The 0.03 inch coaxial gap is in the ballpark of what I got back when I
was designing my 250 lbf engine. I decided that was too difficult to
fabricate so I went with a drilled tube design instead. Cooling small
engines is hard apparently.
The Bartz equation works in general - I used it with educated guesses
about the values and ended up within about 150 degF of the predicted
value of the chamber wall temperature (the engine ran cooler than
predicted). I had included a 1.45x correction factor based on test data
from my 100 lbf engine. I'm sure you know this but the extreme heat
transfer at the throat is only for a very small portion of the engine.
It will be cooler in the chamber and nozzle and assuming you have some
material thickness around the throat, heat will be conducted away toward
cooler parts of the engine. My predicted hg values at the chamber,
throat, and exit respectively were 3.26e-4, 9.34e-4, and 4.83e-4
BTU/s-in^2-degR. I really wanted to know the hot wall temperature but
the only practical place I could put a thermocouple was in the middle
the wall of the chamber region between two cooling holes. The TC
measured 425 degF vs. a predicted value of 590 degF. I designed it with
an allowable hot wall temperature of 700 degF which is really high for
6061-T6 but it still has 10% of its strength left and is not a problem
if planned for, at least in short duration burns < 30 seconds.
-Bob
On 06/27/2017 06:10 PM, Zachary Martinez wrote:
I have considered a hand calculation. However I really have no idea how I would calculate the convective heat transfer coefficient. Should I use the gas side equation because it is on the gas side or the liquid side equation because the surface will be wetted by the liquid? Should I consider the convective heat transfer to the film from the combustion products to be the same as it would be to the wall if there was no film there? I also don't really have a good idea of how to model the radiation heat transfer from the reaction products. RPA is great for this kind of calculation as it looks fairly involved.
Even the Bartz equation is pretty involved in the number of things you need to get right. I have gone through a regenerative design using Bartz a few times on my own both by hand and using Matlab and at the end while I did get an answer, I definitely did not feel very confident in my results. I kept getting impossibly small required fluid flow gaps around .03" when using a coaxial shell design even if copper was used. I have probably spent a month on this problem on and off and was never able to get a different/better number.
Back to the whole point of this. We plan to use 25% film cooling for the engine (I am assuming this means of fuel flow and not of total mass flow someone please let me know.) I am fairly sure the design I am using will be fine thermally based on what I have seen others get away with. However, I have no way to definitively predict the wall temperatures which is especially important since aluminum is being used.
The most reliable hand calculations I have done have been from an energy balance point of view.
Assumptions made in these caclulations:
* Heat flux to the film is equivalent as the gas side heat flux to a
cold wall
* Gas side heat rate was determined by graphically integrating the
heat flux curves from RPA when you put in a wall temp of 300K
* The film absorbs all the energy required for it to evaporate
before it leaves the engine
* At a given time the entire engine is at the same temperature.
I got 4.5 seconds of burning as "safe" i.e. not heating the aluminum as a whole past its weakening temperature. The bad part about these numbers is I never get a throat temperature so I don't know if our copper throat insert is going to be damaged or not and there definitely could be other hot spots in the engine where the aluminum exceeds the safe temperature.
Zachary Martinez
Aerospace & Mechanical Engineering
Missouri S&T
