Post on 17-Apr-2022
transcript
Direct Numerical Simulation of
Drag Reduction with Uniform Blowing
over a Rough Wall
Eisuke Mori1,2, Maurizio Quadrio2 and Koji Fukagata1
1 Keio University, Japan
2 Politecnico di Milano, Italy
11th International ERCOFTAC Symposium on
Engineering Turbulence Modelling and Measurement
Palermo, Sept. 21-23, 2016
E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 2/15
Background
Turbulence
- Huge drag
- Environmental problems
- High operation cost
- How to control?
E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 3/15
Flow control classification(M. Gad-el-Hak, J. Aircraft, 2001)
Flow control
strategies
Passive
Feedback Feedforward
Active
- Uniform blowing
E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 4/15
Uniform blowing (UB)(Sumitani & Kasagi, AIAA J., 1995
Kametani & Fukagata, J. Fluid Mech., 2011)
โข Drag contribution in a channel flow with UB(/US)
โข Excellent performance (about 45% by ๐ฝ๐ = ๐. ๐%๐ผโ)
โข Unknown over a rough wall
๐ช๐ =๐๐
๐๐๐+ ๐๐เถฑ
๐
๐
๐ โ ๐ โ๐โฒ๐โฒ ๐ ๐
(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
๐ฝ๐: Blowing velocity
โ๐๐๐ฝ๐เถฑ
๐
๐
๐ โ ๐ เดฅ๐๐ ๐
E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 5/15
Goal
Investigate the interaction between roughness and UB
for drag reduction
- DNS of turbulent channel flow
- Focus on drag reduction performance and
mechanism
E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 6/15
Numerical procedure
โข Based on FD code (for wall deformation)(Nakanishi et al., Int. J. Heat Fluid Fl., 2012)
โข Constant flow rate, ๐๐๐ = ๐๐ผ๐๐น/๐ = ๐๐๐๐
- so that ๐๐๐ โ ๐๐๐ in a plane channel (K.M.M.)
โข โ๐+ = ๐. ๐, ๐. ๐๐ < โ๐+ < ๐, โ๐+ = ๐. ๐
โข UB magnitude: ๐ = 0, ๐. ๐๐๐, ๐. ๐๐๐
SMOOTH CASEROUGH CASE
E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 7/15
๐ = ๐
Model of rough wall(E. Napoli et al., J. Fluid Mech., 2008)
Roughness displacement
๐น: channel half height
๐ณ๐: Channel length, ๐๐ ๐น๐จ๐: Amplitude of each sinusoid
๐จ๐ = แ๐, ๐๐จ๐ซ ๐ = ๐๐, ๐ , ๐๐จ๐ซ ๐ โ ๐
with rescaling so that
๐ ๐ = ๐. ๐๐๐น
๐ ๐ = ๐น
๐=๐
๐
๐จ๐ ๐ฌ๐ข๐ง๐๐๐ ๐
ฮค๐ณ๐ ๐
๐ ๐ ๐ฆ๐๐ฑ = ๐. ๐๐๐น
(Defined randomly)
E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 8/15
Coordinate transformation(S. Kang & H. Choi, Phys. Fluids, 2000)
Calculation grids: ๐๐ (Cartesian with extra force)
Actual grid points allocation
wall
แ
๐ = ๐๐๐ = ๐๐ ๐ + ๐ + ๐๐
๐ = ๐๐(๐ฅ, ๐ฆ, ๐ง: physical coordinate)
๐ โก ฮค๐๐ฎ โ ๐๐ ๐= โ ฮค๐ ๐ฑ ๐
๐๐ = ๐ซ ๐ฑ , ๐๐ = ๐
๐๐, ๐๐ฎ: displacement of
lower/upper wall
E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 9/15
Post processing
โข Drag coefficient decomposition for rough case
โข Drag reduction rate
๐ ๐ท๐ =โ๐ถ๐ท
๐ถ๐ท,๐=0ร 100 [%]
๐ถ๐ท๐ข๐ =8
Re๐แค
๐เดค๐ข
๐๐ฆ๐2=2
๐ถ๐ท๐๐ =8
Re๐แค
๐๐ข
๐๐ฆ๐2=0
+ แค๐๐ฃ
๐๐ฅ๐2=0
๐ถ๐ท๐๐ = โ16๐๐
๐๐1โ ๐ถ๐ท๐๐ + ๐ถ๐ท๐ข๐
Only focusing on lower side,
subscript โ๐โ omitted hereafter
(Friction component)
(Pressure component)
E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 10/15
Drag reduction rate, ๐น๐ซ
ROUGH CASESMOOTH CASE
Total ๐ ๐ท โ๐๐% โ๐๐% โ๐% โ๐๐%Friction ๐ ๐ท,๐น โ๐๐% โ๐๐% โ๐% โ๐๐%Pressure ๐ ๐ท,๐ - - โ๐% โ๐๐%
E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 11/15
How does friction drag decrease?
Bulk mean streamwise velocity
Black: ๐ = 0Green: ๐ = 0.001Red: ๐ = 0.005
Normalization
based on ๐ = 0
Smooth
Rough
E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 12/15
How does pressure drag decrease?
Pressure contours
๐ด = ๐ ๐ด = ๐. ๐๐๐
๐ ๐ ๐ฆ๐๐ฑ
averaged in the spanwise and time
dashed lines: zero contour
๐+
๐ ๐ ๐ฆ๐ข๐ง
E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 13/15
Stream function
Uniform
Blowing
Solid lines:
๐ = 0Dashed lines:
๐ = 0.005
E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 14/15
In practical applications
Drag reduction amount, โ๐ช๐ซ = ๐ช๐ซ,๐ด=๐ โ ๐ช๐ซ,๐ด=๐.๐,๐.๐
[%]
E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 15/15
Concluding remarks
DNS of turbulent channel flow over a rough wall with
UB
โข UB is effective over rough walls
- Lower drag reduction rate (7%, ๐๐% / 11%, ๐๐% in
rough / smooth case, with ๐ = 0.001, 0.005 )
โข Drag reduction mechanism
- Friction drag by wall-normal convection
(=conventional)
- Pressure drag by prevention of stagnant flow
โข Outlook toward practical applications
- More saving opportunity over rough walls
E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 17/15
Future plans
โข Another drag reduction technique on rough surface
- Spanwise oscillation (ongoing)
โข Assessment of net energy? (should be external flow)
โข Calculation at higher Reynolds number?
โข Other types of rough surfaces (e.g., 3D structure)?
E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 18/15
Uniform blowing (UB)(Sumitani & Kasagi, AIAA J., 1995
Kametani & Fukagata, J. Fluid Mech., 2011)
โข Drag contribution in a channel flow with UB(/US)
โข Excellent performance (about 45% by ๐ฝ๐ = ๐. ๐%๐ผโ)
โข Unknown over a rough wall
๐ช๐ =๐๐
๐น๐๐+ ๐๐เถฑ
๐
๐
๐ โ ๐ โ๐โฒ๐โฒ ๐ ๐ โ ๐๐๐ฝ๐เถฑ
๐
๐
๐ โ ๐ เดฅ๐๐ ๐
(Fukagata et al., Phys. Fluids, 2002)
Viscous
Contribution
(= laminar drag, const.)
Turbulent
contribution
Convective (=UB/US)
contribution
White: vortex core, Colors: wall shear stress
๐ฝ๐: Blowing velocity
Blowing
side
E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 19/15
Governing equations(S. Kang & H. Choi, Phys. Fluids, 2000)
Incompressible Continuity and Navier-Stokes in ๐๐coordinate
๐๐๐๐๐๐
= โ๐บ
๐๐๐๐๐
= โ๐ ๐๐๐๐
๐๐๐โ๐๐
๐๐๐+
๐
๐๐๐
๐๐๐๐๐๐๐๐๐
โ๐ ๐ท
๐๐๐๐น๐๐ + ๐บ๐
๐๐ = โ๐๐ก๐๐ข๐๐๐2
โ ๐๐๐ ๐ข๐๐ข๐
๐๐2โ ๐๐
๐๐
๐๐2๐ฟ๐๐ +
1
๐ ๐2๐๐
๐2๐ข๐๐๐๐๐2
+ ๐๐๐๐๐2๐ข๐
๐๐22 +
1
2
๐ ๐๐๐๐
๐๐2
๐๐ข๐๐๐2
๐๐ =
โ1
1 + ๐๐2
๐๐
๐๐๐+๐๐0๐๐๐
, for j = 1,3
1
1 + ๐, for j = 2
๐๐ = ๐๐ โ ๐ฟ๐2๐ = ๐๐๐๐ข๐๐๐2
where
E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 20/15
Discretization methods
โข Energy-conservative second-order finite difference
schemes (In space)
โข Low-storage third-order Runge-Kutta / Crank-
Nicolson scheme (In time)
+ SMAC method for pressure correction
Discretized in the staggered grid system
E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 21/15
Validation & Verification(B. Milici et al., J. Fluid Mech., 2014)
Bulk mean streamwise velocity Time trace of instantaneous CD,r
Less than 2% of difference
with most resolved one
E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 22/15
How does friction drag decreases?
Reynolds shear stress contour
๐ ๐ ๐ฆ๐๐ฑ
๐ขโฒ+๐ฃโฒ+
*averaged in the spanwise and time
dashed lines: zero contour
๐ด = ๐ ๐ด = ๐. ๐๐๐
E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 23/15
เดฅ๐ distribution (2D contour)
No control case UB 0.5% case
Based on ๐ข๐ in w/o control case
E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 24/15
เดฅ๐ distribution (2D contour)
No control case UB 0.5% case
Based on ๐ข๐ in w/o control case
E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 25/15
Stream function (detailed)
E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 26/15
๐๐ซ๐ฆ๐ฌ distribution
Black: w/o control
Green: UB 0.1%
Red: UB 0.5%
Normalized by ๐ข๐in w/o control case
E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 27/15
๐๐ซ๐ฆ๐ฌ distribution
Black: w/o control
Green: UB 0.1%
Red: UB 0.5%
Normalized by ๐ข๐in w/o control case
E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 28/15
๐๐ซ๐ฆ๐ฌ distribution
Black: w/o control
Green: UB 0.1%
Red: UB 0.5%
Normalized by ๐ข๐in w/o control case
E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 29/15
๐โฒ+๐โฒ+ distribution
Black: w/o control
Green: UB 0.1%
Red: UB 0.5%
Normalized by ๐ข๐in w/o control case
E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 31/15
โข Effective slope = about 0.2
โข k_rms
โข Sand grain roughness
โข 3D?
โข How to calculate skin-friction drag
โข The history of UB
โข Pressure component legend (purple) of smooth case
should be removed
โข More time for drag reduction rate slide