Study of compressible flow through a rotating duct
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Several rotorcraft applications such as circulation control and tip jet driven rotors involve internal spanwise flow along the interior of a rotor blade. This dissertation describes a quasi 1-D numerical model of unsteady flow through a duct rotating about one end along with experimental validations. The numerical model is suitable for inclusion in the conceptual design stage 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. One dimensional Euler equations are solved inside the duct using a finite volume formulation in which the advective fluxes are approximated using the Advective Upwind Splitting Method (AUSM). The model is used to explore the behavior of flow inside a 2 m long duct with a circular crosssection, rotating at tip speeds of up to 260 m/s. In the inviscid limit, at a rotor tip speed of 213 m/s, the model predicted the evolution of a shock which showed periodic oscillations with a time period of approximately 17.5 rotor revolutions. However, when friction was included, a shock did not form until the rotor tip speed was ~ 260 m/s. The effects of suddenly opening a flow control valve at different spanwise stations, x [subscript valve] = 0.0R, x [subscript valve] = 0.5R and x [subscript valve] = R, were also studied numerically. Predictions of both steady and transient flow properties from this model are validated with experiments conducted on a 1.32 m long cylindrical duct, with a cross-sectional diameter of 52 mm, rotating at speeds of upto 1050 RPM (Tip Speed = 145 m/s). Spanwise pressure distribution, duct velocity, temperature, hub forces and moments results from the numerical model showed good correlation with experiments. Considerable internal mass flow rate (~ 0.3 kg/s) was also observed. In the presence of a time-varying valve at the inlet, transient spanwise pressure variations showed periodic fluctuations in pressure which diminished once the valve was fully open. The quasi 1-D model was found to be a much faster computational tool than any conventional 3-D CFD solver to study spanwise flow inside rotor blades. The experiments revealed key information about pressure at the duct's outlet. It was observed that when the duct's inlet is closed, the duct's outlet pressure is less than its ambient value. The knowledge of these boundary conditions is essential in modeling flow through rotating ducts. For more accuracy, the current internal flow solver could be coupled with an external flow code to iteratively obtain boundary conditions at their interface.