tailieunhanh - Application of generalized diffusion theory for calculation of particle distribution in suspension flow between two vertically coaxial cylinders

A problem of motion of suspension in t he gap between two rotating vertically coaxial cylinders was established and stationary case of the problem was numerically investigated. A comparison between the numerical prediction of particle concentration and the experimental data of Phillipset al (1992) was made. | Vietnam J ourna l of Mechanics, VAST, Vol. 27, No. 4 (2005) , pp. 213 - 219 APPLICATION OF GENERALIZED DIFFUSION THEORY FOR CALCULATION OF PARTICLE DISTRIBUTION IN SUSPENSION FLOW BETWEEN TWO VERTICALLY COAXIA L CYLINDERS NGUYEN HO NG PH AN Institute of Mechanics Abst ract. Applications of the generalized diffusion t heory for calcul ation of rotating spherical pa rticle distribut ion in a suspension wit h viscouse fluid , using nonlinear closing relationships are demonstrat ed. A problem of motion of suspension in t he gap between two rot ating vertically coaxial cylinders was established and stationa ry case of t he problem was numerica lly investigated . A comparison between t he numerical pred iction of part icle concentrat ion a nd t he experimental dat a of P hillips et al. (1992) was made. 1. GOV ERNING E QUATIONS The flow of viscous fluid carrying rigid spherical rotating particles, t hat have densit ity coincided wit h density of t he fluid , is decribed by the following equation system [1J: V'· U = O; U=epU1+ (l- ep) U2 ; dep - pdt = - \l · J; ] = pep (U1 - U ) ; p = const; dU _ P& = pg - \i'p - V' x . dw ]dt + ]. (] -) _ A . V' w = - A T + -\l . -T S ; - A - T + -V' x \ ( ) A + -V' . -\ S ; A = pep; -D] = -p ep( l - ep) [-F- - 1 - (V'µ1 ) ] , Dt 1 - ep p ,T where U 1 , U 2 , U - mean volume velocit ies of particles (di spersed phase), fluid (liquid phase) and suspension (mixture), respectively; p - common density of part icles and fluid ; ep - volume concentration of p articles; J - generalized diffusion flux of par t icles; w - mean angular velocity of part icles; j - part icle moment of inert ia; n - number of part icle in an unit volume of suspension; µ 1 - generalized chemical potential of part icles; F - generalized diffusion force; p - thermodynamical pressure; 7 A, r 5 - ant isymmetric and symmetric parts 5 of viscous stress t ensor ; >:A, 3: - ant isymmetric and symmetric parts of moment stress t ensor. The nonlinear const