When Tesla turbines were first introduced it was possible in certain circumstances for them to have superior efficiency to all other types of turbines of the day. That is no longer the case. Most all modern turbines have vastly superior efficiency over a Tesla turbine in all cases. Furthermore, Tesla turbines have always actually had very poor efficiency except under very narrow operating parameters: low flow, low torque, and high speed. The Kw to weight ratio for an efficient Tesla turbine is quite poor. Certainly not something feasible for aircraft. While simple, they have some serious engineering issues, and have never even come close to the theoretical efficiencies. Absolute best case examples have somewhere around 60% efficiency. If they were as good as originally claimed, engineers would be falling all over themselves using them.
The boiling action of the nitrogen is brought about by the input of heat energy to the nitrogen. I don’t mean it has to be hot. It just needs to be above its very low boiling point. Without heat input, the nitrogen would just cool to a temperature below it’s boiling point and not produce any nitrogen gas. It is no different than boiling water producing steam. It just occurs at a much lower temperature. Obviously the best place to obtain the heat energy is from the surrounding air. The issue is a suitable heat exchanger. It must be efficient and effective without being overly large. I see no heat exchanger in your design other than the simple spherical shell of the container.
The amount of energy available from the boiling liquid nitrogen would be directly proportional and equal to the heat energy transferred to the liquid nitrogen to make it boil. No heat energy in (even from ambient temperature air) equals no energy out. Keep in mind heat is a relative term. Anything above absolute zero contains energy in the form of heat. The low boiling point of nitrogen gives a means to extract the heat energy from ambient temperature air.
What is the overall efficiency of this system? Not just the efficiency of the motor itself, but the efficiency of the ground equipment required to produce the liquid nitrogen. I expect the efficiency of the ground equipment to be very poor all by itself. Efficiency is the name of the game when it comes to motors. If it isn’t better than existing turbines then this will be a non-starter. It takes some kind of power input for the equipment to produce liquid nitrogen. Be it a diesel engine or electricity from the grid. You can't ignore this process when calculating the total efficiency.
How much energy per pound is available in the liquid nitrogen? How does it compare to jet fuel? I expect the amount of liquid nitrogen required to sustain a reasonable length flight is going to be more than the aircraft can carry. Energy storage devices that rely upon a simple phase change of the storage medium typically have very low energy density. Boiling liquid nitrogen would fall into this category. On the other hand devices that rely upon a chemical reaction do quite well: IE: gas engines and turbines, batterys, etc. With a quick look on the internet I see that the energy transferred from boiling liquid nitrogen is somewhere around 0.2 MJ/kg. Whereas the energy released from burning jet fuel is somewhere about 43 MJ/kg. That's a huge difference. Jet fuel has over 200 times the energy density of boiling nitrogen.
