Two Methods for Viscous and Inviscid Free-Wake Analysis of Helicopter Rotors

摘要

Two integral equation methods for the free wake analysis of helicopter rotors (for potential and rotational flows, respectively) have been presented. The rotational flow formulation is based upon Helmholtz scalar/vector-potential decomposition. The advantages of the rotational flow formulation over the potential flow formulation have been discussed. The numerical equivalence of the two methods have been demonstrated. It should be noted that (whereas in the potential flow problem viscosity may be introduced only as artificial viscosity) in the rotational-flow formulation the presence of viscosity is consistent with the formulation. Therefore, this formulation is applicable to the solution of time-averaged Navier-Stokes equations: in particular, a simplified thin-wake analysis with an elementary eddy-viscosity model for turbulence is used in the numerical applications. Analysis of the computer times indicates that the new formulation presented here (for rotational flows) has much broader applicability than the formulation for potential flows, while requiring approximately the same amount of computer time.