Hey everyone, I'm back with further adventures in whatever this bizarre thing is! No specific questions this time, but I am fishing for general knowledge on exotic airbreathing engines and how best to implement them. I've been beating my head against this for a few days, so figure it's a good time to reach out and see if I can find someone with a better understanding of supersonic aerodynamics and thermodynamics than I have. In any case, I'll document whatever I do end up doing here.
So my mission is this:
- I want to equip this thing with some kind of exotic engine that accelerates atmosphere when able, and draws on a reservoir of propellant in vacuum.
- High degrees of "space magic" are permissible and somewhat implied by the first point, but I would like the behavior of the engine to seem plausible for its parameters. I want the engine to make some sense conceptually, even if the parameters of its design have to be pretty off-the-wall.
- I would like to cruise up to a fairly high sub-orbit (say 5000-7000 m/s) on the air-breathing mode.
- I would like to do it without any insane thrust spikes at low to mid mach.
- I would like the ascent profile to be challenging enough to hand-fly that it's fun to practice (I'd like to avoid crazy-high thrust margins).
- Space-magic parameters for heat generation etc are welcome. I don't mind if the engine core has to be sun-temperature or something, I don't mind invoking magnetic containment, etc. I just don't want the actual, physical thrust of the engine to be completely "because I said so".
After a few days of research and tinkering I've gotten into the edges of the ballpark of what I'm looking for, but I haven't been able to quite get there. The system that I'm working with now is effectively the DG-S SCRAM code, but extracted from its subsystem, gutted of its fuel parameters, and sloppily retrofitted with a solid state heat source that is directly controlled with the throttle setting. It does fly, and it behaves vaguely in the way I would expect it to: It starts with zero static thrust, builds thrust quickly between M 0.5 and some arbitrarily higher mach (related to maximum core temperature), and loses thrust to decreasing atmospheric density (and thus mass flow), decreasing ram speed (and thus mass flow), and decreasing delta between exhaust velocity and free stream velocity. The problem I can't get away from is I can't approach the upper bounds of speed and altitude I want without having absolutely insane peak thrust on the way there. TWR > 30 insane. It makes sense to me that this would be a problem: Thrust is a function of the difference between free stream velocity and exhaust velocity multiplied by the mass flow. If I want to get to 6 km/s, I am going to need an absolute bare minimum of 6 km/s exhaust velocity. In reality, it's probably going to be more like 9-10 km/s. That means that at lower speeds, the thrust of the engine is only really held back by mass flow, which at low altitude becomes quite high quite quickly. My exhaust velocity does increase with vehicle velocity, but not nearly enough to avoid impractically high thrust between mach 1 and mach 3 or so.
My exhaust velocity math looks like this:
ev= sqrt(2 * (cp * Tb) - (cp * Te))
which is a reorder of
(cp*Tb)=(cp*Te) + (ev^2) / 2
where cp is specific heat at a given pressure, Te is exhaust temperature, and Tb is core temperature. In all honesty I only kind of get what's going on here. I'm mostly working from the equation documented in PDF guide, so I'm not really sure to what extent this does or doesn't make sense. thermodynamics are not a strong subject of mine.
But anyway, while this steep-thrust-curve-with-a-sudden-plateau-as-you-approach-exhaust-velocity behavior makes sense to me based on what I've read, it isn't how the DG-S or XR-2 seem to behave, nor does it quite match the trends in NASA's EngineSim applet, so I figure maybe there's something I'm missing conceptually.
For a start, I was never able to turn up much clarity in my research as to how exhaust velocity behaves in SC/RAM jets. Some sources (EngineSim included, unless I misunderstand it) suggest they have relatively constant exhaust velocities. Other sources (such as Orbiter's own documentation) suggest exhaust velocity increases linear-ish-ly with vessel velocity.
I came to the conclusion that, since air is compressible and should be choking to mach 1 in the nozzle throat (I think?), the static exhaust velocity model is probably more literally realistic. But such an engine could propel a vehicle faster than its exhaust velocity anyway, because the exhaust would be much denser than the free-stream air. Thrust here is being expressed in with respect to mass flow and not volume flow, so I figure the DG-S's increasing-exhaust-velocity approach is simply an abstraction of this high density, lower velocity process, and could be expected to make reasonable predictions about final thrust. But if I'm way off on my understanding of the problem, it might go a long way to explaining why neither this engine nor the expectations I have for SC/RAMjets based on reading seem to line up with the behavior of other SC/RAMjet models.
For another possible lead: all the models I'm comparing to are fueled. Are the ultra-high-minimum-speed and shallow (relatively) power curve of the DG-S and XR-2 SCRAMs a function of fuel mixture somehow, and not representative of how a nuclear ramjet might behave? Those depictions are fictional and I have no real idea how accurate they are as models, but the point is they behave closer to what I'm looking for, and I don't understand why. My implementation is quite literally derived from the DG-S code, stripped of references to a fuel and given a fixed heat source instead. Like I've said though, I have a pretty tenuous grasp on thermodynamics, so who knows what all I broke in the process. I'd post the code, but it's very ugly and I'm probably going to replace it all anyway. Besides, I understand why my code behaves the way it does. What I don't understand is why the DG-S doesn't behave that way.
So all that said, does any of what I'm trying to do make sense? Like I said in the beginning, I'm mostly interested in results: a conceptually plausible-ish engine that is challenging to fly but can deliver a practiced pilot to orbit with minimal burn from fuel reserves. Does it make sense to approach that problem with a nuclear ramjet, presuming crazy science fiction temperatures and pressures are possible? If so, how can I avoid it being crazy overpowered at lower speeds? Is there some other strategy, say magnetoplasmadynamics, that I could massage closer to the results I'm looking for?
