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, Re D = 1.4 × 10 5 and Re λ = 548). Air is slightly heated (20 • 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 vw 2 , uθ 2 , vθ 2 , u 2 θ, v 2 θ and uvθ ). 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 u i u j components are also determined, which enables analysis of the turbulent kinetic energy redistribution mechanisms. The impact of the surrogacy vw 2 = 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 ( k and θ ) are proposed here for use in future studies of the passive scalar in a turbulent round jet. Finally, the budgets of turbulent heat fluxes (u i θ) are presented.

Complete self-preservation on the axis of a turbulent round jet

“…Thiesset et al (2014) reported values of A calculated with (3.1) using the data of Friehe et al (1971), Burattini et al (2005b) and Mi et al (2013) and obtained 39.7, 32.7 and 33.5 respectively, which are in quite good agreement with our calculated value. Using the data of Darisse et al (2015), we found that A = 41 when calculated with (3.1), while the experimental estimate is approximately 42. Finally, using the correction of proposed by Darisse et al (2015), we also calculated A based on (3.1) for the data of Panchapakesan & Lumley (1993) and Hussein, Capp & George (1994) and found 34.8 and 38.8 respectively.…”

“…Using the data of Darisse et al (2015), we found that A = 41 when calculated with (3.1), while the experimental estimate is approximately 42. Finally, using the correction of proposed by Darisse et al (2015), we also calculated A based on (3.1) for the data of Panchapakesan & Lumley (1993) and Hussein, Capp & George (1994) and found 34.8 and 38.8 respectively. While relatively small, the variation of the analytical values between these experiments is likely to reflect the differences in initial conditions, which certainly affect the experimental estimates of R, A U and A I (e.g.…”

“…= T k , where T k represents all remaining terms in the equation of k). The one-point energy budget on the axis of the round jet obtained by Darisse et al (2015) is commensurate with the following transport equation for (δq) 2 (Danaila, Antonia & Burattini 2004;Burattini et al 2005b):…”

“…energy budget rather than an input to this budget. Darisse, Lemay & Benaissa (2015) have recently carried out extensive measurements in a slightly heated turbulent round jet, and provided the budgets for the transport equations of k, the Reynolds stresses and θ 2 (the passive temperature variance). These (one-point) budgets, in particular those of k and θ 2 , are important in the context of s.b.s.…”

“…It should be noted that the axisymmetry applies along the axis so that, e.g., v 2 = w 2 and (δv) 2 = (δw) 2 ). Darisse et al (2015) showed that the energy contributions from the pressure diffusion, turbulent diffusion and molecular diffusion are negligible on the axis of the round jet. It should be stressed that Darisse et al (2015) estimated the pressure diffusion term using the Lumley model (Lumley 1978).…”