Mathematical modelling and optimisation of the formulation and manufacture of aggregate food products

In this PhD study, mathematical modelling and optimisation of granola production has been carried out. Granola is an aggregated food product used in breakfast cereals and cereal bars. It is a baked crispy food product typically incorporating oats, other cereals and nuts bound together with a binder, such as honey, water and oil, to form a structured unit aggregate. In this work, the design and operation of two parallel processes to produce aggregate granola products were incorporated: i) a high shear mixing granulation stage (in a designated granulator) followed by drying/toasting in an oven. ii) a continuous fluidised bed followed by drying/toasting in an oven. In addition, the particle breakage of granola during pneumatic conveying produced by both a high shear granulator (HSG) and fluidised bed granulator (FBG) process were examined. Products were pneumatically conveyed in a purpose built conveying rig designed to mimic product conveying and packaging. Three different conveying rig configurations were employed; a straight pipe, a rig consisting two 45° bends and one with 90° bend. It was observed that the least amount of breakage occurred in the straight pipe while the most breakage occurred at 90° bend pipe. Moreover, lower levels of breakage were observed in two 45° bend pipe than the 90° bend vi pipe configuration. In general, increasing the impact angle increases the degree of breakage. Additionally for the granules produced in the HSG, those produced at 300 rpm have the lowest breakage rates while the granules produced at 150 rpm have the highest breakage rates. This effect clearly the importance of shear history (during granule production) on breakage rates during subsequent processing. In terms of the FBG there was no single operating parameter that was deemed to have a significant effect on breakage during subsequent conveying. A population balance model was developed to analyse the particle breakage occurring during pneumatic conveying. The population balance equations that govern this breakage process are solved using discretization. The Markov chain method was used for the solution of PBEs for this process. This study found that increasing the air velocity (by increasing the air pressure to the rig), results in increased breakage among granola aggregates. Furthermore, the analysis carried out in this work provides that a greater degree of breakage of granola aggregates occur in line with an increase in bend angle.

Grid integration of wave energy & generic modelling of ocean devices for power system studies

The work presented in this thesis covers four major topics of research related to the grid integration of wave energy. More specifically, the grid impact of a wave farm on the power quality of its local network is investigated. Two estimation methods were developed regarding the flicker level Pst generated by a wave farm in relation to its rated power as well as in relation to the impedance angle ψk of the node in the grid to which it is connected. The electrical design of a typical wave farm design is also studied in terms of minimum rating for three types of costly pieces of equipment, namely the VAr compensator, the submarine cables and the overhead line. The power losses dissipated within the farm's electrical network are also evaluated. The feasibility of transforming a test site into a commercial site of greater rated power is investigated from the perspective of power quality and of cables and overhead line thermal loading. Finally, the generic modelling of ocean devices, referring here to both wave and tidal current devices, is investigated.

The Hurst exponent as an indicator of the behaviour of a model monopile in an ocean wave testing basin

With the importance of renewable energy well-established worldwide, and targets of such energy quantified in many cases, there exists a considerable interest in the assessment of wind and wave devices. While the individual components of these devices are often relatively well understood and the aspects of energy generation well researched, there seems to be a gap in the understanding of these devices as a whole and especially in the field of their dynamic responses under operational conditions. The mathematical modelling and estimation of their dynamic responses are more evolved but research directed towards testing of these devices still requires significant attention. Model-free indicators of the dynamic responses of these devices are important since it reflects the as-deployed behaviour of the devices when the exposure conditions are scaled reasonably correctly, along with the structural dimensions. This paper demonstrates how the Hurst exponent of the dynamic responses of a monopile exposed to different exposure conditions in an ocean wave basin can be used as a model-free indicator of various responses. The scaled model is exposed to Froude scaled waves and tested under different exposure conditions. The analysis and interpretation is carried out in a model-free and output-only environment, with only some preliminary ideas regarding the input of the system. The analysis indicates how the Hurst exponent can be an interesting descriptor to compare and contrast various scenarios of dynamic response conditions.

Hollow core photonic crystal fibre as a viscosity and Raman sensor

This PhD thesis investigates the application of hollow core photonic crystal fibre for use as an optical fibre nano litre liquid sensor. The use of hollow core photonic crystal fibre for optical fibre sensing is influenced by the vast wealth of knowledge, and years of research that has been conducted for optical waveguides. Hollow core photonic crystal fibres have the potential for use as a simple, rapid and continuous sensor for a wide range of applications. In this thesis, the velocity of a liquid flowing through the core of the fibre (driven by capillary forces) is used for the determination of the viscosity of a liquid. The structure of the hollow core photonic crystal fibre is harnessed to collect Raman scatter from the sample liquid. These two methods are integrated to investigate the range of applications the hollow core photonic crystal fibre can be utilised for as an optical liquid sensor. Understanding the guidance properties of hollow core photonic crystal fibre is forefront in dynamically monitoring the liquid filling. When liquid is inserted fully or selectively to the capillaries, the propagation properties change from photonic bandgap guidance when empty, to index guidance when the core only is filled and finally to a shifted photonic bandgap effect, when the capillaries are fully filled. The alterations to the guidance are exploited for all viscosity and Raman scattering measurements. The concept of the optical fibre viscosity sensor was tested for a wide range of samples, from aqueous solutions of propan-1-ol to solutions of mono-saccharides in phosphate buffer saline. The samples chosen to test the concept were selected after careful consideration of the importance of the liquid in medical and industrial applications. The Raman scattering of a wide range of biological important fluids, such as creatinine, glucose and lactate were investigated, some for the first time with hollow core photonic crystal fibre.

The design of curved optical waveguides : analytical and numerical analysis

A model for understanding the formation and propagation of modes in curved optical waveguides is developed. A numerical method for the calculation of curved waveguide mode profiles and propagation constants in two dimensional waveguides is developed, implemented and tested. A numerical method for the analysis of propagation of modes in three dimensional curved optical waveguides is developed, implemented and tested. A technique for the design of curved waveguides with reduced transition loss is presented. A scheme for drawing these new waveguides and ensuring that they have constant width is also provided. Claims about the waveguide design technique are substantiated through numerical simulations.

Comparison of deterministic, stochastic and fuzzy logic uncertainty modelling for capacity extension projects of DI/WFI pharmaceutical plant utilities with variable/dynamic demand

The last 30 years have seen Fuzzy Logic (FL) emerging as a method either complementing or challenging stochastic methods as the traditional method of modelling uncertainty. But the circumstances under which FL or stochastic methods should be used are shrouded in disagreement, because the areas of application of statistical and FL methods are overlapping with differences in opinion as to when which method should be used. Lacking are practically relevant case studies comparing these two methods. This work compares stochastic and FL methods for the assessment of spare capacity on the example of pharmaceutical high purity water (HPW) utility systems. The goal of this study was to find the most appropriate method modelling uncertainty in industrial scale HPW systems. The results provide evidence which suggests that stochastic methods are superior to the methods of FL in simulating uncertainty in chemical plant utilities including HPW systems in typical cases whereby extreme events, for example peaks in demand, or day-to-day variation rather than average values are of interest. The average production output or other statistical measures may, for instance, be of interest in the assessment of workshops. Furthermore the results indicate that the stochastic model should be used only if found necessary by a deterministic simulation. Consequently, this thesis concludes that either deterministic or stochastic methods should be used to simulate uncertainty in chemical plant utility systems and by extension some process system because extreme events or the modelling of day-to-day variation are important in capacity extension projects. Other reasons supporting the suggestion that stochastic HPW models are preferred to FL HPW models include: 1. The computer code for stochastic models is typically less complex than a FL models, thus reducing code maintenance and validation issues. 2. In many respects FL models are similar to deterministic models. Thus the need for a FL model over a deterministic model is questionable in the case of industrial scale HPW systems as presented here (as well as other similar systems) since the latter requires simpler models. 3. A FL model may be difficult to "sell" to an end-user as its results represent "approximate reasoning" a definition of which is, however, lacking. 4. Stochastic models may be applied with some relatively minor modifications on other systems, whereas FL models may not. For instance, the stochastic HPW system could be used to model municipal drinking water systems, whereas the FL HPW model should or could not be used on such systems. This is because the FL and stochastic model philosophies of a HPW system are fundamentally different. The stochastic model sees schedule and volume uncertainties as random phenomena described by statistical distributions based on either estimated or historical data. The FL model, on the other hand, simulates schedule uncertainties based on estimated operator behaviour e.g. tiredness of the operators and their working schedule. But in a municipal drinking water distribution system the notion of "operator" breaks down. 5. Stochastic methods can account for uncertainties that are difficult to model with FL. The FL HPW system model does not account for dispensed volume uncertainty, as there appears to be no reasonable method to account for it with FL whereas the stochastic model includes volume uncertainty.

Financial modelling with 2-EPT probability density functions

The class of all Exponential-Polynomial-Trigonometric (EPT) functions is classical and equal to the Euler-d’Alembert class of solutions of linear differential equations with constant coefficients. The class of non-negative EPT functions defined on [0;1) was discussed in Hanzon and Holland (2010) of which EPT probability density functions are an important subclass. EPT functions can be represented as ceAxb, where A is a square matrix, b a column vector and c a row vector where the triple (A; b; c) is the minimal realization of the EPT function. The minimal triple is only unique up to a basis transformation. Here the class of 2-EPT probability density functions on R is defined and shown to be closed under a variety of operations. The class is also generalised to include mixtures with the pointmass at zero. This class coincides with the class of probability density functions with rational characteristic functions. It is illustrated that the Variance Gamma density is a 2-EPT density under a parameter restriction. A discrete 2-EPT process is a process which has stochastically independent 2-EPT random variables as increments. It is shown that the distribution of the minimum and maximum of such a process is an EPT density mixed with a pointmass at zero. The Laplace Transform of these distributions correspond to the discrete time Wiener-Hopf factors of the discrete time 2-EPT process. A distribution of daily log-returns, observed over the period 1931-2011 from a prominent US index, is approximated with a 2-EPT density function. Without the non-negativity condition, it is illustrated how this problem is transformed into a discrete time rational approximation problem. The rational approximation software RARL2 is used to carry out this approximation. The non-negativity constraint is then imposed via a convex optimisation procedure after the unconstrained approximation. Sufficient and necessary conditions are derived to characterise infinitely divisible EPT and 2-EPT functions. Infinitely divisible 2-EPT density functions generate 2-EPT Lévy processes. An assets log returns can be modelled as a 2-EPT Lévy process. Closed form pricing formulae are then derived for European Options with specific times to maturity. Formulae for discretely monitored Lookback Options and 2-Period Bermudan Options are also provided. Certain Greeks, including Delta and Gamma, of these options are also computed analytically. MATLAB scripts are provided for calculations involving 2-EPT functions. Numerical option pricing examples illustrate the effectiveness of the 2-EPT approach to financial modelling.

Feasibility of combined wind-wave energy platforms

The European Union has set out an ambitious 20% target for renewable energy use by 2020. It is expected that this will be met mainly by wind energy. Looking towards 2050, reductions in greenhouse gas emissions of 80-95% are to be sought. Given the issues securing this target in the transport and agriculture sectors, it may only be possible to achieve this target if the power sector is carbon neutral well in advance of 2050. This has permitted the vast expansion of offshore renewables, wind, wave and tidal energy. Offshore wind has undergone rapid development in recent years however faces significant challenges up to 2020 to ensure commercial viability without the need for government subsidies. Wave energy is still in the very early stages of development so as yet there has been no commercial roll out. As both of these technologies are to face similar challenges in ensuring they are a viable alternative power generation method to fossil fuels, capitalising on the synergies is potentially a significant cost saving initiative. The advent of hybrid solutions in a variety of configurations is the subject of this thesis. A singular wind-wave energy platform embodies all the attributes of a hybrid system, including sharing space, transmission infrastructure, O&M activities and a platform/foundation. This configuration is the subject of this thesis, and it is found that an OWC Array platform with multi-MegaWatt wind turbines is a technically feasible, and potentially an economically feasible solution in the long term. Methods of design and analysis adopted in this thesis include numerical and physical modelling of power performance, structural analysis, fabrication cost modelling, simplified project economic modelling and time domain reliability modelling of a 210MW hybrid farm. The application of these design and analysis methods has resulted in a hybrid solution capable of producing energy at a cost between €0.22/kWh and €0.31/kWh depending on the source of funding for the project. Further optimisation through detailed design is expected to lower this further. This thesis develops new and existing methods of design and analysis of wind and wave energy devices. This streamlines the process of early stage development, while adhering to the widely adopted Concept Development Protocol, to develop a technically and economically feasible, combined wind-wave energy hybrid solution.