Extensive study of temperature dissipation measurements on the centerline of a turbulent round jet based on the $$\overline{\theta^{2}}/2$$ θ 2 ¯ / 2 budget

On the basis of a two-point similarity analysis, the well-known power-law variations for the mean kinetic energy dissipation rate and the longitudinal velocity variance u 2 on the axis of a round jet are derived. In particular, the prefactor for ∝ (x − x 0 ) −4 , where x 0 is a virtual origin, follows immediately from the variation of the mean velocity, the constancy of the local turbulent intensity and the ratio between the axial and transverse velocity variance. Second, the limit at small separations of the two-point budget equation yields an exact relation illustrating the equilibrium between the skewness of the longitudinal velocity derivative S and the destruction coefficient G of enstrophy. By comparing the latter relation with that for homogeneous isotropic decaying turbulence, it is shown that the approach towards the asymptotic state at infinite Reynolds number of S + 2G/R λ in the jet differs from that in purely decaying turbulence, although S + 2G/R λ ∝ R −1 λ in each case. This suggests that, at finite Reynolds numbers, the transport equation for imposes a fundamental constraint on the balance between S and G that depends on the type of large-scale forcing and may thus differ from flow to flow. This questions the conjecture that S and G follow a universal evolution with R λ ; instead, S and G must be tested separately in each flow. The implication for the constant C 2 in the k − model is also discussed.

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

Thiesset

Antonia

Djenidi

2014

J. Fluid Mech.

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

2015

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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.

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An empirical expression for on the axis of a slightly heated turbulent round jet

et al. 2019

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Self-preservation analyses of the equations for the mean temperature and the second-order temperature structure function on the axis of a slightly heated turbulent round jet are exploited in an attempt to develop an analytical expression for $\unicode[STIX]{x1D716}_{\unicode[STIX]{x1D703}}$, the mean dissipation rate of $\overline{\unicode[STIX]{x1D703}^{2}}/2$, where $\overline{\unicode[STIX]{x1D703}^{2}}$ is the temperature variance. The analytical approach follows that of Thiesset et al. (J. Fluid Mech., vol. 748, 2014, R2) who developed an expression for $\unicode[STIX]{x1D716}_{k}$, the mean turbulent kinetic energy dissipation rate, using the transport equation for $\overline{(\unicode[STIX]{x1D6FF}u)^{2}}$, the second-order velocity structure function. Experimental data show that complete self-preservation for all scales of motion is very well satisfied along the jet axis for streamwise distances larger than approximately 30 times the nozzle diameter. This validation of the analytical results is of particular interest as it provides justification and confidence in the analytical derivation of power laws representing the streamwise evolution of different physical quantities along the axis, such as: $\unicode[STIX]{x1D702}$, $\unicode[STIX]{x1D706}$, $\unicode[STIX]{x1D706}_{\unicode[STIX]{x1D703}}$, $R_{U}$, $R_{\unicode[STIX]{x1D6E9}}$ (all representing characteristic length scales), the mean temperature excess $\unicode[STIX]{x1D6E9}_{0}$, the mixed velocity–temperature moments $\overline{u\unicode[STIX]{x1D703}^{2}}$, $\overline{v\unicode[STIX]{x1D703}^{2}}$ and $\overline{\unicode[STIX]{x1D703}^{2}}$ and $\unicode[STIX]{x1D716}_{\unicode[STIX]{x1D703}}$. Simple models are proposed for $\overline{u\unicode[STIX]{x1D703}^{2}}$ and $\overline{v\unicode[STIX]{x1D703}^{2}}$ in order to derive an analytical expression for $A_{\unicode[STIX]{x1D716}_{\unicode[STIX]{x1D703}}}$, the prefactor of the power law describing the streamwise evolution of $\unicode[STIX]{x1D716}_{\unicode[STIX]{x1D703}}$. Further, expressions are also derived for the turbulent Péclet number and the thermal-to-mechanical time scale ratio. These expressions involve global parameters that are most likely to be influenced by the initial and/or boundary conditions and are therefore expected to be flow dependent.

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Extensive study of temperature dissipation measurements on the centerline of a turbulent round jet based on the $$\overline{\theta^{2}}/2$$ θ 2 ¯ / 2 budget

Cited by 6 publications

References 43 publications

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

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

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

An empirical expression for on the axis of a slightly heated turbulent round jet

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