Hi Gums,
Here is a cut-away of the TF30 turbojet afterburning engine.
Airflow leaving the fan is split into two flow streams, that which bypasses the core and is ducted (annular duct) to the afterburner, thought of to be a low flow bypass, and the flow stream entering the core of the engine.
The compressor section consists of a 9 stage low-pressure compressor, including the core portion of the three stage fan and a seven stage high-pressure compressor. Interestingly, there are 3 bleed points:
1. A 7th stage bleed which opens in flight at Mach numbers above 1.75
2. A 12th stage bleed which automatically opens to discharge air to the bypass duct when a surge condition is sensed
3. A 16th stage bleed to cool the high-pressure and low-pressure turbine blades.
The differences you experienced between the J57 engine and the F100 engine as to fuel burn and power can really be contributed to technology that came along over time. The J57s had cannular combustors, whereas the F100s had annular combustors which gave the burner folks much more design latitude and creativity to develop high combustor efficiencies. Also, the afterburner technology advanced in design, material capabilities and improved flow patterns resulting in enhanced fuel burn characteristics.
The A-7 aircraft used a non-afterburner TF30 engine in which the bleed systems were probably simplified verses the afterburning engine.
I think the problem with the J58 being modified to an annular bypass system would have been not only added weight, but all the external plumbing changes that would have been required, adding to the overall diameter of the engine.