Table of Contents
Thermal AnalysisWithin the combustion chamber of the rocket engine are combustion gases that exceed 5000 degrees Fahrenheit. This is an extremely harsh environment in which most materials cannot survive for very long before losing their structural integrity. Therefore, it is critical that each component undergoes a thorough thermal analysis to ensure their survival during the firing of the engine. Some of the major components of interest are the chamber casing, nozzle, and injector.
The analysis approach taken on the engine sub-systems has been to first model the phenomena taking place by creating a mathematical model. After creating this model, the results are verified by running simulations using various types of analysis tools and software packages.
Combustion Chamber Heat Flux ModelA matlab script was written to model the transient heat flux from the combustion gases into the chamber casing. It does this by analyzing the properties of the gases, chamber wall, and calculating the convection heat transfer coefficient of the system. The model employs an implicit iterative damping algorithm which steps through time at a specified time step and solves the transient heat flux into the wall. This approach was utlized in order to achieve the most accurate results because the governing equations of the problem are functions of each other. In other words, to solve for the temperature of the wall over time, one must solve the convection coefficient of the system over time. However, the convection coefficient itself is a function of wall temperature. Therefore they loop on each other.
Within each time step of the simulation is an additional loop that compares the wall temperature from the previous time step and the current time step. If the values are not within a given threshold error value, the temperatures are averaged and the calculation does another iteration. After the temperature converges to an acceptable value, it will exit the loop and begin solving the next time step. This computational method is also advantageous because it minimizes the error associated with time steps that are too large.
The ultimate goal of the model is to find the temperature of the wall throughout the burn to determine if it will maintain its structural integrity at high temperatures. The equation that represents the transient wall temperature was derived using the energy balance approach. If the wall does not withstand the stagnation temperature, either a different material will need to be explored or insulation will have to be added. The script can be manipulated to test different chamber materials, thicknesses, combustion gases, etc.
Combustion Chamber Conjugate Heat Transfer Model
Combustion Chamber Insulation SolutionSimulation results suggest that the aluminum casing will not hold its structural integrity over the 7 second burn. Although aluminum has a low melting point, its low cost, low weight, and relative strength are optimal for this design. Therefore, the best solution was to insulate the aluminum from the combustion gases.
The paraffin fuel grain provides natural insulation to the aluminum as it is there for the entirety of the burn. However, adding a .125" layer of insulation throughout the entire chamber mitigates the risk of exposing the wall at the end of the burn due to uneven burning of the wax. This also provides something to cast the fuel grain into. The portion of the insulation that is behind the wax should not be burning at all and therefore its thermal properties are very well understood. It will be more than sufficient to keep the aluminum wall at a low temperature.
The paraffin fuel grain does not extend all the way through the chamber. The pre and post combustion chamber sections therefore do not have that additional protection. For an additional factor of safety, a thicker .25" layer of insulation is added to the inner diameter of the outer insulation in these areas. These areas will be directly subjected to the flame and will therefore burn and ablate away during the burn. Simulating this is nearly impossible and because we do not fully understand the heat transfer properties, we have made the insulation thicker. Together, .375" of insulation should be 100% efficient in insulating the casing and might even be re-usable. Moreover, these inner tubes will create an overlap at the point of contact with the fuel grain. This is too mitigate the leak path that could otherwise result from the mating surface between the phenolic tube and top/bottom surfaces of the fuel grain.
The insulation material is a fine weave cotton fabric base phenolic laminate know as phenolic LE or linen phenolic. Different types of phenolic are widely used in the rocket industry to insulate solid rocket engine casings from the fuel grains within them. This particular type of material has several advantages. It has a fine surface finish and is machinable to very low tolerances. It is rated highly for mechanical strength and has a low tendency to pick up moisture. This is important because it ensures the insulation will not change size as it is exposed to different environments. As mentioned before, the effects of burning on the surface in regards to the temperature distribution within the material are largely unknown and vary greatly depending on the system. To get a better understanding and for validation purposes, different insulation specimens were tested using an oxyacetylene torch. A thermocouple was placed on the back to map temperature as the specimen was exposed to the 1000 degree Fahrenheit flame for a minute. The experiment also allowed us to observe the surface behavior during and after the burn.
Nozzle Conjugate Heat Transfer Model
The rocket nozzle is responsible for transforming the thermal energy in the combustion gases into the kinetic energy that imparts thrust on the rocket engine. It must be able to withstand the extremely high temperatures and heat fluxes stemming from the extremely high mass flow rate. Therefore, the nozzle must be made out of a heat resistant material that will not melt or deform under these conditions. The material chosen for our rocket nozzle is G347 graphite. This is a high density material that is engineered for many applications. It is perfect for our application because it has a very high melting temperature, high mechanical strength, and high thermal conductivity.
Originally, the nozzle was designed to be a slip-fit into the bottom of the chamber. This meant that the outside of the nozzle would be in direct contact with the chamber walls. After combining the results from the turbulent supersonic flow CFD simulation and the transient conjugate heat transfer simulation, it became apparent that the outer wall temperatures of the graphite nozzle could reach temperatures above 1300 degrees kelvin towards the end of the burn. This temperature is well above the temperature that the aluminum casing could take, regardless of the graphite melting temperature.
The CHT model used a coupled solid energy and implicit unsteady solver. The 3-dimensional temperature and local heat transfer coefficient values were exported from the CFD simulation and used as an input for the CHT simulation. The two models could not be solved together because the turbulent flow model was steady state, while the heat transfer model was transient. The transient data is extremely important in the latter model because we want to know the nozzle temperature distribution as a function of time. This allows us to understand the insulation requirements throughout the 7 second burn.
The link to the full animation video can be found here.
Nozzle Insulation Solution
In the best interest of the aluminum casing, it was decided that the .125" of phenolic tube would now extend all the way through the entire chamber. The result was making the outer diameter of the nozzle smaller, and also changing the nozzle retention mechanism which previously was going to involve internal threads.
Another important thermal consideration is the heat transfer through the bottom of the nozzle. The after section of the nozzle is thinner than the rest of it because of the cut-out for the retention mechanism. Therefore, this part will heat up faster than the rest as it has less thermal mass and less distance for conduction to travel from the flame region. After 7 seconds, the average surface temperature in this bottom section is around 1350 degrees Kelvin. This introduces a concern with the nozzle retention plate contacting the graphite. To solve this problem, a thin phenolic region will be placed in between the lip of the graphite and the aluminum retention ring. This phenolic spacer will be more than sufficient to keep the retention plate cool and at high strength. Additionally, there is a small air gap between the inner diameter of the phenolic ring, and the outer diameter of the aft section of the nozzle. Thus, the aluminum retention plate is not in direct contact with the graphite at any point. Lastly, the .125" distance between the nozzle and retention plate also mitigates the risk of a tolerance stack up. If the assembly is loaded and there is a deviation in the axial direction and the components shift either up or down, there is still .125" to work with in either direction.