This paper investigates the validity of azimuthal averaging of 3D temperature fields in the analysis of lateral heat transfer in dense particle packings. This is conducted by synthetic generation of 3D packing surrogates of spheres, cylinders and Raschig rings with tube-to-pellet diameter ratio, 3 < N < 6, using an in-house Rigid Body Dynamics packing algorithm, followed by detailed discrete pellet CFD simulations of heat transfer from wall to bed for laminar, transient and turbulent flow regimes. The CFD results of hydrodynamics and temperature fields are benchmarked against empirical correlations for pressure drop and interphase heat transfer Nusselt number, Nu, offering the best fits with correlations proposed by Eisfeld and Schnitzlein (for cylinders and spheres) and Nemec and Levec (for rings) for pressure drop, and by Gunn and Sun and coworkers for the prediction of Nu. The CFD results demonstrate that fluctuations in local temperature are completely neglected by azimuthal-averaging of 3D temperature fields over the bed volume, leading to more than 150 °C deviations from the local temperature data. Furthermore, it is found that deviations between azimuthally-averaged axial velocity profile and true local velocities are in an analogous fashion transmitted to the temperature field. This is evidenced by the coincidence of the peaks in the deviation profiles of azimuthally-averaged temperature and velocity from the local data over the bed radius. This is due to thermal disequilibrium between fluid and pellet phases which is partially omitted by the azimuthal-averaging of the 3D temperature field and basically neglected in pseudo-homogenous k_er-h_w models.

We investigate forced convective heat transfer in packings of spheres, cylinders and Raschig rings, made of glass, steel and alumina, in relatively narrow tubes. A detailed comparison is made between resolved pellet-scale, azimuthally-averaged temperature profiles, and 2D-axially-dispersed pseudo-homogenous plug flow (2D-ADPF) predictions. The local temperature deviates significantly from azimuthally-averaged profiles, which in turn deviate from 2D-ADPF predictions. We show that the length dependency of effective heat transfer parameters is caused by thermal (non-)equilibrium between fluid and solid phases along the bed and not related to inadequate insulation of the calming section or the thermocouple's cross or an under-developed velocity and thermal field at the bed inlet. The influence of pellet shape and thermal conductivity and tube-to-pellet diameter ratio on k_er and h_w are assessed. We conclude that the models of Specchia/Baldi/Gianetto/Sicardi for all flow regimes and of Martin/Nilles for the turbulent regime are recommended for practical use for spherical particles.

The local flow structure and pressure drop in random packings of Raschig rings are analyzed using sequential Rigid Body Dynamics (RBD) method and Computational Fluid Dynamics (CFD) simulation. Tube-to-pellet diameter ratios, N, between 3 and 6 are investigated for laminar, transitional and turbulent flow regimes (5 ≤ Re_p ≤ 3,000). The computed pressure drops are in good agreement with the empirical correlation of Nemec and Levec (2005), while the Ergun equation exhibited high deviations of more than 60%, even when it is modified to explicitly account for non-sphericity of pellets. This deviation is ascribed to additional sources for eddy formation offered by Rashig rings, compared to spheres and cylinders, which cannot be counterbalanced by the usage of a higher specific surface area. The 3D results of flow structure demonstrate a large influence of packing topology on the velocity distribution: rings oriented parallel to the flow accelerate the local velocity through their axial holes, while rings oriented perpendicular to the flow provide additional space for vortex formation. The flow fields are substantially different from that found in packings of spheres and cylinders, both in terms of volume of backflow regions and velocity hotspots. This implies a higher order of local flow inhomogeneity in azimuthal and axial directions compared to spherical and cylindrical packings. Furthermore, it is found that azimuthal averaging of the 3D velocity field over the bed volume, which has been used to improve classical plug-flow pseudo-homogenous models to account for the role of tortuous velocity fields, cannot reflect the appearance of vortex regions and thereby leads to underestimation of the local axial velocity values by over 500% of the inlet velocity.

Despite the substantial simplicities inherent in pseudo-continuum models of fixed bed reactors, there is a continued interest in the use of such models for predicting fluid flow and transport scalars. In this paper, we aim to quantitatively address the inadequacy of 2D pseudo-continuum models for narrow-tube fixed beds. We show this by comparing with spatially resolved 3D results obtained by a robust and integrated numerical workflow, consisting of a sequential Rigid Body Dynamics and Computational Fluid Dynamics (RBD-CFD) approach. The RBD is founded on a physics-based hard-body packing algorithm, recently proposed by the authors (Moghaddam, E.M., Foumeny, E.A., Stankiewicz, A.I., Padding, J.T., 2018. A Rigid Body Dynamics Algorithm for Modelling Random Packing Structures of Non-Spherical and Non-Convex Pellets. Ind. Eng. Chem. Res. 57, 14988–15007), which offers a rigorous method to handle resting contacts between particles. The methodology is benchmarked for simulations of flow fields in all flow regimes, for 5 ≤ Re_p ≤ 3,000, in random packings of spheres and cylinders with tube-to-pellet diameter ratios, N, between 2.29 and 6.1. The CFD results reveal a remarkable influence of local structure on the velocity distribution at the pellet scale, particularly in low-N packings, where the spatial heterogeneity of the structure is very strong along the bed axis. It is also demonstrated that azimuthal averaging of the 3D velocity field over the bed volume, which has been considered as an advancement over plug flow idealization in classical pseudo-continuum models, cannot reflect the role of vortex regions emerging in the wake of the pellets, and leads to underestimation of the local velocity values by more than 400% of the inlet velocity.

Despite the common use of nonspherical catalyst pellets in chemical engineering applications, the packing structures of such pellets have not been as systematically studied and characterized as spherical packings. We propose a packing algorithm based on rigid body dynamics to simulate packing of nonspherical and possibly nonconvex pellets. The algorithm exerts a hard-body approach to model collision phenomena. The novelty is that the transition between moving and resting particles is controlled by a cutoff on the relative contact velocities, instead of artificially damping linear and angular velocities to stabilize the algorithm. The algorithm is used to synthesize packings of spheres, cylinders, and Raschig rings with tube-to-pellet diameter ratios 3-9.16. The packings are validated in terms of bulk porosity and radial void fraction distribution, finding satisfactory agreement with literature data. Denser packing structures are generated with high restitution coefficients and low friction coefficients. The confining tube walls play an important role, with highly fluctuating bulk porosities in narrow tubes.