High-Precision Numerical Scheme for Vortical Flow

Kei Ito, Tomoaki Kunugi, Hiroyuki Ohshima

Advanced Nuclear System Research and Development Directorate, Japan Atomic Energy Agency, Ibaraki, Japan.
Department of Nuclear Engineering, Kyoto University, Kyoto, Japan.
dvanced Nuclear System Research and Development Directorate, Japan Atomic Energy Agency, Ibaraki, Japan.

DOI: 10.4236/am.2013.410A1004                

Abstract

In this study, a new high-precision numerical simulation scheme for vortical flows (vortex-based scheme) is proposed. This scheme identifies a vortical flow in each computational cell, and then, reconstructs a vortical velocity distribution based on the Burgers vortex model. In addition, a pressure distribution in the vicinity of the vortex center is also reconstructed. The momentum transfer is calculated with the reconstructed velocity and pressure distributions, and therefore, the vortex-based scheme can simulate vortical flows more accurately than the conventional schemes. In fact, as the simulation result of inviscid vortex attenuation problem, the vortex-based scheme shows lower simulation error compared to the conventional discretization schemes. Moreover, also in the numerical simulation of the quasi-steady vortical flow, the simulation accuracy of the vortex-based scheme is superior to those of the conventional schemes.

Keywords

Computational Fluid Dynamics; Numerical Scheme; Vortex Cavitation; Burgers Vortex Theory

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	K. Aoto, N. Uto, Y. Sakamoto, T. Ito, M. Toda and S. Kotake, “Design Study and R&D Progress on Japan SodiumCooled Fast Reactor,” Journal of Nuclear Science and Technology, Vol. 48, No. 4, 2011, pp. 463-471. http://dx.doi.org/10.1080/18811248.2011.9711720
[2]	T. Ezure, N. Kimura, A. Tobita and H. Kamide, “Influences of Fluid Viscosity on the Occurrences of Cavitation Due to Sub-Surface Vortex,” Proceedings of the Seventh Korea-Japan Symposium on Nuclear Thermal Hydraulics and Safety, Chuncheon, 14-17 November 2010, N7P0072.
[3]	T. Ezure, K. Ito, T. Onojima, N. Kimura and H. Kamide, “Fundamental Behavior of Vortex Cavitation in a 1/22 Scaled Upper Plenum Model of Sodium Cooled Fast Reactor,” Proceedings of the Eighth Korea-Japan Symposium on Nuclear Thermal Hydraulics and Safety, Beppu, 9-12 December 2012, N8P1068.
[4]	K. Ito, T. Kunugi, H. Ohshima and T. Kawamura, “Formulations and Validations of a High-Precision Volume-ofFluid Algorithm on Non-Orthogonal Meshes for Numerical Simulations of Gas Entrainment Phenomena,” Journal of Nuclear Science and Technology, Vol. 46, No. 4, 2009, pp. 366-373. http://dx.doi.org/10.1080/18811248.2007.9711542
[5]	K. Ito, T. Kunugi and H. Ohshima, “High-Precision Reconstruction of Gas-Liquid Interface in PLIC-VOF Framework on Unstructured Mesh,” In: A. Kuzumin, Ed., Computational Fluid Dynamics 2010, Springer, Berlin, 2011, pp. 563-567. http://dx.doi.org/10.1007/978-3-642-17884-9_71
[6]	K. Ito, T. Kunugi and H. Ohshima, “A High-Precision Unstructured Adaptive Mesh Technique for Gas-Liquid Two-Phase Flows,” International Journal for Numerical Methods in Fluids, Vol. 67, No. 11, 2011, pp. 1571-1589. http://dx.doi.org/10.1002/fld.2432
[7]	T. Kawamura, H. Takami and K. Kuwahara, “Computation of High Reynolds Number Flow around a Circular Cylinder with Surface Roughness,” Fluid Dynamics Research, Vol. 1, No. 2, 1986, pp. 145-162. http://dx.doi.org/10.1016/0169-5983(86)90014-6
[8]	J. M. Burgers, “A Mathematical Model Illustrating the Theory of Turbulence,” In: R. Mises and T. Karman, Eds., Advance in Applied Mechanics, Academic Press ING., New York, 1982, pp. 171-199.
[9]	K. Sawada, “A Convenient Visualization Method for Identifying Vortex Center,” Transaction of the Japan Society for Aeronautical and Space Sciences, Vol. 38, No. 120, 1995, pp. 102-116.
[10]	D. Sujudi and R. Haimes, “Identification of Swirling Flow in 3-D Vector Fields,” Technical Report AIAA-95-1715, American Institute of Aeronautics and Astronautics, 1995.
[11]	D. Kim and H. Choi, “A Second-Order Time-Accurate Finite Volume Method for Unsteady Incompressible Flow on Hybrid Unstructured Grids,” Journal of Computational Physics, Vol. 162, No. 2, 2000, pp. 411-428. http://dx.doi.org/10.1006/jcph.2000.6546
[12]	T. J. Barth and D. C. Jespersen, “The Design and Application of Upwind Schemes on Unstructured Meshes,” Technical Report AIAA-89-0366, AIAA 27th Aerospace Sciences Meeting, Reno, 9-12 January 1989.
[13]	S. Moriya, “Estimation of Hydraulic Characteristics of Free Surface Vortices on the Basis on Extension Vortex Theory and Fine Model Test Measurements,” Technical Reports of Central Research Institute of Electric Power Industry U97072, 1998.