The Helium Bleed Cycle

[Cunjo Carl]

Hey! I'm still with it . It's been a rough couple seasons, but I'm very slowly improving again.

For long term health reasons I can't quite science like I used to. I've had an idea floating in the back of my head for months though, and I was hoping someone might help me run the numbers? The idea is to slightly boost the efficiency of a simple, cheap pressure fed kerolox engine like the Kestrel (or similarly with the Xombie) by using the Helium that's onboard anyways for pressurizing the prop tanks.

The Helium Bleed Engine

Cycle:
*  Start with high pressure Helium (60 - 200bar) in a COPV stored in LOX (10bar, ~120K)
*  Freely expand He to 50bar
*  Warm He to T_h of ~240K using a heat exchanger in RP1 (~ room temp).
*  Expand He in turbine to 10bar, and T_c ~ 120K
   Use the turbine power to slightly boost the prop pressure using a turbopump
*  'Bleed' the 10bar He back into the prop tanks, like normal, equilibrating it to roughly the prop temps.

Given the He volumetric flow rate = the prop volumetric flow rate, and the assumption of a chunky junky turbopump, what outlet pressure might we get for the propellants? Alternatively, assuming an 8bar chamber pressure with 12bar feed, how low can we get the prop tank pressure?

Is it worth it? Probably not, but curious minds want to know!

[sevenperforce]

I don't have the energy, time, or mental capacity to run the numbers right now, but I like the idea! Back of the envelope says it is good.

[StrandedonEarth]

You start by wanting to improve a pressure-fed engine, but then start mentioning turbines and turbopumps, which are not needed on a pressure-fed engine. 

Although I am curious as to the effect of bleeding helium or hydrogen into the combustion chamber, to boost ISP. It would also cool the exhaust, perhaps allowing it to run closer to stoichiometric.

[Nuke]

dont you need back pressure for those kind of rockets anyway? because for a lot of rockets having the fuel tank pressurized is necessary to maintain structural integrity. 

[sevenperforce]

1 hour ago, StrandedonEarth said:

You start by wanting to improve a pressure-fed engine, but then start mentioning turbines and turbopumps, which are not needed on a pressure-fed engine. 

Right. It's no longer a pressure-fed engine at all; it's now a proper turbopump-fed engine, with correspondingly better performance. 

The trick, as I understand @Cunjo Carl's idea, is to use the temperature differential between the LOX tank and the RP1 tank to operate a heat engine, essentially a helium-based expander-cycle turbopump, and allow the helium to exhaust into the tanks as it ordinarily would. I'm not sure whether the heat differential between the LOX tank and the RP1 tank would provide enough power. 

The Falcon 9/H already expands its COPV helium through a heat exchanger at the engine to increase its volume and use less as a pressurant; it would be straightfoward enough to design a similar setup but use it to run a turbopump before it is dumped into the tank. The question is whether the decreased tank weight, decreased helium requirements, and increased efficiency would outweigh the mass of a turbopump.

1 hour ago, StrandedonEarth said:

Although I am curious as to the effect of bleeding helium or hydrogen into the combustion chamber, to boost ISP. It would also cool the exhaust, perhaps allowing it to run closer to stoichiometric.

Triprop engines are a thing. You'd need a LOT to make it work, though.

50 minutes ago, Nuke said:

dont you need back pressure for those kind of rockets anyway? because for a lot of rockets having the fuel tank pressurized is necessary to maintain structural integrity. 

Yes, you definitely need the back pressure but this way you don't need the weight of pressure-fed tanks.

[Cunjo Carl]

Yep! I guess engineering-wise it's like a halfway point in complexity and performance between the pressure fed and expander/bleed cycles, which is how I approached it. It fills a niche no one asked for, but hey that's why it's new!

For advantages, there's no need for a regenerator (so you can use a simple ablatively cooled chamber), no extreme temperatures or chemical conditions across the turbopump, no chance of saturation in the turbine, the He is inert so you can use leaky seals, and it can work with garden variety kerolox. Just futzing with numbers in my head, I'm thinking we'd get 0.5 - 2 MPa of chamber pressure boost out of it including losses?

I'd love some actual numbers though. I could easily be full of hot air . Like I said, its probably not worth it, but I'm curious what it could do on paper.

 

[sevenperforce]

On 4/7/2020 at 10:39 AM, Cunjo Carl said:

I'd love some actual numbers though. I could easily be full of hot air . Like I said, its probably not worth it, but I'm curious what it could do on paper.

What you need to know is how much helium pressurant a pressure-fed stage needs in comparison to a pump-fed stage of equivalent size. Is it twice as much? Ten times as much? This tells you how much helium you have to work with, and then you can apply a Carnot cycle to determine how much total mechanical energy you can extract from the pressurant mass at your disposal. You can then divide by the total propellant mass to figure out what kind of pressure drop you can produce from that amount of energy, which tells you the pressure reduction (and associated weight reduction) in your tanks.

Note that there is a positive but diminishing feedback loop: the mechanical energy available from your Carnot cycle is an inverse function of the outlet pressure, and the more energy you have, the lower that outlet pressure becomes.

It's entirely possible that pressure-fed kerolox stages already utilize heat from the kerosene to their advantage, at least on one side. If helium pressurant is exhausted into the RP-1 tank directly at LOX temperatures, it will warm and expand, adding supplementary pressurization, meaning you need less of it to get the job done. As a corollary, if you're exhausting helium into the LOX tank after running it through an RP-1 heat exchanger, you're going to warm the LOX, boiling small amounts of it and causing it to self-pressurize.

The helium pressurant system on the Falcon 1, with the Kestrel engine, already used a titanium heat exchanger around the engine to transfer heat to the helium pressurant -- far more than you could get from the RP-1 tank.

[Cunjo Carl]

4 hours ago, sevenperforce said:

What you need to know is how much helium pressurant a pressure-fed stage needs in comparison to a pump-fed stage of equivalent size. Is it twice as much? Ten times as much? This tells you how much helium you have to work with, and then you can apply a Carnot cycle to determine how much total mechanical energy you can extract from the pressurant mass at your disposal. You can then divide by the total propellant mass to figure out what kind of pressure drop you can produce from that amount of energy, which tells you the pressure reduction (and associated weight reduction) in your tanks.

The amount of Helium (mass-wise) should just be found from doing PV=nRT on the propellant tank pressures and temperatures, for a given O:F ratio. Let's rephrase the problem backwards as: for a 12bar propellant pressure at the turbopump outlet, how low can we make the prop tank pressure? For adiabatic isentropic expansion of Helium (monatomic),  Work = mass*Cp*(T1-T2), or in context Work = mass*(5/2)*R*T1*(1-(P2/P1)^(2/5)) . I forgot how to do the VdP work for a turbopump though, and can't surf enough to find out

 

4 hours ago, sevenperforce said:

Note that there is a positive but diminishing feedback loop: the mechanical energy available from your Carnot cycle is an inverse function of the outlet pressure, and the more energy you have, the lower that outlet pressure becomes.

It's true! But there will also be a much stronger negative feedback from:   As we lower the prop tank pressure, we'll need to bring less He (mass wise), and so our available energy will decrease. A slightly higher prop tank pressure (2-4 bar) isn't so bad, because it makes the turbopump way simpler for cavitation reasons, and we can balloon tank the propellants. A 2-4bar prop tank is kinda what I'm hoping for if we have 12 bar propellants coming out of the turbo pump... Not that anyone's having troubles with their balloon tanks at the moment!

 

4 hours ago, sevenperforce said:

It's entirely possible that pressure-fed kerolox stages already utilize heat from the kerosene to their advantage, at least on one side. If helium pressurant is exhausted into the RP-1 tank directly at LOX temperatures, it will warm and expand, adding supplementary pressurization, meaning you need less of it to get the job done. As a corollary, if you're exhausting helium into the LOX tank after running it through an RP-1 heat exchanger, you're going to warm the LOX, boiling small amounts of it and causing it to self-pressurize.

The helium pressurant system on the Falcon 1, with the Kestrel engine, already used a titanium heat exchanger around the engine to transfer heat to the helium pressurant -- far more than you could get from the RP-1 tank.

Absolutely for sure on both accounts! For rocket simplicity, I wanted to avoid having a hot He stream or autogenous pressurization. They'd both help the rocket's overall efficiency *tremendously* though and would make interesting follow-on problems!

Edited April 8, 2020 by Cunjo Carl
error fix

[sevenperforce]

1 hour ago, Cunjo Carl said:

The amount of Helium (mass-wise) should just be found from doing PV=nRT on the propellant tank pressures and temperatures, for a given O:F ratio. Let's rephrase the problem backwards as: <snip>

As we lower the prop tank pressure, we'll need to bring less He (mass wise), and so our available energy will decrease.

This is why I was saying we should start with a known and work forward. We certainly don't want to end up bringing more helium to run our system, so if we start with the amount of helium that comes standard in a pressure-fed stage, and it isn't enough to give us a meaningful pressure drop, then we know we are dead in the water (or, in the alternative, we need to look into something like an engine heat exchanger). 

1 hour ago, Cunjo Carl said:

For rocket simplicity, I wanted to avoid having a hot He stream or autogenous pressurization. They'd both help the rocket's overall efficiency *tremendously* though and would make interesting follow-on problems!

Understood -- although the autogenous pressurization of the LOX tanks on Falcon 1/9/H is a very minor contribution. I will say that of all the hot fluid streams you can possibly have in an orbital launch vehicle, superheated helium is probably the least problematic thing. 

[sevenperforce]

For reference, the "standard" pressure-fed cycle assumes that a heat exchanger will be used at the engine to increase efficiency:

The Apollo Descent Module engine tanks used a helium tank that circulated through the propellant tanks, as you propose, to bring them to ambient temperature before exhausting to increase efficiency.

I'm digging around to try and figure out how much helium is used in a pressure-fed stage that doesn't already run it through a chamber heat exchanger.

 

[Cunjo Carl]

38 minutes ago, sevenperforce said:

For reference, the "standard" pressure-fed cycle assumes that a heat exchanger will be used at the engine to increase efficiency:

The Apollo Descent Module engine tanks used a helium tank that circulated through the propellant tanks, as you propose, to bring them to ambient temperature before exhausting to increase efficiency.

I'm digging around to try and figure out how much helium is used in a pressure-fed stage that doesn't already run it through a chamber heat exchanger.

 

Interesting. I didn't know that was standard! If you know of a reasonable choice of temperature for the heated He entering the prop tanks, please feel free to use it! I agree Helium is probably the most conceivably benign fluid to have hot.

Edit: (with the temp of the He entering the turbine raising accordingly as well, I'd assume)

Edit 2: If T1/T2 stays the same, I think physically we should get the same work per tank volume. So I guess further heating the helium doesn't matter too much except that it lowers our dry mass. No complaints there!

Edited April 8, 2020 by Cunjo Carl

[sevenperforce]

49 minutes ago, Cunjo Carl said:

Interesting. I didn't know that was standard! If you know of a reasonable choice of temperature for the heated He entering the prop tanks, please feel free to use it! I agree Helium is probably the most conceivably benign fluid to have hot.

Edit: (with the temp of the He entering the turbine raising accordingly as well, I'd assume)

Edit 2: If T1/T2 stays the same, I think physically we should get the same work per tank volume. So I guess further heating the helium doesn't matter too much except that it lowers our dry mass. No complaints there!

The biggest consideration (and possible stymie) to your idea is that heating the helium in an exchanger at the engine and then dumping it directly into the tank will immediately do Carnot-cycle work against the propellant, without the need for any turbopump at all.

[Cunjo Carl]

2 hours ago, sevenperforce said:

The biggest consideration (and possible stymie) to your idea is that heating the helium in an exchanger at the engine and then dumping it directly into the tank will immediately do Carnot-cycle work against the propellant, without the need for any turbopump at all.

Er, you shouldn't be able to get anything like Carnot efficiency by dumping a high pressure gas straight into a low pressure chamber! Consider the reverse process.

[mikegarrison]

120K is *way* below the freezing temperature of RP-1. Won't that be a problem?

Sure, helium probably doesn't have much thermal mass, but still, it seems like you might form wax.

Edited April 9, 2020 by mikegarrison

[Cunjo Carl]

5 minutes ago, mikegarrison said:

120K is *way* below the freezing temperature of RP-1. Won't that be a problem?

If we warm up the He somewhere where the RP1 is flowing, the RP1 will never cool down that much because it has so much more thermal mass.

[StrandedonEarth]

Wait..... you want to use the power of the expanding He to add pressure to the props....

There is only so much power available in the pressurized He, no matter which way you use it, and running it through a turbopump will lose some to friction etc.

Sounds similar to a perpetual motion machine, trying to get free power....

I don't think thermodynamics will allow you to get any gain out of this. But the only ways to be sure is to either crunch numbers or build test hardware. OTOH, the whole point of pressure-fed is to KISS. Are there even any RP-1 pressure-fed engines? Modern pressure-feds are usually hypergolic, AFAIK...

[IncongruousGoat]

5 minutes ago, StrandedonEarth said:

Are there even any RP-1 pressure-fed engines? Modern pressure-feds are usually hypergolic, AFAIK...

They weren't even that common historically. The only two I can think of off the top of my head are Kestrel (Falcon 1 upper stage) and the LR-101 (vernier engine used on Atlas, Thor, & Delta).

[sevenperforce]

10 hours ago, Cunjo Carl said:

Er, you shouldn't be able to get anything like Carnot efficiency by dumping a high pressure gas straight into a low pressure chamber! Consider the reverse process.

What I mean is that due to PV=nRT, running the helium through the engine's heat exchanger already increases the pressure and thus the expansion on outlet, and thus increases the available thermodynamic work per unit mass of helium, reducing the needed initial mass of helium. If you step down the pressure in a turbopump, you gain mechanical work which you can use to step up the pressure between the tank and the combustion chamber, but you lose pressurant capacity in the helium. Of course, that's fine -- it is what you were trying to get, anyway -- but my suspicion is that you lose more pressure in the tank than you gain in the turbopump, requiring you to carry more helium. The question is whether the mass of additional helium you need is greater than the mass you save by having less massive tanks.

It may not seem like a Carnot cycle because it's not immediately reversible, but it is reversible in the context of the work it does. If the helium was expanding into a piston inside the propellant tank to fill the volume, it would do the same amount of work but would be reversible.

To a first approximation, I would suspect that the square-cube law will dictate whether you lose or gain with this approach.

 

9 hours ago, IncongruousGoat said:

They weren't even that common historically. The only two I can think of off the top of my head are Kestrel (Falcon 1 upper stage) and the LR-101 (vernier engine used on Atlas, Thor, & Delta).

OTRAG was kerosene plus hypergolic oxidizer. Armadillo's QUAD is room-temp ethanol plus LOX. But yes, most pressure-fed solutions are hypergolic.

[Cunjo Carl]

Oof, I wish I could interact more. I'll be back in a week or two!

[RuBisCO]

So let me get this straight, the advantage over conventional heated helium tank pressurization systems is that the helium can drive the turbo pumps allowing for much higher engine pressures then a normal pressure fed engine could provide.  The problem I see is the amount of hot Helium needed to run the turbines will probably easily exceed the amount of warm helium needed to pressurize the tanks. 

To pressurize 1 m^3 of tank to 2 atm using Helium at 273 K requires 357 g of Helium according to ideal gas law, a Centaur rocket of 20 tons of propellant requires at least 63 m^3 or 22.5 kg of Helium. If these were pressure feed tanks at 10 atm that would come to 113 kg of Helium Needed. Assuming ideal gas law stays correct (which it does not, not even with helium) 1.05 m of helium at 200 atm and 90 K would be needed to store 113 kg of helium, or a sphere 1.26 m wide. For 2 atm case only 0.22 m^3 is needed at 90 K and 200 atm.

Now if someone wants to calculate how much work the helium does going from 200 atm at 0.22 m^3 to 2 atm at 63 m^3 from 90 K to some pre-turbine temperature then to a post turbine temperature of 273 K,please do, I going out for a run now. 

 

[mikegarrison]

Big picture here -- there is no such thing as free work. What you seem to be trying to do is expect that running a pressurized gas through a turbine to drive a fuel pump is more efficient than just using that same pressurized gas to directly pressurize the fuel.

I suppose it might be, but pumps are heavy and complicated and expensive, so is it worth it?

[sevenperforce]

38 minutes ago, mikegarrison said:

Big picture here -- there is no such thing as free work. What you seem to be trying to do is expect that running a pressurized gas through a turbine to drive a fuel pump is more efficient than just using that same pressurized gas to directly pressurize the fuel.

It doesn't necessarily need to be more efficient if you can save a lot of weight by reducing the pressure in the tanks and thus reducing the weight of the tanks. Could also be used to adapt existing pressure-fed engines to work with larger stages (and correspondingly better mass ratios) than would otherwise be possible.

[mikegarrison]

19 minutes ago, sevenperforce said:

It doesn't necessarily need to be more efficient if you can save a lot of weight by reducing the pressure in the tanks and thus reducing the weight of the tanks.

That only works if it's more efficient.

Or ... OK, I think I see what you might be getting at. You are saying you don't need to pressurize the whole fuel tank, just the fuel that is going out the pipe.

Edited April 16, 2020 by mikegarrison

[sevenperforce]

14 hours ago, mikegarrison said:

That only works if it's more efficient.

Or ... OK, I think I see what you might be getting at. You are saying you don't need to pressurize the whole fuel tank, just the fuel that is going out the pipe.

Right. Pressure-fed rockets are hella simple. Helium at super-high pressure pushes against fuel in a tank at lower (but still very high) pressure, which is thus pushed into a combustion chamber at lower pressure. The pressure in the tank must be greater than the pressure in the combustion chamber in order to maintain positive flow.

Unfortunately, this means the tanks must be very strong -- stronger (in an absolute sense, not for their size) than the combustion chamber itself! This means a low chamber pressure (which is inefficient) or a very heavy tank (which hurts mass ratio) or both. For low dV burns (or for stuff where inefficiency is okay, like RCS), this extra weight is not too big a problem, but when you need to squeeze out lots of dV, it hurts you. According to this Rochester Institute of Technology whitepaper which I completely have not vetted, moving from a pressure-fed cycle to a pump-fed cycle can save 90% of tankage weight for burns lasting longer than a minute. So if the weight of a turbopump is less than 90% of your tank weight, you should switch.

On to the maths (or at least back of the envelope maths) for @Cunjo Carl's idea. My suspicion is that the available work-energy in the pressurized helium is going to be the same regardless of whether it is used to run a turbopump or is used to pressurize the entire tank. There might be some inefficiencies on either side that I'm not thinking of, but it's probably going to be roughly the same amount of work-energy at the end of the day.

But localizing the high-pressure region to the turbopump can still have major benefits. If you can reduce the head pressure in the tanks (let's say to halfway between a typical pressure-fed cycle and a typical pump-fed cycle) by putting the helium through a simple turbopump first, you can cut the weight of the tanks to around 55% what they would otherwise be. And since your turbopump has no combustor and is operating on inert helium, it doesn't have to be extraordinarily heavy and it doesn't need to be made of ridiculous corrosion-proof metals. So you should probably come out on top. 

[Cunjo Carl]

So good news for me, I have no idea for how long but my hands cleared up a bit, and the place I consult for is temporarily closed so I got to use some time to brush up on thermo and figure this out instead! It was surprisingly nice to just do something silly.

Also good news for me, my instincts were on point and the engine would work roughly as claimed. Despite this, both I and others pointed out that it probably won't be a terribly popular engine cycle for lack of a proper niche. But at the bottom line the pressure boost numbers wind up looking tantalizingly usable, and the engine would would need only the simplest conceivable turbopump from an engineering perspective (for 20 reasons), which is why I find it interesting. In all cases this cycle would use significantly lighter tanks and less Helium than an equivalent pressure fed, but it has to carry the turbopump. Pressure fed rockets are still considered and tested on occasion by the way, like NASA's 2017 ICPTA! I'll use it for the example. To recap, here's how the cycle works with letters for the subscripts used in the formulas later.

The Helium Pressurant Brayton Cycle (renamed )

The Helium follows this open cycle, in order:
i) Leaves the COPV, decompressing in some regulators (an ignored step for this)
h) Leaves the high temp heat exchanger or regenerator (isobaric expansion)
ad) Leaves the turbopump after doing work (adiabatic expansion)
t) Arrives at the prop tanks, after having gone through an optional second heat exchanger to raise/lower its temp again (isobaric volume change, probably expansion) If no second heat ex is used, T_t = T_ad and this step can be ignored.

Meanwhile, the propellant follows this open cycle, in order:
t) Leaves the prop tanks
c) Arrives at the chamber with its pressure boosted from the turbo pump

With the subscripts from above we can solve for the pressure boost our propellant gets from the turbopump between the tanks P_t to the chamber P_c. This assumes the prop tanks at roughly the same temp and pressure, like on the methalox ICPTA.
P_c = P_t*(1 + Efficiency*CCF*MW_He*(5/2)*(T_h/T_t)*(1-(P_h/P_t)^(-2/5)))
also,
P_c = P_t*(1 + Efficiency*CCF*MW_He*(5/2)*((P_h/P_t)^(2/5)-1))   special case, the formula simplifies when no second heat ex is used. If T_ad < ~180k it's probably smart to remove the CCF correction factor term for methalox.
T_ad = T_h * (P_h/P_t)^(-2/5)
m_He = ~ 100*CCF*MW_He*P_t*V_t/(R*T_t)      (the factor 100 = 10^5 Pa/Bar * (.001 kgmol/mol) SI's weird sometimes)
Helium Savings Factor = m_He,pressureFed/m_He = ~ P_c/P_t

MW is in Daltons, R=8.314, pressure in Bar, everything else is in SI. This is to 0th order. It assumes incompressible propellants and no pressure drops in the prop lines. To fudge factor in some of those losses and account for light weight cheap construction, an abysmal overall turbopump efficiency of 25% seems appropriate. To account for non-idealities, friction, injection pressure loss and tubing heat transfer in the He the actual P_h, T_h and CCF would all be a bit higher than on paper. CCF is the 'cumulative collapse factor', the fudge factor by which the high temp helium we send into the prop tanks is immediately cooled and shrinks... so we need more of it.

Let's check how well this pressurant brayton cycle would work with a real example. Fortunately NASA released some solid hints at numbers to their 2017 ICPTA pressure fed methalox lunar lander, so I plugged in those! Then, I chose a gentle T_h of 200C, which is cool enough to use things like an all-aluminum turbo/tubing, and common elastomeric gaskets/seals. And finally I back-calculated the tank pressure P_t we'd need to produce the ICPTA's same (approx) prop delivery pressure P_c. By pure serendipity, no second heatex is needed with this setup .

P_c = P_t*(1 + Efficiency*CCF*MW_He*(5/2)*(T_h/T_t)*(1-(P_h/P_t)^(-2/5)))
22 = 5*(1 + 0.25*1.5*4*(5/2)*(475/250)*(1-(25/5)^(-2/5)))

The results:  For the same 22bar propellant delivery pressure we can reduce the tank pressure and Helium usage by ~4.5x when switching to a pressurant brayton cycle, even when assuming a 25% efficiency turbopump running on only 200C, 25bar He. Meanwhile a 50% efficient turbopump would reduce the tank pressure and helium usage by ~9x and so on, though I think the 25% efficiency is more plausible. Is it worth it? It sure looks enticing, but probably not! Is it an interesting concept? Heck yeah!