The formula you’ve quoted is for Carnot Efficiency, which expresses the theoretical limit for the efficiency of a ideal heat engine that operates between TH (temperature of heat input, eg flame combustion temperature in a jet engine) and TC (temperature of waste heat stream, eg that of the jet wash as it exits the engine). It doesn’t give the actual efficiency of a real-world engine in terms of work done per unit of fuel/energy consumed (as this is determined by the effectiveness of the physical engine design), but is the maximum possible within this temperature range.
The key item here is that Carnot Efficiency increases proportionally with TH. Preheating the air/fuel mixture will cause a relative increase in the flame temperature within the combustion zone of the engine. For a given exhaust temperature TC, a hotter combustion zone TH allows for a greater volumetric expansion , and therefore, more volume flow and greater thrust.
In short, higher fuel/air temperatures will INCREASE the efficiency of a heat engine, while cold fuel/air will REDUCE efficiency.
As an aside, engine efficiency improvements are made by minimising the temperature of the engine exhaust by maximising the degree of cooling by volumetric expansion in the engine expander sections. Bypass turbofans use this principle by mixing fresh air (bypassed around the combustion chamber and hi-pressure sections) with the exhaust, ie using the waste heat to achieve additional expansion and therefore thrust. Each successive expansion stage requires an additional stage of larger diameter, so given that jet engine weight and length are design constraints, its clear that this optimisation can only be taken so far. Modern jet engines are about as efficient as they will ever be, and improvements going forward will be incremental.
Ahoy, comrade : )
Without saying you are wrong, jut going through the logical chain.
The combustion chamber temperature is not constrained by the available energy, but by the materials.
The Kerosene Stoichiometric adiabatic flame temperature is 2093 Celsius from 20 Celsius.
Means that if you compress it prior of combustion then the temperature of the suction will increase to 550, and the exhaust temperature will increase even more.
So the engine is not constrained by the chamber temperature, but by the heat resistance of the materials.
If the combustion chamber maximum temperature is 1600 Celsius , then the combustion products expand from 550 Celsius to 1600 Celsius .
The compressor end stage pressure and temperature given for an ambient temperature, if you want to increase the efficiency then the pressure needs to be increased, but that will increase the end temperature as well.
Means the best way to increase the pressure if you can cool the compressed air.