Rationale of partially averaged Navier–Stokes model and its applications in turbomachinery: A historical review

The flow patterns in the turbomachinery are highly turbulent, involving various types of unstable flow phenomena. In this paper, Reynolds-averaged Navier–Stokes simulation (RANS) as well as partially averaged Navier–Stokes (PANS), which is a hybrid turbulence model providing a balance solution between computational cost and simulation accuracy, are reexamined with a review toward developing a methodology for the simulation of complex turbulent flows. First, fundamental mathematical formulations and derivation on the RANS and PANS models are introduced systematically. Especially, the rationales of some newly proposed PANS models for simulating unstable flow involving with large-reverse flow, high-shear stress, and high-pressure gradient flows are introduced. Furthermore, recent progress for the unsteady flow using the PANS models in the turbomachinery is mainly summarized with an emphasis on their principles and applicability. Some representative engineering applications of PANS model in hydrofoil, pumps, turbines, and propellers are discussed. It is demonstrated that the PANS models show superior performance in predicting the cavitating flow, flow separation, tip leakage flow, and wake flow. Last, summary comments on the review are drawn. This paper attempts to provide insights and guidelines for the research utilizing the PANS model in turbomachinery. To further promote the study of PANS models in turbomachinery, some further validations on the newly proposed PANS model employed in the compressible turbulent flow in compressors or other turbomachinery are addressed for future research.