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Turbulent drag reduction for a wall with a bump Jacopo Banchetti - - PowerPoint PPT Presentation
Turbulent drag reduction for a wall with a bump Jacopo Banchetti - - PowerPoint PPT Presentation
Turbulent drag reduction for a wall with a bump Jacopo Banchetti & Maurizio Quadrio, Politecnico di Milano EDRFCM 2019, March 2629, 2019 1 Outline Motivation DNS of bump fmow with StTW 2 Outline Motivation DNS of bump fmow with StTW
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Outline
Motivation DNS of bump fmow with StTW
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The streamwise-traveling waves
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10 10 10 1 20 20 20 20 20 30 30 40 4 40 40
ω kx
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1 2 3 1 2 3 4 5
33 45 24 33 42 29 38 13 47 3 32 31
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41 37 34 19 6
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7
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10 47 8 35 24 1 1
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2 24 16 38
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46 47 45 8 16 40 33 30 31 29 24 20 13 23 16 21 44 43 5
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21
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48
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41 45 38 26
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36 18 15 15 31 34 33 19 4
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45 16
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46 44
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45 39 18 3
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14 26 36 14 1
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31 34 27 18
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21 32 36 37 36 1 24 48 44 32 34 29
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28 20 36 40 42 17 42 45 47 15 37 46 40 46 45 46 45 47 46 41 45 46 46 21 40 42 45 43 36
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41
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8 36 33 22 5
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4 35 34 27 32
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3
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33 16 31 34 27 18
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5 21 32 34 0 -6
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3
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22 32 33 33 27 5 22 32 33 33 27 5 0
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The next steps
Besides lacking a suitable actuator, of course!
- Q1 How to interpret results?
- Q2 Effect of Re? Gatti & Quadrio, JFM 2016
- Q3 What about total drag?
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Q1: The energy box
MKE TKE Πp = 0.902
(−0.098)
φℓ = 0.253
(0.014)
Pℓ = 0.649
(−0.112)
−P∆ = 0.292
(−0.058)
φ∆ = 0.292
(−0.058)
ǫ = 0.454
(0.043)
Πc = 0.098
Gatti, Cimarelli, Hasegawa, Frohnapfel & Quadrio, JFM 2018
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Q2: effectiveness is constant with Re
Gatti & Quadrio, JFM 2016
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Q3: What about the airplane total drag?
Prelim results presented at last EDRFCM in Frascati
- Transonic DLR-F6 transport aircraft
- RANS, Spalart-Allmaras model
- Re = 3 × 106, M = 0.75
- StTW accounted for via wall
functions
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Changes in friction AND pressure
Friction drag reduces by 23%, as expected...
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Changes in friction AND pressure
... but total drag reduces by the same amount!
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Outline
Motivation DNS of bump fmow with StTW
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Back to fundamentals: a low-Re, incompressible DNS study
- Incompressible DNS of a channel with a small bump
- Periodic + non-periodic domain
- Second-order FD, immersed boundary
- Reτ = 200, (Lx, Ly, Lz) = (25h, 3.2h, 2h), (Nx, Ny, Nz) = (800, 312, 241)
- With and without StTW
periodic boundary condition inflow
- utflow
X, u Y, v Z, w 11
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Bump instead of a wing profjle
Two (small) bump geometries, one inducing mild separation
2 4 6 8 10 12 0.1 0.2 x/h z/h 12
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Friction coeffjcient (and a poll)
2 4 6 8 10 12 1 2 3 ·10−2 x/h Cf(x) Ref StTW 2 4 6 8 10 120 0.2 0.4 0.6 0.8 1 R(x)
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The mean velocity profjle (no bump)
The maximum velocity shifts towards the actuated side and produces 4% additional drag reduction on the unactuated side! 0.2 0.4 0.6 0.8 1 1.2 1 2 u/Ub z/h Ref StTW
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Pressure drag
−1 −0.5 0.5 ·10−2 ∆Cdp 2 4 6 8 10 12 −20 −10 10 x/h Dp
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Power budget
Periodic Non-Periodic Ref StTW ∆% Ref StTW ∆% Expected Pf 1 0.545 −45.5% 1 0.504 −49.6% −45.5% Pp
- 0.088
0.080 −10.3% 0% Ptot 1 0.545 −45.5% 1.088 0.575 −46.4% −42.2% Preq
- 34.1%Ptot
- 31.2%Ptot
31.3%Ptot Net
- 11.4%Ptot
- 15.3%Ptot
11%Ptot
Table 1: Power per unit area, bump wall with G1
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TKE (left) and TKE production (right)
0.5 1 z/h 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 ·10−2 0.5 1 z/h 0.5 1 z/h 1 2 3 4 5 6 7 8 9 10 0.5 1 x/h z/h 0.5 1 z/h −0.2 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 ·10−2 0.5 1 z/h 0.5 1 z/h 1 2 3 4 5 6 7 8 9 10 0.5 1 x/h z/h
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The separation bubble
0.1 z/h 0.2 0.4 0.6 0.8 1 4.5 4.6 4.7 4.8 4.9 5 5.1 5.2 5.3 5.4 5.5 0.1 x/h z/h
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Conclusions
- Interaction between friction drag reduction and overall drag
- Benefjts of skin-friction drag reduction techniques may be underestimated
- Compressible DNS may reveal larger effects