Modeling Internal Flow Through a Rotating Duct Using Quasi 1-D Euler Equations

A numerical model of the internal flow in a duct rotating about one end is described. One-dimensional Euler equations are solved inside the duct using a finite volume formulation in which the advective fluxes are calculated using the advection upwind splitting method. The model was developed as a fast design tool for helicopter rotor blades with internal spanwise flow. To this end, centrifugal as well as Coriolis effects, frictional losses, duct sweep, and time-dependent duct boundary conditions are modeled, and a spanwise flow control valve can be included. The model is used to explore the behavior of a 2-m-long duct with a circular cross section, rotating at tip speeds of up to 260 m/s. The effects of centrifugal pumping, duct friction, duct sweep, and a flow control valve on the spanwise pressure and velocity distribution, mass flow rate of air through the duct, and torque required to spin the duct are discussed.