My push-pull converter uses a flyback transformer with an air gap. How does changing air gap size affect the secondary output voltage?
All the energy is stored in the gaps between the magnetic core particles or gap in this case. As the gap size increases, flux will start to 'spray' into the area of the windings in proximity to the gap. This will generate high levels of eddy current losses in the wire. To avoid this problem you can wind on a few turns of insulating tape around the middle of the coil former to exclude wire from the region.  The main advantage is it reduces the sensitivity to thermal runaway by moving the losses from the core towards the glass gap when increased.

There is an optimal gap to minimize the sum of  all tradeoffs for increased winding loss, reduced core loss , increased gap coupling leakage  and Eddy current losses.