Direct Numerical Simulation of Drag Reduction with Uniform ...
Transcript of Direct Numerical Simulation of Drag Reduction with Uniform ...
![Page 1: Direct Numerical Simulation of Drag Reduction with Uniform ...](https://reader034.fdocuments.in/reader034/viewer/2022042313/625c394a5539f9325423c573/html5/thumbnails/1.jpg)
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
![Page 2: Direct Numerical Simulation of Drag Reduction with Uniform ...](https://reader034.fdocuments.in/reader034/viewer/2022042313/625c394a5539f9325423c573/html5/thumbnails/2.jpg)
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?
![Page 3: Direct Numerical Simulation of Drag Reduction with Uniform ...](https://reader034.fdocuments.in/reader034/viewer/2022042313/625c394a5539f9325423c573/html5/thumbnails/3.jpg)
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
![Page 4: Direct Numerical Simulation of Drag Reduction with Uniform ...](https://reader034.fdocuments.in/reader034/viewer/2022042313/625c394a5539f9325423c573/html5/thumbnails/4.jpg)
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
![Page 5: Direct Numerical Simulation of Drag Reduction with Uniform ...](https://reader034.fdocuments.in/reader034/viewer/2022042313/625c394a5539f9325423c573/html5/thumbnails/5.jpg)
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
![Page 6: Direct Numerical Simulation of Drag Reduction with Uniform ...](https://reader034.fdocuments.in/reader034/viewer/2022042313/625c394a5539f9325423c573/html5/thumbnails/6.jpg)
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
![Page 7: Direct Numerical Simulation of Drag Reduction with Uniform ...](https://reader034.fdocuments.in/reader034/viewer/2022042313/625c394a5539f9325423c573/html5/thumbnails/7.jpg)
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)
![Page 8: Direct Numerical Simulation of Drag Reduction with Uniform ...](https://reader034.fdocuments.in/reader034/viewer/2022042313/625c394a5539f9325423c573/html5/thumbnails/8.jpg)
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
![Page 9: Direct Numerical Simulation of Drag Reduction with Uniform ...](https://reader034.fdocuments.in/reader034/viewer/2022042313/625c394a5539f9325423c573/html5/thumbnails/9.jpg)
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)
![Page 10: Direct Numerical Simulation of Drag Reduction with Uniform ...](https://reader034.fdocuments.in/reader034/viewer/2022042313/625c394a5539f9325423c573/html5/thumbnails/10.jpg)
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%
![Page 11: Direct Numerical Simulation of Drag Reduction with Uniform ...](https://reader034.fdocuments.in/reader034/viewer/2022042313/625c394a5539f9325423c573/html5/thumbnails/11.jpg)
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
![Page 12: Direct Numerical Simulation of Drag Reduction with Uniform ...](https://reader034.fdocuments.in/reader034/viewer/2022042313/625c394a5539f9325423c573/html5/thumbnails/12.jpg)
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
![Page 13: Direct Numerical Simulation of Drag Reduction with Uniform ...](https://reader034.fdocuments.in/reader034/viewer/2022042313/625c394a5539f9325423c573/html5/thumbnails/13.jpg)
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
![Page 14: Direct Numerical Simulation of Drag Reduction with Uniform ...](https://reader034.fdocuments.in/reader034/viewer/2022042313/625c394a5539f9325423c573/html5/thumbnails/14.jpg)
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
[%]
![Page 15: Direct Numerical Simulation of Drag Reduction with Uniform ...](https://reader034.fdocuments.in/reader034/viewer/2022042313/625c394a5539f9325423c573/html5/thumbnails/15.jpg)
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
![Page 16: Direct Numerical Simulation of Drag Reduction with Uniform ...](https://reader034.fdocuments.in/reader034/viewer/2022042313/625c394a5539f9325423c573/html5/thumbnails/16.jpg)
![Page 17: Direct Numerical Simulation of Drag Reduction with Uniform ...](https://reader034.fdocuments.in/reader034/viewer/2022042313/625c394a5539f9325423c573/html5/thumbnails/17.jpg)
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)?
![Page 18: Direct Numerical Simulation of Drag Reduction with Uniform ...](https://reader034.fdocuments.in/reader034/viewer/2022042313/625c394a5539f9325423c573/html5/thumbnails/18.jpg)
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
![Page 19: Direct Numerical Simulation of Drag Reduction with Uniform ...](https://reader034.fdocuments.in/reader034/viewer/2022042313/625c394a5539f9325423c573/html5/thumbnails/19.jpg)
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
![Page 20: Direct Numerical Simulation of Drag Reduction with Uniform ...](https://reader034.fdocuments.in/reader034/viewer/2022042313/625c394a5539f9325423c573/html5/thumbnails/20.jpg)
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
![Page 21: Direct Numerical Simulation of Drag Reduction with Uniform ...](https://reader034.fdocuments.in/reader034/viewer/2022042313/625c394a5539f9325423c573/html5/thumbnails/21.jpg)
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
![Page 22: Direct Numerical Simulation of Drag Reduction with Uniform ...](https://reader034.fdocuments.in/reader034/viewer/2022042313/625c394a5539f9325423c573/html5/thumbnails/22.jpg)
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
![Page 23: Direct Numerical Simulation of Drag Reduction with Uniform ...](https://reader034.fdocuments.in/reader034/viewer/2022042313/625c394a5539f9325423c573/html5/thumbnails/23.jpg)
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
![Page 24: Direct Numerical Simulation of Drag Reduction with Uniform ...](https://reader034.fdocuments.in/reader034/viewer/2022042313/625c394a5539f9325423c573/html5/thumbnails/24.jpg)
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
![Page 25: Direct Numerical Simulation of Drag Reduction with Uniform ...](https://reader034.fdocuments.in/reader034/viewer/2022042313/625c394a5539f9325423c573/html5/thumbnails/25.jpg)
E.Mori, Fukagata lab. DNS/Drag Reduction/Uniform blowing(UB)/Rough wall 25/15
Stream function (detailed)
![Page 26: Direct Numerical Simulation of Drag Reduction with Uniform ...](https://reader034.fdocuments.in/reader034/viewer/2022042313/625c394a5539f9325423c573/html5/thumbnails/26.jpg)
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
![Page 27: Direct Numerical Simulation of Drag Reduction with Uniform ...](https://reader034.fdocuments.in/reader034/viewer/2022042313/625c394a5539f9325423c573/html5/thumbnails/27.jpg)
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
![Page 28: Direct Numerical Simulation of Drag Reduction with Uniform ...](https://reader034.fdocuments.in/reader034/viewer/2022042313/625c394a5539f9325423c573/html5/thumbnails/28.jpg)
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
![Page 29: Direct Numerical Simulation of Drag Reduction with Uniform ...](https://reader034.fdocuments.in/reader034/viewer/2022042313/625c394a5539f9325423c573/html5/thumbnails/29.jpg)
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
![Page 30: Direct Numerical Simulation of Drag Reduction with Uniform ...](https://reader034.fdocuments.in/reader034/viewer/2022042313/625c394a5539f9325423c573/html5/thumbnails/30.jpg)
![Page 31: Direct Numerical Simulation of Drag Reduction with Uniform ...](https://reader034.fdocuments.in/reader034/viewer/2022042313/625c394a5539f9325423c573/html5/thumbnails/31.jpg)
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