reynolds number

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...

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.

Don't feel the least bit stupid over this, Reynolds number is a
horribly misunderstood thing.

In broad terms, it puts a value on the physical length of an airfoil
and the speed it's traveling. Say you have a 4 foot wing chord, and
the wing is travelling 100 mph will produce a R number around 3.3
million. That same airfoil scaled up to 8 feet will give an R at 6.6
million, or the 4 foot wing at 200 mph also gives 6.6 million, and the
8 foot chord going 200 mph gives an R of 13 million. An airfoil built
half the size, traveling at the same speed as another will give much
less lifting force. (not necessarily half) but that half size airfoil
travelling at twice the speed will act exactly the same as the larger
airfoil at the lower speed.

Reynolds number basically puts a value on the quantity of air working
on a wing for a given unit of time. If you reduce speed or reduce
size, then less air works on it. Increasing speed or increasing size
increases the amount of air working on it.

Hope this helps your understanding
Gerry

On Jun 22, 10:33*am, 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...

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

Gerry van Dyk schreef:
Don't feel the least bit stupid over this, Reynolds number is a
horribly misunderstood thing.

Thanks for reassuring me Gerry, you mailed this while I was replying to
Cavelamb.

(snipped useful explanation)

Reynolds number basically puts a value on the quantity of air working
on a wing for a given unit of time. If you reduce speed or reduce
size, then less air works on it. Increasing speed or increasing size
increases the amount of air working on it.

This is a hard nut to crack, but it looks like it might be the key to my
understanding. Will sleep over it now, and let the information soak this
poor old brain...

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.

At the risk of making things more murky, let me add another point.

Given that bigger wing = higher R = more lift, or higher speed =
higher R = more lift, it also works higher air density = higher R =
more lift. Both lift and drag drop off with altitude, and increase as
you decsend to sea level, IE Renolds number decreases with altitude
and increases going down.

As a thought exercise, think about how fast you'd need to make a wing
travel in water to lift a given weight. It might take only 10 mph to
lift a C-150 in water vs 60 mph in air.. Water is so much more dense
than air, the low speed makes just as many molecules of water contact
the wing during 1 second of time, as air molecules work on it for a
second at 60 mph in air. Therefore, you get the same Reynolds number
at 10 mph in water as 60 mph in air. When moving at an equal Reynolds
number a given wing will give the same lift and drag. In this thought
exercise slow speed thought water gives the same lift and drag as high
speed in air. We've now added fluid density to the equation, all
three factors are part of Reynolds number.

The bottom line is, regardless of the fluid density, physcal size of
the wing, or speed, a given Reynolds number will produce a specific
lift and drag. Change the density, change the size and work out a
speed that will give the same R number, then you will get exactly the
same lift and drag.

Getting back to the question in the other thread, asking about
Reynolds number is engineer-speak for "what wing chord and what speed
will you be running. We'll assume 'standard air' for density, then
we'll select an airfoil that will give you enough lift for the weight
you'll need to pick up."

Hope I didn't just make it worse.
Gerry

On Jun 22, 12:08*pm, jan olieslagers
wrote:
Gerry van Dyk schreef:

Don't feel the least bit stupid over this, Reynolds number is a
horribly misunderstood thing.

Thanks for reassuring me Gerry, you mailed this while I was replying to
Cavelamb.

(snipped useful explanation)

Reynolds number basically puts a value on the quantity of air working
on a wing for a given unit of time. *If you reduce speed or reduce
size, then less air works on it. *Increasing speed or increasing size
increases the amount of air working on it.

This is a hard nut to crack, but it looks like it might be the key to my
understanding. Will sleep over it now, and let the information soak this
poor old brain...

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

jan,

I had a nice graphic that explained the range of effects on Reynolds Number from
the "fall of dew" to Mach 3. Unfortunately I haven't found it - yet.

But getting away from airplane wings for a moment,

How fast does dew fall?
How big is a droplet of water in the morning dew?

At that scale, viscosity (stickiness of the air - and yes, air is "sticky")
effects are the major forces involved.

Accumulate more water into a raindrop.
Now there is enough mass for much higher velocities.
Now the inertial forces predominate.
The wake left behind is fairly clean, but noticeable.

Freeze a bunch of that into hail stones!
Lots of mass - much higher speeds.
Now we start seeing funny things in the shape of the wake - swirling
vortices.

http://en.wikipedia.org/wiki/Von_K%C..._vortex_street
Notice how the animation shows the wake whipping back and forth.


Get enough mass and size, and altitude to fall (ie much higher speeds),
and we see the air ahead of the object starting to pile up - can't get
out of the way fast enough - resulting in super sonic shock waves.

It's all the same air.

The differences are how long (chord length) and fast something is
going through it.


Or, as another pointed out, increase the density of the fluid.

Guys, please, if you really only do have a marginal understanding,
don't post or at least mark it as such. Explaining in entirety what
the Reynolds numbers means will fill one or two chapters in a good
aerodynamics textbook.

What Cavelamb wrote is good, what Jim wrote is, as he said, marginal
understanding, but not wrong, but what Gerry wrote is between
borderline and wrong.

I will try and summarize a bit (but after 7 years of university, it's
probably pretty theoretical):

The Reynolds number is determined as

Re = v * L / nu

v is the speed of the airflow,
L is the "characteristic length" (I'll get into that)
nu is the "cinematic viscosity" (dynamic viscosity divided by density,
which yields roughly 1.5 * 10^-5 m^2/s at ISA MSL conditions - no
fudge factors such as "9346" when using SI. The density effects Gerry
wrote about are 99% due to the impact of density on the dynamic
pressure, and not on Re - and the dynamic viscosity of air and water
are much different to begin with)

Physically speaking, it gives you the relation between viscous and
inertial forces in a fluid (as has been said). Which won't really tell
you anything in the beginning. Very roughly it means whether the
airflow will be laminar or turbulent (see last post by Cavelamb).

This means you can get an infinite number of Re on an airplane, just
as has been written. It cannot (really) be chosen, but is determined
by size and operating conditions of the airplane.

On an airfoil, the characteristic length L is the chord. Wind tunnel
measurements on airfoils are done at certain Re. So if you know your
airflow speed and chord, you can get the right polar to figure out how
your airfoil will behave. Re mostly has an effect on the length of
laminar airflow (transition usually occurs at a certain Re, which is
then not calculated with L, but rather with x, meaning the length of
surface the air has travelled on the airfoil up to this point) and
hence drag, and since laminar and turbulent flow behave differently
with regard to flow separation (check for pictures on Google what this
means), it also has an effect on the maximum lift coefficient the
airfoil will achieve.
In general, higher Re lead to lower drag coefficients and higher max
lift coefficients, but a smaller "laminar bucket", which means the
range of lift coefficients the airfoil can operate in to achieve low
drag is smaller (especially interesting for sailplane and other low-
drag applications).

In short, you need it if you (seriously) want to design an airplane
and estimate its performance.

But the difference between wind tunnel testing and reality is much
greater than the difference between Re = 1 * 10^6 and 2 * 10^6, so it
doesn't really matter for homebuilders. It can become interesting for
builders of high-performance model airplanes and of course
aerodynamically challenging tasks such as designing sailplanes.

Oliver