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

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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.

References

[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