Rocket Thermodynamics (10/19/21)

Thermodynamics, From a Cryogenic Rocket’s Point of View

LOx is probably the world’s best oxidizer. It will oxidize just about anything and everything. It’s nontoxic, not carcinogenic, cheap and widely available. The only caveat is that it is cryogenic, not LH2 temperatures but in the more manageable range of -295 degrees Celsius. LOx is for these reasons, is our oxidizer of choice and it has been the rocket industry’s chosen oxidizer for decades.

Working with cryogens tends to come with very careful design because if the liquid reaches ambient temperature, it will boil, sometimes causing the process of filling a tank to take a few hours for a small tank. Therefore, the process of filling a tank is typically preceded by chilling the cryo tanks with ice. Due to the relatively high thermal conductivity of aluminum, once the temperature of the tank is lowered it’s relatively easy to keep the temperature. Pressurized cryogenic tanks need to have relief valves or burst disks. In our rocket we have a fast-acting relief valve, which gets triggered if we hit a certain pressure and will vent the oxygen above that pressure. Other than needing to use PTFE seals and no other plastics allowed anywhere, and the metals being made brittle at lower temperatures, working with cryogens is pretty straightforward.

On the other end of the temperature spectrum, combustion temperatures in the engine tend to melt uncooled engines, necessitating active cooling, refraction or controlled ablation of the chamber walls, throat and injector face. We solve the injector cooling issue by making our injector out of a material with very high thermal conductivity, allowing the kerosene, which has a high specific heat, to absorb a lot of heat and cool all of the injector face. Note, cooling in this case means <500 degrees, so not something to be touched when in operation. The walls and throat in our case are going to be ablative. In our case, the material is Silica phenolic for the throat and phenolic canvas for the chamber liner. The phenol groups in the phenolic when burned separate the carbon into a different product, forming a carbonaceous foam that tends to burn very slowly, sacrificing itself for the rest of the engine and this happens throughout the chamber liner and throughout our burn. This, along with our film cooling, which due to the lowered mixture ratio around the boundary layer, preserves the engine liner for longer due to lower wall temperatures. At the nozzle essentially the same thing happens but with higher regression rates, higher heat fluxes and better ablation due to the different material.

Other thermal considerations we had were compromising of the tank structure due to aerodynamic heating during flight but that is something we decided was not an issue after consulting some engineers. Other than that, this rocket is fairly straightforward from a thermodynamics standpoint. Turbopump-fed and other more complex systems are far more interesting from a thermal standpoint. I’m thinking of building a regen cooled self-pressurizing test bed rocket that I can launch locally and mess around with. I think the holy grail of small rockets are those that can launch with minimal infrastructure, minimal supervision, no destruction and no explosions most of the time.

Sources:

Physics (2005). Physics. For high school students. GIANCOLI