I was recently asked to investigate a problem for the design and operability of a hot water sphere energy storage vessel that is part of a compressed air energy storage system. The vessel in question was described in the previous article here.
The problem can be simply stated:
We have a large volume of high-pressure hot water, greater than 5,000m3, which we empty periodically to make use of the energy stored in the water. As we empty the vessel, the pressure drops and the water evaporates. If we evacuate the vessel fast enough, could we produce a super-heated liquid that would flash boil and vaporise a large volume of liquid, and create pressure swings and instabilities that would affect the operability of the system?.
The physics of super-heated water and flash boiling is something that can be observed in everyday life. If you heat water in a new glass in a microwave, it is easy to obtain a water temperature above the liquid’s normal boiling point. This is because the glass is smooth, and the nucleation of bubbles is retarded during the heating. If we take the water and add a spoonful of sugar, then the bubbles quickly nucleate on the sugar and the liquid can violently flash boil.
This is a dangerous situation as microwaves can produce a significant degree of superheat and people have been known to be scalded or burnt due to the hot steam produced. Incidentally, this is one of the reasons why food products should be stirred between stages of heating when using a microwave.
Anyway, back to the hot water sphere problem. Research showed that, to understand the physics of the problem, we needed a model for non-equilibrium boiling processes. This model needed to be coupled to the other physical processes of fluid flow, momentum, and heat transfer. The problem was solved using computation fluid dynamics (CFD), which proved that, for the design draining flowrates, the degree of superheating, and hence potential for flash boiling, was not a significant operational issue. The investigation was also able to show at what flowrates the problem of flash boiling would appear.
Very interesting, but so what? I hear you say. Well, the twist is that the non-equilibrium boiling process was previously studied by Albert Einstein (of E=mc2 fame). Einstein had derived the key equations of the departure from equilibrium of a system based on the diffusion processes for gas mixtures. We had used the differential form to solve our hot sphere problem where the local vapour fraction can depart from the thermodynamic equilibrium value.
"Digging deeper, as is my tendency, you will find that Einstein’s equations are also linked to Einstein’s fridge. Bet you didn’t know that Einstein invented a fridge?"
Einstein’s Fridge – Patent 11 November 1930
Einstein’s fridge is a simple thermodynamic cycle that needs only a heat source to produce cooling to the degree that is useful for the everyday kitchen. That’s right, a little bit of heat from any source and you get some useful cold. Einstein, along with former student Leo Szilard, developed this fridge in 1926 after learning that an entire Berlin family was killed due to faulty compressor seals that leaked during the night, resulting in poisoning from the then-toxic refrigerant. Their collaboration resulted in more than 45 patent applications in six different countries.
None of Einstein and Szilard’s alternative designs for refrigerators ever became a consumer product, mostly because, in the intervening time, freon was invented, which was non-toxic and became the accepted way to build a fridge. It wasn’t until many decades later, that freon was discovered to be one of the main causes of ozone destruction in the atmosphere. Alternative refrigerants that are ozone-friendly are now in common use, but unfortunately many of these have been found to be potent greenhouse gases. The law of unintended consequences strikes again!
"So, what has happened to Einstein’s fridge? Interestingly enough, it has become a hot topic in recent times. William Broadway invented a portable fridge system for vaccines based on Einstein and Szilard’s design and won the James Dyson prize in 2016. In 2016, the world health organisation estimated that 1.5 million people could be saved using this technology".
With the development of COVID vaccines and the need for deployment to developing countries where people are remote and refrigeration is not common, the use of Einstein’s fridge will likely become even more important in the coming months and years.
We can see that we can start with trying to solve a simply stated problem and that, with a little effort and know-how, we can find an answer. Along the way, we can learn and discover things that we would hardly have imagined at the start of our journey. How many process engineers have used an equation of Einstein’s in their calculations? It was a first for me.
If you would like to know more, please contact Craig Branch: firstname.lastname@example.org
Additional related reading: ISOBAR James Dyson Award: click here to read