van Wpm Wim Swaaij

Hydrodynamic modelling of dense gas-fluidised beds using the kinetic theory of granular flow: effect of coefficient of restitution on bed dynamics

A radio frequency (RF) glow discharge plasma etch electrode design is disclosed which is capable of creating high power density plasma with uniform etch rates, while providing access for automatic loading semiconductor wafers from outside of the plasma region. The electrode assembly comprises of an electrode to which RF energy is applied surrounded by an insulator, which in turn surrounded a grounded surface all of which have cylindrical symmetry. When placed a small distance from a flat, grounded substrate, the electrode assembly creates a volume which can effectively combine a high power density plasma, while maintaining a sufficient channel for pumping a gas flow and for observing the plasma optically. The same channel is widened for automatic transport of semiconductor wafers from outside of the plasma reactor chamber. Such confined high power density plasma are important for high rate, uniform, anisotropic etching, especially for silicon dioxide.

Dynamic simulation of dispersed gas-liquid two-phase flow using a discrete bubble model.

In this paper a detailed hydrodynamic model for gas-liquid two-phase flow will be presented. The model is based on a mixed Eulerian-Lagrangian approach and describes the time-dependent two-dimensional motion of small, spherical gas bubbles in a bubble column operating in the homogeneous regime. The motion of these bubbles is calculated from a force balance for each individual bubble, accounting for all relevant forces acting on them. Contributions from liquid-phase pressure gradient, drag, virtual mass, liquid-phase vorticity and gravity are considered, whereas direct bubble-bubble interactions are accounted for via an interaction model resembling the collision model developed by Hoomans et al. (1996) to model gas-fluidized beds. The liquid-phase hydrodynamics are described using the volume-averaged, unsteady, Navier-Stokes equations. A preliminary model validation has been performed by comparing the computational results with experimental observations published previously in literature by various authors. The model is shown to predict correctly the motion of a bubble plume in a pseudo-two-dimensional bubble column operated at different superficial gas velocities, provided that a detailed description of the bubble dynamics is incorporated in the model. The effect of bubble column aspect ratio on the hydrodynamic behaviour of the column has also been investigated. Our model predicts the effect of aspect ratio on the flow structure in the bubble column. The importance of the various forces acting on the bubbles will also be discussed and it will be shown that the added mass force and the lift force cannot be neglected in bubble column simulation. Finally, the model has been used to study the start-up behaviour of a two-dimensional bubble column. It will be shown that the history of the gas-liquid two-phase flow significantly affects the flow structure ultimately obtained in a bubble column. This finding has, to our knowledge, not been reported before in literature.

Granular dynamics simulation of segregation phenomena in bubbling gas-fluidised beds

A hard-sphere discrete particle model of a gas-fluidised bed was used in order to simulate segregation phenomena in systems consisting of particles of different sizes. In the model, the gas-phase hydrodynamics is described by the spatially averaged Navier?Stokes equations for two-phase flow. For each solid particle, the Newtonian equations of motion are solved taking into account the inter-particle and particle?wall collisions. The (2D) model was applied to a binary system consisting of particles of equal density, but different sizes where the homogeneous gas inflow velocity was equal to the minimum fluidisation velocity of the bigger particles. Segregation was observed over a time scale of several seconds although it did not become complete due to the continuous back mixing of the bigger particles by the bubbles. An analysis of the dynamics of the segregation in terms of mass fraction distributions is presented. When the particle?particle and particle?wall interactions were assumed to be perfectly elastic and perfectly smooth, segregation occurred very fast and was almost complete due to the absence of bubbles

Computer simulation of the hydrodynamics of a two-dimensional gas-fluidized bed

A first principles model of a gas-fluidized bed has been applied to calculate the hydrodynamics of a two-dimensional (2-D) bed with an orifice in the middle of a porous plate distributor. The advanced hydrodynamic model is based on a two fluid model approach in which both phases are considered to be continuous and fully interpenetrating. Conservation equations for mass, momentum and thermal energy have been solved numerically by a finite difference technique on a mini-computer. Our computer model calculates the porosity, the pressure, the fluidum phase temperature, the solid phase temperature and the velocity fields of both phases in 2-D Cartesian or axisymmetrical cylindrical coordinates. The new feature of the present model is the incorporation of Newtonian behaviour in the gas and solid phases. Our preliminary calculations indicate that the sensitivity of the computed bubble size with respect to the bed rheology (i.e. the solid phase viscosity) is quite small. However the bubble shape appears to be much more sensitive to the bed rheology. Results of the calculations have been compared with data obtained from an experimental cold-flow model (height: 1000 mm, width: 570 mm, depth: 15 mm).

Computational fluid dynamics applied to gas-liquid contactors

In this paper a `hierarchy of models? is discussed to study the fluid dynamic behaviour of gas-liquid bubble columns. This `hierarchy of models? consists of a Eulerian-Eulerian two fluid model, a Eulerian-Lagrangian discrete bubble model and a Volume Tracking or Marker Particle model. These models will be briefly reviewed and their advantages and disadvantages will be highlighted. In addition, a mixed Eulerian-Lagrangian model and a volume tracking model, both developed at Twente University, will be discussed. Some selected results obtained with these models will be presented with emphasis on the results obtained with the volume tracking model. Finally, a brief discussion on advanced experimental techniques, which reflect the recent progress in experimental fluid dynamics, will be presented

Mass transfer with complex reversible chemical reactions—II. parallel reversible chemical reactions

An absorption model has been developed which can be used to calculate rapidly absorption rates for the phenomenon mass transfer accompanied by multiple complex parallel reversible chemical reactions. This model can be applied for the calculation of the mass transfer rates, enhancement factors and concentration profiles for a wide range of processes and conditions, for both film and penetration model. With the aid of this mass transfer model it is demonstrated that the absorption rates in systems with multiple reversible reactions can be substantially greater than the summation of the absorption rates derived for the single systems. This latter fact provides a scientific basis for the application of aqueous mixed amine solutions for industrial sour gas treating. Also it is shown that for kinetic studies by means of absorption experiments for reversible reactions the presence of small amounts of fast reacting contaminants can have an overruling effect on the outcome of the determination of the reaction kinetics. It is shown that the concepts of shuttle mechanism and homogeneous catalysis refer to asymptotic situations, for practical situations intermediate behaviour was observed which was previously not accessible for analysis. Experimentally determined absorption rates of CO, in aqueous solutions of various mixtures of alkanolamines (MMEA-MDEA, MEA-MDEA, DIPA-MDEA and MEA-DEA-MDEA) can be predicted extremely well for the several mass transfer regimes which were studied experimentally. The experiments were carried out in a stirred vessel with a flat surface over a wide range of process conditions.

A three-demensional CFD model for gas-liquid bubble columns.

This paper discusses the development of a three-dimensional Euler?Lagrange CFD model for a gas?liquid bubble column. The model resolves the time-dependent, three-dimensional motion of small, spherical gas bubbles in a liquid. Our model incorporates all relevant forces acting on a bubble rising in a liquid, and accounts for two-way momentum coupling between the phases. The liquid-phase hydrodynamics are described using the volume-averaged Navier?Stokes equations for laminar flow. This three-dimensional CFD model is used to study the effect of the aspect ratio of the bubble column on the flow pattern

Dynamic simulation of gas-liquid two-phase flow: effect of column aspect ratio on the flow structure.

In this paper an Eulerian/Lagrangian model, describing the hydrodynamics of a gas-liquid bubble column, is presented. The model resolves the time dependent, two-dimensional motion of small, spherical gas bubbles in a liquid using the equation of motion. The model incorporates all relevant forces acting on a bubble as it rises through the liquid, and additionally accounts for direct bubble-bubble interactions. The liquid-phase hydrodynamics are described using the volume-averaged Navier-Stokes equations. This model is used to study the hydrodynamic behaviour of bubble columns with aspect ratios ranging from 1.0 to 11.4. In addition to these theoretical results, experimental observations are presented of the flow structure in a pseudo-two-dimensional bubble column with different aspect ratios. A clear transition in the gas-liquid flow pattern could be observed, both experimentally and theoretically, from the well-known `cooling tower? mode of circulation (L/D = 1.0) to the staggered vortices mode of circulation (L/D 2.0). The computational results clearly showed the presence of vortical structures in the liquid phase at aspect ratios exceeding 2.0. These vortical structures in the liquid phase were studied experimentally using neutrally buoyant tracer particles and streak photography. The experimentally observed vortical structures are shown to resemble the computed structures.

Measurements of solids concentration and axial solids velocity in gas-solid two-phase flows.

Several techniques reported in the literature for measuring solids concentration and solids velocity in (dense) gas-solid two-phase flow have been briefly reviewed. An optical measuring system, based on detection of light reflected by the suspended particles, has been developed to measure local solids concentration and local axial solids velocity in dense gas-solid two phase flows. This system has been applied to study hydrodynamics of a cold-flow circulating fluidized bed unit operated in the dense flow regime (uD: 7.5?15 m s?1 and Gs = 100?400 kg m?2 s?). With increasing solids mass flux, at constant superficial gas velocity, lateral solids segregation became more pronounced (i.e. extent of development of core-annulus structure) while the radial profiles of axial solids velocity hardly changed. A decrease in superficial gas velocity, at constant solids mass flux, also augmented the lateral solids segregation. The axial solids velocity decreased over the entire tube radius, although the shape of the profiles showed no strong dependence with respect to the superficial gas velocity. Average solids mass fluxes calculated from the measured local values of solids concentration and solids velocity exceeded the imposed solids mass flux, a finding which could be explained by the downflow observed visually of solid particles close to the tube wall. In addition, cross-sectional averaged solids concentrations obtained on the basis of the optical measuring system and those obtained from the pressure gradient measurements showed satisfactory agreement.

Ensemble correlation PIV applied to bubble plumes rising in a bubble column.

This paper discusses an ensemble correlation, double-exposure single-frame, particle image velocimetry (PIV) technique that can be applied to study dispersed gas?liquid two-phase flows. The essentials of this technique will be reviewed and several important issues concerning the implementation of the PIV technique will be discussed. The capabilities of the newly developed PIV technique will be demonstrated by examining the gas and liquid flow fields induced by a bubble plume rising in a rectangular bubble column.