Travelling waves (DNS) Drag-reducing characteristics Travelling waves of the generalized spanwise Stokes layer: (experiment) experiments and numerical simulations The GSL How do the waves work? Conclusions M.Quadrio Politecnico di Milano Tokyo, March 18th, 2010
Outline Travelling Travelling waves (DNS) 1 waves (DNS) Travelling waves (experiment) 2 Travelling waves (experiment) The GSL How do the waves work? 3 The GSL Conclusions 4 How do the waves work? 5 Conclusions
Outline Travelling Travelling waves (DNS) 1 waves (DNS) Travelling waves (experiment) 2 Travelling waves (experiment) The GSL How do the waves work? 3 The GSL Conclusions 4 How do the waves work? 5 Conclusions
The travelling waves Travelling waves (DNS) c Travelling waves (experiment) The GSL How do the waves work? Conclusions 2h λ y z x Flow δ
The original idea: spanwise wall oscillation Quadrio & Ricco, JFM ’04 Travelling w ( x , y = 0 , z , t ) = A sin ( ω t ) waves (DNS) Travelling waves (experiment) The GSL A + =18 40 + =12 A How do the A + =4.5 waves work? 30 Conclusions Large reductions of 100 * R turbulent friction 20 Unpractical 10 0 200 400 600 800 + T + T opt
The oscillating wall made stationary Viotti, Quadrio & Luchini, ETC 2007 Travelling w ( x , y = 0 , z , t ) = A sin ( κ x ) waves (DNS) Travelling waves (experiment) The GSL Existence of an 40 How do the optimal wavelength waves work? 30 λ opt = U c T opt Conclusions 100 * R Can be 20 A + =12 implemented as a + =6 A A + =12, temporal 10 passive device (sinusoidal riblets) 0 2000 4000 6000 8000 + λ λ + opt
The sinusoidal riblets A new concept under experimental testing Travelling waves (DNS) Travelling waves (experiment) Promising The GSL roughness How do the distribution waves work? Conclusions Better than straight riblets?
The traveling waves: a natural extension Purely temporal forcing Purely spatial forcing Travelling waves (DNS) The oscillating wall: The steady waves: Travelling waves (experiment) w = A sin ( ω t ) w = A sin ( κ x ) The GSL How do the Infinite phase speed Zero phase speed waves work? Conclusions Combined space-time forcing The traveling waves: w = A sin ( κ x − ω t ) Finite phase speed c = ω / κ
Results from DNS (plane channel) Quadrio et al., JFM 2009 5 36 41 43 45 45 46 44 5 -20 -23 -23 -22 -17 -10 -2 Travelling 20 23 8 waves (DNS) 4 15 38 41 44 46 45 36 6 -15 -18 Travelling waves 38 46 -16 -21 4 (experiment) 31 42 45 47 -20 24 45 13 The GSL 3 40 46 -15 -18 2 How do the 15 41 -8 -17 8 15 waves work? k 47 45 47 33 -16 -2 17 Conclusions 2 18 21 29 35 43 45 46 46 32 -7 -14 3 16 44 46 48 48 34 -14 21 30 33 40 45 46 47 40 8 1 -8 -10 13 24 31 1 21 34 37 41 45 45 47 39 31 18 10 3 -3 -6 -9 -9 -1 7 14 19 26 24 16 33 36 40 42 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 34 36 35 33 22 5 -9 4 27 32 0 16 18 22 27 32 34 33 34 33 33 33 32 31 27 21 5 5 0 3 0-6 -3 -9 -7 -7 -9 -7 -7 3 -6 -3 5 0 0 5 21 27 31 32 33 34 33 34 32 27 22 18 16 -3 -2 -1 0 1 2 3 ω
How much power to generate the waves? Travelling waves (DNS) 5 Travelling 71 49 44 43 46 55 67 116 142 146 150 156 162 167 172 waves 153 136 177 4 188 67 50 42 42 53 67 105 129 148 (experiment) 65 40 125 132 157 Map of P in is similar to The GSL 95 49 38 39 129 134 40 179 3 60 37 114 124 141 map of R ! How do the 186 41 102 116 137 171 k 36 waves work? 42 33 43 108 121 152 2 164 149 109 84 51 42 34 31 39 88 97 116 S and G may get very Conclusions 172 48 40 33 31 35 91 143 107 95 64 44 37 30 29 48 58 75 87 103 120 high 106 1 147 93 78 61 40 34 29 24 29 34 39 46 54 62 69 78 82 87 92 96 113 133 173 96 82 59 51 43 35 27 31 37 51 70 89 108 155 97 80 68 62 54 42 31 31 36 52 67 81 110 135 175 87 72 62 51 38 31 28 47 68 85 0 177 166 148 125 93 88 80 78 72 71 72 65 61 56 49 36 39 38 30 39 36 35 32 31 32 31 38 30 10 10 36 36 3539 39 49 56 65 61 71 80 78 88 93 125 148 166 177 -3 -2 -1 0 1 2 3 ω
Power efficiency Travelling waves (DNS) Travelling waves (experiment) The GSL How do the waves work? Conclusions
Power efficiency Travelling waves (DNS) Travelling waves (experiment) The GSL How do the waves work? Conclusions
Power efficiency Travelling waves (DNS) Travelling waves (experiment) The GSL How do the waves work? Conclusions
Power efficiency Travelling waves (DNS) Travelling waves (experiment) The GSL How do the waves work? Conclusions
Outline Travelling Travelling waves (DNS) 1 waves (DNS) Travelling waves (experiment) 2 Travelling waves (experiment) The GSL How do the waves work? 3 The GSL Conclusions 4 How do the waves work? 5 Conclusions
Why? Travelling waves (DNS) Travelling waves (experiment) A proof-of-principle experiment to: The GSL confirm drag reduction How do the waves work? improve understanding of the travelling waves Conclusions
Main design choices Travelling waves (DNS) Travelling Cylindrical pipe waves (experiment) Friction is measured through pressure drop The GSL Spanwise wall velocity: wall movement How do the waves work? Temporal variation: unsteady wall movement Conclusions Spatial variation: the pipe is sliced into thin, independently-movable axial segments
The concept Travelling waves (DNS) Travelling waves (experiment) The GSL How do the waves work? Conclusions Flow traveling wave wall velocity�
A global view Travelling waves (DNS) Travelling waves (experiment) The GSL How do the waves work? Conclusions
Closeup of the rotating segments 60 slabs with 6 independent motors Travelling waves (DNS) Travelling waves (experiment) The GSL How do the waves work? Conclusions
The transmission system Shafts, belts and rotating segments Travelling waves (DNS) Travelling waves (experiment) The GSL How do the waves work? Conclusions
The control system Travelling waves (DNS) Travelling waves (experiment) Slab motion is feedback-controlled The GSL How do the Tachimetric sensors waves work? Vertically-moving reservoir Conclusions
Flow parameters Travelling waves (DNS) Travelling waves Water, Re = 4900 or Re τ = 175 (experiment) Reference pressure drop ≈ 10 Pa! The GSL How do the Anticorrosion device waves work? Conclusions Pressure sensors flooded in water Friction factor verifies Prantl’s empirical correlation
Experimental conditions 0.02 Travelling waves (DNS) Travelling waves 0.015 (experiment) The GSL How do the waves work? 0.01 + k Conclusions s=3 0.005 s=6 0 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 + ω
Drag variation (1) Travelling waves (DNS) Travelling waves (experiment) The GSL How do the waves work? Conclusions
Drag variation (2) Travelling 40 waves (DNS) Travelling waves (experiment) 30 The GSL s=6 How do the 100 * R waves work? 20 Conclusions 10 s=3 0 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 + ω
Comments Travelling waves (DNS) Travelling Quantitative agreement between DNS and experiment is not waves (experiment) expected: The GSL Spatial transient How do the waves work? Cylindrical vs planar geometry Conclusions Difference (small) in Re and A Waveform effects
The discrete waveform i=1 Reference 1 Approximation i=0 0.5 i=2 Travelling waves (DNS) u θ� 0 Travelling waves i=5 (experiment) -0.5 i=3 The GSL i=4 -1 How do the 0 1 2 waves work? x/L Conclusions 1 i=2 i=3 0.5 i=1 u θ� 0 i=4 -0.5 i=0 i=5 -1 0 1 2 x/L
Fourier expansion of the discrete wave s=3 Travelling waves (DNS) Travelling waves √ (experiment) w = 3 3 � + 1 � ˜ � � � � 2 π A sin ω t − κ x 2 sin ω t + 2 κ x + ... The GSL How do the waves work? Conclusions s=6 w = 3 � + 1 � ˜ � � � � π A sin ω t − κ x 5 sin ω t + 5 κ x + ...
Integral representation of the R map Travelling waves (DNS) Travelling waves (experiment) � � R ( ω , κ ) = K ( τ , ξ ) f ω , κ ( τ , ξ ) d τ d ξ The GSL How do the waves work? f ω , κ ( τ , ξ ) is the sinusoidal wave (monocromatic) Conclusions Kernel K empirically determined by fitting DNS results
The monocromatic R map Travelling waves (DNS) Travelling 40 waves (experiment) s=3 The GSL 20 How do the 100 * R waves work? Conclusions 0 -20 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 + ω
The non-monocromatic wave Travelling waves (DNS) Travelling waves The generating wave does not need be monocromatic (experiment) Suppose linear superposition: The GSL How do the � � waves work? f ω , κ + 1 � � ˜ R ( ω , κ ) = K ( τ , ξ ) 2 f ω , − 2 κ d τ d ξ Conclusions
The non-monocromatic ˜ R map Travelling 0.02 waves (DNS) Travelling waves (experiment) 0.015 The GSL How do the waves work? 0.01 + k Conclusions s=3 0.005 0 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 + ω
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