Let’s start with mass flux. Mass flux (

) is simply a measurement of flow over an area at a certain velocity, and has units of mass per time-area. In SI form, this turns out to be

Conveniently, this has the same units as, and is in fact equal to

where

is the density of the stuff, and

is the stuff’s velocity.

In a rocket motor, there is equal pressure throughout the motor, and as the combustion products can be considered relatively homogeneous, it is a reasonable approximation to consider

to be constant. Thus it seems that

is essentially directly proportional to flow velocity

, assuming non-choked conditions.

Perusing a gas dynamics book one day (like all good children of science?), I happened upon our good old friend, Vielle’s Law. Except it was weird. There was something else involved. Zucrow and Hoffman had written it this way:

At first glance, it’s much different from the one I learned from McCreary and Wickman, but really it’s the same thing with an extra constant on the front —

— a constant relating to velocity.

Light bulb goes on. That’s an erosive burning modifier.

Using simple 1-D fluid models, it makes terrific sense. Thus it seems that the addition of Oxamide (or any other burn rate modifier) isn’t just tampering with just the values for

and

— it’s messing with the erosive constant

as well. Man, this is worse than Robert Goulet in that Corn Nuts commercial. Looks like you’ll need a few more test burns, Scott!

After this delightful epiphany, I then continued to ponder. Why is mass flux such a big deal, rather than flow velocity? I mean, it’s not like we can directly measure either one in an operating motor — why pick mass flux to be the anointed child?

Well, for now, I’ve settled on the conclusion that it’s easier to simulate mass flux than it is to simulate flow velocity. Total mass flux can easily be calculated using a simple surface area model, while local flow velocity (note the word local — the equation requires the flow velocity at the propellant element under consideration to solve the new erosive rate) requires many assumptions about path, temperature, and upstream behavior of the gas. Numerical flow code like FLUENT can probably do it. I can’t (easily).

So mass flux is a decent method by which to figure out what the overall picture of the operating motor is, erosive-ly speaking. It also allows the configuration of unique grain designs (double-taper, anyone?) by solving the mass flux at the internal choke point(s), allowing the designer to figure out how fast the odd points will wear away, and perhaps give some insight as to what’s going to happen when the motor comes on. And mass flux seems to have a nice, solid basis in the world of fluid dynamics. But in the end, it’s still just a model. Testing of each unique design is still required.

Darn. Another excuse to fire more rocket motors.