# Does the NK-33 engine require subcooled kerosene so cold that it turns to wax?

It was mentioned in this answer and in several other places on the internet that the kerosene fuel used by NK-33 engines needed to be subcooled enough so that it reached the same density as the LOX, and that this is required so that the turbopumps can run on the same shaft. These statements all trace back to here, where I can not actually find any discussion of subcooled kerosene, much less a discussion of the need to match the density of LOX.

I mentioned this here - it bothers me for two reasons:

1. I think it would be extremely hard to obtain liquid kerosene at a density of 1.17 or 1.18 g/cm3, which is the density of LOX at -310 ℉, the temperature that the NK-33 engines require in order to cool the turbopump bearings. The density of RP-1 is about 0.8 g/cm3 at 25 ℃, and the largest value I’ve seen anywhere is 1.02 g/cm3.
2. I can’t think of any reason why the densities should be equal to run the two turbopumps on the same shaft. The ratio of the mass flows is quite large - perhaps 2.62 LOX/kerosene (from here) so I don’t understand why matching their densities in the two pumps so closely is important.

note: I use the generic “kerosene” since the Russian fuel used to develop the engines can’t officially be called “RP-1”.

I’ve tried to collect as much information as I can on-line, and plot it here. Since I've had to deal with four different temperature scales, and people are accustomed to using different ones, I've just brute-force plotted with all four since I can't do the conversions in my head either.

RP-1 solid blue line from http://www.dtic.mil/dtic/tr/fulltext/u2/290659.pdf. Other data points I’ve found seem to match.

RP-1 dashed red line is an extrapolation of the same line below it’s valid range of -45 ℃ to +25 ℃, just to guide the eye and give the brain something to thing about.

RP-1 comments on consistency (“gel”, “wax”, etc.) are from http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20020018567.pdf. I have included a screenshot of the relevant section below the plots.

LOX solid line from http://booksite.elsevier.com/9780750683661/Appendix_C.pdf. A screen shot of the entry and equation is given below.

LOX data points from http://oxygen.atomistry.com/liquid_oxygen.html

EDIT: additional LOX data points can be found at Spaceflight 101 and here, credit: NASA.

My question is: Does the operation of the NK-33 engine really require equal densities of LOX and kerosene? If so, WHY?? Also if so, what is the actual temperature of the kerosene to acheive this density, and what is its consistency really like, liquid, gel, wax?

NOTE: below is from: http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20020018567.pdf R is temperature in Rankine - which could be called "absolute Fahrenheit" I suppose.

NOTE: below is from http://lpre.de/resources/articles/AIAA-1998-3361.pdf:

NOTE: below is from: http://booksite.elsevier.com/9780750683661/Appendix_C.pdf

• Rankine scale! Wow. – pjc50 Mar 15 '16 at 14:26
• Not sure I've ever seen such a well researched question. – Dewi Morgan Mar 16 '16 at 13:26
• @DewiMorgan I really wanted to get to the bottom of the benefits of subcooling, and asking a SE question is one way to sort it all out. – uhoh Mar 16 '16 at 14:24
• I wonder how hard wax should be pumped and injected to the combustion chamber. – Uwe Sep 16 '17 at 8:36

Confusion abounds. Spaceflight 101 has this to say about the NK-33:

The NK-33 requires sub-cooled Oxygen with a temperature below its boiling point of -183 degrees Celsius to cool the turbopump bearings that would otherwise fail. Also, sub-cooled LOX has a higher density, close to that of Kerosene, reducing required tank volume and overall launch vehicle mass and allowing the engine to use a single rotating shaft for both turbopumps.

So they're flipping the statement, saying the LOX has to be subcooled to get the right density, not the kerosene.

According to Wikipedia (and corroborated by uhoh's diagrams), LOX at any temperature has a higher density than kerosene. So subcooling the LOX increases the density difference. But Spaceflight 101 may have a point. The engine has burns 2.8 kg of oxygen with 1 kg of kerosene. When you make the LOX denser, you bring the volumes of the two closer together, which might make pump design on a common shaft easier.

## Aerojet experiments

Let's see if we can get a statement from source: this AIAA paper by Aerojet details the modifications done by them. It mentions density only once (table 6 on page 16), and that same table lists fuel temperature as -30 °F (-34 °C), so it'd be nowhere near the same density as the LOX. Anyway, this paper confirms the kerosene does not have to be subcooled for the engine to work.

They did tests running the engine with ambient-temperature RP1 and boiling-point LOX, as far as I can see they did burns of up to 140 seconds with this combination. They did no tests with RP-1 subcooled below -37 °F (-38 °C). They also mention the Russians normally used kerosene at above -30 °F (-34 °C).

From this I conclude subcooling of either LOX or propellant is possible, but not necessary on this engine. So the question "Does the NK-33 engine require subcooled kerosene?" can be answered with 'No'.

## Other engines

Single-shaft turbopumps are common in all sorts of rocket engines.

• Kerosene/LOX engines like the RD-0110, which does not use subcooling
• hydrogen/LOX engines like the RD-0120, where the density of LOX and LH are much farther apart than the densities of LOX/RP-1.
• Great! Thank you for the analysis! Somewhere along the way, "density" and "same shaft"became associated, and as often happens on the internet (which Jesse Eisenberg tells us is "written in ink") it propagated. I think you would tend to conlcude that the answer to "Does the NK-33 engine require subcooled kerosene so cold that it turns to wax?" is No? – uhoh Mar 15 '16 at 14:54
• yup. Everyone who talks about the NK-33 turbopump seems to repeat the same sentence, wrongly copied from somewhere. – Hobbes Mar 15 '16 at 15:01
• OK this looks like a pretty definitive answer... – uhoh Mar 15 '16 at 15:15
• (Sorry - Rooney Mara (as Erica Albright) made the statement about the internet being "...written in ink"!) – uhoh Mar 15 '16 at 15:22

There is no problem running Kerosene and Oxygen on the same turbopump shaft, at any temperature. provided both are liquid, the density variations are not sufficient to make any practical difference to the feasibility of a turbopump.

From the OP, the densities of Oxygen and Kerosene are 1.18 and 0.8 g/cm3 , a ratio of 1.475. The pressure produced by a single stage centrifugal pump is proportional to speed of the outer edge of the impeller squared, times the density. Therefore, in order to achieve the same pressure with both propellants in a single shaft turbopump, the diameter of the kerosene impeller would be expected to be sqrt (1.475) = 1.21 times bigger than the oxygen impeller. This is practical to achieve. Note that this is only a rule of thumb, actual impeller diameters may vary slightly to a number of more detailed considerations.

As noted in comments on Russell Borogove's answer, it is not practical to run hydrogen and oxygen on the same turbopump shaft. Oxygen is 16 times denser than hydrogen, so in order to achieve the same pressure the oxygen impeller would have to be a quarter the diameter of the hydrogen impeller, or alternatively the oxygen pump could be single stage and the hydrogen pump 16 stage. But it's more practical just to run the oxygen impeller slower. See video of turbopump on RL-10 hydrogen / oxygen engine showing the turbine at the bottom, the hydrogen pump at the top, and the geared down oxygen pump at the left.

• Thank you for the insightful answer, and also for the cool video! – uhoh Sep 3 '19 at 22:50
• That video is of the RL-10 in the Huntsville museum! (Yes, I recognize individual engines....) space.stackexchange.com/a/10663/6944 – Organic Marble Sep 3 '19 at 23:27

First, the only place I have been able to find the equal density claim is in the NK-33 Wikipedia article. (In fact it originates from the first version). There have never been provided any source for it. On the other hand, this paper seems to suggest that that is indeed the cases, although indirectly.

Polymerization does not necessarily have to be a problem, as RP-1 is by default low on sulphur, alkenes and aromatics. The Russians may have used a stricter specification as well. (The point of which hydrocarbons polymerize is strongly dependent on composition, and pushing it past the "supercooled" range should not be a problem.)

The claim that the NK-33 needed similar densities in order to operate seems odd, as it is not the only closed-cycle engine, just one out of many with a great variety of propellants. The article does however mention a single rotating shaft, so the issue may be a ressult of centrifugal separation of the liquids.

According to Sutton's Rocket Propulsion Elements:

If the two propellants have similar densities (say within 40%) such as NTO & UDMH or LOX and kerosene, and the volume flow of oxidizer and fuel are similar, then the same type of impeller (running at the same speed) can be used on both of them on a single shaft.

It goes on to say that with hydrogen/LOX you definitely want separate shafts. There seems to be a general relationship between impeller speed and propellant density where efficiency is optimal; hydrogen can be pumped on a higher-speed axial impeller while denser propellants want a slower radial or semi-radial impeller. Disclaimer: I am not a hydrodynamicist!

So with a 2.6 LOX:kerosene mass ratio, this seems to say that, within limits, you'd actually want the kerosene less dense in order to achieve more equal volume flow.

• OK that is helpful. I don't have the book handy but I'll see what I can do. Are there any hints of why there is a relationship? Is it related to cavitation at all? (see @Hohmannfan's answer & comments). It looks like the volume ratio here is always going to be greater than 2:1 unless the kerosene is roughly 0C or warmer, far large than the ~40% ballpark mentioned. – uhoh Mar 15 '16 at 12:45
• The 40% is referring to the density relationship; it doesn't say what "similar" actually means for the volume flow, but the book seems to imply that single shaft kerolox pumps are not unusual, so I have to assume that a 2.0 to 2.5 volume ratio is considered "similar". – Russell Borogove Mar 15 '16 at 13:08
• @uhoh it is to do with pressure matching. The pressure is proportional to the velocity of the impeller edge squared times density. Oxygen is 16 times denser than hydrogen, so to get the same pressure from a single shaft turbine, you would need an oxygen impeller 4 times smaller diameter than the hydrogen impeller. Alternatively you could use 16 hydrogen impellers in series. Neither of these are practical. See example video of RL-10 engine . Turbine at bottom, hydrogen pump at top, and geared down oxygen pump at left youtube.com/watch?v=yAg6GSeTBo4 – Level River St Sep 3 '19 at 21:53