Investigation on Strain and Stress Principal Axes in Unsteady DNS Turbine Data

Abstract In the present work, high-fidelity direct numerical simulation (DNS) data has been adopted in conjunction with an extensive post-processing to provide a detailed description of the turbulence characteristics and its production within a low pressure turbine (LPT) cascade blade passage operating with unsteady inflow. Proper orthogonal decomposition is used at first to provide the statistical representation of the flow structures that occur in the blade passage. Different inlet turbulent scales are isolated and a representation of the turbulence produced in the passage is also provided. Principal axes of the Reynolds stress and the strain tensors have been analyzed to provide further insight on the turbulence production. Since each spatial POD mode captures a quota of the Reynolds stress tensor, the POD modes are well suited to provide reduced order models (ROMs) that represent the different scales of turbulence. Namely, four different scales are defined, and the eigenvectors of the stress tensor for each reduced model are discussed. The discussion includes the comparison with the principal axis of the strain rate tensor. It is shown that the spatial locations where the eigenvectors of the strain and stress tensors are aligned lead to the largest production of turbulent kinetic energy. The deterministic periodic perturbations induced at the inlet by the unsteady incoming wakes lead to the largest production of turbulence in the passage region where the highest strain is detected and where the eigenvectors of the two tensors are aligned. In the suction side boundary layers, the highest production is related to the local maximum of the Reynolds shear stress due to the stochastic perturbations. The deterministic perturbations do not contribute to the production of turbulence in the suction side boundary layer, even though their induced stress is not negligible, because the eigenvector directions have a maximum misalignment.