It may or may not be working correctly just because there is no sparks or smoke. The little 9V is not capable of too much in the way of fireworks. But it's a start.So here is the million dollar question , why will the pot and lm317 go wrong when connected to a 10v 1.5a wall adapter or the main large 16v 15a transformer ???, the circuit is obviously working correctly with low current
So before risking any more destruction, let's try to double-check that things are really working as they should. You have two multimeters, I see. Connect one to the LM317 output pin and ground to monitor its output voltage. Connect the second multimeter across the 220 ohm resistor to monitor the reference voltage. You can leave the transistors connected, but disconnect the fan load just to avoid running the little battery down.
Start with the pot at minimum. Both meters should read 1.25V (or thereabouts.) Turn the pot up and watch the output voltage increase, while the reference voltage stays the same at 1.25V. At some point the voltage will reach its maximum, which *should* be about 1.5V less than the battery voltage. If you turn the pot further, the output voltage will stay the same and the reference voltage will go down since the regulator has dropped out of regulation. If you do not get results like this, something may still be wrong.
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I don't know if this will frustrate you or give you confidence, but I did an experiment earlier today. I found some stuff in my junk box where I was experimenting with power supply designs. I was able to fairly quickly lash up a reasonable copy of the circuit you are working from. A few differences, my two transistors are 2N3772s and my emitter ballast resistors are 0.22Ω instead of 0.47Ω.
The outcome of the experiment was that I was able to set it to 12V output and then push 10A into a load with the setup with no drama, other than the transistors getting quite hot of course. The regulation was poor as I expected it would be, the output dropped from 12.0V to 10.3V. The LM317 only needed to provide 161mA of drive current to achieve the 10A, so I got by without heat-sinking it.