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| Mode Shapes of Three-Dimensional State Space Wake Theory | ||||
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Three-dimensional state space modeling of rotor wake expands velocity and pressure perturbation into a truncated Fourier series. Application of potential theory shows the mode shapes are associated Legendre functions. Here illustrated some of lowest orders and degrees of these mode shapes. Large image of poster with 28 mode shapes is available upon certain agreement. Contact Prof. David Peters for details. |
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| Ground effect | ||||
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With new developments, state-space wake model now has capability of analyzing dynamic responses with presence of mass sources. Practical application of such method, such as ground effect analysis, has shown good correlations with flight test data. Here shown is a comparison plot of ground effect factor in hover versus previous formulae, among which Hayden's result was simulated with flight test data. |
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| Finite-state dynamic wake model applications | ||||
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The relationship between the induced velocity and circulation is a
fundamental aspect of the aerodynamics for helicopter rotors and airplane
propellers. The dynamic wake models are currently capable of reproducing
the inflow behavior for typical ascent rates of helicopter rotors. The
wake of helicopter rotors in axial flow has closely spaced trailing vortex
sheets, as shown on the left. The trailing vortex sheets, for propellers,
has larger wake spacing, as shown in the center. Research is currently
being done to expand the application of dynamic wake models to propeller
dynamics, which has a faster free-stream velocity and larger spacing
between the trailing vortex sheets. Alfred Betz determined that the optimal trailing vortex for a lightly loaded propeller is a regular helix of vortex sheets that translate downstream of the propeller as a rigid body, as shown in the figures. Betz also determined the induced velocity profile along the blades that is coincident with this trailing vortex geometry. The exact solution to the circulation along the blades is also known for this optimal system, and the profiles for small and large wake spacing are shown on the right. The analytic solutions provide a comparison for understanding how to correctly apply the dynamic wake models to propeller systems with large wake spacing and high swirl velocities. Further development can then be done to apply the models to real propellers with additional blade dynamics, as opposed to idealized systems. The dynamic wake models are currently used extensively for simulation and design of helicopter rotors. After the current research project is complete, the dynamic wake models can also be applied to propeller mode flight for tiltrotor craft, such as the V-22 Osprey and Bell/Agusta 609. |
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