DOI QR코드

DOI QR Code

테일러 반응기 내의 입자응집과 분해에 관한 수치 연구

Numerical Study of Aggregation and Breakage of Particles in Taylor Reactor

  • 이승훈 (서울대학교 기계항공공학부) ;
  • 전동협 (동국대학교 기계부품시스템공학과)
  • Lee, Seung Hun (School of Mechanical and Aerospace Engineering, Seoul Nat'l Univ.) ;
  • Jeon, Dong Hyup (Dept. of Mechanical System Engineering, Dongguk Univ.)
  • 투고 : 2015.09.15
  • 심사 : 2016.03.08
  • 발행 : 2016.06.01

초록

전산유체역학(CFD)을 이용하여 테일러 반응기 내 입자간 응집과 분해반응을 고려한 유동해석을 수행하였다. 입자크기분포를 파악하기 위하여 모멘트 적분법(QMOM)을 이용하여 집합체 균형방정식(Population Balance Equation)을 계산하였다. 초기 여섯 개의 모멘트를 이용하였으며, 응집커널은 Brownian kernel 과 turbulent kernel의 합을, 그리고 분해커널은 멱법칙 커널(power-law kernel)을 사용하였다. 입자의 초기 부피분율에 따른 최종 입자크기를 예측하였다. 그 결과, 초기 부피분율이 증가할수록 입자의 크기와 초기 성장속도가 증가하는 것을 확인하였다.

Using the computational fluid dynamics (CFD) technique, we simulated the fluid flow in a Taylor reactor considering the aggregation and breakage of particles. We calculated the population balance equation (PBE) to determine the particle-size distribution by implementing the quadrature method-of-moment (QMOM). It was used that six moments for an initial moments, the sum of Brownian kernel and turbulent kernel for aggregation kernel, and power-law kernel for breakage kernel. We predicted the final mean particle size when the particle had various initial volume fraction values. The result showed that the mean particle size and initial growth rate increased as the initial volume fraction of the particle increased.

키워드

참고문헌

  1. Wang, L., Marchisio, D. L., Vigil, R. D. and Fox, R.O., 2005, "CFD Simulation of Aggregation and Breakage Processes in Laminar Taylor-Couette Flow," J. Colloid Interf. Sci., Vol. 282, pp. 380-396. https://doi.org/10.1016/j.jcis.2004.08.127
  2. Kataoka, K., Ohmura, N., Kouzu, M., Simamura, Y. and Okubo, M., 1995, "Emulsion Polymerization of Styrene in a Continuous Taylor Vortex Flow Reactor," Chem. Eng. Sci., Vol. 50, No. 9, pp. 1409-1416. https://doi.org/10.1016/0009-2509(94)00515-S
  3. Dluska, E., Wolinski, J. and Wronski, S., 2005, "Toward Understanding of Two-Phase Eccentric Helical Reactor Performance," Chem. Eng. Technol., Vol. 28, No. 9, pp. 1016-1021. https://doi.org/10.1002/ceat.200500140
  4. Yamada, A., Chung, S. C. and Hinokuma, K., 2001, "Optimized LiFePO4 for Lithium Battery Cathodes," J. Electrochem. Soc., Vol. 148, No. 3, pp. A224-A229. https://doi.org/10.1149/1.1348257
  5. Prosini, P. P., Carewska. M., Wisniewski. P. and Pasquali. M., 2003, "Long-term Cyclability of Nanostructured LiFePO4," Electrochim. Acta., Vol. 48, No. 28, pp. 4205-4211. https://doi.org/10.1016/S0013-4686(03)00606-6
  6. Marchisio, D. L., Soos, M., Sefcik, J., Morbidelli, M., Barresi, A. A. and Baldi, G., 2006, "Effect of Fluid Dynamics on Particle Size Distribution in Particulate Processes," Chem. Eng. Technol., Vol. 29, No. 2, pp. 191-199. https://doi.org/10.1002/ceat.200500358
  7. Nguyen, A. T., Kim, J. M., Chang, S. M. and Kim, W. S., 2010, "Taylor Vortex Effect on Phase Transformation of Guanosine 5-monophosphate in Drowning-out Crystallization," Ind. Eng. Chem. Res., Vol. 49, No. 10, pp. 4865-4872. https://doi.org/10.1021/ie901932t
  8. Smoluchowski, M. V., 1917, "Versuch Einer Mathematischen Theorie der Koagulationskinetik Kolloider Losungen," Zeitschrift f. Physik. Chemie., Vol. 92, pp. 129-142.
  9. Ramkrishna, D. and Mahoney, A. W., 2002, "Population Balance Modeling. Promise for the Future," Chem. Eng. Sci. Vol. 57, pp. 595-606. https://doi.org/10.1016/S0009-2509(01)00386-4
  10. Hulburt, H. M. and Katz, S., 1964, "Some Problems in Particle Technology," Chem. Eng. Sci., Vol. 19, pp. 555-574. https://doi.org/10.1016/0009-2509(64)85047-8
  11. McGraw, R., 1997, "Description of Aerosol Dynamics by the Quadrature Method of Moments," Aerosol Sci. Tech., Vol. 27, pp. 255-265. https://doi.org/10.1080/02786829708965471
  12. Gordon, R. G., 1968, "Error Bounds in Equilibrium Statistical Mechanics," J. Math. Phys., Vol. 9, pp. 655-672. https://doi.org/10.1063/1.1664624
  13. Marchisio, D. L., Vigil, R. D. and Fox, R. O., 2003, "Implementation of the Quadrature Method of Moments in CFD Codes for Aggregation-breakage Problems," Chem. Eng. Sci., Vol. 58, pp. 3337-3351. https://doi.org/10.1016/S0009-2509(03)00211-2
  14. Lemanowicz,a, M., Al-Rashed, M. H., Gierczycki, A. T. and Kocureka, J., 2009, "Application of the QMOM in Research on the Behavior of Solid-liquid Suspensions," Chem. Biochem. Eng. Q., Vol. 23, No. 2, pp. 143-151.
  15. Jerzy, B., Wojciech, O., Łukasz, M., Maciej, M. and Katarzyna, M., 2007, "Break up of Nano-particle Clusters in High-shear Devices," Chem. Eng. Process., Vol. 46, pp. 851-861. https://doi.org/10.1016/j.cep.2007.05.016
  16. Wright, D. L., McGraw, R. and Rosner, D. E., 2002, "Bivariate Extension of the Quadrature Method of Moments for Modeling Simultaneous Coagulation and Sintering of Particle Populations," J. Colloid Interf. Sci., Vol. 236, pp. 242-251.
  17. Jung, W. M., Kang, S. H., Kim, K. S., Kim, W. S. and Choi, C. K., 2010, "Precipitation of Calcium Carbonate Particles by Gas-liquid Reaction: Morphology and Size Distribution of Particles in Couette-Taylor and Stirred Tank Reactors," J. Cryst. Growth, Vol. 312, pp. 3331-3339. https://doi.org/10.1016/j.jcrysgro.2010.08.026
  18. ANSYS, Inc., Fluent 15.0 Theory Manual, 2013.
  19. ANSYS, Inc., Fluent 15.0 Population Balance Module Manual, 2013.
  20. Serra, T., Colomer, J. and Casamitjana, X., 1997, "Aggregation and Breakup of Particles in Shear Flows," J. Colloid Interf.Sci., Vol. 187, pp. 466-473. https://doi.org/10.1006/jcis.1996.4710
  21. Serra, T. and Casamitjana, X., 1998a, "Structure of the Aggregates During the Process of Aggregation and Breakup Under Shear Flow," J. Colloid Interf. Sci., Vol. 206, pp. 505-511. https://doi.org/10.1006/jcis.1998.5714
  22. Serra, T. and Casamitjana, X., 1998b. "Effect of the Shear and Volume Fraction on the Aggregation and Breakup of Particles," A.I.Ch.E. J., Vol. 44, pp. 1724-1730. https://doi.org/10.1002/aic.690440803
  23. Binder, K. and Stauffer, D., 1976, "Statistical Theory of Nucleation, Condensation and Coagulation," Adv. Phys. Vol. 25, No. 4, pp. 343-396. https://doi.org/10.1080/00018737600101402