- Title
- An empirical expression for epsilon(theta) on the axis of a slightly heated turbulent round jet
- Creator
- Lemay, J.; Djenidi, L.; Antonia, R. A.; Benaissa, A.
- Relation
- Journal of Fluid Mechanics Vol. 867, p. 392-413
- Publisher Link
- http://dx.doi.org/10.1017/jfm.2019.164
- Publisher
- Cambridge University
- Resource Type
- journal article
- Date
- 2019
- Description
- 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 ∈θ, the mean dissipation rate of θ̅²/2, where θ̅² 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 ϵκ, the mean turbulent kinetic energy dissipation rate, using the transport equation for (δu)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: η, λ, λθ, RU, RΘ (all representing characteristic length scales), the mean temperature excess Θ0, the mixed velocity–temperature moments uθ², vθ² and θ² and ∈θ. Simple models are proposed for uθ² and vθ² in order to derive an analytical expression for A∈θ, the prefactor of the power law describing the streamwise evolution of ∈θ. 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.
- Subject
- jets; turbulence modeling; temperature structure function; industrial applications
- Identifier
- http://hdl.handle.net/1959.13/1416316
- Identifier
- uon:37033
- Identifier
- ISSN:0022-1120
- Language
- eng
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