Drag-reducing characteristics of the generalized spanwise Stokes layer: experiments and numerical simulations

Transcription

1 (DNS) Drag-reducing characteristics of the generalized spanwise Stokes layer: experiments and numerical simulations M.Quadrio Politecnico di Milano Tokyo, March 18th, 2010

2 Outline (DNS) 1 (DNS)

3 Outline (DNS) 1 (DNS)

4 The travelling (DNS) c Flow 2h λ z y x δ

5 The original idea: spanwise wall oscillation Quadrio & Ricco, JFM 04 (DNS) w(x,y = 0,z,t) = Asin(ωt) 40 A + =18 A + =12 A + =4.5 Large reductions of turbulent friction Unpractical 100 * R T + opt T +

6 The oscillating wall made stationary Viotti, Quadrio & Luchini, ETC 2007 (DNS) w(x,y = 0,z,t) = Asin(κx) Existence of an optimal wavelength λ opt = U c T opt Can be implemented as a passive device (sinusoidal riblets) 100 * R A + =12 A + =6 A + =12, temporal λ + opt λ +

7 The sinusoidal riblets A new concept under experimental testing (DNS) Promising roughness distribution Better than straight riblets?

8 The traveling : a natural extension (DNS) Purely temporal forcing The oscillating wall: w = Asin(ωt) Infinite phase speed Combined space-time forcing The traveling : Purely spatial forcing The steady : w = Asin(κx) Zero phase speed Finite phase speed c = ω/κ w = Asin(κx ωt)

9 Results from DNS (plane channel) Quadrio et al., JFM (DNS) k ω 16

10 k How much power to generate the? (DNS) 5 Map of P in is similar to map of R! S and G may get very high ω

11 Power efficiency (DNS)

12 Power efficiency (DNS)

13 Power efficiency (DNS)

14 Power efficiency (DNS)

15 Outline (DNS) 1 (DNS)

16 Why? (DNS) A proof-of-principle experiment to: confirm drag reduction improve understanding of the travelling

17 Main design choices (DNS) Cylindrical pipe Friction is measured through pressure drop Spanwise wall velocity: wall movement Temporal variation: unsteady wall movement Spatial variation: the pipe is sliced into thin, independently-movable axial segments

18 The concept (DNS) Flow wall velocity traveling wave

19 A global view (DNS)

20 Closeup of the rotating segments 60 slabs with 6 independent motors (DNS)

21 The transmission system Shafts, belts and rotating segments (DNS)

22 The control system (DNS) Slab motion is feedback-controlled Tachimetric sensors Vertically-moving reservoir

23 Flow parameters (DNS) Water, Re = 4900 or Re τ = 175 Reference pressure drop 10 Pa! Anticorrosion device Pressure sensors flooded in water Friction factor verifies Prantl s empirical correlation

24 Experimental conditions (DNS) k s= s= ω +

25 Drag variation (1) (DNS)

26 Drag variation (2) (DNS) * R s=6 10 s= ω +

27 Comments (DNS) Quantitative agreement between DNS and experiment is not expected: Spatial transient Cylindrical vs planar geometry Difference (small) in Re and A Waveform effects

28 The discrete waveform (DNS) u θ i=0 i=1 i=2 i=3 i=4 i=5 Reference Approximation x/l i=2 i=3 0.5 u θ 0 i=1 i=4-0.5 i=0 i= x/l

29 Fourier expansion of the discrete wave (DNS) s=3 s=6 w = 3 { 3 2π A sin ( ωt κx ) sin( ωt + 2κx ) } +... w = 3 {sin π A ( ωt κx ) sin( ωt + 5κx ) } +...

30 Integral representation of the R map (DNS) R(ω,κ) = K (τ,ξ )f ω,κ (τ,ξ )dτdξ f ω,κ (τ,ξ ) is the sinusoidal wave (monocromatic) Kernel K empirically determined by fitting DNS results

31 The monocromatic R map (DNS) 40 s=3 100 * R ω +

32 The non-monocromatic wave (DNS) The generating wave does not need be monocromatic Suppose linear superposition: [ R(ω,κ) = K (τ,ξ ) f ω,κ + 1 ] 2 f ω, 2κ dτdξ

33 The non-monocromatic R map (DNS) k s= ω +

34 Wiggles are predicted! (DNS) 40 s=3 100 * R ω + Wiggles in the experimental data are discretization effects

35 Outline (DNS) 1 (DNS)

36 The spanwise laminar flow (DNS) w(y,t) w(y,x) w(y,x ct)

37 Laminar: the GSL equation (DNS) w t TSL (Stokes) SSL (Viotti et al, PoF 2009) + u w ( 2 x = ν w x ) w y 2 one-way coupling with streamwise flow

38 The analytical solution (DNS) 1 δ h (translates into λ/h Re b ) 2 Linear u profile w(x,y,t) = { AR Ce 2πi(x ct)/λ Ai [ e πi/6 ( 2πuy,w λν ) 1/3 ( y c u y,w ) ]}

39 Spanwise turbulent flow agrees with the GSL (DNS)

40 Using the GSL solution (1) Turbulent (DNS) vs laminar (analytical) δ GSL (DNS) Black points are good δ turb δ lam

41 Using the GSL solution (2) Map of analytical δ GSL (DNS) k ω

42 Using the GSL solution (3) R vs analytical δ GSL (DNS) Black points are good 100 * R o δ lam

43 Outline (DNS) 1 (DNS)

44 The near-wall convection velocity U c Quadrio & Luchini, PoF 2003 (DNS) U c mean vel. convection vel y

45 Near-wall physics 2: the turbulence lifetime T l Quadrio & Luchini, PoF 2003 Space-time autocorrelation of wall friction (DNS) ξ τ

46 How the increase drag (DNS) Waves lock with the convecting structures Steady forcing: c + U + c

47 How the decrease drag (DNS) Drag reduction is proportional to δ GSL (WHY?) Large δ GSL large T Too large a T implies quasi-steady forcing

48 Limit to drag reduction Forcing must be unsteady Oscillating wall (DNS) Forcing on a timescale T l does not yield DR Forcing timescale: oscillation period T 40 A + =18 A + =12 A + = * R T + opt T +

49 Limit to drag reduction Forcing must be unsteady (DNS) Forcing on a timescale T l does not yield DR Timescale: oscillation period T as seen by the convecting structures T = λ U c c

50 Waves and turbulent friction (DNS) Four regions in each half-plane:

51 Outline (DNS) 1 (DNS)

52 (DNS) Streamwise-travelling : Useful for understanding drag-reduction mechanism (Flatland) Extremely energy-efficient Still incomplete understanding Issue of spatial discretization Example

53 Outlook (DNS) Further understanding (why is δ GSL R?) Further increase in efficiency Further development of actuators Explore Re effects

54 Credits (DNS) Pierre Ricco Fulvio Martinelli Claudio Viotti Franco Auteri Arturo Baron Marco Belan Paolo Luchini

55 The scaling issue (1) Drag reduction (DNS) k ω +

56 The scaling issue (2) Do streamwise vorticity fluctuations decrease? (DNS) 0.4 Ref Waves Waves, no GSL The streamwise vorticity fluctuation near the wall is reduced by the spanwise wall oscillation. ω Back y