| Summary: | The thesis presents work across three interlinked areas of investigation into the modelling of multiphase flows, primarily focussed on the evolution of moments. A Lagrangian particle tracking code is used to track the evolution of a phase space probability density function (PDF) over time. From this the effect of point models on the evolution of overall PDFs and their characteristic moments is determined. It is found that difference between point models is generally low, less than 5%, for the majority of low order moments. An experimental section provides a study of the chaaracteristics of a polydisperse particle distribution introduced into a 2D turbulent plane jet. Initially, both the plane jet and 'the dispersed phase delivery system are characterised. Glass beads, with a nominal diameter range of 0-50jJm, are introduced under the influence of gravity into the flow. The delivery location is 25mm downstream of, and 75mm above, the jet exit. Within the developing region of the jet up to 106 measurements of velocity (20) and size are taken at an array of nineteen data points. The central limit theorem (CLT) is utilised to determine the accuracy of high order moments, which is found to be as low as 1% for a moment of order 6. A comparison is made between the results and current turbulence closure models, indicating the difficulties in modelling such terms. The final section of work focuses on the maximum entropy method (MEM) and its use in the calculation of particle distributions from a finite se't of moments. An iterative 1D solution algorithm, readily extendable to mUltiple dimensions, is derived. The stability of the solution technique is demonstrated and the overall accuracy quantified. The use of the MEM with the application of an apriori distribution is demonstrated to provide control over the phase space and prevent non-physical values in the calculated PDF. ,Furthermore, the capability of the algorithm in handling such situations as crossing or impinging particle jets is shown via the calculation of bimodal POFs from a set of moments.
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