I did forget to mention Radzan and Kuo, Renie and Osborn, King, or any of the other myriad of erosive burning papers that have been published in the AIAA journal. Many of the more modern studies rely extensively on numerical simulation techniques (PEM combustion) and assume that the AP/binder gas is premixed before erosivity becomes a problem — so I think the density model still applies.

Granted, I’m not sure of the accuracy of the

model — though the Zucrow and Hoffman text is held in high regard, I’m not aware of anybody firing motors to try and corroborate the equation. Looks like a good static testing exercise

One other thing I did think about last night as I was falling asleep is the fact (duh) that in a core-burning or BATES model, the mass flux is always highest across the face of the grain closest to the nozzle. I’ve been struggling with modeling mass flux in two dimensions (

as a function of grain length, and

as a function of burn depth), but this would simplify things — at least for characterization motors. Don’t know why I didn’t bring that up before.

Maybe a fun experiment would be to try and predict the time at which the aft-most grain gets completely consumed and spit during erosive motor operation. Seems simple enough — make a motor with short aft grains, figure out the rate difference between head end and nozzle end flow, and go from there. Hmm.

There are many models, from simple to wildly complex, to describe erosive burning and related phenomenon such as acceleration affects and resonant burning. The “1+kv” linear approximation isn’t all that good. There are two that I use in my simulations: Lenoir-Robillard(1957)/King(1975) and Kriedler(1964). L-R/K says it is nonlinear and is affected by flow(+), burn rate(-), solid density(-), and length(-). Such as: 1 + Ka V^0.8 exp(-Kb rb rho / V) / L^0.2
Kriedler says there’s a threshold mass flux that depends on pressure, and there’s less erosive affect at higher pressures and higher br exponents. Such as: 1 + (K1 + K2 p)(V-Vth)/p^n.

A good reference is: Razdan and Kuo, 1983, “Erosive Burning of Solid Porpellants”, AIAA.

Here are a couple examples of the non-linear simulation. This one is the L-R/K model which matches the very erosive burn simulation: http://thrustgear.com/MotorSim/bg6gr_38.GIF
This sim is the gradual affect of the Kreidler model which is more useful for mildly erosive propellants: http://thrustgear.com/MotorSim/motorsim_example1.JPG

The only way to find the threshold and constants is to burn several motors with increasing mass flux while trying to hold everything else the same.

-John DeMar