Why aren't expander cycle engines used on lower stages?

Question

Looking at the simplicity of BE-7, I was wondering why dual closed expander cycle engines are not used more commonly and, as far as I know, are not used as lower stage engines at all.

A commonly cited reason is that closed expander cycle engines don't scale well, and it looks like they tap out somewhere around 150 kN. But from here, it seems like open expander cycle engines don't have this limitation. And in fact, BE-3U has 710 kN of thrust.

The problem with open expander cycle, as far as I understand it, is that it is not very efficient (since some portion of the propellant is ejected unburnt). But why not just redirect this propellant to do autogenous pressurization as shown in the diagram below?

It seems to me that this cycle would have similar efficiency to staged combustion engines that do autogenous pressurization (e.g. Raptor), and should be able to achieve thrust similar to that of many low stage engines (e.g. Merlin). All while being extremely simple.

Am I missing something here?

Some more rationale for potential advantages of this design:

1. More efficient than open expander cycle because turbine exhaust is not wasted but returns to the propellant tanks. The assumption here is that most of the returned propellant condenses into liquid as it comes in contact with subcooled propellant in the tanks (which I understand to be the case for autogenous pressurization).
2. There is no need to carry additional pressurant (e.g. highly compressed helium). A small portion of propellant will need to remain in the tanks after all the fuel is burnt to keep it pressurized. But as far as I understand, it will be less than 1% of the fuel.
3. The engine has much less complexity as compared to staged-combustion or gas generator cycle engines - so, is much more reliable.

Answer 1

It seems to me you've got two questions: 1) Why can open-expander-cycle engines be larger than closed-? and 2) Why aren't there more expander-cycle sea level engines? Your question[s] shows you are already aware of the scalability problems that haunt expander engine designers. Before we can look at where such problems originate, let's talk a bit more about how expander-cycle engines operate.

An expander-cycle engine is a pumped engine, but rather than using a gas-generator (which is basically a small rocket engine, but burned with an O/F ratio far off of the stoichiometric ratio to keep exhaust temperatures low) to power its turbopump, an expander cycle uses the phase change of its liquid propellant to provide the pressure needed to run the turbopump. This phase change is induced by regeneratively cooling the combustion chamber, making expander engines extra efficient as it utilizes what would otherwise be waste heat to do the work required to run the turbopump.

The takeaway here is that expander-cycle engines require waste heat to do the work of turning the pump. This is where we start to run into scaling issues. If you double the dimensions of your combustion chamber, you require 8 times the volume of propellant to fill it, but you only have 4 times the surface area from which to obtain waste heat. Eventually as you scale it up, you will run into heat flux issues where you simply cannot obtain enough work from the limited cooling area to pump the volume of propellant required to run the engine.

But you can postpone that issue if you can keep your combustion chamber smaller. This has the delightful advantage of increasing your combustion pressure and consequently your performance. The trick here is preventing backflow problems. If you're piping your turbopump exhaust into your combustion pressure, you need to ensure that the pressure of the exhaust exceeds your chamber pressure or things will begin to flow the wrong way. This limits your chamber pressure, as your turbopump exhaust pressure will never be very high, due to it all coming from the gasification of your propellants.

In fact, it even limits how efficient your turbopumps can be. If you design a pump with a very high pressure-ratio (a ratio of the pressures of the flow driving the pump vs. the flow being driven by the pump), then your pump feeding propellant into the chamber could cause your chamber pressure to exceed your pump exhaust pressure even before combustion begins. And that's a shame, because more efficient turbopumps require less work to drive the same volume of propellant.

All these backpressure problems go away if you disconnect your pump exhaust from the chamber entirely. Now you've got the open expander cycle. Now you can make a higher-pressure chamber and a more efficient pump and you can crank your thrust up. The open expander cycle has another bonus, which is you can provide ullage to your tanks just by venting the boiloff through the pump system and out the nozzle. Another bonus is you also start your pumps spinning, so it's incredibly easy to re-light your engine and you get virtually unlimited ignitions. There's a reason the RL-10 is so successful.

Now onto question two...

Here the speculation begins on my part, simply because well, sea level expanders do exist. Or they're about to. At least, JAXA is building one and I feel pretty confident that they'll succeed. So I'll answer instead "why aren't there more"?

I think the answer is threefold. Firstly, many of the advantages of an open-expander-cycle engine aren't required at sea level. You don't need free ullage, you only need one ignition, and super-high TWRs aren't that helpful. As a result, people have been building gas generator boosters & sustainers for a very long time, and a substantial technology gap has emerged. Why use poorly-known technology when you can use very well-understood technology? Maybe with Mitsubishi's efforts, this technology gap will start to close.

Secondly, expander engines have historically been INCREDIBLY expensive to produce. Since you get more performance by more efficiently cooling your combustion chamber, the regeneratively cooled chambers (and nozzles) are full of very very dense holes. That's very hard to manufacture traditionally This is the same reason the SSME was so costly (among others), and it's why it's often cited that the RL-10s are the most expensive part on any rocket they ride up on. This goes hand-in-hand with the first reason. If you need the advantages of an expander-cycle, the costs may be justified, but they're not for a sea-level booster motor. I believe the cost will begin to go down substantially as additive manufacturing matures and we might start to see more sea-level expanders.

Finally (and my shakiest answer), I think it's also because you can't have as large a nozzle at sea level. If your expansion ratio is much too high, you're going to underexpand your thrust too much and at best loose thrust and at worst destroy your nozzle. I've been saying that expander cycles get their turbopump work out of cooling the combustion chamber, but they also get it out of cooling the nozzle. Not to mention that nozzles are also subject to the square-cube law, and it turns out that big sea-level optimized nozzles just won't give you the work you need to run your larger pumps. Your mileage may vary.

Answer 2

That "Inside the LEO Doghouse" article you found is a very good one. It's written by a guy I kind of work with and if you didn't read the whole thing, it's worth taking the time to.

1. Open expander cycles can still be very efficient. You can get Isp with LOX/LH2 up in the vicinity of 450 s, which is only a few s below RS-25 & RL-10.

2. You have to understand that the biggest performance driver for an expander is the turbopumps. The biggest constraint then is what's backpressuring your turbines. Since in a closed expander, you must dump the turbine discharge into the MCC, your turbine discharge pressure has to be higher than the MCC pressure. That means that the pressure ratio across your turbines will be very limited, on the order of 1.5-2.5. The higher the PR, the more efficient your turbine will run. The only way to increase that PR in a closed expander is to run the MCC at a lower pressure (like RL-10) which limits overall thrust/performance or give your turbine higher pressure fluid going in, but that makes for more work the pump side has to perform which has to be powered by the turbine. That work, of course, has to come from somewhere, which leads me to the next big limiter on expander cycles:

The secondary limiter on expander cycles is the amount of enthalpy you can pick up from cooling your combustion devices. It's easy to make a chamber longer to increase surface area for heat pickup, but ultimately, you're temperature limited by the turbine materials. You're also infringing on your engine envelop that way. Another way is to increase the turbine mass flowrate, but again, that's more work that the pumps have to do. As you scale up in thrust class, these things like heat pickup and pump/turbine work don't scale 1 for 1. It's all very circular and iterative with closed expanders and there's tradeoffs everywhere. Unless we get massive breakthroughs in materials science, there's only so much we can get out of that cycle.

Interestingly, SSME has a chamber pressure in the vicinity of 3,000psi, so you can imagine what the pressure levels in the rest of the engine are like. Before it gets to the chamber, it has to go through all of the coolant lines, the preburners, and finally the injector. Some of that also gets tapped off to power the LPFP and then gets used for tank repress. Coming straight out of the HPFP, the LH2 is at like 7,000 psi! It's insane.

ORRRRRRRR, you can open the turbine discharge up to atmosphere as in an open expander and your turbine PR instantly goes from <2 to >10. With that, many of these issues aren't as bad and you have a lot more room to scale up. I got the cycle to close at around 45klbf for an open expander that I work on, and that is based on real hardware that's actually been tested. There's a lot more room to go even higher than that too if we had different pumps.

Yes, an open expander is less efficient, but not exactly why you think. You're right that the loss in efficiency comes from the amount of propellant that remains unburnt but directing it to the tanks for repress isn't going to do much--it takes so little to repress the tanks so you end up venting the rest. The smarter thing to do is eject that fluid out of a much smaller nozzle so you're at least getting something out of it (like Merlin, even though that's a GG cycle) that often get's used for roll control on a single engine vehicle or attitude control on a multi-engine vehicle. The losses come from the pumps having to put work into that fluid but as you pointed out, that fluid is being ejected unburnt, so you're getting way less work out of it than you put in. Regardless of if you use the propellant for repress, your pumps are still putting work into the fluid that they're not getting back out in combustion. Draw a control volume around your engine and you'll see what I mean.

Another problem is the specific heat of different propellants make some better than others for different cycles. For the expanders that we're talking about, LH2 is going to get you the most enthalpy from cooling the MCC, plus it's effortless to light, but LH2 makes a terrible core stage fuel. And with expander cycles being so sensitive to heat pickup, LH2 having a nice low critical pressure (around 200 psia if I recall) makes it better to work with since you don't have to deal with 2-phase flow in your coolant channels. Methane, on the other hand has a much higher critical pressure (almost 700 psia if I recall) so you can easily run into 2-phase flow in your coolant channels unless your pressures are high enough. 2-phase flow creates unpredictable heat transfer and can lead to hot spots and burn-throughs of the chamber hot wall if it gets bad enough. Methane is also a PITA to light.

You are correct about your additional potential advantages #2 & #3. But as long as we're comparing to SC or GG cycles, there's one more added benefit. Because everything in an expander cycle is so intrinsically coupled together, they're safe in an anomaly. Say your fuel pump begins failing for whatever reason--it's not putting out pressurized fluid, so the turbines don't get what they need and the engine slowly powers down. Say your Ox Pump or Main Ox Valve fail, your mixture ratio will start going down, your coolant won't get enough heat to power the turbines, and the engine shuts down. Say you even have a failure of one of the fuel valves--your mixture ratio is going to go way up and burn through your chamber wall. Once that happens, your coolant leaks out into the chamber instead of going to power the pumps, and you guessed it, the engine shuts down. It's very unlikely that you get a vehicle destroying explosion when an expander has a failure.

The LOX/LH2 open expander I work on bleeds about 2% by mass of the propellant overboard.

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Anton brought up some good points that I missed. However, there are some things I take issue with.

What do you mean with all the ullage talk? The boiloff is the ullage. Another place you definitely don't want 2-phase flow is going into your pumps, so I'm not sure what you mean by running the boiloff through your pumps.

Also, a lot of engines start with the pumps already spinning. That's just called tank-head start like the staged combustion SSME does and that doesn't really have much to do with how easy an engine is to light. The propellant combo has a way larger effect on ease of ignition. And "virtually unlimited" starts is not really a thing that exists. Starting a rocket engine takes a real toll on all of the hardware. Pumps are running off-design, so seals rub, and if they're hydrostatic bearings, those are rubbing too. The chamber takes a beating from the mixture ratio excursions and heterogeneous flow distribution, especially if it has to pass through stoichiometric, and will eventually have a burn-through. That's why # of starts is a very high priority design requirement when we're setting out to develop any new engine.

You're right that RL-10 is an extraordinarily reliable engine though. But it's not the go-to for upper stage engines just because it's an expander. It's because it has excellent performance and reliability. The reliability is key when you're talking about upper stage engines, where you often need multiple starts. Part of that reliability is from it being an expander though--the fewer combustion devices you have, the better. GG's are often used as upper stage engines too though--SpaceX M1vac and J-2X. I also believe that SpaceX's Starship upper stage will also be powered by staged combustion Raptors.

I was told by a company insider once that the RL-10 basically subsidizes everything else at Aerojet until RS-25 restart came along. The cost with additive has made things cheaper though. The entire development program I have been working on for an open expander has been under 18Mil. But simply for hardware and labor, we're only talking about 2-3Mil per copy. It is almost entirely additive. The reason the SSME/RS-25 is about $40M per copy and a 7 year lead time is mostly the nozzle. The nozzle has 1,080 individual coolant tubes that have to be braised together. Much of that work gets done by hand. Until recently, that would take 6 YEARS per nozzle. I think we've got it down to 3 or 4 years now, but not because of additive, just process changes. NASA is incorporating additive into RS-25 bit by bit now to reduce cost, but it's progressing very slowly.

You mention nozzle size at SL too. There are technologies to mitigate that now. Aside from Aerospike, which has been around for a long time, we now have Thrust Augmented Nozzles and Dual-Bell nozzles, but both of those are at least 10 years away from flight readiness.