End burner chamber pressure

Let's say that you have an end-burning APCP motor that starts out with 6" of propellant, right up against the inside face of the nozzle. The diameter
shouldn't matter, but let's say it is 54mm. Let's say that the motor burns ideally - a flat flamefront on the exposed face of the APCP grain, no abberations in the propellant density or composition. Let's assume no burning away of the liner or melting of the case. Let's also assume that there is no erosion of the nozzle.
My question is: as the 6" APCP grain burns from one end to the other, and there is a larger and larger "empty space" in the combustion chamber, does the combustion pressure change (and, therefore, the burn rate)?
-- David
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No, it stays constant.
David wrote:

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wrote:

In theory no. In practice yes, slightly.
--
Jerry Irvine, Box 1242, Claremont, California 91711 USA
Opinion, the whole thing. <mail to: snipped-for-privacy@gte.net>
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David wrote:

No.
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Shouldn't, except for local effects when the propellant is flush or almost flush with the nozzle.
The relationship follows from
GasExpulsionRate = GasProductionRate - GasRetentionRate
Now, GasProductionRate = PropDensity*BurningRateProp*BurningSurfaceArea
Define Discharge Coefficient from
GasExpulsionRate = DischargeCoefficient*P*ThroatArea
At equilibrium chamber pressure,
GasRetentionRate (equ) GasDensity(equ) * BurningRate(equ)*BurningSurfaceArea
Then
P = (PropDensity-GasDensity)*BurningRateProp*BurningSurfaceArea) / (DischargeCoefficient*ThroatArea)
A log/log graph burning rate v pressure is roughly linear for many propellants. For these propellants, there is an empitrical relationship,
BurningRate = a*P^n
n is called the pressure exponent; a is sometimes called the temperature coefficient. n is normally a number between 0 and 1 (though exceptions exist).
Assuming the above, defining
K = BurningSurfaceAres/NozzleThroatArea
and assuming that GasDensity(equ) << PropDensity
a substitution demonstrates that equilibrium chamber pressure is related to K as follows:
Pequ ~ K^[1/(1-n)]
where ~ denotes proportionality
Note that equiliibrium chamber pressure increases geometrically with burning surface area. Also, as n approaches to 1, equilibrium chamber pressure increases without bound.
Propellants with high pressure exponents (e.g.; KClO4 composites and single/double base propellants) are typically hard to use. If the nozzle fouls, they tend to explode. If the nozzle erodes, they tend to fizzle. Progressive burning grains are hard to employ with them as well.
Regards, -Larry (Sorry. My wrists do this...) Curcio

of
burns
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