If you want to make an axial flux PM-generator with no iron in the coils, you can better use a 3-phase winding than a 1-phase winding for two reasons.
The first reason is, that if you rectify a 1-phase current, you get a very fluctuating DC current and so also a fluctuating torque. Batteries don't like a very fluctuating current especially if they are loaded simultaneously with the charging because this results in fast charging and recharging. If you rectify a 3-phase current, there is only a small fluctuation on the DC current. Information about different ways of rectification is given in my public report KD 340.
The second reason is that you can get 50 % more copper in a 1-layer, 3-phase winding than in a 1-layer, 1-phase winding. Information about a 3-phase winding of an 8-pole axial flux generator is given in chapter 9 of my public report KD 341. Once you understand an 8-pole, 3-phase generator, it is easy to understand a 12-pole, a 16-pope or a 20-pole generator. The pole number must be dividable by four if you want to use a 1-layer winding. A 1-layer winding means that all coils are lying in one layer and so there are no crossing coil heads. All my public KD-reports can be copied for free from my website:
www.kdwindturbines.nl at the menu KD-reports.