Vortex Theory Of Axisymmetrical Flows With Free Boundaries

Date of Award




Degree Name

Doctor of Philosophy (Ph.D.)


A three dimensional mathematical model has been developed which is specialized for the study of the hydrodynamics of cavitational flow around axisymmetrical objects. In the model, the obstacle and the stagnant region is substituted by distributed vortices along the obstacle and the free streamsurfaces. The resulting Fredholm integral equations of the second kind are solved by the method of iterations. The convergence and accuracy of the model are tested by comparison of the results with analytical models for two dimensional problem. The model accurately predicts the axisymmetrical flow past a disk with an infinite cavity behind the object. The accuracy of the axisymmetrical solution is checked by comparing the drag coefficient determined analytically with the experimental results. The results compare favorably as the model gives a drag coefficient of 0.825 while the experimental results indicate drag coefficients of 0.81-0.83.The application of the technique presented herein to the three dimensional non-axisymmetrical flow requires significant modification in the numerical methods. However, the theory outlined applies directly to the axisymmetrical jets and the model with minor modifications can be used for the study of jets.


Engineering, Mechanical

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