Two-Scale Methodology for URANS/Large Eddy Simulation Solutions of Unsteady Turbomachinery Flows

A general issue in turbomachinery flow computations is how to capture and resolve two kinds of unsteadiness efficiently and accurately: (a) deterministic disturbances with temporal and spatial periodicities linked to blade count and rotational speed and (b) nondeterministic disturbances including turbulence and self-excited coherent patterns (e.g., vortex shedding, shear layer instabilities, etc.) with temporal and spatial wave lengths unrelated to blade count and rotational speed. In particular, the high cost of large eddy simulations (LES) is further compounded by the need to capture the deterministic unsteadiness of bladerow interactions in computational domains with large number of blade passages. This work addresses this challenge by developing a multiscale solution approach. The framework is based on an ensemble-averaging to split deterministic and nondeterministic disturbances. The two types of disturbances can be solved in suitably selected computational domains and solvers, respectively. The local fine mesh is used for nondeterministic turbulence eddies and vortex shedding, while the global coarse mesh is for deterministic unsteadiness. A key enabler is that the unsteady stress terms (UST) of the nondeterministic disturbances are obtained only in a small set of blade passages and propagated to the whole domain with many more passages by a block spectral mapping. This distinctive multiscale treatment makes it possible to achieve a high-resolution unsteady Reynolds-averaged Navier–Stokes (URANS)/LES solution in a multipassage/whole annulus domain very efficiently. The method description will be followed by test cases demonstrating the validity and potential of the proposed methodology.