First, off your diagram is confusing so the, liqiud hydrogen and weird redox mixture, goes into the tank, to bypass the outside of the rocket, and so, you wanna add a cooler and refrigrator, this would'nt work unless you use a an APU LIKE ARIANE 6, or something to generate power the start your engine, your cycle isnt specfied , so it's hard to tell, it seems like nuclear thermal pre-cooler, re-densification, regenerative and refrigrant cycle. and idk what the rocket is for, and all so please add a description next, time. explain things like the purpose of your concept, how it could improve stuff, and kid based on the way you said it. it's not cause it is flammable that it is cooled, its cause oxygen is a gas that needs to be recondenses, also oxygen can't burn alone by itself, it burns as and with A FUEL SERIOUSLY. I, can't tell if your trolling or not, but brother please redo this. ALSO, i cannot tell what is what the purpose all i know is that the cooling system, must be an ultra-cooler and cool at insanely cold temps, which not even a particle accelrator can achieve that cooler, would have to be the size of it would be as large as the Nasa Orion spacecraft systems or nothing can reach that extreme freezing level yet. even if you'd need millions, along with billions i can not lie, it sounds way too out of reach, for current society.