Radiative Transfer in Packed Spheres

1974 ◽  
Vol 96 (1) ◽  
pp. 52-58 ◽  
Author(s):  
C. K. Chan ◽  
C. L. Tien
Keyword(s):  
Experimental Data ◽  
Optical Properties ◽  
Radiative Transfer ◽  
Qualitative Agreement ◽  
Strong Dependence ◽  
Particle Diameter ◽  
Packed Bed ◽  
Radiative Properties ◽  
Absorption Properties

Radiative transfer through a packed bed of microspheres is analyzed on the basis of a new conceptual model, which combines the continuous and discontinuous models in predicting the scattering and absorption properties of packed microspheres. The basic elements of the formulation consist of the determination of the scattering diagram of a unit cell, the optical properties of a series of thin microsphere layers, and the solution of the two-flux equations. Results show a strong dependence of these radiative properties on the particle diameter and emissivity. Qualitative agreement is shown in the comparison of the predictions with existing experimental data.

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.

Directional Spectral Emittance of a Packed Bed: Correlation Between Theoretical Prediction and Experimental Data

2000 ◽  
Vol 123 (2) ◽  
pp. 240-248 ◽  
Author(s):  
Roge´rio Lopes ◽  
Luı´s M. Moura ◽  
Dominique Baillis ◽  
Jean-Franc¸ois Sacadura
Keyword(s):  
A Priori ◽  
Particle Diameter ◽  
Theoretical Data ◽  
Packed Bed ◽  
Radiative Properties ◽  
Discrete Ordinates ◽  
Spectral Reflectivity ◽  
Spectral Emittance ◽  
Gauss Method ◽  
Isothermal System

Directional spectral emittance of an absorbing and scattering isothermal system of packed spheres is predicted by a radiative model based on the discrete ordinates method. Radiative properties for the bed of packed opaque spheres are obtained using geometric optics laws corrected with a scaling factor to take into account the dependent scattering. This model requires the knowledge of several parameters. Particle diameter and porosity can be easily obtained, but particle hemispherical spectral reflectivity is very difficult to obtain a priori. This particle reflectivity is determined by an identification method (Gauss method of linearization) applied to bidirectional spectral reflectance data obtained from an experimental device using a Fourier transform infrared spectrometer. Directional spectral emittance is measured using a direct radiometric technique that has been recently proposed. For a system of packed opaque spheres at high temperature, good agreement is observed between experimental results of directional spectral and computed theoretical data.

Determination of thermal radiative properties of packed-bed media containing a mixture of polydispersed particles

2009 ◽  
Vol 48 (8) ◽  
pp. 1510-1516 ◽  
Author(s):  
Klaus Jäger ◽  
Wojciech Lipiński ◽  
Helmut G. Katzgraber ◽  
Aldo Steinfeld
Keyword(s):  
Packed Bed ◽  
Radiative Properties ◽  
Thermal Radiative Properties

scholarly journals Sensitivity of aerosol extinction to new mixing rules in the AEROPT submodel of the ECHAM5/MESSy1.9 atmospheric chemistry (EMAC) model

2014 ◽  
Vol 7 (3) ◽  
pp. 3367-3402
Author(s):  
K. Klingmüller ◽  
B. Steil ◽  
C. Brühl ◽  
H. Tost ◽  
J. Lelieveld
Keyword(s):  
Optical Properties ◽  
Radiative Transfer ◽  
Black Carbon ◽  
Atmospheric Chemistry ◽  
Radiative Forcing ◽  
Strong Dependence ◽  
Mixing Rule ◽  
Aerosol Optical Properties ◽  
Volume Average ◽  
Internal Mixing

Abstract. The modelling of aerosol radiative forcing is a major cause of uncertainty in the assessment of global and regional atmospheric energy budgets and climate change. One reason is the strong dependence of the aerosol optical properties on the mixing state of aerosol components like black carbon and sulphates. Using a new column version of the aerosol optical properties and radiative transfer code of the atmospheric chemistry-climate model EMAC, we study the radiative transfer applying various mixing states. The aerosol optics code builds on the AEROPT submodel which assumes homogeneous internal mixing utilising the volume average refractive index mixing rule. We have extended the submodel to additionally account for external mixing, partial external mixing and multi-layered particles. Furthermore, we have implemented the volume average dielectric-constant and Maxwell Garnett Mixing rule. We performed regional case studies considering columns over China, India and Africa, corroborating much stronger absorption by internal than external mixtures. Well mixed aerosol is a good approximation for particles with a black carbon core, whereas particles with black carbon at the surface absorb significantly less. Based on a model simulation for the year 2005 we calculate that the global aerosol direct radiative-forcing for homogeneous internal mixing differs from that for external mixing by about 0.5 W m−2.

Correlation of Measured and Computed Radiation Intensity Exiting a Packed Bed

1996 ◽  
Vol 118 (1) ◽  
pp. 94-102 ◽  
Author(s):  
P. D. Jones ◽  
D. G. McLeod ◽  
D. E. Dorai-Raj
Keyword(s):  
Radiative Transfer ◽  
Radiation Intensity ◽  
Transfer Equation ◽  
Scattering Theory ◽  
Radiative Transfer Equation ◽  
Packed Bed ◽  
Radiative Properties ◽  
Discrete Ordinates ◽  
Measured Intensity ◽  
Participating Media

The spectral and directional distribution of radiation intensity is measured, using a direct radiometric technique, at the exposed boundary of a packed bed of stainless steel spheres. The purpose of these measurements is to provide an experimental data base of radiation intensity with which to correlate intensity field solutions of the radiative transfer equation in participating media. The bed is considered to be one-dimensional, is optically thick, and has measured constant-temperature boundary conditions. Intensity exiting the bed is numerically simulated using a discrete ordinates solution to the radiative transfer equation, with combined mode radiation-conduction solution of the coupled energy conservation equation. Radiative properties for the bed are computed using the large size parameter correlated scattering theory derived by Kamiuto from the general theory of dependent scattering by Tien and others. The measured intensity results show good agreement with computed results in near-normal directions, though agreement in near-grazing directions is poor. This suggests that either radiative transfer near the boundaries of this medium might not be adequately represented by a continuous form of the radiative transfer equation, or that the properties derived from correlated scattering theory are insufficient. In either case, development of a more detailed radiation model for spherical packed beds appears warranted.

A versatile correlation of liquid hold-up under the single-phase trickle flow in a packed bed

1983 ◽  
Vol 48 (12) ◽  
pp. 3356-3369 ◽  
Author(s):  
Vladimír Jiřičný ◽  
Vladimír Staněk
Keyword(s):  
Experimental Data ◽  
Pressure Drop ◽  
Flow Rate ◽  
Single Phase ◽  
Packed Bed ◽  
Critical Values ◽  
Phase Flow ◽  
Two Phase ◽  
Extensive Experimental Data

The paper gives a review of present approaches to the problem of a single- and two-phase flow in a packed bed. A new definititon has been given of the flooding point, which, as far as the theory is concerned, rigorously defines critical values of the quantities in the flooding point. At the same time, the definition enables a unambiguous experimental determination of the flooding point from experimental dependence sof the hold-up or pressure drop on the flow rate of phases. Based on extensive experimental data three alternative forms have been proposed of the versatile correlation of liquid hold-up on the velocity of liquid at the zero velocity of gas. The correlations have been formulated on the principle of automodel properties and define the appropriate relationships in terms of normalized variables related to the newly defined flooding point. The dependences on the geometry parameters of the packing and physical properties of liquid appear in the versatile correlations only implicitly. A new possibility has been shown of inverse utilization of the versatile correlations for the determination of the critical values (the flooding point) from two independent measurements of liquid hold-up in a real apparatus.

Determination of Minimum Fluidization Velocity for Gas-Solid Beds by Experimental Data and Numerical Simulations

2011 ◽  
Author(s):  
Meire Pereira de Souza Braun ◽  
Geraldo Luiz Palma ◽  
Helio Aparecido Navarro ◽  
Paulo Sergio Varoto
Keyword(s):  
Experimental Data ◽  
Numerical Simulations ◽  
Particle Diameter ◽  
Minimum Fluidization Velocity ◽  
Ergun Equation ◽  
Fluidization Velocity ◽  
Minimum Fluidization ◽  
Experimental Apparatus ◽  
Good Agreement

The purpose of this work is to predict the minimum fluidization velocity Umf in a gas-solid fluidized bed. The study was carried out with an experimental apparatus for sand particles with diameters between 310μm and 590μm, and density of 2,590kg/m3. The experimental results were compared with numerical simulations developed in MFIX (Multiphase Flow with Interphase eXchange) open source code [1], for three different sizes of particles: 310mum, 450μm and 590μm. A homogeneous mixture with the three kinds of particles was also studied. The influence of the particle diameter was presented and discussed. The Ergun equation was also used to describe the minimum fluidization velocity. The experimental data presented a good agreement with Ergun equation and numerical simulations.

scholarly journals Impact of mineral dust on shortwave and longwave radiation: evaluation of different vertically-resolved parameterizations in 1-D radiative transfer computations

2018 ◽  
Author(s):  
Maria José Granados-Muñoz ◽  
Michael Sicard ◽  
Roberto Román ◽  
Jose Antonio Benavent-Oltra ◽  
Rubén Barragán ◽  
...  
Keyword(s):  
Optical Properties ◽  
Radiative Transfer ◽  
Aerosol Optical Depth ◽  
Optical Depth ◽  
Mineral Dust ◽  
Radiative Properties ◽  
Radiative Fluxes ◽  
Microphysical Properties ◽  
Aerosol Radiative

Abstract. Aerosol radiative properties are investigated in South-eastern Spain during a dust event on June 16–17, 2013 in the framework of the ChArMEx/ADRIMED (Chemistry-Aerosol Mediterranean Experiment/Aerosol Direct Radiative Impact on the regional climate in the MEDiterranean region) campaign. Particle optical and microphysical properties from ground-based sun/sky photometer and lidar measurements, as well as in situ measurements onboard the SAFIRE ATR 42 French research aircraft are used to create a set of different levels of input parameterizations which feed the 1-D radiative transfer model (RTM) GAME (Global Atmospheric ModEl). We consider three datasets: 1) a first parametrization based on the retrievals by an advanced aerosol inversion code (GRASP; Generalized Retrieval of Aerosol and Surface Properties) applied to combined photometer and lidar data; 2) a parameterization based on the photometer columnar optical properties and vertically-resolved lidar retrievals with the two-component Klett-Fernald algorithm; and 3) a parametrization based on vertically-resolved optical and microphysical aerosol properties measured in situ by the aircraft instrumentation. Once retrieved, the outputs of the RTM in terms of both shortwave and longwave radiative fluxes are contrasted against ground-, satellite- and in situ airborne measurements. In addition, the outputs of the model in terms of the aerosol direct radiative effect are discussed with respect to the different input parameterizations. Results show that calculated atmospheric radiative fluxes differ no more than 7 % to the measured ones. The three parametrization datasets produce aerosol radiative effects with differences up to 10 W m−2 in the shortwave spectral range (mostly due to differences in the aerosol optical depth), and 2 W m−2 for the longwave (mainly due to differences in the aerosol optical depth but also to the coarse mode radius used to calculate the radiative properties). The study reveals the complexity of parameterizing 1-D RTMs as sizing and characterising the optical properties of mineral dust is challenging. The use of advanced remote sensing data and processing, in combination with closure studies on the optical/microphysical properties from in situ aircraft measurements when available, is recommended.

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