Abstract
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 ker-hw models.
Highlights
Tubular fixed bed catalytic reactors with tube-to-pellet diameter ratio, N, in the range of 4 to 10 are extensively employed in process and chemical industries to handle highly exothermic reactions, e.g. oxida tion of n-butane to maleic anhydride [1], and endothermic reactions, e. g. methane steam reforming [2], due to enhancing heat transfer from confining wall to the particulate bed
As evidenced in literature [5,17,18,19,20], the averaged values obtained from pseudo-homogenous models do not suffice to accurately describe the sharp temperature and composition profiles in low-N fixed bed reactor because i) the condition of lateral uniformity of the structures is hardly fulfilled in narrow-tube fixed bed reactors, ii) the plug flow idealization hypothesized in such models obscures the sig nificant roles of flow maldistribution on the local transport processes [19,21,22,23], iii) these models rely strongly on effective transport pa rameters which are described in the form of empirical correlations and computed by solving a multi-variable parameter estimation problem to find the best fit with experimental measurements [16]
Discrete-pellet Computational Fluid Dynamics (CFD) simulations of the hydrodynamics and lateral heat transfer in fixed beds of spheres, equilateral solid cylinder and Raschig rings were performed for laminar, transient and fully turbulent flow regimes
Summary
Tubular fixed bed catalytic reactors with tube-to-pellet diameter ratio, N, in the range of 4 to 10 are extensively employed in process and chemical industries to handle highly exothermic reactions, e.g. oxida tion of n-butane to maleic anhydride [1], and endothermic reactions, e. g. methane steam reforming [2], due to enhancing heat transfer from confining wall to the particulate bed. There are a few studies that use a hard body approach based on Rigid Body Dynamics (RBD) to synthesize random packings of non-spherical particles followed by a supplementary CFD study to analyze local behavior of flow structure and heat and mass transfer in fixed bed reactors [20,40,48,51]. Partopour and Dixon [48] have presented a tailor-made integrated workflow using the Bullet Physics Library for computational generation of randomly packed particulate structures of arbitrary-shaped pellets The authors examined their automated package for the analysis of flow and pressure drop in random packings of spheres, cylinders, Raschig rings, and quadrilobes with five holes. An effort will be made to cast some light on the reasons behind the methodically-driven deviations of radial temperature profile, ob tained from ker-hw pseudo-homogenous heat transfer model, from the pellet-scale temperature field
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