MATHEMATICAL MODELS AND THEIR NUMERICAL SOLUTION FOR THE FLOW FIELD OF HIGH VELOCITY WATER JETS.

摘要

The object of this work is to develop mathematical models and investigate their numerical solutions for the flow-field of high velocity water jets. In order to account for the shear stress exerted by the air on the jet, and for the generated droplet flow field, three multi-component models have been developed. The first of these is called the General Multi-component model. This model assumes that the core water, the generated droplets, and the air surrounding the core, are three distinct flow-fields with concurrent interactions. The Decoupled and Homogeneous models are the other two proposed multi-component models which are more tractable in terms of numerical solution.; An explicit numerical technique, called Method of Lines, together with its applicability to the proposed models has been studied and a sample problem is given. Although the method is explicit, it cannot be applied to some of two phase flow problems due to stability requirements. Thus an alternate explicit numerical technique was developed, which has been successful in cases when the method of lines has failed. It is called the Chorin method and it is tested against a sample problem. The Chorin method seems to be very promising due to its applicability to the water jet models, as well as to many other two-dimensional multi-phase flow problems. The method has been finally applied to the homogeneous model of water jet. Reasonable results have been obtained.