From discretization to regularization of composite discontinuous functions

Discontinuities between distinct regions, described by different equation sets, cause difficulties for PDE/ODE solvers. We present a new algorithm that eliminates integrator discontinuities through regularizing discontinuities. First, the algorithm determines the optimum switch point between two functions spanning adjacent or overlapping domains. The optimum switch point is determined by searching for a “jump point” that minimizes a discontinuity between adjacent/overlapping functions. Then, discontinuity is resolved using an interpolating polynomial that joins the two discontinuous functions. This approach eliminates the need for conventional integrators to either discretize and then link discontinuities through generating interpolating polynomials based on state variables or to reinitialize state variables when discontinuities are detected in an ODE/DAE system. In contrast to conventional approaches that handle discontinuities at the state variable level only, the new approach tackles discontinuity at both state variable and the constitutive equations level. Thus, this approach eliminates errors associated with interpolating polynomials generated at a state variable level for discontinuities occurring in the constitutive equations. Computer memory space requirements for this approach exponentially increase with the dimension of the discontinuous function hence there will be limitations for functions with relatively high dimensions. Memory availability continues to increase with price decreasing so this is not expected to be a major limitation

Analysis of a curved buoyant jet in an enclosure using LES

The objective of this study is to investigate curved buoyant jets in an enclosure using Large Eddy Simulation (LES) methods with an Implicit Turbulent Model (ITM). To accomplish this goal, a numerical solver was written, named DREAMRTM, which is capable of solving three dimensional, transient flows using an accurate monotonic and non-oscillatory upwinding scheme. The three-dimensional Navier-Stokes equations are solved in Cartesian coordinates, with the control volume approach being implemented on a staggered grid. The numerical scheme uses a fractional time step method, with the overall spatial and temporal accuracy being second order.;In ITM simulations, there is no explicit subgrid-scale model (SGS) used for the modeling of the small scale vortical structures. ITM simulations assume that through strict conservation of the fluxing quantities in and out of the cell, the grid resolution is fully capable of capturing the important scales of the flow. The volume averaging techniques used in the ITM methods acts as an implicit subgrid-scale model, and the resolvable scales of the flow are only dependent on the grid resolution within the domain. Comparison of the available experimental data, as well as simulations that used SGS models, to the ITM simulations from DREAMRTM compare favorably for most results.;For the simulations presented in this study, oil is injected at a specified flow rate into a water filled tank, initially taken to be stagnant. Results show that the density stratification tends to damp the amount of turbulence present within the jet near the interface, but overall increases turbulence because of the acceleration of the fuel. Analysis of the curved buoyant jet shows that at an appropriate downstream location, similarity is achieved, and the energy spectrum shows the appropriate inertial subrange characteristics. Impingement of the curved buoyant jet onto the upper wall increases the amount of turbulent present within the enclosure and comparison to vertical buoyant jet simulations with comparable dimensionless parameters shows wall effects may never be completely eliminated from the analysis. Comparison between the curved buoyant jet simulations to the available experimental data from experiments performed explicitly for this study shows good agreement for the buoyant path centerline locations based on the internal densimetric Froude number. The application of these methods to immiscible fluids shows a new dimension to ITM and allows for a high resolution of the resulting flow field without the need for an explicit SGS model. Simulations for the vertical and curved buoyant jet indicate the necessity for small timesteps and increased grid resolution

A level-set model for mass transfer in bubbly flows

A level-set model is presented for simulating mass transfer or heat transfer in two-phase flows. The Navier-Stokes equations and mass transfer (or heat transfer) equation are discretized using a finite volume method on a collocated unstructured mesh, whereas a multiple marker level-set approach is used for interface capturing in bubble swarms. This method avoids the numerical coalescence of the fluid particles, whereas the mass conservation issue inherent to standard level-set methods is circumvented. Furthermore, unstructured flux-limiter schemes are used to discretize the convective term of momentum transport equation, level-set equations, and chemical species concentration equation, to avoid numerical oscillations around discontinuities, and to minimize the numerical diffusion. A convection-diffusion-reaction equation is used as a mathematical model for the chemical species mass transfer at the continuous phase. Because the mathematical analogy between dilute mass transfer and heat transfer, the same numerical model is applicable to solve both phenomena. The capabilities of this model are proved for the diffusion of chemical species from a sphere, external mass transfer in the buoyancy-driven motion of single bubbles and bubble swarms. Results are extensively validated by comparison with analytical solutions and empirical correlations from the literature.Peer ReviewedPostprint (author's final draft

A Finite Volume Model for Predicting Water Vapour Transport in Conjugate Fluid/Porous/Solid Domains

The principle aim of the presented work is to extend the capability of conjugate heat/flow models to include moisture exchange such that applications in food storage/ripening and heating, ventilation, and air conditioning (HVAC) can be simulated. To accomplish this, several modifications were made to an existing finite-volume model developed in-house. The most significant change was the implementation of a mass fraction transport equation to track the evolution of the water vapour field in all regions of the conjugate domain. This approach also required re-formulation of the energy transport model to account for a dry air/water vapour binary mixture. Developments in the porous regions are implemented using the technique of volume averaging, wherein the governing equations are considered macroscopically. A non-equilibrium approach in volume averaging the species and energy transport equations is implemented to allow more versatility for future work. This non-equilibrium versatility is beneficial over traditional equilibrium approaches, as often in agricultural or processing applications, internal moisture and temperature conditions dictate the transfer between constituents. Additionally, these conjugate domains consist of fluid-porous, fluid-solid, and porous- solid interfaces, and interface conditions between governing equations must be developed. Applications in the HVAC industry are chosen for validation, as the model is utilized to predict operating temperatures in evaporative cooling cycles, and study energy and humidity transport throughout these domains

Modelling of freeze layer formation and refractory wear in direct smelting process

The work discussed in this thesis is aimed at examining the formation of freeze layers and refractory wear on water-cooling elements within direct smelting processes through the use of computational modelling techniques. The motivation of performing this work is to examine the cooling of regions of the Smelt Reduction Vessel of the HIsmelt process closer to the molten bath material. HIsmelt is a novel process for the production of pig iron which has been under development by Rio Tinto and is now being commercialised. The previous work performed in this are has been reviewed with particular focus on the refractory wear mechanisms as the solidification algorithms have been thoroughly implemented within the Computational Fluid Dynamics (CFD) framework PHYSCIA used within this work. The governing equations along with the Finite Volume discretisations of these equations are set out within this thesis. Some comment is made about the solution methods used, and how boundary conditions are implemented. The Free-surface flow and Solidification governing relationships are also described as these are important for investigating the formation of freeze layers. The implementation of the refractory wear mechanisms are discussed in some detail. The three mechanisms implemented are for the penetration of slag into the refractory, the corrosion of the refractory by this penetrated slag; and the erosion of the refractory by the bulk flow of slag within the furnace. To be able to reasonably predict refractory wear, it is necessary to make the properties of the materials within the system temperature dependent. During the pilot plant trials at the HIsmelt® Research and Development facility, located in Kwinana Western Australia, accretions formed on the end of the solids injection lances. These accretions have been termed Elephant's Trunks. With the imminent construction of the Development Plant which injects the iron bearing feeds at an elevated temperature rather than at ambient temperatures used on the pilot plant, the formation of these pipe-like accretions under both the cold and hot injection conditions have been examined. This work provides confidence that the freeze layers predicted from the model will reflect those formed within the furnace. To evaluate the effectiveness of the refractory wear mechanisms, data from experimental and the HIsmelt pilot plant have been modelled. Sections of refractory samples from an induction furnace test and a rotary slag test have been modelled. The results are in agreement with the profile and affected regions of the sectioned refractory test pieces. A part of the HIsmelt pilot plant Smelt Reduction Vessel (SRV) has been modelled for the period of campaign 8-1 & 8-2 (just over 20 days). The predicted wear is in agreement with the measurements taken after the vessel had been cooled. To bring together freeze layer formation with the refractory wear mechanisms, a water-cooled element was modelled for the sloping slag section. The results show the growth of a small freeze layer that is consistent with the small freeze layer seen on the upper cooling panels of the pilot plant SRV. This model is an ideal tool to evaluate different water-cooling strategies for HIsmelt and other similar direct smelting processes. This work has developed models that predict the formation of freeze layers and refractory wear within direct smelting processes. The models have focused on slag-refractory interactions and further work would be needed to extend the refractory wear models to account for metal-refractory interactions. To examine spalling, stress calculations could be performed to determine when this may occur