Integrated research in constitutive modelling at elevated temperatures, part 1

Topics covered include: numerical integration techniques; thermodynamics and internal state variables; experimental lab development; comparison of models at room temperature; comparison of models at elevated temperature; and integrated software development

DYNAMIC MESHING AROUND FLUID-FLUID INTERFACES WITH APPLICATIONS TO DROPLET TRACKING IN CONTRACTION GEOMETRIES

The dynamic meshing procedure in an open source three-dimensional solver for calculating immiscible two-phase flow is modified to allow for simulations in two-dimensional planar and axisymmetric geometries. Specifically, the dynamic mesh refinement procedure, which functions only for the partitioning of three-dimensional hexahedral cells, is modified for the partitioning of cells in two-dimensional planar and axisymmetric flow simulations. Moreover, the procedure is modified to allow for computing the deformation and breakup of drops or bubbles that are very small relative to the mesh of the flow domain. This is necessary to avoid mass loss when tracking small drops or bubbles through flow fields. Three test cases are used to validate the modifications: the deformation and breakup of a two-dimensional drop in a linear shear field; the formation and detachment of drops in a two-dimensional micro T-junction channel; and an axisymmetric bubble rising from a pore into a static liquid. The tests show that the modified code performs very well, giving accurate results for much less computational time when compared to corresponding simulations without dynamic meshing. The modified code is then applied to study drop breakup conditions inside a spray nozzle when an emulsion is sprayed to produce a powder. This is done by tracking droplets of various sizes through the flow field within the nozzle and determining conditions under which they break up. The particular interest is in determining the largest drop sizes for which breakup does not occur. The effects of viscosity ratio, capillary number, shear rate, and fluid rheology on the critical drop sizes are determined. Although the code modifications performed for this research were implemented for dynamic mesh refinement of cells close to fluid-fluid interfaces, they may be adapted to other regions in the domain and for other types of flow problems

Identifying Trace Affine Linear Sets Using Homotopy Continuation

We investigate how the coefficients of a sparse polynomial system influence the sum, or the trace, of its solutions. We discuss an extension of the classical trace test in numerical algebraic geometry to sparse polynomial systems. Two known methods for identifying a trace affine linear subset of the support of a sparse polynomial system use sparse resultants and polyhedral geometry, respectively. We introduce a new approach which provides more precise classifications of trace affine linear sets than was previously known. For this new approach, we developed software in Macaulay2

The impact of environmental noise on animal communication:pattern formation in a class of deterministic and stochastic hyperbolic models for self-organised biological aggregations

The collective movement of animalsoccurs as a result of communication between the members of the community. However, inter-individual communication can be aected by the stochasticity of the environment, leading to changes in the perception of neighbours and subsequent changes in  individual behaviour, which then in uence the overall behaviour of the animal aggregations. To investigate the eect of noise on the overall behaviour of animal aggregations, we consider a class of nonlocal stochastic and deterministic hyperbolic models for the collective movement of animals. We show numerically that strong noise does not seem to in uence the spatio-temporal pattern (i.e., travelling aggregations) observed when all neighbours are perceived with the same intensity (i.e., the environment is homogeneous). However, when neighbours ahead/behind are perceived dierently by a reference individual, noise can lead to the destruction of the spatio-temporal pattern. Moreover, we show that the increase in noise can lead to dierent transitions between different spatio-temporal patterns, and these transitions are relatively similar to the transitions between patterns when we perturb deterministically some parameters

User's Manual for HPTAM: a Two-Dimensional Heat Pipe Transient Analysis Model, Including the Startup from a Frozen State

This report describes the user's manual for 'HPTAM,' a two-dimensional Heat Pipe Transient Analysis Model. HPTAM is described in detail in the UNM-ISNPS-3-1995 report which accompanies the present manual. The model offers a menu that lists a number of working fluids and wall and wick materials from which the user can choose. HPTAM is capable of simulating the startup of heat pipes from either a fully-thawed or frozen condition of the working fluid in the wick structure. The manual includes instructions for installing and running HPTAM on either a UNIX, MS-DOS or VMS operating system. Samples for input and output files are also provided to help the user with the code

Large-eddy simulations of a jet in crossflow using Julia

The jet in crossflow (JICF) is a complex flow that has applications in many fields, from pollutant dispersion into air or water to the injection and mixing of fuel in engines. In this thesis, large-eddy simulations, using a stretched-vortex sub-grid model, of a JICF with a non-reactive scalar are performed using a discrete numerical method that is implemented using code written in the computational language Julia. Velocity profiles, trajectories, entrainment, power spectra, turbulent kinetic energy and dissipation of energy are analysed for simulations run at velocity ratios varying between 0.405 and 3.3, crossflow boundary layer thicknesses between 0.28 and 2.06 and Reynolds numbers between 243 and 20500. Simulations are compared to published experimental and simulation-based results, and a full comparison was performed with a simulation provided by Mattner, run on the same computational grid. It was found that the mathematical model used in this thesis performs better at higher velocities and Reynolds numbers. An investigation into the effect of the ratio of average jet inlet velocity to maximum crossflow velocity was performed. It was found that a jet with a higher velocity ratio showed increased penetration into the crossflow. The amount of turbulent kinetic and scalar energy in the system, as well as the amount of dissipation of energy from the system, also increased with velocity ratio. Finally, a comparison of large-eddy simulation (LES) and direct numerical simulation (DNS) of a JICF was performed on the same computational grid for low and moderate Reynolds numbers. At low Reynolds numbers the di↵erences in results between the LES and DNS are minor, although it is not possible to resolve the flow on the computational grid that is used. At moderate Reynolds numbers, above Re = 1 x 10⁴, the differences between the LES and DNS are more pronounced. Deeper jet penetration is seen in the LES than in the DNS, and the distribution of energy in the system is different, with the sub-grid model used in the LES dissipating more energy from the high wavenumber scales.Thesis (M.Phil) -- University of Adelaide, School of Mathematical Sciences, 201

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

Bayesian extreme quantile regression for hidden Markov models

This thesis was submitted for the degree of Doctor of Philosophy and was awarded by Brunel UniversityThe main contribution of this thesis is the introduction of Bayesian quantile regression for hidden Markov models, especially when we have to deal with extreme quantile regression analysis, as there is a limited research to inference conditional quantiles for hidden Markov models, under a Bayesian approach. The first objective is to compare Bayesian extreme quantile regression and the classical extreme quantile regression, with the help of simulated data generated by three specific models, which only differ in the error term’s distribution. It is also investigated if and how the error term’s distribution affects Bayesian extreme quantile regression, in terms of parameter and confidence intervals estimation. Bayesian extreme quantile regression is performed by implementing a Metropolis-Hastings algorithm to update our parameters, while the classical extreme quantile regression is performed by using linear programming. Moreover, the same analysis and comparison is performed on a real data set. The results provide strong evidence that our method can be improved, by combining MCMC algorithms and linear programming, in order to obtain better parameter and confidence intervals estimation. After improving our method for Bayesian extreme quantile regression, we extend it by including hidden Markov models. First, we assume a discrete time finite state-space hidden Markov model, where the distribution associated with each hidden state is a) a Normal distribution and b) an asymmetric Laplace distribution. Our aim is to explore the number of hidden states that describe the extreme quantiles of our data sets and check whether a different distribution associated with each hidden state can affect our estimation. Additionally, we also explore whether there are structural changes (breakpoints), by using break-point hidden Markov models. In order to perform this analysis we implement two new MCMC algorithms. The first one updates the parameters and the hidden states by using a Forward-Backward algorithm and Gibbs sampling (when a Normal distribution is assumed), and the second one uses a Forward-Backward algorithm and a mixture of Gibbs and Metropolis-Hastings sampling (when an asymmetric Laplace distribution is assumed). Finally, we consider hidden Markov models, where the hidden state (latent variables) are continuous. For this case of the discrete-time continuous state-space hidden Markov model we implement a method that uses linear programming and the Kalman filter (and Kalman smoother). Our methods are used in order to analyze real interest rates by assuming hidden states, which represent different financial regimes. We show that our methods work very well in terms of parameter estimation and also in hidden state and break-point estimation, which is very useful for the real life applications of those methods

Spectroscopically Evaluated Rates and Energies for Proton Transfer and Bjerrum Defect Migration in Cubic Ice

Chemistr

Halonitromethane Treatment Using Advanced Oxidation Process: Rates, Mechanisms and Kinetic Modeling

Halonitromethanes (HNMs) are low molecular weight halogenated disinfection-by-products (DBPs) found to be formed during ozonation, chlorination, or chloramination of waters containing natural bromide ion and nitrogenous organic matter. This work identifies the absolute rate constants for the oxidative hydroxyl radical (•OH) and reductive hydrated electron e- aq extinction of HNM compounds. Three forms of HNMs included in this study are the chlorinated, brominated, and mixed halogenated compounds. Electron pulse radiolysis and transient absorption spectroscopy were used to measure •OH and e- aq radical absolute reaction rate constants for a total of nine HNMs. To elucidate the decomposition reaction mechanism, six HNMs were exposed to 60Co gamma (γ) irradiation at various times (absorbed doses). The disappearance of the parent compound in the 60Co irradiated samples was monitored and the mass balance of ionic residuals was determined. Using reaction rate constants and the mechanistic data, a preliminary reaction mechanism was proposed and used in a kinetic model to describe the removal of the HNMs in aqueous solution. The model was then extended to simulate the electron beam process on waters of defined chemical composition and used for estimating the economics of the treatment of trichloronitromethane at large scale