A mathematical model of a swirled turbulent flow in the separation zone of a pneumatic centrifugal device is presented. The model is based on the known k-ω model of turbulence proposed by Wilcox. The influence of rotation of the separation-zone walls, input swirl of the gas flow, and other characteristic parameters on the mean velocity field is demonstrated. A comparison of parameters is performed, which reveals good agreement between the numerical and experimental results for a turbulent fluid flow between parallel disks.
In our days in such fields of manufacturing as precision engineering, electronics, pharmaceutics there is a great interest in creating new materials, obtaining mainly in a powder form. The intensive researches in this area are carried out all over the world. Among the methods of production and processing of powders the pneumatic ones are most perspectives. On the basis of these methods a lot of various construction units are designed and applied in industry. The pneumatic circulating unit (PCU), designed in RIAMM (TSU) [l] is enough perspective for further developments. This unit allows carrying out the combined processes of powder production e.g. mixing, drying, grinding, and classification.The unit consists of (fig. 1) cylindrical-conical chamber 1 with coaxial pipe 2. The circulating motion of powder material is realized by the injection of the last by the compressed air feeding through the noz--zle block 3 in the bottom of the unit, the conveying of powder through the pipe and the precipitation of particles into the packed bed after the separation stage. For the classification of particles by their sizes the build-in vane rotating classifier 4 is applied. The main element of the classifier is the rotor, which generates a powerful centrifugal field around itself by its rotation and allows to achieve a high performance and sharp classification.It should be noticed that the gas flow in the separation zone has a turbulent nature and the turbulent difhsion of particles takes place. The concentration of particles in the flow in the separation zone is about 10 kg/kg and more, thus there are frequent particle-particle collisions and so-called secondary capture of small particles by large ones. All above factors significantly complicate a quantitative examination 2 -0 0 7 air of physical processes proceeding in the unit. The investigation of the classification process is reduced to construction of simplified stochastic models of a "black box" which impossible to be generalized to a wide class of materials. Although in view of considerable progress in the development of the computer technology it becomes more possible to solve the similar problems applying the numerical approaches.In terms of aforesaid in this paper the "interpenetrating and interacting continua" concept is implemented [2] in which base there is a suggestion that more then one phase can exist at the same location at the same time. This suggestion depends on the ideas of time and space averaging. The phases "share" this space; and they may, as they move within it, interpenetrate. In the given activity 2 phases are considered: the carrying -gas and the discrete -particles. Any small volume of the space in question, at any particular time, can be regarded as containing a volume fraction a, of the i-th phase, so that the sum of all a, must be equivalent 1. The interaction between the phases is taken into account by the determination of the drag force of particles. 0-7803-5729-9/99/$10.00 0 1999 IEEE
Abstract. In this paper a two-phase (gas -solid particles) swirling turbulent flow in the separation chamber of a centrifugal apparatus is considered. The results of mathematical modeling of flow at different settings are shown.This paper presents a two-phase (gas -solids) swirling turbulent flow in the separation chamber of the centrifugal apparatus with an additional supply of gas (Fig. 1). Through the section A-A the gas flow is supplied with particles having radial and tangential velocity components. Through the section B-B an additional supply of gas without solid is provided. The flow in the vortex chamber is axisymmetric by its nature.Through the section C-C the swirling flow together with the gas fraction of fine particles leaves the working area of the vortex chamber. Through the section B-B the incoming gas stream filters larger particles of the particulate fraction, returning finer particles to the working zone of the classifier. Large particles, due to the predominance of the centrifugal force over the aerodynamic force, leave the vortex chamber through the cross section B-B. All solid walls of the apparatus can rotate about the axis O-Z, giving additional rotation of the gas flow with the solid phase and thereby aligning the field of circumferential velocity vector components. To describe the swirling gas flow in the separation chamber a set of the Reynolds equations is used. For its closure the generalized Boussinesq model is applied according to which the Reynolds stresses are considered to be proportional to the mean flow strain rate and the coefficient of eddy viscosity νt. Thus, the system of Reynolds equations in the cylindrical coordinate system in the conservative dimensionless form for an incompressible viscous fluid taking into account the axial symmetry (*/* = 0) can be written as follows:*ru r * + * *r (ru 2 r ) + * *z (ru z u r ) − 1 Re * *r r(1 + ν t ) *u r *r + * *z r(1 + ν t ) *u r *z = = u 2 − r *p *r + r Re *ν t *r *u r *r + *ν t *z *u z *r − u r r 2 (1 + ν t ) − 1 N j =1 j j (u r − w rj ) Stk ; a Corresponding author:
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