Max ISP and thrust from HydroLox

[RocketSquid]

So, I was wondering, assuming you can use every trick in the book (afterburning thermal engines, fancy nozzle designs, etc) what is the most thrust and ISP you could pull out of hydrolox? Supposedly, purely chemical engines peak at or below 700 seconds, but I'm wondering how much you can improve that.

[Bill Phil]

We can actually look at this from an energy point of view. How do you maximize energy while limiting mass flow? You can run engines fuel rich, run more efficient cycles, have enormous (and I mean ridiculous) area ratios in the nozzle, and high combustion pressures. Try to minimize mass flow. Thrust goes up with mass flow increase, but ISP goes down.

As per Wikipedia, LH2 has a specific energy of 141.86 megajoules/kg. The issue is, though, that for every kilogram we get energy from, we have to burn it with LOX. If we use a oxidizer to fuel ratio of 4.7, than for every kilogram of hydrogen we burn we also have to add in 4.7 kilograms of LOX. This sums up to 5.7 kilograms. Assuming an efficiency of 60%, we take the energy from 1 kilogram of LH2 (141.86 megajoules) and multiply it by 0.6, and put that into the kinetic energy equation as well as 5.7 kilograms. Then we solve for velocity. You get an exhaust velocity of 5465 m/s, but I'd take that with a some salt, and fudge the numbers to a range of 5250 to 5500 m/s. Now, if we assume a humongous de Laval engine bell, than maybe 6000 m/s...?

Edited August 30, 2016 by Bill Phil

[Kryten]

The space shuttle main engines are going to be pretty close to the max we can get in both categories with current technology, with 1696kn and 452 seconds vacuum Isp respectively. The record for thrust is 2,441KN for the Japanese Le-9, but that uses a relatively low-Isp open cycle and has a much lower chamber pressure so only gets 425s. The Russian KDV-1 has the record for Isp with 462s, but is a tiny upper-stage engine with 74KN thrust. SSME isn't going to be beaten anytime soon, given current LV development trends against expensive high-performance engines and against hydrolox in general.

[RocketSquid]

Okay, how much more could we squeeze out if we superheated the fuel (and possibly the oxidizer) before combustion, as in a LANTR engine?

[Bill Phil]

1 hour ago, RocketSquid said:

Okay, how much more could we squeeze out if we superheated the fuel (and possibly the oxidizer) before combustion, as in a LANTR engine?

Up to 6000 m/s. That's pretty close to LANTR's LoX augmented mode.

[RocketSquid]

Just now, Bill Phil said:

Up to 6000 m/s. That's pretty close to LANTR's LoX augmented mode.

Why would it be less? Superheating the fuel is exactly what LANTR does.

Would superheating the oxidizer in addition to the fuel improve that?

[Kryten]

Where's the energy supposed to come from to superheat the fuel?

[Bill Phil]

3 hours ago, RocketSquid said:

Why would it be less? Superheating the fuel is exactly what LANTR does.

Would superheating the oxidizer in addition to the fuel improve that?

6000 is more of a median. According to Atomic Rockets you could get 6447 m/s from a LANTR with LOX.

It's less because you're still throwing around the Oxygen. And if you're using LANTR, then you're beyond pure chemical engines.

[RocketSquid]

3 hours ago, Bill Phil said:

6000 is more of a median. According to Atomic Rockets you could get 6447 m/s from a LANTR with LOX.

It's less because you're still throwing around the Oxygen. And if you're using LANTR, then you're beyond pure chemical engines.

I wasn't asking pure chemical. I'm mostly asking because even partial chemical typically gives more thrust than pure thermal or electrostatic.

[Bill Phil]

19 minutes ago, RocketSquid said:

I wasn't asking pure chemical. I'm mostly asking because even partial chemical typically gives more thrust than pure thermal or electrostatic.

It's really a question of mass flow then. Exhaust velocity goes down as mass flow and thrust go up,

[shynung]

@Bill Phil @RocketSquid It's mostly a matter of the exhaust gases' molecular mass. A hydrogen-propellant solid-core NTR has a higher specific impulse than a pure chemical hydrolox motor despite lower chamber temperatures (about 2000 K, as opposed to the latter's 4500 K), primarily because it spews hydrogen gas (about 2 amu) whereas the hydrolox motor spews out steam (H2O, about 18 amu).

Generally, for the same chamber temperature and pressure, lighter molecules move faster, which effectively increases specific impulse. This is also why hydrolox motors running rich sometimes have a higher specific impulse than stoichiometric-running motors, despite lower chamber temperature/less energetic combustion, which is because the average molecular mass of the exhaust is lower due to unburned H2 in the exhaust.

On another note, this explains why kerolox rockets have enormous fiery plumes compared to hydrolox ones. I'm willing to bet that the fuel/oxidizer ratio is optimized to burn the kerosene to CO as opposed to CO2, in an attempt to improve specific impulse. The large plume often seen trailing kerolox rockets are therefore, I suspect, the CO in the rocket exhaust reacting with atmospheric oxygen. This fiery plume is not seen in kerolox motors burning higher up, such as F9's second stage, because there aren't any oxygen for the CO to burn with.
 

Edited August 31, 2016 by shynung

[DDE]

15 hours ago, RocketSquid said:

Why would it be less? Superheating the fuel is exactly what LANTR does.

Would superheating the oxidizer in addition to the fuel improve that?

If you can somehow keep your engine from burning up by contact with superheated oxygen...

Basically, any addition to hydrogen - such as a second hydrogen atom - brings I_sp down, hard. That's why NTRs have higher I_sp at lower chamber temperatures; the record-setter is an aluminium-ozone engine at 6000 K. However, ozone has a tendency to explode for no reason, so you're better off with the lithium-fluorine-hydrogen combo at 542 sec practical I_sp.

The Wiki gives a theoretical maximum exhaust velocity of 4462 m/s for hydrolox, which converts to 455 sec; chemistry alone won't get you further.

Edited August 31, 2016 by DDE

[Bill Phil]

2 hours ago, DDE said:

If you can somehow keep your engine from burning up by contact with superheated oxygen...

Basically, any addition to hydrogen - such as a second hydrogen atom - brings I_sp down, hard. That's why NTRs have higher I_sp at lower chamber temperatures; the record-setter is an aluminium-ozone engine at 6000 K. However, ozone has a tendency to explode for no reason, so you're better off with the lithium-fluorine-hydrogen combo at 542 sec practical I_sp.

The Wiki gives a theoretical maximum exhaust velocity of 4462 m/s for hydrolox, which converts to 455 sec; chemistry alone won't get you further.

There are multiple factors. Efficiency, area ratio, which cycle your using, and so on.

If your area ratio is insane, you can get pretty high Isp. Most rockets are limited in that regard, though.

The RL-10-B2's improved isp comes from a larger area ratio and other factors. We're hitting practical limits at the 460s, but there have ben theoretical designs that had higher isp than that.