Uncertainty estimates of turbulent temperature in Rayleigh scattering measurements

Abstract

In time-resolved Rayleigh scattering measurements, shot noise can be the dominant source of uncertainty in each realization, especially when the incident laser energy is relatively small. Because the relative magnitude of the uncertainty increases with decreasing signal level, higher mean temperatures also lead to increased measurement uncertainty. Although it does not affect the measured mean temperature, the uncertainty can lead to an overestimation of the root mean square (rms) of fluctuating temperature if it is not properly accounted for. In this paper, a method is presented to determine the error due to shot noise in Rayleigh scattering turbulent temperature measurements. The uncertainty in the time-resolved temperature is calculated from photon statistics and the mean temperature information. This uncertainty value is then used to estimate the error in the measured rms temperature. Once the error has been determined, it is removed from the measured rms temperature to obtain corrected results. The method was used to estimate the rms of fluctuating temperature in a plane heated air jet. A comparison of the corrected Rayleigh scattering results with those obtained by using a fast-response thermistor shows that accurate measurements can be obtained even when the error levels are in the same order of magnitude of the fluctuating temperature. With application of the same principles, the method can easily be extended to density and pressure measurements.