Development of a multi-time-step vortex particle method for mainrotor–tail rotor interaction

Abstract

A vortex method was conventionally solved using a uniform time-step for simulating a main rotor–tail rotor configuration. Then, the tail rotor advances with larger azimuth than the main rotor does for the same simulation time step since the rotating speed ratio of the tail to main rotor is typically ranged from four to six. Under the restriction that the time step size should be small enough to capture the tail rotor’s unsteady airloads, the uniform time-step method causes excessively fine temporal discretization for the main rotor, which requires more computing efforts. Because fast computing speed is a key feature of a vortex method for simulating a rotor aerodynamics, it is necessary to develop a new methodology which is superior to the uniform time-step method in terms of computing efficiency. In this study, a multi-time step method for the main rotor–tail rotor configuration was proposed. It used coarser time step size for the main rotor and its wake while keeping it fine for the tail rotor. Then, each rotor could advance with a proper azimuth angle independently by adjusting the time-step size ratio between the tail rotor and main rotor. The multi-time-step method was evaluated by simulating four point vortices dynamics and hovering flight of a main rotor–tail rotor configuration. The motion of four point vortices were computed using the multi-time step method: finer time scale for fast rotating vortices, and coarser discretization for slow rotating vortices. Compared to the conventional uniform time-step method, the multi-time step method predicted the position of the point vortices well even with coarse time step for the slow rotating vortices. The effects of an order of the time integration method and extrapolation method were also discussed. Higher order integration method generally predicted the position more accurately, but even the same order method resulted in different accuracy level depending on the number of intermediate time step points, at which the position information were exchanged between the fast and slow vortices. The hovering flight simulation was performed for Yin-Ahmed’s and UH-60A main rotor–tail rotor configurations. The tail rotor–main rotor rotating speed ratios of two and four were adopted to the Yin-Ahmed. The computation was made for the Yin-Ahmed’s main rotor–tail rotor configuration with the rotating speed ratio of four. The time sensitivity analysis showed that even the result of main rotor azimuth, $\Delta\Psi_{MR}=2.5^\circ$ and tail rotor azimuth, $\Delta\Psi_{TR}=10^\circ$ was deviated from the reference result of the finest temporal discretization, $\Delta\Psi_{MR}=1.25^\circ$ and $\Delta\Psi_{TR}=5^\circ$. On the contrary, the multi-time-step method of $\Delta\Psi_{MR}=5^\circ$ and $\Delta\Psi_{TR}=5^\circ$ showed a good correlation with the reference data. In this case, various types of the multi-time-step method were tested, and it turned out that the extrapolation of the main rotor blade movement as well as the main rotor wake position is necessary to secure the accuracy of a solution. Similar analysis was conducted for the scaled UH-60A main rotor–tail rotor configuration, and the accurate result could be obtained by using the multi-time-step method with time step size ratio of four. For both main rotor–tail rotor configurations, the computing time was saved by approximately 3 times using the multi-time-step method of the time step size ratio of four. The results suggest that the multi-time-step method is an efficient way to compute the main rotor–tail rotor interaction fast and accurately.