CFD-based analysis of the wall effect on the pressure drop in packed beds
Systematic methods and tools for managing the complexity
Tools Integration - CAPE Methods & Tools (T4-10)
Keywords: CFD, pressure drop, wall effect, ballistic deposition method, periodic boundary conditions
Pressure drop is of crucial importance for the design and operation of packed bed reactors. There are several works, both experimental and numerical, approaching a correct description of the pressure drop in packed beds. However, the available information regarding the wall effect on pressure drop is contradictory [1]. On the one hand, a wall introduces an additional pressure drop, just because of the wall friction. On the other hand, the pressure drop is reduced due to additional inhomogeneities close to the wall (channelling effect).
The wall effect on the pressure drop was experimentally investigated in [1] and different correlations were examined in which this effect is taken into account. An improved correlation was suggested based on experimental data. Numerical simulations of the flow with low tube-to-particle diameter ratio are useful for the better understanding of the phenomena caused by the wall presence.
In the present work, a commercial CFD tool CFX 10.0 by ANSYS Inc. is used to simulate the single-phase incompressible flow through fixed beds of spheres in arranged and random configurations. The arranged configurations follow the atomic face-centered cubic (FCC) structure in ideal crystals. To construct the random configuration (packing) containing non-overlapping spherical particles, a ballistic deposition method is employed [2]. This method is modified using the Monte Carlo technique leading to results similar to those of most rigorous ballistic deposition algorithms, while requiring significantly less computational time and programming work complexity [3].
The tube-to-particle diameter ratio for the constructed geometries lies between 1 and 10. For this range of ratios, the wall effect on the pressure drop is significant. To simulate the fully developed flow neglecting inlet effects, periodic boundary conditions are imposed along the main flow direction. The use of periodic boundary conditions reduces the necessary computational domain length resulting in a substantial reduction of the required computer power and calculation time.
The hydrodynamic behaviour of the considered packings for different Reynolds numbers is analysed. The pressure drop is calculated and verified against the most common correlations, namely the Ergun, the Carman, the Zhavoronkov and the Reichelt correlation (see [1]). In the last two correlations, the presence of the wall is taken into account for the calculation of the pressure drop.
Furthermore, the channelling effect on the pressure drop is studied. Because of the higher void fraction near the wall in the arranged FCC configurations, stronger channelling is observed as compared to random configurations for the same tube-to-particle diameter ratio. This results in a higher pressure drop for the random configurations which is in accordance with the Zhavoronkov and the Reichelt correlations.
References
[1] Eisfeld, B., Schnitzlein K., 2001. The influence of confining walls on the pressure drop in packed beds. Chemical Engineering Science, 56, 4321–4329.
[2] Coehlo, D., Thovert, J.F., Adler, P.M., 1997, Geometrical and transport properties of random packings of spheres and aspherical particles, Phys. Rev. B, 55, 1959-1978.
[3] Kainourgiakis, M.E., Kikkinides, E.S., Stubos A.K., 2002. Diffusion and flow in porous domains constructed using process-based and stochastic techniques. Journal of Porous Materials, 9, 141-154.
Presented Thursday 20, 08:45 to 09:02, in session Tools Integration - CAPE Methods & Tools (T4-10).
