Author Topic: RP-1, methane, impulse density Q&A  (Read 94628 times)

Offline hkultala

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Re: RP-1, methane, impulse density
« Reply #80 on: 04/15/2016 10:21 am »
Good point. For perfect burning, mixture ratio should be 16.

You mean 8, right?

Whoops, missed some multiplication by 2 in my chemistry.
Quote
Quote
It would seem that RS-68 uses too small mixture ratio;

Maybe it's partly to increase the thrust-to-weight ratio.

Makes T/W ratio of the rocket worse without solids, as the thrust should be about linearily propotional to the propellant density, and it increases more than the propellant weight increases.

2 possibilities come into mind:

1) It's optimized to be used with many solid boosters, not without solids, and with solids the solids have to lift less first stage propellant mass with lower mixture ratios
2) Some cooling-related thing makes the engine T/W not scale with propellant density. The extra unburned H2 makes the engine run cooler and allow less mass to be used for cooling?
« Last Edit: 04/15/2016 10:25 am by hkultala »

Offline RanulfC

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Re: RP-1, methane, impulse density
« Reply #81 on: 04/15/2016 01:31 pm »
Hmm, a thought just occurred to me, wherein cryochilled propane's viscosity could be an advantage.  Are you familiar with the research on metalized gel propellants?  The concept is to add gelling agents like fumed silica to allow you to suspend metal dusts like aluminum powder in the liquid rocket fuel.  Aluminum combustion gives off a great deal of energy for its mass, providing additional heat to the exhaust stream.  But you know, gelling basically means "increasing the viscosity".  With cryochilled propane, you already have increased viscosity vs. "runny" fuels like RP-1 (whether it's sufficient to suspend aluminum particles without gelling agents, that I can't say).

I've never seen any indication of a 'viscosity' issue with cryo-propane. It's denser than when liquid under normal pressure/temperature but nothing that impedes either turbo-pump or pressure fed use. When tested in the RL10 it was less 'viscos' than RP1 and more like LH2 which was a cited advantage in that type of engine.

Did I miss a cite somewhere?

Randy
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Offline RanulfC

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Re: RP-1, methane, impulse density
« Reply #82 on: 04/15/2016 02:06 pm »
To further develop my understanding of the trade between specific impulse and density, I've done a little thought experiment on ground-launch stages.
<snipping some excellent stuff>

So if I read all this right then I get that balancing both impulse and density has not been as straight-forward as even the experts (I'm thinking all the early "when we have hydrogen we can do anything" rocket scientist here :) ) had thought. Further it would seem that in a TSTO system it might be more efficient to consider different propellants for booster and upper stage despite a slightly higher operations costs?

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1.  Except for JP-5 (the composition of which I don't know),

JP-5 or JP-10? JP-5 Material Safety Data Sheets, (MSDS) are available on-line and composition properties sheets IIRC:
http://www.henrycoema.org/LEPC/LEPCPlan/Apdx%20E-Other%20Information/JP5_9942_clr.pdf
http://www.cpchem.com/msds/100000014588_SDS_US_EN.PDF
http://www.atsdr.cdc.gov/toxprofiles/tp121-c3.pdf

JP10's a bit more difficult to find:
http://www.boulder.nist.gov/div838/SelectedPubs/IR%206640%20ms.pdf
http://www.madsci.org/posts/archives/2000-08/966261622.Ch.r.html

If that helps.

Randy
From The Amazing Catstronaut on the Black Arrow LV:
British physics, old chap. It's undignified to belch flames and effluvia all over the pad, what. A true gentlemen's orbital conveyance lifts itself into the air unostentatiously, with the minimum of spectacle and a modicum of grace. Not like our American cousins' launch vehicles, eh?

Offline R7

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Re: RP-1, methane, impulse density
« Reply #83 on: 04/15/2016 02:58 pm »
2) Some cooling-related thing makes the engine T/W not scale with propellant density. The extra unburned H2 makes the engine run cooler and allow less mass to be used for cooling?

Going from O/F 6 to 7

- increases Tc about 100K
- reduces the available coolant franction of total propellant from 1/7 to 1/8 (12.5% less)
- increase the free oxygen species in combustion gases by an order of magnitude.

Even alone none of the three are good news for engine developer. All three together compound each others' problems. Higher Tc would require more cooling and increased oxygen content may require protective oxide layer ... which reduces thermal conductivity ... which requires even more aggressive cooling ... using reduced amount of coolant.

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Offline Proponent

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Re: RP-1, methane, impulse density
« Reply #84 on: 04/15/2016 05:36 pm »
I've never seen any indication of a 'viscosity' issue with cryo-propane. It's denser than when liquid under normal pressure/temperature but nothing that impedes either turbo-pump or pressure fed use. When tested in the RL10 it was less 'viscos' than RP1 and more like LH2 which was a cited advantage in that type of engine.

Attached are liquid viscosities as a function of temperature, from NIST.  I left hydrogen off the plot to avoid compressing the hydrocarbon curves.  Take my word for it, hydrogen's viscosity is pretty low.  The dotted horizontal lines show RP-1's viscosity at a typical temperature of 21oC and at 20oF (266 K), which I believe is the temperature to which SpaceX chilled its RP-1 on CRS-7.  I could imagine that sub-cooling propane too much could cause a viscosity problem (if you're not using viscosity to your advantage, as Rei suggests).  On the other hand, maybe viscosity of propane in the tank doesn't matter too much and it warms up anyway before reaching any turbomachinery or injector, where high viscosity really would be a problem.

I don't have any data for the more exotic fuels.  Cyclopropane is probably quite inviscid even at low temperatures, and it should have a good specific impulse (probably something approaching syntin's, which is three cyclopropane rings and a methyl group stuck together), though it is expensive.

EDIT:  Changed musing on possible unimportance of low-temperature viscosity.  Corrected temperature of chilled RP-1.
« Last Edit: 04/16/2016 03:26 am by Proponent »

Offline Proponent

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Re: RP-1, methane, impulse density
« Reply #85 on: 04/15/2016 05:47 pm »
So if I read all this right then I get that balancing both impulse and density has not been as straight-forward as even the experts (I'm thinking all the early "when we have hydrogen we can do anything" rocket scientist here :) ) had thought. Further it would seem that in a TSTO system it might be more efficient to consider different propellants for booster and upper stage despite a slightly higher operations costs?

Yes, absolutely (though whether the operations costs are just slightly higher or not might be another question).  In fact ideally the mixture ratio of each stage changes during the burn.  At lift-off, the ideal mixture ratio in principle is that corresponding to maximum impulse density.

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JP-5 or JP-10? JP-5 Material Safety Data Sheets, (MSDS) are available on-line and composition properties sheets IIRC ....

Thanks.  What I learn is that JP-5 too is basically kerosene with lots of additives.  I should have guessed that. So, following my scheme, it would have the same color (red) as RP-1.
« Last Edit: 04/15/2016 05:51 pm by Proponent »

Offline Hyperion5

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Re: RP-1, methane, impulse density
« Reply #86 on: 04/16/2016 01:10 am »
Steven Pietrobon:  I think Zubrin himself has fully acknowledged that Ethylene is completely superior to Methane and if he had the whole thing to do over again he would have pushed that instead as it's synthesis is almost as easy as methane, higher hydrocarbons not so much.

Lower hydrogen needs for Ethylene and easier refrigeration (practically none on Mars) are considered even more important then the density and impulse values.  The only reason to go for Methane now is that fact that everyone is developing LNG based engines for launch vehicles now and you could reuse thouse engines on Mars, but even then I suspect a dual fuel engine would be possible and advantageous.

Refrigeration advantages are moot when sharing a thermal environment with LOx.  Ethylene is a moderate problem there, because to maintain it in liquid phase at the same temperature you would need to raise LOx tank pressure to 5+ atmospheres (ethylene freezes at the boiling point of LOx at about 3.5atm). That's manageable, but adds weight.  Zubrin  is currently working on ethylene-N2O green hypergolics - http://www.parabolicarc.com/2015/05/15/pioneer-astronautics/

I've been told on several occasions that Lox-Methane is a very feasible mixture for a Mars mission, with references to the Morpheus lander, though I was curious about its ignition.  The advantages I saw listed were non-toxicity, low cost of propellant, and lower energy use versus hypergolic propellants.  The obvious disadvantages were impulse density and ignition issues.  Aside from gaining hypergolic ignition with an Ethylene-Nitrous Oxide mix, how does its compare with the obvious Lox-Methane and Lox-Ethylene alternatives in terms of advantages and disadvantages?

Offline Proponent

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Re: RP-1, methane, impulse density
« Reply #87 on: 04/16/2016 01:48 pm »
I've been told on several occasions that Lox-Methane is a very feasible mixture for a Mars mission, with references to the Morpheus lander, though I was curious about its ignition.  The advantages I saw listed were non-toxicity, low cost of propellant, and lower energy use versus hypergolic propellants.  The obvious disadvantages were impulse density and ignition issues.  Aside from gaining hypergolic ignition with an Ethylene-Nitrous Oxide mix, how does its compare with the obvious Lox-Methane and Lox-Ethylene alternatives in terms of advantages and disadvantages?

Attached are plots showing the performance of both oxygen and nitrous oxide with light hydrocarbons.  Low-orbit speed on Mars is about 3.5 km/s.  Since the atmosphere is thing and the gravity weak, perhaps 4 km/s is not too optimistic as a delta-V for getting from the surface to low orbit.  The first plot shows that both oxygen and nitrous do pretty well.  Oxygen is better, but nitrous isn't too bad.

On the other hand, the thin atmosphere means that a martian SSTO making a round trip would have a pretty large delta-V to perform in returning to the surface.  Taking an approximate, worst case, suppose the total delta-V to orbit and back is 8 km/s.  Then, as the second plot shows, the performance of nitrous is really rather poor.

Offline S.Paulissen

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Re: RP-1, methane, impulse density
« Reply #88 on: 04/17/2016 05:36 pm »
I've been told on several occasions that Lox-Methane is a very feasible mixture for a Mars mission, with references to the Morpheus lander, though I was curious about its ignition.  The advantages I saw listed were non-toxicity, low cost of propellant, and lower energy use versus hypergolic propellants.  The obvious disadvantages were impulse density and ignition issues.  Aside from gaining hypergolic ignition with an Ethylene-Nitrous Oxide mix, how does its compare with the obvious Lox-Methane and Lox-Ethylene alternatives in terms of advantages and disadvantages?

Attached are plots showing the performance of both oxygen and nitrous oxide with light hydrocarbons.  Low-orbit speed on Mars is about 3.5 km/s.  Since the atmosphere is thing and the gravity weak, perhaps 4 km/s is not too optimistic as a delta-V for getting from the surface to low orbit.  The first plot shows that both oxygen and nitrous do pretty well.  Oxygen is better, but nitrous isn't too bad.

On the other hand, the thin atmosphere means that a martian SSTO making a round trip would have a pretty large delta-V to perform in returning to the surface.  Taking an approximate, worst case, suppose the total delta-V to orbit and back is 8 km/s.  Then, as the second plot shows, the performance of nitrous is really rather poor.

I'm interested in seeing plain N2O myself.  I always wondered at why it was not used given its ease of storage, self pressurization and ability to be A) a monopropellant and B) a ignition source with a reusable catalyst.   It's performance really isn't THAT bad, but in a reusable system that isn't 100% performance optimized I always wondered why it didn't never really saw much consideration. 

I only ask because I've been designing a very amateur-style non-flight pressure-fed rocket motor with kerosene/N2O and found through my amateurish calculations expect a high 240s-range sea-level ISP with autopressurization of the N2O and CO2 pressurization of the kerosene. With helium etc, I would expect quite a bit more; enough to be useful in ISRU situations that don't have TEA-TEB at the ready.
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Offline Proponent

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Re: RP-1, methane, impulse density
« Reply #89 on: 04/18/2016 12:56 pm »
... the thrust should be about linearily propotional to the propellant density ....

Why density?  I would think impulse density most relevant.

Offline Rei

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Re: RP-1, methane, impulse density
« Reply #90 on: 04/19/2016 11:47 pm »
I'm interested in seeing plain N2O myself.  I always wondered at why it was not used given its ease of storage, self pressurization and ability to be A) a monopropellant and B) a ignition source with a reusable catalyst.   It's performance really isn't THAT bad, but in a reusable system that isn't 100% performance optimized I always wondered why it didn't never really saw much consideration. 

It really is.  A typical N2O monoprop will get an Isp around 170 or so.  That's just really, really bad.  Fine for an RCS or small craft's OMS, maybe primary propulsion for a small probe... but you definitely don't want that for a launch vehicle.

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through my amateurish calculations expect a high 240s-range sea-level ISP

One, 240 is still a very bad ISP for a launch vehicle, even sea level.  And two, no, you're not going to get that sort of ISP.  Oh great, now I need to dig out CEA2... let's see.. I'll be generous and give it 200 bar chamber pressure, let's keep the pi/pe figures and mdot the same as from the SSME, basically giving you an SSME-ish N2O monoprop engine... okay, here you go:

Quote
*******************************************************************************

         NASA-GLENN CHEMICAL EQUILIBRIUM PROGRAM CEA2, MAY 21, 2004
                   BY  BONNIE MCBRIDE AND SANFORD GORDON
      REFS: NASA RP-1311, PART I, 1994 AND NASA RP-1311, PART II, 1996

 *******************************************************************************



 prob rocket fac p,bar=200.0 ions pi/pe=1276.851685 mdot=2223.8
 
 reac fuel=N2O moles=1.0  t(k)=300.0
 
 outp short
 end





              THEORETICAL ROCKET PERFORMANCE ASSUMING EQUILIBRIUM

            COMPOSITION DURING EXPANSION FROM FINITE AREA COMBUSTOR

 Pin =  2900.8 PSIA
 MDOT/Ac =  2223.800 (KG/S)/M**2      Pinj/Pinf =  1.003364
 CASE =               

             REACTANT                       MOLES         ENERGY      TEMP
                                                         KJ/KG-MOL      K
 FUEL        N2O                          1.0000000     81671.539    300.000

 O/F=    0.00000  %FUEL=100.000000  R,EQ.RATIO= 0.000000  PHI,EQ.RATIO= 0.000000

                 INJECTOR  COMB END  THROAT     EXIT
 Pinj/P            1.0000   1.0068   1.8334  1276.85
 P, BAR            200.00   198.66   109.09  0.15664
 T, K             1908.42  1907.02  1670.30   305.99
 RHO, KG/CU M    3.6988 1 3.6766 1 2.3049 1 1.8065-1
 H, KJ/KG         1855.63  1853.80  1550.33   7.8034
 U, KJ/KG         1314.91  1313.48  1077.06  -78.903
 G, KJ/KG        -12294.6 -12287.8 -10835.9 -2261.27
 S, KJ/(KG)(K)     7.4146   7.4156   7.4156   7.4156

 M, (1/n)          29.345   29.345   29.344   29.342
 (dLV/dLP)t      -1.00007 -1.00007 -1.00003 -1.00000
 (dLV/dLT)p        0.9998   0.9998   0.9998   1.0000
 Cp, KJ/(KG)(K)    1.3049   1.3046   1.2594   0.9960
 GAMMAs            1.2771   1.2772   1.2901   1.3976
 SON VEL,M/SEC      831.0    830.7    781.4    348.1
 MACH NUMBER        0.000    0.073    1.000    5.522

 PERFORMANCE PARAMETERS

 Ae/At                      8.0991   1.0000   51.862
 CSTAR, M/SEC               1106.7   1106.7   1106.7
 CF                         0.0547   0.7060   1.7370
 Ivac, M/SEC                8993.6   1387.1   1967.5
 Isp, M/SEC                   60.5    781.4   1922.4


 MOLE FRACTIONS

 *NO              0.00676  0.00673  0.00299  0.00000
 NO2              0.00024  0.00024  0.00013  0.00000
 *N2              0.66324  0.66325  0.66515  0.66667
 *O               0.00001  0.00001  0.00000  0.00000
 *O2              0.32974  0.32975  0.33173  0.33333

  * THERMODYNAMIC PROPERTIES FITTED TO 20000.K

That's a vacuum ISP of 203.  From one heck of an advanced N2O engine!  ;)

(CEA2's ISP figures are a bit wierd... one, they're not divided by 9,81, and two the one labeled "Ivac" assumes an infinite length nozzle; in this setup, the Isp is also vacuum).  Also note that CEA2 is generous to begin with; it's calculating equilibrium exhaust properties, there's no frozen combustion involved.

As for returning from LMO to surface in a repeatable manner (the post before yours)... Mars' atmosphere is thin but it's not *that* thin, you can still aerobrake in it just fine.  The main disadvantage vs. Earth is the need for a powered landing.  Also parachutes would be trickier if you want them to be reusable - not only do they have to survive just fine, but be repacked by people in space suits, after having gotten covered in Martian dust and potentially landing on sharp rocks.  You can limit your aerobraking to an aeroshell without any parachutes, but then that means even more propellant needed for landing.

I once ran the numbers up the delta-V requirements for powered landing on Mars, with and without parachutes, but I can't be bothered to dig it up right now.  ;)
« Last Edit: 04/19/2016 11:59 pm by Rei »

Offline S.Paulissen

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Re: RP-1, methane, impulse density
« Reply #91 on: 04/20/2016 02:09 am »
Hah, thanks for that,  and most certainly is ghastly.  But I was not intending to use it ONLY as a mono-prop, I did not do a good enough job to get that across, my bad.  And you are certainly right with 240, being bad, but my number was what seemed achievable with a pressure fed system bi-propellant built by an amateur on a very very low budget, not something you'd launch into space.

I was thinking more along the lines of using the N2O as a monoprop for RCS on a vehicle also using it as an oxidizer with a real fuel like methane or kerosene (likely to former rather than the latter as it's an ISRU fuel).

EDIT: Thank you for pointing me at CEA2.  I cracked it open and put the numbers in as if it was the bi-propellant system I was intending and got 314s at sea level and 325s in vacuum.  I guess that answers my question.
« Last Edit: 04/20/2016 03:07 am by S.Paulissen »
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Offline Robotbeat

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Re: RP-1, methane, impulse density
« Reply #92 on: 04/26/2016 07:49 pm »
To further develop my understanding of the trade between specific impulse and density, I've done a little thought experiment on ground-launch stages.

In 1996, John Whitehead wrote a cute little paper about SSTO mass budgets (4th attachment to this post.  For a few different propellant combinations, he used the rocket equation to calculate the mass ratios needed for a delta-V of 10 km/s (i.e., Earth to LEO with losses).  Then he estimated the masses of engines, tanks, pressurants and residual propellants (the last two can be larger than you expect) as a fraction of burn-out mass.  Let's call the part of the burn-out mass that's not devoted to those four things the available mass (I'm open to suggestions for a better term).  Many subsystems will have to be crammed into this so-called available mass:  landing gear, if any, avionics, etc., etc.  The idea, though, is that the masses of such subsystems will be approximately independent of the propellants chosen.  Hence, the vehicle with the highest available mass fraction should have the largest payload fraction as well.

The name of the game, then, is to choose the propellant combination that maximizes the available mass.

About the same time as Whitehead's paper, Bruce Dunn presented an analysis in a similar spirit (3rd attachment).  Although Dunn's assumptions were perhaps a bit more ad hoc, he covered a wider range of propellants.

I've made a similar calculation similar to Whitehead's.  There are just two major differences.  Firstly, Whitehead assumes that the lift-off thrust-to-weight ratio of the engine is a linear function of propellant density and is 100 for lox/RP-1 and 50 for lox/hydrogen.  In contrast, I assume the ratio is proportional to the impulse density of the propellants (it seems to me this makes more sense; any comments?), taking a value of 123 for lox/RP-1 at a typical mixture ratio (essentially, the NK-33 or the AJ-26).

The second significant difference is that rather than assuming a particular mixture ratio, I adjust the mixture ratio for maximal performance.

Otherwise, to oversimplify slightly, I use pretty much the same assumptions:  10 km/s of delta-V, tanks weigh 10 kg/m3, pressurants and residuals are each 0.25% of the initial propellant load.  Specific impulses come from RPA Lite 1.2.8 and are scaled by 0.95 from ideal vacuum values.  Chamber pressure is 20 MPa and the area expansion ratio is 40:1.  For the time being, propellants are assumed to be at the lower of room temperature and the normal boiling points.

Have a look at the first plot attached.  It shows specific impulses delivered by various fuels1 burned with oxygen as a function of propellant bulk density.  Also shown as grey curves are contours of constant "available mass."  These contours are easily calculated, since all that's required in Whitehead's model is a specific impulse and a propellant density.  The first table, below, gives optimal figures for each of 30 propellant combinations.

Hydrogen does poorly.  If the mixture ratio is allowed to vary during flight in an optimal way, the available mass fraction with hydrogen as a fuel increases2 by about 0.026.  Other fuels don't benefit much from mixture-ratio variation, so the this enough to boost hydrogen to the middle of the table.  But, the substantially larger mass of hydrogen tanks arising from the need to insulate them has been neglected.  Taking this into account would knock hydrogen right back to the bottom of the table.

Speaking of the table, a couple of columns may not be self-explanatory:

* Mix:  Linear function of the mixture ratio, being zero for maximum Isp and unity for maximum impulse density.
* T/W:  Thrust-to-weight ratio of the engine at lift-off (giving the a ratio of 1.3 for the vehicle).
* Den exp: slope of the log Isp-log(bulk density) curve at the optimum; shows the relative importance of density compared to Isp.

People often obsess about maximizing specific impulse.  The Mix column shows that's not generally what you want to do.

The "Den exp" column shows the relative sensitivity of available mass fraction to density as opposed to specific impulse.  For the better performing propellant combinations, it's about 0.23, meaning that a the figure of merit is approximately:

    (specific impulse)(bulk density)0.23

for an SSTO.  This is, of course, somewhat model dependent, but it happens to be about the same as what I estimated from Dunn's results some time ago.

OK, so, what about hydrogen peroxide, with its high density?  Please have a look at the second plot.  This time I've left hydrogen out so as to make the hydrocarbons more visible.  As you easily see, peroxide's density does not raise bulk density enough to make up for its lower specific impulse.  Bruce Dunn told us that a long time ago, but I find it educational to see it graphically.  I also looked at nitric acid, which is even denser (1510 kg/m3) than peroxide (1460 kg/m3).  It, however, suffers from lower specific impulse and lower bulk density than you might expect: the fact that it contains quite a bit of free oxygen means that mixture ratios with nitric acid tend to be low.

If we consider a delta-V of just 4 km/s -- see the third plot and second table -- peroxide looks much better.   As you'll see from the table, the figure of merit at this delta-V, which could correspond to a first stage or a martian SSTO, is something like:

    (specific impulse)(bulk density)0.4 ,

Finally, consider a very low delta-V, like 40 m/s, as shown in the final plot.  In this case, impulse density reigns, and peroxide is the run-away winner.   The associated table shows that the figure of merit is very close to

    (specific impulse)(bulk density) ,

i.e., impulse density, which is just what you expect when delta-V is small compared to exhaust velocity.  Note, though, that we do have to go to very low delta-V's before impulse density dominates.

All of the above is applies to ground-lit stages.  For upper stages, mass will be more important, since the stage's propellant must be accelerated by lower stages.  Hence, the density exponent in the figure of merit will tend to be smaller.



1.  Except for JP-5 (the composition of which I don't know), the color of each curve is the number of carbon atoms, modulo 10, in each fuel's principal chemical component (e.g., 1 for methane, 2 for ethane and ethylene) expressed in the resistor color code.  Solid lines are used for saturated hydrocarbons (alkanes).  The two alkenes, ethylene and proplylene, are shown with dashed lines.

2.  If a different mixture ratio is allowed for each successive 1% of the total propellant volume, the ratio ranges from 17.8 (633 kg/m3) at lift-off to 5.7 (350 kg/m3) at burn-out.  A variable mixture-ratio program helps in two ways.  Firstly, it simply helps with the rocket equation by allowing more impulse to be packed in at the beginning, where mass doesn't matter so much, while going for higher specific impulse at later times.  Secondly, it increases the lift-off thrust-to-weight ratio of the engine, allowing for a smaller engine.

EDIT:  Added "bulk" to very-low-delta-V figure of merit.
Bravo! Impressive analysis. Now can you try subchilling the propellants like Dunn?
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Offline Rei

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Re: RP-1, methane, impulse density
« Reply #93 on: 04/26/2016 10:46 pm »
Quote
, tanks weigh 10 kg/m3

Can this concept be defended?  Mass loadings on the tanks will certainly be different with different propellants at the very least.  Not to mention the x^3/x^2 volume/surface area scaling issue.

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pressurants and residuals are each 0.25% of the initial propellant load

Again, is this defensible?  I certainly wouldn't expect highly voltatile cryogenics to have the same residual as far more viscous, non-volatile liquids.

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Chamber pressure is 20 MPa and the area expansion ratio is 40:1.

Assuming a perfect burn, no frozen combustion?

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Hydrogen does poorly.  If the mixture ratio is allowed to vary during flight in an optimal way, the available mass fraction with hydrogen as a fuel increases2 by about 0.026.

I'm confused by this argument.  On what grounds are you determining "poor performance" and "optimal"?  Maybe I missed something, because your graph rightfully shows hydrogen's ISP vastly superior to the others (but its bulk density, obviously, vastly lower - no shockers there)

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But, the substantially larger mass of hydrogen tanks arising from the need to insulate them has been neglected.

Depends on the context, of course.  On Earth, uninsulated H2 tanks liquefy the surrounding air, causing an extremely rapid heat loss.  On Mars, however, not only is it easier to maintain a much lower radiative equlilibrium, and not only is there far, far less convective losses, but the air doesn't liquefy; like water vapour on LOX tanks, it freezes at LH temperatures, providing an insulative ice that falls off during launch.  It's not immediately obvious that LH tanks for rockets on Mars would require significant, if any, insulation (obviously long-term storage needs insulation)

Quote
* Mix:  Linear function of the mixture ratio, being zero for maximum Isp and unity for maximum impulse density.
* T/W:  Thrust-to-weight ratio of the engine at lift-off (giving the a ratio of 1.3 for the vehicle).
* Den exp: slope of the log Isp-log(bulk density) curve at the optimum; shows the relative importance of density compared to Isp.

I don't see these things in your graphs.

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    (specific impulse)(bulk density)0.23

I can see no justification for the usage of a formula involving a linear multiplication of specific impulse and bulk density.

There's no real mystery here about the optimums for chemical rockets with current propellants.  This has been worked out long, long ago.  Hydrocarbon first stages provide massive thrust (due to the high propellant density) and the tankage costs are kept low (due to the high density and simpler construction) on the massive first-stage tanks.  Hydrogen provides the high ISP needed for subsequent stages to keep the size requirements on the first stage down.

That's not to say that there's no room for improvement - there absolutely is.  But the basics here are no mystery.  Unless you're using solids or you want to destroy the environment and human health by using a fluorine-containing oxidizer, the only obvious choice is LOX - it just performs so much better than its competitors, and its properties are fairly tame (by oxidizer standards, at least... which isn't saying much).  And hydrogen is in a league of its own for upper stages - unless you want to burn it with lithium in a triprop (or totally implausible combinations involving beryllium or boron), there's not much room for improvement.    With the exception of solids, the only real question is "what hydrocarbon do you want to burn with LOX on the first stage, and do you want to work aluminum into the mix?"

When you're talking about SSTOs, the picture doesn't change.  You just can't use the sort of low-ISP high-thrust stage you'd use with a staged rocket.  You still have to use H2 because SSTOs are even more ISP-dependent than staged rockets:

https://en.wikipedia.org/wiki/File:SSTO_vs_TSTO_for_LEO_Mission.tif

You simply can't get a plausible structural coefficient with a low ISP propellant mix.  It just doesn't work.
« Last Edit: 04/26/2016 10:51 pm by Rei »

Offline Robotbeat

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Re: RP-1, methane, impulse density
« Reply #94 on: 04/27/2016 12:22 am »
Quote
, tanks weigh 10 kg/m3

Can this concept be defended?  Mass loadings on the tanks will certainly be different with different propellants at the very least.  Not to mention the x^3/x^2 volume/surface area scaling issue....
The volume/surface area scaling issue does not apply to pressure vessels (unless you run into minimum-gauge issues or decide to use a large amount of insulation). Since rocket tanks are fairly well approximated as pressure vessels, it's appropriate to consider tank masses using the pressure vessel equation. And the pressure vessel equation indeed gives you tank masses with units of kg/m^3, regardless of scale.

If you get really, REALLY tall (like Saturn V first stage size), then you have to start taking into account pressure head (and this can actually allow you to SAVE weight, since you can use a little less ullage pressure and the top of the stage can thus be made a little thinner), but for our purposes here, that's a pretty good estimate.

There are two fairly easy ways to reduce tank mass: Use materials with higher strength-to-weight ratio or operate at lower ullage pressure. This last one is perhaps the biggest reason why pump-fed rocket engines are used instead of pressure-fed.
« Last Edit: 04/27/2016 12:23 am by Robotbeat »
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Offline Robotbeat

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Re: RP-1, methane, impulse density
« Reply #95 on: 04/27/2016 12:35 am »
...

When you're talking about SSTOs, the picture doesn't change.  You just can't use the sort of low-ISP high-thrust stage you'd use with a staged rocket.  You still have to use H2 because SSTOs are even more ISP-dependent than staged rockets:

https://en.wikipedia.org/wiki/File:SSTO_vs_TSTO_for_LEO_Mission.tif

You simply can't get a plausible structural coefficient with a low ISP propellant mix.  It just doesn't work.
STRONGLY disagree. SSTOs are more dry-mass-dependent, and hydrogen's big dry mass penalty is significantly reduced by staging, so if the dry-mass situation looks bad with TSTO, it looks far worse with SSTO.

I think dry mass and total rocket volume is a better stand-in for cost than lift-off mass is, and the only reason you'd use hydrogen for SSTO is if you're trying to minimize lift-off mass. Otherwise, you're far better with another propellant combination.
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Offline Robotbeat

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Re: RP-1, methane, impulse density
« Reply #96 on: 04/27/2016 12:37 am »
Rei, have you read Dunn's report on various SSTO propellant combinations? It is not kind to hydrogen.
http://web.archive.org/web/20120303152352/http://www.dunnspace.com/alternate_ssto_propellants.htm

Hydrogen may have the best Isp, but liquid hydrogen is, in fact, the least dense liquid known to humankind. It has been worshipped by aerospace since Tsiolkovsky, but in no way is it an optimal fuel for a SSTO rocket, particularly a reusable one (where dry mass is yet more important). Please re-examine your prejudices in light of that Dunn report.
« Last Edit: 04/27/2016 12:46 am by Robotbeat »
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Offline Rei

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Re: RP-1, methane, impulse density
« Reply #97 on: 04/27/2016 01:53 am »
Quote
The volume/surface area scaling issue does not apply to pressure vessels (unless you run into minimum-gauge issues or decide to use a large amount of insulation). Since rocket tanks are fairly well approximated as pressure vessels

No, they are not.

Even balloon tanks have an overpressure a fraction of an atmosphere.  As a general rule, the only high pressure tank in a rocket is a helium pressurant which is steadily released to ensure a stable supply of propellant to the turbopumps.

You simply cannot multiply volume by a constant.  That's not at all an accurate representation of tankage mass.  Example: Saturn V first stage = 130 tonnes, holds 1305 cubic meters of propellant = 100kg/m^3.  Second stage = 38 tonnes, 1559 cubic meters = 24kg/m^3.  Third stage = 10 tonnes, 326 cubic meters = 31kg/m^3. 

Not.  Even.  Close.

You simply cannot take some sort of linear scaling parameter with volume to estimate the tankage mass.  Rockets just don't work that way.   Using the posted formula above one would come to the conclusion that Saturn V's hydrogen stages' would be *four times heavier* than they actually were.

Quote
If you get really, REALLY tall (like Saturn V first stage size), then you have to start taking into account pressure head (and this can actually allow you to SAVE weight, since you can use a little less ullage pressure and the top of the stage can thus be made a little thinner), but for our purposes here, that's a pretty good estimate.

And as was just demonstrated above, the Saturn-V first stage is half of an order of magnitude heavier per unit volume, not lighter. 

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This last one is perhaps the biggest reason why pump-fed rocket engines are used instead of pressure-fed.

Which is also why they're not pressure vessels.  Except in balloon tanks internal pressure is only kept high enough to keep the turbos fed.  And even with balloon tanks, it's hardly something one would consider a "pressure vessel".

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Rei, have you read Dunn's report on various SSTO propellant combinations? It is not kind to hydrogen.
http://web.archive.org/web/20120303152352/http://www.dunnspace.com/alternate_ssto_propellants.htm

Hydrogen may have the best Isp, but liquid hydrogen is, in fact, the least dense liquid known to humankind. It has been worshipped by aerospace since Tsiolkovsky, but in no way is it an optimal fuel for a SSTO rocket, particularly a reusable one (where dry mass is yet more important). Please re-examine your prejudices in light of that Dunn report.

All serious efforts toward SSTOs have used hydrogen.  There is a reason for this.  And that reason is in the graph that I posted.

You want to prove NASA wrong?  Start with at least posting something that's been peer-reviewed.  Even with just a cursory glance I can see glaring problems with the stated work, such as how he constrains all systems to have the same propellant volume.  But of course, the author is kind enough to mention this:

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In the current model, most propellant combinations beat hydrogen/oxygen.  This is a direct result of assuming a constant-size rather than constant-mass vehicle for all propellants, regardless of density. 
« Last Edit: 04/27/2016 02:00 am by Rei »

Offline Robotbeat

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Re: RP-1, methane, impulse density
« Reply #98 on: 04/27/2016 01:59 am »
Falcon 9 v1.0 was thought to have an ullage pressure of about 50psi, that's more than just "a fraction of an atmosphere overpressure."

Additionally, Saturn V is a poor example because the different stages were built by different entities. Additionally, the first stage is obviously going to be built much different than the other stages due to the lower penalty for high dry mass first stage (with its big ol' fins, etc). You should be comparing pump-fed upper stages to other pump-fed upper stages.

You have to make some simplifying assumptions, and that's a pretty good one to make.
« Last Edit: 04/27/2016 02:04 am by Robotbeat »
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Offline Rei

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Re: RP-1, methane, impulse density
« Reply #99 on: 04/27/2016 02:17 am »
Falcon 9 v1.0 was thought to have an ullage pressure of about 50psi, that's more than just "a fraction of an atmosphere overpressure."

1) Seriously, why do people on this site use arcane measurements like psi, mmHg, etc?  Use metric people, this isn't the dark ages....

2) Do you have a solid reference for that?  Atlas, the classic example of a balloon tank, was 34kPa:

https://en.wikipedia.org/wiki/SM-65_Atlas

Falcon 9 is partially pressure stabilized, but not to the degree of Atlas (Atlas couldn't even be transported or left on the stand unpressurized)

But let's just say that it's 350 kPa.  Shortly after launch it's pulling 2G.  Say, at 250 tonnes O2.  3,66m diameter = 10,5m cross section.  Thus stress on the bottom of the tank from G forces at launch is around 467kPa just from the fuel.   Now, you could call withstanding 467kPa a "pressure vessel", but it's no more a pressure vessel than any large cylindrical tank.

And all of this is irrelevant anyway, because tanks demonstrably do not have any sort of linear, propellant-ambivalent correspondence between volume and dry mass.  Look up tank masses.  It just doesn't work that way.

Quote
Additionally, Saturn V is a poor example because the different stages were built by different entities. Additionally, the first stage is obviously going to be built much different than the other stages due to the lower penalty for high dry mass first stage (with its big ol' fins, etc). You should be comparing pump-fed upper stages to other pump-fed upper stages.

Okay, okay, let's see, Russia's probably the place to look to for modern, non-hydrogen upper stages... let's say, Proton-M's two uppermost stages?   That's a much more modern rocket than Saturn V, so you can't complain that the Saturn V would be somehow technologically more advanced.  I don't have exact tank sizes but I have propellant masses, and the fuel combination is generally 1,18g/cc.  Stage 3: 4185kg, ~34 m^3; tankage  123kg/m^3.  Briz-M: 2370kg; tankage volume, ballpark 17 m^3; ratio: ~139kg/m^3

It just makes the case for some sort of "constant ratio" even worse.  Want me to make it even worse and compare to an actual modern hydrogen upper stage?

It's just not even remotely realistic to act like there's some sort of fixed ratio.

Now, you can make some sort of general function m(p,v,s) where:

 m = dry mass
 p = propellant scalar factor
 v = propellant volume
 s = stage factor (stages that start their burn further (in terms of delta-V) into the flight have a different ratio of engine mass to tank than lower stages)

Where:
m(p, v, s) = a * p * v^b * s^c

... where a, b,  and c are solved for by regression fitting and p for each propellant combination is determined empirically.  But of course you'll find that newer rockets tend to go under that curve and older rockets over it, so it might be worth adding in a "technology level scalar" in there as well.


« Last Edit: 04/27/2016 01:48 pm by Rei »

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