Dimensional and Mechanical Similarity Analysis of the Flow in Rotating Liquid Film Reactor

Affiliation(s)

Department of Mathematics, Beijing University of Chemical Technology, Beijing, China.

Department of Mathematics, Beijing University of Chemical Technology, Beijing, China.

ABSTRACT

A rotating liquid film reactor (RLFR) is a device of two coaxial rotating conical cylinders with the inner cone rotating and the outer one stationary. A complete mathematical model for the flow between the conical cylinders is built and a dimensional analysis is carried out. It is proved that at each point of the flow field the dimensionless pressure and velocity of the flow are determined by parameters: Reynolds number (*Re*), aspect ratio (Γ), radius ratio (*η*) and wall inclination angle (*α*). Furthermore, a sufficient and a necessary condition are derived from mechanical similarity between RLFR and a manufacturing equipment geometrically similar to RLFR. Finally, a numerical simulation for the distribution of pressure and velocity is performed. The results may provide a theoretical basis for experiment method and numerical simulation of the flow in a RLFR-like device.

Cite this paper

X. Li, L. Xu, J. Zhang and W. Lan, "Dimensional and Mechanical Similarity Analysis of the Flow in Rotating Liquid Film Reactor,"*Open Journal of Fluid Dynamics*, Vol. 3 No. 2, 2013, pp. 33-37. doi: 10.4236/ojfd.2013.32004.

X. Li, L. Xu, J. Zhang and W. Lan, "Dimensional and Mechanical Similarity Analysis of the Flow in Rotating Liquid Film Reactor,"

References

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[6] M. N. Noui-Mehidi, N. Ohmura, K. Nishiyama and K. Takigawa, “Effect of Wall Alignment in a Very Short Rotating Annulus,” Communications in Nonlinear Science and Numerical Simulation, Vol. 14, No. 2, 2009, pp. 613-621. doi:10.1016/j.cnsns.2007.10.004

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[8] X. F. Xu and L. X. Xu, “A Numerical Simulation of Flow between Two Rotating Coaxial Frustum Cones,” Communications in Nonlinear Science and Numerical Simulation, Vol. 14, No. 6, 2009, pp. 2670-2676. doi:10.1016/j.cnsns.2008.08.019

[9] X. F. Xu, P. Wen, L. X. Xu and D. P. Cao, “Occurrence of Taylor Vortices in the Flow between Two Rotating Conical Cylinders,” Communications in Nonlinear Science and Numerical Simulation, Vol. 15, No. 5, 2010, pp. 1228-1239. doi:10.1016/j.cnsns.2009.05.061

[10] Q. S. Li, P. Wen and L. X. Xu, “Transition to Taylor Vortex Flow between Rotating Conical Cylinders,” Journal of Hydrodynamics, Vol. 22, No. 2, 2010, pp. 241- 245. doi:10.1016/S1001-6058(09)60050-0

[1] G. I. Taylor, “Stability of a Viscous Liquid Contained between Two Rotating Cylinders,” Philosophical Transactions Royal Society of London, Vol. 223, No. 605-615, 1923, pp. 289-343. doi:10.1098/rsta.1923.0008

[2] S. Dong, “Direct Numerical Simulation of Turbulent Taylor-Couette Flow,” Journal of Fluid Mechanics, Vol. 587, 2007, pp. 373-393. doi:10.1017/S0022112007007367

[3] S. C. Guo, D. G. Evans, D. Q. Li and X. Duan, “Experimental and Numerical Investigation of the Precipitation of Barium Salfate in a Rotating Liquid Film Reactor,” AIChE Journal, Vol. 55, No. 8, 2009, pp. 2024-2034. doi:10.1002/aic.11818

[4] M. Wimmer, “An Experimental Investigation of Taylor Vortex Flow between Conical Cylinders,” Journal of Fluid Mechanics, Vol. 292, 1995, pp. 205-227. doi:10.1017/S0022112095001492

[5] M. Wimmer, “Taylor Vortices at Different Geometries,” Physics of Rotating Fluids, Vol. 549, 2000, pp. 194-212. doi:10.1007/3-540-45549-3_12

[6] M. N. Noui-Mehidi, N. Ohmura, K. Nishiyama and K. Takigawa, “Effect of Wall Alignment in a Very Short Rotating Annulus,” Communications in Nonlinear Science and Numerical Simulation, Vol. 14, No. 2, 2009, pp. 613-621. doi:10.1016/j.cnsns.2007.10.004

[7] M. N. Noui-Mehidi, N. Ohmura and K. Kataoka, “Dynamics of the Helical Flow between Rotating Conical Cylinders,” Journal of Fluids and Structures, Vol. 20, No. 3, 2005, pp. 331-344. doi:10.1016/j.jfluidstructs.2004.12.001

[8] X. F. Xu and L. X. Xu, “A Numerical Simulation of Flow between Two Rotating Coaxial Frustum Cones,” Communications in Nonlinear Science and Numerical Simulation, Vol. 14, No. 6, 2009, pp. 2670-2676. doi:10.1016/j.cnsns.2008.08.019

[9] X. F. Xu, P. Wen, L. X. Xu and D. P. Cao, “Occurrence of Taylor Vortices in the Flow between Two Rotating Conical Cylinders,” Communications in Nonlinear Science and Numerical Simulation, Vol. 15, No. 5, 2010, pp. 1228-1239. doi:10.1016/j.cnsns.2009.05.061

[10] Q. S. Li, P. Wen and L. X. Xu, “Transition to Taylor Vortex Flow between Rotating Conical Cylinders,” Journal of Hydrodynamics, Vol. 22, No. 2, 2010, pp. 241- 245. doi:10.1016/S1001-6058(09)60050-0