Unsteady Momentum Source Method for Efficient Simulation of Rotor Aerodynamics

Abstract

T HE flow field around a rotor is very complicated as we all understand. Prediction of aerodynamic performance of rotor including not only rotor loading but also rotor wake in computational fluid dynamics (CFD) is still an important issue and also very challenging. Various computational methods based on Euler or Navier–Stokes equations with or without wake modeling were developed to predict the flow field around rotor [1–4]. Unsteady rotor-airframe interaction problems requiring both moving and stationary domains was recently simulated by using various techniques such as overset or Chimera grid or sliding mesh scheme [5–7]. Computational burden becomes rather heavy for a full Navier– Stokes simulation of rotor-airframe interaction because rotating blades and stationary body have to be dealt with simultaneously. Some approaches to mitigate this computational burden were suggested that adopted an actuator disk concept for rotating blades. There are two types of actuator disk methods: a pressure-boundary approach and a momentum-source approach [8–13]. O’Brien and Smith [14] discussed rotor-fuselage interaction models of pressureboundary method and momentum-source method using various load distributions. Schweikhard [15] implemented the time-averaged momentum source method in an unstructured flow solver. These actuator-disk models treat the whole disk plane swept by rotors as pressure jump or momentum source plane so that they yield a timeaveraged representation of the flow. Considering that the flow is essentially unsteady, these actuator-disk models are not expected to simulate properly the unsteady-flow features of the rotor. Recently Boyd and Barnwell [16] developed an unsteady rotor/fuselage interactional model that loosely couples a Generalized Dynamic Wake Theory (GDWT) to thin layer Navier–Stokes code with an overset grid. The GDWT estimates the unsteady blade loading by adopting the inflow model of Peters and He [17]. Tadghighi and Anand [18] developed an unsteady rotor source model for the interactional rotor/fuselage aerodynamics. The blade was represented by an unsteadymomentum source distribution in the form of a lifting-line type representing the loading only along a radial line of the blade. Kim and Park [19] tried an unsteady momentum source method by using a Navier–Stokes solver. Themomentum sourcewas evaluated through the blade element theory with inflow model of Peters andHe [17]. Recently, apart from rotor aerodynamics, a simple momentum source method was used to simulate the flowfield around vortex-generator arrays [20,21]. The momentum source magnitude was determined simply by using only the lift force of the vortex generators with a model constant. According to O’Brien and Smith [14], the momentum source method is known to be more stable numerically than the pressure boundary method in the region where the wake is very close to the rotor disk. Moreover the momentum source method is known to represent the rotor aerodynamics better than the pressure boundary method. In the present study, we develop an unsteady momentum source method for unsteady Navier–Stokes solver without employing additionalmodels for induced velocity and tip loss, which is the very first attempt to the authors’ knowledge. The momentum sources are distributed along radial and chord-wise directions of a rotor. The method suggested is validated by several simulation results.