Specific Impulse vs. Density

[Proponent]

Some time ago I posted some curves of specific impulse as a function of density for a variety of propellant combinations.  Each propellant was at the lower of its boiling point (BP) and room temperature.  By popular demand (as in two people have asked -- hey, for me, that's pretty popular), I've now repeated the calculations with chilled propellants.

The general idea is to cool each propellant to 10 K above its melting point (MP), subject to the viscosity not exceeding 3.3 cP (which is the viscosity of RP-1 at 266 K, which is the temperature of RP-1 in Falcon 9 FT).  The viscosity requirement keeps propane and propylene a few kelvins above MP+10 and RP-1 and JP-10 quite a bit above.  For hydrogen, MP+10 is actually warmer than BP (20 K).  It's cooled to 16 K (MP+2), which is the lowest temperature covered in the NIST table of thermophysical properties.

No cooling is applied to either syntin or boctane, because I have no information on their low-temperature properties.  Syntin, being a big, fat, lumpy molecule (it's three cyclopropane rings stuck together, plus a methyl group) probably can't be cooled much before it becomes molasses anyway.

Otherwise, assumptions are as in the earlier post, including a chamber pressure of 20 MPa and an expansion ratio of 40.  Specific impulses are calculated with RPA Lite.  As before, the grey contour lines show figures of merit for an SSTO with an ideal delta-V of 10 km/s, according to a particular mass model.  Each curve covers the range from peak specific impulse to peak impulse density.

The first plot shows lox with hydrocarbons.  Each fuel, except syntin and boctane, is plotted twice, once for propellants at standard temperatures and once chilled.  Only the standard-temperature curves are labeled, but it's easy to associate each unlabeled curve with a labeled one, because the peak specific impulse remains the same.

You can easily see why Vector Space Systems might be interested in sub-cooled lox-propylene for its microsat launch vehicles.

The second plot includes lox-hydrogen.

EDIT:  Exchanged labels for pentane and butane on first plot.

[envy887]

Nice, thanks!

That does make propene look good when subcooled. Is there any word that Vector is subcooling though? As far as I can tell they use pressurized room-temp propene.

It's interesting that methalox is so far down the chart, even when subcooled. This illustrates the other reasons SpaceX is choosing it for Raptor, including low bulk cost (as LNG), coking issues with RP-1, and temperature similarity with subcooled LOX

[Nilof]

Nice, thanks!

That does make propene look good when subcooled. Is there any word that Vector is subcooling though? As far as I can tell they use pressurized room-temp propene.

It's interesting that methalox is so far down the chart, even when subcooled. This illustrates the other reasons SpaceX is choosing it for Raptor, including low bulk cost (as LNG), coking issues with RP-1, and temperature similarity with subcooled LOX

Another factor may be that Methane has an exceptionally low viscosity.

[Proponent]

Nice, thanks!

That does make propene look good when subcooled. Is there any word that Vector is subcooling though? As far as I can tell they use pressurized room-temp propene.

I doubt you'd want to use propene at room temperature, because its vapor pressure is about 12 atm.   Page 6 of Vector's user guide, version 1.6, states: "The vehicle is fueled with Liquid Oxygen (LOX) and our proprietary densified Liquid Propylene (LPROP)."  I's don't see how a liquid hydrocarbon could be "densified" without being sub-cooled.  I wonder what is proprietary about it.  Since the lox apparently is not sub-cooled, it's presumably at a temperature of about 90 K, just above propene's MP of 88 K but below the 104 K temperature assumed in the Isp-density curves shown in the OP.  The user's guide also mentions Vector's "patented pressurization systems using safe low pressure systems".  I wonder whether the proprietary and patented bits have something to do with managing the fuel's pressure and temperature (and viscosity).

It's interesting that methalox is so far down the chart, even when subcooled. This illustrates the other reasons SpaceX is choosing it for Raptor, including low bulk cost (as LNG), coking issues with RP-1, and temperature similarity with subcooled LOX

As you and Nilof note, there are important considerations that the simple figure of merit plotted above does not take into account.  And I certainly would not take the figure of merit as definitive; it's based on a particular mass model, which is by no means complete or definitive.  That said, while propylene isn't as cheap as methane, it's still cheap.  Methane freezes at 86 K, propene at 88 K, so they're both about equally (in)compatible with sub-cooled lox (MP: 55 K, BP: 90K).  I suspect the main difference between SpaceX's and Vector's requirements arises from the pumping cycles they use.  SpaceX's use of high-pressure staged-combustion probably puts a premium on chemical stability, where propene's double bound might be troublesome.  And, of course, SpaceX wants to make fuel on Mars.

EDIT:  "it's vapor pressure" -> "its vapor pressure" in first sentence.

[Proponent]

Here are the numerical values for the cases plotted above, as well as for the case where the oxygen is at it boiling point but the fuels are sub-cooled.

   Ox.Cond      Fuel   Cond Temp  O.F RelMix Isp Dens Ctemp DenExp MechEff mProp  mEng mTank mFluid mOther
1    MP+10 propylene  MP+16  104 2.79  0.251 349 1069  3926  0.230   0.486  17.6 0.156 0.164 0.0878  0.592
2    MP+10  ethylene  MP+10  114 2.74  0.250 354 1002  3977  0.236   0.493  16.8 0.158 0.168 0.0841  0.590
3    MP+10   propane  MP+17  102 3.13  0.250 347 1064  3804  0.230   0.483  17.8 0.160 0.168 0.0892  0.583
4    MP+10   pentane  MP+10  153 3.03  0.244 346 1080  3827  0.228   0.481  18.1 0.161 0.167 0.0904  0.581
5    MP+10    butane  MP+10  146 3.07  0.254 346 1067  3818  0.229   0.482  18.0 0.162 0.169 0.0900  0.580
6    MP+10    hexane  MP+10  188 3.01  0.259 345 1079  3832  0.228   0.480  18.2 0.162 0.168 0.0909  0.579
7    MP+10     JP-10  MP+97  291 2.71  0.241 340 1153  3910  0.222   0.472  19.1 0.161 0.166 0.0955  0.578
8    MP+10    octane  MP+10  226 2.98  0.252 345 1080  3838  0.228   0.479  18.3 0.163 0.169 0.0914  0.576
9    MP+10    ethane  MP+10  111 3.25  0.261 349 1020  3781  0.233   0.486  17.6 0.164 0.172 0.0878  0.576
10      BP    syntin   <NA>  295 2.59  0.250 347 1042  3987  0.231   0.483  17.8 0.163 0.171 0.0892  0.576
11   MP+10      RP-1  MP+43  266 2.87  0.241 342 1109  3862  0.225   0.475  18.7 0.163 0.169 0.0936  0.574
12      BP   boctane  MP+52  295 2.68  0.249 347 1035  3952  0.231   0.483  17.9 0.165 0.173 0.0894  0.573
13      BP propylene  MP+16  104 2.78  0.256 349 1003  3926  0.233   0.486  17.5 0.166 0.175 0.0877  0.571
14      BP  ethylene  MP+10  114 2.72  0.268 354  944  3976  0.238   0.493  16.8 0.167 0.178 0.0841  0.570
15      BP   propane  MP+17  102 3.12  0.249 347  997  3803  0.233   0.483  17.8 0.171 0.179 0.0892  0.561
16      BP   pentane  MP+10  153 3.02  0.243 346 1011  3826  0.231   0.481  18.1 0.171 0.179 0.0904  0.559
17      BP    butane  MP+10  146 3.06  0.255 346 1000  3818  0.232   0.482  18.0 0.172 0.180 0.0900  0.558
18      BP    hexane  MP+10  188 3.00  0.262 345 1011  3831  0.231   0.480  18.2 0.173 0.180 0.0908  0.557
19      BP     JP-10  MP+97  291 2.70  0.238 340 1078  3909  0.225   0.472  19.1 0.172 0.177 0.0954  0.555
20      BP     JP-10 MP+101  295 2.70  0.238 340 1077  3909  0.226   0.472  19.1 0.173 0.177 0.0954  0.555
21      BP    ethane  MP+10  111 3.24  0.266 349  957  3781  0.235   0.486  17.6 0.174 0.183 0.0878  0.554
22      BP    octane  MP+10  226 2.97  0.254 345 1011  3838  0.231   0.479  18.3 0.174 0.181 0.0914  0.554
23      BP  ethylene     BP  169 2.74  0.250 354  899  3977  0.240   0.493  16.8 0.176 0.187 0.0841  0.553
24      BP      RP-1  MP+43  266 2.86  0.240 342 1038  3862  0.228   0.475  18.7 0.175 0.180 0.0936  0.551
25      BP      RP-1  MP+72  295 2.86  0.241 342 1029  3862  0.229   0.475  18.7 0.176 0.182 0.0936  0.548
26      BP    octane  MP+79  295 2.98  0.256 345  985  3838  0.232   0.479  18.3 0.178 0.186 0.0914  0.545
27   MP+10   methane  MP+10   96 3.62  0.245 352  903  3708  0.239   0.490  17.2 0.180 0.190 0.0859  0.544
28      BP propylene     BP  225 2.81  0.247 349  928  3928  0.236   0.486  17.6 0.180 0.189 0.0878  0.543
29      BP    hexane MP+117  295 3.02  0.263 345  965  3833  0.233   0.480  18.2 0.181 0.188 0.0909  0.540
30      BP   pentane MP+152  295 3.04  0.248 346  947  3828  0.234   0.481  18.1 0.183 0.191 0.0905  0.535
31      BP    ethane     BP  185 3.26  0.262 349  907  3782  0.237   0.486  17.6 0.184 0.194 0.0878  0.534
32      BP   propane     BP  231 3.14  0.251 347  926  3805  0.236   0.483  17.9 0.184 0.193 0.0893  0.533
33      BP    butane     BP  273 3.08  0.256 346  935  3819  0.235   0.482  18.0 0.184 0.192 0.0900  0.533
34   MP+10  hydrogen   MP+2   16 7.44  0.280 421  440  3734  0.301   0.571  10.3 0.192 0.234 0.0515  0.523
35      BP   methane  MP+10   96 3.61  0.272 352  852  3708  0.241   0.490  17.2 0.191 0.201 0.0858  0.522
36      BP   methane     BP  112 3.62  0.261 352  834  3708  0.242   0.490  17.2 0.195 0.206 0.0859  0.513
37      BP  hydrogen     BP   20 7.43  0.290 421  409  3734  0.303   0.571  10.3 0.206 0.252 0.0514  0.491

[acsawdey]

Nice, thanks!

That does make propene look good when subcooled. Is there any word that Vector is subcooling though? As far as I can tell they use pressurized room-temp propene.

It's interesting that methalox is so far down the chart, even when subcooled. This illustrates the other reasons SpaceX is choosing it for Raptor, including low bulk cost (as LNG), coking issues with RP-1, and temperature similarity with subcooled LOX

Another factor may be that Methane has an exceptionally low viscosity.

So SpaceX when switching from RP-1 to methane is switching from Al-Li construction to carbon fiber. Presumedly this is to compensate for the lower bulk density of methane? Also does the lower viscosity of liquid methane increase the efficiency of the turbopump? With staged combustion and the pressures given for Raptor, this could be significant.

Also with respect to the propene -- wouldn't that C=C double bond increase the chance of carbon deposits as well?

[envy887]

Looks like methane is the closest match temperature-wise (at a given viscosity) to 77k LOX, which would help simplify common bulkhead and LOX pipe construction and insulation. Propane and propene both look pretty close though.

From what I can find, propane (as LPG) and propene are roughly $0.50 to $1.00 per kg, compared to methane (as LNG) at $0.15 per kg. Which is a critical factor if you're blowing 50 million kg on a single Mars mission, but likely isn't a major consideration for small launchers like Vector. Filling a Vector rocket probably only costs about $5000 at bulk prices, so the performance is likely more than worthwhile

[R7]

Also does the lower viscosity of liquid methane increase the efficiency of the turbopump?

Lower viscosity -> lower pressure drop in the nozzle cooling channels -> lower pump outlet pressure required -> lower turbine power required -> lower turbopump mass

[Proponent]

Also with respect to the propene -- wouldn't that C=C double bond increase the chance of carbon deposits as well?

I'm sure it would: that's what I meant by "SpaceX's use of high-pressure staged-combustion probably puts a premium on chemical stability, where propene's double bound might be troublesome."