Development of mathematical models of test systems as objects with lumped parameters

Abstract

This paper deals with the problem of constructing a mathematical model for studying the thermal regime of a test system at the design stage. The test system is presented as a complex chemical-technological system, which includes a large number of elements, components and devices, characterized by a variety of functional and thermal relationships. The block-hierarchical method is used for designing the system under consideration. A thermal block diagram of the system has been developed, which includes six interconnected blocks: a thermostat; coolant; heat exchanger; cubic apparatus, medium in apparatus and environment. A mathematical model has been created to estimate the average temperatures in the system, which allows you to calculate the integral characteristics of heat exchange processes (the values average intake temperatures and the values surface average temperatures, average heat fluxes) taking into account the interaction between all blocks of the system. It was assumed that each element of the system under consideration can have thermal connections, both with the environment and with other elements of the system. It was assumed that the element can dissipate its own power, as well as the power supplied for thermal control of the element, which depends on its temperature. The calculation of the temperature fields of bodies and flows of heat carriers was carried out on the basis of models with concentrated parameters, with the assumption that there are no temperature gradients in all directions. The model is represented by a system of ordinary differential equations. The dependences of temperature on time change for two non-stationary modes of a thermostatic system consisting of a hollow device of cubic shape with a volume 3 m3 filled with gas and equipped with a heat exchanger are shown. The developed mathematical model allows solving the problems of temperature stabilization of the test system.