Multigrid Acceleration and Chimera Technique for Viscous Flow Past a Hovering Rotor

ACCURATE simulation of the viscous flow around a helicopter rotor is still a challenging problem. To predict the blade loading accurately, the numerical method must have a capability to capture the vortical wake generated from the rotor blade tip precisely, which significantly affects the aerodynamic performance of the rotor. Therefore, both the numerical scheme with low numerical dissipation and sufficient dense mesh far away from the blade surface are required for rotor computations to simulate the tip vortex with minimal distortion. Furthermore, for a hovering case, a large numerical integration time is needed for the capture of the fully developed vortical wake [1]. In addition, the existence of incompressible flow near the root will also make the convergence slow. Compared with fixed-wing computations, hovering rotor computations not only require more accurate numerical scheme but also will take much more run time to converge. During the past two decades many numerical methods [2–7] have been developed to simulate the viscous flow around a hovering rotor. The methods [2,3] with the single-block structured grid suffer from the grid-quality problem, because the mesh must be stretched and skewed to cover the complete computational domain and to match the periodic boundary condition. To avoid this problem, the chimera technique [4–7] suggested by Benek et al. [8] was introduced into hovering rotor computations. To capture the tip vortex without unphysical distortion and predict the blade loading accurately, some high-order schemes and vortex-adapted chimera methods [6,7] were presented. Although significant advances in the accurate simulation of the tip vortex have been made with these advanced methods, the large computation cost and the low robustness, as well as the complexity make them far away from engineering applications. As mentioned above, hovering rotor computations, especially the computations with high-order methods, require more run time to converge than their fixed-wing counterparts. A few attempts [1,9,10] have been made to use multigrid methods to accelerate the convergence of hovering rotor calculations. Up to now, there is few works concerning the multigrid method for the viscous flow computation about a hovering rotor based on overset grids. The main objective of the present study is to develop an efficient multigrid algorithm coupled with chimera grids for Navier–Stokes computations about a hovering rotor. It should be mentioned that the experience of this work can be extended to accelerate the computation about a rotor in forward flight using moving overset grids,which is themainmotivation of this research. Furthermore, this experience can also be the basis of the future multigrid computation using high-order methods and chimera grids for rotor flows.