The Effect of Turbulence on Momentum and Heat Transport in Packed Beds with Low Tube to Particle Diameter Ratio

2018 ◽  
Vol 16 (11) ◽  
Author(s):  
F. I. Molina-Herrera ◽  
C. O. Castillo-Araiza ◽  
H. Jiménez-Islas ◽  
F. López-Isunza
Keyword(s):  
Thermal Conductivity ◽  
Heat Transport ◽  
Mass Flux ◽  
Flow Model ◽  
Particle Diameter ◽  
Packed Bed ◽  
Diameter Ratio ◽  
Packed Beds ◽  
Measured Temperature ◽  
Orthogonal Collocation

Abstract This is a theoretical study about the influence of turbulence on momentum and heat transport in a packed-bed with low tube to particle diameter ratio. The hydrodynamics is given here by the time-averaged Navier-Stokes equations including Darcy and Forchheimer terms, plus a κ-ε two-equation model to describe a 2D pseudo-homogeneous medium. For comparison, an equivalent conventional flow model has also been tested. Both models are coupled to a heat transport equation and they are solved using spatial discretization with orthogonal collocation, while the time derivative is discretized by an implicit Euler scheme. We compared the prediction of radial and axial temperature observations from a packed-bed at particle Reynolds numbers (Rep) of 630, 767, and 1000. The conventional flow model uses effective heat transport parameters: wall heat transfer coefficient (hw) and thermal conductivity (keff), whereas the turbulent flow model includes a turbulent thermal conductivity (kt), estimating hw via least-squares with Levenberg-Marquardt method. Although predictions of axial and radial measured temperature profiles with both models show small differences, the calculated radial profiles of the axial velocity component are very different. We demonstrate that the model that includes turbulence compares well with mass flux measurements at the packed-bed inlet, yielding an error of 0.77 % in mass flux balance at Rep = 630. We suggest that this approach can be used efficiently for the hydrodynamics characterization and design and scale-up of packed beds with low tube to particle diameter ratio in several industrial applications.

Hydrodynamic Models for Packed Beds with Low Tube-to-Particle Diameter Ratio

2008 ◽  
Vol 6 (1) ◽  
Author(s):  
Carlos O. Castillo-Araiza ◽  
Felipe Lopez-Isunza
Keyword(s):  
Experimental Data ◽  
Effective Viscosity ◽  
Particle Diameter ◽  
Packed Bed ◽  
Diameter Ratio ◽  
Packed Beds ◽  
Hydrodynamic Models ◽  
Viscous Term ◽  
Measured Velocity ◽  
Viscosity Parameter

In the last decade it has been a special interest to incorporate the hydrodynamics in packed bed reactor models. This seems to be important in the case of highly exothermic partial oxidation reactions normally performed in packed beds with low tube/particle diameter ratio (dt/dp< 5) because of the large void distributions in the radial and axial directions, which have a direct impact on the magnitude of radial, angular and axial profiles of the velocity field, and consequently on both, the temperature and concentration profiles in the catalytic reactor. A successful reactor model needs an adequate hydrodynamic description of the packed bed, and for this reason several models additionally incorporate empirical expressions to describe radial voidage profiles, and use viscous (Darcy) and inertial (Forchheimer) terms to account for gas-solid interactions, via Ergun's pressure drop equation. In several cases an effective viscosity parameter has also been used with the Brinkman's viscous term. The use of these various approaches introduce some uncertainty in the predicted results, as to which extent the use of a particular radial voidage expression, or the use of an effective viscosity parameter, yield reliable predictions of measured velocity profiles.In this work the predictions of radial velocity profiles in a packed bed with low tube to particle diameter ratio from six hydrodynamic models, derived from a general one, are compared. The calculations show that the use of an effective viscosity parameter to predict experimental data can be avoided, if the magnitude of the two parameters in Ergun's equation, related to viscous and inertial energy losses, are re-estimated from velocity measurements, for this particular packed bed. The predictions using both approaches adequately fit the experimental data, although the results are analyzed and discussed.

Experimental and Theoretical Modeling of the Effective Thermal Conductivity of Rough Steel Spheroid Packed Beds

2003 ◽  
Vol 125 (4) ◽  
pp. 693-702 ◽  
Author(s):  
G. Buonanno ◽  
A. Carotenuto ◽  
G. Giovinco ◽  
N. Massarotti
Keyword(s):  
Thermal Conductivity ◽  
Effective Thermal Conductivity ◽  
Solid Mechanics ◽  
Packed Bed ◽  
Elementary Cell ◽  
Upper And Lower Bounds ◽  
Packed Beds ◽  
The Finite Element Method ◽  
Two Phase ◽  
Experimental Apparatus

The upper and lower bounds of the effective thermal conductivity of packed beds of rough spheres are evaluated using the theoretical approach of the elementary cell for two-phase systems. The solid mechanics and thermal problems are solved and the effects of roughness and packed bed structures are also examined. The numerical solution of the thermal conduction problem through the periodic regular arrangement of steel spheroids in air is determined using the Finite Element Method. The numerical results are compared with those obtained from an experimental apparatus designed and built for this purpose.

An Experimental Investigation on Forced Convection Heat Transfer From a Cylinder Embedded in a Packed Bed

1994 ◽  
Vol 116 (1) ◽  
pp. 73-80 ◽  
Author(s):  
K. Nasr ◽  
S. Ramadhyani ◽  
R. Viskanta
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Forced Convection ◽  
Convection Heat Transfer ◽  
Particle Diameter ◽  
Packed Bed ◽  
Spherical Particles ◽  
Theoretical Equation ◽  
Convection Heat ◽  
Forced Convection Heat Transfer

Forced convection heat transfer from a cylinder embedded in a packed bed of spherical particles was studied experimentally. With air as the working fluid, the effects of particle diameter and particle thermal conductivity were examined for a wide range of thermal conductivities (from 200 W/m K for aluminum to 0.23 W/m K for nylon) and three nominal particle sizes (3 mm, 6 mm, and 13 mm). In the presence of particles, the measured convective heat transfer coefficient was up to seven times higher than that for a bare tube in crossflow. It was found that higher heat transfer coefficients were obtained with smaller particles and higher thermal conductivity packing materials. The experimental data were compared against the predictions of a theory based on Darcy’s law and the boundary layer approximations. While the theoretical equation was moderately successful at predicting the data, improved correlating equations were developed by modifying the form of the theoretical equation to account better for particle diameter and conductivity variations.

Computing Profiles of Porosity and Surface/Volume Ratio in a Packed Bed Using Monte Carlo Method

2013 ◽  
Author(s):  
Genong Li
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Particle Diameter ◽  
Volume Ratio ◽  
Packed Bed ◽  
Diameter Ratio ◽  
Accuracy Requirement ◽  
Radial Profiles ◽  
Novel Method ◽  
Rigorous Error

Porosity and surface/volume ratio are two important parameters for a packed bed. In cylindrical packed beds at low tube-to-particle diameter ratio, they vary greatly in the radial direction. In the existing literature, radial profiles of porosity and surface/volume ratio have been computed using some analytical equations which involve elliptic integrals. In this paper, a Monte Carlo method is used to compute those profiles. To the authors’ knowledge, the method has never been employed in this context. The procedure of using this novel method is explained in detail. Through a rigorous error analysis based on statistics, the accuracy of the simulation result can be controlled. Before any simulation, the number of sampling points needed in the Monte Carlo simulation can be determined given an accuracy requirement. The method is completely general and can be used to compute profiles of porosity and surface/volume ratio in any packed bed with any shape of packing elements.

Thermophysical Properties of Biporous Heat Pipe Evaporators

2008 ◽  
Vol 130 (2) ◽  
Author(s):  
Tadej Semenic ◽  
Ying-Yu Lin ◽  
Ivan Catton
Keyword(s):  
Thermal Conductivity ◽  
Heat Pipe ◽  
Capillary Pressure ◽  
Linear Function ◽  
Copper Powder ◽  
Thermophysical Properties ◽  
Particle Diameter ◽  
Diameter Ratio ◽  
Vapor Permeability ◽  
Neck Size

Thirty biporous slugs with 3 different cluster diameters and 5 different particle diameters (15 combinations with 2 repetitions) and 12 monoporous slugs with 6 different particle diameters were sintered from spherical copper powder, and thermophysical properties were measured. The neck size ratio for all the particles was approximately 0.4. The porosity of monoporous samples was found to be independent of particle diameter and was equal to 0.28, and the porosity of biporous samples was found to be independent of cluster and particle diameters, and was equal to 0.64. The liquid permeability and maximum capillary pressure of small pores were found to be a linear function of the particle diameter. Similarly, vapor permeability was found to be a linear function of the cluster diameter. The thermal conductivity of monoporous samples was measured to be 142±3W∕mK at 42±2°C, and it was independent of particle diameter. The thermal conductivity of biporous samples was found to be a function of cluster to particle diameter ratio.

An Experimental Evaluation of the Effective Thermal Conductivities of Packed Beds at High Temperatures

1994 ◽  
Vol 116 (4) ◽  
pp. 829-837 ◽  
Author(s):  
K. Nasr ◽  
R. Viskanta ◽  
S. Ramadhyani
Keyword(s):  
Thermal Conductivity ◽  
Effective Thermal Conductivity ◽  
High Temperatures ◽  
Radiation Heat Transfer ◽  
Particle Diameter ◽  
Spherical Particles ◽  
Packed Beds ◽  
Packing Materials ◽  
Bed Temperature ◽  
Thermal Conductivities

Combined conduction and radiation heat transfer in packed beds of spherical particles was investigated. Three different packing materials (alumina, aluminum, and glass) of various particle diameters (2.5 to 13.5 mm) were tested. Internal bed temperature profiles and corresponding effective thermal conductivities were measured under steady-state conditions for a temperature range between 350 K and 1300 K. The effects of particle diameter and local bed temperature were examined. It was found that higher effective thermal conductivities were obtained with larger particles and higher thermal conductivity packing materials. The measured values for the effective thermal conductivity were compared against the predictions of two commonly used models, the Kunii–Smith and the Zehner–Bauer–Schlu¨nder models. Both models performed well at high temperatures but were found to overpredict the effective thermal conductivity at low temperatures. An attempt was made to quantify the relative contributions of conduction and radiation. Applying the diffusion approximation, the radiative conductivity was formulated, normalized, and compared with the findings of other investigators.

Experimental Measurements of the Thermal Conductivity of Nanoparticle Packed Beds

2013 ◽  
Author(s):  
Kevin Clarke ◽  
Muftah Elsahati ◽  
Robert F. Richards
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Silica Nanoparticles ◽  
Metallic Nanoparticles ◽  
Silica Nanoparticle ◽  
Packed Bed ◽  
Experimental Measurements ◽  
Packed Beds ◽  
Copper Nanoparticle ◽  
Sem Imaging

Experimental measurements of heat transfer across packed beds of ceramic and metallic nanoparticles are presented. Round disk-shaped cakes of nanoparticles approximately one millimeter thick and 6.75 millimeters diameter are produced by packing either copper or silica nanoparticles into a mold. The thermal conductivity of these packed beds are then determined using a Guard-Heated Calorimeter under steady state conditions. SEM imaging of the packed beds indicates that the copper nanoparticles are neither monosized nor entirely spherical while the silica nanoparticles, are both highly spherical and monosized. However, both packed beds were found to have very similar effective thermal conductivities. The thermal conductivity of the copper nanoparticle packed bed is found to be 0.054 ± 0.006 W/m°C, while the thermal conductivity of silica nanoparticle packed bed is found to be 0.018 ± 0.007 W/m°C. As a result, it is seen that, at least in this limited comparison, particle material and thermal conductivity (metal with high conductivity, or ceramic with low conductivity), as well as the regularity of the nanoparticle itself (size distribution and sphericity) appear to have a small effect on overall packed bed thermal conductivity.

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