[Gasification] Burning velocity

[Daniel Chisholm]

On Wed, 2006-10-05 at 15:14 -0300, Kevin Chisholm wrote:
> 
> We all know that IC engines with 4" strokes can work at 3600 rpm, but the 
> above "flame speed analysis" says they can't.
> 
> Could someone please tell me what I am missing here?

I suspect that the quoted flame speeds are at atmospheric pressure and
ordinary temperature.  In the higher pressure (density) and higher
temperature gas in a cylinder at the moment of the ignition spark, the
flame speed is likely higher.  And as combustion progresses, not only is
the continuing compression of the rising cylinder increasing the
pressure density and temperature, but the volume is being reduced too.
And the heat addition of the combustion is in turn increasing pressure
and temperature (though not density).

If I had to guess at the mechanics of gas flame speed, I would SWAG that
flame speed is proportional to density (closer particles bump into each
other more frequently), and also to the square root of the absolute
temperature (i.e. mean particle speed - faster particles bump into each
other more frequently).

So if you ignite a charge at ~35BTDC, let's just assume that the
temperature is 400C (from compression), and the volume is about 1/4 of
max.

the flame speed increase due to faster molecules would be
sqrt(700K/300K) = 1.5X

and the increase due to increased density would be 4X (gas is 4X
denser).

Combining these two, this would increase flame speed by 1.5*4 = 6X.  So
hydrogen (300cm/sec at atmos. temp and dens.) would have a flame speed
of about 1800cm/sec, and pure CO (really slow at 30 cm/sec) would be
180cm/sec.

To burn through that inch of headspace (call it 3cm), assuming the worst
case of ignition at the end rather than the centre of the charge, would
take (for slow-burning CO) 3cm/180cm/sec = 1/60th of a second.

But it would actually take less than 1/60th of a second, that 180 cm/s
is the _initial_ burn speed at ~35BTDC condition - remember, the burn
speed is going to be increasing (hotter, denser gas), and the volume
decreasing (piston still compressing), as the piston approaches TDC.

So you see, I've just shown that an engine can run at 3600 rpm.... ;-)



(for an extreme example of this, compare the burn speed of say a
teaspoon of smokeless rifle powder in the open, to the burn speed of the
same amount inside a loaded rifle cartridge.  The former is about one
second of a soft, quiet yellow flame.  The latter is about 0.2-0.5ms,
and anything but a soft quiet flame.  Same thing going on - the burn
rate increases as the charge burns, causing the pressure and temp to
rise, and feed back into still further increasing the burn rate... there
is an initial exponential growth rate)


-- 
- Daniel
Fredericton, NB  Canada