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The role of coherent structures in low-Reynolds-number turbulent wall flows

The role of coherent structures in low-Reynolds-number turbulent wall flows. Genta Kawahara Graduate School of Engineering Science Osaka University. The role of coherent structures in low-Reynolds-number turbulent square duct flow. Genta Kawahara Graduate School of Engineering Science

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The role of coherent structures in low-Reynolds-number turbulent wall flows

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  1. The role of coherent structures in low-Reynolds-number turbulent wall flows Genta Kawahara Graduate School of Engineering Science Osaka University

  2. The role of coherent structures in low-Reynolds-number turbulent square duct flow Genta Kawahara Graduate School of Engineering Science Osaka University M. Uhlmann, A. Pinelli, A. Sekimoto

  3. Role of coherent structures in plane channel Periodic solutions in plane Couette flow(K. & Kida 2001) periodic Regeneration cycle (Jiménez & Moin 1991; Hamilton, Kim & Waleffe 1995) contours u surfaces gentle periodic No regeneration cycle contours u surfaces wx

  4. Role of coherent structures in plane channel Periodic solutions in plane Couette flow(K. & Kida 2001) turbulent turbulent (Moser, Kim & Mansour 1999) periodic gentle periodic laminar Coherent structures ⇒ Prandtl’s wall law (regeneration cycle) (buffer layer)

  5. Other roles of coherent structures Coherent structures in square-duct turbulence Uhlmann, Pinelli, Sekimoto& K.(2007, 2008) Secondary flow of Prandtl's second kind Generation mechanism ・Statistical budget Kajishima, Miyake, Nishimoto （1991） ・Transient growth Biau, Soueid & Bottaro (2008) 1/4 cross-section of square-duct

  6. Coherent structures in square-duct turbulence Uhlmann, Pinelli, Sekimoto& K.(2007, 2008) Near-wall coherent structures ⇒ Secondary flow Reb=Ubh/n > 1100 Ub: bulk mean velocity h: duct half width Reb=1100 Ret=80 Reb=2200 Ret=150

  7. y y h h Velocity and vorticity of mean secondary flow Uhlmann, Pinelli, Sekimoto& K.(2007, 2008) 1/4 cross-section Reb=1100 (Lx=4ph) wx u, v, w z/h z/h

  8. y y h h Velocity and vorticity of mean secondary flow Uhlmann, Pinelli, Sekimoto& K.(2007, 2008) 1/4 cross-section Reb=1500 (Lx=4ph) wx u, v, w z/h z/h

  9. y y h h Velocity and vorticity of mean secondary flow Uhlmann, Pinelli, Sekimoto& K.(2007, 2008) 1/4 cross-section Reb=2200 (Lx=4ph) wx u, v, w z/h z/h

  10. y y h h Velocity and vorticity of mean secondary flow Uhlmann, Pinelli, Sekimoto& K.(2007, 2008) 1/4 cross-section Reb=3500 (Lx=4ph) wx u, v, w z/h z/h

  11. y h Positions of secondary-flow-vortex center Uhlmann, Pinelli, Sekimoto& K.(2007, 2008) 1/4 cross-section maximum point wx of z/h

  12. Positions of secondary-flow-vortex center Uhlmann, Pinelli, Sekimoto& K.(2007, 2008) 1/4 cross-section inner scaling maximum point wx of dy+ dz+ Reb

  13. tw/tw Local wall shear stress Uhlmann, Pinelli, Sekimoto& K.(2007, 2008) local minimum local maximum z+h (z+h)+

  14. Positions of local maximum and minimum Uhlmann, Pinelli, Sekimoto& K.(2007, 2008) inner scaling (z+h)+ local minimum local maximum Reb

  15. Identification of center of streamwise vortices Uhlmann, Pinelli, Sekimoto& K.(2007, 2008) streaks vortices Local maximum point of Laplacian of pressure in cross-streamwise plane Swirl condition Kida & Miura (1998)

  16. y y h h PDF of position of streamwise-vortex center Uhlmann, Pinelli, Sekimoto& K.(2007, 2008) Reb=1500 PDF wx<0 anti-clockwise Secondary flow z/h PDF wx>0 clockwise z/h

  17. y y h h PDF of position of streamwise-vortex center Uhlmann, Pinelli, Sekimoto& K.(2007, 2008) Reb=2200 PDF wx<0 anti-clockwise Secondary flow z/h PDF wx>0 clockwise z/h

  18. twx/tw twx/tw Identification of position of low-velocity streaks Uhlmann, Pinelli, Sekimoto& K.(2007, 2008) Reb=2200 y z x

  19. y h Position and number of low-velocity streaks Uhlmann, Pinelli, Sekimoto& K.(2007, 2008) Position of streaks Reb=1500 wall y/h=1 wall shear stress maximum minimum t+ PDF of vortices z/h

  20. y h Position and number of low-velocity streaks Uhlmann, Pinelli, Sekimoto& K.(2007, 2008) Position of streaks Reb=2200 wall y/h=1 wall shear stress maximum minimum PDF of vortices t+ z/h

  21. Reynolds-number dependence of the roles Uhlmann, Pinelli, Sekimoto& K.(2007, 2008) high Reb Reb=2000

  22. Concluding remarks Roles of near-wallcoherent structures Plane channel 1. Prandtl’s wall law regeneration cycle (periodic solution) 　　⇒ turbulent velocity profile Square duct at low Reynolds number 2. Mean secondary flow constrained streamwise vortices 　　⇒ mean-secondary-flow vortices 3. Wall shear stress constrained low-velocity streaks 　　⇒ local maximum, minimum of wall shear stress

  23. Flow configuration Dimensionless parameters Friction velocity

  24. Direct numerical simulation • Time integration velocity，pressure　→　fractional-step method semi-implicit 3-stage Runge-Kutta method（Verzicco & Orlandi1996） • Spatial discretization pseudo-spectral method streamwise ()： Fourier cross-streamwise ()： Chebyshev

  25. y y h h Positions of secondary-flow-vortex center maximum point （elliptic-type） stagnation point wx of z/h z/h

  26. Positions of secondary-flow-vortex center maximum point （elliptic-type） stagnation point wx of outer scaling inner scaling

  27. Sign selection of coherent vortices trajectories Vortex filament Viscous (Lamb-Oseen) vortex vorticity (red, anti-clockwise; blue, clockwise)

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