Heatsink Thrust Chamber Thermal Analysis

Background

The temperature of combustion inside a rocket engine is extremely high and the rate of heat transfer into the walls of the chamber is substantial. Without a method of transferring heat out of the walls as fast as it is being transferred into the walls, the chamber will increase in temperature until it is compromised. The best method to protect the chamber is to implement regenerative cooling where the chamber wall acts as a heat exchanger between the combustion gas and some of the propellant which serves as a coolant. However this is a significant manufacturing challenge, one that I am not yet prepared to face. Instead, the rocket engine I am working on uses a simplified thrust chamber for short duration testing purposes. I have heard many different names to describe this type of chamber such as “heatsink“, “battleship“, and “copper block“. Fundamentally, this type of chamber is designed to disperse the heat that is transferred into the walls so that it does not concentrate at the innermost wall and destroy it. It will still eventually fail if hotfired for too long, but its ability to spread out the heat it absorbs is what allows it to hotfire for short but useful durations. This necessitates a very thermally conductive material which also ideally has a high specific heat. Thick walls are needed to absorb and store the heat that is transferred. Copper is essentially the best choice and you almost always see it being used in heatsink chambers. Affordability dominates my trades though and aluminum, with its other advantages like workability, was the best choice for my project. There are some examples of aluminum thrust chambers in the amateur community such as Robert Watzlavik’s heatsink and regen LOX/Kerosene engines. I will be taking precautions in my startup and shutdown to keep the aluminum safe from oxygen. It is not strictly necessary for me to know exactly how long I can hotfire. I plan to start conservatively with durations near 1.00s and will inspect for erosion while incrementally increasing duration. Previous experience with a 400psi Kerosene/LOX heatsink engine leads me to believe it will not be a problem to reach 1-2 second durations, however I am curious to see how long I could theoretically hotfire for.

Publicly Released Images of Heatsink Thrust Chambers:

Hotwall Heat Transfer

The hotwall heat transfer coefficient governs how much heat will flow per unit area per temperature differential with units of W/((m^2)*K). Estimating the hotwall htc is core to understanding the heat input to the chamber. Using gas properties from CEA and the known geometry of my chamber, the bartz equation can be used to calculate an estimated Q_in along the length of the chamber. I recommend reading my article on the bartz equation to learn more about this method. Soot deposition and other factors will reduce the real htc and bartz can often be taken as a worst case. To attempt to account for soot resistance I am using a plot I found in Huzel and Huang’s book which puts the soot htc at about 1000-3000 W/((m^2)*K), significantly lowering overall series hotwall htc.

Computation

I am dividing up the solid body of the thrust chamber into small 1x1mm square elements with a “mass” equal to that of the body which would be created by revolving the element about the engine centerline. To simplify the code, heat will transfer only radially not longitudinally. This will also have the effect of skewing the results more conservative (higher peak temperatures) than real life since allowing heat to flow multidirectionally would have the effect of distributing temperature more evenly. The heat transfer area between elements is equal to their width times the circumference at their radius from the engine centerline. The code uses the forward euler method to calculate heat transferred between elements and their temperature change over time. Heat transfer into the innermost elements is calculated according to bartz and then the heat is continuously conducted away into the elements located at larger radii. The outermost elements cannot transfer heat to outside of the system.

Stoke Space Thruster

Results

From what I can tell, 6061 aluminum loses most of its strength after exceeding about 350-400C (623-673K). The melting point is 585C (858K). At an O/F of 1.80 and nominal Pc, the throat peak temperature reaches 600K after about 4-5 seconds of firing. To test the robustness of the model I ran the code multiple times with different time step sizes (dt). Increasing the time step size seems to cause an overprediction in the diffusion of heat (less steep temperature gradient and lower peak temps). I’m not 100% sure I can explain accurately why this is but I suspect this comes down to a core flaw of the simple Euler method I implemented. The change in internal energy of a cell is found by integrating the net q to the cell. q is always net positive but decreasing as the average temperature difference decreases. Due to the Euler method basically taking left Riemann sums for integration it overpredicts q, kind of having the effect of making the material more conductive since more heat is being transferred for a given delta T. As the dt approaches zero, the integration becomes more accurate.