Wave model for longitudinal dispersion: Application to the laminar-flow tubular reactor

The wave model for longitudinal dispersion, published elsewhere as an alternative to the commonly used dispersed plug-flow model, is applied to the classic case of the laminar-flow tubular reactor. The results are compared in a wide range of situations to predictions by the dispersed plug-flow model as well as to exact numerical calculations with the 2-D model of the reactor and to other available methods. In many practical cases, the solutions of the wave model agree closely with the exact data. The wave model has a much wider region of validity than the dispersed plug-flow model, has a distinct physical background, and is easier to use for reactor calculations. This provides additional support to the theory developed elsewhere. The properties and the applicability of the wave model to situations with rapidly changing concentration fields are discussed. Constraints to be satisfied are established to use the new theory with confidence for arbitrary initial and boundary conditions

Wave Concept in the Theory of Hydrodynamical Dispersion - a Maxwellian Type Approach

A new approach to the modelling of chemical reactors and contactors is discussed. This approach argues that the dispersion should, under most circumstances, be based on Maxwell's, rather than Fick's diffusion law. As a pair of first-order partial differential equations of the hyperbolic type and requiring only inlet conditions, the wave model is more realistic physically, has a much wider range of validity and in many practical cases is simpler mathematically. Only mass transfer problems are considered, but the results apply equally well to the hydrodynamic dispersion of heat. It is explained why the standard dispersion model fails in many practical applications and why the new wave model gives much better results

Kinetic Intersections as a Source of Information on Rate Coefficients

C

Gas dynamics and heat transfer in a packed pebble-bed reactor for the 4th generation nuclear energy

Proper analyses of axial dispersion and mixing of the coolant gas flow and heat transport phenomena in the dynamic core of nuclear pebble-bed reactors pose extreme challenges to the safe design and efficient operation of these packed pebble-bed reactors. The main objectives of the present work are advancing the knowledge of the coolant gas dispersion and extent of mixing and the convective heat transfer coefficients in the studied packed pebble-beds. The study also provides the needed benchmark data for modeling and simulation validation. Hence, a separate effect pilot-plant scale and cold-flow experimental setup was designed, developed and used to carry out for the first time such experimental investigations. Advanced gaseous tracer technique was developed and utilized to measure in a cold-flow randomly packed pebble-bed unit the residence time distribution (RTD) of gas. A novel, sophisticated fast-response and non-invasive heat transfer probe of spherical type was developed and utilized to measure in a cold-flow packed pebble-bed unit the solid-gas convective heat transfer coefficients. The non-ideal flow of the gas phase in pebble bed was described using one-dimensional axial dispersion model (ADM), tanks-in-series (T-I-S) model and central moments analyses (CMA) method. Some of the findings of this study are: The flow pattern of the gas phase does not much deviate from the idealized plug-flow condition which depends on the gas flow rate and bed structure of the pebble-bed. The non-uniformity of gas flow in the studied packed pebble bed can be described adequately by the axial dispersion model (ADM) at different Reynolds numbers covers laminar and turbulent flow conditions. This has been further confirmed by the results of tanks in series (T-I-S) model and the central moment analyses (CMA). The obtained results indicate that pebbles size and hence the bed structure strongly affects axial dispersion and mixing of the flowing coolant gas while the effect of bed height is negligible in packed pebble-bed. At high range of gas velocities, the change in heat transfer coefficients with respect to the gas velocity reduces as compared to these at low and medium range of gas velocities. The increase of coolant gas flow velocity causes an increase in the heat transfer coefficient and the effect of gas flow rate varies from laminar to turbulent flow regimes at all radial positions of the studied packed pebble-bed reactor. The results show that the local heat transfer coefficient increases from the bed center to the wall due to the change in the bed structure and hence in the flow pattern of the coolant gas. The results and findings clearly indicate that one value as overall heat transfer coefficient cannot represent the local heat transfer coefficients within the bed and hence correlations to predict radial and axial profiles of heat transfer coefficient are needed --Abstract, page iii

Utilizing Shear Factor Model and Adding Viscosity Term in Improving a Two-Dimensional Model of Fluid Flow in Non Uniform Porous Media

In a packed bed catalytic reactor, the fluid flow phenomena are very complicated because the fluid and solid particle interactions dissipate the energy. The governing equations were developed in the forms of specific models. The shear factor model was introduced in the momentum equation for covering the effect of flow and solid interactions in porous media. A two dimensional numerical solution for this kind of flow has been constructed using the finite volume method. The porous media porosity was treated as non-uniform distribution in the radial direction. Experimentally, the axial velocity profiles produce the trend of having global maximum and minimum peaks at distance very close to the wall. This trend is also accurately picked up by the numerical result. A more comprehensive shear factor formulation results a better velocity prediction than other correlations do. Our derivation on the presence of porous media leads to an additional viscosity term. The effect of this additional viscosity term was investigated numerically. It is found that the additional viscosity term improves the velocity prediction for the case of higher ratio between tube and particle diameter

Doctor of Philosophy

dissertationComputational fluid dynamic modeling was performed to describe and analyze the various processes occurring in three chemically reacting gas-particle flows: chemical vapor synthesis of tungsten carbide and aluminum nanopowders, flame synthesis of silica nanopowder, and a novel flash ironmaking process based on the direct gaseous reduction of iron oxide concentrate particles. The model solves the three-dimensional turbulent governing equations of overall continuity, momentum, energy, and species transport including gas-phase chemical kinetics. For modeling nanopowder synthesis, the particle size distribution is obtained by solving the population balance model. The particle nucleation rate is calculated based on chemical kinetics or homogeneous nucleation theory. The particle growth rate is calculated by vapor condensation, Brownian coagulation or a combination of both, depending on the type of material. The quadrature method of moments is used to numerically solve the population balance. For modeling the flash ironmaking reactor, a simplified chemical reaction mechanism for hydrogen-oxygen combustion is used to calculate realistic flame temperatures. The iron oxide concentrate particles are treated from a Lagrangian viewpoint. First, the chemical vapor synthesis of tungsten carbide nanopowder was simulated. Using available experimental data, a parametric study was conducted to determine the nucleation and growth rate constants. Second, the flame synthesis of silica nanopowder was simulated. A single value of the collision efficiency factor was sufficient to reproduce the magnitude as well as the variations of the average particle diameter with different experimental conditions. Third, the chemical vapor synthesis of aluminum nanopowder was simulated. Comparison of model predictions with the available experimental data showed good agreement under different operating conditions without the need of adjustable parameters. For modeling the flash ironmaking reactor, experiments reported in the literature for a nonpremixed hydrogen je t flame were simulated for validation. Model predictions showed good agreement with gas temperature and species concentrations measurements. The model was used to design a nonpremixed hydrogen-oxygen burner. The distributions of velocity, temperature, and species concentrations, and the trajectories of iron oxide concentrate particles in a lab flash reactor were computed and analyzed

Utilizing Shear Factor Model and Adding Viscosity Term in Improving a Two-Dimensional Model of Fluid Flow in Non Uniform Porous Media

In a packed bed catalytic reactor, the fluid flow phenomena are very complicated because the fluid and solid particle interactions dissipate the energy. The governing equations  were developed in the  forms of  specific  models. The shear factor  model was introduced in the momentum equation for covering the effect  of  flow  and  solid  interactions  in  porous  media.   A  two  dimensional numerical  solution  for  this  kind  of  flow  has  been  constructed  using  the  finite volume  method.  The  porous  media  porosity  was  treated  as  non-uniform distribution  in  the  radial  direction.  Experimentally,  the  axial  velocity  profiles produce  the  trend  of  having  global  maximum  and  minimum  peaks  at  distance very close to the wall. This trend is also accurately picked up by the numerical result. A more comprehensive shear factor formulation results a better velocity prediction than other correlations do. Our derivation on the presence of porous media leads to an additional viscosity term. The effect of this additional viscosity term was investigated numerically. It is found that the additional viscosity term improves  the  velocity  prediction  for  the  case  of  higher  ratio  between  tube  and particle diameter

The application of a time delay model to chemical engineering operations

Methods are developed for describing flow and transport phenomena in chemical process equipment in terms of random time delays that are undergone by material or energy elements in passing through the process. It is shown how these methods may be applied to typical chemical engineering processes including exchange processes in packed beds, distillation and multiple reactions in complex flow regimes. A new mixing concept, dynamic dispersion, is defined which may be used to account, in a formal way, for the disparity that sometimes exists between the behaviour of a process in the steady state and predictions based on the axial dispersion concept

Experimental study of natural convection heat transfer and gaseous dynamics from dual-channel circulation loop

This research focuses on establishing a range of scaled separate and integral effects experiments for studying thermal-hydraulic behavior occurring within a component or region of the prismatic very high-temperature reactor (VHTR) such as plenum-to-plenum heat transfer and gaseous dynamics during natural circulation. Natural circulation of the coolant is the leading capability for VHTR to transport the decay heat from the core to the reactor vessel during accident scenarios. To address this need, a scaled-down facility is designed and developed with only two channels with upper and lower plena. The emphasis is placed on high-resolution and high-fidelity experimental data for local heat transfer and gaseous dispersion measurements utilizing sophisticated techniques under different operating conditions. These techniques are 1) non-invasive flush wall mounted heat transfer coefficient probe to measure reliably the heat flux and surface temperature along the flow channels, and by measuring simultaneously these two variables and the flowing fluid, the heat transfer coefficient can be obtained, 2) radial temperature sensor adjuster to measure radial temperature variations of the coolant along the flow channels, and 3) advanced gaseous tracer technique to accurately measure the residence time distribution (RTD) in an of flow systems by injecting pulse change gas tracer and then monitoring its concentration at the exit. The measured RTD is utilized to quantify the gas dispersion and identify the degree of mixing in the system. The obtained local heat transfer and gaseous dispersion data in this study will provide high spatial and temporal resolutions benchmarking data for validating heat transfer and gaseous dispersion computations and correlations that are integrated with CFD simulations --Abstract, page iv