Conference rusure::math

    727.0 opened quite a can of worms.
    
    What is a flame?  It is a region in space in which violent phase
    transitions are occuring (solid to liquid to gas) resulting in
    a lot of kinetic energy (heat and motion) and electromagnetic 
    energy (light and ionization).  How do you model such a situation?
    You must consider the chemistry of the interactions (including but
    not limited to the energy produced by the reaction, the relation
    between the reaction rate and chemical densities, pressures and
    temperatures; and if you have more than one reaction going on you
    have to relate all of them).  In addition, the pressures, densities
    and temperatures of the gases will depend on thermodynamic and 
    fluid dynamic laws (which can be summarized by the Navier-Stokes
    equations *but* these equations can not be solved in general). 
    So we need (at least) a hydro-chemical thermodynamic model.
    
    Punch line:  Few people have come up with such models and even
    fewer have been able to squeeze useful physical information out
    of these models (even with computer simulations).
    
    So what do we do?  We say hot air rises and that's why flames look
    the way they do!  :-)
    
    In the past few years, computer models of flames have been in vogue.
    In fact, I think that there was even an article in Scientific American
    a few years back.
                     

Let me rephrase the first question as a (simple) thought experiment to
get at the specific things I'm trying to figure out.

Suppose I have an enclosed box (say a cube) of air.  Let's say that the
sides, bottom, and top conduct heat and that I'm performing the experiment
on the earth's surface (i.e. in a gravitational field).

If I heat the bottom of the box (near the center say), a circulation of air
flow will start inside the box.  The flow is that the
hot air will rise near the center, and move out when it hits the top, then
it will cool and fall, finally being drawn back to the center and up the
plume again ... (I think; am I right ?)  

Some questions:

Is gravity necessary to this process or would the same
thing happen in a gravity free environment ?

If gravity is NOT necessary, then why do we say that hot air RISES ?
Might it not be more correct to say that air moves away from a heat source ?

If I heat the side of the box in a gravitational field, do I get a different
flow pattern (all other things being equal) ?

Is the high heat conductivity of the sides of the box essential to this process
or would I get the same kind of flow if no heat were conducted away ? Of course,
the bottom must still conduct or we couldn't heat the system.

What is the mechanism of the 'rising' ?  Does it have something to do with the
fact that heated molecules are faster and try to get rid of their additional
kinetic energy by moving up against a gravity gradient or what ?  Why should
the net momentum of the faster heated molecules be away from the heat source
while this is not true for the cooler molecules ?

Do you see what I'm getting at ?

re.2:

>If I heat the bottom of the box (near the center say), a circulation of air
>flow will start inside the box.  The flow is that the
>hot air will rise near the center, and move out when it hits the top, then
>it will cool and fall, finally being drawn back to the center and up the
>plume again ... (I think; am I right ?)  

Sounds right.

>Is gravity necessary to this process?

Gravity IS necessary.  The hotter gas is less dense, and rises like a bubble.
Note that it's not simply the more energetic molecules that rise -- the energy
can be transferred between molecules, and percolates to the top.  The cooler
air has greater density and sinks, displacing the warm air.

If you heat the side of a box in a gravitational field, you'll also get a flow.
BUT without a gravitational field, the heat will simply dissipate, and you'll
have a temperature gradient within the box, with no macroscopic air motion.

>Is the high heat conductivity of the sides of the box essential?

In a way, yes.  If the sides and top were insulators, the air inside the box
would eventually reach the same temperature as the bottom.


re.0:

I'm curious about a zero-G flame.  Would there be enough convection and osmosis
for the carbon dioxide to dissipate, and oxygen to approach the flame?

    Re .0:
    
    > What's going on at the molecular level ? 
    
    Consider a bit of air.  The air is less dense at the top of this bit
    than at the bottom.  Now consider a molecule moving randomly.  It hits
    other molecules periodically, and changes direction.  If it moves down,
    it is more likely to hit molecules because the air is more dense. If it
    moves up, it is less likely to be stopped.
    
    So there is a tendency for molecules to rise -- except that this would
    change the density.  So what happens is they fall into a general
    equilibrium.  But hotter molecules are moving faster and get more
    advantage out of the phenomenon described above, so they move upward
    more than slower molecules.
    
    
    				-- edp

I believe the reason hot air is less dense and hence rises, is that its
molecules are moving around faster, bumping into each other more, and
hence increasing the average distance between molecules.

I suspect that maybe burning would not proceed very well in no-gravity,
unless a fan were present to produce an air flow.

/Eric

Burning can take place in gravity-neutral environments, but the situation
is much more complex than in a gravity environment. What happens is that minute
irregularites in the gas flow will cause local 'storms' to occur, in which
heavier and lighter gasses move past each other in opposite directions in
adjacent, parallel channels to and from the combustion point. Much like the 
flow of water in gaseous, liquid, and solid states in a thundercloud. 

    For those who are interested in flames in 0-g environment can read
    A House In Space in which is described what happened when one of
    the astronauts in the SKYLAB lit a candle.  Basically the flame
    was spherical and did not last very long because lack of convection
    did not allow sufficient oxygen to enter the flame and support it.
    
    	John Hooker
    	SDO (619)292-1818
    	aiwest::hooker

1.  Go to the circus.
1.5 Buy an air-filled balloon.
2.  Buy a HELIUM balloon with a string; don't just fill it with air. Use Helium.
3.  Tie the string of the He balloon to a suitable attachment on the floor of
	your car so that it is suspended in the middle of the cockpit.  
4.  Tie the string of the air balloon to the ceiling, maybe a clothes hook.
Or tape it to the ceiling so that it is suspended.
4.5Drive forward.

5.  Note that when you accelerate, the helium balloon goes forward and the
air balloon goes backward.  Note that when you turn left the He balloon
goes left and the air balloon goes right.


A balloon suspended in air feels pressure from inside and out.  the pressure
from the outside on the top is less than that on the bottom because it is
under less pressure because there is less atmosphere above it pressing it
down from gravitational attraction.  
(vertical components of)Pressure * area = force_down.  So the force
on the underside of the balloon is more than on top.  If the resultant force
up is less than the weight of the balloon (because it is an air balloon)
the resultant force accelerates the ballon towards the earth (also
impeded by drag) and the balloon falls.  If the resultant air-pressure force
is greater than the weight of the balloon (because it's filled with He,
which weighs less than air at the same pressure), then the force
(summa (vertical components of pressure on top and bottom)-balloon weight)
accelerates it upward, also slowed by drag.

Heated air is less dense than unheated air at the same pressure.  So the
force on it from the other air pushes it up.

Tom

Oops forgot the car.
Accelerating forward makes a de-facto gravitational field with a 
gradient pointing backwards.  From there on everything else is the same
as in gravity.  Turning right makes it point left.
Tom

re .8:

The lighter-than-air balloon moving forward is a delightfully
counter-intuitive result !  I had to think about this for a while
before I believed it.  I think you should have mentioned that the
reason the acceleration makes the balloon move forward is that the
pseudo gravitational field creates a new static air pressure distribution
inside the car with the isobaric lines forming an angle arctan( a/g ) with
the ground plane.  The ballon then moves to bring the string normal to
these isobaric lines.

In reality, might not the balloon oscillate a while around
the new string angle and maybe even initially move backwards (until the
new pressure distribution is established) ?  After all the air has
to flow to the back of the car when we first start accelerating.

I think some kind of experimental setup that demonstrated this effect
could be a real surprise to physics students !  I love this kind of
thing (counter-intuitive behavior).

You know, I'm still not convinced that gravity has much to do with the question
in .0 that I originally raised (about why hot air rises).  Let me think about
this a bit more.

>Turning right makes it point left.

Don't you mean '... it point right' ? The principle seems the same for
tangential acceleration except that the isobars will be arcs of circles,
right ?

re: -.1
yeah, i got it right in the original , but wrong in the later reply.
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Note 727.8              physics questions about flames                   8 of 11
COUGAR::JANZEN "Tom LMO2/O23 296-5421"               32 lines  17-JUL-1987 14:19
                 -< Integrate forces on sphere along vertical >-
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5.  Note that when you accelerate, the helium balloon goes forward and the
air balloon goes backward.  Note that when you turn left the He balloon
goes left and the air balloon goes right.

    re .10:
    
    > I think some kind of experimental setup that demonstrated this effect
    > could be a real surprise to physics students !
      
    It certainly was when they did it for our class at MIT.
                                                   
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    re .10:
    
    > You know, I'm still not convinced that gravity has much to do with
    > the question in .0 that I originally raised (about why hot air rises).
                   
    Well, there _is_ experimental evidence that without gravity, hot
    air does not rise (either Skylab or the Shuttle).
    
                                                   
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    JUST ANOTHER SOMETHING TO 
    
    CONSIDER ABOUT GRAVITY AND HOT AIR
    
    HOT AIR BALLOONS FLY (OR RISE) STRICTLY
    
    BECAUSE THE HOT AIR IS LIGHTER THAN
    
    THE AIR AROUND IT . KIND OF LIKE WHY 
    
    A HELIUM BALLOON FLOATS ONLY THE HOT AIR 
    
    IS A TEMPORARY LIGHTER THAN AIR SITUATION
    
    NOT PERMANENT LIKE HELIUM. THE ATMOSPHERIC PRESSURE
    
    CAUSED BY GRAVITY CAUSES THEM TO RISE.