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N EAR - WALL ENSTROPHY GENERATION IN A DRAG - REDUCED TURBULENT CHANNEL FLOW WITH SPANWISE WALL OSCILLATIONS Pierre Ricco 1 , Claudio Ottonelli, Yosuke Hasegawa, Maurizio Quadrio 1 Sheffield, 2 Onera Paris, 3 Tokyo, 4 Politecnico Milano

  1. N EAR - WALL ENSTROPHY GENERATION IN A DRAG - REDUCED TURBULENT CHANNEL FLOW WITH SPANWISE WALL OSCILLATIONS Pierre Ricco 1 , Claudio Ottonelli, Yosuke Hasegawa, Maurizio Quadrio 1 Sheffield, 2 Onera Paris, 3 Tokyo, 4 Politecnico Milano ERCOFTAC/PLASMAERO Workshop, Toulouse, 10 December 2012 5 D ECEMBER 2012 WALL - OSCILLATION DRAG - REDUCTION PROBLEM 1-28

  2. T URBULENT DRAG REDUCTION A CTIVE OPEN - LOOP TECHNIQUE Energy input into system Pre-determined forcing N UMERICAL APPROACH Direct numerical simulations of wall turbulence Fully-developed turbulent channel flow ( Re τ = u τ h /ν = 200) Compact finite-difference scheme along wall-normal direction Spectral discretization along streamwise and spanwise directions S PANWISE WALL OSCILLATIONS New approach: Turbulent enstrophy Transient evolution C ONSTANT DP / DX τ w is fixed in fully-developed conditions GAIN: U b increases 5 D ECEMBER 2012 WALL - OSCILLATION DRAG - REDUCTION PROBLEM 2-28

  3. T URBULENT DRAG REDUCTION A CTIVE OPEN - LOOP TECHNIQUE Energy input into system Pre-determined forcing N UMERICAL APPROACH Direct numerical simulations of wall turbulence Fully-developed turbulent channel flow ( Re τ = u τ h /ν = 200) Compact finite-difference scheme along wall-normal direction Spectral discretization along streamwise and spanwise directions S PANWISE WALL OSCILLATIONS New approach: Turbulent enstrophy Transient evolution C ONSTANT DP / DX τ w is fixed in fully-developed conditions GAIN: U b increases 5 D ECEMBER 2012 WALL - OSCILLATION DRAG - REDUCTION PROBLEM 2-28

  4. T URBULENT DRAG REDUCTION A CTIVE OPEN - LOOP TECHNIQUE Energy input into system Pre-determined forcing N UMERICAL APPROACH Direct numerical simulations of wall turbulence Fully-developed turbulent channel flow ( Re τ = u τ h /ν = 200) Compact finite-difference scheme along wall-normal direction Spectral discretization along streamwise and spanwise directions S PANWISE WALL OSCILLATIONS New approach: Turbulent enstrophy Transient evolution C ONSTANT DP / DX τ w is fixed in fully-developed conditions GAIN: U b increases 5 D ECEMBER 2012 WALL - OSCILLATION DRAG - REDUCTION PROBLEM 2-28

  5. T URBULENT DRAG REDUCTION A CTIVE OPEN - LOOP TECHNIQUE Energy input into system Pre-determined forcing N UMERICAL APPROACH Direct numerical simulations of wall turbulence Fully-developed turbulent channel flow ( Re τ = u τ h /ν = 200) Compact finite-difference scheme along wall-normal direction Spectral discretization along streamwise and spanwise directions S PANWISE WALL OSCILLATIONS New approach: Turbulent enstrophy Transient evolution C ONSTANT DP / DX τ w is fixed in fully-developed conditions GAIN: U b increases 5 D ECEMBER 2012 WALL - OSCILLATION DRAG - REDUCTION PROBLEM 2-28

  6. T URBULENT DRAG REDUCTION A CTIVE OPEN - LOOP TECHNIQUE Energy input into system Pre-determined forcing N UMERICAL APPROACH Direct numerical simulations of wall turbulence Fully-developed turbulent channel flow ( Re τ = u τ h /ν = 200) Compact finite-difference scheme along wall-normal direction Spectral discretization along streamwise and spanwise directions S PANWISE WALL OSCILLATIONS New approach: Turbulent enstrophy Transient evolution C ONSTANT DP / DX τ w is fixed in fully-developed conditions GAIN: U b increases 5 D ECEMBER 2012 WALL - OSCILLATION DRAG - REDUCTION PROBLEM 2-28

  7. S PANWISE WALL OSCILLATIONS G EOMETRY Ww = A sin � T t � Lz 2 π Ly y x Lx Mean flow z U 2 b , o − U 2 C f , r − C f , o R = b , r C f , r = U 2 b , o Why does the skin-friction coefficent decrease? C f = 2 τ w / ( ρ U 2 b ) decreases → study why U b increases 5 D ECEMBER 2012 WALL - OSCILLATION DRAG - REDUCTION PROBLEM 3-28

  8. S PANWISE WALL OSCILLATIONS G EOMETRY Ww = A sin � T t � Lz 2 π Ly y x Lx Mean flow z U 2 b , o − U 2 C f , r − C f , o R = b , r C f , r = U 2 b , o Why does the skin-friction coefficent decrease? C f = 2 τ w / ( ρ U 2 b ) decreases → study why U b increases 5 D ECEMBER 2012 WALL - OSCILLATION DRAG - REDUCTION PROBLEM 3-28

  9. S PANWISE WALL OSCILLATIONS G EOMETRY Ww = A sin � T t � Lz 2 π Ly y x Lx Mean flow z U 2 b , o − U 2 C f , r − C f , o R = b , r C f , r = U 2 b , o Why does the skin-friction coefficent decrease? C f = 2 τ w / ( ρ U 2 b ) decreases → study why U b increases 5 D ECEMBER 2012 WALL - OSCILLATION DRAG - REDUCTION PROBLEM 3-28

  10. S PANWISE WALL OSCILLATIONS G EOMETRY Ww = A sin � T t � Lz 2 π Ly y x Lx Mean flow z U 2 b , o − U 2 C f , r − C f , o R = b , r C f , r = U 2 b , o Why does the skin-friction coefficent decrease? C f = 2 τ w / ( ρ U 2 b ) decreases → study why U b increases 5 D ECEMBER 2012 WALL - OSCILLATION DRAG - REDUCTION PROBLEM 3-28

  11. A VERAGING OPERATORS S PACE : HOMOGENEOUS DIRECTIONS � L x � L z 1 f ( y , t ) = f ( x , y , z , t ) d z d x L x L z 0 0 P HASE N − 1 � f ( y , τ ) = 1 � f ( y , nT + τ ) N n = 0 T IME � T � f � ( y ) = 1 f ( y , τ ) d τ T 0 G LOBAL � h [ f ] g = � f � ( y ) d y 0 5 D ECEMBER 2012 WALL - OSCILLATION DRAG - REDUCTION PROBLEM 4-28

  12. A VERAGING OPERATORS S PACE : HOMOGENEOUS DIRECTIONS � L x � L z 1 f ( y , t ) = f ( x , y , z , t ) d z d x L x L z 0 0 P HASE N − 1 � f ( y , τ ) = 1 � f ( y , nT + τ ) N n = 0 T IME � T � f � ( y ) = 1 f ( y , τ ) d τ T 0 G LOBAL � h [ f ] g = � f � ( y ) d y 0 5 D ECEMBER 2012 WALL - OSCILLATION DRAG - REDUCTION PROBLEM 4-28

  13. A VERAGING OPERATORS S PACE : HOMOGENEOUS DIRECTIONS � L x � L z 1 f ( y , t ) = f ( x , y , z , t ) d z d x L x L z 0 0 P HASE N − 1 � f ( y , τ ) = 1 � f ( y , nT + τ ) N n = 0 T IME � T � f � ( y ) = 1 f ( y , τ ) d τ T 0 G LOBAL � h [ f ] g = � f � ( y ) d y 0 5 D ECEMBER 2012 WALL - OSCILLATION DRAG - REDUCTION PROBLEM 4-28

  14. A VERAGING OPERATORS S PACE : HOMOGENEOUS DIRECTIONS � L x � L z 1 f ( y , t ) = f ( x , y , z , t ) d z d x L x L z 0 0 P HASE N − 1 � f ( y , τ ) = 1 � f ( y , nT + τ ) N n = 0 T IME � T � f � ( y ) = 1 f ( y , τ ) d τ T 0 G LOBAL � h [ f ] g = � f � ( y ) d y 0 5 D ECEMBER 2012 WALL - OSCILLATION DRAG - REDUCTION PROBLEM 4-28

  15. A VERAGING OPERATORS S PACE : HOMOGENEOUS DIRECTIONS � L x � L z 1 f ( y , t ) = f ( x , y , z , t ) d z d x L x L z 0 0 P HASE N − 1 � f ( y , τ ) = 1 � f ( y , nT + τ ) N n = 0 T IME � T � f � ( y ) = 1 f ( y , τ ) d τ T 0 G LOBAL � h [ f ] g = � f � ( y ) d y 0 5 D ECEMBER 2012 WALL - OSCILLATION DRAG - REDUCTION PROBLEM 4-28

  16. M EAN FLOW 25 0.35 0.3 20 0.25 15 U � 0.2 �� R 0.15 10 0.1 5 0.05 0 0 0 1 2 0 25 50 75 100 125 150 175 10 10 10 y T Scaling by viscous units Mean velocity increases in the bulk of the channel Mean wall-shear stress is unchanged Optimum period of oscillation T ≈ 75 5 D ECEMBER 2012 WALL - OSCILLATION DRAG - REDUCTION PROBLEM 5-28

  17. M EAN FLOW 25 0.35 0.3 20 0.25 15 U � 0.2 �� R 0.15 10 0.1 5 0.05 0 0 0 1 2 0 25 50 75 100 125 150 175 10 10 10 y T Scaling by viscous units Mean velocity increases in the bulk of the channel Mean wall-shear stress is unchanged Optimum period of oscillation T ≈ 75 5 D ECEMBER 2012 WALL - OSCILLATION DRAG - REDUCTION PROBLEM 5-28

  18. M EAN FLOW 25 0.35 0.3 20 0.25 15 U � 0.2 �� R 0.15 10 0.1 5 0.05 0 0 0 1 2 0 25 50 75 100 125 150 175 10 10 10 y T Scaling by viscous units Mean velocity increases in the bulk of the channel Mean wall-shear stress is unchanged Optimum period of oscillation T ≈ 75 5 D ECEMBER 2012 WALL - OSCILLATION DRAG - REDUCTION PROBLEM 5-28

  19. M EAN FLOW 25 0.35 0.3 20 0.25 15 U � 0.2 �� R 0.15 10 0.1 5 0.05 0 0 0 1 2 0 25 50 75 100 125 150 175 10 10 10 y T Scaling by viscous units Mean velocity increases in the bulk of the channel Mean wall-shear stress is unchanged Optimum period of oscillation T ≈ 75 5 D ECEMBER 2012 WALL - OSCILLATION DRAG - REDUCTION PROBLEM 5-28

  20. M EAN FLOW 25 0.35 0.3 20 0.25 15 U � 0.2 �� R 0.15 10 0.1 5 0.05 0 0 0 1 2 0 25 50 75 100 125 150 175 10 10 10 y T Scaling by viscous units Mean velocity increases in the bulk of the channel Mean wall-shear stress is unchanged Optimum period of oscillation T ≈ 75 5 D ECEMBER 2012 WALL - OSCILLATION DRAG - REDUCTION PROBLEM 5-28

  21. T URBULENCE STATISTICS 0.2 uv � 7 , �� φ = 3 π 0.15 4 6 � 0.1 φ = π w 2 5 � 2 0.05 � 4 , � vw � 0 3 � v 2 � -0.05 φ = 0 2 , � -0.1 φ = π u 2 � 1 4 � -0.15 0 -1 -0.2 0 1 2 0 1 2 10 10 10 10 10 10 y y Turbulence kinetic energy decreases Streamwise velocity fluctuations are attenuated the most vw in created, �� vw � New oscillatory Reynolds stress term � = 0 5 D ECEMBER 2012 WALL - OSCILLATION DRAG - REDUCTION PROBLEM 6-28

  22. T URBULENCE STATISTICS 0.2 uv � 7 , �� φ = 3 π 0.15 4 6 � 0.1 φ = π w 2 5 � 2 0.05 � 4 , � vw � 0 3 � v 2 � -0.05 φ = 0 2 , � -0.1 φ = π u 2 � 1 4 � -0.15 0 -1 -0.2 0 1 2 0 1 2 10 10 10 10 10 10 y y Turbulence kinetic energy decreases Streamwise velocity fluctuations are attenuated the most vw in created, �� vw � New oscillatory Reynolds stress term � = 0 5 D ECEMBER 2012 WALL - OSCILLATION DRAG - REDUCTION PROBLEM 6-28

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