Many ways to make a burn tube...the one shown was the last one I worked with. Flared at the inlet and tapered at the outlet, it was the quietest (still bloody loud) and smoothest running one I made. ~240000btu judging by fuel burn IIRC.
Not necessarily preheated...an ignition source will add heat which will vaporize "some" fuel and the resulting combustion will generate MORE heat, which will heat the tube up and help SUSTAIN the combustion when the ignition source is removed.
I don't happen to have any sunflower oil on hand

... but the residential oil burners that use a pump and atomizer nozzle (such as you drew) use ~300psi to atomize heating oil...which around here, is nothing more than diesel fuel with a red dye added.
Most waste oils need to be preheated and still require significant pressure for atomization. A good burner for waste oils is either the Turk burner , or the babington babington....the turk is significantly simpler to build, but the babington can run for longer periods of time without service.
Judging by the drawing you made, I'm thinking you should have a look at a Turk burner.
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