RE: [ATM] basic questions about cooling fans

["Timm Simpkins" <poduck@poducksworld.com>]

To add a little bit to this already excellent reply, boundary layers come in
two flavors, laminar and turbulent.  Since the flow of the fluid (air) in
this case is basically nonexistent, no boundary layer really exists.  Air
either has to be moving over a surface, or a surface has to be moving
through the air in order to create a true boundary layer.  This layer is
called the boundary layer because it adheres to the surface of an object and
acts as a boundary between the object and the surrounding fluid.  It is not
because the air bounds the object.

Since Mark already explained very well what the actual problem is, I'll just
leave this as a correction to a logically derived wrong conclusion.  It may
seem like the phrase boundary layer applies since the air is on the boundary
of the mirror, but that's not what it's called.  Don't ask me what you might
call it, maybe stagnant air.

One clarification needs to be made though.  If you start blowing air from
behind the mirror to the front, you most likely will create a turbulent
boundary layer.  There should be a boundary layer of some sort, and it's
most likely not going to be laminar.

-----Original Message-----
From: atm-bounces@atmlist.net [mailto:atm-bounces@atmlist.net] On Behalf Of
Mark Holm
Sent: Saturday, May 22, 2004 9:13 AM
To: atm@atmlist.net
Subject: Re: [ATM] basic questions about cooling fans

Thomas A Simmons wrote:

>I was wondering how long it would take before someone commented
>on Bryan Greer's articles.

Actually, on the very same day the May issue arrived in my mail box, I wrote
a strongly worded message to the list suggesting (almost demanding) that
every atm should read these articles.

I am going to take this opportunity to recap something I wrote a few months
back, because I notice that confusion/ignorance over this point is common.

The optical distortion caused by "tube currents", mirror boundary layer and
atmospheric "turbulence" is caused by non uniform refractive index of the
air along the path that light travels to get from a celestial object to our
eye.  It is exactly the same effect as if you put pieces of clear and well
polished, but different refractive index glass in the light path.  Light
traveling through each region of different refractive index takes a slightly
different time to pass through.  After passage, light waves that had a
certain phase relationship, imposed when they left the celestial object, now
have a different phase relationship that bears only a scrambled version of
the original relationship.

An aside:  We are often told that the speed of light is a constant.  This is
true if you are talking about the speed of light in a vacuum.  When light
passes through materials, it slows down.  The amount by which it slows down
depends on the electromagnetic environment inside the material, and is
exactly equal to the number we call the refractive index.

The refractive index of air is close to 1.  That is, it isn't too terribly
different from the refractive index of a vacuum, but it isn't exactly 1.

The refractive index of air depends on the chemical composition of air and
on its density (how many molecules are in a given volume).  Except for water
vapor content, the chemical composition of air is pretty uniform both on
small and large scales.  Water vapor content usually is pretty constant on
small scales, so changing water vapor content usually isn't a big player in
degrading telescope images.

Density, the other player in air's refractive index is given to a rather
good approximation by the universal gas law

PV = nRT

Density, for this purpose, is number of molecules per volume of air, so the
equation rearranges to

n/V = P/RT

n/V is the number of molecules per volume
R is a constant (called the universal gas constant.  It shows up in a lot of
chemical thermodynamic equations.)

So, the factors that influence air's refractive index on a small scale are
Pressure, P, and Temperature, T.

Notice that velocity is nowhere to be found in these equations.  It does not
matter whether the air is moving or not.  Turbulence (chaotic motion) of air
does not cause bad seeing, unless it involves pressure gradients or
temperature gradients.

The thing about pressure is that pressure differences in air even out very
quickly on small scales.  Pressure differences propagate at the speed of
sound and bulk pressure differences rapidly induce air movement that quickly
damps out the pressure differences.  Pressure differences are of course
associated with all air movement, but the amount of pressure difference
associated with low speed air movement on small scales is very small.
Running a fan in front of a telescope mirror induces pressure differences in
the vicinity of the fan blades, but 1. those pressure differences are small,
and 2. they damp out very quickly, so that, a short distance from the fan
(millimeters) the pressure differences have dropped to a small level.  Thus,
unless you have a monster fan at work, the pressure differences caused by
the fan will cause only quite small refractive index differences in the air.

Temperature is a different story.  Heat propagates slowly through air.  It
is quite possible (and quite common) to have significant temperature
differences across small distances, and for those temperature differences to
take a long time to dissipate.

When we see atmospheric distortion of telescope images, whether the source
is inside the scope or up in the sky, we are seeing primarily the effect of
different air temperatures along the light path.  The distortions are
usually in motion, because the air is usually in motion, moving the
different temperature parcels of air about in the light path.  It isn't the
motion per se that causes the distortion, it is the temperature differences.
If we froze the motion, we would still have distortion because the air
column would still be non uniform in temperature.  Freezing the motion would
just give a static distortion instead of dynamic.

To eliminate the distortion one needs to eliminate the temperature
differences.  This is where fans become our ally.  Moving air and mixing it
up is the quickest way to even out temperature differences in it.  We can
homogenize the air inside our telescopes, and immediately in front of the
mirrors to a very great extent using fans.  We can also greatly speed the
equilibration of solids (mirrors) with the surrounding air temperature, thus
greatly reducing a big cause of air temperature difference in our
telescopes.

To minimize the temperature differences in the atmosphere outside our
telescopes, our only hope is finding a good observing site.  It doesn't have
to be Mona Kea to be an improvement.  Grassy fields are better than parking
lots.  Heated buildings are bad.  The top of a hill is usually better than a
valley (cold air pools in valleys).  The top of a hill is usually better
than the side of a hill (cold air flows down the side of hills.)

It is often true that, at night, the greatest temperature differences in air
are found in the first couple of meters above the ground.  A lot of that
nasty seeing is happening only a few feet over your head!!!  Get up on a
hilltop, or build an observing platform a meter or two tall, and a lot of
bad seeing will be put under your feet.

Mark Holm
mdholm@telerama.com


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