When you started the thread, I went over in my mind what goes into a modern afterburning engine to make it work reasonably seamlessly for the pilot... Variable bypass for cooling and flow control, variable nozzle area to control pressure and EGT, flame holder and injector design, ignitors, light-off detectors that automatically cut burner fuel supply if the thing doesn't light off right away or if the burner blows out, etc etc... I figure you ought to be able to make it function with just a tube, flame holder, injectors, and igniters, but it won't run right and you'll have to be very concerned with temps and what it does to the engine. To make a simple model turbine burner, you'll probably end up doing a LOT of static ground testing (with and without forced airflow to simulate flight conditions) just to keep the thing from blowing up or melting inflight. Buying one that's already been tweaked is probably a better idea.
Ironically, the more complex you make the system, the less testing you'll need because you'd be able to adjust the various parts on the fly. Have bypass airflow automatically increase when the ignitors are running. Have fuel flow tied to igniter operation. Have igniters run on a timing system where they only operate for 2 or 3 seconds if a light-off is not detected, and cut it all off at 20-30 seconds if there is a good light-off. Use at least a two-step variable nozzle, closed down for normal operation and opened up for burner operation. Or tie nozzle area to EGT. Point being that a simple design with very few adjustments will be reliable but will take a hell of a lot of manual testing and tweaking to get to run right, while a very complex system could work pretty well with little operator input.
Again, I'd probably just buy one that someone else had already tested. Reliable full-scale afterburners took decades to perfect and only became truly reliable with the advent of full-authority digital engine control units. Even the F-15Cs in use at Tyndall AFB for training have a pretty high burner blow-out rate with the older engine control units, while an F-15E can do a tailslide with the pilot running the throttle from idle to burner and back, without the engine quitting. It's far more complex but much more reliable.
