MATHEMATICAL MODELING OF THE PROCESS EVAPORATION OF MULBERRY FRUITS JUICE

Abstract

When evaporating the juice of mulberry fruits, a differential equation was obtained for changing the amount of liquid over time, expressed as a material balance, converted to the liquid level in the separator of the evaporator, an expression for the density of the liquid, its flow rates at the inlet and outlet of the apparatus, the differential equation for changing the temperature of the liquid over time. Using the reference data of the state of water and steam, equations for the temperature, enthalpy of liquid and dry steam are obtained. A system of equations has been obtained - a mathematical model of the dynamics of the process of liquid evaporation in a single-vessel vacuum evaporator. Using the SIMULINK part of the MATLAB program, a computer model for solving equations was compiled. Some results of studies of the evaporation of mulberry juice on a five-case vacuum evaporator are given, the optimal number of stages of the complex is found. Since the calculation of the process of evaporation of water vapor is associated with the thermodynamic parameters of the state of water, it is necessary to obtain equations for the dependence of the boiling point of water, the heat of vaporization of water, the enthalpy of steam, the enthalpy of water on pressure. Experimental data have been obtained for a long time, they are successfully used, however, there are no uniform empirical equations used by all researchers. Using the capabilities of the MATLAB program, by statistical processing of tabular data, we obtain empirical equations in the form of polynomials for the state of water and water vapor, describing the real picture with an accuracy of 98% or more.