A few thoughts.......correct me if I'm wrong.
1. I've read that somewhere around 80% of the thrust from a "Turbo-Fan" jet engine is from the fan/compressor blades, 20% from the hot expanding gases or jet plume.
2. Heat, materials and cost will keep this a paper project for a very long time, machining cost might be kept in check DIY.
3. Ducted propellers & fans driven by piston engines might get you 80% of where you want to be. I read about some guy in Florida working on a light aircraft piston driven jet type fan. Read about it in "Kit Planes" about eight years ago.
4. Let us know what your research on this topic yields, interesting subject.
5. You might want to check out over the counter products, do you really want a flame thrower? Would you rather have an axle spinner?
6. Picture below is food for thought.