Liquid metal turbulent flow dynamics in a cylindrical container with free surface: experiment and numerical analysis

The liquid metal flow in induction crucible models is known to be unstable, turbulent and difficult to predict in the regime of medium frequencies when the electromagnetic skin-layer is of considerable extent. We present long term turbulent flow measurements by a permanent magnet incorporated potential difference velocity probe in a cylindrical container filled with eutectic melt In-Ga-Sn. The parallel numerical simulation of the long time scale development of the turbulent average flow is presented. The numerical flow model uses an implicit pseudo-spectral code and k-w turbulence model, which was recently developed for the transitional flow modelling. The results compare reasonably to the experiment and demonstrate the time development of the turbulent flow field and the turbulence energy.

Liquid metal turbulent flow dynamics in a cylindrical container with free surface: experiment and numerical analysis

The liquid metal flow in inducation crucible models is known to be higly unstable and turbutlen in the regim e of medium frequecies when the elctronmagnetic skin-layer is of considerable extent. We present long term turbulent flow measurements by a permanent magnet incorporated potential difference veolocity probe in a cylindirical container filled with eutecti mlt In-Ga-SN. The parallel numerical simulation of the long time scale development of the turbulen average flow is presented. The numerical lfow model uses a pseud-spectral code and k-w turbulence model, which was recently developed for the transitional flow modelling. The result compare reasonably to the experiment and demonstrate the time development of the turbulent flow field.

Thermoelectric MHD in dendritic solidification

The effects of a constant uniform magnetic field on dendritic solidification were investigated using an enthalpy based numerical model. The interaction between thermoelectric currents on a growing crystal and the magnetic field generates a Lorentz force that creates flow. The need for very high resolution at the liquid-solid boundary where the thermoelectric source originates plus the need to accommodate multiple grains for a realistic simulation, make this a very demanding computational problem. For practical simulations, a quasi 3-dimensional approximation is proposed which nevertheless retains essential elements of transport in the third dimension. A magnetic field normal to the plane of growth leads to general flow circulation around an equiaxed dendrite, with secondary recirculations between the arms. The heat/solute advection by the flow is shown to cause a change in the morphology of the dendrite; secondary growth is promoted preferentially on one side of the dendrite arm and the tip velocity of the primary arm is increased. The degree of approximation introduced is quantified by extending the model into 3-dimensions, where the full Navier-Stokes equation is solved, and compared against the 2-dimensional solution.

Development of a model to predict the life of pneumatic conveyor bends subject to erosive wear

The erosion processes resulting from flow of fluids (gas-solid or liquid-solid) are encountered in nature and many industrial processes. The common feature of these erosion processes is the interaction of the fluid (particle) with its boundary thus resulting in the loss of material from the surface. This type of erosion in detrimental to the equipment used in pneumatic conveying systems. The puncture of pneumatic conveyor bends in industry causes several problems. Some of which are: (1) Escape of the conveyed product causing health and dust hazard; (2) Repairing and cleaning up after punctures necessitates shutting down conveyors, which will affect the operation of the plant, thus reducing profitability. The most common occurrence of process failure in pneumatic conveying systems is when pipe sections at the bends wear away and puncture. The reason for this is particles of varying speed, shape, size and material properties strike the bend wall with greater intensity than in straight sections of the pipe. Currently available models for predicting the lifetime of bends are inaccurate (over predict by 80%. The provision of an accurate predictive method would lead to improvements in the structure of the planned maintenance programmes of processes, thus reducing unplanned shutdowns and ultimately the downtime costs associated with these unplanned shutdowns. This is the main motivation behind the current research. The paper reports on two aspects of the first phases of the study-undertaken for the current project. These are (1) Development and implementation; and (2) Testing of the modelling environment. The model framework encompasses Computational Fluid Dynamics (CFD) related engineering tools, based on Eulerian (gas) and Lagrangian (particle) approaches to represent the two distinct conveyed phases, to predict the lifetime of conveyor bends. The method attempts to account for the effect of erosion on the pipe wall via particle impacts, taking into account the angle of attack, impact velocity, shape/size and material properties of the wall and conveyed material, within a CFD framework. Only a handful of researchers use CFD as the basis of predicting the particle motion, see for example [1-4] . It is hoped that this would lead to more realistic predictions of the wear profile. Results, for two, three-dimensional test cases using the commercially available CFD PHOENICS are presented. These are reported in relation to the impact intensity and sensitivity to the inlet particle distributions.

Computational issues in the modelling of materials-based manufacturing processes

The manufacture of materials products involves the control of a range of interacting physical phenomena. The material to be used is synthesised and then manipulated into some component form. The structure and properties of the final component are influenced by both interactions of continuum-scale phenomena and those at an atomistic-scale level. Moreover, during the processing phase there are some properties that cannot be measured (typically the liquid-solid phase change). However, it seems there is a potential to derive properties and other features from atomistic-scale simulations that are of key importance at the continuum scale. Some of the issues that need to be resolved in this context focus upon computational techniques and software tools facilitating: (i) the multiphysics modeling at continuum scale; (ii) the interaction and appropriate degrees of coupling between the atomistic through microstructure to continuum scale; and (iii) the exploitation of high-performance parallel computing power delivering simulation results in a practical time period. This paper discusses some of the attempts to address each of the above issues, particularly in the context of materials processing for manufacture.

Mechanism of motion of an optical fiber aligned by a solder droplet

Solder is often used as an adhesive to attach optical fibers to a circuit board. In this proceeding we will discuss efforts to model the motion of an optical fiber during the wetting and solidification of the adhesive solder droplet. The extent of motion is determined by several competing forces, during three “stages” of solder joint formation. First, capillary forces of the liquid phase control the fiber position. Second, during solidification, the presence of the liquid-solid-vapor triple line as well as a reduced liquid solder volume leads to a change in the net capillary force on the optical fiber. Finally, the solidification front itself impinges on the fiber. Publicly-available finite element models are used to calculate the time-dependent position of the solidification front and shape of the free surface.

Multiscale modeling of the onset of freckle formation during vacuum arc remelting

A multiscale model for the Vacuum Arc Remelting process (VAR) was developed to simulate dendritic microstructures during solidification and investigate the onset of freckle formation. On the macroscale, a 3D multi-physics model of VAR was used to study complex physical phenomena, including liquid metal flow with turbulence, heat transfer, and magnetohydrodynamics. The results showed that unsteady fluid flow in the liquid pool caused significant thermal perturbation at the solidification front. These results were coupled into a micromodel to simulate dendritic growth controlled by solute diffusion, including local remelting. The changes in Rayleigh number as the microstructure remelts was quantified to provide an indicator of when fluid flow channels (i.e. freckles) will initiate in the mushy zone. By examining the simulated microstructures, it was found that the Rayleigh number increased more than 300 times during remelting, which suggests that thermal perturbation could be responsible for the onset of freckle formation.

Effect of bend orientation on life and puncture point location due to solid particle erosion of a high concentration flow in pneumatic conveyors

An investigation into predicting failure of pneumatic conveyor pipe bends due to hard solid particle impact erosion has been carried out on an industrial scale test rig. The bend puncture point locations may vary with many factors. However, bend orientation was suspected of being a main factor due to the biased particle distribution pattern of a high concentration flow. In this paper, puncture point locations have been studied with different pipe bend orientations and geometry (a solids loading ratio of 10 being used for the high concentration flow). Test results confirmed that the puncture point location is indeed most significantly influenced by the bend orientation (especially for a high concentration flow) due to the biased particle distribution and biased particle flux distribution.

Modeling the diffusion of solid copper into liquid solder alloys

During the soldering process, the copper atoms diffuse into liquid solders. The diffusion process determines integrity and the reworking possibility of a solder joint. In order to capture the diffusion scenarios of solid copper into liquid Sn–Pb and Sn–Cu solders, a computer modeling has been performed for 10 s. An analytical model has also been proposed for calculating the diffusion coefficient of copper into liquid solders. It is found that the diffusion coefficient for Sn–Pb solder is 2.74 × 10− 10 m2/s and for Sn–Cu solder is 6.44 × 10−9 m2/s. The modeling results reveal that the diffusion coefficient is one of the major factors that govern the rate at which solid Cu dissolve in the molten solder. The predicted dissolved amounts of copper into solders have been validated with the help of scanning electron microscopic analysis.

The development of dynamic CFD model of the magnetic semi-levitation of liquid metals

In the casting of reactive metals, such as titanium alloys, contamination can be prevented if there is no contact between the hot liquid metal and solid crucible. This can be achieved by containing the liquid metal by means of high frequency AC magnetic field. A water cooled current-carrying coil, surrounding the metal can then provide the required Lorentz forces, and at the same time the current induced in the metal can provide the heating required to melt it. This ‘attractive’ processing solution has however many problems, the most serious being that of the control and containment of the liquid metal envelope, which requires a balance of the gravity and induced inertia forces on the one side, and the containing Lorentz and surface tension forces on the other. To model this process requires a fully coupled dyna ic solution of the flow fields, magnetic field and heat transfer/melding process to account for. A simplified solution has been published previously providing quasi-static solutions only, by taking the irrotational ‘magnetic pressure’ term of the Lorentz force into account. The authors remedy this deficiency by modelling the full problem using CFD techniques. The salient features of these techniques are included in this paper, as space allows.

Mathematical modelling of the solidification of liquid tin with electromagnetic stirring

It is well known that during alloy solidification, convection currents close to the so-lidification front have an influence on the structure of dendrites, the local solute concentration, the pattern of solid segregation, and eventually the microstructure of the casting and hence its mechanical properties. Controlled stirring of the melt in continuous casting or in ingot solidification is thought to have a beneficial effect. Free convection currents occur naturally due to temperature differences in the melt and for any given configuration, their strength is a function of the degree of superheat present. A more controlled forced convection current can be induced using electro-magnetic stirring. The authors have applied their Control-Volume based MHD method [1, 2] to the problem of tin solidification in an annular crucible with a water-cooled inner wall and a resistance heated outer one, for both free and forced convection situations and for various degrees of superheat. This problem was studied experimentally by Vives and Perry [3] who obtained temperature measurements, front positions and maps of electro-magnetic body force for a range of superheat values. The results of the mathematical model are compared critically against the experimental ones, in order to validate the model and also to demonstrate the usefulness of the coupled solution technique followed, as a predictive tool and a design aid. Figs 6, refs 19.

Dynamics of an axisymmetric electromagnetic ‘crucible’ melting

Different industrial induction melting processes involve free surface and melt-solid interface of the liquid metal subject to dynamic change during the technological operation. Simulation of the liquid metal dynamics requires to solve the non-linear, coupled hydrodynamic-electromagnetic-heat transfer problem accounting for the time development of the liquid metal free boundary with a suitable turbulent viscosity model. The present paper describes a numerical solution method applicable for various axisymmetric induction melting processes, such as, crucible with free top surface, levitation, semi-levitation, cold crucible and similar melting techniques. The presented results in the cases of semi-levitation and crucible with free top surface meltings demonstrate oscillating transient behaviour of the free metal surface indicating the presence of gravity-inertial-electromagnetic waves which are coupled to the internal fluid flow generated by both the rotational and potential parts of the electromagnetic force.

The numerical simulation of fire spread within a compartment using an integrated gas and solid phase combustion model

An integrated fire spread model is presented in this study including several sub-models representing different phenomena of gaseous and solid combustion. The integrated model comprises of the following sub-models: a gaseous combustion model, a thermal radiation model that includes the effects of soot, and a pyrolysis model for charring combustible solids. The interaction of the gaseous and solid phases are linked together through the boundary conditions of the governing equations for the flow domain and the solid region respectively. The integrated model is used to simulate a fire spread experiment conducted in a half-scale test compartment. Good qualitative and reasonable quantitative agreement is achieved between the experiment and numerical predictions.

CFD approach for solid mechanics analysis

A cell-centred finite volume(CC-FV) solid mechanics formulation, based on a computational fluid dynamics(CFD) procedure, is presented. A CFD code is modified such that the velocity variable is used as to the displacement variable. Displacement and pressure fields are considered as unknown variables. The results are validated with finite element(FE) and cell-vertex finite volume(CV-FV) predictions based on discretisation of the equilibrium equations. The developed formulation is applicable for both compressible and incompressible solids behaviour. The method is general and can be extended for the simultaneous analysis of problems involving flow-thermal and stress effects.

Modelling induction melting energy savings

Electromagnetic processing of liquid metals involves dynamic change of the fluid volume interfacing with a melting solid material, gas or vacuum, and possibly a different liquid. Electromagnetic field and the associated force field are strongly coupled to the free surface dynamics and the heat-mass transfer. We present practical modelling examples of the flow and heat transfer using an accurate pseudo-spectral code and the k-omega turbulence model suitable for complex and transitional flows with free surfaces. The 'cold crucible' melting is modelled dynamically including the melting front gradual propagation and the magnetically confined free surrounding interface. Intermittent contact with the water-cooled segmented wall and the radiation heat losses are parts of the complex problem.