Gaussian model for emission rate measurement of heated plumes using hyperspectral data. (February 2018) - Grauer, Samuel J.; Conrad, Bradley M.; Miguel, Rodrigo B.; Daun, Kyle J.
Highlights: A Gaussian plume model is proposed for remote gas sensing by hyperspectral imaging. Present models implicitly assume a uniform distribution of emissions within the plume. Synthetic hypercubes are generated for a commercial camera with a plume simulation. Gaussian profiles of state variables improve column density estimates by 14%. Abstract: This paper presents a novel model for measuring the emission rate of a heated gas plume using hyperspectral data from an FTIR imaging spectrometer. The radiative transfer equation (RTE) is used to relate the spectral intensity of a pixel to presumed Gaussian distributions of volume fraction and temperature within the plume, along a line-of-sight that corresponds to the pixel, whereas previous techniques exclusively presume uniform distributions for these parameters. Estimates of volume fraction and temperature are converted to a column density by integrating the local molecular density along each path. Image correlation velocimetry is then employed on raw spectral intensity images to estimate the volume-weighted normal velocity at each pixel. Finally, integrating the product of velocity and column density along a control surface yields an estimate of the instantaneous emission rate. For validation, emission rate estimates were derived from synthetic hyperspectral images of a heated methane plume, generated using data from a large-eddy simulation. Calculating the RTE with Gaussian distributions of volume fraction and temperature, instead of uniform distributions, improved the accuracy of column density measurement by 14%. Moreover, the mean methane emission rate measured using our approach was within 4% of the ground truth. These results support the use of Gaussian distributions of thermodynamic properties in calculation of the RTE for optical gas diagnostics.