DOI QR코드

DOI QR Code

Force Analysis on the Nano/Micro Particle in a Flow using Immersed Boundary-Lattice Boltzmann Method

가상경계-격자 볼츠만 방법을 이용한 유동장내 나노/마이크로 입자에 작용하는 힘의 해석

  • Jo, Hong Ju (Division of Biomedical Engineering, Yonsei University) ;
  • Lee, Sei Young (Division of Biomedical Engineering, Yonsei University)
  • 조홍주 (연세대학교 미래캠퍼스 의공학부) ;
  • 이세영 (연세대학교 미래캠퍼스 의공학부)
  • Received : 2021.11.23
  • Accepted : 2022.02.08
  • Published : 2022.02.28

Abstract

Immersed boundary-Lattice Boltzmann Method (IB-LBM) is used for the analysis of flow over the circular cylinder in the concept of fluid-structure interaction analysis (FSI). Recently, IB-LBM has shown the enormous possibility for the application of various biomedical engineering fields, such as the movement of a human body or the behavior of the blood cells and/or particle-based drug delivery system in blood vessels. In order for the numerical analysis of the interaction between fluid and solid object, immersed boundary method and lattice Boltzmann method are coupled to analyze the flow over a cylinder for low Reynolds laminar flow (Re=10, 20, 40 and 100) with Zhu-He boundary condition at the boundary. With the developed IB-LBM, the flow around the cylinder in the uniform flow is analyzed for the laminar flow and the drag and lift coefficients and recirculation length are compared to the previous results.

Keywords

Acknowledgement

이 논문은 2021년도 정부(교육부)의 재원으로 한국연구재단의 지원을 받은 4단계 BK21 사업(II21SS7606007)과 기본연구(SGER)지원사업(NRF-2016R1D1A1A02937019)의 지원을 받아 수행됨.

References

  1. Kweon J, Choi H. Sectional lift coefficient of a flapping wing in hovering motion. Phys. Fluids 2010;22(7):071703. https://doi.org/10.1063/1.3471593
  2. Farhat C, Van der Zee KG, Geuzaine P. Provably second-order time-accurate loosely-coupled solution algorithms for transient nonlinear computational aeroelasticity. Comput. Methods Appl. Mech. Eng. 2006;195(17-18):1973-2001. https://doi.org/10.1016/j.cma.2004.11.031
  3. Strychalski W, Copos CA, Lewis OL, Guy RD. A poroelastic immersed boundary method with applications to cell biology. J. Comput. Phys. 2015;282:77-97. https://doi.org/10.1016/j.jcp.2014.10.004
  4. Ferrari M. Cancer nanotechnology: opportunities and challenges. Nat. Rev. Cancer. 2005;5(3):161-71. https://doi.org/10.1038/nrc1566
  5. Lee S-Y, Ferrari M, Decuzzi P. Shaping nano-/micro-particles for enhanced vascular interaction in laminar flows. Nanotechnol. 2009;20(49):495101. https://doi.org/10.1088/0957-4484/20/49/495101
  6. Lee T-R, Choi M, Kopacz AM, Yun S-H, Liu WK, Decuzzi P. On the near-wall accumulation of injectable particles in the microcirculation: smaller is not better. Sci. Rep. 2013;3(1):1-8.
  7. Liu H, Kawachi K. A numerical study of undulatory swimming. J. Comput. Phys. 1999;155(2):223-47. https://doi.org/10.1006/jcph.1999.6341
  8. Namkoong K, Choi H, Yoo J. Computation of dynamic fluid-structure interaction in two-dimensional laminar flows using combined formulation. J. Fluids Struct. 2005;20(1):51-69. https://doi.org/10.1016/j.jfluidstructs.2004.06.008
  9. Bavo AM, Rocatello G, Iannaccone F, Degroote J, Vierendeels J, Segers P. Fluid-structure interaction simulation of prosthetic aortic valves: comparison between immersed boundary and arbitrary Lagrangian-Eulerian techniques for the mesh representation. PloS one. 2016;11(4):e0154517. https://doi.org/10.1371/journal.pone.0154517
  10. Peskin CS. The immersed boundary method. Acta numer. 2002;11:479-517. https://doi.org/10.1017/s0962492902000077
  11. Mohd-Yusof J. For simulations of flow in complex geometries. Ann. Res. Briefs 1997;317:35.
  12. Uhlmann M. An immersed boundary method with direct forcing for the simulation of particulate flows. J. Comput. Phys. 2005;209(2):448-76. https://doi.org/10.1016/j.jcp.2005.03.017
  13. Lee S-Y, Ferrari M, Decuzzi P. Design of bio-mimetic particles with enhanced vascular interaction. J. Biomech. 2009;42(12):1885-90. https://doi.org/10.1016/j.jbiomech.2009.05.012
  14. McNamara GR, Zanetti G. Use of the Boltzmann equation to simulate lattice-gas automata. Phys. Rev. Lett. 1988;61(20):2332. https://doi.org/10.1103/PhysRevLett.61.2332
  15. Yu D, Mei R, Luo L-S, Shyy W. Viscous flow computations with the method of lattice Boltzmann equation. Prog. Aerosp. Sci. 2003;39(5):329-67. https://doi.org/10.1016/S0376-0421(03)00003-4
  16. Schmieschek S, Shamardin L, Frijters S, Kruger T, Schiller UD, Harting J, et al. LB3D: A parallel implementation of the Lattice-Boltzmann method for simulation of interacting amphiphilic fluids. Comput. Phys. Commun. 2017;217:149-61. https://doi.org/10.1016/j.cpc.2017.03.013
  17. Feng Z-G, Michaelides EE. The immersed boundary-lattice Boltzmann method for solving fluid-particles interaction problems. J. Comput. Phys. 2004;195(2):602-28. https://doi.org/10.1016/j.jcp.2003.10.013
  18. Niu X, Shu C, Chew Y, Peng Y. A momentum exchange-based immersed boundary-lattice Boltzmann method for simulating incompressible viscous flows. Phys. Lett. A 2006;354(3):173-82. https://doi.org/10.1016/j.physleta.2006.01.060
  19. Dupuis A, Chatelain P, Koumoutsakos P. An immersed boundary-lattice-Boltzmann method for the simulation of the flow past an impulsively started cylinder. J. Comput. Phys. 2008;227(9):4486-98. https://doi.org/10.1016/j.jcp.2008.01.009
  20. Wu J, Shu C. Implicit velocity correction-based immersed boundary-lattice Boltzmann method and its applications. J. Comput. Phys. 2009;228(6):1963-79. https://doi.org/10.1016/j.jcp.2008.11.019
  21. Kang SK, Hassan YA. A comparative study of direct-forcing immersed boundary-lattice Boltzmann methods for stationary complex boundaries. Int. J. Numer. Methods Fluids 2011;66(9):1132-58. https://doi.org/10.1002/fld.2304
  22. Wang Z, Fan J, Luo K. Combined multi-direct forcing and immersed boundary method for simulating flows with moving particles. Int. J. Multiph. Flow 2008;34(3):283-302. https://doi.org/10.1016/j.ijmultiphaseflow.2007.10.004
  23. Champion JA, Katare YK, Mitragotri S. Particle shape: a new design parameter for micro-and nanoscale drug delivery carriers. J. Control. Release 2007;121(1-2):3-9. https://doi.org/10.1016/j.jconrel.2007.03.022
  24. Tasciotti E, Liu X, Bhavane R, Plant K, Leonard AD, Price BK, et al. Mesoporous silicon particles as a multistage delivery system for imaging and therapeutic applications. Nat. Nanotechnol. 2008;3(3):151-7. https://doi.org/10.1038/nnano.2008.34
  25. Zhang Q, Jiang Q, Li N, Dai L, Liu Q, Song L, et al. DNA origami as an in vivo drug delivery vehicle for cancer therapy. ACS nano. 2014;8(7):6633-43. https://doi.org/10.1021/nn502058j
  26. Lee SY, Hyun JY. Analysis of force acting on the non-spherical particle near a wall. Biomed. Eng. Lett. 2015;5(4):289-95. https://doi.org/10.1007/s13534-015-0205-z
  27. Mohamad A. Lattice Boltzmann Method: Springer; 2011.
  28. 조홍주. 가상 경계 격자 볼츠만 방법을 이용한 2차원 원형실린더 주변 유동 분석 및 검증: 연세대학교; 2020.
  29. Bao YB, Meskas J. Lattice Boltzmann method for fluid simulations. Department of Mathematics, Courant Institute of Mathematical Sciences, New York University. 2011;44.
  30. Fang J, Diebold M, Higgins C, Parlange MB. Towards oscillation-free implementation of the immersed boundary method with spectral-like methods. J. Comput. Phys. 2011;230(22):8179-91. https://doi.org/10.1016/j.jcp.2011.07.017
  31. Yang X, Zhang X, Li Z, He G-W. A smoothing technique for discrete delta functions with application to immersed boundary method in moving boundary simulations. J. Comput. Phys. 2009;228(20):7821-36. https://doi.org/10.1016/j.jcp.2009.07.023
  32. Guo Z, Zheng C, Shi B. Discrete lattice effects on the forcing term in the lattice Boltzmann method. Phys. Rev. E 2002;65(4):046308. https://doi.org/10.1103/PhysRevE.65.046308
  33. Zou Q, He X. On pressure and velocity boundary conditions for the lattice Boltzmann BGK model. Phys. Fluids 1997;9(6):1591-8. https://doi.org/10.1063/1.869307
  34. Rohde M, Kandhai D, Derksen J, Van den Akker HE. A generic, mass conservative local grid refinement technique for lattice-Boltzmann schemes. Int. J. Numer. Methods Fluids 2006;51(4):439-68. https://doi.org/10.1002/fld.1140
  35. Cai Y, Li S, Lu J. An improved immersed boundary-lattice Boltzmann method based on force correction technique. Int. J. Numer. Methods Fluids 2018;87(3):109-33. https://doi.org/10.1002/fld.4484
  36. Dennis S, Chang G-Z. Numerical solutions for steady flow past a circular cylinder at Reynolds numbers up to 100. J. Fluid Mech. 1970;42(3):471-89. https://doi.org/10.1017/S0022112070001428
  37. Nieuwstadt F, Keller H. Viscous flow past circular cylinders. Comput Fluids 1973;1(1):59-71. https://doi.org/10.1016/0045-7930(73)90026-1
  38. He X, Doolen G. Lattice Boltzmann method on curvilinear coordinates system: flow around a circular cylinder. J. Comput. Phys. 1997;134(2):306-15. https://doi.org/10.1006/jcph.1997.5709
  39. Pepona M, Favier J. A coupled Immersed Boundary-Lattice Boltzmann method for incompressible flows through moving porous media. J. Comput. Phys. 2016;321:1170-84. https://doi.org/10.1016/j.jcp.2016.06.026
  40. Tritton DJ. Experiments on the flow past a circular cylinder at low Reynolds numbers. J. Fluid Mech. 1959;6(4):547-67. https://doi.org/10.1017/S0022112059000829
  41. Nishioka M, Sato H. Measurements of velocity distributions in the wake of a circular cylinder at low Reynolds numbers. J. Fluid Mech. 1974;65(1):97-112. https://doi.org/10.1017/S0022112074001273
  42. Tao S, He Q, Chen J, Chen B, Yang G, Wu Z. A non-iterative immersed boundary-lattice Boltzmann method with boundary condition enforced for fluid-solid flows. Appl. Math. Model. 2019;76:362-79. https://doi.org/10.1016/j.apm.2019.06.026
  43. Kim DK, Hyun JY, Kim SC, Kim HS, Lee SY. Inertial effects on cylindrical particle migration in linear shear flow near a wall. Microfluid. Nanofluidics 2016;20(5):1-10. https://doi.org/10.1007/s10404-015-1676-z