How much does water injection improve thrust of a jet engine?

Question

In 1961 a Navy F4 Phantom Skyburner broke the world speed record with the aid of a water injection system to boost thrust. Water injection was also commonly used to improve take-off performance of many aircraft of that era.

The application in question would be a steam thrust mechanism for a hypersonic propulsion system.

Modern jet engines compress air, raising its temperature to around 1000 K, before heating it to around 2000 K from combustion of fuel.

This would be a pressure or volume gain of around 2 to 1.

Water to steam results in a pressure or volume gain of 1600 to 1.

Hypersonic aircraft surfaces routinely are heated by friction to over 2000 K.

Question 1: why are they even bothering to burn fuel when plenty of heat energy is available from aerodynamic friction?

Question 2: how much thrust would be generated from water to steam vs combustion/heating at those speeds?

That's where the issue is. Essentially, the steam motor would be a rocket. Mass flow would be much less but thermal expansion, 1600 vs 2!

The Rolls-Royce Olympus 101 early jet engine generated around 11,000 lbs of thrust, 9300 lbs from momentum thrust and 1800 lbs from pressure thrust. What sort of numbers would the "steam engine" generate in comparison$^1$?

$^1$ peroxide as monopropellant may be used as a reference. (Temperature of decomposition into steam around 1250 K).

Answer 1

When used 60 years ago on the B-52 and 707, water injection increased thrust by about 30%. Enough water was carried on the 707 for about 5 minutes of takeoff and climb. Its system and the water added weight that could no longer be justified when engines became more powerful. The Concorde was slightly underpowered in dry thrust to be able to operate on 12,000' runways and this was addressed by adding about 20% more afterburning thrust. Considering these examples, the effect of water injection is not insignificant, but it seems it is no longer ever the preferred option. Besides system weight, another drawback is that it is not environmentally friendly and due to the cooling, not all fuel is combusted, leaving soot and pollutants.

Note that water injection increases thrust by accelerating the water mass (and also increases engine performance by cooling); similarly, the mass of added fuel in afterburning also accounts for part of the added wet thrust. In this sense, given that afterburning engines get around two thirds more thrust, effectively by quadrupling fuel consumption, when a significant portion of that thrust is from accelerating the fuel mass, not just from combustion, it is understandable that we might start to wonder if we should swap a few hundred gallons of fuel for water.

I think the numbers on SFC (specific fuel consumption) for afterburing engines are worth commenting on here because the inefficiency is insane, whereas water is rather cheap. For afterburning turbofan engines, fuel flow usually quadruples in reheat. The SFC in the F-16's FW100 increases from 0.76 dry to 1.94 wet - dry thrust being 17,800 lbs and 29,160 lbs wet. When calculating with FW100 thrust figures, dry fuel burn at sea level is 225 lb/minute, but in reheat/wet it's 943 lb/min. So by more than quadrupling the fuel burn, the result is just 64% more or 11360 lbs additional thrust. Considering the F-16 has 7000 lbs internal fuel, this is a heavy price to pay for 64% more (sea level) thrust and it certainly makes an additional 30% thrust from water injection sound appealing at first glance.

As far as actually commercially "budgeting" for wet thrust, the Concorde was the only afterburning commercial aircraft, so it would be interesting to know how close they were to adopting water injection. It would appear the weight savings with afterburners was more important than the cost savings of a heavier water injection system.

For the purpose of civil experimental aircraft it would be extremely interesting to see how water injection could be employed and if a similar 30% boost is achievable. Given that the small TJ-150 engine produces 337 lbs max thrust and probably burns 50 GPH at sea level, the prospect of getting an additional 100 lbs thrust for minimal cost or weight, even for a few minutes, would be very appealing.

Edit: I should also add that the Honeywell TPE331 turboprop engine gains an additional 10% power - Augmented 5 min Rating - from water methanol injection.

Answer 2

With pure jet engines the air density is a major factor in thrust. By injecting water the density is increased. I worked on both the B52G and KC135A military aircraft using J57 engines. Both had water injection which was used on takeoff. Loss of water injection during take off was a emergency that pilots feared. Each engine had a regulator valve to control the amount of water going to that engine. A defective valve would cause the that engine to use far more water than normal resulting in the water supply being exhausted during the take off roll or shortly after the wheels leaving the runway.

Later versions of both aircraft used turbofan engines which did not use water injection.