reynolds number

jan olieslagers wrote:
It's been puzzling me for a long while and there it is again popping up
in the "WIG airfoils" thread: what is this sacred Reynolds number?
I tried our alther friend en.wikipedia but its theory was quite beyond
my level of education* and its examples of oil in a pipe were not really
illuminating - not to mention the spermatozoa and the Major League
Baseball.

Is it a property of the wing, or of the whole plane, or do the fuselage
and wing and empennage &C each have their own Reynolds number?
I seem to understand this figure is a measure of aerodymanic quality?
Given a plane's weight and engine power, will it be faster (or slower)
for a higher Reynolds number?

Excuse my stupidity,
KA


*I am only a modest Solaris sysadmin, never went to university...

Detailed explanation at:
http://www.aerodrag.com/Articles/ReynoldsNumber.htm

Here's a simple example for a wing with a 10 feet chord at 100 mph
flying speed, at Sea Level and "Standard Day" conditions.

Re = 9346 x 100 x 10 = 9346 x 1000 = 9,346,000.


Reynold's Magic Number basically shows the ratio between inertial
forces and viscous forces in a fluid.

Think of it as (how fast it's moving) / (how sticky it is).

At low R, viscous forces predominate. (and generally laminar flow)
At high R, is dominated by inertial forces. (resulting in higher sheer
forces and turbulence)


Straight from wiki...

If an airplane wing needs testing, one can make a scaled down model of the wing
and test it in a wind tunnel using the same Reynolds number that the actual
airplane is subjected to. If for example the scale model has linear dimensions
one quarter of full size, the flow velocity would have to be increased four
times to obtain similar flow behaviour.

Alternatively, tests could be conducted in a water tank instead of in air
(provided the compressibility effects of air are not significant). As the
kinematic viscosity of water is around 13 times less than that of air at 15 °C,
in this case the scale model would need to be about one thirteenth the size in
all dimensions to maintain the same Reynolds number, assuming the full-scale
flow velocity was used.

The results of the laboratory model will be similar to those of the actual plane
wing results. Thus there is no need to bring a full scale plane into the lab and
actually test it. This is an example of "dynamic similarity".

Reynolds number is important in the calculation of a body's drag
characteristics. A notable example is that of the flow around a cylinder. Above
roughly 3×106 Re the drag coefficient drops considerably. This is important when
calculating the optimal cruise speeds for low drag (and therefore long range)
profiles for airplanes.

cavelamb schreef:

Detailed explanation at:
http://www.aerodrag.com/Articles/ReynoldsNumber.htm

Thank you Richard, you really did your best but I only feel more stupid,
this text still leaves me confused. At one time the Reynolds factor
seems a property of the plane, and one Questair plane can even have two
values for it, another time it seems a property of the wing and yet
another time the Reynolds factor is different for various places of the
wing. Excuse my being confused!

Here's a simple example for a wing with a 10 feet chord at 100 mph
flying speed, at Sea Level and "Standard Day" conditions.

Re = 9346 x 100 x 10 = 9346 x 1000 = 9,346,000.

This sounds like "it is a property of a given wing at a certain speed"
OK, I can digest that. So just like drag, Re will go up by speed
squared. And it might vary with atmospheric conditions, I'm still with
you, great!

Reynold's Magic Number basically shows the ratio between inertial
forces and viscous forces in a fluid.

Think of it as (how fast it's moving) / (how sticky it is).

OK, how sticky it is depends on the wing (airfoil and "smoothness" I
should think, and speed is speed. OK, got that.

At low R, viscous forces predominate. (and generally laminar flow)
At high R, is dominated by inertial forces. (resulting in higher sheer
forces and turbulence)

This much I gathered from the Wiki page, but I still don't get the
point. Given the mission (design a plane with so much max gross, with
xxx HP engine power, and make it go as fast as you can) is it possible
to determine an optimal Reynolds number for the wing or for the damned
plane or its f....g mother in law?

Or why is this Reynolds factor important, and where does one apply it?

Thanks for bearing with me,
KA

jan olieslagers wrote:
Or why is this Reynolds factor important, and where does one apply it?

My rough understanding:

It is useful to aircraft designers who want to first build small models.
The flow over small models will generally remain laminar over a larger
portion of the small model than the full-sized aircraft. Reynolds number
can be used as an _estimate_ of the amount that turbulent flow contributes
to aspects like drag. (The equation, Re = V*L/nu, doesn't even include
surface roughness; hence the approximation aspect of its nature.)

One could use the Reynolds number equation to estimate when the flow goes
from laminar to turbulent. In fact since length L is in the equation, there
are an infinite number of Reynolds numbers for a body! For example, at the
leading edge of a wing, the length L starts at 0, so Re = 0. That indicats
laminar flow at that point (in theory!) Then Re gets larger as the flow
moves along the wing because the L in the equation gets larger. If one
could factor in wing surface roughness and how much the fluid is already
edging toward turbulence before it even reached the leading edge of the
wing, then one could presumably estimate the value of L when the flow
transitions to turbulent flow (or laminar separation from the surface) for
a given V.

So when you see some publication saying that Re is, for example, 1,000,000
for a wing of length L in a fluid moving at speed V, they mean that is the
value Re reaches at the trailing edge of the wing. Roughly halfway along
that wing Re would be about 500,000 for the same V.

I can't think of anyone other than aircraft designers and testers needing
an understanding of the number.

A different example...

A golf ball operates at a very low Re (small length and low speed),
so it's form drag would be very high - without the dimples.

The dimples trip the boundary layer forcing a premature turbulent transition
in the boundary layer. This turbulent layer provides a high energy boundary
layer that reduces form drag by reducing the boundary layer thickness.
The dimples, in effect, increase the Re.

Back to wings:

In choosing airfoils (and thus wing areas), Re is important because all airfoils
do not work equally well
at all Re.

Laminar airfoils generally don't work very well at exceptionally low Re.

The 5 digit NACA series, as an example, don't do well below Re of 2 million.

On that little low wing single seater I was sketching on a while back, the
wing tips are only 24" chord. At landing and take off speeds ( 40 mph?)
the tips aren't making very much lift!

That leads to higher take off speeds (or a larger wing?), lousy aileron response
at low speed, and makes it very easy to encounter a tip stall (roll on take off
any one?).

But the rest of the wing, due to longer chord looked to be fine.

So my "solution" was to change from a 23015 airfoil at the root to a
2412 (a 4 digit - or turbulent flow airfoil) at the tips.
(That would be a lofting nightmare - without CAD)

This airplane was also supposed to operate at higher than "usual" altitudes
(12,ooo+ feet for cruise) the same thing could have happened in cruise.

The thinner (lower density) air lowers Re to the point that we could possibly
encounter high speed tip stalls...


Now, does that mean that small chord wings can not operate at low speeds?
Of course not.
But we left wing size, efficiency and altitude out of the question.


Richard