The persistence of wake vortices analyzed through the long-term evolution of the Crow instability

Transcription

1 The persistence of wake vortices anayzed through the ong-term evoution of the Crow instabiity Hoy JOHNSON* Vincent BRION Laurent JACQUIN WakeNet-Europe Workshop

2 Introduction Cam atmospheric conditions (ow turbuent dissipation ) are the worst case scenario for ATM because of the persistence of wake vortices ε cam tt/tt 00 Characteristic timescae tt 00 = 2222bb22 ΓΓ tt/tt 00 Crow In this case, the Crow instabiity determines the eary evoution of the fow 2

3 Introduction The Crow instabiity eads to the connection of the WV and to the formation of vortex rings Crow rings The subsequent evoution of those rings has been argey negected in the iterature, whie recent work (Leweke & Wiiamson, 2011) shows that the evoution can be dramatic. 3

4 Leweke & Wiiamson s experimenta work (2011) Water tank experiment Observation (PIV) of the evoution Second reconnection : return of the origina vortex pair?!? In the present work, we first try to reproduce the evoution shown by Leweke using DNS of the Navier-Stokes equations. From Leweke and Wiiamson,

5 Method for DNS 1 - Initia veocity fied + ε 2-D Base fow Linear mode λλ 8bb ε <<1 perturbation ampitude w/r base fow 2 - Expore the infuence of εε Reason for DNS (and not, say, LES) - No initia turbuence (start with aminar fow) - Aowed by rather ow Reynods number (Re 1000) 5

6 Non-inear growth of the Crow mode Perturbation energy growth G(t) = E'(t) E'(0) 2 - Non-inearities 1 - Linear growth ε =10 3 ( 0,1% ) Drop-off at t 9t 0 «pinching of the vortices» first non-inear phenomenon after Crow /t 0 6

7 Long-term dynamics of the Crow instabiity Initia = Direct mode ε =10 3 French computationa centre GENCI Project 7

8 Sef-sustained dynamics of the vortex ring t/t DNS Bird s eye view 8

9 Sef-sustained dynamics of the vortex ring t/t DNS L L = 0.24 Theory From Dhanak and Bernardinis, 1981 L = 0.2 Quasi-perpetua periodic evoution if hardy disturbed 9

10 Dynamics of an eiptic vortex ring t/t DNS L L = 0.24 Theory From Dhanak and Bernardinis, 1981 L = 0.2 Quasi-perpetua periodic evoution if hardy disturbed 10

11 Dynamics of an eiptic vortex ring t/t DNS L L = 0.24 Theory From Dhanak and Bernardinis, 1981 L = 0.2 Quasi-perpetua periodic evoution if hardy disturbed 11

12 Dynamics of an eiptic vortex ring t/t DNS L L = 0.24 Theory From Dhanak and Bernardinis, 1981 L = 0.2 Quasi-perpetua periodic evoution if hardy disturbed 12

13 Dynamics of an eiptic vortex ring t/t DNS L L = 0.24 Theory From Dhanak and Bernardinis, 1981 L = 0.2 Quasi-perpetua periodic evoution if hardy disturbed 13

14 Dynamics of an eiptic vortex ring t/t DNS L L = 0.24 Theory From Dhanak and Bernardinis, 1981 L = 0.2 Quasi-perpetua periodic evoution if hardy disturbed 14

15 Dynamics of an eiptic vortex ring t/t DNS L L = 0.24 Theory From Dhanak and Bernardinis, 1981 L = 0.2 Quasi-perpetua periodic evoution if hardy disturbed 15

16 Dynamics of an eiptic vortex ring t/t DNS L L = 0.24 Theory From Dhanak and Bernardinis, 1981 L = 0.2 Quasi-perpetua periodic evoution if hardy disturbed 16

17 Dynamics of an eiptic vortex ring t/t DNS L L = 0.24 Theory From Dhanak and Bernardinis, 1981 L = 0.2 Quasi-perpetua periodic evoution if hardy disturbed 17

18 Resuts from a rea fied experiment 18

19 Long-term dynamics of the Crow instabiity : summary The vortex dynamics after inking is very compex. In cam atmospheric conditions, the vortices are ikey to remain powerfu for a ong time εε = instabiity ring dynamics Γ inking ΓΓ tt/tt 0 We observed a quasi-stabe regime of periodic vortex deformations, which is backed up by eiptic vortex ring theory. The case of Leweke (reformation of the vortices) coud not be reproduced by our DNS (one waveength computed), may be singuar 19

20 How can we disrupt this dynamics in order to reduce risks? Linear stabiity theory : «the adjoint mode is optima for perturbation growth» Adjoint operator : ( q 1, Aq 2 )= ( A + q 1,q 2 ) scaar product ( q 1,q 2 )= q * V 1. q 2 dv 20

21 Linear stabiity theory appied to the Crow instabiity Perturbation energy growth G(t) = E'(t) E'(0) Adjoint mode growth (transient then exponentia) Direct mode growth (exponentia) /t 0 21

22 Non-inear growth of the adjoint Crow mode Linear growth Non-inear growth : ε =10 3 ( 0,1% ) ε = ( 3% ) 2 different behaviours : - exponentia then drop-off (same as for direct mode ε <<1 - by-pass of the Crow growth ε <1 22

23 Crow instabiity deveopment from the adjoint mode Adjoint mode ε = French computationa centre GENCI Project 23

24 By-pass of the Crow instabiity Adjoint mode ε = French computationa centre GENCI Project 24

25 Search for the critica ampitude Δk Δk Δkk = Measure of the fow disruption Critica ampitude 1% < ε C < 2,2% 25

26 Efficiency comparison with white noise How robust is the adjoint perturbation? test response to white noise keeping the same tota energy Noise 1 : Crow waveength, random distribution in space adjoint ε=10-3 Noise 2 : random distribution in wavenumber and space noise 1 noise 2 26

27 Discussion In a rea ife situation, using the adjoint perturbation : 1 - How strong woud the perturbation have to be? in terms of Lift = ρ U Impuse I wake = Γb I pert = V ω x dv I pert I wake = = 6.5% 2 - Where woud it need to be paced? b pert b = y pert b = on-going research b = 50m adjoint perturbation ΔLL = 6.5% bb pppppppp =2.8m y pert = 21. 8m 27

28 Concusion 1 - In cam atmospheric conditions, wake vortices can persist much onger than expected, in the form of rings. The effect of higher Reynods number on this dynamics must be investigated. 2 The effect of the initia ampitude of perturbation has been investigated by DNS 3 - The adjoint Crow mode with sufficient ampitude (εε 2%) dissipates the vortices without even estabishing the Crow instabiity 4 - The necessary strength of the perturbation seems feasibe, the ony remaining question is that of the impementation 28