Journal of Mechanical Science and Technology

The Korean Society of Mechanical Engineers (대한기계학회)
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Elliptic Feature of Coherent Fine Scale Eddies in Turbulent Channel Flows

  • Kang Shin-Jeong (Department of Mechanical and Aerospace Engineering, Tokyo Institute of Technology) ;
  • Tanahashi Mamoru (Department of Mechanical and Aerospace Engineering, Tokyo Institute of Technology) ;
  • Miyauchi Toshio (Department of Mechanical and Aerospace Engineering, Tokyo Institute of Technology)
  • Published : 2006.02.01
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Abstract

Direct numerical simulations (DNS) of turbulent channel flows up to $Re_{\tau}=1270$ are performed to investigate an elliptic feature and strain rate field on cross sections of coherent fine scale eddies (CFSEs) in wall turbulence. From DNS results, the CFSEs are educed and the strain rate field around the eddy is analyzed statistically. The principal strain rates (i.e. eigenvalues of the strain rate tensor) at the CFSE centers are scaled by the Kolmogorov length $\eta$ and velocity $U_k$. The most expected maximum (stretching) and minimum (compressing) eigenvalues at the CFSE centers are independent of the Reynolds number in each $y^+$ region (i. e. near-wall, logarithmic and wake regions). The elliptic feature of the CFSE is observed in the distribution of phase-averaged azimuthal velocity on a plane perpendicular to the rotating axis of the CFSE $(\omega_c)$. Except near the wall, phase-averaged maximum $(\gamma^{\ast}/\gamma_c^{\ast})$ and minimum $(\alpha^{\ast}/\alpha_c^{\ast})$ an eigenvalues show maxima on the major axis around the CFSE and minima on the minor axis near the CFSE center. This results in high energy dissipation rate around the CFSE.

Keywords

References

  1. Ashurst, W. T., Kerstein, A. R., Kerr, R. M. and Gibson, C. H., 1987, 'Alignment of Vorticity and Scalar Gradient with Strain Rate in Simulated Navier-Stokes Turbulence,' Phys. Fluids, Vol. 30, pp. 2343-2353 https://doi.org/10.1063/1.866513
  2. Blackburn, H.M., Mansour, N.N. and Cantwell, B. J., 1996, 'Topology of Fine-scale Motions in Turbulent Channel Flow,' J. Fluid Mech., Vol. 310, pp. 269-292 https://doi.org/10.1017/S0022112096001802
  3. Hunt, J. C. R, Wray, A. A. and Main, P., 1988, 'Eddies, Stream and Convergence Zones in Turbulent Flows,' Center for Turbulence Research Report, CTR-S88, pp. 193
  4. Jimenez, J. and Wray, A. A., 1998, 'On the Characteristics of Vortex Filaments in Isotropic Turbulence,' J. Fluid Mech., Vol. 373, pp. 255-285 https://doi.org/10.1017/S0022112098002341
  5. Jimenez, J., Wray, A. A., Saffman, P. G. and Rogallo, R. S., 1993, 'The structure of Intense Vorticity in Isotropic Turbulence,' J. Fluid Mech., Vol. 255, pp. 65-90 https://doi.org/10.1017/S0022112093002393
  6. Kang, S. -J., Tanahashi, M. and Miyauchi, T., 2004, 'Coherent Fine Scale Eddies and Large-scale Structures in wall Turbulence,' Advances in Turbulence X, pp. 603-606
  7. Kim, J., Moin, P. and Moser, R. D., 1987, 'Turbulence Statistics in Fully Developed Channel Flow at Low Reynolds Number,' J. Fluid Mech., Vol. 1777, pp. 133-166 https://doi.org/10.1017/S0022112087000892
  8. Mansour, N. N., Kim, J. and Moin, P., 1988, 'Reynolds-stress and Dissipation-rate Budgets in a Turbulent Channel Flow,' J. Fluid Mech., Vol. 194, pp. 15-44 https://doi.org/10.1017/S0022112088002885
  9. Miyauchi, T., Tanahashi, M., Takata, N. and Iwase, S., 2002, 'Scalar Dissipation Rate and Coherent Fine Scale Eddies in Turbulence,' Proc. Int Symp. Dynamics and Statistics of Coherent Structures in Turbulence : Roles of Elementary Vortices, Tokyo Japan, pp. 249-258
  10. Miyauchi, T., Kang, S. -J. and Tanahashi, M., 2005, 'Coherent Fine Scale Eddies in the Logarithmic Region of Turbulent Channel Flows,' Proc. IUTAM Symp. Elementary Vortices and Coherent Structures,' Fluid Mechanics and Applications, Kluwer Academic Publishers, in print
  11. Orszag, S. A., 1971, 'Numerical Simulation of Incompressible Flows with Simple Boundaries,' Stud. Appl. Math., Vol. 50, pp. 293-327
  12. Prochazka, A. and Pullin, D. I., 1998, 'Structure and Stability of Non-symmetric Burgers Vortices,' J. Fluid Mech., Vol. 363, pp. 199-228 https://doi.org/10.1017/S0022112098008866
  13. Soria, J., Sondergaard, Cantwell, B. J., Chong, M. S. and Perry, A. E., 1994, 'A Study of the Fine-scale Motions of Incompressible Time-developing Mixing Layers,' Phys. Fluids, Vol. 6, pp. 871-884 https://doi.org/10.1063/1.868323
  14. Tanahashi, M., Miyauchi, T. and Yoshida, T., 1996, 'Characteristics of Small Scale Vortices Related to Turbulent Energy Dissipation,' Proc. 9th International Symposium on Transport Phenomena, Vol. 2, pp. 1256-1261
  15. Tanahashi, M., Miyauchi, T. and Matsuoka, K., 1997, 'Coherent Fine Scale Structure in Temporally Developing Turbulent Mixing Layers,' Proc. 2nd Int. Symp. on Turbulence, Heat and Mass Transfer, Vol. 2, pp. 451-470
  16. Tanahashi, M., Miyauchi, T. and Ikeda, J., 1999, 'Identification of Coherent Fine Scale Structure in Turbulence,' Proc. IUTAM Symp., Fluid Mechanics and Applications, Vol52, Kluwer Academic Publishers, pp. 131-140
  17. Tanahashi, M., Iwase, S. and Miyauchi, T., 2001, 'Appearance and Alignment with Strain Rate of Coherent Fine Scale Eddies in Turbulent Mixing Layer,' J. of Turbulence, 2, No. 6 https://doi.org/10.1088/1468-5248/2/1/006
  18. Tanahashi, M., Tsukamoto, Y., Iwase, S. and Miyauchi, T., 2002a, 'Coherent Fine Scale Eddies and Energy Cascade in Homogeneous Isotropic Turbulence,' 2002a, Proc. Int Symp. Dynamics and Statistics of Coherent Structures in Turbulence : Roles of Elementary Vortices, Tokyo Japan, pp. 259-268
  19. Tanahashi, M., Ootsu, M., Fukushima, M. and Miyauchi, T., 2002b, 'Measurement of Coherent Fine Scale Eddies in Turbulent Mixing Layer by DPIV,' Engineering Turbulence Modeling and Measurements, Vol. 5, pp. 525-534
  20. Tanahashi, M., Kang, S. -J., Miyamoto, T., Shiokawa, S. and Miyauchi, T., 2004, 'Scaling Law of Fine Scale Eddies in Turbulent Channel flows up to $Re_{\tau}=800$,' Int. J. Heat and Fluid Flow, Vol. 25, pp. 331-340 https://doi.org/10.1016/j.ijheatfluidflow.2004.02.016