Rocket Injectors (11/9/21)
The heart of the rocket engine is the injector and it has several functions: it meters the propellant, impinges the propellant, and atomises it, all while preventing instability and cooling itself using the propellant. There are many types of injectors but they all do the same thing. In some engines the injector is fused to the manifolds but for now we’ll consider only engines in which the manifolds are separate from the injector.
The metering of the injectors is done using specifically metered orifices either screwed in or designed into the injector face. The metering is what keeps the specific mass ratio, pressure and amount of propellant in the chamber and is entirely dependent on the feed system conditions coupled with the orifice sizes relative to the total surface area of the holes in the injector and the ratio of the oxidizer holes and the fuel holes. Typically this is found using Bernoulli’s equation in relation to the Cd - the discharge coefficient, which is an empirically derived correctional constant that clumps in the friction of the hole and the viscous/turbulent effects.
A properly designed injector prevents combustion instabilities by inducing a pressure drop which is induced via the complex paths and smaller pipe sizes, increasing the surface area of the boundary layers so instead of one large surface area call it S1 which would be the internal surface area of the propellant line it would be Sa + Sb + … + Sn for n number of channels and in a well designed injector n would be the sufficient number of channels to cause a pressure drop. This typically depends on the length of the channels and the pressure drop caused by the manifolds as well. The pressure drop should be at least 20% of the chamber pressure. Typically this figure is much greater, sometimes up to 150% of the chamber pressure. This is imperative because the combustion produces thrust, which can allow the flames to propagate upstream, burning the feed system and causing an explosion. Although if things are that bad it will have a hard time even sustaining itself without major combustion instabilities. These are caused by several factors, including resonant frequencies, uneven chamber heating, and feed system frequencies. Typically the engineer just decides to just fire the engine in presence of a microphone and then they can analyze the audio to see what instabilities exist and fix them using either acoustic chamber liners, baffles or many other solutions. These things are typically analyzed after the fact due to the massive amounts of complexity involved in the process.
Atomization of the propellant is a two step process typically which includes turning the liquid propellant into little droplets. That happens with the injection from the orifices due to the surface tension of the fluid as well as the turbulence involved, which cause little droplets to form. The absolute perfect medium for combustion is a gas mixture which is superbly easy to ignite and will burn extremely well. The second step is to essentially impinge the two propellants which serves to shrink the droplet size into fine mist. It’s hard to be specific about the specific molecule size but typically the smaller the droplets, the better. This leads to conditions asymptotically approaching perfect combustion efficiency which is typically achieved using gas-gas engines which are more powerful and complex typically incorporating pre burners. For example, the SpaceX Raptor engine is a gas-gas engine. This injection tech is moot for gas-gas engines and is entirely directed towards liquid-liquid engines.
Cooling of the injector is straightforward and involves picking a material with as high of a thermal conductivity as is possible to manufacture. In our case that was Cu145 which is a copper alloyed with a bit of tellurium, giving it 90% of the thermal conductivity of pure copper with 3x the tensile strength which improves the machinability which is related to both the thermal conductivity and the tensile strength. The cooling is achieved by running the propellant through the channels in the injector which cool it instantaneously. Typically this is a steady-state process and so transients are ignored in analysis but the temperatures at the face of the injector reach 6000 degrees fahrenheit. Pretty much cooling is about having the channels go through as much of the body of the injector as possible, with bias given to the fuel as the liquid oxygen has a low heat capacity, meaning it will not cool anywhere near as well as the kerosene. There are some times in which that was the right choice for some projects but it is very rare.
That in essence, is the basic science and theory behind injectors. While I didn’t design our injector, I learned much more about the subject in recent months in preparation for my next development program which will be a reusable lander style rocket similar to vehicles built for the Northrop Grumman Lunar Landing Challenge which was designed to launch a new type of space industry which unfortunately has failed at its objective. It did however lead to some very interesting stories.
NASA SP-194 (1972). Liquid Propellant Rocket Combustion Instability - Harrje. D.T
RPE George Sutton 1984.