Pressure-fed Hydrogen Rocket Engine

[Enthalpy]

Injecting hydrogen in the divergent of an engine downstream dense propellants was experimented long ago. But if the dense propellants are pressure-fed, I claim one can build a (mainly) oxygen-hydrogen engine without pumps. This isn't normally done because hydrogen pressure tanks are too heavy.

Figures are just examples to help understand and check. From pressure tanks, scalable 1kg/s oxygen is fed in the chamber and burns only 28g/s alkane at 80bar and 1056K. Expansion to 27.2bar converts half the enthalpy available in the hot gas, so the gas can't flow upstream, and it builds a vacuum downstream a sharp obstacle. There, hydrogen ducts end facing downstream, which sucks the hydrogen from 1+1bar in the lightweight tank.

261g/s hydrogen burn in the much oxygen left in the hot gas, the rest of the expansion accelerates the combustion products. 1bar exit provides 3459m/s = 353s and 0.233bar exit 3895m/s = 397s. Less than pumps achieve, but far better than pressure-fed dense propellants, and with reasonable tank mass.

I computed with hydrogen burning at constant 27.2bar. This isn't optimum. Some pressure increase is acceptable and improves the performance. How much is a difficult question (and topical at scramjets) and I won't put the necessary time in it. The first expansion to 27.2bar is overkill too. So the performance I indicate is pessimistic.

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The engine can have one chamber but many convergents, throats and starts of divergent. This lets build one injector per divergent start, for instance to have one hydrogen injector around each hot gas stream, or a more sophisticated section like a flower. All streams can then converge in a common end of divergent built as usual, cooled if needed by hydrogen or oxygen. At an atmospheric stage, an atmospheric insert and a wider nozzle, as at the RD-0120, improve very much the small expansion.

Graphite tanks are very desirable. Alkanes outperform minimally their amines homologues, high strain or unsaturation improve only 1s. The chamber's walls need some cooling by the oxygen.

The RD-170's gas generator can inspire the chamber here, including wall cooling, but I would leave a common room to the slightly oxygen-rich flames and inject most oxygen further downstream as I suggested there, possibly without swirl
scienceforums
and then ignition doesn't need pyrophorics, something like Diesel glow plugs would suffice
nasaspaceflight
28g/s alkane need active cooling of the chamber's walls to leave 823K = 550°C at hydrogen injection. This was to ignite permanently the hydrogen in the quick stream, but I forgot cooling by hydrogen. More alkane can help stabilize the hydrogen flame. Pilot flames with alkane at hydrogen injection can help too, or staged hydrogen injection, or some local recompression shocks.

Alkanes with an at least C₄ unbranched tail have a low autoignition. Or Pmdta ignites at only +155°C in air. Farnesane stays liquid around -100°C. Heavy by-products of an alkylation unit shouldn't be bad.

To pressurize the hydrogen tank, a fluid can circulate in heat exchangers between the chamber and the tank, or an electric pump can scoop some liquid hydrogen, send it to a heat exchanger at the chamber, and to the top of the tank. Or the divergent, just upstream hydrogen injection, is a milder place than the chamber.

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Some ideas here apply to scramjets too, especially the many streams, each with hydrogen suction or injection, which ease the mixture and shorten the engine. Some ignition methods apply too. Check also
chemicalforums

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A sketch should come, maybe some more figures.

Marc Schaefer, aka Enthalpy

[Enthalpy]

And here's a sketch of a pressure-fed hydrogen engine. No scale, but the dimensions I checked are all favourable. Only few injectors and streams are displayed. The many streams should join their divergents, and some hydrogen be injected where they don't.

Angles between the streams shorten the engine, while slow upstream oxygen turns easily.

The oxygen injectors could protrude from the side instead, reach nearly the centre, with shorter injectors between the longest ones. This circulates less oxygen in the head where the fuel might freeze, but this doesn't happen at RD-170's gas generator.

Whether the many hydrogen moles ignite in the warm oxygen? The progressive evaporation gives a chance. Staged injection can help, or a pilot flame can burn a bit of dense fuel with lower ignition temperature like Pmdta or Diesel oil. A small compression wave could converge to an ignition point.

An optional atmospheric insert, no displayed but very useful, can be ablatively cooled. I like the RD-0120 discardable inner divergent in this role because the flow is stable at intermediate pressures too.

Pressurizing helium can be stored in the oxygen and dense fuel vessels, as graphite here doesn't favour spheres much. The vessels are bigger, but remain much smaller than the hydrogen tank(s). Some sprinkler provides isothermal expansion then. Or the hydrogen can keep helium cold in a small separate pressure vessel to save good mass.

Marc Schaefer, aka Enthalpy

[dimreepr]

How can one go faster, than the propellent???

[exchemist]

1 hour ago, dimreepr said:

How can one go faster, than the propellent???

Is this a trick question? I'd have thought the answer is "easily" - if you mean faster relative to some external observer.

[Enthalpy]

Elements for a pressure-fed hydrogen engine.

At the left part, a small bump in the stram's walls provoques a mild compression wave whose amplitude increases at the centre and could approach the pre-chamber's stagnation temperature to ignite the fuel present there, displayed is auxiliary hydrogen. The streams have nearly cylindrical symmetry, so the structure around them and the hydrogen feed don't.

Can the main hydrogen ignite alone? Maybe if it evaporates slowly enough. The auxiliary hydrogen keeps much oxygen hot for a local flame. Some fuels ignite more easily: Pmdta ignites at +155°C, before it boils under 1atm, heavy alkanes too, keeping the oxygen hot.

Hydrogen must burn at the maximum pressure that keeps the oxygen flow and the suction. This results from hydrogen evaporation, oxygen cooling, combustion, and the stream profile design. No attempted prediction from me. Ideally, most hydrogen would burn at subsonic speed, with De Laval profiles, or at least the combustion would make a compression xave. Throttling worsens the design difficulty.

A fairing after the structure eases assembly and cooling. It can leak some hydrogen. Its makes the intricate part of the shape, so the stream walls have cylindrical symmetry and can be mounted by screwing.

The right part depicts the already mentioned flower injector. One stream with that injector replaces several smaller ones. I hope the flowers can be deep-drawn from a sheet or electroformed, and welded to the thicker elements by friction or diffusion.

Marc Schaefer, aka Enthalpy

[Enthalpy]

Hi everyone, thanks for your interest!

On 4/25/2021 at 4:06 PM, dimreepr said:

How can one go faster, than the propellent???

As Exchemist says, speeds are relative to an observer. Apparently, you took implicitly an observer at the rocket's start point, and then the rocket moves faster than the exhaust gas, somewhere at the second stage. The best chemical engine spews gas at 4560m/s while satellites move with 7800m/s on low Earth orbit.

If an observer moves at the rocket's speed at some time, for instance if he's in a space station joined by a rocket, then the same rocket is slow and the gas is fast.

The events, for instance the rocket's acceleration, don't change whether one observer or the other measures the speeds, so a rocket continues to accelerate by expelling gas, even if for some observers the rocket is already faster than it expels gas.

You can view it like that: as the already fast rocket continues to expel gas, the gas is less fast relative to the observer at the start point, so the rocket gets faster, because the sum of their momentums is zero.

[dimreepr]

On 4/27/2021 at 8:41 AM, Enthalpy said:

Hi everyone, thanks for your interest!

As Exchemist says, speeds are relative to an observer. Apparently, you took implicitly an observer at the rocket's start point, and then the rocket moves faster than the exhaust gas, somewhere at the second stage. The best chemical engine spews gas at 4560m/s while satellites move with 7800m/s on low Earth orbit.

If an observer moves at the rocket's speed at some time, for instance if he's in a space station joined by a rocket, then the same rocket is slow and the gas is fast.

The events, for instance the rocket's acceleration, don't change whether one observer or the other measures the speeds, so a rocket continues to accelerate by expelling gas, even if for some observers the rocket is already faster than it expels gas.

You can view it like that: as the already fast rocket continues to expel gas, the gas is less fast relative to the observer at the start point, so the rocket gets faster, because the sum of their momentums is zero.

Does that work if the observer is on the rocket?

[swansont]

On 4/25/2021 at 10:06 AM, dimreepr said:

How can one go faster, than the propellent???

The short answer is that momentum is conserved. In the rocket frame, the exhaust has momentum in one direction, so the rocket recoils in the other. This works for any frame where the exhaust has a velocity opposite of the rocket’s

In any other frame, the exhaust has less momentum than an equal amount of mass on the rocket, since it’s moving slower, so the rocket has to have gained momentum.

[Enthalpy]

On 4/30/2021 at 3:04 PM, dimreepr said:

Does that work if the observer is on the rocket?

The rocket accelerates. The observer wouldn't be linked to an inertial frame then (aka free-falling). This can become quite more complicated.

[IDNeon]

Can we get off the semantics and onto the topic again?

I am interested in the idea but biggest flaw seems to be the 91atm pressure vessel.

How big does it have to be? I have the equation for this if I know the internal diameter. But likely it will be 0.05meters thick of titanium.

Other problem. At what temperature? 

Metallurgy is a limiting factor.

US solved hydrogen problems and the solutions centered around solving metallurgical problems.

Are you keeping hydrogen at 91atm down stream?

If not how does Metallics react to change from -400C to whatever temperature the hydrogen reaches at this pressure? 

Engineering problems always have solutions. 

So I'm less interested in the specifics and more interested in how it integrates into the whole system.

[dimreepr]

On 4/30/2021 at 5:52 PM, swansont said:

The short answer is that momentum is conserved. In the rocket frame, the exhaust has momentum in one direction, so the rocket recoils in the other. This works for any frame where the exhaust has a velocity opposite of the rocket’s

In any other frame, the exhaust has less momentum than an equal amount of mass on the rocket, since it’s moving slower, so the rocket has to have gained momentum.

On 5/2/2021 at 5:37 PM, Enthalpy said:

The rocket accelerates. The observer wouldn't be linked to an inertial frame then (aka free-falling). This can become quite more complicated.

I think I get it (thanks), at any given moment we're not moving unless pushed.

 

[Enthalpy]

On 5/2/2021 at 6:52 PM, IDNeon said:

I am interested in the idea but biggest flaw seems to be the 91atm pressure vessel. How big does it have to be? At what temperature? [...]

Hi IDNeon, thanks for your interest!

My description doesn't specify a propellant amount, so the tank size adapts to the target design. For a given tank shape, the thickness increases proportionally to the diameter and to the ratio of accepted stress vs internal pressure. This implies that the ratio between tank mass and propellant mass depends on the accepted stress, the pressure and also the shape.

Previously, I optimized more seriously all pressures for pressure-fed oxygen and a dense fuel. With maraging steel tanks (lighter than titanium alloy, easier to construct, cheaper) the best chamber pressure is 36bar for an atmospheric stage, about 20bar for a vacuum stage. Graphite fibre tanks allow more pressure, optimized to 40bar and 25bar, and remain lighter than steel.

One precious optimization is to let the pressure drop in the tanks as a stage goes empty, as the engines must throttle anyway. This saves helium mass, and even more helium tank mass. I compute with helium in a separate spherical tank (sometimes toroidal) that is usually at 90K (cooled by oxygen) even if a part flows to the storable fuel tank. I always take helium at the propellant temperature, despite hot helium would save mass. Here, helium would rather by at 20K to save helium tank mass, cooled by the available hydrogen, and warm to 90K in the oxygen tank.

Pressurizing hydrogen doesn't work to my opinion. I estimated the mass of the strong hydrogen tank and of the gaseous hydrogen left in the tank at 20K, and even at 5bar for a vacuum stage, the inert mass is catastrophic. I didn't follow if Sea Dragon solved this problem after I revealed it.

It's the central point of this thread: the engine I propose doesn't pressurize the hydrogen, it sucks it instead. This makes a light hydrogen tank at 1+1bar.

Because this design is more sensitive to pressure, and because only the oxygen is pressurized and uses colder helium from a lighter tank, the optimum pre-chamber pressure is higher. I didn't reoptimize it and took 80bar arbitrarily. Maybe it's 60bar, I don't know, but the optimum is wide.

On 5/2/2021 at 6:52 PM, IDNeon said:

[...] At what temperature? Metallurgy is a limiting factor. [...]

The oxygen pressure vessel is at 90K, easy for steel as for graphite fibres. The helium pressure vessel is at 20K if possible, I didn't re-check if graphite fibres serve at this temperature, maraging steel is fine. The hydrogen tank is at low pressure, and nearly all aluminium alloys are just fine for 20K.

Most literature about rocketry dates back to the 1950s. Most difficulties are solved now, most attempts are abandoned, notably the exotic propellants. Cryogenic alloys are well known and no source of headache.