Direct Numerical Simulation of

Drag Reduction with Uniform Blowing

over a Two-dimensional Roughness

Eisuke Mori1, Maurizio Quadrio2 and Koji Fukagata1

1 Keio University, Japan

2 Politecnico di Milano, Italy

European Drag Reduction and Flow Control Meeting

Rome, Apr. 3-6, 2017

E.Mori, M.Quadrio, K.Fukagata DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 2/18

Uniform blowing (UB)

Drag contribution in a channel flow with UB(/US)

Excellent performance (about 45% by = . %)

Unknown over a rough wall

=

+

(Fukagata et al., Phys. Fluids, 2002)

Viscous

Contribution

(= laminar drag, const.)

Turbulent

contribution

Convective (=UB/US)

contribution

On a boundary layer, White: vortex core, Colors: wall shear stress

: Blowing velocity

(Kametani & Fukagata, J. Fluid Mech., 2011)

E.Mori, M.Quadrio, K.Fukagata DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 3/18

UB over a rough wall

Experimental results so far

Similar to the smooth-wall cases

- Schetz and Nerney, AIAA J., 1977

- Voisinet, 1979

Opposite behavior

(drag increased, turbulent intensity suppressed)

- Miller et al., Exp. Fluids, 2014

Contradicting remarks exist

E.Mori, M.Quadrio, K.Fukagata DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 4/18

Goal

Investigate the interaction between roughness and UB

for drag reduction using numerical simulation

- DNS of turbulent channel flow

- Drag reduction performance and mechanism

- Combined effect of UB and roughness

E.Mori, M.Quadrio, K.Fukagata DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 5/18

Numerical procedure

Based on FD code (for wall deformation)(Nakanishi et al., Int. J. Heat Fluid Fl., 2012)

Constant flow rate, = / =

- so that in a plane channel (K.M.M.)

+ = . , . < + < , + = .

UB magnitude: = , . %, . %, %

SMOOTH CASEROUGH CASE

E.Mori, M.Quadrio, K.Fukagata DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 6/18

=

Model of rough wall

Roughness displacement

: channel half height: Channel length, : Amplitude of each sinusoid

= , = , ,

with rescaling so that

= .

=

=

= .

(Defined randomly)

(E. Napoli et al., J. Fluid Mech., 2008)

E.Mori, M.Quadrio, K.Fukagata DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 7/18

The result of the base flow

+~6.5

Transitionally-rough regime

+ =

= 2ave ( + ,)ave: Overall drag coefficient: of the rough wall side

,: of the smooth wall side

E.Mori, M.Quadrio, K.Fukagata DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 8/18

The result of UB

ROUGH CASESMOOTH CASE

Total, % % % % % %

= 1 ,ctr,nc

,ctr: controlled

,nc: no control

E.Mori, M.Quadrio, K.Fukagata DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 9/18

The result of UB

ROUGH CASESMOOTH CASE

Total, % % % % % %

Friction, % % % % % %Pressure, - - % % %

E.Mori, M.Quadrio, K.Fukagata DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 10/18

Bulk mean streamwise velocity

Friction drag reduction mechanism

Black: = 0Green: = 0.1%Red: = 0.5%Blue: = 1%

+nc: normalization

with no control case

SMOOTH CASE

ROUGH CASE

+

E.Mori, M.Quadrio, K.Fukagata DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 11/18

How does pressure drag decrease?

Pressure contours averaged in the spanwise and timedashed lines: zero contour

+nc

= %

=

+

+

E.Mori, M.Quadrio, K.Fukagata DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 12/18

Smoothing effect

Wall-normal velocity contours averaged in the spanwise and timedashed lines: zero contour

+nc

+

+

= %

=

+ = 38

+ = 20

E.Mori, M.Quadrio, K.Fukagata DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 13/18

Velocity defect

Outer layer similarity with UB

Base flow (No controlled) of

one-side rough wall1% UB case of

one-side rough wall

Smooth side

Rough side

: distance from a wall to the minimum RMS location

(K. Bhaganagar et al.,

Flow, Turbul. Combust., 2004)

E.Mori, M.Quadrio, K.Fukagata DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 14/18

Comparison with smooth case

Velocity defect

1% UB case of

both-side smooth wall

1% UB case of

one-side rough wall

Smooth

side

Rough

side

Suction

side

Blowing

side

E.Mori, M.Quadrio, K.Fukagata DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 15/18

Comparison with smooth case

Velocity defect

1% UB case of

both-side smooth wall

1% UB case of

one-side rough wall

Same tendency, but quantitatively weakened

E.Mori, M.Quadrio, K.Fukagata DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 16/18

Stevensons law of the wall

Plots using Stevensons law of the wall (Stevenson, 1963)2

+ 1 +

++ 1 =1

ln + +

+

Modified law is suggested:

2

+ 1 +

++ 1 =1

ln + + +

Roughness function

+

E.Mori, M.Quadrio, K.Fukagata DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 17/18

Normalization by +

Drag reduction,

= , ,

Drag reduction rate,

nc: no control

ctr: controlled becomes similar when plotted with

+

E.Mori, M.Quadrio, K.Fukagata DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 18/18

Concluding remarks

DNS of turbulent channel flow is performed

over a rough wall with UB

UB is effective over a rough wall

- Almost same in drag reduction rate, but larger in drag

reduction amount (when normalized by +nc)

Drag reduction mechanisms are considered

- Friction drag is reduced by wall-normal convection

- Pressure drag is reduced by smoothing effect

Combined effect (UB + roughness) slightly exists

Modified Stevensons law of the wall is suggested

Thank you for your kind attention

E.Mori, M.Quadrio, K.Fukagata DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 21/18

Background

Turbulence

- Huge drag

- Environmental problems

- High operation cost

- How to control?

E.Mori, M.Quadrio, K.Fukagata DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 22/18

Flow control classification(M. Gad-el-Hak, J. Aircraft, 2001)

Flow control

strategies

Passive

Feedback Feedforward

Active

- Uniform blowing

E.Mori, M.Quadrio, K.Fukagata DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 23/18

Governing equations(S. Kang & H. Choi, Phys. Fluids, 2000)

Incompressible Continuity and Navier-Stokes in coordinate

=

=

+

+

= 2

2

2 +

1

2

22

+ 2

22 +

1

2

2

2

=

1

1 + 2

+0

, for j = 1,3

1

1 + , for j = 2

= 2 = 2

where

E.Mori, M.Quadrio, K.Fukagata DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 24/18

Coordinate transformation(S. Kang & H. Choi, Phys. Fluids, 2000)

Calculation grids: (Cartesian with extra force)

Actual grid points allocation

wall

= = + +

= (, , : physical coordinate)

=

= , =

, : displacement of lower/upper wall

E.Mori, M.Quadrio, K.Fukagata DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 25/18

Post processing

Drag coefficient decomposition for rough case

Drag reduction rate

=

,=0 100 [%]

=8

Re

2=2

=8

Re

2=0

+

2=0

= 16

1 +

Only focusing on lower side,

subscript omitted hereafter

(Friction component)

(Pressure component)

E.Mori, M.Quadrio, K.Fukagata DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 26/18

Discretization methods

Energy-conservative second-order finite difference

schemes (In space)

Low-storage third-order Runge-Kutta / Crank-

Nicolson scheme (In time)

+ SMAC method for pressure correction

Discretized in the staggered grid system

E.Mori, M.Quadrio, K.Fukagata DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 27/18

Validation & Verification

Bulk mean streamwise velocity Time trace of instantaneous

Less than 2% of difference

from the most resolved case

E.Mori, M.Quadrio, K.Fukagata DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 28/18

Stevensons law of the wall

Plots using Stevensons law of the wall (Stevenson, 1963)2

+ 1 +

++ 1 =1

ln + +

+

Normalized by local Normalized by Stevensons law