Direct numerical simulation of turbulent flow around an impulsively started circular cylinder by using mesh-free vortex method

International Journal of Mechanical Engineering
© 2015 by SSRG - IJME Journal
Volume 2 Issue 11
Year of Publication : 2015
Authors : Amirreza Mohammadian, Suresh Akella, A.M.K Prasad
How to Cite?

Amirreza Mohammadian, Suresh Akella, A.M.K Prasad, "Direct numerical simulation of turbulent flow around an impulsively started circular cylinder by using mesh-free vortex method," SSRG International Journal of Mechanical Engineering, vol. 2,  no. 11, pp. 13-18, 2015. Crossref,


Direct numerical simulation of turbulent flow, wake flow, using the random vortex method involving vortex blobs is presented and implemented in this paper. The method is used to perform highresolution simulations of incompressible twodimensional, Navier-Stokes fluid flows. In the random vortex method, vorticity of the flow field is the primary variable. After generation on the cylinder wall, it is followed in two separate fractional time step in a Lagrangian approach, namely convection and diffusion. In this paper, the developed random vortex method applied to the flow past one impulsively started circular cylinder. the flow simulations are carried out in the high Reynolds number Re=140000. Instantaneous velocity vector field and Instantaneous velocity and position of each vortex element in the flow at same time are plotted. The code has been validated by using experimental data to demonstrate accuracy of produced solution without the effects of grid-based numerical diffusion.


Turbulence, Vortex, Random vortex, mesh-free, Vorticity.


[1] Anderson, C. and Greengard C. (1985), On vortex methods, SIAM J. Numer. Anal., 22,413-440.
[2] Beale, J.T. and Majda, A. (1982), Vortex methods. I: Convergence in three dimensions, Math.Comp., 39, 1-27.
[3] Bouard. R and Coutanceau. M (1980), The early stage of development of the wake behind an impulsively started cylinder for 40 < Re < 104. J . Fluid Mech. 101, 583.
[4] Cantwell, B. J. and Coles, D. (1979), A flying hot wire study of the turbulent near wake of a circular cylinder at Re=140000. , PH.D. Thesis, California institute of technology.
[5] Chorin, A.J. (1973), Numerical study of slightly viscous flow, J. Fluid Mech., 57, 785-796.
[6] Cottet, G.H. and Mas-Gallic, S. (1990), A particle method to solve the Navier-Stokes system, Numerische Mathematik, 57, 805-827.
[7] Dutta .P. K. (1980), Computational and Theoretical Fluid Dynamics Division National Aerospace Laboratories, Bangalore 560 017, INDIA
[8] Fogelson, A. L. and R. H. Dillon (1993), Optimal smoothing in function-transport particle methods for diffusion equations, J. Comput. Phys, 109, 155-163.
[9] Goodman, J. (1987), Convergence of the random vortex method, Comm. Pure Appl. Math.40, 189-220.
[10] Hald, O.H. (1987), Convergence of vortex methods for Euler equations. III, SIAM J. Numer. Anal., 24, 538-582.
[11] Kida, t and Kimura, k. (1997), Transient flow around an impulsively started two-dimensional circular cylinder by deterministic vortex methods, Department of Energy Systems Engineering, Osaka Prefecture University, Gakuen-cho, Sakai 599-8530, JAPAN
[12] Leonard . A. (1980), Vortex methods for flow simulation, J. Comput. Phys. 37, 289-335.
[13] Long, D-G. (1988), Convergence of the random vortex method in two dimensions, JAMS, 1,779-804.
[14] Lorena A. Barba (2004), Vortex Method for computing high- Reynolds number flows: Increased accuracy with a fully mesh-less formulation, Doctor of philosophy thesis, California Institute of Technology, Pasadena, California
[15] Mortazavi, I., P. Micheau, and A. Giovannini (1996), Numerical convergence of the random vortex methods for complex flows. In Vortex flows and related numerical methods II, Proceedings of the second international workshop on vortex flows and related numerical methods, volume 1. European Series in Applied and Industrial Mathematics (ESAIM), Montreal, Canada.
[16] Puckett, E. G. (1989) . A study of the vortex sheet method and its rate of convergence. SIAM Journal on Scientific and Statistical Computing, 10, 298-327.
[17] Roberts, S. (1985), Accuracy of the random vortex method for a problem with non -smooth initial conditions, J. Comput. Phys, 58, 29-43.
[18] Sarpkaya (1989), Computational methods with vortices - The 1988 Freeman scholar lecture, J. Fluid Engr., 115, 5-52.