What happens to turbulent drag reduction at higher Re ? Davide Gatti 1 , 2 , Maurizio Quadrio 1 1 Dept. for Aeronautical Sciences and Technologies, Politecnico di Milano 2 Center for Smart Interfaces, TU-Darmstadt EFMC IX, Rome, September 2012
Skin-friction drag reduction and high Re • Several techniques are under development • DNS and experiments at low Re , applications at high Re • Focus on active techniques, spanwise forcing • Drop of max. drag reduction R m as Re grows (data for 200 < Re τ < 1000) • Literature (Choi AIAA J. 02, Touber JFM12) suggests R m ∼ Re − 0 . 20 τ
What happens at high Re ? Numerical / experimental information for spanwise forcing 50 40 30 100 R m 20 10 0 1000 2000 3000 Re τ
What happens at high Re ? Numerical / experimental information for spanwise forcing 50 40 30 100 R m 2 20 1 10 0 1000 2000 3000 Re τ
Several attack strategies ✻ exceeds present modeling skills RANS high we did non succeed with standard models Modeling error LES Touber JFM 2012 : high computational cost prohibitive computational costs DNS for a parametric study none Experiments difficulties measuring drag, spatial transient
Our workaround DNS of turbulence in channels of reduced size • No modeling errors (like in full DNS) • Discretization errors like in full DNS, but... • ...truncation of large scales is potentially larger!
Neither minimal nor full 8 6 7 3 = + x L L + z = 1884
Neither minimal nor full 0 5 2 = + x L L + z = 100
Neither minimal nor full 0 0 0 2 = + x L L + z = 1000
Choosing the simulation time Larger fluctuations of the space-averaged wall shear (Ω) 7 6 5 MFU Full Jim´ enez & Moin, JFM 1991 0 200 400 600 800 1000 tU p / h Need to compromise between space and time average σ Ω σ Ω = C √ T sim
Drag reduction with error bars (oscillating wall, A + = 12 , T + = 125) 45 40 DNS asymptote 35 100 R 30 25 Our "small" box Standard "large" box 20 5 6 7 10 10 10 Box size (length*width) +
The oscillating wall, up to Re τ = 1000 A + = 12 40 30 100 R 20 10 200 DNS 200 1000 0 0 50 100 150 200 250 300 T +
The travelling wave A + = 12 , λ + x = 1256 5 30 -20 36 41 43 45 45 46 44 5 -20 -23 -23 -22 -17 -10 -2 0 30 0 20 23 8 0 40 20 4 15 38 41 44 46 45 36 6 -15 -18 10 10 38 46 -16 -21 4 31 42 45 47 -20 24 45 13 -10 3 40 46 -15 -18 0 2 20 0 40 15 41 0 -8 -17 0 8 15 1 κ - k 47 45 47 33 -16 -2 17 0 3 2 18 21 29 35 43 45 46 46 32 -7 -14 3 16 30 44 46 48 48 34 -14 21 30 33 40 10 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 -6 -7 -9 -7 -3 5 0 0 5 3 21 27 31 32 33 34 33 34 32 27 22 18 16 -3 -2 -1 0 1 2 3 ω ω
The travelling wave, up to Re τ = 2000 A + = 12 , λ + x = 1256 200 DNS 200 1000 40 2000 100 R 20 0 -0.2 -0.1 0 0.1 0.2 0.3 + ω
Effect of Re : maximum R 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 25 29.2 20 15 100 200 400 1000 2000 10000 Re τ
Effect of Re : region at high- ω 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 15 100 200 400 1000 2000 10000 Re τ
Conclusions ... of suggestive nature! • Doable strategy for higher- Re parametric studies • Decreasing trend of max R confirmed: R ∼ Re − 0 . 22 τ • Low- Re effects identified • More optimistic view: R ∼ Re − 0 . 08 τ
Effect of Re : region at high- ω 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 15 100 200 400 1000 2000 10000 Re τ
Full DNS confirms the slow decrease! 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 Full DNS 15 100 200 400 1000 2000 10000 Re τ
Open questions • Generality? • What happens at even higher Re ? • How to achieve real (non-suggestive) results?
Box size L + L + z = L + x = 1000 ÷ 2000 x / 2 Criteria: • “Healthy” turbulence up to y d apart from wall if L + z = 3 y + L + x ≈ h + and d (Florez and Jim´ enez, PoF 2010) • At least one wavelength long L x = 2 π/κ x
Simulation data T + Simulation time: sim = 12000 ÷ 24000 ∆ x + = 2∆ z + = 10 ∆ y + < 4 Resolution: Grid points: 128 × Re τ / 2 × 64 192 × Re τ / 2 × 96
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
Effects on input power κ x = 0 -70 L + x 3746 -75 • ◦ 666 • ◦ 1000 100 P in / P 0 • ◦ 1326 -80 ◦ • 2000 -85 -90 85 90 95 100 105 110 115 120 T +
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