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Mathematical model of electromagnetic radiation of flame

DOI 10.18127/j15604128-201807-05

Keywords:

M.A. Vaganov – Ph.D.(Eng.), Associate Professor, Saint-Petersburg State University of Aerospace Instrumentation
E-mail: ma.vaganov@gmail.com
S.V. Kulakov – Dr.Sc.(Eng.), Professor, Saint-Petersburg State University of Aerospace Instrumentation
E-mail: svk25@mail.ru
O.D. Moskaletz – Ph.D.(Eng.), Senior Research Scientist, Associate Professor, Saint-Petersburg State University of Aerospace Instrumentation
E-mail: molegd@mail.ru


The electromagnetic radiation formed in the combustion process is considered in this paper as signal carrying information about the processes occurring in the combustion center. The main characteristic of this radiation is its spectrum. The spectral composition of the radiation is determined by the conditions under which the combustion process takes place. Accordingly, it carries information about these conditions.
Traditionally, optical spectra are represented by a combination of continuous and linear spectra. The continuous component of the spectral distribution is broadband radiation and it can be described using Planck's law. As for the spectral «lines», they are not lines per se. These «lines» are narrow-band modulated oscillations having both amplitude and angular modulation. For this reason their adequate description can be performed within the framework of narrow-band stationary random processes.
Therefore, an approach to the mathematical description of the flame electromagnetic radiation in the framework of the theory of sta-tionary random processes is proposed in this paper proposes. An optical radiation falling on the aperture of the spectral device is con-sidered as variable (depending on t) random field in two-dimensional space (x, y) in the framework of this approach. Accordingly, the space-time random field at the aperture of the spectral device can be characterized by three correlation functions - two spatial and one temporal.
An expression in the form of a power series is proposed to estimate the influence of the field distribution irregularity on the input aperture of the spectral device on the results of spectroscopic measurements.
Since the main task of spectroscopy is to obtain information about time changes, i.e. about the dynamics of the functions of sources (combustion centers), the main attention should be paid to the transformation of random processes by the spectral device. In particular, when analyzing separate spectral lines, their oscillations can be described in the form of narrow – band stationary random processes, and their realizations-in the form of analytical signals.
On the basis of these studies, models of signals generated by combustion centers and model of noise against the background which these signals act can be proposed. It will open the way for the creation of more advanced equipment for early detection of fire centers with increased probability of correct detection of fires and reduced probability of false alarm.

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