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ON diffusion VELOCITY AND THE MASS CONSERVATION EQUATION FOR COMPONENTS

Applied Mathematics and Mechanics(English Edition) 1991年第11期12卷 1075-1082页

作者：刘大有吴邦贤 Multiphase Reaction Laboratory Academia Sinica: Institute of Mechanics Academia Sinica BeijingMultiphase Reaction Laboratory Academia Sinica Institute of Engineering Thermophvsics. Academia Sinica Beijing

The mass migration velocity(absolute velocitv) of component i in a multicomponent flow is equal to the convection velocity (frame velocity) plus the diffusion velocity (relative velocity). The diffusion velocity as well as the corresponding diffusion coefficient depends on how the convection velocity is adopted.In turbulent flow, the mass migration velocity of component i is( muss-weighted time average velocity). The diffusion velocity consists of turbulent diffusion velocity and molecular diffusion velocity is the simple lime average velocity of component i and a is a certain convection velocity). So, the part of turbulent diffusion velocity is independent of what convection velocity is taken.In the mdss conservation equation for component i, the expression for the diffusion term on its right-hand side will change when the convection velocity on its left-hand side changes. In turbulent flow, there could be no diffusion terms, or a turbulent diffusion term only or both the turbulent and molecular diffusion terms when or any velocity other than these two is taken as the convection velocity. The case, in which there could he molecular diffusion only without turbulent diffusion, occurs in laminar flow. The molecular diffusion term always depends on the adoption of convection velocitv.In two-phase flow, the value of the molecular diffusion term is often near or even exceeds that of the turbulent diffusion term, which is quite different from the case in gas mixture flow.

关键词： molecular diffusion turbulent diffusion diffusion and convection diffusion equation

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Modeling and Simulation of Heterogeneous Catalyzed Propylene Polymerization

引用

Chinese Journal of Chemical Engineering 2007年第4期15卷 545-553页

作者：刘兴高 State Key Laboratory of Industrial Control Technology Institute of Industrial Control Department of Control Science and Technology Zhejiang University Hangzhou 310027 China

A novel mathematical model for single particle slurry propylene polymerization rising heterogeneous Ziegler-Natta catalysts has been developed to describe the kinetic behavior, the molecular weight-distribution, the monomer concentration, the degree of polymerization, the polydispersity index （PDI）, etc. This model provides a more valid mathematical description by accounting for the monomer diffusion phenomena at two levels as multigrai model counts, and obtains results that are more applicable to the conditions existing in most polymerizations of industrial interest. Considering that some models on the mesoscale phenomena are so complex that some existingmodeling aspects have to be simplified or even neglected to make the model convenient for use in interesting engineering studies, it is very important to put some effort into determining what sort of numerical analysis works bestfor these problems. For this reason, special *** to these studies to explorean efficient algorithm usingadaptive grid-point spacing in a tlnlte-ditterence technique to tlgure out more practical mass transport models andconvection-diffusion models efficiently. The reasonable outcomes, as well as the significant computation time saving, have been achieved, thereby displaying the advantage of this calculation method.

关键词： modeling and simulation propylene polymerization mass transfer diffusion and convection

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