부유 입자를 해석하기 위한 운동량 교환/가상영역-격자볼츠만 방법

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전석윤;윤준용;김철규;신명섭
Jeon, Seok Yun;Yoon, Joon Yong;Kim, Chul Kyu;Shin, Myung Seob

  • 투고 : 2015.04.04
  • 심사 : 2015.12.07
  • 발행 : 2016.06.01

초록

본 연구에서는 격자볼츠만 방법을 기반으로 유체-입자 상호작용에 대한 수치계산을 수행하였다. 유체 유동은 격자볼츠만 방법을 이용하였으며, 유동장 내에서의 고체입자 운동은 계산점(node) 기반의 가상영역으로 간주하여 해석하였다. 유체-입자의 상호작용은 격자볼츠만 방법의 지배방정식에 국부적으로 운동량 교환량을 추가하여 해석하며, 가상영역 내에 위치한 고체입자의 병진 및 회전 운동은 뉴턴 운동 방정식과 오일러(Euler) 방정식을 이용한다. 구성된 상호작용 모델의 유효성을 검증하기 위하여 중립상태에서의 부유 입자운동 및 단 입자의 침강에 대한 수치계산을 수행하였으며, 기존 연구들과의 비교를 통하여 본 연구의 유체-입자 상호작용 모델이 갖는 신뢰성과 효용성을 평가하였다.

키워드

격자볼츠만 방법;유체-고체입자 상호작용;운동량 교환 모델;부유입자

참고문헌

  1. Hu, H. H., 1996, "Direct Simulation of Flows of Solid-liquid Mixtures," International Journal of Multiphase Flow, Vol. 22, pp. 335-352. https://doi.org/10.1016/0301-9322(95)00068-2
  2. Peskin, C. S., 1977, "Numerical Analysis of Blood Flow in the Heart," Journal of Computational Physics, Vol. 25, pp. 220-252. https://doi.org/10.1016/0021-9991(77)90100-0
  3. Glowinski, R., Pan, T. W., Hesla, T. I., Joseph, D. and Periaux, J., 2001, "A Fictitious Domain Approach to the Direct Numerical Simulation of Incompressible Viscous Flow Past Moving Rigid Bodies: Application to Particulate Flow," Journal of Computational Physics, Vol. 169, pp. 363-426. https://doi.org/10.1006/jcph.2000.6542
  4. Yu, Z. and Shao, X., 2007, "A Direct-forcing Fictitious Domain Method for Particulate Flows," Journal of Computational Physics, Vol. 227, pp. 292-314. https://doi.org/10.1016/j.jcp.2007.07.027
  5. Fadlun, E. A., Verzicco, R., Orlandi, P. and Mohd-Y., 2000, "Combined Immersed-boundary Finite-difference Methods for Three-dimensional Complex Flow Imulations," Journal of Computational Physics, Vol. 161, pp. 35-60. https://doi.org/10.1006/jcph.2000.6484
  6. Chen, S. and Doolen, G. D., 1998, "Lattice Boltzmann Method for Fluid Flows," Annual Review of Fluid Mechanics, Vol. 30, pp. 329-364. https://doi.org/10.1146/annurev.fluid.30.1.329
  7. Aidun, C. K. and Clausen, J. R., 2010, "Lattice-Boltzmann Method for Complex Flows," Annual Review of Fluid Mechanics, Vol. 42, pp. 439-472. https://doi.org/10.1146/annurev-fluid-121108-145519
  8. Ladd, A. J., 1994, "Numerical Simulations of Particulate Suspensions Via a Discretized Boltzmann Equation: Part 1. Theoretical Foundation," Journal of Fluid Mechanics, Vol. 271, pp. 285-309. https://doi.org/10.1017/S0022112094001771
  9. Ladd, A. J., 1994, "Numerical Simulations of Particulate Suspensions Via a Discretized Boltzmann Equation: Part 2. Numerical Results," Journal of Fluid Mechanics, Vol. 271, pp. 311-339. https://doi.org/10.1017/S0022112094001783
  10. Aidun, C. K., Lu, Y. N. and Ding, E. J., 1998, "Direct Analysis of Particle Suspensions with Inertia Using the Discrete Boltzmann Equation," Journal of Fluid Mechanics, Vol. 373, pp. 287-311. https://doi.org/10.1017/S0022112098002493
  11. Chopard, B. and Marconi, S., 2002, "Lattice Boltzmann Solid Particles in a Lattice Boltzmann Fluid," Journal of Statistical Physics, Vol. 107, pp. 23-37. https://doi.org/10.1023/A:1014542116996
  12. Guo, Z. and Shu, C., 2013, Lattice Boltzmann Method and its Applications in Engineering, World Scientific, Singapore, pp. 66-78.
  13. Joseph, D. D., Lundgren, T. S., Jackson, R. and Saville, D.A., 1990, "Ensemble Averaged and Mixture Theory Equations for Incompressible Fluid-Particle Suspensions," International Journal of Multiphase Flow, Vol. 16, pp. 35-42. https://doi.org/10.1016/0301-9322(90)90035-H
  14. Feng, J., Hu, H. H. and Joseph, D. D., 1994, "Direct Simulation of Initial Value Problems for the Motion of Solid Bodies in a Newtonian Fluid. Part 2. Couette and Poiseuille Flows," Journal of Fluid Mechanics, Vol. 277, pp. 271-301. https://doi.org/10.1017/S0022112094002764
  15. Zou, Q. and He, X., 1997, "On Pressure and Velocity Boundary Conditions for the Lattice Boltzmann BGK Model," Physics of fluids, Vol. 9, pp. 1591-1598. https://doi.org/10.1063/1.869307
  16. Niu, X. D., Shu, D., Chew, Y. T. and Peng, Y., 2006, "A Momentum Exchange-Based Immersed Boundary-Lattice Boltzmann Method for Simulating Incompressible Viscous Flow," Physics Letters A, Vol. 354, pp. 173-182. https://doi.org/10.1016/j.physleta.2006.01.060
  17. Wan, D. and Turek, S., 2006, "Direct Numerical Simulation of Particulate Flow Via Multigrid FEM Techniques and the Fictitious Boundary Method," International Journal for Numerical Methods in Fluids, Vol. 51, pp. 531-566. https://doi.org/10.1002/fld.1129
  18. Nie, D. and Lin, J., 2010, "A LB-DF/FD Method for Particle Suspensions," Communications in Computational Physics, Vol. 7, pp. 544-563.