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Numerical simulation of the vorticesmerging process in the extended

near-field of an aircraft wake

Laurent NybelenHenri Moet, Roberto Paoli, Guihlem Chevalier

WakeNet2 EuropeWG7 - Workshop at ONERA Toulouse

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Outline of the presentation• Introduction

- Wake vortex physics- Objectives

• Analysis of the merging process of two co-rotating vortices inthe extended near-field

- Configuration and initial condition- 2D / Stable merging- 3D / Unstable merging, development of the elliptic instability- Reynolds number effects

• Conclusion

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Wake vortex physics

• aircraft wake : intense vortices• wake vortices compact regions

of air, strong rotational motion

• lifting surface in a fluid⇒ vortex originating fromsurface discontinuity (wing tip,flap, horizontal tailplane)

• hydrodynamically generatedpressure difference (fluidacceleration)

suction

pressure

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Wake vortex physics : phenomenology ⇒ near field : x/c=O(1) - roll up / concentraded vortices(wing tip, flap, nacelle, fuselage, horizontal tailplane,...)

⇒ extented near field : x/B=O(1) - completion of roll-up - merging of primary co-rotating vortices - reduction of vortices number ⇒ far field : x/B=O(10) - symmetrical pair of counter-rotating vortices - mutual induction, linear instability ⇒ dispersion regime: x/B=O(100) - vortex decay - atmospheric conditions / instablities nonlinear phase

(downstream distance x - aerodynamic chord c - wing span B)

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Objectives of the study• Obtain a better understanding of the mechanism governing the evolution of wake vortices in the extended near-field of the wake

• Characterize the merging process in the extended near-field• Parametric study to check the sensitivity using

– different initial vortex profiles– different Reynolds numbers

2D/stable merging 3D/unstable merging

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Numerical tool

Numerical tool solving Navier-Stokes equations : three dimensional unsteadyflows on structured grids (uniform/no uniform mesh)

⇒ NTMIX3D : - finite difference approximation - spatial discretization : 6th order compact scheme (Lele, JCP, 1992)

Large Eddy Simulation (LES) :subgrid scale : Filtered Structured Function model (Ducros et al., JFM , 1996)

⇒ Numerical tool proved to be suitable for treating unsteady vortex flows subjected to instability mechanisms (linear stability analysis) (Laporte ,INPT Thesis, 2002 / Moet, INPT Thesis, 2003)

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Lamb-Oseen model :

⇒ 1 characteristic length scale : rc

Jacquin VM2 model (Fabre et Jacquin, PoF, 2004) :

⇒ 2 characteristic length scales : a1 and a2

)))/(exp(1(2

),( 2crr

rtrv η

πθ −−Γ

=

vθ (r,t) =Ω0 r

(1+ (r /a1)4)(1+α)/4 (1+ (r /a2)

4)(1−α)/4

Initial vortex profile

Generic configuration :System of a two co-rotating and symmetrical (same core size and circulation)vortices, without axial velocity

Initial configuration

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3D 2D/3Da/b=0.15

2D 2D 2D 2D a/b=0.1

240000 10000 5000 1500 750ReΓ = Γ/ν

Points number of the mesh grid• 2D simulation ⇒ Ο(1.6×105)

• 3D simulation ⇒ Ο(6×106)

DNS LES

Mesh grid and configurations

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2D/stable merging : dynamics

Global dynamics (Jacquin VM2initial vortex system)

• isocontours of vorticity deformed : elliptic forms • exchange of their vorticity• creation of vorticity filaments• merging

Configuration : a/b0=0.15 ReΓ=10000

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Step 1 :1st diffusionphase t*=1

Step 2 : Convective phaset*=4

Step 3 : 2nd diffusion phase t*=4.5

Step 4 :Final phase t*=5. 3

• Initial separation distance (a/b)0 = 0.15

• Turnover period of the system : tc=2π2b2/Γ

• ReΓ=10000

2D/stable merging: dynamics

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• The merging process starts when the critical ratio a/b is reached at (beginning of phase 2)

(a/b)crit=0.24±0.01

Good agreement with theorical/experiments (Meunier andal., PoF, 2002) and experiments/numerical (Leweke andal., ODAS, 2001)

2D/stable merging: analysis

• Identical slope of separation distance during the convective phase

Reynolds number independence !

Initial ratio (a/b)0=0.1

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⇒ The final vortex profile has two characteristic length scales no matter the initial conditions are used!

Configuration : (a/b)0=0.15 ReΓ=10000

2D/stable merging : final vortex profile

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Development of a short wavelengthinstability due to the strain fieldinduced by one vortex on the other⇒ Wavy displacement of the vortexcore

⇒ Unstable modes saturate the flow becomes turbulent

3D/unstable merging: dynamics

Global dynamics(a/b)0=0.15 ReΓ=10000

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3D/unstable merging: analysis

1.4163.294.5240000

3.296.52.47510000

JacquinVM2λ/a

JacquinVM2σ*

Lamb-Oseenλ/a

Lamb-Oseen

σ*ReΓ

⇒ At high Reynolds number : good agreement with the theoreticalprediction (Le Dizes and Laporte, JFM, 2002) in the initial case of Lamb-Oseen vortices⇒ The growth rate of the short wavelength instability is higher of 30% foran initial system of Jacquin VM2 vortex (Fabre et Jacquin, PoF, 2004). Butthe wavelength of the most unstable mode of the elliptic instability is notidentical

Spectral decomposition of the kinetic energy :• to extract the growth rate σ* of the instability during the linear phase• to identify the most unstable mode characterized by a wavelength λ/a

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Evolution of the characteristic parameters, b the distance separation andthe ratio a/b during the unstable merging.

⇒ The unstable merging process is decomposed in two phases⇒ Little difference between the two initial condition cases

3D/unstable merging

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⇒ A profile quasi-similar and describes by two length scales no matter the initial conditions !

Configuration : (a/b)0=0.15 ReΓ=10000

3D/unstable merging : final vortex profile

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Conclusion2D/stable merging :• No difference of the two-dimensionnal dynamic flow between the two initialvortex model• For all Reynolds number considered here, we obtain a same threshold ratio• Purely convective phase which is independent of the Reynolds number.

3D/unstable merging :• The growth rate of the short wavelength instability during the linear phase ishigher in the case of initial condition with Jacquin VM2 vortices

• The 3D/unstable merging is quicker than the 2D/stable merging• The structure of the final vortex seems to be intrinsic of the physical mergingphenomenom

Which will be the effect of an axial velocity on the merging process ?Interaction or/and apparition of others instability mechanisms ?