Measurement and modeling of homogeneous axisymmetric turbulence

Abstract

A new method for modeling the unknown correlations in Reynolds stress transport equations is developed taking the kinematic relationship of turbulence tensors in homogeneous axisymmetric turbulence. Both the rapid-straining and the return-to-isotropy process of homogeneous axisymmetric turbulence are studied with the aim of improving Reynolds stress closures. The partition of the stress dissipation is also studied to assess the possible existence of local isotropy for turbulence at small scales. Homogeneous, axisymmetric turbulence is a simple flow, where the axes of anisotropy of the Reynolds stresses and dissipation tensor are found to be aligned. Using the theory of barycentric coordinates, the relationship between the Reynolds stress and dissipation tensors is derived, satisfying restrictions for the limiting states of turbulence and its assumed behavior for large Reynolds number and arbitrary anisotropy. The role of the anisotropy in constraining models for the turbulent dissipation rate and the pressure–strain correlations is discussed. Comparisons of the resulting closure based on barycentric coordinates with the experimental data for axisymmetric flow measurements of Ertunç and Durst (On the high contraction ratio anomaly of axisymmetric contraction of grid-generated turbulence, Phys. Fluids. 20, February 2008) are good within the limitations of the data.

Keywords:

• turbulence—transport model
• Reynolds stress
• realizability
• second-order closure

Acknowledgments

The first author is grateful to Prof. Ulrich Rüde for motivation to take part in the Bavarian Graduate school of Computational Engineering.