Wake-Vortex Topology & Decay New Insights from Observation & Simulation

Transcription

1 Wake-Vortex Topology & Decay New Insights from Observation & Simulation Frank Holzäpfel, Takashi Misaka,, and Ingo Hennemann Institut für f r Physik der Atmosphäre Deutsches Zentrum für f r Luft- und Raumfahrt Oberpfaffenhofen LES codes, post-processing capabilities vortex descent & circulation decay vortex topology pressure waves - double rings - vortex bursting - vortex funnels turbulent mixing detrainment Vortragstitel 1

2 LES codes LESTUF finite differences, second order Boussinesq-approximated Navier-Stokes equations modified Smagorinsky SGS closure MGLET finite volume, fourth order compact scheme, massive parallel Boussinesq-approximated / anelastic Navier-Stokes equations Lagrangian dynamic subgrid scale model

3 initial conditions pre-runs of stably stratified turbulence 3 initializations of passive tracers 512 m * =0.01 N * =0.35 L t* = m 384 m N * * 0 M 0.01 L/M L/M L/M 0.05 L L/M L 0.23 L L L A Lamb-Oseen vortices 0 = m²/s b 0 = 47.1 m r c /span = 5% 2 m/s rms fluctuations at r c

4 initial conditions pre-runs of stably stratified turbulence 3 initializations of passive tracers 512 m * =0.01 N * =1.0 L t* = m 384 m N * * 0 M 0.01 L/M L/M L/M 0.05 L L/M L 0.23 L L L A Lamb-Oseen vortices 0 = m²/s b 0 = 47.1 m r c /span = 5% 2 m/s rms fluctuations at r c

5 post processing vortex tracking curvature radii search direction: correction: pressure minimum segment length 1.5 b 0 find optimal plane iterative search of inscribed circle

6 vortex descent (MGLET) excessive descent distances > 16 b 0 (2500 ft) in neutral atmosphere far beyond 1000 ft in Reduced Vertical Separation Minimum (RVSM) airspace prevented by stable stratification typically prevailing in tropopause region

7 vortex topology 2-phase decay: shortening of vortex segments in flight direction topology caused by mutual velocity induction redistribution of 5-15 by vortex stretching and compression and / or collision of pressure waves * = 0.05, N * = 0, L t * = 0.41

8 circulation decay characteristics LESTUF MGLET good agreement in stable stratification large uncertainties in neutral strat. neutral - weak stratification: three-phase decay of circulation to vortex line: diffusion phase rapid decay phase ring diffusion phase

9 effects of integral turbulence length scales ( * = 0.23) with increasing L t : more rapid decay in diffusion phase 3-phase decay concealed more complex topology * = 0.23, N * = 0, L t * = 0.85

10 effects of integral turbulence length scales ( * = 0.23) primary vortices conduct work on turbulent eddies by means of vortex stretching energy of primary vortices reduced (cf. turbulence theory) more intense eddies faster decay in diffusion phase weak effect of in ground proximity L t /b 0 < 1: consider and L t * = 0.23, N * = 0 Holzäpfel et al., Aerospace Science & Technology 7 (2003)

11 effects of integral turbulence length scales ( * = 0.4) for L t /b 0 > 1 effect of L t runs into saturation LES in large domains required

12 vortex topology large domain m³ * = 0.4, N * = 0, L t * = 2.2

13 detrainment / sinusoidal oscillations / hollow vortex cores / vortex bursting / vortex funnels? photo series Frank Holzäpfel 2007

14 Vortex Bursting Spalart (1998): "phenomenon where the region marked by ice crystals or smoke contracts in portions of the vortices and expands in others" P.R. Spalart, Airplane trailing vortices, Annu. Rev. Fluid Mech. 30, 107, 1998.

15 Vortex Bursting reported from flight experiments visualized by smoke 1,2 or contrails 3 in towing tank 4 and numerical simulations 5 always connected with abrupt change of diameter of marker around vortex core traveling frequently along the vortex axis in either direction sometimes two bursts would travel toward each other, eventually colliding and leaving behind an intensely marked disk-like parcel of tracer 2 sometimes also termed puff or pancake 6 in vortex core region also funnel-shaped features surrounded by pancakes 3 no explanation of the causes & structure of the bursts until Moet et al. 5 suggested collision of pressure waves emanating from the location of vortex linking 1 H. Chevalier, Flight test studies of the formation and dissipation of trailing vortices, J. Aircr. 10, 14, I. Tombach, Observations of atmospheric effects on vortex wake behavior, J. Aircr. 10, 641, A. P. Brown, On the specification of wake vortex encounter gust-fields from flight data, AIAA Paper T. Sarpkaya and J. J. Daly, Effect of ambient turbulence on trailing vortices, J. Aircr. 24, 399, H. Moet, F. Laporte, et al., Wave propagation in vortices and vortex bursting, Phys. Fluids 17, P. R. Spalart, Airplane trailing vortices, Annu. Rev. Fluid Mech. 30, 107, 1998.

16 vortex topology neutral stratification pressure waves helical instabilities double rings vortex bursting? Side view animation not available in pdf Top view * = 0.01, N * = 0, L t * = 0.85, tracer initialized in half oval, domain laterally extended to 512 meshes

17 pressure waves - helical instabilities - double rings - vortex bursting? photo Sven Lüke, 16 Nov. 2006, 8:53, t*=5.6 t*=5.9 t*=6.2 initiation of helical instability due to vortex linking collision collision reorganization t*=6.5 on t*=6.8 t*=7.3 bur stin g bursting t*=8.2 t*=10.0 t*=11.4 second Institut vortex für Physik der Atmosphäre linking

18 pressure waves - helical instabilities - double rings - vortex bursting? photo Sven Lüke, 16 Nov. 2006, 8:53, t*=5.6 t*=5.9 t*=6.2 initiation of helical instability due to vortex linking collision collision reorganization t*=6.5 t*=6.8 t*=7.3 reorganizati colliding pressure onwaves temporarily & locally bur stin g bursting increase r c and decrease 5-15 subsequent reorganization of vortex tracer distribution indicates no vortex bursting t*=8.2 t*=10.0 t*=11.4 second Institut vortex für Physik der Atmosphäre linking

19 vortex topology cruise conditions (weakly stably stratified) Side view animation not available in pdf Top view * = 0.01, N * = 0.35, L t * = 0.95, tracer in half oval

20 Vortex Bursting Radiative Transfer Simulation with libradtran/mystic T. Zinner, M. Schönegg, MIM, LMU vortex bursting: - visualized by passive tracer - caused by collisions of secondary vorticity structures propagating along vortex lines - not related to local vortex decay max. ice water content 0.2 g/m³, eff. radius 25 m t * = 4.6, * = 0.01, N * = 0.35, L t * = 0.95 t * = 2.3, * = 0.23, N * = 0.35, L t * = 0.75

21 vortex bursting Vortex / puffs Bursting / pancake vortices Side view animation not available in pdf Top view * = 0.01, N * = 0.35, L t * = 0.95, tracer initialized in half oval

22 Vortex Bursting u r c 5-15 t * = 4.6, * = 0.01, N * = 0.35, L t * = 0.95

23 Vortex Bursting v spreading of tracer caused by secondary vorticity structures propagating along the vortex lines c 5-15 vortex bursting not related to local vortex decay t * = 4.6, * = 0.01, N * = 0.35, L t * = 0.95

24 Vortex Bursting & Vortex Funnels Anthony P. Brown, AIAA Paper photo: DLR Falcon research a/c

25 Evaluation of detrainment Control volume and tracer distribution Tracer contour ( * = 0.01, N * = 0.35, L t * = 0.95) Axial distribution of tracer concentration Primary wake Section 2 Secondary wake Control volume for primary wake Folie 26 W&F 2. Statustreffen > W1 > D. Fischenberg >

26 detrainment of tracer from primary wake similar to circulation decay half-value times coincide ~ 40% of tracer remains with primary vortices low sensitivity on initial tracer distribution

27 detrainment of tracer from primary wake vertical/horizontal extent and axial variance (c thres = 5%) z * y * secondary wake: N< high & slender N> shallow & wide

28 Current Work & Outlook Current Work & Outlook interaction with ground & crosswind wall-resolving LES Anton Stephan

29 Current Work & Outlook interaction with ground & crosswind FAR-Wake case animation not available in pdf head-, crosswind, surface roughness

30 Current Work & Outlook flying through LES domain... Front view Perspective view animation not available in pdf

31 Conclusions 3-phase decay in neutral to weak stratification... and long-lived vortex (double) rings excessive descent distances in low turbulence / neutral stratification integral turbulence length scales may affect decay in diffusion phase vortex decay related to stretching of environmental vorticity curvature radii finally approach r /b 0 1 vortex bursting is related to the collision of secondary vorticity structures propagating along vortex lines propagating secondary vorticity structures may generate vortex funnels tracer detrainment goes along with circulation decay low sensitivity on initial tracer distribution F. Holzäpfel, T. Misaka, I. Hennemann, "Wake-Vortex Topology, Circulation, and Turbulent Exchange Processes," AIAA Paper , extended version submitted to Physics of Fluids.