Transactions of the Korean Society of Mechanical Engineers B (대한기계학회논문집B)

The Korean Society of Mechanical Engineers (대한기계학회)
권호 표지
DOI QR코드

DOI QR Code

Simulations of the Unsteady Viscous Flow Around an Impulsively Started Cylinder Using Improved Vortex Particle Method

개선된 입자와법을 이용한 급 출발하는 실린더 주위의 비정상 점성 유동 시뮬레이션

  • Published : 2000.05.01
Download PDF
⟨ Previous Next ⟩

Abstract

We solve the integral representation of the Navier-Stokes equations in a lagrangian view by tracking the particles, which have vortex strengths. We simulate the unsteady viscous flow around an impulsively started cylinder using the vortex particle method. Particles are advanced via the Biot-Savart law for a lagrangian evolution of particles. The particle strength is modified based on the scheme of particle strength exchange. The solid boundary satisfies the no-slip boundary condition by the vorticity generation algorithm. We newly modify the diffusion scheme and the boundary condition for simulating an unsteady flow efficiently. To save the computation time, we propose the mixed scheme of particle strength exchange and core expansion. We also use a lot of panels to ignore the curvature of the cylinder, and not to solve the evaluation of the surface density. Results are compared to those from other theoretical and experimental works.

Keywords

References

  1. Bar-Lev, M. and Yang, H, T., 1975, 'Initial Flow Field Over An Impulsively Started Circular Cylinder,' J. of Fluid Mech. Vol. 72, pp. 625-647 https://doi.org/10.1017/S0022112075003199
  2. Beale, J. T. and Majda, A., 1985, 'Higher Order Accurate Vortex Methods with Explicit Velocity Kernels,' J. of Comput. Phys. Vol. 58, pp. 188-208 https://doi.org/10.1016/0021-9991(85)90176-7
  3. Blasius, H. 1908. 'Grenzchichten in Flussigkeiten mit kleiner Reibung,' Z. angew. Math. Phys. Vol. 56, p. 1
  4. Bouard, R. and Contauceau, M., 1980, 'The Early Stage of Development of the Wake Behind an Impulsively Started Cylinder for $40{\le}Re{\le}10^4$,' J. Fluid Mech. Vol. 101, pp. 583-607 https://doi.org/10.1017/S0022112080001814
  5. Chorin, A. J., 1973, 'Numerical Study of Slightly Viscous Flow,' Journal of Fluid Mechanics, Vol. 57, pp. 785-796 https://doi.org/10.1017/S0022112073002016
  6. Christiansen, J. P., 1997, 'Vortex Methods for Flow Simulation,' J. Comput. Phys. Vol. 135, pp. 189-197 https://doi.org/10.1006/jcph.1997.5701
  7. Degond, P. and Mas-Gallic, S., 1989, 'The Weighted Paricie Method for Convection-Diffusion Equations, Part I : The Case of an Isotropic Viscosity, Part II : The Anisotropic Case,' Math. Comput. Vol. 53, pp. 485-526 https://doi.org/10.2307/2008716
  8. Greengard, C., 1985, 'The Core Spreading Vortex Method Approximates the Wrong Equation,' J. Comput. Phys. Vol. 61, pp. 345-348 https://doi.org/10.1016/0021-9991(85)90091-9
  9. Knio, O. M. and Ghoniem, A. F., 1991, 'Three-Dimensional Vortex Simulation of Rollup and Entrainment In A shear Layer,' J. Comput. Phys. Vol. 97, pp. 172-223 https://doi.org/10.1016/0021-9991(91)90044-L
  10. Koumoutsakos, P., Leonard, A., and Pepin, F., 1994, 'Boundary Conditions for Viscous Vortex Methods,' J. Comput. Phys. Vol. 113, pp. 52-61 https://doi.org/10.1006/jcph.1994.1117
  11. Koumoutsakos, P., 1993, 'Direct Numerical Simulations of Unsteady Separated Flows Using Vortex Method,' Ph.D. thesis, Caltech
  12. Leonard, A., 1980. 'Vortex Methods for Flow Simulation,' J. of Comput. Phys. Vol. 37, pp. 289-335 https://doi.org/10.1016/0021-9991(80)90040-6
  13. Lighthill, M. J., 1963, 'Introduction. Boundary Layer Theory,' J. Rosenhead Ed., Oxford Univ. Press, New York, pp. 54-61
  14. Pepin, F., 1990, 'Simulation of the Flow Past an Impulsively Started Cylinder Using a Discrete Vortex Method,' Ph.D. thesis, Caltech
  15. Stickland, J. H., Kempka, S. N., Wolfe, W. P., 1995, 'Viscous Diffusion of Vorticity in Unsteady Wall Layers Using the Diffusion Velocity Concept,' Proceedings of the Forum on Vortex Methods for Engineering Applications, Albuquerque, NM. Feb. pp. 22-24
  16. Ta Phuoc Loc and Bouard, R., 1985, 'Numerical Solution of the Early Stage of the Unsteady Viscous Flow Around a Circular Cylinder: a Comparison with Experimental Visualization and Measurement,' J. of Fluid Mech., Vol. 160, pp. 93-117 https://doi.org/10.1017/S0022112085003408