Core Spreading Vortex Method for Simulating 3D Flows Around Bluff Bodies
DOI:
https://doi.org/10.5614/j.eng.technol.sci.2014.46.4.7Abstract
This paper presents the development of core spreading vortex element method, which is a mesh-free method, for simulating 3D viscous flow over bluff bodies. The developed method simulates external flow around complex geometry by tracking local velocities and vorticities of particles introduced within the fluid domain. The viscous effect is modeled using core spreading method coupled with the splitting spatial adaption scheme, and a smoothing interpolation scheme for overlapping issue and population control, respectively. The particle's velocity is calculated using Biot-Savart formulation. To accelerate computation, Fast Multipole Method (FMM) is employed. The solver is validated, for both unbounded and bounded flows at low Reynolds numbers, using a number of benchmark problems. For unbounded case, simulation of the collision of two vortex rings was performed. To test the performance of the method in simulating bounded flow problem, simulation of flow around a sphere was carried out. The results are found to be in good agreement with those reported in literatures and also simulations using other diffusion model.Downloads
References
Ramussen T.R, A penalization Interface Method for 3D Particle Vortex Methods, Master Thesis, Mechanical Engineering, Technical University of Denmark, 2008.
Li G., M1/4ller U.K., van Leeuwen J.L., Liu H, Body dynamics and hydrodynamics of swimming fish larvae: a computational study, Journal of Experimental Biology,vol.215, pp.4015-4033, 2012.
Mattia G., Chatelain P., Rees W. M., Koumoutsakos P., Simulations of single and multiple swimmers with non-divergence free deforming geometries, Journal of Computational Physics, vol.230, pp.7093-7114, 2011.
Eric D.T., The hydrodynamics of eel swimming II. Effect of swimming speed, Journal of Experimental Biology, vol.207, pp.3265-3279, 2004.
Kajtar J. B., Monaghan P.P., On the swimming of fish like bodies near free and fixed boundaries, European Journal of Mechanics - B/Fluids, vol.33, pp.1-13, 2012.
Barba L.A., Vortex Method for Computing High-Reynolds Number Flows: Increased Accuracy with a Fully Mesh-less Formulation, PhD dissertation, Department of Aeronautical Engineering, California Institute of Technology, California, 2004.
Cottet G.-H. and Poncet P., Advances in direct numerical simulations of 3D wall-bounded ,ows by vortex-in-cell methods, Journal of Computational Physics, vol.193, pp.136-158, 2004.
KamemotoK., On Contribution of Advanced Vortex Element Methods Toward Virtual Reality of Unsteady Vortical Flows in the New Generation of CFD, Brazilian Congress of Thermal Sciences and Engineering,vol.26, pp.368-378, 2005.
PloumhansP.and WinckelmansG.S., Vortex Methods for High-Resolution Simulations of Viscous Flow Past Bluff Bodies of General Geometry, Journal of Computational Physics, vol.165, pp.354-406, 2000.
Greengard C., The core-spreading vortex method approximations the wrong equation, Journal of Computational Physics, Vol.61, pp.345-348, 1985.
Yokota R., Validation of Vortex Methods as a Direct Numerical Simulation of Turbulence, PhD Dissertation, Mechanical Engineering, Keio University, Yokohama, 2009.
Rossi L., Merging computational elements in vortex simulations, SIAM Journal on Scientific Computing, vol.18, pp.1014-1027,1997.
Rossi L., Resurrecting core-spreading vortex methods: a new scheme that is both deterministic and convergent, SIAM Journal on Scientific Computing, vol.17, pp.370-397, 1996.
Huang M. J., Su H. X., Chen L. C., A fast resurrected core-spreading vortex method with no-slip boundary conditions, Journal of Computational Physics, vol.228, pp.1916-1931, 2005.
GreengardL.and RokhlinV., A Fast Algorithm for Particle Simulations, Journal of Computational Physics, vol.73, pp.325-348, 1987.
Chatelain P., Reconnection of Colliding Vortex Rings, Physical Review Letter, Department of Aeronautical Engineering, California Institute of Technology, California, 2003.
Kim. Y. C, Vortex-in-cell method combined with a boundary element method for incompressible viscous flow analysis, International Journal of Numerical Methods in Fluids, vol.69, pp.1567-1583, 2011.
Johnson T. A. and Patel V. C., Flow Past a Sphere Up To Reynolds Number of 300, Journal of Fluid Mechanics, vol.378, pp.19-70, 1999.
Taneda S., Studies on wake vortices (III). Experimental investigation of the wake behind a sphere at low Reynolds "number, Reports of Research Institute of Applied Mechanics, vol.4, pp.99-105, 1956.