Fourth-order Spectral Statistics in the Developing Shear Layers of Hot Supersonic Jets

Abstract

Novel non-intrusive measurements are presented to lend insight into behavior of 4 th order velocity fluctuation spectral statistics and space-time correlations in the developing shear layer of hot supersonic jets. Fourth-order statistics are dominated by the chaotic motion of large-scale coherent structures, which appear largely as the 'skirts' of probity density. Due to the interest in predicting the power spectral spectral density of acoustic density fluctuations, a mean-square quantity, 4 th order statistics hold direct application in acoustic analogies. Despite this, limited data exist for fourth-order spectral correlations of velocity, particularly in hot supersonic jets. A Doppler-based measurement technique with a frequency resolution of 125kHz is employed to obtain time-resolved measurements and used to determine 2 nd and 4 th order space-time correlations, integral timescales, convection velocities and auto-spectra on the lip line of a hot (TTR=1.6 and TTR=2) supersonic perfectly expanded jet at M d =1.65. Comparator data obtained in the same facility using laser Doppler velocimetry is analyzed with respect to 4 th order terms indicating the importance of the 4 th order correlation in the region of immediate interface between the potential core and the shear layer.

The separation of radiating and non-radiating near-field pressure fluctuations in supersonic jets

“…The overall convection velocity U c relative to the fully expanded jet velocity is of the order of U c =U j % 0:5 (U j is the fully expanded jet speed, and U j =c 0 % 2:0 at the current operating conditions). This agrees well with experimental measurements at similar conditions [27,31,30]. The results also suggest that high-frequency fluctuations are generally convected at a higher phase velocity as compared to lowfrequency fluctuations.…”

“…It should be noted that very few flow measurements are available for supersonic hot jets. Also, relatively large differences exist between these measurements even at similar operating conditions due to the use of different experimental techniques and other limitations and uncertainties [25][26][27][28][29][30].…”

Laser Doppler Velocimetry in Supersonic Round Jets

“…Recently, LDV has been used by Brooks et al 16 to measure turbulent statistics in a new facility with cold and electrically heated over-expanded supersonic jets. Doppler Global Velocimetry, a derivative technique of LDV, has been used by the same researchers in Ecker et al 17 to obtain fourth-order statistics and velocity spectra with a frequency resolution that exceeds 100 kHz.…”

Laser velocimetry for turbofan inlet distortion applications

“…Technological advances in laboratory techniques for opticalbased flow measurements have been staggering in recent years. These developments have led to unprecedented temporal response in flow velocimetry (Ecker et al, 2014a(Ecker et al, , 2014bBeresh et al, 2017), the ability to measure flow velocity, temperature and pressure without probes or the addition of seeding particles (Doll et al, 2017) and a number of fundamental aerodynamics discoveries (e.g. confirmed existence of coherent wavepackets in supersonic jets Cavalieri et al (2013), presence of reverse flow in flat-plate turbulent boundary layers Willert et al (2018)).…”