Open AccessA Computer Model of the Dynamics of a Heterogeneous Liquid-Solid Medium in a Technological Apparatus with Bubbling
Author(s) -
Olga Oliynyk,
Yurii Taranenko
Publication year - 2020
Publication title -
metrologìâ ta priladi
Language(s) - English
Resource type - Journals
eISSN - 2663-9564
pISSN - 2307-2180
DOI - 10.33955/2307-2180(2)2020.51-56
Subject(s) - suspension (topology) , viscosity , vibration , mechanics , liquid medium , laminar flow , field (mathematics) , liquid phase , particle (ecology) , equations of motion , materials science , process engineering , simulation , computer science , chemical engineering , thermodynamics , classical mechanics , engineering , physics , acoustics , composite material , mathematics , oceanography , homotopy , pure mathematics , geology
The article is devoted to the development of a computer model of the dynamics of a heterogeneous liquid-solid medium in a technological apparatus with bubbling. In a heterogeneous bubbler medium, the known methods of environmental control are difficult to implement and practically unsuitable for control in the flow of the medium; therefore, new approaches to the implementation of the software and hardware complex of information systems are necessary.
Existing mathematical not take into account the change in the concentration of the liquid due to the formation of solid suspensions included in the bubbling of the liquid by flue gases and the dynamics of the behavior of gas bubbles in the vibration field of the apparatus. Vibration measuring instruments could solve the problem by taking into account changes in the density and viscosity of the components of the medium.
The developed mathematical model of a heterogeneous liquid-solid medium, which ensures the accuracy of information in information systems, is based on the model of vibration frequency methods for monitoring the concentration of the solid fraction of suspensions, based on the use of the behavior of the solid phase of the suspension in a vibration field.
Based on the equation of motion of a particle in a vibrational field for the case of a spherical shape of the particle, which is in free conditions under a laminar regime of motion, taking into account the dependence of the density of the suspension on the density of the solid phase and liquid, the viscosity of the suspension on the viscosity of the liquid and density of the solid phase, a new differential equation is obtained.
The obtained equation of dynamics of a heterogeneous liquid-solid medium in a technological apparatus with bubbling is solved by a software solution in the Python environment, with the introduction of the sympy library using complex Conjugation and simplification.
Relations are obtained for controlling the concentration of the suspension formed in the technological apparatus after bubbling flue gases through a liquid layer. The presented results of the software implementation of the model confirm that with an increase in the frequency of the vibrational field, the relative amplitude of the solid phase decreases, and therefore its effective mass participating in the vibrations of the medium.