Analysis of turbulence anisotropy in a mixing tank

The objective of this paper is to analyze the gap between the local turbulence and the 3D isotropic state in a mixing tank stirred with a Rushton turbine. Experiments were carried out using the PIV technique, and phase average treatment permits the calculation of the six components of the Reynolds stress tensor. In order to quantify the gap between the measured local turbulence and the 3D isotropic state, methods based on tensorial analysis are developed. In a turbulent flow, three representations are able to characterize the turbulence anisotropy: representation based on two eigenvalues (s–t)(s–t) of the anisotropy tensor; the Lumley–Newman triangle based on two invariants (II –III   ) of the anisotropy tensor; a representation based on the axisymmetry invariant AA and the two-dimensional invariant GG. These three visual methods, that quantify the degree of anisotropy from two independent variables are developed and used in the impeller stream region, and the distribution of the turbulence state is thus described. A parameter is proposed to quantify the anisotropy level.