Can high pressure mist of water be sprayed into jet engine exhaust, to create steam, to increase velocity? Would the steam generated from high pressure water being injected into the jet engine exhaust increase velocity?
Spraying water into the exhaust stream will cool down the exhaust flow. The energy needed to heat and evaporate the water needs to come from somewhere, after all. The cooler and denser exhaust flow will slow down, so its impulse will become lower, reducing thrust. While the mass flow will go up, its speed will be reduced. Since water enters the flow as a liquid and leaves the nozzle as a gas, its evaporation enthalpy is irretrievably lost and removes energy from the exhaust stream. The slightly higher mass flow in combination with a lower speed will result in a lower impulse.
If you spray water into the intake flow (or after the first few compressor stages), the same evaporation enthalpy will allow a higher mass flow in the intake, so a higher mass flow in the combustion chamber can be achieved. Also, the cooling of the intake air allows to add more fuel in the combustion process, so more thrust can be created. Of course, this is bought with higher fuel flow.
Water injection in the exhaust could work if:
- The water is fully evaporated before it exits the engine exhaust. The fuel injected in the combustion chamber must also be fully evaporated for effective combustion, and this does take some time end effort - and temperatures in the combustor are higher than in the exhaust.
- The injected steam counteracts the effect of the exhaust jet contracting due to extraction of heat to vaporise the water (it does not seem to, see edit below).
Older type military jets used to use water injection back in the days when jet engines were narrow, noisy pipes. Not really required anymore since high bypass ratio turbofans were invented: almost all energy in the hot flow is used for driving the fan blade and the bypass air. Injecting water mist in the engine could still convert some waste heat into free thrust - free if we're not considering the extra infrastructure, tanks, piping etc.
Re-using exhaust waste heat is an old idea first applied with the turbo-charger, patented by Alfred Büchi in 1905. In power stations, this principle is used in combined-cycle power plants to increase overall efficiency:
A combined-cycle power plant uses both a gas and a steam turbine together to produce up to 50 percent more electricity from the same fuel than a traditional simple-cycle plant. The waste heat from the gas turbine is routed to the nearby steam turbine, which generates extra power.
A steam turbine extracts rotational energy from the hot gas turbine exhaust flow. This works for combined-cycle power plants because of the dynamics of the heat transfer, injecting water directly into a gas turbine exhaust does not do much for thrust. There are better ideas:
- Inject water in the compressor, which cools down the flow and increases air density. Since the internal volume of the engine is fixed, increased density means a higher air mass flow through the engine. The science behind this is further explained in this NACA document of 1947. It mentions water/air ratios of 0.05, resulting in a further 5% increase in the total mass flow.
- Inject fuel in the exhaust stream! In the old turbojets there was still a lot of oxygen in the exhaust stream, combined with the high temperatures this gives afterburner thrust.
- Use a bypass fan and extract more energy from the exhaust for the turbine that drives the fan.
Steam expands, but cooler exhaust gas contracts. Injecting the water increases the mass flow with the water weight. Is the total effect beneficial? By means of a back-of-the-envelope check, we could consider a volume of exhaust gas at high temperature, and check how the volume changes after injecting water to create steam.
If we take 10 m$^3$ exhaust gas (air) at 1000K, and inject an amount of water m$_w$ in it so that temperature lowers to 800K, the exhaust gas will contract. How much water do we inject, and does the resulting superheated steam have a higher volume than the contraction due to temperature? All at constant pressure of 100 kPa.
- 10 m$^3$ exhaust gas (air) at 1000K weighs 3.8 kg (source)
- at 1000K, C$_p$ of air is 1.14 kJ/kg.K (source)
- in order to bring 3.8 kg air from 1000 to 800 K, we need to extract $1.14 \cdot 200 \cdot 3.8 $ = 866 kJ
- to transform 1 kg water @ 300 K to Steam @ 800 K, we need 3444 kJ: C$_p$ of water, enthalpy of phase transition water -> vapour, C$_p$ of steam (source).
- so we need to inject 866/3444 = 0.25 kg of water.
The exhaust air has reduced in volume: 3.8 kg air @ 800K is 8.26 $m^3$, so it has lost 1.74 $m^3$ from density increase.
1 kg superheated steam at 800K has a volume of 3.5 m$^3$ (source), so 0.25 kg takes 0.25 $\cdot$ 3.5 = 0.88 m$^3$.
- Exhaust volume has reduced from 10 to (8.26 + 0.88) = 9.14 m$^3$ = 8.6%.
- Mass has increased from 3.8 kg to (3.8 + 0.25) = 4.05 kg = 6.6%
Because of the decrease in total volume, jet exhaust velocity will be lower. Thrust is mass flow * exhaust velocity - the increase in mass flow does not compensate for the decrease in velocity.