As a liquid cools from a temperature in a tank that is above its boiling point outside in a chamber, some will flash to vapor, which would drive all the fluid out of the chamber out through a bell nozzle. This mix of vapor and liquid can then can be directed into the periphery of a circular chamber with a exit in the center and a small nozzle at the periphery pointing in the opposite direction of the fluid flow. The vapor will leave through the center exit and the liquid, being denser then the vapor, will exit out the opening at the periphery at a speed of the fluid mix. This speed can be reduced in another nozzle to create very high pressures, since the pressure is proportional to the density and the speed squared. This high pressure fluid could be used in a liquid jet cutter or sent into a high pressure rocket chamber. Ideally, for highest efficiency, the exit at the center should untwist the spinning vapor, converting its rotary motion into linear motion leading out of the sphere. One way is with vanes, another is by using letting the vapor exit through a nozzle off center pointing in the opposite direction of the fluid flow.

Thermodynamics can be used to calculate the exhaust velocity of such a system. For the case of water expanding to sea level pressure, start with liquid water at its boiling point at pressure P. The water is partially flashed to steam and expanded isentropically down to 100,000 N / m^2, through an ideal nozzle. How fast is it going?

This can be solved by finding the entropy of saturated liquid water at P and at 100,000 N / m^2 and vapor at 100,000 N / m^2, then solving for the fraction of water that remains liquid under the assumption entropy is constant. From this, subtract the enthalpies to get the kinetic energy of the exhaust, from which the exhaust velocity can be calculated. This is for sea level, at lower pressures the difference in enthalpy would be greater, so the exhaust velocity would be greater. The static pressure of a moving liquid entering an ideal nozzle is half the density times the velocity squared. For water:

Water pressure = 1 / 2 * 1000 kg / m^3 * velocity^2
Water pressure = 500 kg / m^3 * velocity^2
 
Boiling Hot Water Flow
Pressure ( N / m^2 ) Fraction Liquid Velocity ( m / s ) Water Pressure ( N / m^2 )
1,000,000 0.86 260 33,800,000
3,000,000 0.78 424 89,888,000
5,000,000 0.73 517 133,645,000
9,000,000 0.67 643 206,725,000
11,000,000 0.65 692 239,432,000
13,000,000 0.63 738 272,322,000
15,000,000 0.61 781 304,981,000
17,000,000 0.59 823 338,665,000
20,000,000 0.55 892 397,832,000
22,000,000 0.50 983 483,145,000
22,090,000 0.48 1,016 516,128,000

 

For a rocket engine, in the simple case the vapor in the center exits either through its own nozzle to the atmosphere or downstream of the throat of the main bell nozzle. There is a net gain at low pressures because a bit of liquid expanding drives the large remaining portion of the liquid to a high pressure. The optimal pressure gain produced by this is roughly proportional to the piping efficiency, proportional to the density of the liquid and inversely proportional to the density of the vapor. For cryogenic fuels like liquid oxygen and liquid methane where at their boiling points their liquid is about 250 times as dense as their vapor, with a piping efficiency of 0.3, the optimal pressure produced is about 66 atmospheres. Because part of the liquid was not pressurized and actually had its pressure drop; the overall effective pressure is about half that, 33 atmospheres. This can in effect be used to turn a pressure fed rocket with a tank pressure of 10 atmospheres into a pressure fed rocket with a combustion pressure of ( 33 + 10 ) = 43 atmospheres. The pressure boost can be calculated at pumped rocket, where the injector is idealized to see the pressure before the reactants are injected into the combustion chamber. The efficiency is considered to be 0.15 to approximate the loss of thrust caused by part of the reactants having a pressure drop.

This basic principle can be used in a version with an additional propellant. Water can be used as the pressurizer by entraining fuel and oxidizer into the engine. The water vapor is partly wasted; however, since the water is cheaper than the fuel, the engine operates at a lower cost. This adds more pressure, about 80 atmospheres, to the combustion chamber because the water is boiled off at a higher temperature than cryogenic fuels. This is essentially a very efficient form of water injection. This is only useful on the first stage; since the water will lower the average exhaust velocity to about two kilometers per second, depending on the liquid propellants and water fraction; it is only cost effective when the craft is moving less than two kilometers per second relative to its launch site.

Another version that can be used without an additional pressurant is to heat the propellant with the rocket engine, flash it to liquid / vapor, then entrain this extremely high energy liquid part back before the propellant gets heated. This will create a net pressure gain if the piping is well crafted and if the propellant is heated up sufficiently by the engine. In effect it is a self pressurizing part steam engine. This might seem like the propellant is pushing on itself and no work can be done; but, consider a conventional steam engine.

Water at atmospheric pressure is pumped to a high pressure and injected into a chamber, where it is heated and boiled into steam. The steam is then expanded and part of the energy goes into pumping the water to a high pressure and the rest is used for another purpose. In a part steam engine, water at atmospheric pressure is pumped to a high pressure and injected into a chamber, where it heated and partly boiled into steam. The part that is steam is then expanded and part of the energy goes into pumping the water to a high pressure and the rest is used for another purpose. Because only part of the water is turned into steam, less energy is available for pumping; but, if the system is well crafted and enough water is turned into steam, there will still be enough energy to pump the water to a high pressure and have some energy left over for other purposes. In this case, instead of the steam being expanded, turning a turbine for energy which then turns a pump; the steam could be expanded and the water that is entrained by the steam can then in turn entrain the water before it is injected into the chamber. In the case of a rocket engine, the other purpose is to enter the combustion chamber at an intermediate pressure which is higher than the pressure at which it left the tank; but, lower than the pressure at which it was heated by the rocket engine.

In this version, because of the extra level of entrainment the piping efficiency will be lower; in fact the extra extrainment loss might stop the engine from developing a pressure gain at all at low propellant heating, on the other hand there is no vapor loss and a greater part of the fuel is boiled off, so the overall pressure boost might be higher in the end, reaching 70 atmospheres. Basically this is a more sophisticated version that may develop a higher performance; but, might not be worth it as the first version is good enough.

This type of seperator can also be used to obtain liquid from a high pressure vapor. In this case, the high pressure vapor is directed into the periphery of the circular chamber and most will leave through the exit at the center. Since the velocity of the fluid is high, its pressure is low and its temperature is also therefore low, so some of it will condense into liquid. This liquid can then exit out another nozzle at the periphery, pointing in the opposite direction of the vapor nozzle at the periphery.
 
  Invention   Rocket      Resume