A procedure for rotor performance, flowfield and interference - A perspective

The momentum source method as applied to rotor calculations is presented. The Navier-Stokes equations and the blade element theory are coupled implicitly to yield a self contained method for generating rotor performance, as well as the near and far wake. The two-dimensional airfoil characteristics of the rotor blades and the local velocity of the flow are the basis for the computation of the momentum sources. The method has been subjected to a number of difficult applications including multiple rotors and the results compare well with available data. Introduction The flowfield of a rotor is complex. Even an isolated rotor is dominated by the mutual, aerodynamic interference effects of the blades. Therefore, all rotor techniques, to be successful, must consider interference effects. The importance of interference cannot be overstated when complete configurations are considered [l]. Also, in situations where the interference effects are the main focus, the flow regimes could well be in the neighborhood of incompressible Mach numbers, such as in the case of the flow underneath the fuselage of a hovering rotor or under the wings of a hovering tilt rotor. In general, the absolute velocity of the fluid is in the low subsonic range and algorithms used must be capable of solving the elliptic governing equations that characterize the flow in this regime. An algorithm which satisfies the above mentioned requirements and is suitable for rotorcraft analysis is the the subject of discussion here. Rajagopalan [2, 3, 4, 5, 6, 7, 8, 9, 10, 111 and his co-authors have demonstrated that a spinning ro tor can be sufficiently represented by time-averaged momentum sources in the governing flow equations. This method is intermediate in complexity and accuracy between the freevortex methods [12], based on the potential flow assumption, and the Euler-NavierStokes methods [13, 14, 15, 16, 17, 18, 191 with a body-fitted grid around the rotating blades embedded in a global flowfield grid. Use of the momentum sources to represent the rotating blades, admittedly, compromises the reality of the simulation very close to the blades by not resolving the (chord wise and span-wise) boundary layer flow on the rotor. However, the ability to solve some of the current important problems, such as the fountain-flow interference effects of a tilt-rotor, while avoiding the need for super computer type numerical computations, makes this procedure useful. The essential details of this method can be divided into three parts: The method used for solving the fluid flow equations, the evaluation of the forces generated by the rotating rotor blades and the coupling between them. Any numerical algorithm that solves the Navier-Stokes equations is adequate for obtaining the flowfleld. The classical blade element theory yields the correct forces on the rotating blades once the local vector velocity field is known. It is the coupling that is non-traditional and requires explanation. Navier-Stokes equations are a derived statement of the Newton’s Second Law for fluid flow in the form of conservation of momentum. The rotor blades by virtue of their motion, impart a certain amount of momentum to the fluid surrounding them. Thus, it is natural to hypothesize that the presence of the spinning rotor blades can be modeled as sources in the Navier-Stokes equations. If this model is made to be an implicit function of the rotor’s geometric and aerodynamic characteristics, in addition to the local flow conditions that change as the flow evolves, the coupling between the modeled rotor and the flow would be strong. This integral coupling between the rotor forces and the conservation of momentum equations ensures a balance of local momentum throughout the iterative process. Conservation of local momentum, also implies global linear and an-