Journal of Mechanical Science and Technology

The Korean Society of Mechanical Engineers (대한기계학회)
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Analysis of Hagen-Poiseuille Flow Using SPH

  • Min, Oakkey (Division of Electrical and Mechanical Engineering, Yonsei University) ;
  • Moon, Wonjoo (Research Team of Design for Structural Integrity, Division of Electrical and Mechanical Engineering, Yonsei University) ;
  • You, Sukbeom (Product Design Team, Samsung SDI Co., Ltd.)
  • Published : 2002.03.01
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Abstract

This paper shows how to formulate the transient analysis of 2-dimensional Hagen-Poiseuille flow using smoothed particle hydrodynamics (SPH). Treatments of viscosity, particle approximation and boundary conditions are explained. Numerical tests are calculated to examine effects caused by the number of particles, the number of particles per smoothing length, artificial viscosity and time increments for 2-dimensional Hagen-Poiseuille flow. Artificial viscosity for reducing the numerical instability directly affects the velocity of the flow, though effects of the other parameters do not produce as much effect as artificial viscosity. Numerical solutions using SPH show close agreement with the exact ones for the model flow, but SPH parameter must be chosen carefully Numerical solutions indicate that SPH is also an effective method for the analysis of 2-dimensional Hagen-Poiseuille flow.

Keywords

References

  1. Bonet, J. and Kulasegram, S., 2000, 'Correction and Stabilization of Smooth Particle Hydrodynamics Methods with Applications in Metal Forming Simulations,' Int. J. Numer. Meth. Engng., Vol. 47, pp. 1189-1214 https://doi.org/10.1002/(SICI)1097-0207(20000228)47:6<1189::AID-NME830>3.0.CO;2-I
  2. Libersky, L. D., Petschek, A. G., Carney, T. C., Hipp, J. R. and Allahdadi, F. A., 1993, 'High Strain Lagrangian Hydrodynamics: A Three-Dimensional Response,' J. Comput. Phys., Vol. 109, pp. 67-75 https://doi.org/10.1006/jcph.1993.1199
  3. Lucy, L. B., 1997, 'A Numerical Approach to the Testing of the Fission Hypothesis,' Astron. J., Vol. 82, pp. 1013-1020 https://doi.org/10.1086/112164
  4. Min, O., Lee, J., Kim, K., Park, H., 1996, 'An Application of Smoothed Particle Hydrodynamics in Analysis of Dynamic Elasto-Plastic Deformation,' Proc. of 2nd ISIE '96, pp. 392-397
  5. Min, O., Lee, J., Kim, K. and Lee, S., 2000, 'A Contact Algorithm in the Low Velocity Impact Simulation with SPH,' KSME Int. J., Vol. 114, pp. 705-714
  6. Monaghan, J. J. and Gingold, R. A., 1983, 'Shock Simulation by the Particla method SPH,' J. Comput. Phys., Vol. 52, pp. 374-389 https://doi.org/10.1016/0021-9991(83)90036-0
  7. Monaghan, J. J. and Kocharyan, A., 1994, 'SPH simulation of multi-phase flow,' J. Comput. Phys., Vol. 87, pp. 225-235 https://doi.org/10.1016/0010-4655(94)00174-Z
  8. Morris, J. P., Fox, P. J. and Yi, Z., 1997, 'Modeling Low Reynolds Number Incompressible Flow Using SPH,' J. Comput. Phys., Vol. 136, pp. 214-226 https://doi.org/10.1006/jcph.1997.5776
  9. Morris, J. P., 2000, 'Simulating Surface Tension with Smoothed Particle Hydrodynamics,' Int. J. Numer. Meth. Fluids., Vol. 33, pp. 333-353 https://doi.org/10.1002/1097-0363(20000615)33:3<333::AID-FLD11>3.0.CO;2-7
  10. Petschek, A. G. and Libersky, L. D., 1993, 'Cylindrical Smoothed Particle Hydrodynamics,' J. Comput. Phys., Vol. 109, pp. 76-83 https://doi.org/10.1006/jcph.1993.1200
  11. Randles, P. W. and Libersky, L. D., 1996, 'Smoothed Particle Hydrodynamics: Some Recent Improvements and Applications,' Comput. Methods Appl. Mech. Engrg., Vol. 139, pp. 375-408 https://doi.org/10.1016/S0045-7825(96)01090-0
  12. Takeda, H., Miyama, S. M. and Sekiya, M., 1994, 'Numerical Simulation of Viscous Flow By Smoothed Particle Hydrodynamics,' Prog. Theor. Phys., Vol. 92, pp. 939-960 https://doi.org/10.1143/PTP.92.939