Budgets of turbulent kinetic energy, Reynolds stresses, variance of temperature fluctuations and turbulent heat fluxes in a round jet

Abstract

The self-preserving region of a free round turbulent air jet at high Reynolds number is investigated experimentally (at$x/D=30$,$\mathit{Re}_{D}=1.4\times 10^{5}$and$\mathit{Re}_{{\it\lambda}}=548$). Air is slightly heated ($20\,^{\circ }\text{C}$above ambient) in order to use temperature as a passive scalar. Laser doppler velocimetry and simultaneous laser doppler velocimetry–cold-wire thermometry measurements are used to evaluate turbulent kinetic energy and temperature variance budgets in identical flow conditions. Special attention is paid to the control of initial conditions and the statistical convergence of the data acquired. Measurements of the variance, third-order moments and mixed correlations of velocity and temperature are provided (including$\overline{vw^{2}}$,$\overline{u{\it\theta}^{2}}$,$\overline{v{\it\theta}^{2}}$,$\overline{u^{2}{\it\theta}}$,$\overline{v^{2}{\it\theta}}$and$\overline{uv{\it\theta}}$). The agreement of the present results with the analytical expressions given by the continuity, mean momentum and mean enthalpy equations supports their consistency. The turbulent kinetic energy transport budget is established using Lumley’s model for the pressure diffusion term. Dissipation is inferred as the closing balance. The transport budgets of the$\overline{u_{i}u_{j}}$components are also determined, which enables analysis of the turbulent kinetic energy redistribution mechanisms. The impact of the surrogacy$\overline{vw^{2}}=\overline{v^{3}}$is then analysed in detail. In addition, the present data offer an opportunity to evaluate every single term of the passive scalar transport budget, except for the dissipation, which is also inferred as the closing balance. Hence, estimates of the dissipation rates of turbulent kinetic energy and temperature fluctuations (${\it\epsilon}_{k}$and${\it\epsilon}_{{\it\theta}}$) are proposed here for use in future studies of the passive scalar in a turbulent round jet. Finally, the budgets of turbulent heat fluxes ($\overline{u_{i}{\it\theta}}$) are presented.