Mixing and scalar dissipation rate statistics in a starting gas jet

Abstract

We quantify the temporal development of the mixing field of a starting jet by measuring the mixture fraction and the scalar dissipation rate and their statistics in an isothermal, impulsively started, gaseous jet. The scalar measurements are performed using planar laser induced fluorescence and, with appropriate processing of the resulting images, allow scalar dissipation rate measurements within 20%. The probability density functions of the mixture fraction, measured within a region of the order of 3 times the Batchelor length scale of the flow, are bimodal and skewed around a well-mixed radial location, which depends on the downstream distance and the time after the start of injection. The instantaneous distributions of the scalar dissipation rate reveal regions of high mixing at the jet periphery and at the developing vortex ring. The normalised probability density function (pdf) of the scalar dissipation rate at various flow positions and times after the start of injection has the same characteristic shape but differs from the usually suggested lognormal distribution at both low and high dissipation values; the same, also, holds true for the pdf conditioned on different values of the mixture fraction. The mean of the scalar dissipation rate conditional on mixture fraction shows a variation across the mixture fraction range, which differs between flow locations and times after the start of injection; however, at later times and for larger downstream distances the conditional mean between flow locations has similar distributions. Implications of the measurements for the auto-ignition of gaseous jets are examined and demonstrate that near the nozzle exit or at earlier times conditions are un-favourable for auto-ignition.

Mixing and scalar dissipation rate in a decaying jet

“…Such skewness has been observed in several different turbulent flows [21][22][23][24], as well as in the starting jet [12].…”

“…values. As suggested in [12], the generalised Gumbel distribution can be a better fit. The form of the distribution for a normalised variable is 𝛱 𝜃 = 𝑎× 𝑒𝑥𝑝 𝜋/2×𝑏 × 𝜃 − 𝑐 − 𝜋/2×𝑒𝑥𝑝 𝑏× 𝜃 − 𝑐 : here 𝑎 = 2.065 , 𝑏 = 0.9038 and 𝑐 = 0.2799 fitted the data andthis fitting is also drawn in Fig.…”

“…The flow configuration of the measurements has been discussed in detail elsewhere [11][12][13]. Briefly, a fast acting, automotive-type gas injector (KEIHIN DM4 62cc) injected an unsteady gas jet, installed inside a 300 mm long fused silica cylinder with internal diameter of 80 mm.…”

“…However, measured PDFs [11][12][13][14][15] show differences from the lognormal distribution at both low and high values of SDR. The PDF typically has a longer tail at low rates, and falls-off more quickly at high rates, as compared to the lognormal distribution.…”

Laser ignition of methane jets in homogenous and isotropic turbulence

“…In the present study, Point 1 is located on the centreline and 5 diameters downstream the nozzle exit, point 2 is located 1 diameter off the centreline and 5 diameters downstream the nozzle exit, while point 3 is located on the centreline and 10 diameters downstream the nozzle exit. According to the mixture fraction of a starting jet measured in [17], and considering the 10 ms delay between the injection and laser triggering signals of the present study, the local mixture fraction at point 1 should be much higher than stoichiometric, while the mixture at point 2 should be near stoichiometric. The local mixture fraction at point 3 is expected to be in between points 1 and 2.…”