Void fraction random variations

Dixon and coworkers [25] have performed several CFD simulations of fixed beds with catalyst particles of different geometries (Figure 15.9). The vast number of surfaces and the problems with meshing the void fraction in a packed bed have made it necessary to limit the number of particles and use periodic boundary conditions to obtain a representative flow pattern. Hollow cylinders have a much higher contact area between the fluid and particles at the same pressure drop. However, with a random packing of the particles, there wiU be a large variation... 

In addition to these pressure drop models, models to represent spreading of liquid in packed beds because of spatial variation in flow resistance are needed. In a randomly packed bed, the void fraction is not uniform. This implies that some flow channels formed within a packed bed offer less resistance to flow than other channels of equal cross-sectional area. Liquid will tend to move toward channels of lower resistance, leading to higher liquid hold-up in such channels. Thus, even if the initial liquid distribution is uniform, inherent random spatial variation of the bed leads to non-uniform liquid flow. Yin et al. (2000) assumed that the dispersion coefficient for liquid phase volume fraction is linearly proportional to the adverse gradient of... 

It is often assumed that the void fraction e is constant throughout the bed. However, there will always be a certain wall effect. This is illustrated in figure 4.8. Even in a random packing, the variations in void fraction increase toward the wall. In a layer with a thickness of half the particle diameter, adjacent to the wall, the void fraction is higher than average. 

Figure 4.8. Radial variation of void fraction in randomly packed beds of spheres, as a function of (05 d-r)ld, for did = 20.

Kondelik, P. J., J. Horak and J. Tesarova. Heat and Mass Transfer in Heterogeneous Catalysis. Variations of Local Void Fraction in Randomly Packed Beds of Equilateral Cylinders. Inc. Eng. Chem. Proc. Des. Devel. 7 (1968) 250-252. 

---