The Effect of Near-Wall Vortices on Wall Shear Stress in Turbulent Boundary Layers

Abstract

The objective of the present study is to explore the relation between the near-wall vortices and the shear stress on the wall in two-dimensional channel flows. A direct numerical simulation of an incompressible two-dimensional turbulent channel flow is performed with spectral method and the results are used to examine the relation between wall shear stress and near-wall vortices. The two-point correlation results indicate that the wall shear stress is associated with the vortices near the wall and the maximum correlation-value location of the near-wall vortices is obtained. The analysis of the instantaneous diagrams of fluctuation velocity vectors provides a further expression for the above conclusions. The results of this research provide a useful supplement for the control of turbulent boundary layers.

The objective of the present study is to explore the relation between the near-wall vortices and the shear stress on the wall in two-dimensional channel flows. A direct numerical simulation of an incompressible two-dimensional turbulent channel flow is performed with spectral method and the results are used to examine the relation between wall shear stress and near-wall vortices. The two-point correlation results indicate that the wall shear stress is associated with the vortices near the wall and the maximum correlation-value location of the near-wall vortices is obtained. The analysis of the instantaneous diagrams of fluctuation velocity vectors provides a further expression for the above conclusions. The results of this research provide a useful supplement for the control of turbulent boundary layers.

Cite this paper

nullS. Guo and W. Li, "The Effect of Near-Wall Vortices on Wall Shear Stress in Turbulent Boundary Layers,"*Engineering*, Vol. 2 No. 3, 2010, pp. 190-196. doi: 10.4236/eng.2010.23027.

nullS. Guo and W. Li, "The Effect of Near-Wall Vortices on Wall Shear Stress in Turbulent Boundary Layers,"

References

[1] J. Shen, E. Malkiel and J. Katz, “Using digital holographic microscopy for simultaneous measurement of 3D near wall velocity and wall shear stress in a turbulent boundary layer,” Experiment in Fluids, Vol. 45, No. 6, pp. 1023-1035, 2008.

[2]
G. Arthur, Kravchenko, H. Choi and P. Moin, “On the relation of near-wall streamwise vortices to wall skin friction in turbulent boundary layers,” Physics of Fluid A, Vol. 5, No. 12, pp. 3307-3309, 1993.

[3]
E. P. Hammond, T. R. Bewley and P. Moin, “Observed mechanisms for turbulence attenuation and enhancement in opposition-controlled wall-bounded flows,” Physics of Fluid, Vol. 10, No. 9, pp. 2421-2423, 1998.

[4]
Y. Chang, S. S. Collis and S. Ramakrishnan, “Viscous effects in control of near-wall turbulence,” Physics of Fluid, Vol. 4, No. 11, pp. 4069-4080, 2002.

[5]
J. Kim, “Control of turbulent boundary layers,” Physics of Fluid, Vol. 15, No. 5, pp. 1093-1105, 2003.

[6]
J.-I. Choi, C. X. Xu and H. J. Sung, “Drag reduction by spanwise wall oscillation in wall-bounded turbulent flows,” AIAA Journal, Vol. 40, No. 5, pp. 842-850, 2002.

[7]
K. Kim and H. J. Sung, “DNS of turbulent boundary layer with time-periodic blowing through a spanwise slot,” The 5th Aslan computational fluid dynamics conference, Busan, Korea, 30 June-3 July, pp. 1471-1478, 2003.

[8]
K.-S. Choi, “Near-wall structure of turbulent boundary layer with spanwise oscillation,” Physics of Fluid, Vol. 14, No. 7, pp. 2530-2542, 2002.

[9]
Y. S. Park, S. H. Park and H. J. Sung, “Measurement of local forcing on a turbulent boundary layer using PIV,” Experiments in Fluids, Vol. 34, pp. 697-707, 2004.

[10]
S. Chen, G. Eyink and R. E. Ecke, “Physical mechanism of the two-dimensional enstrophy cascade,” Physical Review Letters, Vol. 91, pp. 24501, 2003.

[11]
W. Kramer, H. J. H. Clercx and G. J. F. van Heijst, “On the large-scale structure and spetral dynamics of two- dimensional turbulence in a periodic channel,” Physics of Fluids, Vol. 20, pp. 1-15, 2008.

[12]
J. Jimenez, “Transition to turbulence in two-dimensional Poiseuille flow,” Journal of Fluid Mechanics, Vol. 218, pp. 265-297, 1990.

[13]
X. L. Li, Y. W. Ma and D. X. Fu, “High efficient method for incompressiable N-S equations and analysis of two- dimensional turbulent channel flow,” Acta Mechanica Sinica, Vol. 33, No. 5, pp. 576-586 (in Chinese), 2001.

[14]
J. Kim, P. Moin and R. Moser, “Turbulence statistics in fully developed channel flow at low Reynolds number,” Journal of Fluid Mechanics, Vol. 177, pp. 133-166, 1987.

[15]
L. Kleiser and U. Schumann, “Treatment of incompressibility and boundary layer conditions in 3D numerical spectral simulation of plane channel flows,” E. H. Hirschel, Ed., Proceedings of the 3rd GAMM Conference on Numerical Method in Fluid Mechanics, Brunswick, Germany, pp. 165-173, 1980.

[16]
Z. W. Hu, C. L. Morfey and N. D. Sandham, “Wall pressure and shear stress spectra from direct simulations of channel flow,” AIAA Journal, Vol. 44, No. 7, pp. 1541- 1549, 2006.