicated fuselage wake simulations by DLR and CENAERO using RANS methods showed that the prediction of the correct flow topology in the wake of the fuselage is sensitive to the turbulence model but also to the level of grid refinement. Final calculation results after dedicated grid refinement/adaptation agree reasonably well with the experimental data. Routine prediction of lift-carry-over effect from wing to fuselage will remain a challenge because of the large efforts needed in gridding. The experiments by TUM-AER with- and without landing gear did not indicate an important effect on wake structure and wake instability. Interesting simulations of wake roll-up with and without simulated velocity defect in the wake were made by UCL. With simulated velocity defect, longitudinal instabilities develop in the thin wake during the wake roll-up phase, which become wrapped around the vortex and lead to a modified circulation profile and some reduction in the circulation strength Γ5-15.

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5.3 Synthesis of main WP3 results The effect of ground proximity on airfoil lift was investigated with a vortex panel method, and showed that the ground effect becomes important when h/c<0.5 (so very close to the ground). Subsequently the span loading of various shaped wings at different heights above the ground was simulated with a modified lifting line theory. The results from these engineering method type calculations were very useful to define realistic initial span-loading conditions for wake roll-up studies with 2D DNS. Results also helped to define interesting test conditions for the experiments. 2D DNS wake roll-up simulations showed that the effect of ground proximity on wake roll-up remains small when h/b0> 0.25. At higher Reynoldsnumber, with vortices created close to the ground (h/b0=0.25), the 2D DNS simulations predict high intensity secondary vortices (emanating from the separating boundary layer at the ground) interacting with the primary vortices. It is expected that the complex dynamics predicted would not occur in a 3D simulation. A 3D vortex filament numerical simulation of vortices created above the ground, with a given amplitude of the Crow instability, was made by UCL to mimic experiments made by IRPHE. A good comparison with the experiments was found. The comparison of LES simulations by CENAERO and a benchmark DNS by UCL showed the importance of using adequate sub-grid turbulent models in LES. The superiority of the multi-scale Smagorinsky sub-scale model was well demonstrated. 2D LES simulations by UCL of a 2-vortex system created at two wingspans above the ground show a very good correspondence with of the IRPHE water tank experiments. Subsequent 3D LES simulations also showed the development of short-wavelength elliptic instabilities on the secondary vortices, in good agreement with the experiments. Numerical simulations by CENAERO/UCL and UPS-IMFT of a vortex pair descending into ground effect agree well and confirm an enhanced decay of vortices shortly after reaching the rebound height, as is also observed in lidar experiments. Numerical simulations with cross- and head-wind show an even more rapid decay in wind conditions, again in agreement with analysed lidar data. The numerical simulations are very helpful for explaining the mechanisms which lead to the enhanced decay. The numerical simulations by UPS-IMFT of a counter rotating 4-vortex system, descending into ground effect, show an even faster decay due to the interaction of the inner vortices with the (equally signed) separating vortices from the ground.

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Dedicated towing tank experiments of 2- and 4-vortex systems created in ground proximity were made. Flow visualisations and measurements showed a complex interaction between the primary vortex and the secondary vorticity created by the interaction with the ground, leading to a “bursting” of the main vortex. A very demanding spatial LES simulation by UCL gave results in good qualitative agreement with the experiments. Compared with 2D and 3D time developing LES simulation, the spatial simulation shows more complex 3-D interaction with the ground and therefore displays an earlier and more violent transition to turbulence. The analysis of the Frankfurt data-base with lidar measured wakes, done by DLR and NLR, yielded useful results on the effect of crosswind on wake evolution. These results have been used to improve the wake prediction models P2P (DLR) and P-VFS (UCL). The ground effect parameterizations of the wake vortex models of UCL (DVM/PVM) and DLR (D2P/P2P) have been further developed. The devised parameterizations of both models were adapted, based on numerical simulation data and field measurement data (mainly acquired at Frankfurt Airport). The model performances have been tested against the Frankfurt field measurement data, showing a significant improvement of wake vortex prediction skills in ground proximity for both models. Both models are intended to be used as a tool for assessing safety for revised dynamic (weather dependent) aircraft separation strategies that are currently under investigation by e.g. EUROCONTROL in projects like CREDOS (cross-wind dependent aircraft separations).

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References

1 Anon.: FAR-Wake, Fundamental Research on Aircraft Wake Phenomena, Description of Work, FP6-012238, January 2005.

2 T. Leweke: Previous work and present knowledge on vortex instabilities and decay, FAR-Wake deliverable D1.0, July 2005.

3 L. Nybelen; R. Paoli; G. Chevalier: Previous work and present knowledge on vortex interactions with jets and wakes, FAR-Wake deliverable D2.0, July 2005.

4 L. Dufresne; G. Winckelmans: Previous work and present knowledge on wake vortices near the ground, FAR-Wake deliverable D3.0, July 2005.

5 Name: Final report on vortex instabilities and decay, FAR-Wake deliverable D1.F (this report was not yet issued when Final Synthesis Report was completed).

6 T. Schönfeld; J.-F. Boussuge: Final Report on vortex interactions with jets and wakes, FAR-Wake deliverable D2.F, May 2008.

7 Name: Final Report on wake evolution near the ground, FAR-Wake Deliverable D3.F, May 2008.

8 A.C. de Bruin: Framework definition, wake characterisation and Synthesis planning for the FAR-Wake project, FAR-Wake deliverable D4.1, August 2005, NLR-CR-2005-411.

9 A.C. de Bruin; F. Laporte: Synthesis of FAR-Wake results, Intermediate results after 1st year of the project, FAR-Wake deliverable D4.2-1, June 2006, NLR-CR-2006-033.

10 A.C. de Bruin: Synthesis of FAR-Wake results, Intermediate results after 2nd year of the project, FAR-Wake deliverable D4.2-2, April 2007, NLR-CR-2007-019.

11 T. Leweke: FAR-Wake Periodic Activity Report, Reporting period 1, February 2005 – 31 January 2006, April 2006.

12 T. Leweke: FAR-Wake Periodic Activity Report, Reporting period 2, February 2006 – 31 January 2007, April 2007.

13 D. Fabre; J. Fontane; P. Brancher; S. le Dizès; C. Roy; T. leewke; R. Fernandez-Feria; L. Parras; C. del Pino: Synthesis on vortex meandering, FAR-Wake deliverable D1.1.1, May 2008.

14 S. Le Dizès; D. Fabre: Linear asymptotic stability analysis of specific vortices, FAR-Wake Technical Report TR1.1.1-1, January 2006.

15 J. Fontane; P. Brancher; D. Fabre: Stochastic forcing of the Lamb-Oseen vortex, FAR-Wake Technical Report TR1.1.1-2, January 2008.

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16 R. Fernandez-Feria; C. del Pino; L. Parras: Spatial stability analysis of specific vortices, FAR-Wake Technical Report TR1.1.1-3, October 2006.

17 C. Roy; T. Leweke: Experiments on vortex meandering, FAR-Wake Technical Report TR1.1.1-4, May 2008.

18 C. del Pino; L. Parras; R. Fernandez-Feria: Non-parallel spatial stability of Batchelor vortex, Physics of Fluids (2008, submitted).

19 L. Parras; R. Fernandez-Feria: Spatial stability and the onset of absolute instability of Batchelor vortex for high swirl numbers, JFM 583, pp. 27-43 (2007).

20 M. Abid: Nonlinear mode selection in a model of trailing line vortices, JFM (2008, submitted).

21 J. Fontane; P. Brancher; D. Fabre: Stochastic forcing of the Lamb-Oseen vortex, JFM (2008, submitted).

22 S. Le Dizès; D. Fabre: Large Reynolds number asymptotic analysis of viscous centre modes in vortices, JFM 585, pp 153-180 (2007).

23 D. Fabre; S. Le Dizès: Viscous and inviscid centre-modes in vortices: the vicinity of the neutral curves, JFM 603, pp 1-38 (2008).

24 A. Antkowiak; P. Brancher: On vortex rings around vortices: an optimal mechanism, JFM 578, pp 295-304 (2007).

25 Name: Wave propagation phenomena and vortex bursting associated with end effects, FAR-Wake deliverable D1.1.2 (this report was not yet issued when Final Synthesis Report was issued).

26 P. Meunier: Axial propagation of vortex perturbations, FAR-Wake Technical Report TR1.1.2-1, March 2006.

27 L. Nybelen; J.F. Boussuge: Temporal DNS on end effects and vortex waves, FAR-Wake Technical Report TR1.1.2-2, September 2007.

28 D. Fabre; D. Sipp; L. Jacquin: Kelvin waves and the singular modes of the Lamb-Oseen vortex, FAR-Wake Technical Report TR1.1.2-3, February 2006 (also published in JFM, Vol. 551, pp 235-274 (2006).

29 B. Leclaire; D. Sipp; O. Thomas: free-flight B20 catapult: end-effects analysis, FAR-Wake Technical Report TR1.1.2-4, June 2008.

30 L. Nybelen; J.F. Boussuge: Temporal DNS on vortex bursting and assessment, FAR-Wake Technical Report TR1.1.2-5, February 2008.

31 T. Lonfils; R. Cocle; G. Daeninck; C. Cottin; G. Winckelmans: Numerical investigations of end-effects associated with accelerated/decelerated wings: time-developing and space-developing simulations, FAR-Wake Technical Report TR1.1.2-6, September 2007.

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32 S. Le Dizès; L. Lacaze: An asymptotic description of vortex Kelvin modes, JFM, Vol. 542, pp 69-96 (2005).

33 H. Moet; F. Laporte; G. Chevalier; T. Poinsot : Wave propagation in vortices and vortex bursting, Physics of Fluids 17, 054109 (2005).

34 S. Le Dizès; T. Leweke; C. Roy; N. Schaeffer; L. Lacaze; L. Nybelen; H. Deniau; R.R. Trieling; A. Elsenaar; G.J.F. van Heijst; J.P.J. Jaarsveld; A.P.C. Holten; L.M. Gonzáles; V. Theofilis; M.C. Thompson; K. Ryan: Short-wave instabilities in two-vortex systems, FAR-Wake deliverable D1.2.1, May 2008.

35 L.M. González; V. Theofilis: Temporal stability analysis of two-vortex systems, FAR-Wake Technical Report TR1.2.1-1, January 2008.

36 S. Le Dizès; L. Lacaze: Linear stability analysis of the elliptic instability in vortices with axial flow, FAR-Wake Technical Report TR1.2.1-2, October 2005.

37 N. Schaeffer; C. Roy; S. Le Dizès, M. Thomson: Temporal DNS of short-wave instabilities in vortex pairs with axial flow, FAR-Wake Technical Report TR1.2.1-3, April 2008.

38 C. Roy; T. Leweke: Experiments on short-wavelength instability in vortex pairs, FAR-Wake Technical Report TR1.2.1-4, May 2008.

39 J.P.J. van Jaarsveld; A.P.C. Holten; A. Elsenaar; R.R. Trieling; G.J.F. van Heijst: Wind tunnel experiments on wake-vortex decay in external turbulence, FAR-Wake Technical Report TR1.2.1-5, April 2008.

40 L. Nybelen; H. Deniau; J.F. Boussuge: Spatial DNS of two-vortex systems, FAR-Wake Technical Report TR1.2.1-6, February 2008.

41 L. Lacaze; K. Ryan; S. Le Dizès: Elliptic instability in a strained Batchelor vortex, JFM 577, 341-361 (2007).

42 C. Roy; N. Schaeffer; S. Le Dizès; M.C. Thomson: Stability of a pair of co-rotating vortices with axial flow, Physics of Fluids (2008, submitted).

43 N. Schaeffer; S. Le Dizès: Nonlinear dynamics of the elliptic instability, Physical Review Letters (2008, submitted).

44 C. Roy; T. Leweke; M.C. Thompson; K. Hourigan: Elliptic instability in vortex pairs with axial core flow, Physical Review Letters (2008, in preparation).

45 L.M. Conzález; V. Theofilis, R. Gómez-Blanco: Finite-element numerical methods for viscous incompressible BiGlobal linear instability analysis on unstructured meshes, AIAA Journal 45 (4), pp 840-854 (2007).

46 L.M. Conzález; V. Theofilis: On the eigenmodes of a co-rotating vortex dipole, AIAA Journal (2008, in preparation).

47 L.M. Conzález; J. de Vincente; V. Theofilis: High-order finite element methods for global viscous linear instability analysis of internal flows, 18th AIAA Computational Fluid Dynamics Conference, Miami, June 25-28, 2007, AIAA paper 2007-3840.

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48 M. Ren; A. Elsenaar; G.J.F. van Heijst; A.K. Kuczaj; B.J. Geurts: Decay or collapse: aircraft wake vortices in grid turbulence. In: Proceedings of the 6th Euromech Fluid mechanics Conference, Stockholm, Sweden (2006).

49 L. Nybelen; R. Paoli: Direct and large-eddy simulations of merging in co-rotating vortex system, AIAA Journal (2008, submitted).

50 H. Deniau; L. Nybelen: Strategy for spatial simulation of co-rotating vortices, International Journal for Numerical methods in Fluids (2008, submitted).

51 Name: Medium- and long-wavelength instabilities, FAR-Wake deliverable D1.2.2 (this report was not yet issued when Final Synthesis Report was completed).

52 Name: Temporal CFD studies of 4-vortex systems, FAR-Wake Technical Report TR1.2.2-1 (this report was not yet issued when Final Synthesis Report was completed).

53 O. Desenfans; T. Lonfils, G. Daeninck, R. Cocle, L Bricteux; L. Dufresne; G. Winckelmans: Numerical simulations of counter-rotating four-vortex systems, FAR-Wake Technical Report TR1.2.2-2, January 2007.

54 L.M. Conzáles; V. Theofilis: Temporal stability analysis of 4-vortex systems by Floquet methods, FAR-Wake Technical Report TR1.2.2-4, January 2008.

55 V. Brion; D. Sipp; L. Jacquin: Analysis of transient growth in dipolar vortices, FAR-Wake Technical Report TR1.2.2-5, May 2008.

56 R. Konrath; C.F. von Carmer; K.-P. Mach; P. Anschau: Validation experiment with 4-vortex wake in SVA Potsdam, FAR-Wake Technical Report TR1.2.2-6, April 2008.

57 A. Allen; C. Breitsamter: Experimental study of the DLR F13/F13X models in TUM-AER wind tunnels, FAR-Wake Technical Report TR1.2.2-7, September 2007.

58 D. Fabre; L. Jacquin; A. Loof : Optimal perturbations in a four-vortex aircraft wake in counter-rotating configuration, JFM, Vol. 451, pp. 319-328, 2002.

59 G. Winckelmans; R. Cocle;, L. Dufresne; R. Capart: Vortex methods and their application to trailing wake vortex simulations, Comptes Rendus Physique, special issue on “Aircraft trailing vortices”, Académie des Sciences, Paris, Vol. 6, No. 4-5, 2005, pp. 467-486.

60 R. Cocle; L. Dufresne; G. Winckelmans: Investigation of multiscale subgrid scale models for LES of instabilities and turbulence in wake vortex systems, in “Complex Effects in Large Eddy Simulations” (eds. S.C. Kassinos, C.A. Langer, G. Iaccarino, P. Moin), Lecture Notes in Computational Science and Engineering 56, pp 141-159 (2007).

61 L. Dufresne; R. Baumann; T. Gerz; G. Winckelmans; H. Moet; R. Capart; R. Cocle; L. Nybelen: Large-eddy simulation of wake vortex flows at very high Reynolds numbers: a comparison of different methodologies. First issued as AWIATOR report D1.1.4-16 August 2005; to be submitted as a paper to Aerosp. Sci. Tech.

62 V. Brion; D. Sipp; L. Jacquin: Optimal amplification of the Crow instability, Physics of Fluids 19, 111703 (2008).

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63 A. Allen; C. Breitsamter: Investigation on the wake characteristics of a four vortex system, Aerospace Science and Technology (2008, submitted).

64 A.C. de Bruin: Estimation of exhaust velocities and temperatures for various operation phases of a modern high by-pass turbofan, FAR-Wake deliverable D2.1.1-1b, NLR-CR-2005-641, November 2005.

65 A.C. de Bruin: Analysis of near wake data with- and without simulated jets, Airbus-UK experiments from C-Wake project, FAR-Wake deliverable D2.1.1-1, NLR-CR-2005-642, February 2006.

66 P. Margaris; D. Marles; I. Gursul: Synthesis on single vortex/ cold engine jet interactions, FAR-Wake Deliverable D2.1.1-2, January 2007.

67 L. Nybelen, R. Cocle; G. Winckelmans; T. Lonfils; C. Cottin: Cold-jet effects in relevant multi-vortex configurations, including wake roll-up, FAR-Wake Deliverable D2.1.1-3, May 2008.

68 P. Margaris; D. Marles; I. Gursul: Experiments on single vortex / jet interaction, FAR-Wake Technical Report TR2.1.1-1, February 2006.

69 O. Labbé: LES of cold turbulent jet/vortex interaction, FAR-Wake Technical Report TR2.1.1-2, January 2007.

70 L. Nybelen; J.F. Boussuge; T. Schönfeld: LES of turbulent cold jet/vortex interaction, FAR-Wake Technical Report TR2.1.1-3, August 2006.

71 D. Marles; P. Margaris; I. Gursul: Experiments on Vortex Pair/Jet interaction, FAR-Wake Technical Report TR2.1.1-4, January 2007.

72 L.L.M. Veldhuis; R. de Kat; G.E. Elsinga: Towing tank experiments of cold jet-vortex interaction on a generic wing-flap model, FAR-Wake Technical Report TR2.1.1-5, Jan 2007.

73 C. Cottin; G. Winckelmans; T. Lonfils; R. Cocle: Roll-up of a temporally-evolving wing wake in presence of jets, FAR-Wake Technical Report TR2.1.1-6, October 2007.

74 D. Marles; I. Gursul: Experiments on vortex / pulsed jet interaction, FAR-Wake Technical Report TR2.1.1-7, January 2008.

75 P. Margaris; D. Marles; I. Gursul: Experiments on interaction of a jet with a trailing vortex, AIAA Paper AIAA-2007-1123, presented at 45th Aerospace Science Meeting and Exhibition, January 2007, Reno, NV.

76 P. Margaris; D. Marles; I. Gursul : Experiments on jet/vortex interaction, Experiments in Fluids 44, 261-278 (2008).

77 E. Coustols; O. Labbé; P. Molton; D. Sipp; L. Nybelen; A. Boguslawski: Single vortex/ hot jet interactions including stability of resulting flow, FAR-Wake deliverable D2.1.2, May 2008.

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78 A. Boguslawski; A. Tyliszczak; J. Bijak: LES and experiments on stability of a hot jet, FAR-Wake Technical Report TR2.1.2-2, April 2006.

79 D. Sipp: Synthesis on stability analysis of vortex with temperature variations resulting from hot jet/ single vortex interaction, FAR-Wake Technical Report TR2.1.2-3, October 2006.

80 O. Labbé: LES of hot turbulent jet/ vortex interactions, FAR-Wake Technical Report TR2.1.2-4, September 2006.

81 L. Nybelen; T. Marger; J.F. Boussuge; T. Schonfeld: LES of turbulent hot jet/vortex interaction, FAR-Wake Technical Report TR2.1.2-5, December 2006.

82 L. Jacquin; P. Molton: Experiments on cold/ hot jet-vortex interaction, FAR-Wake Technical Report TR2.1.2-6, September 2006.

83 D. Sipp; D. Fabre; S. Michelin; L. Jacquin: Stability of a vortex with a heavy core, JFM, Vol. 526, pp. 67-76 (2005).

84 L. Coquart; D. Sipp; L. Jacquin: Mixing induced by Rayleigh-Taylor instability in a vortex, Physics of Fluids, Vol. 17, 021703 (2005).

85 L. Jacquin; C. Pantano: On the persistence of trailing vortices, JFM, 2002, 471: 159-168.

86 S. Melber-Wilkending; L. Georges; A. Allen: Effect of fuselage on the structure of the wake vortex system including RANS simulations of fuselage/wing/HTTP system, FAR-Wake Deliverable D2.2.1-1, January 2007.

87 G. Schrauf; C. Hünecke: On the influence of the wing-fuselage vortex, FAR-Wake Technical Report TR2.2.1-1, Jan 2008.

88 T. Louagie; L. Georges, P. Geuzaine; S. Melber: Hybrid RANS-LES simulations of the TAK fuselage wake, FAR-Wake Technical Report TR2.2.1-3, April 2008.

89 A. Allen; C. Breitsamter: Characterisation of landing gear and its influence on the wake system, FAR-Wake Deliverable D2.2.2-1, September 2006.

90 A. Allen; C. Breitsamter; C. Cottin; G. Winckelmans; T. Lonfils; R. Cocle: Wake flows generated by wings and wing elements (including wing-tip device), and their influence on the wake system, FAR-Wake Deliverable D2.2.2-2, October 2007.

91 A. Allen; C. Breitsamter: Wind tunnel measurements of wing element wakes, FAR-Wake Technical Report TR2.2.2-2, September 2006.

92 C. Cottin; G. Winckelmans; T. Lonfils; R. Cocle: Roll-up of a temporally-evolving wing wake with velocity deficit, FAR-Wake Technical Report TR2.2.2-3, September 2007.

93 G. Daeninck; O. Desenfans; G. Winckelmans: Span loading variations and wake roll-up in ground effect, FAR-Wake Deliverable D3.1.1-1, September 2006.

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94 G. Winckelmans; L. Bricteux, M. Duponcheel; T. Lonfils; G. Daeninck; L. Georges; P. Geuzaine; A. Giovannini; H. Boisson; T. Leweke; C. Cottin: 3D instabilities of two- and four-vortex systems in ground effect, FAR-Wake Deliverable D3.1.1-2, April 2008.

95 A. Giovanni; L. Georges; P. Geuzaine; M. Duponcheel; L. Bricteux; T. Lonfils; G. Winckelmans: Effect of wind conditions on the evolution of a two-vortex system near the ground, FAR-Wake Deliverable D3.1.1-3, July 2007.

96 J. Sereno; J.M. Chaves; J.C.F. Pereira: Quantification of uncertainty in a 2D vortex pair near the ground in cross-flow, FAR-Wake Deliverable D3.1.1-4, part 1, February 2006.

97 J.C.F. Pereira; J. Sereno: Uncertainty quantification in a 2D vortex pair near the ground with and without crosswind, FAR-Wake Deliverable D3.1.1-4, part 2, January 2007.

98 T. Lonfils; G. Daeninck; G. Winckelmans: 3D filament simulations of Crow-like instabilities in ground effect, FAR-Wake Technical Report TR3.1.1-1, September 2006.

99 L. Georges; P. Geuzaine; M. Duponcheel; L. Bricteux; T. Lonfils; G. Winckelmans: LES of two-vortex system in ground effect (longitudinally uniform wakes), FAR-Wake Technical Report TR3.1.1-2, October 2006.

100 A. Giovannini; H. Boisson: LES calculations of a 4 vortex system IGE, FAR-Wake Technical Report TR3.1.1-3, October 2006.

101 C. Cottin; T. Leweke: Water tank experiments on vortex pairs IGE, FAR-Wake Technical Report TR3.1.1-4, April 2008.

102 C. Cottin; T. Leweke: Experiments on vortex pair dynamics in ground effect, presented at the 6th EUROMECH Fluid mechanics Conference, 26-30 June, 2006, Stockholm.

103 M. Duponcheel; C. Cottin; G. Daeninck; T. Leweke; G. Winckelmans: Experimental and numerical study of counter-rotating vortex pair dynamics in ground effect, 18th Congrès Français de Mécanique, Grenoble, August 2007.

104 R. Konrath; C.F. von Carmer; G. Schrauf; K. Schmidt; G. Winckelmans, C. Cottin; O. Desenfans; G. Daeninck; R. Cocle: Dynamics and decay of spatially-evolving two- and four-vortex wakes near the ground, FAR-Wake Deliverable D3.1.2, May 2008.

105 R. Konrath; C.F. von Carmer: Towing-tank PIV measurements on 2- and 4-vortex systems IGE, FAR-Wake Technical Report TR3.1.2-2, April 2008.

106 C. Cottin; O. Desenfans; G. Daeninck; G. Winckelmans: Towing-tank visualizations of two-vortex systems in ground effect, FAR-Wake Technical Report TR3.1.2-3, December 2006.

107 G. Daeninck; R. Cocle; G. Winckelmans: LES calculations of spatially evolving wakes in ground effect, FAR-Wake Technical Report TR3.1.2-4, December 2006.

108 F. Holzäpfel; M. Steen: Impact of weather conditions and ground effects on wake-vortex evolution near the ground in real conditions, FAR-Wake Deliverable D3.2-1, February 2007.

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109 A.C. de Bruin: Analysis of wake transport and decay data from near ground lidar measurements, FAR-Wake Deliverable D3.2-2, December 2006.

110 F. Holzäpfel; I. de Visscher; G. Winckelmans: Assessment of combined ground effects and meteorology on wake vortex transport and decay NGE and IGE and improvement of the models P2P and PVM, including performance analysis, FAR-Wake Deliverable D3.3.1, February 2008.

111 G. Winckelmans; R. Cocle ; L. Dufresne ; R. Capart : Summary description of the models used in the Vortex Forecast System (VFS), VFS version with added improvements done after completion of the Transport Canada funded project. Technical report, Université Catholique de Louvain (UCL), April 2005.

112 F. Holzäpfel: Probabilistic Two-Phase Aircraft wake-vortex model: Further development and assessment, Journal of Aircraft, Vol. 43, No. 3, 2006, pp 800-708.

113 F. Holzäpfel; M. Steen: Aircraft Wake-Vortex Evolution in Ground Proximity: Analysis and Parameterization, AIAA Journal 45(1), pp 218-227 (2007).

114 T. Gerz; F. Holzäpfel; W. Bryant; F. Köpp; M. Frech; A. Tafferner; G. Winckelmans: Research towards a wake-vortex advisory system for optimal aircraft spacing, Comptes Rendus Physique 6 (4/5), Special issue on Aircraft trailing vortices, 501-523 (2005).

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23.

1.1

3.1.

23.

23.

3Pa

rtne

rIR

PHE

THE

THE

/EXP

CFD

/EXP

(2)/T

HE

EXP

EXP

A-D

EXP

EXP

EXP

CEN

AER

OC

FDC

FDC

ERFA

CS

CFD

CFD

CFD

CFD

CU

TE

XP

/CFD

DLR

EX

P(2

)/CFD

CFD

EXP

Ana

lysi

sA

naly

sis

IST

CFD

NLR

EXP

Ana

lysi

sO

NER

AC

FDC

FD/T

HE

CFD

EX

P/C

FDTU

Del

ftE

XPTU

E-FD

LE

XP

/CFD

/TH

EE

XP

/CFD

TUM

-FLM

EX

PE

XPU

-Bat

hE

XP(8

)U

CL

CFD

CFD

(3)

CFD

CFD

CFD

(2)

EX

P/C

FDA

naly

sis

UM

ATH

EU

PMTH

ETH

EU

PS-IM

FTTH

ETH

EC

FD

NLR

-CR

-20

08

-02

3

54

Tabl

e 2:

Ove

rvie

w o

f exp

loita

ble

resu

lts

Sub-

ta

sk

Sub-

resu

lt pr

actic

al

impl

icat

ion

diffi

culty

to

exp

loit

scie

ntifi

c in

tere

st

com

men

t

111

Impr

oved

un

ders

tand

ing

of

vorte

x ce

ntre

mod

e in

stab

ilitie

s m

inor

m

ediu

m/

high

hi

gh

Vor

tex

cent

re m

ode

inst

abili

ties

for

spec

ific

vorti

ces

with

or

with

out

axia

l co

re

flow

ha

ve

been

in

vest

igat

ed

in

deta

il in

clud

ing

the

diff

eren

ces

in s

tabi

lity

betw

een

para

llel a

nd n

on-

para

llel f

low

. 11

1 Im

prov

ed

unde

rsta

ndin

g of

vo

rtex

mea

nder

ing

mec

hani

sm

med

ium

m

ediu

m/

high

hi

gh

Com

bine

d th

eore

tical

and

exp

erim

enta

l w

ork

expl

ains

the

or

igin

of

the

vorte

x m

eand

erin

g m

echa

nism

. It

aris

es f

rom

a

trans

ient

gro

wth

of

a vo

rtex

disp

lace

men

t in

stab

ility

mod

e,

unde

r the

act

ion

of e

xter

nal t

urbu

lenc

e ef

fect

s. a

s ob

serv

ed in

w

ind

tunn

els.

Seem

s no

t ea

sily

exp

loita

ble,

nor

hav

e a

larg

e im

pact

on

airc

raft

sepa

ratio

n di

stan

ce

112

Com

plet

e m

appi

ng

of

norm

al

inst

abili

ty

mod

es

for

Lam

b-O

seen

vor

tex

min

or

med

ium

/ hi

gh

high

M

ode

forc

ing

seem

s no

t eas

ily p

ossi

ble

on a

rea

l airc

raft.

The

ne

wly

obs

erve

d cr

itica

l lay

er m

ode

seem

s to

pla

y a

role

in th

e re

cept

ivity

of

vo

rtex

core

s to

ex

tern

al

dist

urba

nces

(e

.g.

ambi

ent t

urbu

lenc

e ef

fect

s)

112

grou

p ve

loci

ty

of

trave

lling

w

aves

hi

gh

min

or

med

ium

A

goo

d co

rrel

atio

n be

twee

n th

eory

and

exp

erim

enta

l re

sults

(I

RPH

E) o

f fr

eque

ncie

s an

d tra

vel

spee

d ha

s be

en o

bser

ved.

Th

e re

sults

are

im

porta

nt t

o un

ders

tand

the

end

eff

ects

in

expe

rimen

tal f

acili

ties

112

Impr

oved

CFD

cap

abili

ties

for

sim

ulat

ion

of tr

avel

ling

wav

es

med

ium

m

inor

hi

gh

ON

ERA

, U

PS-I

MT,

C

ERFA

CS

and

UC

L ap

plie

d th

eir

num

eric

al c

odes

to

the

prob

lem

of

trave

lling

wav

es a

long

vo

rtice

s.

121

Impr

oved

un

ders

tand

ing

of

ellip

tic i

nsta

bilit

ies

in 2

-vor

tex

co-

or c

ount

er r

otat

ing

syst

ems

and

with

- and

with

out a

xial

flow

med

ium

TB

D

high

A

par

amet

ric i

nves

tigat

ion

of e

llipt

ic i

nsta

bilit

y m

echa

nism

s fo

r co

- an

d co

unte

r- r

otat

ing

vorti

ces

with

var

ious

mag

nitu

de

of a

xial

cor

e flo

w h

as b

een

mad

e. T

his

impr

oved

the

phys

ical

un

ders

tand

ing

of t

he r

ole

of s

uch

inst

abili

ties

durin

g vo

rtex

mer

ging

and

the

effe

cts

on th

e pr

oper

ties

of th

e fin

al m

erge

d vo

rtex.

Lin

ear s

tabi

lity

resu

lts w

ere

supp

orte

d by

tem

pora

l and

sp

atia

l num

eric

al s

imul

atio

ns. W

ith a

xial

cor

e flo

w th

e si

nuou

s in

stab

ilitie

s ar

e su

ppre

ssed

. Co-

rota

ting

vorti

ces

disp

lay

high

er

ampl

ifica

tion

rate

s th

an c

ount

er ro

tatin

g vo

rtice

s an

d at

hig

her

Rey

nold

snum

ber

com

bina

tions

of

Kel

vin

mod

es o

f di

ffer

ent

NLR

-CR

-20

08

-02

3

55

Sub-

ta

sk

Sub-

resu

lt pr

actic

al

impl

icat

ion

diffi

culty

to

exp

loit

scie

ntifi

c in

tere

st

com

men

t

labe

ls b

ecom

e un

stab

le a

nd m

ake

the

flow

sus

cept

ible

to

a la

rge

rang

e of

wav

enum

bers

, wha

teve

r the

axi

al fl

ow.

121

Bi-G

loba

l ei

genv

alue

m

etho

d fo

r dip

ole

vorte

x co

nfig

urat

ions

TB

D

TBD

hi

gh

A B

i-Glo

bal

eige

nval

ue m

etho

d ha

s be

en d

evel

oped

tha

t si

mul

tane

ousl

y pr

ovid

es

the

eige

nval

ues

and

the

spat

ial

stru

ctur

e of

the

eige

nmod

es. T

he p

roce

dure

can

be

appl

ied

to

arbi

trary

wak

e vo

rtex

flow

fie

lds.

The

bene

fits

over

mor

e cl

assi

cal m

etho

ds sh

ould

be

furth

er a

sses

sed.

12

2 Pr

ogre

ss in

CFD

sim

ulat

ions

of

2- a

nd 4

-vor

tex

syst

ems

high

m

ediu

m

high

Th

e av

aila

bilit

y of

pow

erfu

l C

FD m

etho

ds o

pens

the

way

to

asse

ss t

he t

ime

for

rapi

d w

ake

deca

y of

a c

erta

in d

esig

ned

wak

e to

polo

gy.

It en

able

s to

ass

ess

the

bene

fits

of c

erta

in

solu

tions

an

d th

eir

resi

stan

ce

agai

nst

exte

rnal

tu

rbul

ence

ef

fect

s, pr

ior t

o th

eir f

inal

test

ing

(e.g

. in

fligh

t).

122

A s

pace

-dev

elop

ing

LES

of a

4-

vorte

x w

ake

m

inor

hi

gh

high

U

CL

mad

e a

very

cha

lleng

ing

LES

sim

ulat

ion

of a

spa

ce

deve

lopi

ng 4

-vor

tex

syst

em (Γ

2/Γ1=

-0.3

, b2/b

1=0.

3). A

larg

e lif

t co

effic

ient

had

to b

e as

sum

ed in

ord

er to

lim

it th

e si

ze o

f th

e co

mpu

tatio

nal b

ox. T

he s

patia

l dev

elop

ing

sim

ulat

ion

show

s a

mor

e ra

pid

deca

y th

an t

he t

empo

ral

deve

lopi

ng s

imul

atio

n.

This

eff

ect

is e

xpec

ted

to b

e le

ss w

hen

lift

coef

ficie

nt i

s re

duce

d (le

ss h

elic

al w

ake

stru

ctur

e).

The

calc

ulat

ion

show

s th

at sp

atia

l sim

ulat

ions

may

bec

ome

doab

le in

nea

r fut

ure.

12

2 M

ore

prac

tical

vor

tex

stre

ngth

ra

tio

for

coun

ter-

rota

ting

4-vo

rtex

syst

ems

coul

d st

ill

prov

ide

an

enha

nced

gro

wth

ra

te

high

m

ediu

m

med

ium

LE

S si

mul

atio

ns b

y U

CL

sugg

est t

hat a

4-v

orte

x sy

stem

with

a

circ

ulat

ion

stre

ngth

rat

io o

f Γ 2

/Γ1=

-0.2

ins

tead

of Γ 2

/Γ1=

-0.3

co

uld

still

giv

e a

cons

ider

able

adv

anta

ge a

nd i

s m

uch

easi

er

impl

emen

ted

in p

ract

ice.

122

Opt

imum

lo

ng

wav

elen

gth

forc

ing

of 4

-vor

tex

syst

ems

(at

wak

e sy

mm

etry

pla

ne)

high

TB

D

high

A

n an

alys

is o

f op

timum

per

turb

atio

n of

cou

nter

-rot

atin

g 2-

vorte

x sy

stem

s sh

owed

in

tere

stin

g tra

nsie

nt

grow

th

of

norm

ally

st

able

lo

ng

wav

elen

gth

dist

urba

nces

w

hen

appr

opria

tely

dis

turb

ed n

ear

the

wak

e sy

mm

etry

pla

ne.

This

re

sults

in a

sig

nific

antly

enh

ance

d C

row

mod

e am

plitu

de a

t a

give

n w

ake

vorte

x lif

e-tim

e.

211/

21

2 R

educ

ed p

eak

vorti

city

due

to

inte

ract

ion

of

a je

t w

ith

the

med

ium

/ hi

gh

med

ium

m

ediu

m

Expe

rimen

tal d

ata

from

Airb

us a

nd U

BA

and

CFD

sim

ulat

ions

by

ON

ERA

and

CER

FAC

S re

veal

tha

t pe

ak v

ortic

ity i

s

NLR

-CR

-20

08

-02

3

56

Sub-

ta

sk

Sub-

resu

lt pr

actic

al

impl

icat

ion

diffi

culty

to

exp

loit

scie

ntifi

c in

tere

st

com

men

t

vorte

x re

duce

d an

d vo

rtex

core

siz

e is

incr

ease

d w

hen

a su

ffic

ient

ly

stro

ng (b

ut re

alis

tic) j

et is

pla

ced

suff

icie

ntly

clo

se to

a v

orte

x (e

.g. a

fla

p ed

ge).

Espe

cial

ly d

urin

g ta

ke-o

ff th

is c

ould

hav

e a

sign

ifica

nt e

ffec

t on

(red

uced

) wak

e ha

zard

. 21

1 Se

nsiti

vity

of

je

t-vor

tex

inte

ract

ion

to r

elat

ive

posi

tion

and

orie

ntat

ion

of th

e je

t

high

m

ediu

m

med

ium

Th

e ef

fect

of

je

t-vor

tex

inte

ract

ion

on

the

final

w

ake

char

acte

ristic

s (c

ross

-flo

w v

eloc

ity p

rofil

e) a

ppea

rs to

dep

end

criti

cally

on

the

jet p

ositi

on a

nd o

rient

atio

n w

ith re

spec

t to

the

vorte

x (o

r vo

rtice

s). I

n ge

nera

l the

eff

ect o

f th

e je

t lea

ds to

a

mor

e be

nign

wak

e be

caus

e of

enh

ance

d di

ffus

ion.

How

ever

, fr

om th

e ex

perim

ents

of T

UD

, thi

s is

not

alw

ays

the

case

. The

je

t m

ay i

nflu

ence

vor

tex

mer

ging

lea

ding

to

a sm

alle

r vo

rtex

core

afte

r rol

l-up.

21

1 Te

mpo

ral

and

spat

ial

LES

sim

ulat

ion

of

jet

vorte

x in

tera

ctio

ns

star

ting

from

ex

perim

enta

l dat

a

high

hi

gh

med

ium

LE

S si

mul

atio

ns o

n je

t- vo

rtex

inte

ract

ion

wer

e m

ade

by U

CL

and

CER

FAC

S st

artin

g fr

om e

xper

imen

tal d

ata,

as p

rovi

ded

by

Airb

us.

In p

rinci

ple

this

off

ers

the

poss

ibili

ty t

o ex

tend

nea

r w

ake

mea

sure

d da

ta to

far d

owns

tream

, pro

vide

d ac

cura

te a

nd

suff

icie

ntly

reso

lved

inflo

w d

ata

are

avai

labl

e.

212

Effe

ct o

f hot

jets

no

ne

n.a.

hi

gh

Bas

ed o

n th

e ex

perim

enta

l an

d C

FD r

esul

ts i

t se

ems

that

the

ef

fect

of

jet

tem

pera

ture

on

the

final

wak

e ch

arac

teris

tics

is

very

min

or. T

he h

ot je

t beh

aves

as

a pa

ssiv

e sc

alar

. The

refo

re,

activ

e us

e of

jet t

empe

ratu

re a

s a

mea

ns to

redu

ce w

ake

vorte

x ha

zard

see

ms

not

prac

ticab

le.

Alth

ough

not

use

ful

for

the

wak

e-vo

rtex

issu

e, t

he o

bser

ved

Ray

leig

h-Ta

ylor

ins

tabi

lity

mec

hani

sms

lead

ing

to a

stro

ng fi

lam

enta

tion

of th

e co

re fl

ow,

coul

d pe

rhap

s w

ell b

e us

ed a

s a

mea

ns to

enh

ance

mix

ing

or to

pr

omot

e co

mbu

stio

n ef

ficie

ncy.

21

2 D

ata

set o

f ex

perim

enta

l res

ults

on

ho

t an

d co

ld

jet-v

orte

x in

tera

ctio

n

med

ium

m

inor

hi

gh

The

data

set

pro

duce

d by

ON

ERA

on

the

inte

ract

ion

of a

si

mpl

e je

t flo

w w

ith th

e w

ake

of a

sim

ple

stra

ight

win

g is

ver

y us

eful

for C

FD c

ode

valid

atio

n.

221

Effe

ct o

f fu

sela

ge o

n th

e w

ake

char

acte

ristic

s, du

e to

lift-

carr

y-ov

er

effe

ct

from

w

ing

to

fuse

lage

med

ium

TB

D

med

ium

B

ased

on

Airb

us a

naly

sis

the

lift c

arry

-ove

r ef

fect

fro

m w

ing

to f

usel

age

can

have

a s

igni

fican

t ef

fect

on

initi

al l

ater

al

spac

ing

of v

ortic

ity c

entro

ids

and

thus

on

over

all

wak

e si

nk

spee

d an

d de

cay.

NLR

-CR

-20

08

-02

3

57

Sub-

ta

sk

Sub-

resu

lt pr

actic

al

impl

icat

ion

diffi

culty

to

exp

loit

scie

ntifi

c in

tere

st

com

men

t

221

Impr

oved

C

FD

mod

ellin

g of

fu

sela

ge w

ake

flow

m

ediu

m

med

ium

hi

gh

The

wak

e of

an

isol

ated

fuse

lage

was

mea

sure

d by

TU

M-A

ER

and

com

pute

d by

DLR

and

CEN

AER

O.

Cal

cula

tions

on

a co

arse

gr

id

show

so

me

impr

ovem

ent

whe

n ad

vanc

ed

turb

ulen

ce m

odel

s ar

e us

ed (

e.g.

Rey

nold

s St

ress

Mod

ellin

g).

Subs

eque

nt g

rid a

dapt

atio

n an

d re

finem

ent

stud

ies

show

grid

ef

fect

s ar

e ev

en m

ore

impo

rtant

. O

n th

e fin

e m

eshe

s th

e pr

edic

ted

flow

top

olog

y is

in

reas

onab

le a

gree

men

t w

ith t

he

expe

rimen

t. 22

1 C

ontri

butio

ns

to

half-

mod

el

test

ing

med

ium

m

inor

m

ediu

m

Num

eric

al s

imul

atio

ns b

y D

LR f

or t

he K

AT

mod

el i

n fr

ee-

fligh

t, w

ith w

ind

tunn

el w

alls

incl

udin

g a

peni

che

wer

e m

ade.

Th

e im

porta

nce

for

the

wak

e-vo

rtex

issu

e is

th

e sh

own

diff

eren

ce in

vor

tex

posi

tion

in w

ind

tunn

el c

ompa

red

to f

ree-

fligh

t. Th

e re

sults

are

als

o in

tere

stin

g fo

r the

dev

elop

men

t and

va

lidat

ion

of h

alf-

mod

el c

orre

ctio

n te

chni

ques

. 22

1/22

2 C

ompu

ted

flow

fie

ld a

roun

d an

is

olat

ed la

ndin

g ge

ar

min

or

n.a.

m

ediu

m

A R

AN

S si

mul

atio

n by

DLR

show

s the

com

plex

flow

topo

logy

in

the

wak

e of

a la

ndin

g ge

ar. I

t pro

duce

s ha

rdly

any

lift

but a

co

mpl

ex s

yste

m o

f tra

iling

vor

tices

that

will

inte

ract

with

the

wak

e-ro

ll-up

beh

ind

a w

ing.

22

2 ef

fect

of

land

ing

gear

on

wak

e ev

olut

ion

min

or

min

or

med

ium

Th

e ne

ar w

ake

up to

x/b

=1 o

f th

e TA

K h

alf-

mod

el w

ith-

and

with

out

a la

ndin

g ge

ar h

as b

een

inve

stig

ated

by

TUM

-AER

, us

ing

hotw

ire p

robe

s. Th

e w

ake

of th

e la

ndin

g ge

ar is

vis

ible

as

a tu

rbul

ence

regi

on w

ith w

eak

stre

amw

ise

vorti

city

. Spe

ctra

l an

alys

is o

f th

e ho

t-wire

sig

nals

sho

ws

mai

nly

broa

dban

d tu

rbul

ence

with

out p

refe

rred

freq

uenc

y pe

aks.

22

2 ef

fect

of a

win

glet

m

ediu

m

med

ium

m

ediu

m

It is

wel

l kno

wn

that

a w

ingl

et in

fluen

ces

the

span

-load

ing

of

an a

ircra

ft an

d th

us th

e di

strib

utio

n of

the

vorti

city

she

d by

a

win

g. I

n th

e ex

perim

ents

by

TUM

-AER

the

vor

ticity

pea

k fr

om t

he w

ingt

ip v

orte

x is

hig

her

than

for

the

win

g w

ith

win

glet

. How

ever

, thi

s res

ults

can

pro

babl

y no

t be

gene

ralis

ed.

222

Num

eric

al s

imul

atio

n of

wak

e ro

ll-up

in

th

e pr

esen

ce

of

a re

alis

tic v

eloc

ity d

efec

t in

the

w

ing

traili

ng e

dge

wak

e

med

ium

m

ediu

m

high

U

CL

mad

e te

mpo

ral

LES

sim

ulat

ions

of

w

ake

roll-

up

initi

aliz

ed f

rom

a f

inite

thi

ckne

ss v

ortic

ity s

heet

with

- an

d w

ithou

t a s

imul

ated

vel

ocity

def

ect i

n th

e w

ing

wak

e. D

urin

g th

e ro

ll-up

pha

se th

e ve

loci

ty d

efec

t trig

gers

sev

eral

inst

abili

ty

NLR

-CR

-20

08

-02

3

58

Sub-

ta

sk

Sub-

resu

lt pr

actic

al

impl

icat

ion

diffi

culty

to

exp

loit

scie

ntifi

c in

tere

st

com

men

t

mec

hani

sms.

Afte

r ro

ll-up

the

vor

tex

stru

ctur

e (v

eloc

ity a

nd

vorti

city

pro

files

) is h

owev

er q

uite

sim

ilar.

31

1 En

gine

erin

g m

etho

d re

sults

ob

tain

ed

for

wak

e ge

nera

tion

near

the

grou

nd

high

m

inor

lo

w

The

engi

neer

ing

anal

ysis

mad

e by

UC

L at

sta

rt of

the

proj

ect

gave

pr

actic

al

guid

elin

es

for

the

mor

e ex

tend

ed

CFD

si

mul

atio

n of

w

akes

in

gr

ound

ef

fect

, bu

t al

so

for

the

inte

rpre

tatio

n of

IG

E ex

perim

ents

and

for

ris

k as

sess

men

t st

udie

s (u

sual

ly

base

d on

en

gine

erin

g ty

pe

wak

e-vo

rtex

trans

port

and

deca

y si

mul

atio

ns).

It sh

ows

that

rol

l-up

is o

nly

influ

ence

d by

gro

und

effe

ct w

hen

the

initi

al h

eigh

t h/b

of

the

vorti

ces i

s les

s tha

n 0.

5.

311

Re-

conn

ectio

n of

wak

e vo

rtice

s w

ith th

e gr

ound

m

inor

hi

gh

high

N

umer

ical

sim

ulat

ions

by

UC

L sh

ow th

at, d

epen

ding

on

initi

al

pertu

rbat

ion

leve

l of C

row

inst

abili

ty, v

ortic

es m

ay re

-con

nect

w

ith t

he g

roun

d. T

he r

esul

ts a

re i

n go

od a

gree

men

t w

ith

expe

rimen

ts b

y IR

PHE.

31

1 A

dequ

ate

sub-

grid

m

odel

ling

for L

ES si

mul

atio

ns

high

m

inor

hi

gh

In a

ser

ies

of n

umer

ical

sim

ulat

ions

by

CEN

AER

O a

nd a

be

nchm

ark

DN

S si

mul

atio

n by

UC

L th

e su

perio

rity

of t

he

mul

ti-sc

ale

Smag

orin

sky

sub-

scal

e m

odel

was

dem

onst

rate

d an

d th

is m

odel

is th

eref

ore

to b

e re

com

men

ded.

31

1 En

hanc

ed d

ecay

of

two-

vorte

x sy

stem

s IG

E hi

gh

min

or

high

N

umer

ical

sim

ulat

ions

by

CEN

AER

O s

how

the

rap

id d

ecay

on

set

to o

ccur

soo

n af

ter

rebo

und

of t

he v

ortic

es I

GE.

For

vo

rtice

s rel

ease

d at

h/b

0=1

the

rapi

d de

cay

sets

in a

t τ*=

2.8.

31

1 C

ompu

ted

effe

ct o

f he

ad-w

ind

and

cros

s-w

ind

on w

ake

vorte

x de

cay

high

m

ediu

m

high

N

umer

ical

si

mul

atio

ns

by

CEN

AER

O

and

UPS

-IM

FT

of

vorti

ces

rele

ased

IG

E (h

/b0=

1) i

n fu

lly d

evel

oped

cro

ssw

ind

(rat

io b

etw

een

cros

s-w

ind

at in

itial

hei

ght a

nd in

itial

sink

spee

d of

the

vorti

ces

OG

E is

equ

al to

uni

ty),

show

that

the

onse

t of

rapi

d de

cay

is t

hen

even

ear

lier τ*

=2.0

. Th

e do

wns

tream

vo

rtex

appe

ars

to d

ecay

a li

ttle

fast

er th

an th

e up

win

d vo

rtex.

W

ith h

eadw

ind

the

over

all

effe

ct o

n de

cay

is s

imila

r th

an i

n cr

oss-

win

d.

311

Enha

nced

de

cay

of

4-vo

rtex

syst

ems I

GE

high

m

ediu

m

med

ium

N

umer

ical

sim

ulat

ions

by

UPS

-IM

FT o

f a

4-vo

rtex

syst

em

with

Γ2/Γ

1=-0

.3 I

GE

show

a m

uch

mor

e ra

pid

deca

y of

the

4-vo

rtex

syst

em c

ompa

red

to a

2-v

orte

x sy

stem

. The

circ

ulat

ion

deca

ys to

hal

f its

orig

inal

val

ue a

t τ*=

1.7,

com

pare

d to

τ*=

6

NLR

-CR

-20

08

-02

3

59

Sub-

ta

sk

Sub-

resu

lt pr

actic

al

impl

icat

ion

diffi

culty

to

exp

loit

scie

ntifi

c in

tere

st

com

men

t

for

the

2-vo

rtex

syst

em.

This

sho

ws

the

pote

ntia

l be

nefit

of

coun

ter-

rota

ting

4-vo

rtex

syst

ems

IGE.

How

ever

cur

rent

ly 4

-vo

rtex

syst

ems

are

mos

tly c

o-ro

tatin

g an

d it

rem

ains

to

be

inve

stig

ated

whe

ther

thes

e sh

ow a

lso

rapi

d de

cay

IGE.

31

1 Ex

perim

enta

l PI

V

data

an

d flo

w-v

isua

lisat

ion

resu

lts o

f 2-

vorte

x sy

stem

s IG

E

med

ium

m

inor

hi

gh/

med

ium

Th

e ex

perim

enta

l res

ults

fro

m I

RPH

E on

vor

tex

pairs

cre

ated

by

two

impu

lsiv

ely

rota

ted

plat

es c

an b

e us

ed f

or c

ompa

rison

w

ith C

FD re

sults

. The

exp

erim

enta

l dat

a w

ith fo

rcin

g of

Cro

w

mod

es a

re q

uite

uni

que

and

coul

d be

rel

ated

to li

near

sta

bilit

y pr

edic

tions

. 31

1 St

ocha

stic

2D

NS

sim

ulat

ions

TB

D

TBD

m

ediu

m

A s

toch

astic

2D

Nav

ier

Stok

es s

imul

atio

n te

chni

que

has

been

de

velo

ped

an a

pplie

d to

the

wak

e vo

rtex

IGE

prob

lem

. Th

e so

lutio

n of

the

coup

led

syst

em o

f equ

atio

ns is

at l

east

103 ti

mes

fa

ster

tha

n a

clas

sica

l M

onte

-Car

lo s

imul

atio

n. I

t is

how

ever

no

t ful

ly c

lear

how

the

resu

lts o

f th

is r

athe

r un

ique

app

roac

h ne

ed to

be

inte

rpre

ted

and

expl

oite

d.

312

Flow

vi

sual

isat

ion

resu

lts

of

spac

e de

velo

ping

w

akes

ge

nera

ted

at

diff

eren

t he

ight

s ab

ove

the

grou

nd

med

ium

m

ediu

m

high

V

ery

inte

rest

ing

flow

vi

sual

isat

ions

of

2-

vorte

x sy

stem

s cr

eate

d at

diff

eren

t hei

ght a

bove

the

grou

nd w

ere

prod

uced

by

UC

L (to

win

g ta

nk)

and

IRPH

E (im

puls

ivel

y ro

tate

d pl

ate)

. Th

ese

show

how

the

vor

tices

ind

uce

flow

sep

arat

ion

at t

he

grou

nd a

nd h

ow th

e as

soci

ated

turb

ulen

ce is

wra

pped

aro

und

the

vorti

ces.

In t

he w

ater

tan

k te

sts

a di

stur

banc

e, t

rave

lling

w

ith t

he w

ake

gene

ratin

g m

odel

spe

ed,

can

be o

bser

ved

espe

cial

ly fo

r wak

es c

reat

ed v

ery

clos

e to

the

grou

nd. F

or lo

w

initi

al a

ltitu

des

h/b 0

=<0.

25 th

e ro

ll-up

pro

cess

is s

igni

fican

tly

affe

cted

by

the

grou

nd.

312

Com

puta

tion

of

a sp

atia

lly

evol

ving

wak

e IG

E m

ediu

m

high

hi

gh

In a

seq

uenc

e of

2D

tem

pora

l 3D

tem

pora

l an

d 3D

spa

tial

sim

ulat

ions

of

the

wak

e fr

om a

n el

liptic

ally

load

ed w

ing

IGE

(h/b

0=0.

25)

the

diff

eren

ce b

etw

een

and

the

limita

tions

of

each

m

odel

ling

met

hod

have

bee

n ni

cely

illu

stra

ted

by U

CL.

To

enab

le t

he s

imul

atio

n of

the

spa

tially

evo

lvin

g w

ake

a ra

ther

la

rge

lift c

oeff

icie

nt h

as to

be

assu

med

to m

aint

ain

the

leng

th

of th

e co

mpu

tatio

nal b

ox su

ffic

ient

ly sm

all.

31

2 V

ortic

es

crea

ted

clos

e to

th

e m

ediu

m/

min

or

high

C

ombi

ned

flow

vis

ualis

atio

n an

d LE

S si

mul

atio

n re

sults

sho

w

NLR

-CR

-20

08

-02

3

60

Sub-

ta

sk

Sub-

resu

lt pr

actic

al

impl

icat

ion

diffi

culty

to

exp

loit

scie

ntifi

c in

tere

st

com

men

t

grou

nd

high

th

at v

ortic

es c

reat

ed v

ery

clos

e to

the

gro

und

expe

rienc

e a

quic

k an

d vi

olen

t int

erac

tion

with

the

grou

nd, l

eadi

ng q

uick

ly

to

flow

tu

rbul

ence

an

d a

rapi

d de

cay.

Th

eref

ore

vorte

x se

gmen

ts c

reat

ed v

ery

clos

e to

the

grou

nd w

ill n

ot p

ose

a ris

k to

follo

win

g ai

rcra

ft.

32

Ana

lyse

d da

ta f

rom

Fra

nkfu

rt IG

E lid

ar

mea

sure

men

t ca

mpa

ign

high

m

inor

m

ediu

m

The

anal

ysis

of

the

Fran

kfur

t da

ta r

esul

ted

in m

any

usef

ul

resu

lts o

n w

ake

trans

port

and

deca

y in

gro

und

effe

ct, i

nclu

ding

th

e ef

fect

of

cros

s-w

inds

. Th

is i

s ve

ry u

sefu

l fo

r m

odel

ling

thes

e flo

ws

and

for

defin

ing

safe

ai

rcra

ft se

para

tions

, de

pend

ing

on c

ross

-win

d co

nditi

on.

33

Ass

essm

ent

and

real

-tim

e m

odel

ling

high

m

inor

lo

w

Sign

ifica

ntly

im

prov

ed

disc

rete

an

d pr

obab

ilise

d w

ake

trans

port

and

deca

y m

odel

s ha

ve

been

de

vise

d by

U

CL

(DV

M/P

VM

) an

d D

LR (

D2P

/P2P

). Th

ese

are

of g

reat

val

ue

for

asse

ssin

g pr

oper

saf

e se

para

tion

dist

ance

s be

twee

n ai

rcra

ft de

pend

ing

on w

eath

er/w

ind

cond

ition

s.

NLR-CR-2008-023

61

a) q=0.4, k= 1.5, m=-1 mode b) q=1, k=2, m=-1 Figure 1: Comparison of temporal spectra of theory (circles) and computed with spectral method (stars). Two different cases, both for Re=106 (IRPHE and IMFT, Ref. 14).

Figure 2: 3D structure of a viscous centre mode for the Batchelor vortex (UMA, Ref. 16). Contour surfaces are for a perturbation azimuthal velocity corresponding to 0.4.

NLR-CR-2008-023

62

Figure 3: Azimuthally averaged profiles of swirl velocity (left) and axial velocity defect (right). Circles are the experimental data, lines are the least square fits (VM2 model for Uθ and Gaussian for W). Experiments by IRPHE (Ref. 17).

a) ellipses for α= 6 (left), 9 (middle) and 12 deg (right),

U= 46 (line), 67 (squares) and 91 cm/s (circels).

b) Transverse vortex positions for α= 9 deg and U=67 cm/s

Figure 4: Distribution of transverse vortex centre positions, evaluated from high-speed dye visualisation of vortex core position in water tunnel tests by IRPHE (Ref.17). Coordinates are in cm and centred at mean vortex position.

NLR-CR-2008-023

63

Figure 5: The six most energetic modes in the vortex core at x/c=11.2 behind a wing profile in a water tank, computed from a time series of high-speed PIV vorticity fields for α=6 deg and U=46 m/s (IRPHE, Ref. 17).

NLR-CR-2008-023

64

Figure 6: Optimal non-dimensional time as function of wave number. Results from Antkowiak & Brancher (Ref. 24) for a Gaussian vortex are compared to results from IRPHE (Ref. 17).

a) vortex generating plate b) dye visualisation in c) Kelvin-wave excitation (impulsive motion, θω &= ) cross-plane device

Figure 7: Creation of unperturbed and perturbed vortex by impulsive motion of a plate (IRPHE, Ref. 26)

NLR-CR-2008-023

65

Figure 8: Dye visualisation of a travelling wave (end-effect) for different non-dimensional times: ωmaxt=0 (0.5)4.5. Experiments by IRPHE (Ref. 26) with impulsively rotated sharp edged plate.

Figure 9: Comparison between experimental and numerical dispersion of a Gaussian vortex. In experiments (symbols) excitation length is either 40 cm (red symbols) or 10cm (blue symbols). The numerical results correspond to the counter-rotating mode (black), the modes with critical layer (blue and pink) or the retrogade viscous modes (green). Results from IRPHE, Ref. 26.

Figure 10: Wave propagation velocity max,* / θVVV prpprop = as function of initial magnitude of

vortex core radius variation. Results from DNS simulations by CERFACS at ReΓ=104 (Ref. 27). Red line from theory (Ref. 32) and blue line from IRPHE experiment (Ref. 26).

NLR-CR-2008-023

66

a) without random excitation b) with small white noise excitation

Figure 11: Iso-vorticity contours along a vortex core showing a travelling wave initiated by a sudden increase in vortex core radius (3D-LES by CERFACS, Ref. 27).

Figure 12: Vortex bursting phenomena observed in flight (NLR and Airbus in Awiator flight tests) and simulation results of colliding pressure waves along a Lamb-Oseen vortex by CERFACS, using a DNS code (Ref. 30).

a) (rc2-rc1)/rc1=0.5 b) (rc2-rc1)/rc1=1.0

Figure 13: Computed circulation profiles at different times at the mid-collision location, for two different amplitudes of simulated colliding pressure waves (CERFACS, Ref. 30).

Vortex bursting observed in flight Awiator Flight tests (NLR and Airbus)

NLR-CR-2008-023

67

Figure 14: Decay of perturbation energy of travelling waves, depending on initial amplitude. Computed with the ONERA DNS code FLUDILES for m=1 (left) and m=2 (right) disturbance modes (Ref. 29).

a) linear regime (ε=0.01) at T=9.85 b) non-linear regime (ε=0.5) at T=9.85

Figure 15: 3D fields of DNS computed perturbations in axial vorticity for small (ε=0.01) and strongly perturbed (ε=0.5) Lamb-Oseen vortex. Perturbation is for m=1 mode at ReΓ=103. The weakly perturbed flow is still in the linear regime, the strongly perturbed flow is in the non-linear regime, leading to much more complex disturbance and a faster propagation of disturbances.

Figure 16: A numerical simulation of end effects for a suddenly stopped elliptically loaded wing. Simulation by UCL, using the VIC-PFM code (Ref. 31).

NLR-CR-2008-023

68

Figure 17: Temporal LES simulation of the wake of an accelerated elliptical wing, showing the cross-linking of vorticity across the wake symmetry plane (required to compensate the change in circulation strength) and a propagating disturbance along the vortex core (UCL, Ref. 31).

Figure 18: Spatial LES simulation of the same accelerated elliptical wing as shown in Figure 17, showing the travelling waves introduced by the acceleration (computation UCL, Ref. 31).

Figure 19: The amplitude functions of axial velocity for the leading and second eigenmode of a 2-vortex system, at axial wave number α=3, ReΓ=3180 and initial axial flow magnitude U0=0.25. BiGlobal eigenvalue results from UPM (Ref. 35).

Figure 20: Dependence of amplification rate and frequency on axial wave number α for different initial axial flow magnitudes U0, at ReΓ=3180. BiGlobal eigenvalue result from UPM (Ref. 35).

ωi ωr

NLR-CR-2008-023

69

Figure 21: Growth rate of principle coupling modes from linear stability analysis for a Batchelor vortex at Re=20000 in a strain field of strength ε = 0.01 and various axial velocity W0 (IRPHE, Ref. 36).

Figure 22: Temporal DNS of co-rotating vortex pairs with axial flow. Example of computed growth rate levels for the different modes at Re=31400, a/b=0.168 (IRPHE, Ref.37).

NLR-CR-2008-023

70

Figure 23: Temporal 3D DNS at Re=12600 of the merging process of co-rotating vortices with axial core flow (w0=0.6) at initial distance b/a=5 (IRPHE, Ref. 37). Top figure shows vortex pair before, bottom figures show results after merging, without- (blue) and with core flow (red) and for a hypothetical 2D merging (black). The green line is for a different less unstable axial core flow (w0=0.3).

NLR-CR-2008-023

71

Figure 24: Temporal evolution of co-rotating vortex merging, Re=12500, (b/a)0=5 (IRPHE, Ref. 37). Initial situation was perturbed with most amplified mode. 2D computation (figure left), 3D without axial flow (middle) and 3D with axial flow w0=0.6 (right).

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a) test set-up b) profiles at z/c=5.6

c) Dye visualisation d) sketch of perturbation

e) growth inferred from dye visualisation f) growth rate compared with numerical stability analysis of the experimental flow

Figure 25: Test set-up and results for short-wavelength elliptic instability in counter rotating vortices compared with theory (ReΓ=15800, a/b=0.16, W0=0.44, IRPHE, Ref. 38).

Figure 26: Side view (a) and top view (b) of the test set-up (schematic) used by Technical University Eindhoven (TUE-FDL), for measuring wakes behind single vortices and vortex pairs in various levels of grid turbulence. H=1.05, W=0.7 and L=8 m.

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Figure 27: Turbulence grid with 0.1m large flow agitators on rotatable rods (TUE-FDL).

a) core size growth b) standard deviation of vortex position

with respect to mean position

Figure 28: Correlation between vortex radius growth and vortex life time and between standard deviation of distance to mean vortex position (scaled with vortex core radius at initial measurement position Δx=0.26 m) and normalised life time (based on urms and Γ0), Isolated vortex tests, TUE-FDL (Ref. 39).

Figure 29: Vortex core positions (left) and correlation (showing flow symmetry) between vertical position of left and right vortex, showing Crow mode type displacements. Vortex pair created with tip separation d0=0.03 m and measurements are at 3.82 m downstream (TUE-FDL, Ref.39)

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Figure 30: The status of vortex pair (left) as function of t* and ε* for all open grid cases. The angle of Crow mode oscillation with respect to horizontal axis (all grid types). TUE-FDL, Ref.39.

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Figure 31: Spatial evolution of co-rotating vortices with axial flow, through the development of short wavelength instabilities, DNS simulation by CERFACS, Ref. 40. Initial vortex spacing is 10 core radii, ReΓ =104, ratio between axial velocity W and maximum azimuthal velocity V0 is 1.5, ratio between axial velocity in vortex core and V0 is 0.54.

Figure 32: LES simulation of optimal long wavelength forcing of a 4-vortex system with a long wavelength disturbance in the symmetry plane (simulations by ONERA and DLR, Ref. 52).

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Figure 33: Comparison of counter-rotating 4-vortex results at τ*=2.9, for two different circulation strength ratios (temporal LES calculation by UCL, Ref. 53).

Figure 34: Temporal LES simulation of a counter-rotating 4-vortex system, showing the formation of omega loops and transition to turbulence (calculation by UCL, Ref. 53, for Γ2/Γ1=-0.3, b2/b1=0.3).

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Figure 35: Space developing simulation with VIC-PFM method of UCL (Ref. 53) of a counter rotating 4-vortex system with Γ2/Γ1=-0.3, b2/b1=0.3. Results are for a large enough simulation time, with well developed wake flow. Top figure displays a top-view, bottom figure a side-view.

Figure 36: Optimal perturbation with adjoint of the Crow mode, using a long-wavelength perturbation strategy, showing a promising way for enhanced vortex dissipation (ONERA, Ref. 55).

Optimal perturbation

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Figure 37: Initial perturbation of ωx and ωz (left), leading to a near-optimum transient growth of the most amplified Crow instability mode (k=0.9, ReΓ=3600, a/b=0.2, ONERA, Ref. 55). Comparison of energy growth of the k=0.9 Crow mode (right): modal mode (long-dash), optimum forcing with adjoint mode (thick solid) and non optimal forcing with ωx and ωz as shown in left figure (thin solid).

Figure 38: The DLR F13 and F13X model shape for generating a 4-vortex system during wind tunnel tests at TUM-AER (Ref. 57) and water-tank tests by DLR (Ref. 56). Figure right shows the deformation of wing tip vortex in TUM-AER windtunnel, due to interaction with the tail vortex (Γ2/Γ1=-0.3, b2/b1=0.3).

Figure 39: The vortex trajectories (left) and the decay of peak vorticity of the wing tip vortex (right) for tests at different Reynolds number with the large F13X model in the wind tunnel of TUM-AER (Ref. 57).

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Figure 40: The water towing tank of SVA at Potsdam while the F13 model is towed (DLR).

Figure 41: Cross-flow velocity vectors and streamwise vorticity for 2-vortex system at x/b=1.1 (left) and at x/b=166 (right). Results from towing tank tests (DLR).

Figure 42: Cross-flow velocity vectors and streamwise vorticity for 4-vortex system (Γ2/Γ1= -0.3) at x/b=1.7 (left) and at x/b=101 (right). Results from towing tank tests (DLR).

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a) vorticity (Approach Idle) b) vorticity (Thrust for Level Flight)

c) total pressure coefficient Cp,t d) total pressure coefficient Cp,t (Approach Idle, jet areas in red) (Thrust Level Flight, jet areas in red)

Figure 43: Analysis of Airbus wind tunnel data showing the effect of thrust level on vorticity and total pressure (4-engine aircraft, half-wake at x/b=1.3, analysis by NLR, Ref. 65).

x/b= 0.35 x/b= 0.7 x/b= 1.05 x/b= 1.4 x/b= 1.75

Figure 44: Time-averaged flow visualisation (average of 10 images) from water tunnel, showing the process of merging of the jet (red dye injected) and the wing tip vortex (yellow dye) at different downstream positions. Results from U-Bath for h/Dj= 6.7 and R= 0.13 (Ref. 68).

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Figure 45: Effect of jet strength (Rj=Uj/U) on time-averaged iso-vorticity contour plots. Results from U-Bath (Ref. 68) for h/Dj= 4 at x/b= 1.05 and a) Rj=0, b) Rj =0.13, c) Rj =0.34, d) Rj =0.78.

Figure 46: Flow visualisation results at x/c= 4 and x/c=24, showing the sensitivity to jet position with respect to the equally strong flap and wing tip vortex (U-Bath, Ref. 71).

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Figure 47: The effect of jet strength on vortex merging, depending on jet position (experiments by U-Bath, Ref. 71).

Figure 48: Single vortex-jet interaction at x/c= 16. a) Time-averaged and instantaneous maximum cross-flow velocity magnitude, b) vorticity, c) schematic test set-up. Shaded area is the initial vortex core radius at x/c=0.5.

Merger Delayed

c)

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Figure 49: Temporal simulation with FLUDILES code of cold jet-vortex merging showing the different stages in relation to the evolution of turbulent kinetic energy. In support of the interpretation of the ONERA experiments shown in Figure 62 (ONERA, Ref. 69).

a) cruise condition

b) approach c) take-off

Figure 50: Temporal LES of cold jet vortex interaction for cruise, approach and take-off thrust conditions, showing effect of trust level on jet-vortex interaction (CERFACS, Ref. 70).

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a) cruise phase (Δh =0.145b) b) cruise phase (Δh =0.29b)

c) approach phase a) take-off phase

Figure 51: Development of circulation profile Γ(r)/Γ0 with non-dimensional time τ . Results from LES simulations by CERFACS (Ref. 70).

Figure 52: Jet influence on tangential velocity distribution is rather sensitive on model angle of attack. The red-lines are the fitted results with a double Gaussian model. Results from water tank tests with the SWIM-J model (TU-Delft, Ref. 72).

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Figure 53: Initial conditions for time developing LES simulations by UCL for a propelled wake configuration (Ref. 73). Top figure: vorticity; middle figure: axial velocity; bottom figure: transverse vorticity norm.

a) propelled wing wake

b) non-propelled wing wake

Figure 54: Comparison of wake at x/b=2.4 with- and without jets. From temporal LES simulation by UCL (Ref. 73). Left figures compare longitudinally averaged axial vorticity fields and right figures compare the averaged deficit (blue) or excess (yellow) velocity.

Figure 55: Comparison of LES simulation results at x/b= 2.4, for propelled wing (left) and non-propelled wing configuration (right). Temporal LES simulations by UCL (Ref. 73).

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a) initial condition for axial vorticity b) initial condition for velocity deficit

c) axial vorticity at x/b=1.3 (temporal) d) velocity deficit at x/b=1.3 (temporal)

e) axial vorticity at x/b=1.3 (spatial) f) velocity deficit at x/b=1.3 (spatial)

Figure 56: LES simulation results by UCL of wake roll-up behind a multi-vortex wake configuration with jets (Ref. 67). Simulations initiated from the experimental data at x/b=0.3. Comparing spatial and temporal developing LES results with the experimental data (from Airbus) at x/b= 1.3.

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Figure 57: The computed circulation and velocity profile for the completely rolled-up vortex at x/b= 19.3. Results from temporal LES simulation by UCL, initiated from Airbus wind tunnel data for a 4 engine aircraft configuration in high lift condition (Ref. 67).

a) high thrust b) zero thrust

Figure 58: Time evolution of vortex core radius centred on the flap vortex (solid line) and on the wing tip vortex (dashed line). Time developing LES simulations starting from Airbus supplied wind tunnel data (CERFACS, Ref. 67, τ=0 corresponds to x/b=0.3, τ=0.5 to x/b=16).

a) Sta=0.3 b) Sta=0.4 c) Sta=0.5

Figure 59: Example of the results of a parametric study for the effect of the forcing frequency on the evolution of a bi-furcating hot jet (Sta is the Strouhal number for the axial forcing, based on jet diameter and jet velocity). LES simulations by CUT, Ref. 78.

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Figure 60: Rayleigh-Taylor instability (RTI) and centrifugal instability (CTI) for the two-parameter (C,b) family of vortices with a hot core (top figure), with b being the ratio between hot jet and vortex core radius and C defining the density ratio of the hot jet. Figure a) shows amplification rate for CTI (m=0, n=0, k→∞); figure b) shows location of unstable CTI eigenmode; figure c) shows RTI amplification rate for (m=3, n=0, k=0); figure d) shows corresponding frequency ωr/m; figure e) shows most amplification rate for most amplified RTI mode and figure f) the corresponding m/n mode. Above the dotted line CTI is more unstable than RTI (ONERA, Ref. 79).

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Figure 61: Iso-density contour plots from a 2D DNS simulation of the most unstable Rayleigh-Taylor instability (an m=3 mode with ωr=2.82) developing in a vortex with a cold core (ONERA, Ref. 79). a) t= 2π /ωr= 0.157, b) t= 11, c) t=20.4, d) t= 34.5.

Figure 62: Example from experimental data of cold- and hot-jet vortex interaction showing iso-contours of axial velocity close behind a NACA 0012 wing. The hot and cold jet have a different jet velocity in order to maintain the same axial impulse (experiments by ONERA, Ref. 82).

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a) dj/b=0.21, x/b=8

b) dj/b=0.10, x/b=5 c)dj/b=0.05, x/b=3

Figure 63: Iso-contours of flow temperature for various jet-vortex spacing distance dj/b, showing that hot jet mainly acts as a passive scalar (ONERA, Ref. 82).

Figure 64: The large sensitivity of the vorticity centroid to details of the wing-fuselage lift carry-over. Left figure shows fictitious load distribution as derived from half-wake 5-hole rake experiments in DNW-LST wind tunnel, right figure shows the effect of modified load distribution (red) on the position of the vorticity centroid. Airbus test data from Awiator project (see Ref. 87).

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a) geometries considered b) Experimental vorticity at x/b=0.37 (TUM-AER)

c) RANS (SA model, CENAERO), coarse (left), fine grid (middle) and RANS-DES (right).

d) RANS (TAU, DLR): k-ω model, coarse mesh (left), RSM model, coarse mesh (middle), k-ω model, adapted mesh (right)

Figure 65: Iso-vorticity contours from RANS simulations by CENAERO and DLR of the wake flow behind an isolated fuselage, showing importance of turbulence modelling and grid refinement (calculations by CENAERO and DLR, Ref. 88 and Ref. 86).

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a) x/b=0.02

b) x/b= 1.0

c) x/b= 4.7 Figure 66: Effect of landing gear (right) on axial vorticity (top), turbulence intensity Tux (bottom), from hot-wire measurements by TUM-AER (Ref. 89 and Ref. 90).

Increased turbulence due to landing gear

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Figure 67: RANS simulation of the complex vortex flow topology around an isolated landing gear (calculations by DLR, Ref. 86).

a) initial condition for axial vorticity of elliptically loaded wing

b) initial condition for axial velocity

no velocity defect with velocity defect

c) axial vorticity at τ =0.02

no velocity defect with velocity defect

d) axial vorticity at τ =0.25

Figure 68: Temporal LES simulations by UCL of wake roll-up of an elliptic loaded wing (Ref. 92), with- and without simulated wake velocity defect. Simulation made for ReΓ= 104.

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a) τ =0.05 b) τ =0.08

c) τ =0.10 d) τ =0.25

Figure 69: Temporal evolution of the wake, shown by iso-contours of the total vorticity norm ω for simulated wake with velocity defect (UCL, Ref. 92).

Figure 70: Results from temporal LES simulations of wake rollup by UCL (Ref. 92), showing longitudinally and azimuthally averaged profiles of circulation and tangential velocity. Dashed line is the reference case without velocity defect (ReΓ= 104). Solid line (ReΓ= 104) and dash=dot line (ReΓ= 106) are for cases with simulated velocity defect.

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Figure 71: Distribution of pressure coefficient and streamlines around a NACA0012 airfoil at 0 deg (left) and 10 deg (middle) angle of attack at three distances h/c from the ground (panel method calculation by UCL, Ref. 93). Figure right shows lift coefficient as a function of angle of attack at different distances h/c from the ground.

Figure 72: Effect of Reynolds number on the roll-up of a wake vortex sheet generated by an elliptic wing in ground effect (h/b=0.25). 2D time developing DNS simulations by UCL (Ref. 93).

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a) side-view

b) top-view

Figure 73: Comparison of vortex filament simulation (UCL, left figures, Ref. 98), with forced Crow mode experimental data from IRPHE (right figures). Vortices released at h/b0= 6, initial amplitude a0=0.0417b0 and wavelength λ/b0=5. Comparison is made at τ*=3.8.

a) τ = 4.7, initial perturbation a0/b0=0.01 b) τ = 9.8, initial perturbation a0/b0=0.001

Figure 74: Simulation of Crow mode in ground effect. Depending on initial amplitude the vortex linking may occur just above ground or not, leading to very different interaction with the ground. UCL simulations with 3D vortex filament method, vortices released at h/b= 6 (Ref. 98). Note that low initial perturbation case (right figure) is shown at a two times larger time than the high initial perturbation case.

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a) τ*=0.48 b) τ*=1.62

c) τ*=2.29 d) τ*=2.96

e) Decay of kinetic energy f) decay of circulation strength

Figure 75: LES simulation of a two-vortex system initiated at one vortex spacing above the ground and inducing turbulent flow separation at the ground underneath (CENAERO, Ref. 99).

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a) τ*=0.32 b) τ*=0.48

c) decay of circulation strength

Figure 76: LES of a 4-vortex system (Γ2/Γ1=-0.3, b2/b1=0.3) released at h/b1=1 above ground in zero wind conditions (UPS-IMFT, Ref. 100).

Figure 77: Side view dye visualisation of vortices created at h/b0=2 above ground and moving into ground effect at different ReΓ (IRPHE, Ref. 101). Showing development of short wavelength instabilities, depending on Reynolds number.

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Figure 78: Longitudinal cross-section of a primary vortex at t*=2 (left, showing probably centrifugal like instabilities) and at t*=5.2 (right, showing probably elliptical instabilities). Corresponding vorticity plots are shown in bottom figures (IRPHE, Ref. 101, ReΓ=5200).

a) ReΓ= 5200 b) ReΓ= 2500 Figure 79: Volume LIF visualizations for vortices created at h/b0= 2 and two Reynolds numbers (IRPHE, Ref.101). Fluorescein (gree dye) injected on the ground and Rhodamine (red dye) visualizes one of the primary vortices.

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Figure 80: Observed growth rate of Crow instability for vortices created at h/b0= 6 with sinuously disturbed wake generator (wave-length 4.8b0 and initial amplitude 0.04b0 (ln(A/b0)=-3.2), b0= 0.025m). Measurements by IRPHE (Ref. 101).

Figure 81: Comparison of experimental (IRPHE, Ref. 101) and computed (UCL, Ref. 103) results at t*= 4, for vortices created at h/b=2 above the ground at ReΓ= 3500. PIV measurements (top left), 3D simulation (top middle), flapping plate simulation (top right), LIF visualisation (bottom left), axial vorticity perturbation in a slice of 3D simulation (bottom middle). 3D simulation result at t*=7.8 (bottom right).

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a) vortices in cross-wind τ*=1.53 b) vortices in headwind τ*=2.96

c) decay of Γ5-15. d) decay of total circulation Γmax.

Figure 82: Effect of head- or crosswind on vortex decay IGE. Wind at initial vortex height h=b0 is equal to initial sink velocity of the vortices. LES simulations by CENAERO and UCL, Ref. 95.

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a) crosswind V(h)= V0, τ*=1.06 b) crosswind V(h)= V0, τ*=2.06

c) crosswind V(h)= 2V0, τ*=1.09 d) crosswind V(h)= 2V0, τ*=2.10

Figure 83: LES simulations of vortex pair in two different levels of crosswind (IMFT, Ref. 95). Crosswind at initial vortex altitude h=b0 is V0 or 2V0. (V0 is the initial vortex sink speed).

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a) vortex trajectories

c) vertical positions against time

b) lateral displacement

d) decay of Γ5-15 with time

Figure 84: Comparison of wake behaviour in crosswind (Ref. 95), from LES simulations by UCL (filtered Smagorinsky model for crosswind R=V(h)/V0 = 1 only) and IMFT (Dynamic Mix model, for two levels of crosswind: R=1 and R=2).

y/b0

z/b0

z/b0

t*

t*

y/b0

t*

0155 /ΓΓ −

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a) τ*=1.59 b) τ*=3.18

Figure 85: Average vorticity contours with 10% random circulation variation of the left vortex. Quantification of the effect of uncertainties with Polynomial Chaos Expansion solutions of the Navier-Stokes equations (IST, Refs. 96-97).

a) 2-vortex model in water-tank b) test set-up

c) development of separating vorticity layer at ground (model height h/b=0.25)

Model carriage: Speed ≤ 1.5 m/s

Tank cross section: 1x1m2

Additional floor installed to investigate ground effects

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Figure 86: Towing tank PIV measurements of 2-vortex system IGE (DLR, Ref. 105).

Figure 87: Vortex trajectories (red) and circulation decay (blue) development for system of co-rotating vortices (Γ2/Γ1= 0.3, b2/b1=0.3) released at different heights above the ground (ground is at bottom of the figures). From PIV measurements with F13 model (DLR, Ref. 105).

Figure 88: Vortex trajectories (red) and circulation decay (blue) development for system of counter-rotating vortices (Γ2/Γ1= -0.3, b2/b1=0.3) released at different heights above the ground (ground is at bottom of the figures). From PIV measurements with F13 model (DLR, Ref. 105).

Figure 89: Towing-tank flow visualisation of a wake generated in ground effect at h/b0= 0.25 (UCL, Ref. 106).

t* ≈ 0.045 t* ≈ 0.19

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Figure 90: Spatial developing wake roll-up of an elliptically loaded wing IGE (h/b= 0.25, CL=6, 50 million grid points, UCL, Ref. 107).

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2D 3D time-developing 3D-spatial developing (vorticity field) (spatial averaged vorticity) (temporal averaged

vorticity)

Figure 91: Comparison of 2D, 3-D time developing and 3D-spatial developing wake evolution (h0/b=0.25, no wind, UCL, Ref. 107).

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a) WakeFRA site, showing position of sensors b) scatter plot of lateral vortex

positions for all over flights

c) Scatter plot of average lateral transport d) Normalised circulation evolution with time. of vortices as function of crosswind at z*=0.6b0

Figure 92: Results from WakeFRA test campaign (DLR, Ref. 108).

y [m]

t [s]

VWV [m/s]

v [m/s]

Γ*

t*

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a) minor crosswind, v* ≈ 0 b) weak crosswind, v* ≈ 1.0

Figure 93: Examples from WakeFRA dataset (symbols) showing a different rebound already in mild cross-wind conditions and comparison with predictions from the modified D2P and P2P model (DLR, Ref. 108).

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Figure 94: Wake decay of B747 vortices created at 50 to 60m above ground according to WakeFRA data measured by Airbus and DLR at Frankfurt Airport in 2004. Analysis made by NLR (Ref. 109).

Figure 95: Compilation of final observed wake positions (B747 sub-set of WakeFRA 2004 data, analysed by NLR, Ref. 109).

0

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Γf [m2/s]25L, port25L, starb25R, port25R, starbinitial

Final observation

Initial observation

0 2 4 6 8 NM

final position w.r.t. runway

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25R, starbaircraft (25R)

1st building (25R)2nd building (25R)

25R (25L)

zmax

High rebound in windshear

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final distance to lidar

WV from 25Lalmost drifted to 25R

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Figure 96: Example of in-depth case-by-case checking of vortex characteristics and weather conditions (including cross-checking of lidar and SODAR-RASS wind profiles) for the B747 sub-set of the 2004 WakeFRA data (NLR, Ref. 109).

Figure 97: Asymmetric rebound behaviour of vortices depending in cross-wind, observed in WakeFra data. Left figure shows rebound height z*

min from analysis by DLR (Ref. 108), right figure shows difference in rebound height for port and starboard vortex for B747 vortices (NLR, Ref. 109).

-30

-20

-10

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(zp-zs)r [m]

25L25R

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Figure 98: Comparison between LES and DVM results for a case with crosswind. Results from the previous VFS method are shown in top figures and from DVM with improved IGE model in the bottom figures. Solid lines are the DVM results (blue for port and red for starboard vortex), crosses are LES results. Results from UCL (Ref. 111).

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Figure 99: Onset of more rapid decay of vortices shortly after reaching the rebound height zmin at t*=t*g+0.25, as observed in WakeFra dataset, and adaptation of P2P model for rapid decay IGE (DLR, Ref. 108).

)*(*exp

)*(*exp*)( *

2*2

2

*1

*1

2*

155 TtR

TtRAt

−−

−−

−−=Γ − νν

diffusion

rapid decay

)*(*exp

)*(*exp*)( *

2*2

2

*1

*1

2*

155 TtR

TtRAt

−−

−−

−−=Γ − νν

diffusion

rapid decay

Γ00 = Γ(t*=tg*+0.25)

⇒−= 1**2 gtT 25.0** += gtt

being the time of minimum vortex height*gt

effective onset of decay

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Figure 100: Modified parameters as applied in the P2P model (DLR, Refs. 108, 112 and 113) for the secondary vortex in cross-wind conditions. The secondary vortex is released when the primary vortex has reached height zsec and the initial strength of the secondary vortex is a fraction of the primary vortex strength at height zsec (Γsec/Γ). Both parameters are a function of crosswind magnitude.

Lee-side vortex rebounds earlier

Lee-side secondary vortex is stronger

synthesis of eu far-wake project results · project synthesis task. results and conclusions...

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