Turbulent Drag Reduction at Moderate Reynolds Numbers via Spanwise - PowerPoint PPT Presentation

Introduction Flow Unit for Drag Reduction Results Conclusions Davide Gatti 1 , 2 , Maurizio Quadrio 1 Turbulent Drag Reduction at Moderate Reynolds Numbers via Spanwise Velocity Waves 1 POLITECNICO DI MILANO 2 CENTER OF SMART INTERFACES Technische Universit¨ at Darmstadt

Introduction Flow Unit for Drag Reduction Results Conclusions Turbulent skin-friction Drag Reduction Motivation • Economical benefits • Environmental benefits • Better understanding of turbulence Our focus • The effects of Re on a particular control strategy 1/17

Introduction Flow Unit for Drag Reduction Results Conclusions A promising strategy Streamwise-traveling waves of spanwise wall velocity (Quadrio et al. , JFM 2009) w w ( x , t ) = A sin( κ x x − ω t ) c = ω κ x 2h λ y z x Flow δ 2/17

Introduction Flow Unit for Drag Reduction Results Conclusions High performances R = P 0 − P Drag reduction rate: P 0 � L x � L z � T 1 ∂ w Input power: P in = ∂ y d t d x d z w w L x L z T 0 0 0 S = R − P in Power saving rate: P 0 3/17

Introduction Flow Unit for Drag Reduction Results Conclusions High drag reduction achievable (Quadrio et al. , JFM 2009) 5 0 3 w w ( x , t ) = A sin( κ x x − ω t ) -20 36 41 43 45 45 46 44 5 -20 -23 -23 -22 -17 -10 -2 c = ω 0 30 κ x 0 20 23 8 0 40 4 0 15 38 41 44 46 45 36 6 -15 -18 2 10 10 $% λ 38 46 -16 -21 4 " ! # &'() 31 42 45 47 -20 24 45 13 -10 3 δ 40 46 -15 -18 0 2 20 0 0 15 41 0 -8 -17 0 8 15 4 κ 1 - k 47 45 47 33 -16 -2 17 0 3 2 18 21 29 35 43 45 46 46 32 -7 -14 3 16 0 44 46 48 48 3 34 -14 21 30 33 40 0 0 0 45 46 47 40 8 1 -8 -10 1 13 24 20 40 10 31 1 21 34 37 41 45 45 47 39 31 18 10 0 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 20 2 0 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 0 16 18 22 27 32 34 33 34 33 33 33 32 31 27 21 5 0 5 3 0 -6 -3 -7 -7 -9 -7 -9 -7 -6 -3 5 0 0 3 5 21 27 31 32 33 34 33 34 32 27 22 18 16 -3 -2 -1 0 1 2 3 ω ω 4/17

Introduction Flow Unit for Drag Reduction Results Conclusions What happens at high Re ? Two possible scenarios 50 Unknown 40 Zone 30 100 R 20 ”Well-known” Zone 10 ◦ • Numerical • ◦ Experimental 0 0 500 1000 1500 2000 2500 3000 Re τ 5/17

Introduction Flow Unit for Drag Reduction Results Conclusions What happens at high Re ? Two possible scenarios 50 Unknown 40 Zone 30 100 R 1 20 ”Well-known” 2 Zone 10 ◦ • Numerical • ◦ Experimental 0 0 500 1000 1500 2000 2500 3000 Re τ 5/17

Introduction Flow Unit for Drag Reduction Results Conclusions Several means of investigation ✻ exceeds present modeling skills RANS high our attempt: Smagorinsky model fails Modeling error LES Touber and Leschziner, JFM 2012 : high computational costs and low reliability prohibitive computational costs DNS for a parametric study none Experiments difficult drag measurements and more 6/17

Introduction Flow Unit for Drag Reduction Results Conclusions Our approach Up to Re τ = 2000 with DNS of channels of reduced size Pros Cons • No modeling errors • Discretization errors at the large scales • No resolution errors 7/17

Introduction Flow Unit for Drag Reduction Results Conclusions Neither minimal nor full 0 0 0 2 = + x L L + z = 1000 8/17

Introduction Flow Unit for Drag Reduction Results Conclusions Neither minimal nor full 8 6 7 3 = + x L L + z = 1884 8/17

Introduction Flow Unit for Drag Reduction Results Conclusions Neither minimal nor full 0 5 2 = + x L L + z = 100 8/17

Introduction Flow Unit for Drag Reduction Results Conclusions Simulation time Larger fluctuations of the space-averaged wall shear (Ω) σ Ω Ω treated as a measure: σ Ω = C √ T sim optimal compromise between space and time average 7 6 5 MFU Full Jim´ enez & Moin, JFM 1991 0 200 400 600 800 1000 tU p / h 9/17

Introduction Flow Unit for Drag Reduction Results Conclusions Effects on drag reduction κ x = 0 (oscillating wall) 45 • Reduced 100 R DNS 40 35 30 25 L + x × L + z 20 10 5 10 6 10 7 ours full 10/17

Introduction Flow Unit for Drag Reduction Results Conclusions Effects on drag reduction κ x = 0 (oscillating wall) 45 • Reduced 100 R DNS 40 35 30 25 L + x × L + z 20 10 5 10 6 10 7 ours full 10/17

Introduction Flow Unit for Drag Reduction Results Conclusions Wave parameters λ + x = 1256 30 5 -20 36 41 43 45 45 46 44 5 -20 -23 -23 -22 -17 -10 -2 0 30 0 20 23 8 0 0 0 4 15 38 41 44 46 45 36 6 -15 -18 4 2 0 10 1 38 46 -16 -21 4 31 42 45 47 -20 24 45 13 3 0 40 46 -15 -18 0 2 1 - 20 40 0 0 15 41 0 -8 -17 8 15 κ 1 - k 47 45 47 33 -16 -2 17 30 2 18 21 29 35 43 45 46 46 32 -7 -14 3 30 16 44 46 48 48 34 -14 21 10 30 33 40 0 0 45 46 47 40 8 1 -8 -10 13 24 20 40 0 31 1 1 21 34 37 41 45 45 47 39 31 18 10 0 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 20 2 0 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 0 16 18 22 27 32 34 33 34 33 33 33 32 31 27 21 5 0 3 5 0 -6 -3 -7 -7 -9 -7 -9 -7 -6 -3 5 0 0 3 5 21 27 31 32 33 34 33 34 32 27 22 18 16 -3 -2 -1 0 1 2 3 ω ω 11/17

Introduction Flow Unit for Drag Reduction Results Conclusions Drag reduction λ + x = 1256 100 R 50 40 30 20 Re τ 10 • ◦ 200 � 1000 0 △ 2000 � -10 ω + -0.2 -0.1 0 0.1 0.2 0.3 12/17

Introduction Flow Unit for Drag Reduction Results Conclusions Input power λ + x = 1256 0 100 P in / P 0 Re τ 200 • ◦ 1000 � -50 2000 � △ -100 -150 ω + -200 -0.2 -0.1 0 0.1 0.2 0.3 13/17

Introduction Flow Unit for Drag Reduction Results Conclusions Reynolds effect 100 R 40 55 20 50 45 0 ω + 49 40 −0.2 −0.1 0 0.1 0.2 0.3 35 100 R 36.5 R max ∼ Re − 0 . 22 30 Reduced 25 29.2 20 15 100 200 400 1000 2000 10000 Re τ 14/17

Introduction Flow Unit for Drag Reduction Results Conclusions Reynolds effect 100 R 40 55 20 50 45 0 ω + 40 −0.2 −0.1 0 0.1 0.2 0.3 35 100 R R ∼ Re − 0 . 08 30 22 .4 25 19.7 20 Reduced 15 100 200 400 1000 2000 10000 Re τ 15/17

Introduction Flow Unit for Drag Reduction Results Conclusions Reynolds effect 100 R 40 55 20 50 45 0 ω + 40 −0.2 −0.1 0 0.1 0.2 0.3 35 100 R R ∼ Re − 0 . 08 30 25 20 21. 7 20.5 DNS 15 100 200 400 1000 2000 10000 Re τ 15/17

Introduction Flow Unit for Drag Reduction Results Conclusions “Conclusions” R ∼ Re − 0 . 22 τ 16/17

Introduction Flow Unit for Drag Reduction Results Conclusions “Conclusions” ...or even better! R ∼ Re − 0 . 08 τ S increases with Re 16/17

Introduction Flow Unit for Drag Reduction Results Conclusions A broader result Need for extensive parametric studies focusing on optimal parameters gives a limited view! 17/17

Davide Gatti 1 , 2 , Maurizio Quadrio 1 Turbulent Drag Reduction at Moderate Reynolds Numbers via Spanwise Velocity Waves 1 POLITECNICO DI MILANO 2 CENTER OF SMART INTERFACES Technische Universit¨ at Darmstadt 17/17

Box size L + L + z = L + x = 1000 ÷ 2000 x / 2 Criteria: • “Healthy” turbulence up to y d apart from wall z = 3 y + if L + L + x ≈ h + and d (Florez and Jim´ enez, PoF 2010) • At least one wavelength long L x = 2 π/κ x 17/17

Simulation data T + sim = 12000 ÷ 24000 Simulation time: ∆ x + = ∆ z + = 10 ∆ y + < 4 Resolution: Grid points: 128 × Re τ / 2 × 64 192 × Re τ / 2 × 96 17/17

Effects on wall skin friction Fixed wall 9 Dean 8 ◦ • Re τ = 200 � Re τ = 1000 7 � △ Re τ = 2000 C f × 10 3 6 5 4 3 0 2 4 6 8 10 12 × 10 6 L + x × L + z 17/17

Effects on input power κ x = 0 -70 L + x 3746 -75 • ◦ 666 • ◦ 100 P in / P 0 1000 • ◦ 1326 -80 • ◦ 2000 -85 -90 85 90 95 100 105 110 115 120 T + 17/17