Resuspension by vortex rings

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Sharyl Cain
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1 Resuspension by vortex rings Stuart Dalziel A prototype for resuspension in turbulent flows? UNIVERSITY OF CAMBRIDGE

2 collaborators Nastja Bethke (BNP Paribas) Ian Eames (UCL) Rick Munro (Nottingham) Anna Mujal (UPC)

3 outline Introduction resuspension, wakes Vortex rings modelling, solid boundaries Particle beds crater formation, shapes & scalings Time dependence shear at bed, impact on ring development Other configurations cross-flow, uncompacted beds, underlying structure Conclusions

4 outline Introduction resuspension, wakes Vortex rings modelling, solid boundaries Particle beds crater formation, shapes & scalings Time dependence shear at bed, impact on ring development Other configurations cross-flow, uncompacted beds, underlying structure Conclusions

with a particle layer Hydrodynamics Lift and drag

5 resuspension How does dust get suspended? Ballistic mechanism Collision of moving particles with a particle layer Hydrodynamics Lift and drag forces due to velocity differences Buoyancy forces u Lift Drag Buoyancy

6 hydrodynamics u Lift Drag Lift ~ f u 2 a 2 Drag ~ f u 2 a 2 or ua Buoyancy ~( p f )ga 3 Cohesion Rolling/sliding resistance Critical velocity Buoyancy dust sand pebbles No motion until Large particles : Drag ~ Rolling/sliding Medium particles: Lift ~ Buoyancy Small particles: Lift ~ Cohesion

7 Shields parameter lift stress area ~ or buoyancy buoyancy Resuspension: c Generically Steady turbulent flow t p gd 2 u* gd p u 2

8 wakes

9 Shields parameter lift stress area ~ or buoyancy buoyancy Resuspension: c Generically Steady turbulent flow t p gd 2 u* gd p u 2 Impact i p U 2 gd

10 modelling Critical impact Shields parameter 2 fuc c ga Viscous sublayer p f U d U ~ 2 U d ~ U

11 modelling For small particles V s 1 p f 18 f g 2 a Re s Va s ga p Critical Shields parameter c U 3 Re 1 2 f c s ~ p f ga Res Res 1

12 modelling c Re s

13 wakes Re ~ 850

14 ideas Simplify the wake problem Resuspension by vortex rings Can raindrops have wakes? Resuspension by droplets

15 collision with particles

16 outline Introduction resuspension, wakes Vortex rings modelling, solid boundaries Particle beds crater formation, shapes & scalings Time dependence shear at bed, impact on ring development Other configurations cross-flow, uncompacted beds, underlying structure Conclusions

17 vortex rings

18 parameters 100 W 700 mm/s 0.55 LD t Re W D t 0.25 ar d 1000 m

19 vortex rings Plug of fluid forced through an orifice

20 vortex rings Vortex sheet wraps up

21 vortex rings Circulation half what you might expect L U UL t udx udx 1 UL 2

22 vortex rings

23 propagation Circular line R Kelvin (1867), a << R R 2a W 8R 1 ln 4 R a 4 Assuming thin core gives an error of around 5% in W 0

24 propagation Spherical vortex (Hill 1894) i 3 U r b r 4b h W 2 4b 15 5b r h

25 finite core size Norbury (1973) W R W 2 2 ˆ R A R a e

26 Norbury

27 Norbury W R W 2 2 ˆ Wˆ

28 solid wall 2a 2R Re 4800 ar0.35

29 approaching a wall

30 approaching a wall

31 approaching wall Ek dz K k W R dt 4 R Z R 2Z E k 2Z Kk dr dt 4 RZ R Z Complete elliptic integrals sin k K k k x dx sin E k k x dx 0 4Rr z Z rr 2 2

32 solid wall

33 solid wall Re 4800 ar 0.35

34 solid wall

35 outline Introduction resuspension, wakes Vortex rings modelling, solid boundaries Particle beds crater formation, shapes & scalings Time dependence shear at bed, impact on ring development Other configurations cross-flow, uncompacted beds, underlying structure Conclusions

36 bed velocity solid Theoretical

37 bed velocity solid Boundary layer unsteady forcing

38 Shields parameter lift stress area ~ or buoyancy buoyancy Resuspension: c Generically Steady turbulent flow Impact Bed t b i p gd 2 u* gd p u W 2 2 p gd 2 U b gd p

39 the particles Nominally spherical Nominally monodisperse Negligible cohesion Depth: 10 mm Scraped to level/compact

40 the particles 90 m 250 m 1000 m acrylic

41 the splash

42 the splash: cartoon D t

43 the splash: cartoon D t

44 particle motion Bed-load transport or resuspension? Flow separation

45 crater formation

46 critical conditions c p U 2 c gd U c maxu r b c 3 Re 1 s ~ 1 5 Re 2 s Res 1 Re p Va p Re s Va s ga p Actual settling velocity Stokes settling velocity

47 craters

48 measurement technologies (2)

49 craters 250m 2.9U c 5.3U c 7.3U c

50 crater volume 250m V hh da A 0 40 L 70 mm

51 PE 250m 1 E 1 2 p v p g hh0 da 2 E E E p k c A k 3 2 E f ad DU

52 shape 250m R e h e

53 shape 250m

54 shape 250m R d R e h d 1 10 hd h e

55 shape 250m R d R e h d 1 10 hd h e

56 shape 250m h E E e k c E E E p k c E ~ h R R R 2 p e 0 e 0 ~ R R E E e 0 k c

57 craters 90m 2.2U c 3.5U c 250 m 2.9U c 5.3U c 5.7U c 7.3U c

58 craters 90m h E E e k c E E E p k c R R E E e 0 k c E ~ h R R R 2 p e 0 e 0 ~

59 craters 1000m 1.6U c 3.6U c 250 m 2.9U c 5.3U c 5.1U c 7.3U c

60 craters 1000m

61 craters 1000m Deep craters Exceed angle of repose? collapse? Max measured slope ~21 Angle of repose ~ 24

62 craters 1000m h E E e k c E E E p k c R R E E e 0 k c E ~ h R R R 2 p e 0 e 0 ~

63 outline Introduction resuspension, wakes Vortex rings modelling, solid boundaries Particle beds crater formation, shapes & scalings Time dependence shear at bed, impact on ring development Other configurations cross-flow, uncompacted beds, underlying structure Conclusions

64 the effect on the ring vectors & colour: 250μm contours: solid boundary

65 bed velocity 90m

66 bed velocity - solid

67 bed velocity particles 90 m 1000 m Boundary layer thinner? particle mobility? bed permeability? solid

68 flow within bed a Ub r w p h 1 w rur r r z 0 2 p 2 U u ~ ~ ~ c r Ub r r a k Uc 1 Uc d wp ~ h~ h 2 2 a a p m/s 10 w O O U b

69 reticulated foam

70 reticulated foam

71 reticulated foam

72 reticulated foam

73 outline Introduction resuspension, wakes Vortex rings modelling, solid boundaries Particle beds crater formation, shapes & scalings Time dependence shear at bed, impact on ring development Other configurations cross-flow, uncompacted beds, underlying structure Conclusions

74 cross flow 250m

75 uncompacted particles

76 uncompacted 90m

77 corrugated boundary

78 conclusions Resuspension linked with separation Self-similarity of crater shapes Avalanching if too steep Flow within porous bed may contribute to resuspension Porosity/permeability influence bed velocity

15. Physics of Sediment Transport William Wilcock

15. Physics of Sediment Transport William Wilcock (based in part on lectures by Jeff Parsons) OCEAN/ESS 410 Lecture/Lab Learning Goals Know how sediments are characteried (sie and shape) Know the definitions