Anisotropy analysis of vortex breakdown states via direct numerical simulation

Modeling highly swirling flows via second-moment closure approaches requires properly characterizing the turbulence dissipation tensor. In the present work, we investigate bubble-type and regular conical vortex breakdown states through direct numerical simulation. Consequently, we analyze the anisotropic features of the Reynolds stress and dissipation rate tensors using componentiality contours on the standard anisotropy maps. The anisotropy analysis reveals that the turbulence dissipation process exhibits a less significant departure from isotropic states than Reynolds stresses. Still, non-negligible anisotropy levels are envisaged around the breakdown-induced stagnation point, within the shear layer region, and at the top end of the central recirculation zone, highlighting the need for ad-hoc anisotropic modeling. Hence, we test a set of algebraic dissipation tensor models against the direct numerical simulation data, and we find out that blended formulations governed by the local turbulent Reynolds number can potentially identify the most anisotropic dissipation regions. However, this approach tends to revert to the classical isotropic treatment under the current formulation. Thus, improving both the blending function and the anisotropic contribution term is necessary. On the other hand, algebraic models directly relating the dissipation tensor to Reynolds stress anisotropies show worse agreement with the reference database, suggesting that the small-scale anisotropies instead descend from mean local flow field properties.