Pergamon Mechanics Research Communications, Vol. 26, No. 3, pp. 379-384, 1999 Copyright© 1999Elsevier ScienceLid Printedin the USA. All rights reserved 0093-6413/99/$-secfrontmatter PII S0093-6413(99)00037-3 A NUMERICAL MODEL FOR PREDICTION OF THE AIR-CORE SHAPE OF HYDROCYCLONE FLOW J. Romero and R. Sampaio Department of Mechanical Engineering, Catholic University of Rio de Janeiro Rua Marquis de S~o Vicente 225 - Gdlvea 224453-900, Rio de Janeiro - R.L, Brazil (Received 1 7 March 1998; accepted for print 10 March 1999) Introduction 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, such as [1], [10], [4] and [3] 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 experimentally in [2], where it is possible to get satisfactory answers. Mathematical model for the fluid flow The fluid flow in the hydrocyclone is modeled by using the Navier-Stokes equations, (continuity and momentum conservation). Because of the rotational fluid movement, a low pressure region is created in the central part of the devices, so an air-core of an unknowing nature is produced. The air-core shape can vary with the time or due to the hydrocyclones parameters and operational conditions. This makes the dynamic problem to a free boundary problem. Therefore beyond the calculation of the velocity and pressure fields, it should be approximated the free boundary shape and localization (liquid-air interface). Due to the operation condition and geometry of the equipment, the flow is turbulent and anisotropic difficulting the turbulent diffusion modeling. By applying the Reynolds decomposition in the conservation's equations of the 379