SEMI-EMPIRICAL MATHEMATICAL MODEL OF NITROGEN OXIDES EMISSION FROM LOW-EMISSION COMBUSTION CHAMBER AS A PART OF AUTOMATIC CONTROL SYSTEM OF AN AERO ENGINE

Abstract

The article is devoted to the problem of automatic control of nitrogen oxide emissions from a low-emission combustion chamber (LECC) of a gas turbine engines' (GTE) new generation. Since the measurement technologies have not reached the required level of availability today, and the reliability of the automatic control system (ACS) depends on the validity of input information about the engine state, it is proposed to use the built - in predictive mathematical model of the LECC. The model equations are functions of the measured parameters. The compact design requirements and significant nonlinearity of combustion determine the stochastic nature of the LECC. Taking into account the strict ICAO standards for the emission of harmful substances, all this leads to a narrow range of stable operating modes, limited, on the one hand, by the normalized level of nitrogen oxide emissions, and, on the other hand, by unacceptable modes of flame blowout or vibration combustion (thermoacoustic vibrations). It is proposed to build into the ACS a hybrid model of the processes of generating harmful emissions in the MEKS GTE, consisting two parts. The first semi-empirical submodel combines the physical equation of Zeldovich and the generalized empirical coefficient calculating as a function of several critical variables. This submodel allows generating training samples for the second submodel in case of insufficient experimental data. The second submodel is based on a neural network. The article discusses the development and testing of the first submodel, which identification algorithm is based on the accepted hypothesis of the possibility of applying the principle of superposition in describing the interaction of diffusion and homogeneous flames. The algorithm is based on the Zeldovich equation, which makes it possible to determine the dependence of the generation of nitrogen oxides on the composition of the air-fuel mixture using the distribution function of the probability density of its pulsations depending on the value of the integral equivalent ratio φ, which characterizes the concentration of fuel in the mixture. A feature of the LECC is the presence in the flame tube of longitudinal acoustic waves, excited by the release of heat during combustion, having a frequency equal to natural frequency of the gas-air column. These acoustic waves are leading to fluctuations of φ and causing the harmonic fluctuations in the mathematical expectation of the mixture composition. In this work the numerical modeling of the distribution of the inhomogeneity and pulsation of the fuel-air mixture concentration over the area of the flames in the CFX package allowed to obtain the characteristics of the mathematical expectations and dispersion, as well as the natural frequencies of the object. The distribution functions of the probability density of pulsations of the mixture concentration for diffusion and homogeneous circuits are calculated analytically, taking into account the acoustics of the combustion chamber. The analysis of the effect of dispersion of acoustic waves on the form of the resulting probability density curves in diffusion and homogeneous plumes is carried out.