Item 1302
OTHER:
Aerodynamics - General - Swirl (slipstream rotation)
"This rotational velocity represents an energy loss that accounts for an increase in the induced power of 2% to 3%. .... This loss can be eliminated by using coaxial, counterrotating rotors."
[Source ~ RWP3 p.14] (Swirl recovery)
My Thoughts:
There is a small swirl component of the velocity in the rotor wake, induced by the spinning rotor. I believe that this should be slightly advantageous for coaxial and intermeshing rotors and slightly disadvantageous for interleaving rotors. The reason is that if the upper and lower blades have the same pitch, then the angle of attack in the lower blade will be less, due to the downwash from the upper blade. The swirl should reduce this angle of attack difference slightly when the blades are moving in opposite directions.
Reprint of Georgia Tech Web Page:
Swirl: Swirl is caused by the forces (tangential to the plane of rotation) exerted by the rotor on the fluid. There are two types of tangential forces. The first caused by viscous drag, which causes the fluid particles to follow the blade as is the case for the wake behind a truck following the truck. The kinetic energy imparted to the fluid for this useless swirling motion is already accounted for in the profile power estimates, since Cd includes both skin friction drag and form drag.
The second tangential force is simply induced drag, which is caused by the rotation of the lift vector by the inflow angle f. This also causes the fluid particles to follow the blade and swirl. The fluid particles thus follow a spiral trajectory as they spin and descend. Swirl accounts for only about 1% of the total power. It may be crudely estimated as follows.
We consider a fluid particle that descends through the rotor disk. In an coordinate system attached to the blade, the particle will have an angular velocity
W as it approaches the rotor disk. Underneath the rotor disk, the same particle will only have an angular velocity (W-w), where w is the angular velocity associated with swirl. Then, from Bernoulli equation in this rotating coordinate system,
The above equation relates the pressure jump across an annulus of the rotor disk with the swirl underneath that annulus disk. The thrust produced by this annulus disk, according to the momentum theory is p. A= 2 (v) v DA. Thus,
Solving for
w, we get
The above expression may be used to find the magnitude of the swirl velocity and direction when required.
The power dumped into the wake associated with this swirl velocity is given by the integral:
Here the lower limit of the integral is set to r/R= 
Swirl accounts for only 1% to 2% of the total power. The present treatment is adequate for estimating these small losses.
Swirl may be only 0.2% of the total power.
[Source ~ AH p.50]
See; Technical Documents on ABC; Forward Flight Performance of a Coaxial Rigid Rotor, page 6, ~ May 1971, by V. M. Paglino
The method of calculation that Sikorsky used was referred to as "Yawed Blade Element Theory"
See also;
More;
NACA Technical note 1210.
Have hard copy.Blade-Element Theory for Propeller in Forward Flight Have hard copy.
My Speculative Question Regarding Vibration:
The downwash from the 3 or 4 upper blades will strikes the lower blades at a rate of 3 or 4 times per rotor rotation. In addition, the upper blades may experience a downdraft from the lower blades. This may result in a vibration of the lower and the upper blades. In both cases there will probably be a rotational component to the downwash and downdraft. In the coaxial and intermeshing configurations (interleaving configuration not included) might the increase in the horizontal component, due to the swirl, tend to work with the increase in the vertical component, due to the thrust, tend to reduce any change in the Angle of Attack and thereby reduce the vibration?
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Last Revised: February 4, 2007