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What I found decades ago working in the industry, was that thermochem code-based Isp was not reliable. That is because (1) chemists known nothing about real nozzle efficiency performance, and (2) thermochem codes generally do not include an option for modeling incomplete combustion. For those that do, few users know to use the option, or what values to plug in.
Regarding item 1, go see what I just posted over at "exrocketman", which is "How Propulsion Nozzles Work" dated 11-12-18. It covers both conventional nozzles (whether conical or curved bell), and the axisymmetric aerospike (which would be somewhat representative of the linear aerospike as well.) That article makes painfully clear why free expansion designs are just not appropriate for vacuum operation. They essentially have an altitude limit, beyond which the streamlines diverge too sharply. The low efficiency just kills the high expansion effects.
Regarding item 2, this is best generated from test data. You can run thermochem codes at multiple pressures to generate chamber c* velocity as a function of pressure, but it is theoretical only! It takes the curve-fitted form c*o = Ko P^mo where Ko and mo are curve fit constants. c*o is theoretical c*.
From actual test runs at various pressures, you can generate actual c* data, and curve fit that vs pressure, too. It takes the same form c* = K P^m, where again k and m are your curve fit constants. The ratio of c* to c*o is your c* efficiency. It, too, curve fits well as a K P ^ m variation, precisely because both c* and c*o curve fit well that way. These c* predictions are independent of the backpressure effects that modify CF, and thus Isp, as altitudes change.
In decent engine designs big enough to push a missile, whether liquid or solid, c* efficiency is generally a high value in the vicinity of 98%. Can be less, can never exceed 100%. Most rocket folks in the early days correlated c* efficiency (or more usually just delivered actual c*) vs a parameter called L*.
L* = chamber volume / throat area, which is scale-dependent as dimension^1, while chemistry is not. It's strongly related to both residence time and scale. So small engines feature different correlations than big ones. And it's all experimental: there is no way to calculate c* efficiency a priori, except by correlation from real, actual test data.
Here is the relationship between chamber deliverable c* and motor/stage deliverable Isp, using a realistic nozzle CF. For no massflow dumped overboard instead of going through the nozzle, Isp = CF c* / gc, where gc is the "gravity constant" for inconsistent mass and force units. Solids and pressure-fed liquids and hybrids inherently meet the “no massflow dumped overboard” criterion.
Pumped liquids and hybrids almost invariably tap off hot gas to drive turbine(s) that drive the pump(s). Depending on the details of the engine "cycle", somewhere between zero and a significant fraction “f” of the massflow drawn from tankage gets dumped overboard as wasted drive gas.
You cannot reconcile estimated Isp with actual stage mass ratio unless you account for that dumped gas !!! So for the case where f is not zero, the relationship for stage Isp becomes Isp = CF c* / gc (1+f). In this, combustion completeness is part of c*, and independent of altitude operation. CF doesn’t care about combustion completeness, but inherently reflects how the nozzle actually operates vs altitude. The dump fraction f may or may not be a constant. Its trend is set by the turbopump cycle. Splitting apart and experimentally correlating those effects like this is precisely why ballistics are done this way.
So the discrepancies between your thermochem-predicted Isp's and actual vehicle Isp data trace to at least (!!!) three sources: (1) nozzle efficiency (usually but not always near 98%), (2) c* efficiency (max near 98%), and (3) engine cycle dumped massflow fraction f. I didn't work liquids, so I don't have a feel for f vs cycle, but I'd guess it's a number that falls in the 0-10% range.
The other two do not simply multiply theoretical Isp. To get it right, you need to do the ballistics right, and you have to do it with real c* (or c* efficiency) data from actual testing. For conventional nozzles, the kinetic energy efficiencies correlate easily. For free-expansion designs, such efficiencies do not correlate simply and easily, and they are really low at high altitudes into vacuum.
GW
GW Johnson
McGregor, Texas
"There is nothing as expensive as a dead crew, especially one dead from a bad management decision"
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Regarding item 1, go see what I just posted over at "exrocketman", which is "How Propulsion Nozzles Work" dated 11-12-18. It covers both conventional nozzles (whether conical or curved bell), and the axisymmetric aerospike (which would be somewhat representative of the linear aerospike as well.) That article makes painfully clear why free expansion designs are just not appropriate for vacuum operation. They essentially have an altitude limit, beyond which the streamlines diverge too sharply. The low efficiency just kills the high expansion effects.
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GW
I'm still reading through your post on Exrocketman, http://exrocketman.blogspot.com/2018/11 … -work.html, but I have a question about the aerospike. The intent of the aerospike is to have both good performance at sea level and vacuum. For instance the F9 first stage Merlin Engine has a sea level Isp of 282s and a vacuum Isp of 312s. It's that vacuum performance that's poor. In comparison, the Merlin Vacuum used on the second stage has a vacuum Isp of 342s.
The aerospike would not be able to match the full 342s vacuum Isp of the Merlin Vacuum but it could get closer to it than the 312s of the sea level Merlin.
Bob Clark
Old Space rule of acquisition (with a nod to Star Trek - the Next Generation):
“Anything worth doing is worth doing for a billion dollars.”
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Well, if you look at the update to that article, I did verify that it was possible for a free expansion design to equal or slightly exceed the performance of a separation-limited conventional design, across a wide range of altitudes.
Such simply cannot be "designed for vacuum" as you seem to think, but only for a definite high altitude where the ambient pressure is not zero. In real vacuum, the boundary streamline divergence approaching 90 degrees just wipes out the nozzle efficiency, and thus the thrust. That simply cannot be avoided.
What I reported in the article, and confirmed in the update, is that there is no fluid-mechanical optimum design for any of the free-expansion approaches. It boils down to whether what you can really build (and expect to survive) is more important than the slight average improvement across the mid-range of the high altitudes.
Or not; it may not actually be worth it. The article and its update so states, and does not take up practicality or survivability. All that was addressed was the fluid mechanics.
GW
GW Johnson
McGregor, Texas
"There is nothing as expensive as a dead crew, especially one dead from a bad management decision"
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For SpaceNut re #29 above ....
In past years (as I understand it) the NewMars forum had a review process for applications for membership in the forum.
I'd like to ask for a collective review of that idea.
How did the system work (way back then) and why did it fail?
The registration process seems to be effectively unrestricted right now.
An interview could be requested by an applicant.
The interview could be requested with an existing member who has agreed to serve as a gatekeeper.
If I were to serve as a gatekeeper, for example, I would ask the application a set of questions which would be agreed upon by the forum community.
Among these might be:
Why are you interested in NewMars forum? (eg, are you wanting to sell something?)
How could you contribute to the forum?
(th)
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