Turbulent drag reduction for a wall with a bump Jacopo Banchetti & Maurizio Quadrio, Politecnico di Milano EDRFCM 2019, March 26–29, 2019 1
Outline Motivation DNS of bump fmow with StTW 2
Outline Motivation DNS of bump fmow with StTW 3
The streamwise-traveling waves 4 5 20 40 0 1 - 36 41 43 45 45 46 44 5 -20 -20 -23 -23 -22 -17 -10 -2 20 40 10 0 0 20 23 8 0 4 15 38 41 44 46 45 36 6 -15 -18 0 0 2 38 46 -16 - -21 4 -10 31 42 45 47 -20 24 45 13 0 3 40 46 -15 -18 2 1 0 15 41 -8 -17 8 15 30 k x 47 30 45 47 33 -16 -2 17 -10 0 20 0 4 2 18 21 29 35 43 45 46 46 32 -7 -14 3 20 0 16 40 20 44 46 48 48 34 10 -14 21 30 33 40 0 45 46 47 40 8 1 -8 -10 13 24 0 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 10 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 16 18 22 27 32 34 33 34 33 33 33 32 31 27 21 3 5 5 0 0 -6 -3 -9 -7 -7 -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
The next steps Besides lacking a suitable actuator, of course! • Q1 How to interpret results? • Q2 Effect of Re ? Gatti & Quadrio, JFM 2016 5 • Q3 What about total drag?
Q1: The energy box Gatti, Cimarelli, Hasegawa, Frohnapfel & Quadrio, JFM 2018 6 φ ℓ = 0 . 253 Π c = 0 . 098 (0 . 014) MKE TKE P ℓ = 0 . 649 ( − 0 . 112) ǫ = 0 . 454 (0 . 043) Π p = 0 . 902 ( − 0 . 098) −P ∆ = 0 . 292 ( − 0 . 058) φ ∆ = 0 . 292 ( − 0 . 058)
Q2: effectiveness is constant with Re Gatti & Quadrio, JFM 2016 7
Q3: What about the airplane total drag? Prelim results presented at last EDRFCM in Frascati • Transonic DLR-F6 transport aircraft • RANS, Spalart-Allmaras model • StTW accounted for via wall functions 8 • Re = 3 × 10 6 , M = 0 . 75
Changes in friction AND pressure Friction drag reduces by 23%, as expected... 9
Changes in friction AND pressure ... but total drag reduces by the same amount! 9
Outline Motivation DNS of bump fmow with StTW 10
Back to fundamentals: a low- Re , incompressible DNS study • Incompressible DNS of a channel with a small bump • Second-order FD, immersed boundary • With and without StTW 11 • Periodic + non-periodic domain • Re τ = 200, ( L x , L y , L z ) = ( 25 h , 3 . 2 h , 2 h ) , ( N x , N y , N z ) = ( 800 , 312 , 241 ) Z, w outflow Y, v inflow X, u periodic boundary condition
Bump instead of a wing profjle Two (small) bump geometries, one inducing mild separation 12 0 . 2 z/h 0 . 1 0 0 2 4 6 8 10 12 x/h
Friction coeffjcient (and a poll) 13 3 · 10 − 2 1 Ref StTW 0 . 8 2 0 . 6 C f ( x ) R ( x ) 1 0 . 4 0 . 2 0 120 0 0 2 2 4 4 6 6 8 8 10 10 12 x/h
The mean velocity profjle (no bump) The maximum velocity shifts towards the actuated side and produces 4% 14 additional drag reduction on the unactuated side! 2 Ref StTW z/h 1 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 2 0 1 u/U b
Pressure drag 15 · 10 − 2 0 . 5 0 ∆ C dp − 0 . 5 − 1 10 0 D p − 10 − 20 0 2 4 6 8 10 12 x/h
Power budget 1.088 0.088 0.080 Periodic P tot 1 0.545 0.575 - P req - - Net - - Table 1: Power per unit area, bump wall with G 1 - 16 - Ref StTW P p StTW Expected P f Ref 1 0.545 Non-Periodic 1 ∆% ∆% − 45 . 5 % − 49 . 6 % − 45 . 5 % 0 . 504 − 10 . 3 % 0 % − 45 . 5 % − 46 . 4 % − 42 . 2 % 34 . 1 % P tot 31 . 2 % P tot 31 . 3 % P tot 11 . 4 % P tot 15 . 3 % P tot 11 % P tot
TKE (left) and TKE production (right) 17 · 10 − 2 · 10 − 2 1 2 . 2 1 2 . 2 2 2 z/h z/h 0 . 5 0 . 5 1 . 8 1 . 8 0 0 1 . 6 1 1 1 . 6 1 . 4 z/h z/h 1 . 4 0 . 5 0 . 5 1 . 2 1 . 2 0 0 1 1 1 1 0 . 8 z/h z/h 0 . 5 0 . 5 0 . 8 0 . 6 0 . 4 0 . 6 0 0 1 1 0 . 2 0 . 4 z/h z/h 0 0 . 5 0 . 5 0 . 2 − 0 . 2 0 0 0 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 x/h x/h
The separation bubble 18 0 . 1 1 0 . 8 z/h 0 . 6 0 0 . 1 0 . 4 z/h 0 . 2 0 0 4 . 5 4 . 6 4 . 7 4 . 8 4 . 9 5 . 1 5 . 2 5 . 3 5 . 4 5 . 5 5 x/h
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 19
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