Large eddy simulation of turbomachinery flows using a high-order implicit residual smoothing scheme

Abstract

A recently developed fourth-order accurate implicit residual smoothing scheme (IRS4) is investigated for the large eddy simulation of turbomachinery flows, characterized by moderate to high Reynolds numbers and subject to severe constraints on the maximum allowable time step if an explicit scheme is used. For structured multi-block meshes, the proposed approach leads to the inversion of a scalar pentadiagonal system by mesh direction, which can be done very efficiently. On the other hand, applying IRS4 at each stage of an explicit Runge–Kutta time scheme allows to increase the time step by a factor 5 to 10, leading to substantial savings in terms of overall computational time. With respect to standard second-order fully implicit approaches, the IRS4 does not require approximate linearization and factorization procedures nor inner Newton-Raphson subiterations. As a consequence, it represents a better cost-accuracy compromise for the numerical simulations of turbulent flows where the maximum time step is controlled by the lifetime of the smallest resolved turbulent structures. Numerical results for the well-documented high-pressure VKI LS-89 planar turbine cascade illustrate the potential of IRS4 for significantly reducing the overall cost of turbomachinery large eddy simulations, while preserving an accuracy similar to the explicit solver even for sensitive quantities like the heat transfer coefficient and the turbulent kinetic energy field.