Approximation Methods for Analysis and Formation of Mechanisms for Regulating Heat and Mass Transfer Processes in Heat Equipment Systems

Abstract

The need to increase the accuracy of decisions and the depth of analysis of complex heat power systems determines the relevance of modeling and regulation of heat and mass transfer processes with the development of theoretical models and the development of a new methodology. Uncertainty of the environment increases the significance of the problems of insufficient efficiency of the available numerical approaches to the modeling of dynamic processes and the regulation of heating elements. Therefore, the aim of the article was to develop the applied aspects of the theory of solving nonlinear problems, provisions of the analytical methodology and the methods for regulating stepwise thermodynamic processes based on adapted tools for approximating generalized and step functions. The following tasks were solved: the structure of mechanisms was determined, including regulators of the energy efficiency of the flare device of the boiler unit with an expanded combustion zone; a model of integration-balancing regulation of heat transfer with four types of unsteady processes determined by indicators of changes in the direction and sign of the entropy of the effects of the regulators is proposed. Quantitative meters of energy efficiency of combustion and heat transfer processes in boiler units have been developed. Mathematical adapted and developed technical and organizational methods for solving problems: approximation of the original functions (generalized Dirac and stepwise) by a sequence of recursive periodic functions; simulation of spasmodic heat transfer processes based on step functions; structuring the mechanism for regulating heat transfer, including four types of regulators; empirical modeling of the assessment and regulation of energy efficiency, taking into account the directivity and severity of the effects of regulators displayed by derivatives of higher orders of approximation of energy efficiency functions. The results were obtained: mathematical ones were adapted and new approximation models for generalized functions were built; quantitative measuring instruments of process dynamics for regulating the technical and organizational mechanisms of heat transfer were obtained.

Mathematical Foundations for Modeling a Zero-Carbon Electric Power System in Terms of Sustainability

“…In other words, for any values of the parameter (even arbitrarily large, but finite values) there will always be ω < ω 1 for which the values of the function constructed by Kotelnikov will differ from π, and there will always be ω > ω 1 , for which its values will be non-zero. Moreover, it is important to note that the indicated difference with increasing T does not tend to zero, but to approximately 0.281 [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. Mathematical tools for approximating functions make it possible to evaluate and more accurately control jump-like processes.…”

“…Alyukov et al [5][6][7][8][9][10][11] make it possible to predict the influence of individual factors on the operation of an enterprise as a whole. V. Balakrishnan et al, A. Alabugin, and A. Nikitin showed that new control algorithms with increased accuracy significantly reduce the impact of forecasting errors [12][13][14]. In the economic ecosystems of a number of developing countries, researchers have identified the insufficient decarbonization of industrial territories.…”

Methodological Foundations for Modeling the Processes of Combining Organic Fuel Generation Systems and Photovoltaic Cells into a Single Energy Technology Complex

“…At many domestic enterprises of industrial heat and power engineering, evolutionary methods of modernization of individual elements of equipment with a low level of innovation of technologies and results prevail. Investment decisions on new construction and technical re-equipment projects are often made without modeling the processes of transition to technologies and organizational methods of energy saving based on the factors of the new industrial revolution [22].…”

“…In such a digital economy, it is necessary to use open educational platforms based on large databases [21]. Especially they are necessary for analyzing the possibilities of advanced combination of resources based on the organization of ETC with the inclusion of objects of distributed energy, other multipurpose productions and participation in projects of such transformation of research and educational complexes of type 4.0 [22,23]. The considered methods solve a complex of problems of the organization of processes of high-tech development with use of integration of the diversified resources.…”