The objective of the present work was to investigate three dimensional unsteady vortex dominated flows using the spectral difference (SD) method and finite volume (FV) method. The simulations were carried out over a circular cylinder, a delta wing and a spiral-shaped wind turbine. SD method was used to demonstrate its potential in Large Eddy Simulation (LES) of flow over a cylinder and also to predict the mean and instantaneous flow structure over a delta wing. FLUENT and MUSIC (2nd order FV solvers) were used to study the flow behavior in a spiral-shaped wind turbine designed to extract maximum power out of it.Large eddy simulation of the flow over a circular cylinder at Reynolds number ReD = 2580 was studied with a high-order unstructured SD method. Grid and accuracy refinement studies were carried out to assess numerical errors. The mean and fluctuating velocity fields in the wake of a circular cylinder were compared with PIV experimental measurements. The numerical results are in an excellent agreement with the measurements for both the mean velocity and Reynolds stresses. Other wake characteristics such as the re-circulation bubble length, vortex formation length and maximum intensity of the velocity fluctuations have also been predicted accurately. The numerical simulations demonstrated the potential of the high-order SD method in large eddy simulation of physically complex problems.Computational simulations were performed for a 50o sweep delta wing at 15o degree angle of attack and a moderate Reynolds number of Re = 2x105 using SD method. A preliminary study was carried out to demonstrate once again the potential of high order spectral difference method in a highly vortex dominated flow. Comparisons were made with high resolution PIV images and numerical simulations performed by Raymond and Visbal. The numerical results were examined to provide a description of the mean and instantaneous flow structure over the delta wing including the separated vortical flow and vortex breakdown. The results suggest the importance of grid resolution on the upper surface of the delta wing, to obtain a better accuracy of the vortex structure.2nd order FV method was used to study the flow in a Tornado Type Wind Turbine (TTWT) which uses a strong Rankine vortex to generate low pressure at the turbine base. The primary aim was to design the spiral shaped turbine in order to broaden the usability of wind energy. Two solvers, FLUENT and MUSIC, both utilizing the 2nd order FV method were used to perform the CFD analysis. Grid refinement study was carried out to assess numerical errors. The effect of different parameters, like diameter of the spiral, height of the turbine and blockage effect, on the vortex strength were studied. The numerical results were compared with the experiment results. The distribution of pressure was within 5-10% of experiment values but the values are not small enough to extract high power out of the turbine.
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