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 JAMP  Vol.2 No.6 , May 2014
Dimensional Analysis and Dissipation Rate Estimation in the Near Wake of a Circular Cylinder
Abstract: A particle image velocimetry (PIV) experiment is performed for dissipation rate estimation in the near wake behind a circular cylinder with diameter D of 12 mm and corresponding Reynolds number of 7100. Considering the limitation of PIV resolution, a large eddy PIV method based on idea of large eddy simulation (LES), is used for more accurate estimation of dissipation rate. Based on the dynamic equilibrium assumption in the inertial subrange, the dissipation rate of the subgrid scales is approximated by the subgrid scale (SGS) flux, computed from PIV velocity fields and Smagorinsky model for SGS stress. A dimensional analysis about the integral length scale and the Kolmogorov length scale is discussed firstly to verify whether the dynamic equilibrium assumption holds or not.
Cite this paper: Zhang, X. , Wei Zhong, W. , Yang, J. and Liu, M. (2014) Dimensional Analysis and Dissipation Rate Estimation in the Near Wake of a Circular Cylinder. Journal of Applied Mathematics and Physics, 2, 431-436. doi: 10.4236/jamp.2014.26052.
References

[1]   Saarenrinne, P. and M. Piirto, (2000) Turbulent Kinetic Energy Dissipation Rate Estimation from PIV Velocity Vector Fields. Experiments in Fluids, 29, S300-S307. http://dx.doi.org/10.1007/s003480070032

[2]   Sheng, J., Meng, H. and Fox, R.O. (2000) A Large Eddy PIV Method for Turbulence Dissipation Rate Estimation. Chemical Engineering Science, 55, 4423-4434. http://dx.doi.org/10.1016/S0009-2509(00)00039-7

[3]   Jong, J.D., et al. (2009) Dissipation Rate Estimation from PIV in Zero-Mean Isotropic Turbulence. Experiments in Fluids, 46, 499-515. http://dx.doi.org/10.1007/s00348-008-0576-3

[4]   Aronson, D. and L?fdahl, L. (1993) The Plane Wake of a Cylinder: Measurements and Inferences on Turbulence Modeling. Physics of Fluids A, 5, 1433-1437. http://dx.doi.org/10.1063/1.858579

[5]   Hao, Z., et al. (2008) Approximations to Energy and Temperature Dissipation Rates in the Far Field of a Cylinder Wake. Experimental Thermal and Fluid Science, 32, 791-799. http://dx.doi.org/10.1016/j.expthermflusci.2005.08.008

[6]   Mi, J. and Antonia, R. (2010) Approach to Local Axi-symmetry in a Turbulent Cylinder Wake. Experiments in Fluids, 48, 933-947. http://dx.doi.org/10.1007/s00348-009-0779-2

[7]   Browne, L.W.B., Antonia, R.A. and Shah, D.A. (1987) Turbulent Energy Dissipation in a Wake. Journal of Fluid Mechanics, 179, 307-326. http://dx.doi.org/10.1017/S002211208700154X

[8]   Smagorinsky, J. (1963) General Circulation Experiments with the Primitive Equation I the Basic Experiment. Monthly Weather Review, 91, 99-164. http://dx.doi.org/10.1175/1520-0493(1963)091<0099:GCEWTP>2.3.CO;2

[9]   Ong, L. andWallace, J. (1996) The Velocity Field of the Turbulent Very Near Wake of a Circular Cylinder. Experiments in Fluids, 20, 441-453. http://dx.doi.org/10.1007/BF00189383

[10]   Ma, X., Karamanos, G.S. and Karniadakis, G.E. (2000) Dynamic and Low-Dimensionality of a Turbulent Near Wake. Journal of Fluid Mechanics, 410, 29-65. http://dx.doi.org/10.1017/S0022112099007934

[11]   Zhou, T., et al. (2006) Comparisons between Different Approximations to Energy Dissipation Rate in a Self-Preserving Far Wake. Physical Review E, 74, 056308. http://dx.doi.org/10.1017/S0022112099007934

 
 
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