MATHEMATICAL DESCRIPTION IN THE FLUID FLOW FLUCTUATIONSTHROUGH A ROTARY-PULSE CAVITATION APPARATUS

Abstract

Rotary pulse devices are used for grinding various materials in liquids, preparing highly dispersed suspensions and emulsions, intensifying mass transfer processes, homogenizing and disinfecting liquids. There are several ways to calculate the rotary-impulse apparatus parameters; however, to implement any of them, it is necessary to know the fluid movement patterns both in the rotor and stator channels, and outside the apparatus.

The article is devoted to theoretical studies of fluid movement through a rotary-impulse apparatus. As a result of the research, a growth pattern in the amplitude and period of pulsations of the total fluid flow through the apparatus has been revealed as the greatest common divisor of the numbers of its rotor and stator channels increases.

A sinusoidal function Q_sin(t) to describe the pulsation of liquid flow Q through a rotary-pulse apparatus is proposed. The coefficients of the function Q_sin(t) are the average fluid flow through the apparatus, the amplitude and period of the pulsations. Using mathematical statistics methods, it has been established that the function Q_sin(t) has a strong correlation (coefficient r ≥ 0.85) with the instantaneous flow rate values Q and can be used to determine the processed material flow parameters at the inlet and outlet of the rotary-impulse apparatus.