# How would exhaust heat recovery into the combustion chamber affect the efficiency of a jet engine?

So, a jet engine basically sucks in air, heats it up and spits it out, right? The hotter the air gets, the faster the exhaust velocity and thus the more efficient (Higher specific impulse).

Now my question is how this all gets affected if you use a heat recovery system, either a heat pump or a simple heat exchanger. Let's ignore the annoying practicalities of metals melting and all that stuff and just look at the theoretical side.

If you recover heat from the exhaust and put it back into the combustion chamber how does this affect the efficiency of the engine? If we were to apply the heat into the combustion chamber using a heat pump, pumping heat from the exhaust into the chamber could we get even higher efficiencies? While "Yes/No" answers would suffice I would be much more interested in a thermodynamic explanation and possibly even some estimations of the theoretical efficiency which could be reached using the Carnot cycle for pumping the heat.

Onto the practical, has anything like this been experimented with? To my knowledge we don't have heat pumps capable of operating at 2000 degrees Celsius and pumping heat quickly enough to compare to any type of engine, but maybe someone has experimented with simple heat exchangers like how rocket engines use regenerative cooling (for different purposes though, but still similar to this).

• What efficiency are you implying, fuel efficiency or thermodynamic and/or propulsion efficiency? Heat recovery is very beneficial for the fuel efficiency! Feb 26, 2020 at 7:30
• You would probably make the engine too heavy to fly. Heat recovery is used in gas turbine electric generators (which are basically jet engines). Here's what the equipment looks like: en.wikipedia.org/wiki/Heat_recovery_steam_generator Mar 26, 2020 at 18:21

Extracting heat from the exhaust will cool and compress it, slowing it down and reducing thrust. Recirculating the heat back into or downstream of combustion will raise the temperature at that point and on downstream to the extraction point. The inevitable thermodynamic losses mean that the returned heat does not quite compensate for the heat drawn out and overall efficiency will fall a little.

What does improve efficiency is to draw through additional air mass in order to increase the exhaust mass flow, even at the expense of lower overall velocity and temperature. This is what the bypass turbofan does.

A more radical modification is to swap the combustion chamber for a heat exchanger and heat the gas via hot fluid from an external source; the hotter the fluid the better. I have seen this proposed for the hydrogen turbopump in some versions at least of the SABRE air-breathing rocket engine. It was also proposed for nuclear-powered bombers in the 1950s, though I cannot recall if those included turbojets as well as ramjets.

A couple of remarks:

1. The reaction jet engine produces thrust in the exhaust nozzle. In a subsonic engine the exhaust gas first accelerates in the convergent section of the nozzle then it expands in the divergent section. Expanding, the gas looses not only kinetic energy but it cools down as well. Since the thrust is developed in the last section of the nozzle then having a heat exchanger further down would actually reduce the thrust by reducing the ability of the gas to expand.
2. There is a reactive jet engine that uses heat exchanger. Is called Sabre and the developer tried to solve the problem of suborbital flight using one engine only. At takeoff the engine functions as a reaction jet. Once the speed exceeds the range of usability of the axial compressor, then a heat exchanger placed in the air intake cools down the air to maintain the efficiency of the axial compressor even at supersonic speeds. The airflow through the engine remains subsonic. However, on exhaust the afterburner provides the extra thrust required to maintain speeds in the vicinity of Mach5 to 7. This engine burns hydrogen and uses liquid helium as coolant, or so the developer says. This is a bold undertaking from a private developer.
3. To answer your question: The Sabre is an example of using a heat exchanger in the air intake. The only cooling in the exhaust is meant to keep the hot side operational and not to extract energy from exhaust gas because that will affect the thrust.
• I might quibble with 1. a little bit. I would say the reaction is generated along the entire path from the burner can outlet aft, but mostly between the turbine and nozzle as the flow is forced to accelerate by the convergence. Also non-afterburning engines don't have a divergent nozzle section. It narrows down to the nozzle outlet and that's it. The "divergent" part is just open space. The divergent nozzle section is only present on an afterburner nozzle and only while in reheat. Jan 7, 2020 at 17:14
• The reactive force in the reaction jet happens in two places only: in the axial compressor and in the divergent stage of the exhaust nozzle. The turbofan takes advantage of compressor thrust by employing fan stages. The exhaust nozzle is formed by a fixed diffuser cone at the interior and an adjustable shell at exterior. Even when the adjustable shell is fully closed it still forms a ring shaped divergent nozzle. Usually the nozzle convergent side is missing because the turbine extracts work from exhaust gas hence recompressing the gas after the turbine would decrease efficiency. Jan 7, 2020 at 17:52
• So basically, any attempt at recovering heat would result in a decreased expansion and thus decreased thrust and efficiency? Jan 8, 2020 at 16:50
• If you cool the exhaust gas, the speed decreases (speed depends on temperature) and the flow vein contracts; it gets denser and slower. Won’t exert more pressure on the walls of the divergent nozzle (in fact the pressure will decrease because of contraction), therefore less thrust will be achieved. However, if you cooled the intake air, then denser air entered the compressor. The air will then be compressed and heated the same, but starting from a lower temperature the final state will result in higher pressure. Jan 8, 2020 at 21:34
• Am I reading this correctly? The heat exchanger is cooling the intake air, right? That would make sense, since you want the intake air as dense as possible. Jan 25, 2020 at 19:43

Theoretically, in an infinitely efficient system, there would be no net difference. The energy lost in the exhaust would be added back to the combustion chamber to be lost again in the exhaust. Maybe, you could use this heat exchange side engine to run another system without losing engine power. But, there is never something for nothing. Although I've read that the cowled radiator for the piston engine spitfire did produce a small amount of thrust as a biproduct.

This is all predicated by the fact that the heat energy is dumped back into the whole system in or after the combustion chamber. If it's before the the compressors, it would lower the density of the air coming in. Your thrust is based on the mass of the air being accelerated. If it dumped into the compressors, that energy may be lost to the peak amount that the compressors can increase density and pressure. It would be lost in the current way compressors shed excess heat. If the compressors could be made of material that did not need to be protected from excess heat, then there would be no need for the heat exchanger adding heat. It would already be there as a biproduct of compression. Therefore, you would not need to rob it from the exhaust.

• The "Meredith" system used in the Spitfire radiators was just an embryonic thermal ramjet: gas channelled through an asymmetric duct and heated in the middle. Feb 25, 2020 at 17:19
• Efficiency of the combustion zone is greater if the compressor delivers cooler air. Turbocharged piston engines sometimes have an intercooler stage after initial compression. Feb 25, 2020 at 17:23