In this thesis the following aspects have been investigated:\ud (i) the numerical solutions for unsteady 2-dimensional,\ud incompressible viscous fluid flows induced by a harmonically\ud oscillating cascade, and (ii) the fluid flows in industrial cyclones and their separation efficiencies. In the first part of the thesis we deal with fluid flows induced by harmonically oscillating cascades of cylinders with different cross sectional shapes. Numerical solutions for large amplitude oscillations of a cascade of normal flat plates are obtained by using a finite-difference method\ud and it is found that solutions are in good agreement with some related experimental results. For small amplitude oscillations a perturbation method, series truncation technique and finite-difference methods are used to obtain solutions for cascades of normal flat plates and square cylinders. By assuming that the streaming Reynolds number is 0(1) then the outer streaming flows for cascades of square cylinders, normal flat plates and circular\ud cylinders are investigated numerically for the streaming Reynolds number Rs up to 70. Conformal mapping, grid generation and boundary element methods are used to deal with the different geometries in order to determine the outer potential flows. For small values of the streaming Reynolds number it is found experimentally that the\ud flow remains symmetrical and the numerically predicted fluid flow is in good agreement with the experimental results. As the value of the streaming Reynolds number increases then it is found experimentally that the flow develops asymmetries and this occurs when 8<R <9, and\ud the numerically predicted results are also in good agreement with the experimental data. A stability analysis is presented for the outer streaming flow for the cascade of circular cylinders which reveals the reasons for the break-down in the symmetry.\ud \ud In the second part of the thesis the fluid flow In industrial cyclones has been investigated numerically. The influence of various aspects of the design parameters of the cyclone have been studied numerically and some important factors which affect the separation\ud efficiency of the cyclone are identified. Numerical results are also compared with some existing experimental data and there is good agreement. Correlations for both the loss factor and d50, the 50% cut-off particle diameter, with other parameters and operating conditions of the cyclone performance have been developed using a regression method with the existing experimental results. Finally,\ud the separation efficiency of a small personal cyclone (10mm in diameter) is also investigated
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