MATHEMATICAL MODELS OF THE THERMAL PROTECTION COATING OF THE GAS GENERATOR OF THE HYDROGEN STORAGE AND SUPPLY SYSTEM
DOI:
https://doi.org/10.33042/2522-1809-2024-4-185-159-165Keywords:
gas generator, hydrogen storage and supply system, thermal protection coatingAbstract
The article describes the properties of the thermal protection coating of the gas generator of the hydrogen storage and supply system by two transfer functions with Hurwitz polynomials of the third order. Obtaining such transfer functions is based on the solution of the non-stationary heat conduction equation, represented in operator form using the integral Laplace transform, and in which approximating spline functions in the form of second-order polynomials are used. The article gives the solution of the non-stationary thermal conductivity equation, which describes the thermal processes in the heat-protective coating of the gas generator of the hydrogen storage and supply system under the thermal effect of a fire. This solution comes in the operator form for the surface temperature of the heat-protective coating on the side of the gas generator wall. The peculiarity of this decision is the presence of hyperbolic functions of an irrational argument in its composition. The structural and dynamic scheme of the thermodynamic system ‘gas generator wall – heat-protective coating’ is presented, the feature of which is the presence of two entrances. The signal at the scheme’s first input reflects the thermal effect of the fire, and the signal at the second input reflects the thermal state of the gas generator cavity. An equivalent mathematical transition to the description of thermal processes in the heat-protective coating of the gas generator of the hydrogen storage and supply system was carried out. This transition happened due to the use of spline functions, which approximate the hyperbolic functions of the irrational argument and are polynomials of the second order. The article gives a verbal interpretation of the algorithm for determining the transfer functions of the heat-protective coating of the gas generator of the hydrogen storage and supply system and also an example of its implementation. Furthermore, it shows that for the given conditions of functioning of the gas generator heat-protective coating, the relative errors in approximation of hyperbolic functions by second-order polynomials do not exceed 1.7 %, and the average relative error when equivalent replacement of transfer functions does not exceed 3.8 %.
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