Conditional statistics of the turbulent/non-turbulent interface in a jet flow

Abstract

AbstractUsing two-dimensional high-speed measurements of the mixture fraction $Z$ in a turbulent round jet with nozzle-based Reynolds numbers $R{e}_{0} $ between 3000 and 18 440, we investigate the scalar turbulent/non-turbulent (T/NT) interface of the flow. The mixture fraction steeply changes from $Z= 0$ to a final value which is typically larger than 0.1. Since combustion occurs in the vicinity of the stoichiometric mixture fraction, which is around $Z= 0. 06$ for typical fuel/air mixtures, it is expected to take place largely within the turbulent/non-turbulent interface. Therefore, deep understanding of this part of the flow is essential for an accurate modelling of turbulent non-premixed combustion. To this end, we use a composite model developed by Effelsberg & Peters (Combust. Flame, vol. 50, 1983, pp. 351–360) for the probability density function (p.d.f.) $P(Z)$ which takes into account the different contributions from the fully turbulent as well as the turbulent/non-turbulent interface part of the flow. A very good agreement between the measurements and the model is observed over a wide range of axial and radial locations as well as at varying intermittency factor $\gamma $ and shear. Furthermore, we observe a constant mean mixture fraction value in the fully turbulent region. The p.d.f. of this region is thus of non-marching character, which is attributed physically to the meandering nature of the fully turbulent core of the jet flow. Finally, the location and in particular the scaling of the thickness $\delta $ of the scalar turbulent/non-turbulent interface are investigated. We provide the first experimental results for the thickness of the interface over the above-mentioned Reynolds number range and observe $\delta / L\sim R{ e}_{\lambda }^{- 1} $, where $L$ is an integral length scale and $R{e}_{\lambda } $ the local Reynolds number based on the Taylor scale $\lambda $, meaning that $\delta \sim \lambda $. This result also supports the assumption often made in modelling of the stoichiometric scalar dissipation rate ${\chi }_{st} $ being a Reynolds-number-independent quantity.