A new model for granular porous media: Part II. Numerical solution of steady state incompressible Newtonian flow through periodically constricted tubes

Abstract

A numerical method for the solution of the problem of steady state, incompressible Newtonian flow through periodically constricted tubes is developed. All terms of the Navier‐Stokes equation are retained, including the nonlinear inertia terms. Sample calculations for a uniform periodically constricted tube, the geometry of which is connected with the modeling of a packed bed of sand are given, including streamlines, axial and radial velocity profiles, pressure profiles, and the dimensionless pressure drop versus Reynolds number relation. The effect of some geometric characteristics of periodically constricted tubes on their friction factor is investigated numerically, and comparison of some existing experimental data with calculated ones is made.

Deep Bed Filters

“…As before, for small values of C ,typically 50 x 10-6 vol/vol, and for reasonably practical filter °run times (for txample 2Oh) the value of 1r2 becomes very small, of the order of 10-• Consequently, csech ~ 2 becomes very large and the term in brackets approaches 1 There is thus a linear relationship between head loss and time as in the case of the uniform filter.…”

“…Such surface deposits form a discontinuous cake on the face of the filter material 6 tgd give rise to an exponential rise in head loss with time (Ives ,1 ). This can be due to head loss caused by deposits on the inlet surface of the filter material in addition to the deposits within the pores.…”

Flow of dispersed particles through porous media — Deep bed filtration

“…Constricted tube model (Petersen, 1958;Houpeurt, 1959;Payatakes et al, 1973a;Payatakes et al, 1973b;Newman, 1977, 1979;Venkatesan and Rajagopalan, 1980) describes voids of porous media as a collection of pore spaces connected by constrictions such that the basic flow channel through the media is assumed to consist of two half-pores joined by a constriction and aligned along the direction of the main flow (Fig. 4c).…”

A solution birefringence study of polymer elongation in spatially periodic stretching flows

“…Other investigators have employed continuum models to solve for the flow fields in periodic tubes and channels, with the goal to theoretically explain the pressure drop/flow rate relationship of polymeric fluids in porous media [30][31][32]. These workers have typically solved the equations of motion with nonNewtonian constitutive relationships such as that of the well-known Oldroyd Model B fluid [33].…”