Packed Bed Of Spheres Research Articles

A new model of solid-phase effective thermal conductivity in local thermal non-equilibrium simulation for packed beds of rough spheres in convective flow

This work proposes a new method to calculate the solid-phase effective conductivity in a two-equation local thermal non-equilibrium (LTNE) model for a packed sphere bed under convection. Considered parameters include the surface roughness, the slope of the surface asperity, the applied force, and the hardness of the sphere. The framework of this method is described and constructed both numerically and mathematically. First, structured unit cells in simple cubic and face-centered cubic arrangements are considered to represent mono-sized packed spheres of different porosities. The inter-sphere apparent contact region is found to be surrounded by a stagnant-fluid ring whose outer boundary divides the inner conductive region from the uncoupled outer convective region. Both the apparent contact region and the stagnant-fluid ring are included in the calculation of the solid-phase effective conductivity. Numerical simulations accounting for the inter-sphere contact resistance and the interior constriction/spreading resistance are conducted to evaluate the effective thermal conductivity over a unit cell with respect to various parameters. In addition, a semi-empirical mathematical equation is formulated with deviations from the numerical results within 3%. The present semi-empirical model for the prediction of the solid-phase effective conductivity associated with packed rough spheres is validated by the excellent agreement with experiments under a stagnant environment. The present method is expected to provide accurate evaluation of the solid-phase effective conductivity in a two-equation LTNE convective heat transfer model for packed beds of mono-sized spheres.

Electrophoresis of a soft charged particle in a sparsely packed bed

ABSTRACTIn this study, the migration of a single charged spherical hydrogel (polyelectrolyte) micro/nanoparticle is considered in an electrolyte solvent medium where several identical micro/nanoparticles are suspended. Each particle can be modeled as a charged linearly elastic fibrous spherical solid saturated with a Newtonian electrolyte. In this study, a new analytical approach is proposed for finding the steady response of the soft charged hydrogel sphere to a DC electric field using the perturbation method. It is possible to obtain a closed form for the electrophoretic mobility of a single sphere within a sparsely packed sphere bed for a wide range of electric double layer thickness. The response of each hydrogel sphere toward the external fields includes both the particle translation and infinitesimal deformation in the polymeric skeleton of a hydrogel sphere. The hydrodynamics inside a sphere and the corresponding strain of the solid phase are studied by adopting field equations from the theory of biphasic mixtures. This study highlights that factors like fixed charge density, dielectric constants, elasticity coeffcients of polymer skeleton influence the mobility and deformation of the particle. This study has a close relevance to an electric field induced drug delivery in biological media.

Experimental study on helium pressure drop across randomly packed bed for fusion blanket

Pebble beds are used in many tritium breeder designs of fusion blanket, which is purged by a flow of low velocity helium. In this paper, experimental study of the pressure drop of helium through packed sphere beds was carried out. The pebbled beds were sealed in a rectangular container. The spheres of five different diameters varied from 0.5mm to 2.0mm. The Darcy regime and Forchheimer regime were identified within the range 2.47<Re<27.59. The transition region was identified and discussed in detail. The pressure drop was characterized by Kozeny-Carman constants or Ergun's constants for the experimental range. Some commonly used correlations were evaluated by the experimental data.

Nanoparticle transport in heterogeneous porous media with particle tracking numerical methods

In this article, transport and retention of nanoparticles that flow in suspension through packed beds with unconsolidated spheres and through consolidated Berea sandstone are numerically explored. The surfaces exhibit electrical charge heterogeneity where particles can deposit blocking the surrounding surface deposition sites. The lattice Boltzmann method with Lagrangian particle tracking are the techniques employed. Four ideal patterns of surface charge heterogeneity are adopted for the packed sphere beds, while a real distribution of charge heterogeneity is determined for the Berea core through micro-CT image segmentation. It is found that particle breakthrough curves do not reach a plateau, unless the pore surfaces are completely saturated. Surface saturation also enhances particle propagation because of the surface blocking mechanism, reducing the effective particle deposition rate. In addition, surface saturation mitigates the effect of the pattern of heterogeneity on particle retention, which might be pronounced when blocking is not taken into account. It is also observed from the case of Berea core that the heterogeneity of the mineralogical surfaces disturbs particle transport depending on the physicochemical properties of the surfaces. Likewise, similarity of the mineralogical surface properties is a prerequisite for the commonly used patch-wise model with Langmuirian blocking to reproduce nanoparticle breakthrough in such porous media.

Study of geometries of active magnetic regenerators for room temperature magnetocaloric refrigeration

Room temperature magnetic refrigeration has attracted substantial attention during the past decades and continuing to increase the performance of active magnetic regenerators (AMR) is of great interest. Optimizing the regenerator geometry and related operating parameters is a practical and effective way to obtain the desired cooling performance. To investigate how to choose and optimize the AMR geometry, a quantitative study is presented by simulations based on a one-dimensional (1D) numerical model. Correlations for calculating the friction factor and heat transfer coefficient are reviewed and chosen for modeling different geometries. Moreover, the simulated impacts of various parameters on the regenerator efficiency with a constant specific cooling capacity are presented. An analysis based on entropy production minimization reveals how those parameters affect the main losses occurring inside the AMR. In addition, optimum geometry and operating parameters corresponding to the highest efficiency for different geometries are presented and compared. The results show that parallel plate and micro-channel matrices show the highest theoretical efficiency, while the packed screen and packed sphere beds are possibly more practical from the application point of view.

Modeling of Effective Stagnant Thermal Conductivity of Porous Media

Based on one-dimensional analysis of heat conduction, a general formula for the effective stagnant thermal conductivity of spatially periodic porous media is derived without assuming local thermal equilibrium. Furthermore, we discuss the contribution of the contact area between particles to the effective stagnant thermal conductivity in detail, and the modification of the formula is proposed to predict the actual effective stagnant thermal conductivity for the porous media. The present results are in good agreement with experimental results of Nozad et al. (1985, “Heat Conduction in Multi-Phase Systems I: Theory and Experiments for Two-Phase Systems,” Chem. Eng. Sci., 40(5), pp. 843–855) for a packed-sphere bed.

Selective laser melting of La(Fe,Co,Si)13 geometries for magnetic refrigeration

Magnetic cooling prototypes based on the magnetocaloric effect require the magnetic refrigerant to be shaped into geometries that enable quick and efficient heat-transfer to the transfer fluid. Simple solutions include a stack of parallel-plates or a bed of packed-spheres. Here, we demonstrate how more sophisticated geometries can be made by using selective laser melting, a rapid prototyping technique to form three-dimensional shapes. Using excellent magnetocaloric La(Fe,Co,Si)13 as starting-powder we made two geometries: a wavy-channel block with a high surface-to-volume ratio and an array of fin-shaped rods which eliminate unwanted heat conduction along the magnetic part. After annealing treatment, the geometries are intact and can survive more than 106 cycles of applying a magnetic field while still maintaining good magnetocaloric properties. This fabrication approach shows promise for making near-net shaped magnetic refrigerants with superior heat transfer properties and performance.

Determining the minimum mass and cost of a magnetic refrigerator

An expression is determined for the mass of the magnet and magnetocaloric material needed for a magnetic refrigerator and these are determined using numerical modeling for both parallel plate and packed sphere bed regenerators as function of temperature span and cooling power. As magnetocaloric material Gd or a model material with a constant adiabatic temperature change, representing an infinitely linearly graded refrigeration device, is used. For the magnet a maximum figure of merit magnet or a Halbach cylinder is used. For a cost of $40 and $20 per kg for the magnet and magnetocaloric material, respectively, the cheapest 100 W parallel plate refrigerator with a temperature span of 20 K using Gd and a Halbach magnet has 0.8 kg of magnet, 0.3 kg of Gd and a cost of $35. Using the constant material reduces this cost to $25. A packed sphere bed refrigerator with the constant material costs $7. It is also shown that increasing the operation frequency reduces the cost. Finally, the lowest cost is also found as a function of the cost of the magnet and magnetocaloric material.

Pore-scale simulations on relative permeabilities of porous media by lattice Boltzmann method

Pore-scale simulations of two phase flows in a packed-sphere bed and in a carbon paper gas diffusion layer (GDL) are carried out using the free energy multiphase lattice Boltzmann method (LBM). The simulations are performed based on the detailed microstructure of the porous media under periodic boundary conditions such that the average phase saturations in the porous medium remain constant. A comparison of the simulated and measured relative permeabilities for the packed sphere bed as a function of non-wetting phase saturation is performed, and effects of the wettability and the anisotropic characteristics of relative permeabilities of the GDL are investigated.

Imaging of Individual Polymers Undergoing Flow in a Bed of Small Spheres

Flexible DNA molecules are imaged by fluorescence microscopy while undergoing convection through micron-sized pores of a packed sphere bed. To circumvent the high pressures of a closed channel design, an open channel microfluidic device is selected such that sphere wicking drives convection. Image analysis yields the average level of chain stretching and the average DNA migration rate as a function of Deborah number De for ratios of sphere diameter to coil radius of gyration of order 1 to 10. Visualizations also reveal the transient localized conformations and trajectories of individual molecules, which can migrate only by traversing coil-sized pore constrictions. Two De (flow) transitions are noted: the first, at De ∼ 0.3, leads to limited chain stretching, while the second, at De ∼ 1, leads to gross chain stretching via a mechanism of entanglement about sphere contact points. Entangled chains adopt elongated “U”- and “J”-shaped conformations, which are relaxed by “pulley-like” sliding over entanglement ...

A Monte Carlo simulation of photon propagation in fluorescent poly(ethylene glycol) hydrogel microsensors

A Monte Carlo simulation of photon propagation through fluorophore-containing poly(ethylene glycol) hydrogel networks is described. Poly(ethylene glycol) (PEG) hydrogel microspheres are being studied for fluorescent biosensing of small molecular weight analytes such as glucose and paraoxon. A computational approach to assess the fluorescent output from these sensors was developed, in particular investigating the impact of sphere characteristics such as size, scattering, and fluorophore concentrations on sensor response. Monte Carlo simulations of both individual spheres and packed sphere beds were developed to model photon propagation through homogeneous, water-swollen PEG hydrogel microspheres with encapsulated fluorescein isothiocyanate (FITC) and tetramethylrhodamine isothiocyanate (TRITC) dyes. Experimental studies using an integrating sphere were conducted to determine the hydrogel optical properties used in the simulation and spectrofluorimetry studies performed to verify assumptions made in the model regarding quantum yield. Changes in fluorescence quantum yield, hydrogel scattering and absorption coefficients ( μ s and μ a), hydrogel scattering anisotropy ( g), and depth of the sphere bed were used to predict optimum sphere size, gel chemistry, and collection geometry.

Flow Through a Finite Packed Bed of Spheres: A Note on the Limit of Applicability of the Forchheimer-Type Equation

The variation of the pressure drop measured as a function of the fluid velocity through a packed bed of spheres is presented and discussed in the range of particle Reynolds number 30–1500. Based on previous studies, the observed limit of validity of the so-called Forchheimer law may be attributed to the concomitant effects of the finite character of the tested bed and of the transition of flow regime which is marking the beginning of the fully developed turbulent flow regime. The limit of validity of the Forchheimer-type law was formerly noticed by several authors.

Modified Zehner-Schlunder models for stagnant thermal conductivity of porous media

Modified Zehner-Schlunder models are proposed for calculations of the stagnant thermal conductivity of two types of porous media with spatially periodic structures. The area-contact model is developed to take into consideration finite area contacts between spheres in a packed-sphere bed. It is shown that results based on the area-contact model are in better agreement with experimental data than those based on the original Zehner-Schlunder model especially at high solid/fluid thermal conductivity ratios. The phase-symmetry model is developed for a sponge-like porous medium where each phase is continuously connected and phase symmetry must be maintained in the expression of the stagnant thermal conductivity. The characteristics of these two models are illustrated.

Prediction of location of particles in the wall region of a randomly packed bed of spheres

Presentation d'une nouvelle correlation basee sur le principe des couches cylindriques concentriques d'egale epaisseur

The evaluation of temperature jump distances and thermal accommodation coefficients from measurements of the thermal conductivity of UO 2 packed sphere beds

The results of thermal conductivity measurements on UO 2 80 μm diameter microsphere beds in helium, argon and krypton over a range of temperatures and pressures are reported. These and previous results on UO 2 microsphere beds in helium, krypton and nitrogen obtained at Oak Ridge National Laboratory (ORNL) were analysed in terms of a previously developed model which enables thermal accommodation coefficients (TAC) and temperature jump distances to be evaluated. Values derived from ORNL results tend to be in reasonable agreement with the corresponding, rather sparse data reported previously. In particular, in the case of helium, TAC's are in reasonable agreement with the direct measurements of Ullman et al. and exhibit a similar decrease with increasing temperature. However the TAC and temperature jump distance values derived from the Harwell measurements are respectively larger and smaller than the comparable ORNL figures. Also, in the case of helium, the TAC increases with pressure in contrast with values obtained from the ORNL data which are pressure independent. These differences are attributed to the differing surface finishes that are achieved during the manufacturing processes employed in the two laboratories.

Fully-developed, forced convective flow through an annular packed-sphere bed with wall effects

An analysis is performed for a fully-developed, forced convective flow through a packed-sphere bed between concentric cylinders maintained at different temperatures. The radial variations of the porosity and permeability in the bed near the walls, known as wall effects, are approximated by exponential functions. The Brinkman model with variable permeability is used as the momentum equation. An analytical solution based on the method of matched asymptotic expansions is obtained for the velocity distribution. It is shown that velocity overshoots occur in the variable permeability bed near the inner and outer cylinders. Because of the non-uniform porosity variation near the walls, the stagnant thermal conductivity of the bed also varies in the radial direction accordingly. A mixing length theory, proposed recently by Cheng and Vortmeyer for the transverse thermal dispersion, is employed to obtain the radial temperature distribution and the Nusselt number of the annular bed. Computations of the heat transfer characteristics were carried out based on three velocity models, i.e. Brinkman's model with variable and constant permeabilities as well as the plug flow model. It is found that with the mixing length theory, theoretical predictions of the heat transfer characteristics based on the three velocity models are in good agreement with the existing experimental data. The predicted temperature profiles, based on the Brinkman model with a variable permeability, agree the best with temperature data.

Comparison of coolant flow predictions with those measured on a full-scale mockup of a pebble bed reactor core

In a companion paper, a mathematical model for the analysis of coupled thermal-hydraulic problems in steady-state, axisymmetric pebble bed nuclear reactor cores was presented. In this paper, predictions by the computer code PEBBLE, which is based on the previously reported model, are compared with flow measurements from the full-scale mockup of the Oak Ridge National Laboratory Pebble Bed Reactor Experiment. The code PEBBLE is shown to adequately predict distributions and magnitudes of velocity and pressure for high Reynolds number flows in packed sphere beds. Limitations of the code and its ability to adequately calculate flow distributions in large pebble bed power reactors are discussed.