A Modified Fifth-Order WENO-HLLC Riemann Solver for Transonic Viscous Flows around Helicopter Rotor in Hover

Li Xu,Jingjing Cai,Fengfeng Zhao,Rodrigo Nicoletti

doi:10.1155/2022/2180845

Abstract

This paper presents a modified fifth-order WENO-HLLC Riemann solver for the transonic compressible viscous flows around the helicopter rotor in hover. The HLLC approximate Riemann solver is proposed to discrete the convection term involving grid velocity of the Navier-Stokes equations. In order to solve the interface flow accurately, a modified fifth-order WENO scheme is presented by designing the smoothness indicators based on L 1 norm measurement. The improved WENO scheme can provide the optimal approximation order even at critical points. Numerical accuracy and robustness are validated by several benchmark inviscid flow problems. Then the numerical properties of the WENO-HLLC solver in conjunction with the implicit LU-SGS time integration method with high efficiency are further validated by simulating transonic viscous flows over RAE2822 airfoil and ONERA-M6 wing. The results show that the accuracy of calculating shock, discontinuity, and the vortex is significantly improved. Finally, the method is developed to compute the transonic vortex flow around the helicopter rotor with a domain discretized by overset grids. The results indicate that the proposed method is very robust and effective in acquiring high resolution for vortex wake.

Highlights

Rotor is the key component of a helicopter, which provides the lift to overcome the weight of the helicopter and the thrust during forward flight and the control force of helicopter balance, flight, and lifting. e aerodynamic performance of the rotor largely determines the flight quality, stability, maneuverability, vibration, and noise level of the helicopter
En, the numerical properties of the proposed WENOHLLC method are studied for steady transonic viscous compressible flows over the RAE2822 airfoil and ONERAM6 wing
The method is applied to the steady transonic vortex flow around the helicopter rotor with a domain discretized by overset grids

Summary

Introduction

Rotor is the key component of a helicopter, which provides the lift to overcome the weight of the helicopter and the thrust during forward flight and the control force of helicopter balance, flight, and lifting. e aerodynamic performance of the rotor largely determines the flight quality, stability, maneuverability, vibration, and noise level of the helicopter. In the field of helicopter aerodynamics and computational fluid dynamics (CFD), the accurate prediction for rotor flow field with vortex wake is still one of the most complex and challenging problems [3]. A low dissipation numerical method will be developed to calculate the transonic vortex field of the hovering rotor. The HLLC Riemann solver in combination with an overlapping grid system is developed to calculate three dimensional compressible viscous transonic flow field of the hovering rotor. To increase the accuracy of first-order HLLC scheme, an improved fifth-order weighted essentially nonoscillatory (WENO) scheme is proposed to reconstruct the left and right states of the Riemann solution.

Governing Equations

Numerical Formulation

Convergence Order of the New Fifth-Order WENO