MATHEMATICAL MODEL OF HYDRODYNAMIC CONDITIONS OF THE LIQUID FLOW AROUND THE CONIC SURFACE IN THE CYLINDRICAL CHANNEL

Abstract

Membrane methods are widespread in the processing of liquid food media. Development and implementation of new membrane equipment involves the reasonable choice of its parameters, including the sizes of several structural elements. Mathematical modeling makes it possible to select the parameters of the developed membrane equipment at the design stage on the basis of the creation and study of appropriate mathematical models. Particular interest is in the mathematical models of hydrodynamic conditions in the internal channel of the tubular ceramic membrane filter when it contains elements of various geometric shapes, aiming to reduce the influence of "concentrated polari-zation" on the productivity of the processing of liquid food media. The use of hydrodynamic elements enables to increase locally the flow rate of the product, which leads to a decrease of detained substance layer on the membrane surface and intensifies the membrane process. The hydrodynamic element in the form of conic surface has been selected. The basic analytical dependences have been examined. They helped to determine the hydrodynamic conditions, such as flow rate (Reynolds criterion) and loss of pressure, depending on the viscosity and geometric dimensions of the hydraulic resistance in the form of a conic surface in the cylindrical channel. The method of calculation of hydrodynamic conditions of the liquid flow around the conic surface in the cylindrical channel has been considered. The mathematical model of hydrodynamic conditions with hydraulic resistance in the form of a conic surface in the cylindrical channel has been created with MathCAD. The calculation of hydrodynamic conditions by the example of the movement of low concentrated water solution in the internal channel of the tubular ceramic membrane filter has been done. The rational sizes of geometric dimensions of a conic surface have been chosen.

Keywords

• mathematical model
• hydrodynamic conditions
• conic surface
• membrane methods