Effect of varying composition on temperature reconstructions obtained from refractive index measurements in flames

Optical methods (such as holographic interferometry, speckle photography, speckle shearing interferometry, moiré deflectometry, rainbow Schlieren deflectometry and Talbot interferometry, and so forth) have the potential for accurately measuring the entire temperature field associated with multidimensional flames, which may be difficult to do using other techniques. These interferometric or deflectometric techniques first determine the refractive index in flames, and thereafter infer the temperature distribution. The relationship between the refractive index and temperature is obtained by using a state equation and the Gladstone-Dale relation. However, a potential source of error arises since the local composition of the flame being studied is usually unknown. In a previous investigation, we examined the occurrence of this error by assuming the local flame composition to be the same as that of air at the local temperature. This was examined through one-dimensional simulations of counterflow flames. We found that while calculating the temperature from the measured refractive index this assumption could lead to significant errors for some flames and to minimal errors in other flames. This investigation quantifies those errors in the context of two-dimensional flames in both planar and axisymmetric geometries. It is found that the refractive index values of a mixture are nearly identical with those of the refractive index of air for partially premixed flames (PPFs). The maximum error lies in the range of 6.3 to 10.7% for one-dimensional (1-D) counterflow PPFs, and between 6.1 to 8.0% for two-dimensional (2-D) planar and axisymmetric PPFs (for equivalence ratios in the range of 1.5 ≤ φr ≤ 2.0). For nonpremixed flames, however, the maximum error can have values up to 33.8% and 34.5% for the 1-D and 2-D configurations, respectively. Therefore, the accurate inference of the temperature of nonpremixed flames from the measured refractive index distribution requires that an alternative approach be developed. We have developed an interpolation method that reduces the maximum error from 34.5% to 9.8% for these flames, and is associated with even smaller errors in most other regions of these flames.