A-priori study of subgrid-scale models for the flow field in the rotor exit region of a centrifugal turbomachine

The present article deals with a-priori evaluation of two popular subgrid-scale (SGS) models, i.e. Smagorinsky and similarity, for the complicated flow field of a centrifugal turbomachine. Comparison of Smagorinsky and similarity models for various turbulent flows shows that accuracy of these models is inferior for complicated turbomachinery flow. The estimated SGS model coefficients, correlation coefficient among exact and modeled SGS quantities and the functionality between SGS stress/dissipation and resolved flow parameters are different features of SGS models which are examined for Smagorinsky and similarity models. The calculated model coefficients for the rotor exit flow are significantly smaller than their classical values to avoid over-estimation of SGS dissipation. Back-scattering of turbulent energy and spectral shortcut mechanisms are two possible reasons for this reduction of models coefficients. Investigation of instantaneous SGS dissipation shows that about 40% of flow samples in the rotor exit region have back-scattering of energy. This large density of back-scattering significantly reduces the performance of fully-dissipative models such as the Smagorinsky model. Joint probability density functions of exact vs. modeled SGS stress/dissipation show that the similarity model is capable of back-scattering prediction and has a considerably larger correlation coefficient than that of the Smagorinsky model. The present article shows that the Smagorinsky model performance improves in the presence of straining (in the jet-wake interacting regions) while the minimum correlation coefficient occurs in the core region of jets and wakes with smallest straining. Weak functionalities between Smagorinsky-modeled SGS stress/dissipation with the resolved strain rate tensor, particularly in the case of cross components, show the necessity for modifying Smagorinsky model in such a complicated flow field to allow for spectral shortcut and energy back-scattering mechanisms.