Application of the Method of Approximating Polynomials for the Determination of the Temperature and Concentration of Hot Carbon Dioxide from Its Transmission Spectrum

Abstract

An advanced method of approximating polynomials for simultaneous determination of the temperature and concentration of a hot gas from its spectral characteristics is presented. The technique has been approved with application of the most correct measurements of carbon dioxide transmission function at temperatures 500–1770 K and partial pressures \( {\uprho}_{{\mathrm{CO}}_2} \) = 0.17–1 atm. An arbitrary number (≥2) of spectral centers is used to solve unambiguously the inverse optical problem for the transmission function in the measured spectral region. The influence of the value of the transmission function on its approximation error by the polynomial of a fixed degree is analyzed. Dependences of errors in determining the temperature and concentration of carbon dioxide on the values of its transmission function and the number of the employed spectral centers are obtained. The accuracy of determining experimental values of the thermodynamic parameters with allowance for the error of measuring the transmission function is increased.