The subset sum problem in Keno modelling

Aspects of Keno modelling throughout the Australian states of Queensland, New South Wales and Victoria are discussed: the trivial Heads or Tails and the more interesting Keno Bonus, which leads to consideration of the subset sum problem. The most intricate structure is where Heads or Tails and Keno Bonus are combined, and here, the issue of independence arises. Closed expressions for expected return to player are presented in each case.

CFD and experimental modelling of an impinging jet for thunderstorm downburst simulation

A thunderstorm downburst in its simplest form can be modelled as a steady flow impinging air jet. Although this simplification neglects some important atmospheric and physical parameters it has proven to be a useful tool for understanding the kinematics of these events. Assuming this simple impinging jet model also allows numerical models to be developed which can be directly compared with experimental results to validate the use of CFD. Confidence gained from these simulations will allow the use of more complex atmospheric impinging jet models that cannot be directly validated. Thunderstorm downbursts are important for wind engineers because in many parts of the world they produce the design wind speeds used in design standards, but are not structurally represented in these documents.

Modelling of a magnetocaloric system for cooling in the kilowatt range

A numerical time-dependent model of an active magnetic regenerator (AMR) was developed for cooling in the kilowatt range. Earlier numerical models have been mostly developed for cooling power in the 0.4 kW range. In contrast, this paper reports the applicability of magnetic refrigeration to the 50 kW range. A packed bed active magnetic regenerator was modelled and the influence of parameters such as geometry and operating parameters were studied for different geometries. The pressure drop for AMR bed length and particle diameter was also studied. High cooling power and coefficient of performance (COP) were achieved by optimization of the diameter of the magnetocaloric powder particles and operating frequency. The optimum operating conditions of the AMR for a cooling capacity of 50 kW was determined for a temperature span of 15 K. The predicted coefficient of performance (COP) was found to be ∼6, making it an attractive alternative to vapour compression systems.

Numerical studies on CFRP strengthened steel columns under transverse impact

Strengthening of metallic structures using carbon fibre reinforced polymer (CFRP) has become a smart strengthening option over the conventional strengthening method. Transverse impact loading due to accidental vehicular collision can lead to the failure of existing steel hollow tubular columns. However, knowledge is very limited on the behaviour of CFRP strengthened steel members under dynamic impact loading condition. This paper deals with the numerical simulation of CFRP strengthened square hollow section (SHS) steel columns under transverse impact loading to predict the behaviour and failure modes. The transverse impact loading is simulated using finite element (FE) analysis based on numerical approach. The accuracy of the FE modelling is ensured by comparing the predicted results with available experimental tests. The effects of impact velocity, impact mass, support condition, axial loading and CFRP thickness are examined through detail parametric study. The impact simulation results indicate that the strengthening technique shows an improved impact resistance capacity by reducing lateral displacement of the strengthened column about 58% compared to the bare steel column. Axial loading plays an important role on the failure behaviour of tubular column.

Fouling of waste heat recovery : numerical and experimental results

Numerical results are presented to investigate the performance of a partly-filled porous heat exchanger for waste heat recovery units. A parametric study was conducted to investigate the effects of inlet velocity and porous block height on the pressure drop of the heat exchanger. The focus of this work is on modelling the interface of a porous and non-porous region. As such, numerical simulation of the problem is conducted along with hot-wire measurements to better understand the physics of the problem. Results from the two sources are then compared to existing theoretical predictions available in the literature which are unable to predict the existence of two separation regions before and after the porous block. More interestingly, a non-uniform interface velocity was observed along the streamwise direction based on both numerical and experimental data.

The mathematical modelling of cheese ripening

A mathematical model is developed for the ripening of cheese. Such models may assist predicting final cheese quality using measured initial composition. The main constituent chemical reactions are described with ordinary differential equations. Numerical solutions to the model equations are found using Matlab. Unknown parameter values have been fitted using experimental data available in the literature. The results from the numerical fitting are in good agreement with the data. Statistical analysis is performed on near infrared data provided to the MISG. However, due to the inhomogeneity and limited nature of the data, not many conclusions can be drawn from the analysis. A simple model of the potential changes in acidity of cheese is also considered. The results from this model are consistent with cheese manufacturing knowledge, in that the pH of cheddar cheese does not significantly change during ripening.

Two-scale computational modelling of water flow in unsaturated soils containing irregular-shaped inclusions

The focus of this paper is two-dimensional computational modelling of water flow in unsaturated soils consisting of weakly conductive disconnected inclusions embedded in a highly conductive connected matrix. When the inclusions are small, a two-scale Richards’ equation-based model has been proposed in the literature taking the form of an equation with effective parameters governing the macroscopic flow coupled with a microscopic equation, defined at each point in the macroscopic domain, governing the flow in the inclusions. This paper is devoted to a number of advances in the numerical implementation of this model. Namely, by treating the micro-scale as a two-dimensional problem, our solution approach based on a control volume finite element method can be applied to irregular inclusion geometries, and, if necessary, modified to account for additional phenomena (e.g. imposing the macroscopic gradient on the micro-scale via a linear approximation of the macroscopic variable along the microscopic boundary). This is achieved with the help of an exponential integrator for advancing the solution in time. This time integration method completely avoids generation of the Jacobian matrix of the system and hence eases the computation when solving the two-scale model in a completely coupled manner. Numerical simulations are presented for a two-dimensional infiltration problem.

Modelling of the evaporation of a droplet suspended in a binary atmosphere

The process of spray drying is applied in a number of contexts. One such application is the production of a synthetic rock used for storage of nuclear waste. To establish a framework for a model of the spray drying process for this application, we here develop a model describing evaporation from droplets of pure water, such that the model may be extended to account for the presence of colloid within the droplet. We develop a spherically-symmetric model and formulate continuum equations describing mass, momentum, and energy balance in both the liquid and gas phases from first principles. We establish appropriate boundary conditions at the surface of the droplet, including a generalised Clapeyron equation that accurately describes the temperature at the surface of the droplet. To account for experiment design, we introduce a simplified platinum ball and wire model into the system using a thin wire problem. The resulting system of equations is transformed in order to simplify a finite volume solution scheme. The results from numerical simulation are compared with data collected for validation, and the sensitivity of the model to variations in key parameters, and to the use of Clausius–Clapeyron and generalised Clapeyron equations, is investigated. Good agreement is found between the model and experimental data, despite the simplicity of the platinum phase model.

Mathematical modelling of the impaction and spreading of spray droplets on leaves

This thesis concerns the development of mathematical models to describe the interactions that occur between spray droplets and leaves. Models are presented that not only provide a contribution to mathematical knowledge in the field of fluid dynamics, but are also of utility within the agrichemical industry. The thesis is presented in two parts. First, thin film models are implemented with efficient numerical schemes in order to simulate droplets on virtual leaf surfaces. Then the interception event is considered, whereby energy balance techniques are employed to instantaneously predict whether an impacting droplet will bounce, splash, or adhere to a leaf.

Numerical studies of gypsum plasterboard and MGO board lined LSF walls exposed to fire

Fire resistance of cold-formed light gauge steel frame (LSF) wall systems is enhanced by lining them with single or multiple layers of wall boards with varying thermal properties. These wall boards are gypsum plasterboards or Magnesium Oxide (MgO) boards produced by different manufacturers. Thermal properties of these boards appear to show considerable variations and this can lead to varying fire resistance levels (FRL) for their wall systems. Currently FRLs of wall systems are determined using full scale fire tests, but they are time consuming and expensive. Recent research studies on the fire performance of LSF wall systems have used finite element studies to overcome this problem, but they were developed based on 1-D and 2-D finite element platform capable of performing either heat transfer or structural analysis separately. Hence in this research a 3-D finite element model was developed first for LSF walls lined with gypsum plasterboard and cavity insulation materials. Accurate thermal properties of these boards are essential for finite element modelling, and thus they were measured at both ambient and elevated temperatures. This experimental study included specific heat, relative density and thermal conductivity of boards. The developed 3-D finite element model was then validated using the available fire tests results of LSF walls lined with gypsum plasterboard, and is being used to investigate the fire performance of different LSF wall configurations. The tested MgO board exhibited significant variations in their thermal properties in comparison to gypsum plasterboards with about 50% loss of its initial mass at about 500 ºC compared to 16% for gypsum plasterboards. Hence the FRL of MgO board lined LSF wall systems is likely to be significantly reduced. This paper presents the details of this research study on the fire performance of LSF wall systems lined with gypsum plasterboard and MgO board including the developed 3-D finite element models, thermal property tests and the results.

Prediction of masonry compressive behaviour using a damage mechanics inspired modelling method

Masonry under compression is affected by the properties of its constituents and their interfaces. In spite of extensive investigations of the behaviour of masonry under compression, the information in the literature cannot be regarded as comprehensive due to ongoing inventions of new generation products – for example, polymer modified thin layer mortared masonry and drystack masonry. As comprehensive experimental studies are very expensive, an analytical model inspired by damage mechanics is developed and applied to the prediction of the compressive behaviour of masonry in this paper. The model incorporates a parabolic progressively softening stress-strain curve for the units and a progressively stiffening stress-strain curve until a threshold strain for the combined mortar and the unit-mortar interfaces is reached. The model simulates the mutual constraints imposed by each of these constituents through their respective tensile and compressive behaviour and volumetric changes. The advantage of the model is that it requires only the properties of the constituents and considers masonry as a continuum and computes the average properties of the composite masonry prisms/wallettes; it does not require discretisation of prism or wallette similar to the finite element methods. The capability of the model in capturing the phenomenological behaviour of masonry with appropriate elastic response, stiffness degradation and post peak softening is presented through numerical examples. The fitting of the experimental data to the model parameters is demonstrated through calibration of some selected test data on units and mortar from the literature; the calibrated model is shown to predict the responses of the experimentally determined masonry built using the corresponding units and mortar quite well. Through a series of sensitivity studies, the model is also shown to predict the masonry strength appropriately for changes to the properties of the units and mortar, the mortar joint thickness and the ratio of the height of unit to mortar joint thickness. The unit strength is shown to affect the masonry strength significantly. Although the mortar strength has only a marginal effect, reduction in mortar joint thickness is shown to have a profound effect on the masonry strength. The results obtained from the model are compared with the various provisions in the Australian Masonry Structures Standard AS3700 (2011) and Eurocode 6.

Spatial and temporal variability in midge (Nematocera) assemblages in shallow Finnish lakes (60−70 °N) : community-based modelling of past environmental change

Multi- and intralake datasets of fossil midge assemblages in surface sediments of small shallow lakes in Finland were studied to determine the most important environmental factors explaining trends in midge distribution and abundance. The aim was to develop palaeoenvironmental calibration models for the most important environmental variables for the purpose of reconstructing past environmental conditions. The developed models were applied to three high-resolution fossil midge stratigraphies from southern and eastern Finland to interpret environmental variability over the past 2000 years, with special focus on the Medieval Climate Anomaly (MCA), the Little Ice Age (LIA) and recent anthropogenic changes. The midge-based results were compared with physical properties of the sediment, historical evidence and environmental reconstructions based on diatoms (Bacillariophyta), cladocerans (Crustacea: Cladocera) and tree rings. The results showed that the most important environmental factor controlling midge distribution and abundance along a latitudinal gradient in Finland was the mean July air temperature (TJul). However, when the dataset was environmentally screened to include only pristine lakes, water depth at the sampling site became more important. Furthermore, when the dataset was geographically scaled to southern Finland, hypolimnetic oxygen conditions became the dominant environmental factor. The results from an intralake dataset from eastern Finland showed that the most important environmental factors controlling midge distribution within a lake basin were river contribution, water depth and submerged vegetation patterns. In addition, the results of the intralake dataset showed that the fossil midge assemblages represent fauna that lived in close proximity to the sampling sites, thus enabling the exploration of within-lake gradients in midge assemblages. Importantly, this within-lake heterogeneity in midge assemblages may have effects on midge-based temperature estimations, because samples taken from the deepest point of a lake basin may infer considerably colder temperatures than expected, as shown by the present test results. Therefore, it is suggested here that the samples in fossil midge studies involving shallow boreal lakes should be taken from the sublittoral, where the assemblages are most representative of the whole lake fauna. Transfer functions between midge assemblages and the environmental forcing factors that were significantly related with the assemblages, including mean air TJul, water depth, hypolimnetic oxygen, stream flow and distance to littoral vegetation, were developed using weighted averaging (WA) and weighted averaging-partial least squares (WA-PLS) techniques, which outperformed all the other tested numerical approaches. Application of the models in downcore studies showed mostly consistent trends. Based on the present results, which agreed with previous studies and historical evidence, the Medieval Climate Anomaly between ca. 800 and 1300 AD in eastern Finland was characterized by warm temperature conditions and dry summers, but probably humid winters. The Little Ice Age (LIA) prevailed in southern Finland from ca. 1550 to 1850 AD, with the coldest conditions occurring at ca. 1700 AD, whereas in eastern Finland the cold conditions prevailed over a longer time period, from ca. 1300 until 1900 AD. The recent climatic warming was clearly represented in all of the temperature reconstructions. In the terms of long-term climatology, the present results provide support for the concept that the North Atlantic Oscillation (NAO) index has a positive correlation with winter precipitation and annual temperature and a negative correlation with summer precipitation in eastern Finland. In general, the results indicate a relatively warm climate with dry summers but snowy winters during the MCA and a cool climate with rainy summers and dry winters during the LIA. The results of the present reconstructions and the forthcoming applications of the models can be used in assessments of long-term environmental dynamics to refine the understanding of past environmental reference conditions and natural variability required by environmental scientists, ecologists and policy makers to make decisions concerning the presently occurring global, regional and local changes. The developed midge-based models for temperature, hypolimnetic oxygen, water depth, littoral vegetation shift and stream flow, presented in this thesis, are open for scientific use on request.

Environmental factors affecting the occurrence of periglacial landforms in Finnish Lapland: a numerical approach

Determination of the environmental factors controlling earth surface processes and landform patterns is one of the central themes in physical geography. However, the identification of the main drivers of the geomorphological phenomena is often challenging. Novel spatial analysis and modelling methods could provide new insights into the process-environment relationships. The objective of this research was to map and quantitatively analyse the occurrence of cryogenic phenomena in subarctic Finland. More precisely, utilising a grid-based approach the distribution and abundance of periglacial landforms were modelled to identify important landscape scale environmental factors. The study was performed using a comprehensive empirical data set of periglacial landforms from an area of 600 km2 at a 25-ha resolution. The utilised statistical methods were generalized linear modelling (GLM) and hierarchical partitioning (HP). GLMs were used to produce distribution and abundance models and HP to reveal independently the most likely causal variables. The GLM models were assessed utilising statistical evaluation measures, prediction maps, field observations and the results of HP analyses. A total of 40 different landform types and subtypes were identified. Topographical, soil property and vegetation variables were the primary correlates for the occurrence and cover of active periglacial landforms on the landscape scale. In the model evaluation, most of the GLMs were shown to be robust although the explanation power, prediction ability as well as the selected explanatory variables varied between the models. The great potential of the combination of a spatial grid system, terrain data and novel statistical techniques to map the occurrence of periglacial landforms was demonstrated in this study. GLM proved to be a useful modelling framework for testing the shapes of the response functions and significances of the environmental variables and the HP method helped to make better deductions of the important factors of earth surface processes. Hence, the numerical approach presented in this study can be a useful addition to the current range of techniques available to researchers to map and monitor different geographical phenomena.

Contribution of geophysical surveys to groundwater modelling of a porous aquifer in semiarid Niger: An overview

Subsurface geophysical surveys were carried out using a large range of methods in an unconfined sandstone aquifer in semiarid south-western Niger for improving both the conceptual model of water flow through the unsaturated zone and the parameterization of numerical a groundwater model of the aquifer. Methods included: electromagnetic mapping, electrical resistivity tomography (ERT), resistivity logging, time domain electromagnetic sounding (TDEM), and magnetic resonance sounding (MRS). Analyses of electrical conductivities, complemented by geochemical measurements, allowed us to identify preferential pathways for infiltration and drainage beneath gullies and alluvial fans. The mean water content estimated by MRS (13%) was used for computing the regional groundwater recharge from long-term change in the water table. The ranges in permeability and water content obtained with MRS allowed a reduction of the degree of freedom of aquifer parameters used in groundwater modelling.

A numerical study of projectile impact on thin aluminium plates

This article deals with a simulation-based Study of the impact of projectiles on thin aluminium plates using LS-DYNA by modelling plates with shell elements and projectiles with solid elements. In order to establish the required modelling criterion in terms of element size for aluminium plates, a convergence Study of residual velocity has been carried Out by varying mesh density in the impact zone. Using the preferred material and meshing criteria arrived at here, extremely good prediction of test residual velocities and ballistic limits given by Gupta et al. (2001) for thin aluminium plates has been obtained. The simulation-based pattern of failure with localized bulging and jagged edge of perforation is similar to the perforation with petalling seen in tests. A number Of simulation-based parametric studies have been carried out and results consistent with published test data have been obtained. Despite the robust correlation achieved against published experimental results, it would be prudent to conduct one's own experiments, for a final correlation via the present modelling procedure and analysis with the explicit LS-DYNTA 970 solver. Hence, a sophisticated ballistic impact testing facility and a high-speed camera have been used to conduct additional tests on grade 1100 aluminium plates of 1 mm thickness with projectiles Of four different nose shapes. Finally, using the developed numerical simulation procedure, an excellent correlation of residual velocity and failure modes with the corresponding test results has been obtained.