Line-of-sight (LOS) variations of temperature and concentrations of CO and H 2 O within a simulated high-pressure ame are deduced using an inverse analysis. In this work, synthetic spectral transmittances, acquired by a Fourier transform infrared spectrometer along a single LOS, represent the experimental data. The theoretical basis of the analysis is that spectral variations in the absorption coef cient contain information about spatial variations in temperature and species concentrations. The Marquardt-Levenberg method is used to solve for the temperature and species concentrations. Accurate spatial variations of temperature and species concentrations can be recovered when changes in the spectral transmittances caused by noise are smaller than those changes caused by spatial variations in temperature and species concentrations. The recovered centerline temperatures and species concentrations are, respectively, within 5 and 20% of the synthetic values, when the variations in spectral transmittance caused by noise are about the same as that caused by spatial variations in temperature and species concentrations. As temperature increases, a redistribution in the molecular states decreases the spectral absorptances, thereby causing the analysis to become more sensitive to the effects of noise.
Nomenclaturec = speed of light, m/s E = rotational energy of lower state F = spectral transmittance g = normalized rovibrational (rotational-vibrational) line shape function h = Planck's constant k = Boltzmann's constant L = 0.0025 m, half of path length m P = order of power series used to approximate partial-pressure pro les m T = order of power series used to approximate temperature pro les N = number of molecules per cm 3 per atm N d = number of data points in measurement N np = number of gaseous species present along the line of sight that is not being quanti ed N p = number of half-periods used to calculate integral over the wave number range N r = number of rovibrational transitions N s = number of species N x = order of quadrature used in the integral along path length N = order of quadrature used in convolution integral P = pressure, atm P i,m = coef cients for partial pressure of ith species Q = partition function S = line intensity T = temperature, K T m = coef cients for temperature pro le w l = weights for Gauss-Legendre quadrature X n (x) = row vector of species mole fractions, Xn = ( ) X , X , X N CO H O 2 2 x = distance along the line of sight from the center of the ame z = x/L = absorption coef cient p = half-width at half-height of spectral line, cm 1 max = maximum retardation of moving mirror, cm n = half-period of instrument line shape, cm 1 = wave number, cm 1 = standard deviation = temperature exponent for p 2 = sum of squares, Eq. (11) = Gaussian distribution function Subscripts i = ith species j= jth rovibrational transition k, l = index for quadrature noise = quantity affected by noise r = reference state t = total true = true quantity 0 = rovibrational line center Superscripts 1, 2 = steps 1 and 2 of d...