- Title
- Transport equation for the mean turbulent energy dissipation rate on the centreline of a fully developed channel flow
- Creator
- Tang, S. L.; Antonia, R. A.; Djenidi, L.; Abe, H.; Zhou, T.; Danaila, L.; Zhou, Y.
- Relation
- Journal of Fluid Mechanics Vol. 777, p. 151-177
- Publisher Link
- http://dx.doi.org/10.1017/jfm.2015.342
- Publisher
- Cambridge University Press
- Resource Type
- journal article
- Date
- 2015
- Description
- The transport equation for the mean turbulent energy dissipation rate ⋶ along the centreline of a fully developed channel flow is derived by applying the limit at small separations to the two-point budget equation. Since the ratio of the isotropic energy dissipation rate to the mean turbulent energy dissipation rate ⋶iso/⋶ is sufficiently close to 1 on the centreline, our main focus is on the isotropic form of the transport equation. It is found that the imbalance between the production of ⋶ due to vortex stretching and the destruction of ⋶ caused by the action of viscosity is governed by the diffusion of ⋶ by the wall-normal velocity fluctuation. This imbalance is intrinsically different from the advection-driven imbalance in decaying-type flows, such as grid turbulence, jets and wakes. In effect, the different types of imbalance represent different constraints on the relation between the skewness of the longitudinal velocity derivative S₁,₁ and the destruction coefficient G of enstrophy in different flows, thus resulting in non-universal approaches of S₁,₁ towards a constant value as the Taylor microscale Reynolds number, Rλ, increases. For example, the approach is slower for the measured values of S₁,₁ along either the channel or pipe centreline than along the axis in the self-preserving region of a round jet. The data for S₁,₁ collected in different flows strongly suggest that, in each flow, the magnitude of S₁,₁ is bounded, the value being slightly larger than 0.5.
- Subject
- channel flow; turbulence theory; turbulent flows; energy dissipation
- Identifier
- http://hdl.handle.net/1959.13/1332354
- Identifier
- uon:26852
- Identifier
- ISSN:0022-1120
- Language
- eng
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