Background Rotors for propulsion are commonly used for vertical takeoff and landing (VTOL) vehicles such as helicopters. The rotor operates in a complex flow field, and there are several important fluid mechanics phenomena that occur on the rotor at the same time. Although a rotor is essentially two or three rotating wings or blades that generate lift, drag, and a pitching moment to produce thrust and torque when the forces are integrated along the entire blades, the linear momentum equation can be used to approximate the thrust force generated by the rotor. The following setup was used for the experiments to measure thrust and torque using a load cell, as well as flow velocity above and below:
Mach Number and Reynolds Number
When the rotor is spinning at a high rotational speed, 2 the blades "see" very different flow conditions depending on the blade location. The freestream velocity ahead of a spinning blade is equal to, U. = Sur where r is the blade radius and varies from r=0 at the center of the hub to r= 1.205 m at the blade tip. The freestream velocity is critical to determining the flow regime or behavior based on the Mach number, M = U/ a, and the Reynolds number, Re = U«c/ v where c is the local blade chord, and v is the kinematic viscosity of the air at sea level, 1.470x10 mʻ/s. The air density, p is 1.225 kg/mand the speed of sound, a is 344 m/s.
Experimental Conditions
The experimental rotor was operated at several rotational speeds from 250 to 1,250 RPM and blade pitch angles, 0 = 0, 3, and 6 degrees. The rotor diameter is 2.41 m. For the calculations below. assume that the rotor variables are as follows: 12 = 1,000 RPM and 6 = 6°. Under these conditions, the rotor thrust was measured directly with a load cell as T = 375 N. The average velocity of the flow 5 cm above the rotor plane (station 1) was measured with a probe as Vi = 6.7 m/s, and the average velocity 5 cm below the rotor plane (station 2) was measured as 12 = 11.1 m/s, and the acceleration of the flow from station 1 to 2 was calculated as 16.8 m/s.
Calculations and Discussion
Mach number. Sketch a rotor blade as discussed in class, showing a linear freestream velocity profile as a function of blade radius. (1) Assuming 12 = 1,000 RPM, find the location, r on the blade where the flow transitions from incompressible to compressible flow. Remember for compressible flow, M > 0.3 holds true. (2) Discuss the implications of having both incompressible and compressible flow on the same blade.