insidersource
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It is very challenging. The fuel burn improvement of the 737 example is directly linked to the bypass ratio increase. Commercial jets increase bypass ratio by fitting a bigger fan. On a fighter jet if you increase bypass ratio but keep the diameter the same then the thrust reduces. To improve both thrust and fuel efficiency is then extremely challenging.I don't think it's that challenging. The F414 burns 0.84lb/hr/lbf, so you're only talking ~5% fuel burn improvement. There's been quite an improvement in turbine engines since the F414 was designed. For example, the CFM56-2 (737 classic) burns 0.386-0.396lb/hr/lbf while the -7B (737NG burns 0.356-0.386lb/hr/lbf at takeoff. That's a ~10% improvement at the low range.
The older F404 actually has around 3% better fuel burn than the F414 as it has a higher bypass ratio of 0.34 versus 0.25.
The RB199 actually has 15% better fuel burn than the F414 in a similar size engine. But the RB199 has 30% less dry thrust due to its higher bypass ratio 1.1
If you keep bypass ratio constant there has only been a 5% fuel burn improvement over the last 30 years. The F414 actually has great fuel efficiency for an engine with such a low bypass ratio.
It would be nearly impossible for Korea to improve fuel burn by 5% AND increase thrust beyond the current F414. If they do manage to achieve this then the engine will probably be running so hot that the aircraft needs a new engine every month. Massively trading durability to achieve higher performance like what the USSR did for decades.