Item 1003

OTHER: Aerodynamics - General - Reynolds Number [Re | RN]

General:

The flow of air or water past an object depends on the velocity, the density and the viscosity of the fluid as well as the size of an object. For a given boat moving through the water, at very small speeds, the flow is laminar [very smooth] and it gets more and more turbulent as the speed increases. A smaller boat would have less turbulence than a larger boat at the same speed. To scale the behaviour of different boats and in different fluids, it was discovered that the fluid behaviour is very similar when the same Reynolds number is obtained.

R = v r D/h where v is the fluid velocity, r is the fluid density, D is the characteristic size of the object and h is the viscosity. The more viscous the fluid, the more drag it exerts. Molasses is much more viscous than water. The viscosity varies with temperature. Here are some examples.

fluid

temperature oC

h (Pa-s)

water

0

1.8x10-3

water

20

1x10-3

air

20

1.8x10-5

glycerine

20

1.5

Description:

The Reynolds number determines the type of flow (whether laminar or turbulent), which in turn determines where the flow separates from the wing, which in term affects the lift, drag and moment coefficients. We note that as Reynolds number increases, the maximum lift coefficient increases; but this does not occur indefinitely; when flows become very turbulent, the maximum lift coefficient begins to drop.

General:

Reynolds number = chord (ft) x speed (mph) x 9360; at sea level. Re = c x MPH x 9360

Reynolds number = chord (ft) x speed (fps) x 6378; at sea level. Re = c x fps x 6378

Note: the highest Reynolds number is 2.45 x 106. This is on the UniCopter, with 700 RRPM, 6" chord, azimuth 90º and 125 mph. On the retreating side at 75% of R the Reynolds number is 0.90 x 106.

 Chord length:

The only negative to the narrow chord, so far, is the mention somewhere that a chord should never be less than 5". Has to do with the Reynolds Number (proportional to chord times velocity).

My thoughts:

The greatest air velocity over the airfoil will be experienced at azimuth-90º. At other azimuths between 0 to 180 the resultant of the forward velocity and the rotational velocity will be less, but the airfoil will probably be perceived as having a longer chord.

 FORM: Tangential Velocity:

This form could be easily expanded to calculate the Reynolds number.

 Outside Web Sites:

See: OTHER: Aerodynamic - Web Sites

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Last Revised: April 5, 2007