Statistical tomography for scalar turbulence measurements using line of sight optical techniques
Turbulence has been an intriguing subject for several decades with past studies focusing on understanding the transition to turbulence and characterizing turbulence using statistical tools. In present research rainbow schlieren deflectometry (RSD), a line of sight optical technique, is used and its high spatio-temporal resolution measurement capability is demonstrated through transitional hydrogen gas jet diffusion flame experiments wherein hitherto unknown secondary instability in flame surface is captured by employing 23 microseconds exposure time and 400 micro-meter/pixel resolution at 2000 Hz image sampling rate. Significant effects of buoyancy previously thought unimportant are identified and a conceptual view of transitional jet diffusion flames illustrating various instabilities is developed. The quantitative characterization of turbulent flow requires local scalar field statistics. However, RSD provides path integrated measurements that must be deconvoluted to obtain the local field statistics. For round turbulent jets, Abel inverse transform can be used to deconvolute time averaged local field quantities such as mean refractive index difference. Based on critical evaluation of four techniques two point formula, a semi-analytical approach, is recommended to evaluate the improper integral in Abel inverse transform with best accuracy and minimum error propagation. For deconvolution of second moment statistics (scalar fluctuation intensity) from path integrated measurements cross beam correlation (CBC) algorithm is presented and analyzed using noise free synthetic scalar turbulent data. CBC algorithm is found to yield accurate reconstruction only in fully developed turbulent flows and it required knowledge of statistics at inlet boundary that are generally unknown. To overcome limitations of CBC algorithm, a novel spectral analysis algorithm is developed and verified using synthetic scalar turbulent data. The algorithm provided local field statistics (mean and variance) at high accuracy using path integrated data in only one line of sight. Present implementation was limited to time averaged axisymmetric turbulent flow although its extension to asymmetric flow is feasible. Spectral analysis algorithm was applied for measurements in a turbulent helium jet with diameter, d = 2.96 mm at Reynolds number, Re = 3500 and Richardson's number, Ri =0.0000102335. Mean, variance, autocorrelation function, and power spectra of local scalar properties are presented to characterize the turbulent flow.