Coupling of an Unsteady Aerodynamics Model with a Computational Fluid Dynamics Solver

Momentum source methods are an efficient means of representing airfoils in Navier-Stokes computational fluid dynamics (CFD) simulations. Momentum source terms are added to the Navier-Stokes equations instead of resolving the solid boundary of the airfoil with a mesh. These source terms are calculated using an aerodynamics model. This approach is useful where the overall performance and mid- to far-field influence of a wing or rotor are desired and details of the flowfield near the blade are not the objective of the simulation. One example is simulation of rotorcraft operations where the objective may be to assess an operation's feasibility in terms of control margins, rather than to inform rotor design decisions. Coupling an aerodynamics model to a CFD solver is straightforward in cases where the airflow relative to the blade is steady. Unsteady conditions require an unsteady aerodynamics model, complicating the coupling with the CFD solver. A coupling method is proposed whereby the incident velocity is extracted from the CFD solution and corrected using a theory-based approximation for the unsteady induced velocity. The steady-state momentum source method is demonstrated for two- and three-dimensional simulations, and the unsteady coupling method is validated against experiments on a pitching airfoil and verified for blade-vortex interactions. The unsteady coupling method enables meaningful incident velocities to be extracted from unsteady flowfields, as shown by agreement with experiments and simulations using analytical expressions for the incident velocity in place of the CFD solver.