I know there is an immense amount of engineering that goes into the shape of rocket motor nozzles. Maximizing the impulsive force transferred to the vehicle during combustion of the fuel.
I am wondering if a sort of flat plate design is feasible and maybe maximal? A plate with some large number of small combustion points. Each one shaped in a small scale to maximize it’s individual thrust. Might it be easier to engineer the maximum thrust of a smaller nozzle area? Then multiply that added efficiency over a large number of nozzles in a plate? Is there an inherent energy loss of multiple combustion points compared to one point?
I know there may be issues of proper fuel delivery across all the points that may be difficult. But is there any value to the basic concept?
So it is instructive to first look at the general one dimensional (rocket) thrust equation:
With F as the force, q the mass flow rate, Ve the exhaust velocity, P a the pressure of the ambient atmosphere, P e the pressure of the exhaust gases, and A e the area of the nozzle exit plane. One purpose of the expansion portion of the nozzle (after the throat, also referred to as the “nozzle exit cone” even though it generally isn’t conical) is to capture additional expansion of the exhaust products from the plume after it passes through the nozzle throat and convert it into impulse (which is the second component of the right hand side of the equation), but the primary impulse comes from just the momentum transfer of products from the chamber (where combustion occurs) through the nozzle throat (the first component). A second function is to allow for steering the rocket via thrust vectoring, either by physically gimbaling the nozzle exit cone, or by altering the flow properties in the cone via some kind of diverter or spraying extra fluid into the nozzle to cause shock waves (called liquid thrust vector injection).
There is a lot of engineering that goes into determining the optimal shape of the cone (generally a de Laval type diverging nozzle) for a given ambient condition (far more than just indicated by this 1D equation because the flow is a 2D complex axisymmetric or fully 3D phenomenon) to get as much efficiency as possible, but there are also a lot of tradeoffs. At ground level and low atmosphere the nozzle expansion efficiency doesn’t add that much because so much of the expansion is limited by the ambient pressure; in high altitude and vacuum conditions where the ambient pressure is effectively zero, you theoretically get an advantage by making the nozzle cone very long and capturing the full expansion of the still-hot exhaust products; however, all of that length is inert mass (and requires packaging in an interstage structure and space from the downstage) so in practice the length of the expansion portion of the nozzle even a high altitude/vacuum application is limited by practicalities. Some tricks can be played here such as having extensible exit cones that package up short but deploy to make a much longer expansion nozzle, but in general there are diminishing returns past a certain length in terms of what can be gained by expansion that make it not worth the additional mass.
As far as making a plate that is essentially a bunch of tiny combustion chambers with nozzle cones machined into it, or a plate that is a bunch of tiny chambers, you’d end up with a lot of extra mass for the same combustion volume, which is obviously inefficient. You also wouldn’t be able to gimbal the nozzles individually, although I suppose you could steer via differential thrust (reducing thrust on some nozzles and increasing them through others). You often see rockets that have a few smaller engines (either with one nozzle cone per combustion chamber or occasionally sporting two or more nozzles per chamber); these are generally less efficient but allow for better vectoring control or to prevent combustion instability problems that can come with larger combustion chambers.
An alternative nozzle design is the aerospike or plug nozzle:
These essentially turn the exit cone inside out, so the ambient pressure is holding the exhaust on the outside and the expansion is pushing against the spike or plug on the inside. These are less efficient overall but have the advantage of automatically compensating for change in ambient pressure as the vehicle ascends. No aerospike engine has yet flown on a production space launch rocket, but suborbital vehicles have flown with aerospike engines, and alternative aerospike engines were developed for the Space Transportation System (STS “Shuttle”) under IRAD by Rocketdyne (not accepted for political reasons), and a linear areaspike was developed and qualified for the X-33 Advanced Technology Demonstratorl which was a proof of concept for the Lockheed VentureStar Reusable Launch Vehicle (RLV) intended to replace Shuttle before the program was cancelled in 2001.
Everything you want to know about the fundamentals of rocket propulsion, suitable for the enthusiast:
Rockets are, at their most fundamental, heat engines–no different than gasoline engines or jet turbines. As such, it’s helpful to think of them in those terms.
All heat engines take a hot, high-pressure gas and expand to a cold, low-pressure gas, performing mechanical work in the process. Rockets achieve this with their nozzle: the products of the combustion chamber exit the throat, expanding as they travel the length of the nozzle, and pushing on the curved sides of it. This pushes the rocket forward. When it finally exits (ideally, at the ambient air pressure), it has expanded by dozens to hundreds of times.
This runs into some practical issues of course. Two of them, both related:
The hot gas is so hot that it may melt the nozzle
The gas is wasting that heat that goes into the nozzle, decreasing efficiency
The first problem is solved in several different ways, from intentionally limiting the combustion temperature, to running coolant through the nozzle walls, to using extremely heat resistant materials, to using ablative surfaces that get slowly vaporized.
The second is largely helped by having a large nozzle. Square-cube scaling helps here: double the dimensions of the nozzle, and take roughly 8x the flow, but has only 4x the surface area. So the losses are less.
As a result, my expectation is that a large array of small combustors would not be very efficient. The gas would lose an enormous amount of heat due to the large surface area of the nozzles, and be difficult to cool for the same reason. One reason aerospikes have never really taken off is due to these cooling issues.
I worked in NASA Glenn’s Rocket Engine Test Facility for several years. I can tell you that the bulk of the research is getting the fuel and oxidizer to mix and ignite properly. You can’t just run the two into the combustion chamber. They squirt out of injectors that allow the two streams to impinge in mid air. We tested countless schemes involving combinations of fuel and oxidizer holes and their angles. Some were just holes. others were slots others were holes annular to each other. We actually did early work on hydrogen/oxygen engines a long time ago. A single firing test would involve how fast you ramp up the pressures and how and when to ignite. The flame for each injector couple must ignite and stabilize. After that, as one scientist told me, there is nothing more to learn.
The Shuttle engines have hundreds of these pairs (or triples, quads or whatever). You are basically proposing to place a small nozzle on each unit. That won’t work. The flame temperatures are well above material science and the walls must be cooled. The cold fuel and oxidizer is typically run through hollow walls of thousands of complex holes to carry away the heat. The fuel pressures also have to balance the combustion chamber pressures (2000 psi or so) to keep the walls of each passage from collapsing. Far easier to do this on one large nozzle rather than 200 small ones. The Shuttle throat is plated in pure gold to transfer every last bit of heat as possible.
Thanks for the reply.
I don’t see the gimble system as any problem. You can have a 3 or 4 cornered plate, with a central pivot point and actuators at the corners. I was vaguely aware of the specific design concepts of a single large nozzle. Your reply supplied a lot of additional specific information that I will need to chew on. The mass issue is very fuzzy. It is very difficult to suppose the trade offs. I am thinking the plate having the small nozzles being very closely spaced. Less than an inch apart if that is feasible. Maybe a ceramic material with minimal metal support frame behind. The central pivot point and actuators giving support. There might be an overall shroud/nozzle around the plate. My basic wondering about the concept, is if at a certain scale that multiple smaller combustion chambers, can be shaped more efficiently at small scale. I notice that there seems to be a top end. Rather than just making a bigger motor/nozzle, they employ multiple motors. Maybe going the opposite direction from this point may be more efficient. There would be a smaller volume in the individual nozzles to deal with all the complexities of the movement of the gases.
Also a great reply. Thanks so much. I did consider how difficult it might be to distribute fuel and oxidizer to so many chambers. But was really just wondering about the overall thrust that might be gained if all other technical difficulties were solvable.
Not really. The limits at the top end are due to the difficulty in maintaining combustion stability. The Russians never pursued nozzles as large as the F1 due to their inability to solve the combustion problems (they pursued efficiency in a different way).
Exceptionally large engines have been proposed; for example, the Sea Dragon. Unclear whether they could have solved the stability issues, but if it could have been built it would have been reasonably efficient given the cycle (a relatively poor pressure fed cycle).
Each nozzle would be so close to another that there might be positive or negative effects to each one. Almost as if the surrounding nozzles were creating a flow constriction either positive or negative to the scheme.
Quite the opposite. From a thermodynamic standpoint, the smaller chambers will lose more thermal energy by conduction through the chamber walls than larger ones. There are also viscous flow losses that are more significant with very small channels, and of course there is a minimum physical size that you could have injectors, igniters, et cetera. The mass flow rate scales as an area but the inert mass of the chamber scales with volume which, all things being equal benefits the larger engine, notwithstanding all of the extra mass that this manifold-integrated chamber has that is not structurally necessary. This would be extraordinarily inefficient even without consideration of the complexity of somehow milling all of these tiny chambers and nozzles. And even if you could make it work, you wouldn’t want to gimbal the entire manifold plate, as it would have a huge amount of inertia and geometric inefficiency that would result in ludicrously inadequate vectoring slew rates; you’d want to use differential thrust (by turning on and off thrusters in various parts of the plate) rather than trying to articulate it.
Sea Dragon was actually a pressure-fed design and operated at relatively low pressure, gaining efficiency (such as it was) by scale. Combustion instability rises with pressure because of high gradients within the chamber; if the average pressure is low, the degree of instability is limited. The downside is that it can only be scaled down to a certain level before having to switch over to a pump-fed system, and Sea Dragon has vastly more payload than anyone had interest in using.
I don’t understand what you are trying to say here.
I have not worked on Rocket Engines but have worked on Research Projects involving Gasification Injectors / burners by Pratt and Whitney / Rocketdyne. Have worked on gas turbine buckets and gasifier injectors.
Wanted to highlight a few considerations that may have some bearing here :
99% + pure Oxygen : Many rocket failures are due to a mishap somewhere in the oxygen system. Oxygen is the prima donna when it comes to injector designs : there are NO oxygen compressors (liquid oxygen is pumped and vaporized), the piping and path for oxygen has to avoid any sharp bends - it needs to be smooth, otherwise oxygen will eat up stainless steel like candy. Incolloy provides some protection against oxygen but incolloy is extremely difficult to machine and making an array of nozzles will be difficult.
So an array of small nozzles will require intricate tubing / piping of oxygen, which will be very difficult to implement / unsafe.
As the fuel and the oxygen exit the nozzle, they start reacting and the temperature starts rising. The highest temperature is a little distance away from the nozzle face. Higher fuel/oxygen velocity in the nozzle moves the high temperature zone away from the nozzle face. The nozzle face temperature determines the life of the nozzle.
Multiple nozzles will require how the highest temperature zone from one nozzle effects the other, and the zone will likely move closer to the face.
Injector cooling : There is cooling water, steam, air and multiple other media available on land based system but for rockets, the fuel+oxygen are the cooling media (before combustion takes place). It gets tricky to cool when you have multiple nozzles and one failure will lead to cascading failures.
During the Space Race, the Soviets didn’t have any individual engines as large as the Saturn’s, so their (attempted) moon rocket just had a whole huge mess of smaller engines. One problem they faced was that it was very difficult to control that many engines: If the engines on one side are producing a little more thrust than on the other side, the rocket will veer off.
In the end, they traded one stability problem for another. However, it should be noted that there’s nothing inherently problematic with having lots of engines. You have to handle small failures gracefully, and take more care to avoid resonances and the like. The tools for modeling this were poor in the 60s, and especially poor in the 60s Soviet Union.
The Soviet N1 rocket had 30 engines on the first stage and failed in four out of four launch attempts. The Falcon Heavy however has 27 first-stage engines and succeeded on three out of three flights. The SpaceX Super Heavy booster will have 33 engines but has not yet flown.
Another problem with the N1 is that the engines were truly single-use. Therefore they weren’t capable of a “static fire” that might have uncovered any defects. The only quality testing they got was by taking samples from each batch, testing those, and hoping they were representative.
Thrust imbalance on engines of those size isn’t really a problem; as long as the engines are delivering adequate overall impulse, any imbalance can be compensated by normal thrust vectoring, and indeed some multi-engine stages can lose one or more engines in flight and continue onto a nominal mission just by increasing the burn time to achieve the necessary delivered impulse. (This is different on really large external boosters such as the Shuttle Solid Rocket Boosters where a thrust imbalance of less than 2% will result in negative structural margins or the Atlas V AJ-60A side boosters, which is why the motor segments are produced in matched sets and the total propellant weight is closely controlled to prevent imbalance.)
The biggest problem with multi-engine rockets is that all of the propellant feed systems and individual dynamics of the engines can result in destructive resonance conditions that can disrupt propellent flows or even damage an engine, as occurred multiple times on the Saturn S-II stage. The N-1 had some significant problems with this because of the large number of engines and primitive tools for modeling such a complex dynamic system with so many interconnected elements.
The other problem with having many engines is that the reliability has to be correspondingly higher; a single engine with a individual 99.7% reliability rating translates to 98.5% system reliability with five engines or 91.4% with 30 engines, even without consideration for system failures caused by interactions between the engines. Of course, if the engine can tolerate one or more engines out through most or all flight regimes then you earn back reliability but there are significant tradeoffs with more engines. On the other hand, smaller engines are inherently advantageous in terms of propellant-specific impulse and specific thrust just because larger combustion chambers will inevitably have larger zones of incomplete combustion within them, and also tend to be more difficult to get to a steady state condition at given operating pressure level.
@am77494 highlights some of the practical issues with trying to build this kind of integrated manifold, and in general I just don’t think this is a practical idea even if you could somehow design it to be as mass efficient as larger individual engines.
