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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

Reply to
David
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Reply to
Jeff Taylor

No.

Reply to
Dave Grayvis

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) Let's say that you have an end-burning APCP motor that starts out with 6" of

Reply to
Larry Curcio

In theory no. In practice yes, slightly.

Reply to
Jerry Irvine

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