This year we experienced a record-breaking January in Austria – the coldest since 30 years. Our heat pump system produced 14m3 of ice in the underground tank.
The volume of ice is measured by Mr. Bubble, the winner of The Ultimate Level Sensor Casting Show run by the Chief Engineer last year:
The classic, analog level sensor was very robust and simple, but required continuous human intervention:
So a multitude of prototypes had been evaluated …
The challenge was to measure small changes in level as 1 mm corresponds to about 0,15 m3 of ice.
Mr. Bubble uses a flow of bubbling air in a tube; the measured pressure increases linearly with the distance of the liquid level from the nozzle:
Mr. Bubble is fine and sane, as long as ice is growing monotonously: Ice grows from the heat exchanger tubes into the water. The heat exchanger does not float due to buoyancy, as it is attached to the supporting construction. The design makes sure that not-yet-frozen water can always ‘escape’ to higher levels to make room for growing ice. Finally Mr. Bubble lives inside a hollow cylinder of water inside a block of ice. As long as all the ice is covered by water, Mr. Bubble’s calculation is correct.
But when ambient temperature rises and the collector harvests more energy then needed by the heat pump, melting starts at the heat exchanger tubes. The density of ice is smaller than that of water, so the water level in Mr. Bubble’s hollow cylinder is below the surface level of ice:
Mr. Bubble is utterly confused and literally driven over the edge – having to deal with this cliff of ice:
When ice is melted, the surface level inside the hollow cylinder drops quickly as the diameter of the cylinder is much smaller than the width of the tank. So the alleged volume of ice perceived by Mr. Bubble seems to drop extremely fast and out of proportion: 1m3 of ice is equivalent to 93kWh of energy – the energy our heat pump would need on an extremely cold day. On an ice melting day, the heat pump needs much less, so a drop of more than 1m3 per day is an artefact.
As long as there are ice castles on the surface, Mr. Bubble keeps underestimating the volume of ice. When it gets colder, ice grows again, and its growth is then overestimated via the same effect. Mr. Bubble amplifies the oscillations in growing and shrinking of ice.
In the final stages of melting a slab-with-a-hole-like structure ‘mounted’ above the water surface remains. The actual level of water is lower than it was before the ice period. This is reflected in the raw data – the distance measured. The volume of ice output is calibrated not to show negative values, but the underlying measurement data do:
Only when finally all ice has been melted – slowly and via thermal contact with air – then the water level is back to normal.
In the final stages of melting parts of the suspended slab of ice may break off and then floating small icebergs can confuse Mr. Bubble, too:
So how can we picture the true evolution of ice during melting? I am simulating the volume of ice, based on our measurements of air temperature. To be detailed in a future post – this is my cliffhanger!
elkemental Force 
Interesting challenge. This is when school book physics has to make place for real world engineering. Could you measure the decreasing volume of air in the ice tank or is the quantity of water variable as well?
The total volume of water varies a bit – it increases due to condensation of water from the air – but this is not an important effect.
But the tank is also not air-tight and temperature of the air varies from place to place. Actually, if we wanted to optimize operations more, it would even be beneficial to open the insulated lid automatically in phases of ‘warmer’ weather – this would be typically the same phases when the ice decreases rapidly because of the heating ‘from inside’.
Of course we have the high-tech solution in mind: A 3D grid of wires with temperature sensors in the the tank and above the surface – or nano-bots who know their position ;-) – who would determine the position of the surface and then calculate the volume.
Great to see that you have given this ample thought! It occurred to me that one way to measure air volume in a “closed” tank is to measure its resonance. Hit the tank and measure the sound frequency and even if the tank is open (like an open drum) it would work. Another random thought.
The shape of the volume of air would be irregular and asymmetrical – even without ice … because of the various connections of tubes, wires, pumps etc. No nice standing waves to be expected ;-) The insulated lid (from styrofoam) might also absorb sound waves rather than reflect them.
But from a practical perspective this measurement of volume is not really needed: The important and critical parameter is the minimum allowed brine inlet temperature (allowed by the heat pump vendor) – which is easy to measure. When the block of ice grows, there is a temperature gradient within the ice when the heat pump is on. When brine temperature is below, typically, ~ -10°C, the heat pump will stop working. This limit will be reached before the tank is fully ‘exhausted’. As water can always ‘escape’ to the top and the tank is only filled to 90% to hold the increasing volume of ice, it could theoretically freeze to 100% without damaging the tank … and then the whole ground around it could freeze as well. But before, brine temperature is likely to be too low anyway.
So our main objective in designing such systems is that 1) the tank is large enough that this situation will only occur once in, say, 10-20 years – and heating heating with a backup heating element with a ‘COP’ of only 1 for a few days will not hurt the economic assessment (compared to building an even bigger tank). 2) Lots of heat exchanger tubes have to traverse the volume evenly so that most of the volume can actually be used before brine temperature becomes too low.
I love it. I really don’t understand thermodynamics and you live and breathe it! Madame Joule :)