A parametric study of the validity of the weak-line and strong-line limits of infrared band absorption

Abstract

A current version of the NASA band model was used to calculate the errors in the weakline and strong-line band absorption limits for a wide range of temperatures, pressures, path lengths, and species concentrations. The weak-line limit is valid under the condition 2u/β « 1. The strong-line limit is valid under the opposite conditions of the weak-line limit, i.e. 2u/β » 1. These two conditions are not always easily related to physical parameters such as temperature, pressure, path length, and species concentration. Therefore, the band model was used in a parametric study to calculate the weak-line limit and strong-line limit errors as a function of the temperature (100 K - 3000 K), pressure (0.0001 - 10.0 atm), path length (1 cm - 10 km), and species concentration (0.00033 - 1.0) for atmospheric and jet-exhaust-plume conditions. The results were generated in the form of spectral graphs (500 - 5000 cm⁻¹) of the limit error superimposed with the general-case absorptivity, and as contour graphs of the band-integrated limit error. The error in the contour graphs was plotted versus temperature and pressure for a given path length and species concentration. The contour graphs were generated for the 2.7 μm and 6.3 μm H₂O bands, the 2.7 μm and 4.3 μm CO₂ bands, and the medium wave (3.0 - 5.0 μm) and long wave (8.0 - 12.0 μm) bands. In the spectral graphs, the greatest error in both limits tends to occur in the core of the absorption bands when the absorption bands are small and in the band wings when the bands are relatively wide. The weak-line error generally occurs in localized pressure-temperature regimes in the contour graphs. The error is generally small at low and high temperatures and pressures, but can be significant at intermediate pressures and temperatures. The weak-line error also increases steadily with path length. The strong-line error, on the other hand, was not nearly as predictable as the weak-line error. At short path lengths, the strong-line error exhibits a linear behavior with respect to pressure. However, at longer path lengths, the strong-line error appeared saddle shaped as a function of both pressure and temperature.