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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
