A numerical model for prediction of the air-core shape of hydrocyclone flow

Hydrocyclones are used extensively for solid particles separation and classification in the minerals processing industry. By means of the tangential fluid feeding and solid particle, a strong rotational movement takes place inside the equipment, that charged a centrifugal field. Because of this field, the solid particles are suspended in the fluid and tend to move towards the walls. As well, by the high tangential velocity of the fluid in the central part of the device, the pressure decreases until a values smaller than atmospheric pressure. A low pressure region is starting, causing the formation of an air-core in the central line. In spite of the simple geometry and operation, explaining the detailed mechanisms of the work is extremely complicated. One difficulty in finding the actual flow of the hydrocyclones is the necessity of specifying the form and location of the air-core surface. In the usual models applied to an hydrocyclone, the interface that bounds the air-core is modeled as a fixed cylindrical surface, that greatly simplifies the problem. This simplification avoids the necessity of the calculation of an unknowing boundary that modifies the domain, where the field equations must be solved. Nevertheless, such a simplification can produce bad results. Many research works have studied theoretical models to approximate the air-core radius. In this work, it is considered the air-liquid interface being a Young-Laplace type. With an iterating process the air-core radius is updated, in order to minimize the error in the Young-Laplace jump condition. The results obtained for velocity field are compared with those obtained expemerimentally in a previous paper, where it is possible to get satisfactory answers.