Analysis of turbulence structures and the validity of the linear Boussinesq hypothesis for an infinite tube bundle

The basis of many turbulence models in computational fluid dynamics is the linear Boussinesq hypothesis that assumes an alignment between the mean strain rate tensor and the Reynolds stress tensor. The validity of this main assumption is analyzed for the test case of an infinite tube bundle with periodic boundary conditions at Re b ≈ 34 , 800 . This work focuses on the application of five methods based on the Reynolds-averaged Navier–Stokes equations and two scale resolving methods and their ability to accurately reproduce the mean velocity field and the Reynolds stresses. In addition, their capability to predict the anisotropic behavior of the turbulent flow is analyzed. The results indicate that only scale resolving methods are able to predict the turbulent flow field properly for the case under investigation. The results of the large eddy simulation are used to further analyze the distribution of the validity parameter ρ RS and the anisotropic turbulence field. Only small areas between the tubes are identified in which alignment occurs and the linear Boussinesq hypothesis is therefore fully valid.