Is it impossible to prevent the combustion instability by injecting the reactants at the choking condition for the liquid rocket engine?

To an old timer like me who was one of the pioneers in much of the rocket engine research during the Saturn V F-1 engine development at Princeton University (around 1966 – 71), I’m glad to see renewed public interest in these topics. My feelings are that the private rocket companies now-a-days are doing some good things with their new designs and strategies. I can only hope their social strategies and other relevant decisions can match it.

To the question, there are different kinds of combustion instability in liquid propellant rocket engines. Simple categories are “low frequency,” “intermediate frequency,” and “high frequency.” The first is caused by acoustic effects in the plumbing associated with moving the liquid propellants. For instance, there can be acoustic coupling between a turbo pump and a particular length of pipe with associated elbows and tees. Or other vibrations can serve to cause acoustic coupling with the plumbing. It’s easy to see that the suggestion of the questioner doesn’t really address such phenomenon. A summary of this kind of phenomenon can be found in this reference: Harrje

Intermediate instability occurs when chamber pressure irregularities instigate an acoustic coupling with the propellant feed plumbing, and here, one might think there would be some merit to the questioner’s suggestion. However, there are enormous practical difficulties, primarily because of the extraordinary high pressure ratios required to choke a flow in a liquid system. In fact, required pressures for nozzles venting to atmospheric pressure would require thousands of psi, or 20 – 30 mega Pascals, or pressure ratios of well over a thousand. In contrast, for air, the critical pressure ratio is only a little over two. Since the combustion chamber may already be operating at thousands of psi, we run into an insurmountable hurdle. In addition, such high pressures will involve supercritical flow during expansion, often producing two phase flows, sometimes with thermodynamic non-equilibrium. For more details on producing choked flow using liquid systems, as sometimes done in nuclear power plants, see Muftuoglu.

Thus, the questioner’s suggestion for acoustical feed coupling to the combustion chamber seems beyond reach for existing systems, especially since traditional acoustic methods work well. Since the acoustics are usually understood, these methods usually involve a re-design, or the attachment of quarter-wave tubes or Helmholtz devices into the plumbing.

High frequency combustion instability, sometimes called screech, or nonlinear instability, is more troublesome and more difficult to understand, predict, and remedy. We do know that it occurs when the combustion energy release is coupled with the acoustic modes of fluid vibration of the combustion chamber volume. There is no significant coupling to the feed system. In fact, the frequencies at which this instability occur closely match those acoustic solutions, which are much higher than those experience with the feed system. But the details of how energy is transferred from the phsico-chemical combustion processes to the acoustic modes seems at best abstruse. These processes involve liquid stream breakup, the formation of populations of drops, diffusion of chemical species, transport of heat, momentum, and species, as well as unsteady motions.

As far as the question goes, we can stop here, but those interested can read a little further for the story on how the difficult issue of high frequency combustion instability is addressed.

There was considerable theoretical and experimental work done at Princeton in the 60’s and 70’s concerning this phenomena. Most effort was focused on the Sensitive Time Lag theory, originally developed by Professor Luigi Crocco, an Italian engineer who joined with a group of other experts on most issues concerning liquid, and solid propellant chemical rockets, as well as those involving electrically propelled rockets, using plasmas. Crocco’s own father made a name for himself in fluid dynamics, and Luigi had already made his own name in the same field. Martin Summerfield was there, with his solid propellant group, along with Irving Glassman, S.I. Chen, Harvey Lam, and Robert Jahn.

Crocco’s approach was highly mathematical, all done from an analytic point of view, with little resort to numerical analysis, since back then, computers were relatively primitive. The basic equations were the Navier Stokes set with chemical combustion and state equations. Many clever mathematical strategies were necessary, with appropriate simplification by hopefully realistic assumptions. But bottom line, the theory was never developed to the point where simple enough results could be used by the designers. Most of our funding came from NASA, and the effort extended over a couple decades. Although many Ph.D.’s and resulting professorships at Universities were generated, and many of the results diffused to other areas such as aircraft noise, fire research and other combustion areas, as well as to the field of analytic studies in applied mathematics, some of us and others apart from the Princeton group (especially Rocketdyne Research, Georgia Tech, and JPL in CA) settled on brute force techniques, achieved by simply placing apparatus within the combustion chamber that increased the dissipation caused by the violent pressure and velocity oscillations that are the mainstay of the instabilities. In other words, the problem was never really solved fundamentally, as well as, say with the acoustical understanding of low and intermediate frequency instability, but we learned how to minimize the damage, and even prevent it from happening. Indeed, such damage could be catastrophic, blowing up a rocket engine within milliseconds of ignition. Dave Harrje had his share of blow ups on his rocket test stand, at noise levels that made your blood boil.

Two practical methods were most common, one by the use of so-called acoustic liners (back then also called “screech” liners), and the other by the use of baffles.

The liners consisted of a perforated wall sometimes placed slightly removed from the chamber’s true wall – forming many Helmholtz resonators - or with deeper perforations placed against the chamber wall – forming quarter-wave tubes. Pressure oscillations in the chamber induced flow in and out of the perforations, causing jets that dissipate energy, and this behavior is analogous to the action of a Helmholtz resonator or quarter wave tubes in the other kinds of instability involving feed systems.

Baffles were perhaps more commonly used than liners, and these were simply protrusions placed in the regions where velocity oscillations tend to be large, for the particular acoustic mode excited. These baffles create much random turbulence, dissipating energy and destroying any large organized velocity oscillations. I believe the F-1 engine used baffles, protruding from the injector end of the chamber.

Finally, the shape of the entire combustion chamber became a useful tool. For instance, short chambers put the longitudinal acoustic modes at frequencies incompatibly high for the combustion process, and a short, pancake shape makes a geometry that would encourage tangential acoustic modes, which can be addressed through the use of baffles that need not be very long. Putting a central plug in the chamber might discourage radial modes, etc. Many such ideas can be found in the above referenced manual edited by Harrje.

Much work is still being done towards a theoretical understanding of high frequency combustion instability, although most of it makes use of the enormous computation power of the latest computers. The workers are now from many other countries, some regarded as “undeveloped.” I myself am not aware of how much new rocket engine designs are based on such numerical studies, and how much they are based on the old standbys, baffles and liners.

Although I believe I’ve answered the question adequately, I realize I’ve gone far beyond, with hope that the questioner would think it adds to his interest behind the question. I’ve done it for historical reasons on a topic dear to me, and in fact, I’m one of the authors of the manual referenced here. I’m perfectly willing to shorten this answer, if required.

Very good idea, indeed. I am nort sure if someone already used that design in the actual engine, but it is worth noting that by removing the propagation of disturbances upstream through the injector would cutt off any backpressure-induced instability.

Also, one may conclude that throttling such an engine would be a challenge, since chocking the injector removes the possibility of flow control through any given injector nozzle. Maybe turning a number of nozzles on or off could be a solution.

Let's now look at the conditions for establishing a choked fuel and oxidizer flow.

Since pressure differential across the injector is a major condition for choking, given the high chamber pressures, would it be possible to attain such pressures using realistic turbopump design? Is there a stability margin for safe engine startup, shutdown and other transient events? Would cavitation appear after the choked section?

Next, the local speed of sound in the choked area varies with the fluid temperature. Steady-state engine operation would rather quickly establish thermal equilibrium (within tens of seconds), but careful design should take into account what happens with the fluid being injected when these equilibrium conditions are not met.

Then there is the question of closed-cycle designs. The gas generator exhaust that is fed into the combustion chamber has properties closely tied to the turbine operating conditions. The turbine itself runs on pressure and temperature differential between its inlet and outlet side. If the task is to have that exhaust flow choked on its injector too, than any adjustments should be made in the gas generator upstream of the turbine. Since turbine runs turbopumps, some fuel presure and flow controll issues could arise if not aressted on time.

Again, your reasoning is fair, and to help make the case, remember that a conceptually similar idea appeared in the design of the supersonic inlet of the SR-71 engines. There, a choked area is deliberately created where one would expect only decelarating inlet section. That way, any pressure instabilities originating in the air compressor could not move upstream to the inlet spike and lip, and therefore no disturbances are felt there. I guess they had to come up with some solution for notorious air compressor instability problems on the P&W J58 engine, even by means of sacrificing total pressure recovery in the process.