Computational modelling of bubbles, droplets and particles in metals reduction and refining

A multi-phase framework is typically required for the CFD modelling of metals reduction processes. Such processes typically involve the interaction of liquid metals, a gas (often air) top space, liquid droplets in the top space and injection of both solid particles and gaseous bubbles into the bath. The exchange of mass, momentum and energy between the phases is fundamental to these processes. Multi-phase algorithms are complex and can be unreliable in terms of either or both convergence behaviour or in the extent to which the physics is captured. In this contribution, we discuss these multi-phase flow issues and describe an example of each of the main “single phase” approaches to modelling this class of problems (i.e., Eulerian–Lagrangian and Eulerian–Eulerian). Their utility is illustrated in the context of two problems – one involving the injection of sparging gases into a steel continuous slab caster and the other based on the development of a novel process for aluminium electrolysis. In the steel caster, the coupling of the Lagrangian tracking of the gas phase with the continuum enables the simulation of the transient motion of the metal–flux interface. The model of the electrolysis process employs a novel method for the calculation of slip velocities of oxygen bubbles, resulting from the dissolution of alumina, which allows the efficiency of the process to be predicted.

Numerical simulation of incompressible flow problems using an unstructured staggered mesh method

A number of two dimensional staggered unstructured discretisation schemes for the solution of fluid flow and heat transfer problems have been developed. All schemes store and solve velocity vector components at cell faces with scalar variables solved at cell centres. The velocity is resolved into face-normal and face-parallel components and the various schemes investigated differ in the treatment of the parallel component. Steady-state and time-dependent fluid flow and thermal energy equations are solved with the well known pressure correction scheme, SIMPLE, employed to couple continuity and momentum. The numerical methods developed are tested on well known benchmark cases: the Lid-Driven Cavity, Natural Convection in a Cavity and Melting of Gallium in a rectangular domain. The results obtained are shown to be comparable to benchmark, but with accuracy dependent on scheme selection.

Modelling metal powder production by the gas atomisation process

Metal powder in the range of 10-100 microns is widely employed in the production of Raney nickel type catalysts for hydrogenation reactions and hydrogen fuel cell manufacture. In this presentation we examine the modelling of powder production in a gas atomisation vessel using CFD techniques. In a fully coupled Lagrangian-Eulerian two phase scheme, liquid meal particles are tracked through the vessel following atomisation of a liquid nickel-aluminium stream. There is full momentum, heat and turbulence transport between particles and surrounding argon gas and the model predicts the position of solidification depending on particle size and undercooled condition. Maps of collision probability of particles at different stages of solidification are computed, to predict the creation of satellite defects, or to initiate solidification of undercooled droplets. The model is used to support experimental work conducted under the ESA/EU project IMPRESS.

Levitated liquid droplets in AC and DC magnetic field

Electromagnetic levitation of liquid metal droplets can be used to measure the properties of highly reactive liquid materials. Two independent numerical models, the commercial COMSOL and the spectral-collocation based free surface code SPHINX, have been applied to solve the transient electromagnetic, fluid flow and thermodynamic equations, which describe the levitated liquid motion and heating processes. The SPHINX model incorporates free surface deformation to accurately model the oscillations that result from the interaction between the electromagnetic and gravity forces, temperature dependent surface tension, magnetically controlled turbulent momentum transport. The models are adapted to incorporate periodic laser heating at the top of the droplet, which is used to measure the thermal conductivity of the material. Novel effects in the levitated droplet of magnetically damped turbulence and nonlinear growth of velocities in high DC magnetic field are analysed.

Magnetic damping of levitated liquid droplets in AC and DC field

The intense AC magnetic field required to produce levitation in terrestrial conditions, along with the buoyancy and thermo-capillary forces, results in turbulent convective flow within the droplet. The use of a homogenous DC magnetic field allows the convective flow to be damped. However the turbulence properties are affected at the same time, leading to a possibility that the effective turbulent damping is considerably reduced. The MHD modified K-Omega turbulence model allows the investigation of the effect of magnetic field on the turbulence. The model incorporates free surface deformation, the temperature dependent surface tension, turbulent momentum transport, electromagnetic and gravity forces. The model is adapted to incorporate a periodic laser heating at the top of the droplet, which have been used to measure the thermal conductivity of the material by calculating the phase lag between the frequency of the laser heating and the temperature response at the bottom. The numerical simulations show that with the gradual increase of the DC field the fluid flow within the droplet is initially increasing in intensity. Only after a certain threshold magnitude of the field the flow intensity starts to decrease. In order to achieve the flow conditions close to the ‘laminar’ a D.C. magnetic field >4 Tesla is required to measure the thermal conductivity accurately. The reduction in the AC field driven flow in the main body of the drop leads to a noticeable thermo-capillary convection at the edge of the droplet. The uniform vertical DC magnetic field does not stop a translational oscillation of the droplet along the field, which is caused by the variation in total levitation force due to the time-dependent surface deformation.

A note on the prediction of liquid hold-up with the stratified roll wave regime for gas/liquidco-current flow in horizontal pipes.

This note presents a simple model for prediction of liquid hold-up in two-phase horizontal pipe flow for the stratified roll wave (St+RW) flow regime. Liquid hold-up data for horizontal two-phase pipe flow [1, 2, 3, 4, 5 and 6] exhibit a steady increase with liquid velocity and a more dramatic fall with increasing gas rate as shown by Hand et al. [7 and 8] for example. In addition the liquid hold-up is reported to show an additional variation with pipe diameter. Generally, if the initial liquid rate for the no-gas flow condition gives a liquid height below the pipe centre line, the flow patterns pass successively through the stratified (St), stratified ripple (St+R), stratified roll wave, film plus droplet (F+D) and finally the annular (A+D, A+RW, A+BTS) regimes as the gas rate is increased. Hand et al. [7 and 8] have given a detailed description of this progression in flow regime development and definitions of the patterns involved. Despite the fact that there are over one hundred models which have been developed to predict liquid hold-up, none have been shown to be universally useful, while only a handful have proven to be applicable to specific flow regimes [9, 10, 11 and 12]. One of the most intractable regimes to predict has been the stratified roll wave pattern where the liquid hold-up shows the most dramatic change with gas flow rate. It has been suggested that the momentum balance-type models, which give both hold-up and pressure drop prediction, can predict universally for all flow regimes but particularly in the case of the difficult stratified roll wave pattern. Donnelly [1] recently demonstrated that the momentum balance models experienced some difficulties in the prediction of this regime. Without going into lengthy details, these models differ in the assumed friction factor or shear stress on the surfaces within the pipe particularly at the liquid–gas interface. The Baker–Jardine model [13] when tested against the 0.0454 m i.d. data of Nguyen [2] exhibited a wide scatter for both liquid hold-up and pressure drop as shown in Fig. 1. The Andritsos–Hanratty model [14] gave better prediction of pressure drop but a wide scatter for liquid hold-up estimation (cf. Fig. 2) when tested against the 0.0935 m i.d. data of Hand [5]. The Spedding–Hand model [15], shown in Fig. 3 against the data of Hand [5], gave improved performance but was still unsatisfactory with the prediction of hold-up for stratified-type flows. The MARS model of Grolman [6] gave better prediction of hold-up (cf. Fig. 4) but deterioration in the estimation of pressure drop when tested against the data of Nguyen [2]. Thus no method is available that will accurately predict liquid hold-up across the whole range of flow patterns but particularly for the stratified plus roll wavy regime. The position is particularly unfortunate since the stratified-type regimes are perhaps the most predominant pattern found in multiphase lines.

Double-electron above threshold ionization of helium

We present calculations of intense-field multiphoton ionization processes in helium at XUV wavelengths. The calculations are obtained from a full-dimensional integration of the two-electron time-dependent Schrödinger equation. A momentum-space analysis of the ionizing two-electron wavepacket reveals the existence of double-electron above threshold ionization (DATI). In momentum-space two distinct forms of DATI are resolved, namely non-sequential and sequential. In non-sequential DATI correlated electrons resonantly absorb and share energy in integer units of Ïlaser.

Positronium scattering by Ne, Ar, Kr and Xe in the frozen target approximation

A full-electron coupled-state treatment of positronium (Ps)- inert gas scattering is developed within the context of the frozen target approximation. Calculations are performed for Ps(Is) scattering by Ne and Ar in the impact energy range 0-40 eV using coupled pseudostate expansions consisting of nine and 22 Ps states. The purpose of the pseudostates is primarily to represent ionization of the Ps which is found to be a major process at the higher energies. First Born estimates of target excitation are used to complement the frozen target results. The available experimental data are discussed in detail. It is pointed out that the very low energy measurements (less than or equal to2 eV) correspond to the momentum transfer cross section sigma(mom) and not to the elastic cross section sigma(el). Calculation shows that sigma(mom), and sigma(el) diverge very rapidly with increasing energy and consequently comparisons of the low-energy data with ITel can be very misleading. Agreement between the calculations and the low-energy measurements of anion as well;as higher energy (greater than or equal to15 eV) beam measurements of the total cross section, is less than satisfactory. Results for Ps(1s) scattering by Kr and Xe in the static-exchange approximation are also presented.

Spin asymmetries in spatially resolved processes of ionization of heavy atoms by relativistic electrons

The triple-differential cross section for ionization of a heavy atom is shown to depend on the spin of the incident electron even if this is polarized entirely parallel or antiparallel to its direction of propagation, the atom is unpolarized, and the spins of the ejected electrons are not resolved. Quantitative predictions for the spin asymmetry are presented in a relativistic distorted-wave Born approximation. Simple physical models are introduced to understand both these results and further symmetry properties involving the reversal of a spatial momentum component also.

Triply differential single ionization cross sections in coplanar and non-coplanar geometry for fast heavy ion-atom collisions

We have performed a kinematically complete experiment and calculations on single ionization in 100 MeV/amu C6+ + He collisions. For electrons ejected into the scattering plane (defined by the initial and final projectile momentum vectors) our first- and higher-order calculations are in good agreement with the data. In the plane perpendicular to the scattering plane and containing the initial projectile axis a strong forward-backward asymmetry is observed. In this plane both the first-order and the higher-order calculations do not provide good agreement neither with the data nor amongst each other.

Electron impact excitation of A1 XIII: A relativistic approach

Energy levels, radiative rates, collision strengths, and effective collision strengths for all transitions up to and including the n = 5 levels of AlXIII have been computed in the j j coupling scheme including relativistic effects. All partial waves with angular momentum J less than or equal to 60 have been included, and resonances have been resolved in a fine energy grid in the threshold region. Collision strengths are tabulated at energies above thresholds in the range 170.0 less than or equal to E less than or equal to 300.0 Ryd, and results for effective collision strengths, obtained after integrating the collision strengths over a Maxwellian distribution of electron velocities, are tabulated over a wide temperature range of 4.4 less than or equal to log T-e less than or equal to 6.8 K. The importance of including relativistic effects in a calculation is discussed in comparison with the earlier available non-relativistic results.

Electron impact excitation of Al XIII: Collision strengths and rate coefficients

Collision strengths for all transitions up to and including the n = 5 levels of Al XIII have been computed in the LS coupling scheme using the R-matrix code. All partial waves with angular momentum L less than or equal to 45 have been included, and resonances have been resolved in a fine energy grid in the threshold region. Collision strengths are tabulated at energies above thresholds in the range 162.30 less than or equal to E less than or equal to 220.0 Ry, and results for the 1s-2s and 1s-2p transitions are compared with those of previous authors. Additionally, effective collision strengths, obtained after integrating the collision strengths over a Maxwellian distribution of electron velocities, are tabulated over a wide temperature range of 4.40 less than or equal to log T-e less than or equal to 6.40 K.

Energy dependence for pair production with electron capture in relativistic heavy-ion collisions

In 'Charge transfer from the negative-energy continuum: alternative mechanism for pair production in relativistic atomic collisions', Eichler (1995 Phys. Rev. Lett. 75 3653) proposes an alternative mechanism for capture by pair production, and from it derives an analytic expression for the total cross section with a surprisingly strong energy dependence. We show that, in fact, there is no alternative mechanism; rather the above mechanism may be more transparently viewed as an ionization-like transition in one centre with inclusion of continuum distortion by the second centre. We further show that to Centre the initial and final states on the target and projectile leads to confusion in the momentum transfer vectors, and hence, respectively that the alleged high-energy behaviour is erroneous.

Plane wave and Coulomb asymptotics

A simple plane wave solution of the Schrodinger-Helmholtz equation is a quantum eigenfunction obeying both energy and linear momentum correspondence principles. Inclusion of the outgoing wave with scattering amplitude f asymptotic development of the plane wave, we show that there is a problem with angular momentum when we consider forward scattering at the point of closest approach and at large impact parameter given semiclassically by (l + 1/2)/k where l is the azimuthal quantum number and may be large (J. Leech et al., Phys. Rev. Lett. 88. 257901 (2002)). The problem is resolved via non- uniform, non-standard analysis involving the Heaviside step function, unifying classical, semiclassical and quantum mechanics, and the treatment is extended to the case of pure Coulomb scattering.

Chemical abundances and winds of massive stars in M31: a B-type supergiant and a WC star in OB 10

We present high quality spectroscopic data for two massive stars in the OB 10 association of M31, OB 10-64 (B0 la) and OB 10-WRI (WC6). Medium resolution spectra of both stars were obtained using the ISIS spectrograph on the William Herschel Telescope. This is supplemented with Hubble Space Telescope STIS UV spectroscopy and Keck I HIRES data for OB 10-64. A non- local thermodynamic equilibrium (LTE) model atmosphere and abundance analysis for OB 10-64 is presented, indicating that this star has similar photospheric CNO, Mg and Si abundances to solar neighbourhood massive stars. A wind analysis of this early B-type supergiant reveals a mass-loss rate of (M)over dot = 1.6 x 10(-6) M-circle dot yr(-1), and v(infinity) = 1650 km s(-1). The corresponding wind momentum is in good agreement with the wind momentum-luminosity relationship found for Galactic early-B supergiants. Observations of OB 10-WRI are analysed using a non-LTE, line-blanketed code, to reveal approximate stellar parameters of log L/L-circle dot similar to 5.7, T-* - 75 kK, v(infinity) similar to 3000 km s(-1), (M)over dot/(M-circle dot yr(-1)) similar to 10(-4.3) adopting a clumped wind with a filling factor of 10 per cent. Quantitative comparisons are made with the Galactic WC6 star HD 92809 (WR23) revealing that OB 10-WR1 is 0.4 dex more luminous, though it has a much lower C/He ratio (similar to0.1 versus 0.3 for HD 92809). Our study represents the first detailed, chemical model atmosphere analysis for either a B-type supergiant or a Wolf- Rayet (WR) star in Andromeda, and shows the potential of how such studies can provide new information on the chemical evolution of galaxies and the evolution of massive stars in the local Universe.