Heat exchange engineering Advances in design and operation

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Predictive characterization of mean voidage in packed beds

Abstract-A generalized mean voidage correlation has been derived to provide reliable prediction of mean voidage in packed beds of spherical and cylindrical particles. From geometrical considerations, the correlation is extended to cover beds of hollow cylindrical pellets. NOMENCLATURE d j internal diameter do outer diameter dp dp, particle diameter equivalent sphere diameter d, diameter ratio d, tube diameter f empirical factor H height of cylindrical particle n exponent Greek symbols f m mean voidage of packed bed f h mean voidage of bed of hollow cylindrical particles 4> sphericit

Fixed bed reactors of non-spherical pellets: Importance of heterogeneities and inadequacy of azimuthal averaging

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 ≤ Rep ≤ 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.</p

Fixed bed reactors of non-spherical pellets: Importance of heterogeneities and inadequacy of azimuthal averaging

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 ≤ Rep ≤ 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.Large Scale Energy StorageIntensified Reaction and Separation SystemsComplex Fluid Processin

Hydrodynamics of narrow-tube fixed bed reactors filled with Raschig rings

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 ≤ Rep ≤ 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.Large Scale Energy StorageIntensified Reaction and Separation SystemsComplex Fluid Processin

Multiscale modelling of wall-to-bed heat transfer in fixed beds with non-spherical pellets: From particle-resolved CFD to pseudo-homogenous 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 ker and hw 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.Large Scale Energy StorageComplex Fluid Processin