A J-tube style RMH doesn't need a secondary air intake there. It has enough oxygen for complete combustion, it just needs sufficient turbulent mixing for oxygen and fuel gases to meet in hot conditions. The sharp right-angle turns in the J-tube have been found to do that well, especially with some refinements near the beginning of the burn tunnel, the "p-channel" and "tripwire". Search on those terms for details.
If you want to experiment, you can't get any feel for how well this would work without first building one by the book, then adding just that one modification. Anything else will be meaningless in research terms.
Location: Southern alps, on the French side of the french /italian border 5000ft elevation
posted 4 years ago
To follow what Glenn says.
J tube rockets always have too much excess oxygen in their flue gases. And furthermore, if you add air at that point, it's verry bad, because you would be cooling the fire. Which would decrease the efficiency of the burn.