Here are the specs for the regeneratively cooled engine:

Fuel:                Kerosene
Oxidizer:            Liquid Oxygen (LOX)
Mixture ratio:       1.8
Thrust:              100 lbf
Chamber pressure:    200 psia
Chamber diameter:    2.16 inches
Chamber length:      3.44 inches
Nozzle throat dia.:  0.72 inches
Nozzle exit dia.:    1.22 inches
Injector pairs:      6
Fuel injection dia.: 0.038 inches
Oxidizer inj. dia.:  0.041 inches
Chamber temperature: 5400 Deg R (4940 Deg F)
Chamber material:    6061-T6 aluminum

Here is the complete design spreadsheet in OpenOffice format and in MS Excel format.

There were a lot of tradeoffs to consider in the design of the regen engine. I had to reject many of the traditional design methods (annular, helical, brazed tubes) because they were not feasible to fabricate with my basic machine shop equipment. I made some conical forms hoping to expand annealed copper pipe but it didn't work out too well. The plan was to get the force the copper pipe over the mandrel and then braze tubing around the outside in a helical pattern. My attempts at brazing were less than useful however.

The design I settled on is a solid wall chamber with cross-drilled coolant passages. The hardest part was coming up with a scheme that would keep the wall temperatures at a reasonable limit for aluminum. According to MIL-HDBK-5, 700 degF is about the useful limit of 6061-T6. At that temperature the yield strength is 8% and the ultimate strength is 10% of the room temp values. This requires significantly thicker walls than you would normally require but it turns out that the required wall thickness, 0.05 inches at the throat, is about the minimum I would feel comfortable maintaining while cross drilling holes.

A traditional one or two-pass coolant tube design required really tiny holes that I would never be able to drill. Instead, I went with just one "tube", alternating up and down in 10 total passes (see the drawings for an image of the solid model). This allows for a fairly large coolant hole since the cross sectional area is sized for the entire fuel flow. This keeps the velocity high enough for cooling with a total pressure drop across the coolant jacket at a manageable 85 psi. The approx 0.14 inch diameter holes should be fairly easy to cross drill. For simplicity, the same hole diameter is used throughout the chamber, converging, and diverging sections of the nozzle. There will be a cap at the nozzle exit to enclose the tube reversal slots. The injector face will serve the same purpose at the other end of the chamber. Grafoil sheet serves as a pretty good high temperature gasket. The holes on the outside of the chamber for the converging portion of the nozzle will have to be plugged somehow.

The Analysis section contains the final results of many thermal analysis runs, using the evaluation version of Mayasim TMG. Since everything in the engine is symmetrical, you only need to model a single tube. Also, I found that you don't need a very fine grid for thermal analysis. Once I figured out how to apply the boundary conditions in TMG, it went pretty quick.

The single tube in 10 passes complicates the analysis somewhat since I had to evaluate the heat transfer at different chamber wall and coolant temperatures. Since practically all of the material and fluid properties vary with temperature, this proved to be pretty complicated. The thermal analysis shown is a run with properties calculated at an average temperature.

Some comments on the design parameters:

The pressure drop across the cooling jacket varies significantly depending on the temperature the coolant properties are evaluated at. After considerable calculation, I modified the spreadsheet to use average, min, or max temperature properties where appropriate. It was surprisingly difficult to find fluid properties of kerosene at various temperatures. I'm well within the bulk coolant capacity of the fuel but I'm a bit worried about the bulk temperature of the fuel (325 degF) at the cooling jacket exit causing deposits on the cooling tube walls. I plan to use Jet A for the fuel so I have good access to the thermodynamic properties.

I took credit based on NASA SP-125 for thermal resistance from the carbon deposits on the walls due to kerosene combustion. Testing with embedded thermocouples will show whether this was a reasonable assumption or not. I also found that 1D thermal analysis was quite a bit more conservative than necessary. I played around a bit with a fin factor (described in Hill & Peterson, p. 430) that takes into account the fin-like geometry of a coolant tube. I was able to select a fin factor based on my geometry that, when applied to a 1D analysis, almost exactly matched the 2D TMG analysis. Since I can't link the TMG analysis to the spreadsheet, this made the spreadsheet a lot easier to use.

For the injector, I'm using 6 unlike split triplets. There is a good AIAA paper that describes the split triplet in detail - "Effect of Momentum Ratio on the Mixing Performance of Unlike Split Triplet Injectors", Journal of Propulsion and Power, Vol. 18, No. 4, July-August 2000. The split triplet is attractive for me from a fabrication point since my oxidizer holes are in the middle and this keeps them from pointing toward the wall as they did in my uncooled chamber. I'd like to put additional fuel holes near the chamber walls but the holes are already getting too small as it is. I don't have good heat transfer estimates for the injector face so that is definitely a potential weak point. There's tons of great material in the NASA SP papers regarding injector design. Some other good references are the NACA RM and TM reports. The Swiss Propulsion Lab has an excellent collection of links in the publications section.