# Why do pressure fed engines have combustion instabilities?

Reading about the Sea Dragon idea, I came upon this argument against it, which sounds compelling, but relies on more detailed knowledge than I have:

Those are to be pressure-fed to avoid "complexity". Complexity? How about combustion instability from runaway pressure waves the size of houses? It took seven years to stop combustion issues from killing the F1 on test stands, and if it hadn't been started in the late fifties as a research project, it would have delayed the entire moon program.

AFAIK, the Sea Dragon would have a pressurized bag of Helium at around 60 psi which acts as the pusher of the cryogenic liquids into the engine. It seems completely counter-intuitive that this would have more mechanical problems than a turbine driven system.

Why is this? What causes an astoundingly simple pressure driven engine to suffer from major pressure instabilities propagating from the engine?

• Just as a reference and recommended reading from days of yore: Harrje, Reardon (1972) - NASA SP-194 Liquid Propellant Rocket Combustion Instability. – Deer Hunter Aug 3 '13 at 18:45
• It is interesting to note that "combustion instability" varies from just a little bit of vibration to highly entertaining yet dangerous and expensive explosions. A very fine question! – Deer Hunter Aug 3 '13 at 18:48
• Alan, F-1 and J-2 were pump-fed. You're thinking about SM and LM engines. – Deer Hunter Aug 3 '13 at 18:59
• @SF. Um, no. That's not how rocket engines work. The propellant in the combustion chamber needs to be at high pressure. The chamber is not sealed, so the combustion event doesn't increase the pressure like it does in an internal combustion engine. The combustion increases the temperature, which provides the energy that is turned into velocity by expansion through the nozzle, but without pressure none of that works. The combustion chamber is fed by a high-pressure source or stored at low pressure and pumped up. 60 psi is probably feed pressure to the turbopumps. – Adam Wuerl Sep 4 '13 at 17:45
• @SF. and AlanSE Those are good enough questions I thought they deserved their own thread: Why do pump and pressure fed liquid engines need to operate at high pressures? – Adam Wuerl Sep 6 '13 at 21:45

In the pressure fed rocket engines the propellant (both the oxidizer and the fuel) is fed to the combustion chamber by the pressurized gas (usually Helium) and it does not contain any complexity such as fed pump or turbo pumps

The presence of the turbo pump prevents the pressure wave reaching the propellant tank. But in a pressure fed rocket engine contains only the valve that opens and closes under pressure

The valve opens if the pressure in the combustion chamber is less then the pressure in the propellant tank(which is thick walled because they need to withstand high pressure)

The valve closes if the pressure in the combustion chamber is more than the pressure in the propellant tank (to prevent the pressure waves reaching the propellant tank )

with a direct pressure-fed cycle is that any variation in pressure will result in double the change in the whole loop, amplifying the oscillation. There's no turbine between the injectors and the containers to stop that oscillation from propagating

During the combustion process the pressure in the combustion chamber increases(flow velocity decreases) at the same time the amount of propellant injection from the injector decreases and suddenly the flow velocity increases(combustion chamber pressure decreases) the injectors, injects more propellents that burns outside the nozzle.

To be theoretical the fuel residence time in a combustion chamber is given by the Characteristic length(usually denoted by L*)(minimum length that the fuel will remain in the combustion chamber and nozzle for complete combustion to take place)

$$L^*= {{q*V*t_s}\over A}$$

q is the propellant mass flow rate, V is the average specific volume, and $t_s$ is the propellant stay-time A is the sonic throat area

so the propellent flow rate is a function of the pressure difference between the combustion chamber and the propellant tank and as the propellant rate increases as a result of low pressure (when compared to the pressure in the fuel tank) in the combustion chamber the characteristic length also increases(since the nozzle length remains constant) result in the instabilities in the fuel combustion and the combustion occurs outside the nozzle

The issue with Sea Dragon and pressure instability is that the likelihood of pressure instability increases exponentially as the size of the combustion chamber and nozzle diameter increases linearly. Sea Dragon's bell was supposed to be over 75 feet in diameter and put out 350 meganewtons of force (about 5000% more than an F-1 engine). The F-1s had huge issues with combustion stability, which were eventually solved.

Truax wasn't concerned with combustion stability because the engine was going to be a pintle injector type. He believed the natural combustion stability of the pintle injector would allow enormous engines to be highly stable at a variety of pressures. (Variable pressure was a key part of his design, because it allowed a much simpler and sloppier system in which pressure started high and slowly dwindled down as the tanks emptied.)

TRW (who built the rockets for the Apollo lander) later validated his belief. In that paper they point out that pintle injectors have demonstrated stable combustion with motors varying in scale by 50,000:1. So, Truax was probably right.

On an interesting side note, the Soviets had the same problem with combustion stability that we did. This is why early Soviet engines used four smaller combustion chambers instead of one 1 big one. The Soviet's inability to develop large engines was what lead to the N1 (their moon rocket) to have so many engines (33 in the first stage, I believe). Which then led to enormous plumbing problems, which led to the failure of the N1, which led to the failure of the Soviet Moon program.

• This is good info (and the linked TRW paper is a great read), but I'm skeptical that behavior of pintle injector engines up to 2900kN says much about what they'll do at 120 times that level. – Russell Borogove Sep 7 '16 at 3:49
• Even if the pintle injector doesn't stack up at sea dragon sizes, this is an an excellent answer and shows how foresightful Truax was. So, it would seem true to say that instability is what makes for the attraction to clusters? I always wondered at the complexity of some of the clustered designs. – WetSavannaAnimal Mar 20 '18 at 0:56
• @WetSavannaAnimalakaRodVance: Of course, more engines means a greater chance of at least one of the many doing something like exploding, which leads to other forms of instability – Sean Jun 23 '18 at 16:40
• Also, the Sea Dragon proposal doc shows what looks like a conventional showerhead injector in the first stage engine; do you have a citation for Truax considering pintle injection for SD? – Russell Borogove yesterday