Abstract
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.
Highlights
Effective solid phase thermal conductivity [WmÀ1KÀ1] Effective axial thermal conductivity [WmÀ1KÀ1] Effective radial thermal conductivity [WmÀ1KÀ1] Fluid thermal conductivity [WmÀ1KÀ1] Pellet thermal conductivity [WmÀ1KÀ1]
Effective parameter optimization has been conducted for 168 case studies, including the packing structures of spheres, cylinders and Raschig rings with different N for the full range of ReP and different pellet materials to investigate the effect of bed length on the effective heat transfer model parameters, i.e. ker and hw
To compute Peer and Bi, we applied a nonlinear least squares (NLLS) method, which uses an initial guess for the effective parameters, whereby the radial temperature profile is predicted using Eqs. (1)–(10) at locations corresponding to the measurements, i.e
Summary
Effective (axial) solid phase thermal conductivity [WmÀ1KÀ1] Effective axial thermal conductivity [WmÀ1KÀ1] Effective radial thermal conductivity [WmÀ1KÀ1] Fluid thermal conductivity [WmÀ1KÀ1] Pellet (solid) thermal conductivity [WmÀ1KÀ1]. As shown by Vortmeyer and Haidegger (1991) and Wen and Ding (2006), there is a large disagreement between the predicted values and literature correlations for the effective radial Peclet number, Peer = Gcpdpv/ker, and the apparent wall Nusselt number, Nuw = hwdpv/kf, versus particle Reynolds number, Rep (see Nomenclature for clarification of the meaning of symbols) These empirical correlations thoroughly reflect the impact of catalyst shape, tube-to-pellet diameter ratio and operating conditions and, are not recommended for extrapolation (Magnico, 2009; Nijemeisland and Dixon, 2001). Packing algorithms include Discrete Element Methods (DEM) (Dong et al, 2017; Flaischlen and Wehinger, 2019; Guo et al, 2019; Ruiz et al, 2019; Singhal et al, 2017b), Monte-Carlo methods (Behnam et al, 2013) and Rigid Body Dynamics (RBD) tools such as the open-source graphical soft-
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