A novel high-order scheme for numerical simulation of wake flow over helicopter rotors in hover

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• A novel WENO-K scheme using Gauss-Kriging reconstruction with an optimized hyper-parameter is extended to numerical simulation of three-dimensional unsteady compressible viscous flows dominated by tip vortices over hovering rotors. • A multi-start distance decreasing method is proposed to accelerate the update of overset relationship and a method of multilayer fringes are presented to support any-order flux-reconstruction on artificial boundaries. • A massively parallelizable simulation method features high-order accuracy and low dissipation for unsteady vortex flows over rotors in hover is established based on WENO-K scheme and an automatically partitioned dynamic overset grid system. • Numerical results demonstrate that the proposed method outperforms the WENO-JS method and can preserve vortex wake to a larger wake age with a more accurate trajectory of vortex core with only 4.1% additional computational cost compared to WENO-JS scheme. Accurate prediction of tip vortices is crucial for predicting the hovering performance of a helicopter rotor. A new high-order scheme (we call it WENO-K) proposed by our research group is employed to minimize numerical dissipation and extended to numerical simulation of unsteady compressible viscous flows dominated by tip vortices over hovering rotors. WENO-K is referred to as an adaptively optimized WENO scheme with Gauss-Kriging reconstruction, and its advantage is to reduce dissipation in smooth regions of flow while preserving high-resolution around discontinuities. Here WENO-K scheme is adopted to reconstruct left and right state values within the Roe Riemann solver updating the inviscid fluxes on a structured dynamic overset grid. To minimize the accuracy loss for high-order reconstruction on artificial boundaries of overset grid, a method of multilayer fringes is proposed to carry out interpolation between background grid and blade grid. Massively parallel computing considering automatic load balance on averagely partitioned overset grid is developed to reduce the wall-clock time of an unsteady simulation. Numerical results for Caradonna-Tung (C-T) rotor in hover at the conditions of subsonic and transonic tip Mach numbers show that the thrust coefficient error for the result of WENO-K scheme is no more than 3%. Compared with WENO-JS scheme, WENO-K scheme achieves about 40% improvement on accuracy of predicting rotor thrust with only 4.1% extra computational cost. More importantly, WENO-K scheme can capture more sophisticated unsteady flow structures and resolve tip vortices to a larger wake age with an increment of about 270° compared to WENO-JS scheme.