(DNS) Drag-reducing characteristics of the generalized spanwise Stokes layer: experiments and numerical simulations M.Quadrio Politecnico di Milano Tokyo, March 18th, 2010
Outline (DNS) 1 (DNS) 2 3 4 5
Outline (DNS) 1 (DNS) 2 3 4 5
The travelling (DNS) c Flow 2h λ z y x δ
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 30 20 10 0 T + opt 200 400 600 800 T +
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 40 30 20 10 0 A + =12 A + =6 A + =12, temporal λ + opt 2000 4000 60008000 λ +
The sinusoidal riblets A new concept under experimental testing (DNS) Promising roughness distribution Better than straight riblets?
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)
Results from DNS (plane channel) Quadrio et al., JFM 2009 5 36 41 45 45 46 44-20 -23 43 5-17 -23-22 -10-2 (DNS) 20 23 8 4 15 31 38 38 41 44 46 45 36 46 42 45 47 6-15 -18-16 -21 4-20 k 3 15 24 40 45 46 47-15 -18 2 41-8 -17 8 15 13 45 47 33-16 -2 17 2 18 21 29 35 43 45 46 46 32-7 -14 3 16 44 46 48 34-14 21 30 33 40 45 46 47 40 8 1-8 -10 13 24 1 21 31 37 41 45 454739 1810-9 31-3 -9 7 34 1419 3-6 -1 26 24 16 33 42 36 40 42 42 36 14 1-7 1 24 28 20 32 36 37 38 37 36 26 1-8 -1 19 29 29 24 16 0 35 36 33 22 5-9 4 34 27 32 16 18 22 27 32 34 334 33 3231 27 21 5 30-3-6-7 -7-9 -9-7 -6-3 03 5 21 273132 33 3433 34 32 27 22 18-3 -2-1 0 1 2 3 ω 16
k 188 186 164 153 149 147 136 134 109 107 106 95 95 84 64 44 37 30 29 93 78 61 4034 2924 2934 39465462 69 788287 9296 113 96 82 59 51 43 35 27 31 37 97 80 68 62 54 42 31 31 36 52 67 81 110 135 177 166 148 125 93 88 80 78 72 71 6561 56 49 3936 38 3632 3531 10 30 10 31 32 3539 36 38 39 49 5661 65 71 780 88 93 125 148 166 71 67 65 60 51 48 40 36 40 42 34 31 33 31 50 42 42 53 51 49 44 43 46 55 67 116 142 146 150 156 162 167 172 49 38 39 42 33 35 39 48 58 75 87 87 72 62 51 38 31 28 47 68 85 37 40 70 89 67 88 91 103 105 129 148 108 116 120 114 133 124 41 102 116 137 43 97 121 125 129 143 132 141 152 108 155 157 171 172 173 175 177 177 179 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 4 3 2 1 0-3 -2-1 0 1 2 3 ω
Power efficiency (DNS)
Power efficiency (DNS)
Power efficiency (DNS)
Power efficiency (DNS)
Outline (DNS) 1 (DNS) 2 3 4 5
Why? (DNS) A proof-of-principle experiment to: confirm drag reduction improve understanding of the travelling
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
The concept (DNS) Flow wall velocity traveling wave
A global view (DNS)
Closeup of the rotating segments 60 slabs with 6 independent motors (DNS)
The transmission system Shafts, belts and rotating segments (DNS)
The control system (DNS) Slab motion is feedback-controlled Tachimetric sensors Vertically-moving reservoir
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
Experimental conditions (DNS) 0.02 0.015 k + 0.01 s=3 0.005 s=6 0-0.3-0.2-0.1 0 0.1 0.2 0.3 ω +
Drag variation (1) (DNS)
Drag variation (2) (DNS) 40 100 * R 30 20 s=6 10 s=3 0-0.3-0.2-0.1 0 0.1 0.2 0.3 ω +
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
The discrete waveform (DNS) u θ 1 0.5 0-0.5-1 1 i=0 i=1 i=2 i=3 i=4 i=5 Reference Approximation 0 1 2 x/l i=2 i=3 0.5 u θ 0 i=1 i=4-0.5 i=0 i=5-1 0 1 2 x/l
Fourier expansion of the discrete wave (DNS) s=3 s=6 w = 3 { 3 2π A sin ( ωt κx ) + 1 2 sin( ωt + 2κx ) } +... w = 3 {sin π A ( ωt κx ) + 1 5 sin( ωt + 5κx ) } +...
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
The monocromatic R map (DNS) 40 s=3 100 * R 20 0-20 -0.3-0.2-0.1 0 0.1 0.2 0.3 ω +
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
The non-monocromatic R map (DNS) 0.02 0.015 k + 0.01 s=3 0.005 0-0.3-0.2-0.1 0 0.1 0.2 0.3 ω +
Wiggles are predicted! (DNS) 40 s=3 100 * R 20 0-20 -0.3-0.2-0.1 0 0.1 0.2 0.3 ω + Wiggles in the experimental data are discretization effects
Outline (DNS) 1 (DNS) 2 3 4 5
The spanwise laminar flow (DNS) w(y,t) 0 0.2 0.4 0.6 0.8 1 w(y,x) 0 0.2 0.4 0.6 0.8 1 w(y,x ct) 0 0.2 0.4 0.6 0.8 1
Laminar: the GSL equation (DNS) w t TSL (Stokes) SSL (Viotti et al, PoF 2009) + u w ( 2 x = ν w x 2 + 2 ) w y 2 one-way coupling with streamwise flow
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 ) ]}
Spanwise turbulent flow agrees with the GSL (DNS)
Using the GSL solution (1) Turbulent (DNS) vs laminar (analytical) δ GSL (DNS) Black points are good δ turb 16 14 12 10 8 6 4 2 0 0 2 4 6 8 10 12 14 16 δ lam
Using the GSL solution (2) Map of analytical δ GSL (DNS) 0.025 0.02 3.5 k + 0.015 0.01 3.5 0.005 +17.5 0-0.3-0.2-0.1 0 0.1 0.2 0.3 ω 10.5 3.5
Using the GSL solution (3) R vs analytical δ GSL (DNS) Black points are good 100 * R 50 40 30 20 10 0-10 o -20-30 0 2 4 6 8 10 12 14 16 18 20 + δ lam
Outline (DNS) 1 (DNS) 2 3 4 5
The near-wall convection velocity U c Quadrio & Luchini, PoF 2003 (DNS) U c + 20 15 10 5 mean vel. convection vel. 0 10 0 10 1 y + 10 2
Near-wall physics 2: the turbulence lifetime T l Quadrio & Luchini, PoF 2003 Space-time autocorrelation of wall friction (DNS) 4506 2253 ξ + 0-2253 -50 0 50 τ + 100 150 200
How the increase drag (DNS) Waves lock with the convecting structures Steady forcing: c + U + c
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
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 + =4.5 100 * R 30 20 10 0 T + opt 200 400 600 800 T +
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
Waves and turbulent friction (DNS) Four regions in each half-plane:
Outline (DNS) 1 (DNS) 2 3 4 5
(DNS) Streamwise-travelling : Useful for understanding drag-reduction mechanism (Flatland) Extremely energy-efficient Still incomplete understanding Issue of spatial discretization Example
Outlook (DNS) Further understanding (why is δ GSL R?) Further increase in efficiency Further development of actuators Explore Re effects
Credits (DNS) Pierre Ricco Fulvio Martinelli Claudio Viotti Franco Auteri Arturo Baron Marco Belan Paolo Luchini
The scaling issue (1) Drag reduction (DNS) 0.025 0.02 k + 0.015 0.01 +12-8 0.005 +5-7.5 0-0.3-0.2-0.1 0 0.1 0.2 0.3 ω +
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 + 0.3 0.2 0.1 Back 0 10 0 10 1 y + 10 2