Turbulent time scales in a nonpremixed turbulent jet flame by using high-repetition rate thermometry

High-repetition-rate (10-kHz), single-point laser Rayleigh scattering thermometry was used to measure temperature and thermal dissipation rate fluctuations in a turbulent nonpremixed jet flame at a Reynolds number of 15,200. The measurements were made along the jet-flame centerline for downstream locations in the vicinity of the flame tip and were aimed at obtaining one-dimensional (1D) energy and dissipation spectra and estimates of the integral and Batchelor scales. The signal-to-noise ratios of the measured correlations, energy spectra, and dissipation spectra were significantly improved by using two detectors to measure redundant scattering signals from the same point, followed by computing the cross-correlation of these signals. Measurements of the integral scales show good agreement with measurements in isothermal jets except near the stoichiometric flame length, where the flame scales are smaller. These smaller scales are attributed to the state relationship between temperature and mixture fraction. The cutoff frequency of the dissipation range (i.e., the Batchelor frequency) is determined from the 1D thermal dissipation spectra. The experimentally determined cutoff frequencies agree with those estimated using nonreacting jet scaling laws, provided an appropriate local Reynolds number is used that is significantly smaller than the jet exit Reynolds number. The resulting 1D energy and dissipation spectra at all downstream stations collapse when properly normalized and fit well to model spectra at a Taylor Reynolds number near 55. This Reynolds number is considerably smaller than the corresponding nonreacting jet value of 150. The measured energy and dissipation spectra exhibit significant overlap at intermediate frequencies, which indicates that the largest scales of the dissipation range may be significantly influenced by the large, energy containing scales. The time-series data are also used to determine the influence of the probe resolution on the temperature variance and mean 1D thermal dissipation rate. It is shown that the resolution requirements are similar to those in nonreacting jet flows, provided the difference in the local Reynolds number is considered.