Dear jdsewell,
We've gotten into (almost) more of an aerospace discussion now, although what we're talking about is certainly still a valid and interesting mechanical problem. I'd like to get back to memepe for a moment, since he (or she) asked the original question and I'm not sure has ever gotten a satisfactory reply. The real expert here was SteamJetPE, who apparently has had a career (or some portion thereof) in designing these things; I think the most important facts we learned from him were that design methods are to a large extent proprietary, and that empirical data is an important part of the methods. So, no matter what we do, we're going to have to experiment some to achieve our design goal. Now, I'll throw in my two cents' worth to get us started, based purely on "thought experiments", not real-world experimental processes: Intuitively, I would suggest that a) the driving flowstream should fill the receiving venturi throat, so that flow velocity is as nearly constant as possible throughout; b) the gap between the driving tube exit and the throat is the most critical dimension to be determined, but it must be fairly long (maybe, at least the throat diameter?) so that good induction and mixing will occur at and within the driving flowstream boundary; c) the higher the driving flowstream velocity the better, because it means you've done a good job of reducing fluid static pressure, and because it means greater downstream momentum imparted to the gas molecules picked up at the boundary of the driving flowstream; d) the larger the venturi intake the better, up to a point. memepe, please accept that for what it's worth (possibly, about two cents). One other point: this feels like the kind of thing that doesn't scale especially well, so I'm guessing that optimizing a small model probably doesn't guarantee optimum results when you double or quadruple the dimensions. Again, this is purely intuitive, not experientially based.
Now, getting back to your idea, which (I think) amounts to a thrust augmentor with added fuel injection. Theoretically, this should work -- remember, though, that adding energy via combustion is not in itself enough to improve thrust performance. You have to provide something that will communicate forward momentum back to the body of the device. Presumably, the dowstream skirt of the venturi will perform this function, but to do so, you'll have to make sure that it's a sufficiently long cone to take up the expansion of the exhaust gas without the exhaust stream separating from the cone wall. In other words, adding fuel for combustion increases the static pressure in the flowing gas, and you want to effectively convert that static pressure into rearward momentum of the gas stream (and corresponding reaction momentum into the cone and thereby through bracing into the rest of the device). This is likely to take a pretty long cone, because of the already high rearward velocity of the gases.
Your mention of ramjet design suggests a slightly different approach (though maybe this is closer to what you really had in mind) -- provide a ramjet type diffuser leading into an expansion chamber, with flameholders, etc. followed by a nozzle for re-acceleration. I have seen (now expired) patent drawings of a whole chain of these things "boosting" air input into each other, (supposedly) to gain efficiency as you go along. Such multi-stage "combustor chains" are probably excessive, but providing a single-stage "ramjet afterburner" would seem reasonably efficient and certainly doable. For efficient combustion, you would have to achieve oxygenation equivalent to at least a 30lb/lb air/fuel ratio, taking into account the added fuel and air and the unconsumed oxygen still available in the driving exhaust stream (as utilized in conventional built-in jet afterburners). Obviously, "some experimentation required".
LarryC