Large scale structures in skin friction drag reduction by spanwise wall oscillation Qiang Yang and Yongmann M. Chung School of Engineering and Centre for Scientific Computing University of Warwick September 22, 2014 Q. Yang & Y. M. Chung (Warwick) Large structures in spanwise wall oscillation September 22, 2014 1 / 21 Introduction Drag reduction by spanwise wall oscillation Spanwise wall oscillation can have as much as 40% drag reduction (DR) at Reτ = 200 (Jung et al. [1992]); Cf , C f ,0 are the skin friction for control and no-control flows, respectively. DR = 1 − where C f and C f ,0 Simple formula (no need for feedback): w = A sin(ωt) (or w = A sin( 2π T t)), where w is spanwise wall velocity; A is the spanwise peak wall velocity; ω is the wall oscillation frequency ( T is the wall oscillation period). Q. Yang & Y. M. Chung (Warwick) Large structures in spanwise wall oscillation September 22, 2014 2 / 21 Introduction Simulation set up Cases Reτ Rem Lx × Ly × Lz Nx × Ny × Nz ∆x+ ∆y+ ∆z+ CH200 CH400 CH800 CH800L CH1600 200 400 800 800 1600 3150 7000 15700 15700 34500 16h × 2h × 6h 16h × 2h × 6h 12h × 2h × 4h 24h × 2h × 8h 12h × 2h × 4h 320 × 140 × 240 640 × 240 × 480 960 × 384 × 640 3840 × 384 × 1280 1920 × 800 × 1280 10.0 10.0 10.0 5.0 10.0 0.4 ∼ 6.0 0.4 ∼ 7.2 0.4 ∼ 9.7 0.4 ∼ 9.7 0.4 ∼ 9.2 5.0 5.0 5.0 5.0 5.0 Computational domain sizes and grid resolutions for DNS. Using an in-house second-order accuracy FVM code in both space and time (Hurst et al. [2014]). CH800 (236 millions points) was simulated in local cluster Minerva at Warwick University. CH1600 (∼ 2 billion points) was simulated on HECToR (and Archer). Q. Yang & Y. M. Chung (Warwick) Large structures in spanwise wall oscillation September 22, 2014 3 / 21 Introduction Reynolds number effect for spanwise wall oscillation 1 0.9 100 T+ 50 40 0.8 DR C f / C f,0 500 200 60 Reτ=200 Reτ=400 Reτ=800 Reτ=1600 20 0.7 0.6 0.5 Reτ=200 Reτ=400 Reτ=800 Reτ=1600 0 0 500 1000 t 1500 2000 -20 0 0.05 + 0.1 0.15 0.2 ω+ Initial response of skin friction C f for T + = 100 at four Reynolds numbers (left) and DR changes with oscillation frequencies and Reynolds numbers (right); . As Reynolds number increases from Reτ = 200 to 1600: Maximum DR decreases; Optimal oscillation frequency shifts towards a higher value. Q. Yang & Y. M. Chung (Warwick) Large structures in spanwise wall oscillation September 22, 2014 4 / 21 Introduction Large scale structures in no control flows 32 1.5 ++ rms0 rms0 uwv rms 2 Reτ=200 Reτ=400 Reτ=800 Reτ=1600 1 1 0.5 00 -1-1 10 10 0 10 0 10 1 10 1 10 + + yy 2 10 2 10 3 10 3 10 0 urms plots (left) and 2D spectra kx kz Φuu at y+ = 15 (right). The logarithmic region keeps developing to form an outer peak in urms profile. A spectra handle (Hoyas and Jiménez [2006]) in premultiplied spectra kx kz Φuu becomes clearer at Reτ = 800 (lines) and Reτ = 1600 (shaded). Q. Yang & Y. M. Chung (Warwick) Large structures in spanwise wall oscillation September 22, 2014 5 / 21 Introduction Large scale structures in no control flows 32 1.5 ++ rms0 rms0 uwv rms 2 Reτ=200 Reτ=400 Reτ=800 Reτ=1600 1 1 0.5 00 -1-1 10 10 0 10 0 10 1 10 1 10 + + yy 2 10 2 10 3 10 3 10 0 urms plots (left) and 2D spectra kx kz Φuu at y+ = 15 (right). The logarithmic region keeps developing to form an outer peak in urms profile. A spectra handle (Hoyas and Jiménez [2006]) in premultiplied spectra kx kz Φuu becomes clearer at Reτ = 800 (lines) and Reτ = 1600 (shaded). Q. Yang & Y. M. Chung (Warwick) Large structures in spanwise wall oscillation September 22, 2014 6 / 21 Introduction Large scale structures in no control flows 1D premultiplied spectra kx Φuu (left) and kz Φuu (right). Inner peak scales well in wall units, with λx+ ≈ 1000 and λz+ ≈ 100. The outer site penetrates deeply into the near wall region. Q. Yang & Y. M. Chung (Warwick) Large structures in spanwise wall oscillation September 22, 2014 7 / 21 Introduction Large scale structures in no control flows 1D premultiplied spectra kx Φuu (left) and kz Φuu (right). Inner peak scales well in wall units, with λx+ ≈ 1000 and λz+ ≈ 100. The outer site penetrates deeply into the near wall region. Q. Yang & Y. M. Chung (Warwick) Large structures in spanwise wall oscillation September 22, 2014 8 / 21 Introduction Large scale structures in no control flows 1D premultiplied spectra kx Φuu (left) and kz Φuu (right). Inner peak scales well in wall units, with λx+ ≈ 1000 and λz+ ≈ 100. The outer site penetrates deeply into the near wall region. Q. Yang & Y. M. Chung (Warwick) Large structures in spanwise wall oscillation September 22, 2014 9 / 21 Visualisation Visualisation for CH1600 Visualisation for channel flow at Reτ = 1600 with and without spanwise wall oscillation (movie). Q. Yang & Y. M. Chung (Warwick) Large structures in spanwise wall oscillation September 22, 2014 10 / 21 Spectra & decomposition Spectra change (kx kz Φuu ) No control cases 2D spectra kx kz Φuu at y+ = 15 (left) and 1D spectra kx Φuu (right). The inner peak shifts towards smaller scales by wall oscillation. Energy in the large scales is also modified by wall oscillation. Q. Yang & Y. M. Chung (Warwick) Large structures in spanwise wall oscillation September 22, 2014 11 / 21 Spectra & decomposition Spectra change (kx kz Φuu ) Controlled at T + = 100 2D spectra kx kz Φuu at y+ = 15 (left) and 1D spectra kx Φuu (right). The inner peak shifts towards smaller streamwise scales by wall oscillation. Energy in the large scales is also modified by wall oscillation. Q. Yang & Y. M. Chung (Warwick) Large structures in spanwise wall oscillation September 22, 2014 12 / 21 Spectra & decomposition Inner/Outer decomposition 1 1 Reτ=200 Reτ=400 Reτ=800 Reτ=1600 0.6 0.8 (1-y)(1-uv0) -uv0 0.8 0.4 0.2 0.6 0.4 0.2 0 0 0 0.2 0.4 y/h 0.6 0.8 1 0 0.2 0.4 y/h 0.6 0.8 1 Turbulent shear stress distribution, −uv0 (left) and the wall distance weighted form, (1 − y)(−uv0 ) (right). Contribution to C f is considered by using the formula from Fukagata et al. [2002]: Cf = 6 +6 Re Z 1 (1 − y)(−uv)dy 0 Q. Yang & Y. M. Chung (Warwick) = 6 +6 Re | Z yp 0 (1 − y)(−uv)dy + 6 {z } | inner Large structures in spanwise wall oscillation Z 1 yp (1 − y)(−uv)dy {z } outer September 22, 2014 13 / 21 Spectra & decomposition Inner/Outer decomposition 1 1 Reτ=200 Reτ=400 Reτ=800 Reτ=1600 0.6 0.8 (1-y)(1-uv0) -uv0 0.8 0.4 0.2 0.6 0.4 0.2 0 0 0 0.2 0.4 y/h 0.6 0.8 1 0 0.2 0.4 y/h 0.6 0.8 1 Turbulent shear stress distribution, −uv0 (left) and the wall distance weighted form, (1 − y)(−uv0 ) (right). Contribution to C f is considered by using the formula from Fukagata et al. [2002]: Cf = 6 +6 Re Z 1 (1 − y)(−uv)dy 0 Q. Yang & Y. M. Chung (Warwick) = 6 +6 Re | Z yp 0 (1 − y)(−uv)dy + 6 {z } | inner Large structures in spanwise wall oscillation Z 1 yp (1 − y)(−uv)dy {z } outer September 22, 2014 14 / 21 Spectra & decomposition Inner/Outer decomposition 1 40 30 0.6 DR C f / C f0 0.8 0.4 Outer Inner Laminar 0.2 0 500 1000 1500 2000 20 Outer Inner Total 10 0 Reτ 500 1000 1500 2000 Reτ Contribution to skin friction, C f , from turbulent shear stress in the inner region and outer region. (. . . no control; — T + = 100). As Reynolds number increases: Laminar component to C f deceases; Inner contribution for controlled cases remains almost constant; C f reduction in the outer region is very large and remains almost constant. Q. Yang & Y. M. Chung (Warwick) Large structures in spanwise wall oscillation September 22, 2014 15 / 21 Spectra & decomposition Spectra decomposition (kx kz Φuv ) 2 Reτ=800 Reτ=1600 LevelkxkzΦuv/uτ 2 1 no control: + T =100: 0.0025 0.1 0.005 Reτ=800 Reτ=1600 λz + -uv, (-uv)L, (-uv)S 103 102 no control: T+=100: 0.002 0.0015 0.001 0.0005 0 0 0.2 0.4 0.6 0.8 1 y/h 1 10 2 10 10 3 4 10 λ+x 2D spectra kx kz Φuv at y+ = 15 (left) and decomposed turbulent shear stress, −uv (right). Spectra filter size λx /h = 3 and λz /h = 0.5. Decomposed large scales, −uvL , for no control cases are scaled well in outer units. Significant turbulent shear stress reduction comes from the large scales, −uvL . Q. Yang & Y. M. Chung (Warwick) Large structures in spanwise wall oscillation September 22, 2014 16 / 21 Spectra & decomposition Spectra decomposition (kx kz Φuv ) 2 Reτ=800 Reτ=1600 LevelkxkzΦuv/uτ 2 1 no control: + T =100: 0.0025 0.1 0.005 Reτ=800 Reτ=1600 λz + -uv, (-uv)L, (-uv)S 103 102 no control: T+=100: 0.002 0.0015 0.001 0.0005 0 0 0.2 0.4 0.6 0.8 y/h 1 10 2 10 10 3 4 10 λ+x 2D spectra kx kz Φuv at y+ = 15 (left) and decomposed turbulent shear stress, −uv (right). Spectra filter size λx /h = 3 and λz /h = 0.5. Decomposed large scales, −uvL , for no control cases are scaled well in outer units. Significant turbulent shear stress reduction comes from the large scales, −uvL . Q. Yang & Y. M. Chung (Warwick) Large structures in spanwise wall oscillation September 22, 2014 17 / 21 Spectra & decomposition Spectra decomposition (kx kz Φuv ) 2 Reτ=800 Reτ=1600 LevelkxkzΦuv/uτ 2 1 no control: + T =100: 0.0025 0.1 0.005 Reτ=800 Reτ=1600 λz + -uv, (-uv)L, (-uv)S 103 102 no control: T+=100: 0.002 0.0015 0.001 0.0005 0 0 0.2 0.4 0.6 0.8 1 y/h 1 10 2 10 10 3 4 10 λ+x 2D spectra kx kz Φuv at y+ = 15 (left) and decomposed turbulent shear stress, −uv (right). Spectra filter size λx /h = 3 and λz /h = 0.5. Decomposed large scales, −uvL , for no control cases are scaled well in outer units. Significant turbulent shear stress reduction comes from the large scales, −uvL . Q. Yang & Y. M. Chung (Warwick) Large structures in spanwise wall oscillation September 22, 2014 18 / 21 Conclusion Conclusions Cases CH800 (NO) CH1600 (NO) CH800 (WO) Type no control no control T + = 100 laminar 7% 4% 10% (0% ↓) small scales 57% 57% 54% (31% ↓ ) large scales 36% 39% 36% (25% ↓ ) Contribution to skin friction, C f , from laminar, small scales and large scales. The effect of large scales becomes important as Reynolds number increases. Wall oscillation can also significantly weaken the large scales, even though those structures are far away from the wall. The interaction between the small and large scales may explain the Reynolds number effect in spanwise wall oscillation. Q. Yang & Y. M. Chung (Warwick) Large structures in spanwise wall oscillation September 22, 2014 19 / 21 Conclusion Acknowledgements Thank You Q. Yang & Y. M. Chung (Warwick) Large structures in spanwise wall oscillation September 22, 2014 20 / 21 References W. J. Jung, N. Mangiavacchi, and R. Akhavan. Suppression of turbulence in wall-bounded flows by high-frequency spanwise oscillations. Physics of Fluids A, 4(8): 1605–1607, 1992. M. Quadrio, P. Ricco, and C. Viotti. Streamwise-travelling waves of spanwise wall velocity for turbulent drag reduction. Journal of Fluid Mechanics, 627:161–178, 2009. E. Hurst, Q. Yang, and Y. M. Chung. The effect of Reynolds number on turbulent drag reduction by streamwise travelling waves. Journal of Fluid Mechanics, under review, 2014. K. C. Kim and R. J. Adrian. Very large-scale motion in the outer layer. Physics of Fluids, 11(2):417422, 1999. N. Hutchins and I. Marusic. Evidence of very long meandering features in the logarithmic region of turbulent boundary layers. Journal of Fluid Mechanics, 579:1–28, 2007. S. Hoyas and J. Jiménez. Scaling of the velocity fluctuations in turbulent channels up to Reτ = 2003. Physics of Fluids, 18:011702, 2006. R. Mathis, N. Hutchins, and I. Marusic. Large-scale amplitude modulation of the small-scale structures in turbulent boundary layer. Journal of Fluid Mechanics, 628: 311–337, 2009. B. Ganapathisubramani, N. Hutchins, J. P. Monty, D. Chung, and I. Marusic. Amplitude and frequency modulation in wall turbulence. Journal of Fluid Mechanics, 712:61–91, 2012. M. Bernardini and S. Pirozzoli. Inner/outer layer interactions in turbulent boundary layers: A refined measure for the large-scale amplitude modulation mechanism. Physics of Fluids, 23(6):061701, 2011. Q. Yang & Y. M. Chung (Warwick) Large structures in spanwise wall oscillation September 22, 2014 20 / 21 Conclusion L. Agostini and M. A. Leschziner. On the influence of outer large-scale structures on near-wall turbulence in channel flow. Physics of Fluids, 26:075107, 2014. K. Fukagata, K. Iwamoto, and N. Kasagi. Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows. Physics of Fluids, 14(11):L73–L76, 2002. Q. Yang & Y. M. Chung (Warwick) Large structures in spanwise wall oscillation September 22, 2014 20 / 21 Conclusion Density spectra covariance of Fourier coefficients: Rbi, j (κ,t) = hubi (κ,t)b u j (κ 0 ,t)i = hubi (κ,t)b u j (−κ,t)i = hubi (κ,t)b u∗j (κ,t)i, κ ∈ [−∞, ∞]. (1) one-sided energy spectra: Ei j (κ,t) ≡ Ei j (κx , κz ,t) = Ri j (κx , κz ,t) + Ri j (−κx , κz ,t) + Ri j (−κx , −κz ,t) + Ri j (κx , −κz ,t) = ubi (κx , κz ,t)b u∗j (κx , κz ,t) + ubi (−κx , κz ,t)b u∗j (−κx , κz ,t) (2) + ubi (−κx , −κz ,t)b u∗j (−κx , −κz ,t) + ubi (κx , −κz ,t)b u∗j (κx , −κz ,t) = ubi (κx , κz ,t)b u j (−κx , −κz ,t) + ubi (−κx , κz ,t)b u j (κx , −κz ,t) + ubi (−κx , −κz ,t)b u j (κx , κz ,t) + ubi (κx , −κz ,t)b u j (−κx , κz ,t). one-sided energy density spectra: Φi, j (κ,t) = Ei, j (κ,t)/dκ. Q. Yang & Y. M. Chung (Warwick) Large structures in spanwise wall oscillation (3) September 22, 2014 20 / 21 Conclusion 1D spectra validation 2.5 103 2 1.5 Φuu/(uτν) 10 kxΦuu/u2τ 1 10-1 10-3 1 -5 10 0.5 10-7 -9 10 -3 10 -2 10 10 0 -1 -3 -2 10 10 + 8 6 6 u2 ∫Φuudk/u2τ -1 kx 8 4 2 0 10 + kx 4 2 -3 10 -2 10 10 -1 0 -1 10 0 10 + kx Q. Yang & Y. M. Chung (Warwick) Large structures in spanwise wall oscillation 10 y 1 10 2 + September 22, 2014 20 / 21 Conclusion 2D spectra validation Q. Yang & Y. M. Chung (Warwick) Large structures in spanwise wall oscillation September 22, 2014 20 / 21 Conclusion Spectra size Table: Contribution to C f : spectra filter size test. Cases (1)λx ≥ 3h and λz ≥ 0.5h : Reτ = 800(NC) Reτ = 800(Osci) (2)λx ≥ 3h: Reτ = 800(NC) Reτ = 800(Osci) (3)λz ≥ 0.5h: Reτ = 800(NC) Reτ = 800(Osci) (4)λx ≥ h: Reτ = 800(NC) Reτ = 800(Osci) (5)λz ≥ h: Reτ = 800(NC) Reτ = 800(Osci) Q. Yang & Y. M. Chung (Warwick) laminar turbulence (S) turbulence (L) 7.3% 10.0% (0% ↓) 57.2% 53.8% (30.6% ↓ ) 35.5% 36.2% (25.1% ↓ ) 7.3% 10.0% (0% ↓) 44.0% 43.5% (27.3% ↓ ) 48.7% 46.5% (29.6% ↓ ) 7.3% 10.0% (0% ↓) 38.1% 30.8% (30.8% ↓ ) 54.6% 54.2% (26.9% ↓ ) 7.3% 10.0% (0% ↓) 27.3% 26.1% (28.0% ↓ ) 65.4% 63.3% (28.7% ↓ ) 7.3% 10.0% (0% ↓) 56.6% 53.5% (30.4% ↓ ) 36.1% 36.5% (25.6% ↓ ) Large structures in spanwise wall oscillation September 22, 2014 20 / 21 Conclusion Spectra decomposition Accumulative energy uu for Reτ = 800 and Reτ = 1600. Spectra filter size: λx /h = 3 and λz /h = 0.5 (dash dot lines). 0 100 10 Level∫Φuudk Level∫Φuudk 0.9 0.6 0.3 3 2 1 0.9 0.6 0.3 y 10-1 y 10-1 3 2 1 10-2 10 -2 -3 10 -3 10 -1 0 10 10 10 1 λx /h -1 10 10 0 λz /h Around 30% uu energy is contained in large scales near the wall. More than 50% uu energy is contained in large scales in the outer region. Q. Yang & Y. M. Chung (Warwick) Large structures in spanwise wall oscillation September 22, 2014 20 / 21 Conclusion Spectra decomposed field Q. Yang & Y. M. Chung (Warwick) Large structures in spanwise wall oscillation September 22, 2014 20 / 21 Conclusion Location for Inner/Outer decomposition 1 40 30 0.6 DR C f / C f0 0.8 0.4 Outer Inner Laminar 0.2 0 500 1000 1500 2000 20 Outer Inner Total 10 0 Reτ 500 1000 1500 2000 Reτ Contribution to skin friction, C f from turbulent shear stress in the inner region and outer region. (. . . no control; — T + = 100). Q. Yang & Y. M. Chung (Warwick) Large structures in spanwise wall oscillation September 22, 2014 21 / 21