МАТЕМАТИЧЕСКАЯ МОДЕЛЬ МИКРОВОЛНОВОГО НАГРЕВА ОБРАБАТЫВАЕМОЙ СРЕДЫ И ТЕРМОПРЕОБРАЗОВАТЕЛЕЙ ДЛЯ КОНТРОЛЯ РАСПРЕДЕЛЕНИЯ ТЕМПЕРАТУРЫ МОДЕРНИЗИРОВАННЫМ КАЛОРИМЕТРИЧЕСКИМ МЕТОДОМ
Authors: Кувшинов Н.Е. 
Published: February 2025

В статье предложена математическая модель микроволнового нагрева обрабатываемой среды и матрицы дискретных термопреобразователей из поглощающего материала, размещённых в рабочей камере лабораторной СВЧ технологической установки, реализующей модернизированный калориметрический метод контроля распределения интенсивности электромагнитного поля. Результаты численной проверки модели на примере сушки биологических отходов показывают возможность её применения для определения момента достижения требуемого процента влажности в обрабатываемых средах. Для этого предварительно проведены калибровочные измерения диэлектрических характеристик обрабатываемой среды и их зависимости от влажности и температуры, которые заложены в разработанную модель. В заключении рассмотрены перспективы применения модели и метода для различных приложений.

Introduction. To implement controlled microwave heating (MH), it is necessary to use complex temperature control systems, which are currently don't have distributed sensors or require interruption of the technological process for measurements. Existing non-contact thermometers, pyrometers and thermal imagers for monitoring MH have drawbacks, namely, the thermometer yields an average value over the entire surface or measures the temperature in one local area, while pyrometers and thermal imagers provide excessive detailing of the thermal image of the objects surface. The aim of the research is to develop a mathematical model of the MH of the investigated medium (IM) and thermo-converters (TC) in the working chamber, which allows one to judge on the distribution of the microwave field intensity over the IM and the change in dielectric properties along the height of its layer by the temperature distribution in the TC matrix to determine the level of completeness of the technological process of MH of IM by comparing them with the previously known dielectric parameters of the IM at each stage. To build a control system, there was used a calorimetric method, advanced by the author by using fiber-optic sensors. To control the temperature, it uses a set of thermo-converters heated by the energy of the microwave field that has passed through the processed medium. The changes in the field allow one to judge on the energy absorbed in the medium, and by the location of the temperature of a specific zone, recalculated according to a certain algorithm, to take into account the known dielectric losses. In general case, when the parameters of the medium are unknown, the nature of the heating of the thermo-converters allows to obtain primary data on the features of the MH process. Typically, such systems are built on the principle of process control on the basis of an embedded mathematical model, developed for the advanced calorimetric method. Findings. The paper presents a mathematical model of the MH process of the medium and thermo-converters in the working chamber; a numerical experiment was carried out with the use of the proposed advanced calorimetric method for temperature control and the developed model in the process of drying biological waste from poultry farms and stud farms; the perspectives for the practical implementation of the advanced calorimetric method in various applications were discussed. In the framework of the numerical experiment, taking into account the priori known features of the dependences of the dielectric constant of poultry manure and horse manure on humidity and temperature, there were obtained the following findings: for the processes of drying poultry manure and horse manure with a height of 6 cm, it is reasonable to use MH at a frequency of 2450 MHz; MH can be turned off at a temperature of thermo-converters of 80 °C, such a temperature of thermo-converters is achieved at a moisture content of poultry manure and horse manure of 10%, which is the target drying value; controlling the drying process does not require direct measurement of the temperature of the medium.