DOI QR코드

DOI QR Code

Behavior of a Heavy Particle in the Shear Flow Near a Flat Wall

벽 근처 전단 유동 내의 입자의 운동

  • 정재달 (연세대학교 기계공학과) ;
  • 조성기 (연세대학교 기계공학과) ;
  • 이창훈 (연세대학교 기계공학과)
  • Published : 2006.08.01

Abstract

The motion of a small rigid particle in the shear flow near a stationary flat wall is investigated in the context of Stokes flow. The lift force proposed by Saffman and later modified by Mclaughlin and Mei is considered in the prediction of the particle motion far away from the wall. Later, the expression of the lift force is modified to take into account the effect of wall. In the analysis, gravity, lift and drag acting on a small rigid particle near the wall are taken into account. Both analytical and numerical results for the terminal velocities, distances from the wall and trajectories of the particle are presented. In addition, we extended the present analysis to turbulent near-wall flow in the vicinity of the wall.

Keywords

References

  1. Bagchi, P. and Balachandar, S., 2002, 'Effect of Free Rotation on the Motion of a Solid in Linear Shear Flow at Moderate Re,' Physics of Fluid, Vol. 14, No. 8, pp. 2719-2737 https://doi.org/10.1063/1.1487378
  2. Cherukat, P. and Mclaughlin, J.B, 1994, 'The Inertial Lift on a Rigid Sphere in a Linear Shear Flow Field Near a Flat Wall,' J. Fluid Mech. 263, pp. 1-18 https://doi.org/10.1017/S0022112094004015
  3. Cox, R. G. and Brenner, H., 1968, 'The Lateral Migration of Solid Particles in Poiseuille Flow: I. Theory,' Chem. Engng Sci. Vol. 23, p. 147 https://doi.org/10.1016/0009-2509(68)87059-9
  4. Cox, R. G. and Hsu, S. K., 1977, 'The Lateral Migration of Solid Particles in a Laminar Flow Near a Plane,' Int. J. Multiphase Flow, Vol. 3, pp. 201-222 https://doi.org/10.1016/0301-9322(77)90001-5
  5. Dandy, D. S. and Dwyer, H. A., 1990, 'A Sphere Flow at Finite Reynolds Number: Effect of Shear on Particle Lift, Drag, and Heat Transfer,' J. Fluid Mech., Vol. 216, pp. 381-409 https://doi.org/10.1017/S0022112090000477
  6. Gavze, E. and Shapiro, M., 1998, 'Motion of Inerial Spheroidal Particles in a Shear Flow Near Solid Wall with Special Application to Aerosol Transport in Microgravity,' J. Fluid Mech., Vol. 371, pp. 59-79 https://doi.org/10.1017/S0022112098002109
  7. Goldman, A. G., Cox, R. G. and Brenner, H., 1967, 'Slow Viscous Motion of a Sphere Parallel to a Plane Wall,' Chem. Engng Sci., Vol. 22, pp. 637-653 https://doi.org/10.1016/0009-2509(67)80047-2
  8. Happel, J. and Brenner, H., 1973, Low Reynolds Number Hydrodynamics. Martinus Nijhoff
  9. Lataste, J., Huilier, D., Burnage, H. and Bednar, J., 2000, 'On the Shear Lift Force Acting on Heavy Particles in a Turbulent Boundary Layer,' Atmospheric Environment, Vol. 34, pp. 3963-3971 https://doi.org/10.1016/S1352-2310(00)00169-2
  10. Lee, C., Yeo, K. and Choi, J.-I., 2004, 'Intermittent Nature of Acceleration in Near Wall Turbulence,' Phusical Review Letters, Vol. 92, No.144-502 https://doi.org/10.1103/PhysRevLett.92.144502
  11. Marchioli, C. and Soldati, A., 2002, 'Mechanisms for Particle Transfer and Segregation in a Turbulent Boundary Layer,' J. Fluid Mech., Vol. 468, pp. 283-315 https://doi.org/10.1017/S0022112002001738
  12. Maxey, M.R. and Riley, J.J., 1983, 'Equation of Motion for a Small Rigid Sphere in a Nonuniform Flow,' Physics of Fluid, Vol. 26, pp. 1211-1224
  13. Mclauhglin, J.B., 1991, 'Inertial Migration of a Small Sphere in Linear Shear Flows,' J. Fluid Mech., Vol. 224, pp. 262-274 https://doi.org/10.1017/S0022112091001751
  14. Mei, R., 1992, 'An Approximate Expression for the Shear Lift Force in a Spherical Particle at Finite Reynolds Number,' Int. J. Multiphase Flow, Vol. 18, pp. 145-147 https://doi.org/10.1016/0301-9322(92)90012-6
  15. Miyazaki, K., Bedeaux, D. and Bonet Avalos, J., 1995, 'Drag on a Sphere in Slow Shear Flow,' J. Fluid Mech., Vol. 296, pp. 373-390 https://doi.org/10.1017/S0022112095002163
  16. Pozrikidis, C., 1997, Introduction to theoretical and computational fluid dynamics, Oxford University Press
  17. Saffman, P.G., 1965, 'The Lift Force in a Small Sphere in a Slow Shear Flow,' J. Fluid Mech, 22(2), pp. 385-400 https://doi.org/10.1017/S0022112065000824
  18. Wang, Q., Squires, K., Chen, M. and Mclaughlin, J.B., 1997, 'On the Role of the Lift Force in Turbulence Simulation of Particle Deposition,' Int. J. Multiphase Flow, Vol. 23, pp. 749-763 https://doi.org/10.1016/S0301-9322(97)00014-1
  19. Williamson. J. H., 1980, 'Low Storage Runge-kutta Schemes,' J. Comput. Phys. Vol. 35, pp. 48-56 https://doi.org/10.1016/0021-9991(80)90033-9
  20. Ziskind, G., Fichman, M. and Gutfinger, C., 1998, 'Effects of Shear in Particle Motion Near a Surface Application to Resuspension,' J. Aerosol Sci., Vol. 29, pp. 323-338 https://doi.org/10.1016/S0021-8502(97)10009-X

Cited by

  1. Design of Reduced Shear Stress with High-Viscosity Flow Using Characteristics of Thin Film Flow on Solid Surfaces vol.38, pp.12, 2014, https://doi.org/10.3795/KSME-B.2014.38.12.1027