Numerical Calculation of Unsteady Transonic Potential Flow over Helicopter Rotor Blades

The small disturbance potential equation appropriate to a helicopter in forward flight is derived. This equation then is solved for the flow over a nonlifting transonic rotor blade, using a completely implicit scheme that is an extension of the Murman-Cole mixed difference technique. The flow in the tip region is most unsteady in the decelerating flow region, after the blade passes the \J/ - 90°azimuthal station. The unsteadiness appears to be caused by expansion and compression waves that move slowly upstream of the blade as the relative incident flow decelerates. The influence of aspect ratio, advance ratio, and Mach number on this process is discussed.