De Laval Nozzles

[LorneGifford]

Hi Everyone

I've joined the forum in the hope someone can help me understand if it is possible to generate a liquid vapour exhaust flow from a gaseous entry in a De Laval subsonic to supersonic nozzle.  Using methane as a working fluid with a relatively low entry temperature (about 200 K, but it's on my other computer) and reasonable 4 bara entry and 0.25 bara exit pressures, the standard formula calculate exit temperature below 95 K that puts methane in its liquid phase.  However, I'm guessing a shock wave would exist in real life at the gas-liquid transition part way down the diverging nozzle at which the working fluid decelerates to subsonic, rises in temperature (kinetic to thermal energy) and comes out the exhaust as a gas at pretty much entry conditions.

Anyway of avoiding this, perhaps by removing kinetic energy just before the gas-liquid interface, and having the exhaust in a liquid phase?  I think the only way to do it is to remove the kinetic energy, otherwise what comes out the back would be the same state as what goes in the front.

The reason for the interest is because De Laval nozzles generate supercooled exhaust flow with the right entry conditions.  A nice supercooled liquid sounds ideal for an inflow of thermal energy from low grade temperature sources.

[LorneGifford]

A heat engine that used the following cycle would by all classical reasoning violate the second law of thermodynamics: 

Overcritical gaseous methane 30 bara and 275 K through a De Laval subsonic to supersonic fixed stator impulse turbine, exhaust ends up 143 K, 4 bara and zero kinetic energy gas state after the turbine,
Exhaust from turbine into a De Laval nozzle at 4 bara to 0.25 bara with outlet transition into a liquid phase due to low exhaust temperature and removal of the kinetic energy that would otherwise generate a thermal shock transition back to gas,
Liquid methane exhaust from nozzle at 95 K and 0.25 bara pressurised to 30 bara and reheated to 275 K entry conditions through a heat exchanger.

A closed cycle with one thermal source, no heat sink and positive mechanical energy surplus, but it violates the second law of thermodynamics.  However, I'm not sure the second law would be applicable at above supersonic speeds, where the energy flow can only go in one direction; down the diverging section of the nozzle.  Reverse flow is blocked by the inability of a shock wave to travel back up the nozzle at greater than the speed of sound.

[LorneGifford]

The theoretical way of generating a cold sink for use in an ambient Organic Rankine Cycle engine without voilating the second law of thermodynamics - ie entropy of the system increases.

[LorneGifford]

So, does anyone have any thoughts on this device? 

I've included a turbine at the bottom of the liquid column to remove energy from the system so that there is kinetic (to electrical) energy removal to balance the thermal energy input.  And overall I'd suggest this appears to be a theoretical way of removing energy from an ambient environment without needing a cold sink and without violating the laws of thermodynamics or entropy.  For entropy you need to consider the whole system, as although the working fluid is in a closed cycle, the ambient heat source is part of the overall entropy calculation.