Challenges in Modeling of Turbulence in the Tip Region of Axial Turbomachines

The flow and turbulence in turbomachines are characterized by spatially and temporally nonuniform strain rate fields and tendency to develop partially understood large-scale instabilities. Consequently, the applicability of popular Reynolds stress models in Reynolds-averaged Navier-Stokes simulations of turbomachinery flows is questionable and requires validation under relevant conditions. Experimental studies performed in the Johns Hopkins University optical refractive index-matched facility have investigated the complex flow and turbulence in the blade tip region of several axial turbomachines, including two waterjet pumps and an aviation compressor. The comprehensive databases obtained for different flow conditions and tip geometry using high-resolution particle image velocimetry are used in this article to examine the characteristics of turbulence in the vicinity of the tip leakage vortex (TLV). The results reveal several common features in the spatial distribution of the extremely anisotropic Reynolds stress tensor, suggesting that there are similarities in the mechanisms involved among the different machines. Of the quantities that could be measured accurately, both the local production and mean-flow advection rates appear to govern the evolution of turbulence in the passage. The dissipation rate also appears to be a major factor, but it cannot be measured accurately because of its dependence on motions at small scales that are not resolved by the measurements. The turbulent transport terms are important only in limited cases and locations. The strain rate tensor components, which appear to play primary roles in the production of turbulent kinetic energy (TKE), display common features in the spatial distributions of regions with high contraction, extension, and shear under different conditions. Some but not all of the inhomogeneity and anisotropy in the distributions of Reynolds stresses can be related to the corresponding local production rates. There is disagreement near the TLV core, where the persistent presence of multiple interacting vortices contributes significantly to the elevated TKE there. Lack of a clear functional correlation between the Reynolds stresses and mean strain rates is ubiquitous in all cases, resulting in widely spatially varying positive and negative values for the eddy viscosity. However, surprisingly, results from different machines and conditions have similar spatial distributions of individual stress and strain rate components and, accordingly, the eddy viscosity.