Earth, Air, Water, and Ice.

In my attempts at Ice Storage Heat Source popularization I have been facing one big challenge: How can you – succinctly, using pictures – answer questions like:

How much energy does the collector harvest?


What’s the contribution of ground?


Why do you need a collector if the monthly performance factor just drops a bit when you turned it off during the Ice Storage Challenge?

The short answer is that the collector (if properly sized in relation to tank and heat pump) provides for about 75% of the ambient energy needed by the heat pump in an average year. Before the ‘Challenge’ in 2015 performance did not drop because the energy in the tank had been filled up to the brim by the collector before. So the collector is not a nice add-on but an essential part of the heat source. The tank is needed to buffer energy for colder periods; otherwise the system would operate like an air heat pump without any storage.

I am calling Data Kraken for help to give me more diagrams.

There are two kinds of energy balances:

1) From the volume of ice and tank temperature the energy still stored in the tank can be calculated. Our tank ‘contains’ about 2.300 kWh of energy when ‘full’. Stored energy changes …

  • … because energy is extracted from the tank or released to it via the heat exchanger pipes traversing it.
  • … and because heat is exchanged with the surrounding ground through the walls and the floor of the tank.

Thus the contribution of ground can be determined by:

Change of stored energy(Ice, Water) =
Energy over ribbed pipe heat exchanger + Energy exchanged with ground

2) On the other hand, three heat exchangers are serially connected in the brine circuit: The heat pump’s evaporator, the solar air collector, and the heat exchanger in the tank. .

Both of these energy balances are shown in this diagram (The direction of arrows indicates energy > 0):

Energy sources, transfer, storage - sign conventions

The heat pump is using a combined heat source, made up of tank and collector, so …

Ambient Energy for Heat Pump = -(Collector Energy) + Tank Energy

The following diagrams show data for the season containing the Ice Storage Challenge:

Season 2014 - 2015: Monthly Energy Balances: Energy Sources, Transfer, Storage

From September to January more and more ambient energy is needed – but also the contribution of the collector increases! The longer the collector is on in parallel with the heat pump, the more energy can be harvested from air (as the temperature difference between air and brine is increased).

As long as there is no ice the temperature of the tank and the brine inlet temperature follow air temperature approximately. But if air temperature drops quickly (e.g. at the end of November 2014), the tank is still rather warm in relation to air and the collector cannot harvest much. Then the energy stored in the tank drops and energy starts to flow from ground to the tank.

2014-09-01 - 2015-05-15: Temperatures and ice formation

2014-09-01 - 2015-05-15: Daily Energy Balances: Energy Sources, Transfer, Storage

On Jan 10 an anomalous peak in collector energy is visible: Warm winter storm Felix gave us a record harvest exceeding the energy needed by the heat pump! In addition to high ambient temperatures and convection (wind) the tank temperature remained low while energy was used for melting ice.

On February 1, we turned off the collector – and now the stored energy started to decline. Since the collector energy in February is zero, the energy transferred via the heat exchanger is equal to the ambient energy used by the heat pump. Ground provided for about 1/3 of the ambient energy. Near the end of the Ice Storage Challenge (mid of March) the contribution of ground was increasing while the contribution of latent energy became smaller and smaller: Ice hardly grew anymore, allegedly after the ice cube has ‘touched ground’.

Mid of March the collector was turned on again: Again (as during the Felix episode) harvest is high because the tank remains at 0°C. The energy stored in the tank is replenished quickly. Heat transfer with ground is rather small, and thus the heat exchanger energy is about equal to the change in energy stored.

At the beginning of May, we switched to summer mode: The collector is turned off (by the control system) to keep tank temperature at 8°C as long as possible. This temperature is a trade-off between optimizing heat pump performance and keeping some energy for passive cooling. The energy available for cooling is reduced by the slow flow of heat from ground to the tank.

How Does It Work? (The Heat Pump System, That Is)

Over the holidays I stayed away from social media, read quantum physics textbooks instead, and The Chief Engineer and I mulled over the fundamental questions of life, the universe and everything. Such as: How to explain our heat pump system?

Many blog postings were actually answers to questions, and am consolidating all these answers to frequently asked questions again in a list of such answers. However, this list has grown quickly.

An astute reader suggested to create an ‘animation’ of the gradual evolution of the system’s state. As I learned from discussions, one major confusion was related to the role of the solar collector and the fact that you have to factor in the history of the heat source: This is true for every heat pump system that uses a heat source that can be ‘depleted’, in contrast to a flow of ground water at a constant temperature for example. With the latter, the ‘state’ of the system only depends on the current ambient temperature, and you can explain it in a way not too different from pontificating on a wood or gas boiler.

One thing you have to accept though is how a heat pump as such works: I have given up to go into thermodynamical details, and I also think that the refigerator analogy is not helpful. So for this pragmatic introduction a heat pump is just a device that generates heating energy as an output, the input energy being electrical energy and heat energy extracted from a rather cold heat source somewhere near the building. For 8kW heating power you need about 2kW electrical energy and 6kW ambient energy. The ratio of 8kW and 2kW is called the coefficient of performance.

What the typical intro to heat pumps in physics textbooks does not point out is that the ambient heat source actually has to be able to deliver that input energyduring a whole heating season. There is no such thing as the infinite reservoir of energy usually depicted as a large box. Actually, the worse the performance of a heat pump is – the ratio of output heat energy and input electrical energy, the smaller are the demands on the heat source. The Chief Engineer has coined the term The Heat Source Paradox for this!

The lower the temperature of the heat source, the smaller the coefficient of performance is: So if you run an air source heat pump in mid-winter (using a big ventilator) then less energy is extracted from that air source than a geothermal heat pump would extract from ground. But if you build a geothermal heat source that’s too small in relation to a building’s heating demands, you see the same effect: Ground freezes, source temperature decreases, performance decreases, and you need more electrical energy and less ambient energy.

I am harping on the role of the heat source as the whole point of our ‘innovation’ is our special heat source that has two components, both of them being essential: An unglazed solar collector and an underground water / ice tank plus the surrounding ground. The solar collector allows to replenish the energy stored in the tank quickly, even in winter, and the tank is a buffer: When no energy is harvested by the collector at ambient temperatures below 0°C water freezes and releases latent heat. So you can call that an air heat pump with a huge, silent and mainentance-free ‘absorber’ plus a buffer that provides energy for periods of frost and that allows for storing all the energy you don’t need immediately. Ground does provide some energy as well, and I am planning to post about my related simulations. It can be visulized as an extension of the ice / water energy storage into the surroundings. But the active volume or area of ground is smaller than for geothermal systems as most of the ambient energy actually comes from the solar collector: The critical months in our climate are Dec-Jan-Feb: Before and after, the solar collector would be sufficient as the only heat source. In the three ‘ice months’ water is typically frozen in the tank, but even then the solar collector provides for 75-80% of the ambient energy needed to drive the heat pump.

Components are off-the-shelf products, actually rather simple and cheap ones, such as the most stupid, non-smart brine-water heat pump. What is special is 1) the arrangement of the heat exchanger in the water tank and 2) the custom control logic, that is programming of the control unit.

So here is finally the series of images of the system’s state, shown in a gallery and with captions: You can scroll down to see the series embedded in the post, or click on the first image to see an enlarged view and then click through the slide-show.

Information for German readers: This post contains the German version of this slide-show.

Ice Storage Challenge: High Score!

Released from ice are brook and river
By the quickening glance of the gracious Spring;
The colors of hope to the valley cling,
And weak old Winter himself must shiver,
Withdrawn to the mountains, a crownless king.

These are the first lines of the English version of a famous German poem on spring, from the drama Faust, by Johann Wolfgang von Goethe. Weird factoid about me: I was once inclined to study literature, rather than physics. But finally physics won, so this is a post about joyful toying with modeling heat transport in ice and water.

After 46 days we had a high score: The ice cube, generated by our heat pump, stopped growing at about 15m3. About 10mof water remained unfrozen. After the volume of ice had been in a steady state for a a while, we turned on the solar collector again to return to standard operations.

Where did the energy for the heat pump come from before?

The lid of the tank is insulated against ambient air, the solar collector was not operational, and no ice had been created: The remaining energy has to be provided by the 5th element that cannot be shut off: 1) water 2) ice, 3) ambient air, 4) solar radiation … 5) ground.

Normally ground supplies about 15 W per m2 surface area – deduced from monitoring the power transported with the brine flow and energy accounting for the tank. The active interface between tank and ground below frost depth is about 35 m2. This results in about 0,5 kW in total, thus just 12 kWh per day, much lower than the ~ 50 kWh ambient energy fed into the heat pump.

After much deliberation and playing with the heat transfer equation we came up with this description of the evolution of the ice cube:

Phase 1: Growth of ice into water.

  • Ice starts to grow from the heat exchanger tubes into the remaining water. These tubes are installed in a meandering pattern, traversing the storage tank.
  • At some point the thick layers of ice covering adjacent parts of the pipes touch each other. The surface of this solid ice cube is smaller than the interface between the meandering ice formations and water before. The power needed by the heat pump has to be pushed through a smaller surface – which is only possible if the temperature gradient within the ice gets larger. As the temperature at the ice-water interface has to be 0°C, the temperature at the heat exchanger has to decrease. This is exactly what we see from monitoring data – brine temperature drops well below 0°C.
  • Side-effect: Due to the lower brine temperature the coefficient of performance  decreases slightly. So more of the total heating energy needs to be provided by the electrical input. We call this the heat source paradox: The worse performance is, the more you spare the energy stored in the heat source. Thanks to this self-protection mechanism, the energy in the tank will not suddenly drop to zero.
Ice in the water tank, 2015-03-30

Evolution of the volume of ice, ambient temperature and brine temperature over time. The ice is now quickly melting again – in March the collector is already harvesting enough energy again for balancing heating demands!

Phase 2: Ice touching ground.

  • As long as there is some water between ice and ground, the water temperature is 0°C. This is the temperature ground ‘sees’ and the temperature which is relevant for the low heat transport from ground to water.
  • Ice touches some surfaces of the cuboid tank – the ones where the heat exchanger tubes are closest to the surface. Now ground is directly connected to ice with its temperatures < 0°C. The temperature gradient between ground and ice provides for a higher flow of energy. This is also indicated by the evolution of the temperature in the ground below the tank: While temperatures of undisturbed ground and the region below the tank had been aligned before, ground temperature beneath the tank still kept getting lower – although a few meters away from the tank ground is already warming up again.
  • If enough heat is delivered by ground, no more heat is needed by freezing the remaining water in the tank. When ground temperature reaches zero, it can even freeze – which happens with geothermal systems, too. We might have extended the ice storage into ground.
Temperatures in ground, beneath the water tank.

The temperature sensor closest to the tank in 30 cm underneath. A few meters from the tank ground is already warming up again (following the standard ‘yearly temperature wave’), but below the tank the temperature is still getting lower – as highlighted by the blue rectangle.

Heat transport within ice is actually more efficient than transport in water: Ice has 4 times the heat conductivity of water, and 10 times the thermal diffusivity. The latter is a measure for the time a deposited ‘lump of heat’ will be spread in space:

Heat eqnSo we have built a very efficient cold bridge between the heat exchanger and ground. Everything is consistent with the poetry of the differential equation of heat transfer.

I marvel at the intriguing and mathematically appealing physics in my backyard!

When we grow up, we'll be eggplants!

For the backyard (‘Office desk farming’). Happy Easter everybody!

The Ice Storage Challenge

The more we enjoyed our spring-like winter, the more we were worried if we will ever see much ice in our underground water tank this heating season.

Snowdrops in the garden

So we did what I had announced – we switched off the solar collector completely: Since February 1st our heat pump has been extracting heat energy from the tank only.

Ice started to grow from the heat exchanger pipes into the bulk of the tank, our re-purposed root cellar. These images have been taken at Day 9; showing the part of the pipes above water level:

Ice in the underground water tank, 2015-02-09Ice in the underground water tank, 2015-02-09The density of ice is about 10% lower than the density of water, and the supporting construction needs to make sure that this home-grown iceberg does not start to float. The visible tip of a floating iceberg would be equivalent to those 10% of the total volume. If the whole bulk of ice has to remain under water, the water level increases gradually. There is a tiny heater in the right place, to prevent the formation of a continuous slab of ice that would trap the not-yet-frozen water.

From the change in water level we determine the volume of ice:

Volume of ice in the water tank over time, 2015-03-06The volume of the tank is about 27m3, so it can hold about 25m3 of ice. Now a bit more than half of it is frozen. About 0,3m3 of ice has been created per day, and the rate is slowing down as the weather gets milder and milder. We need less than 70kWh heating energy per day, for space heating and hot water.

The water level has now raised above the top part of the tubes shown in the previous image – and some interesting new structures have emerged which are not directly related to heat pump operations (Image taken at Day 25):

Ice in the underground water tank, 2015-02-25

If it rains heavily, some water trickles down into the former cellar which still uses the original ‘ceiling’ built decades ago. The rain water hits the bulk of ice and is frozen as well.

Next part of this story: High Score!


More data: Our documentation of measurement data now covers two full seasons (since autumn 2012) plus this season until end of January.

A Sublime Transition

Don’t expect anything philosophical or career-change-related. I am talking about water and its phase transition to ice because …

…the fact that a process so common and important as water freezing is not fully resolved and understood, is astonishing.


There are more spectacular ways of triggering this transition than just letting a tank of water cool down slowly: Following last winter’s viral trend, fearless mavericks turned boiling water vapor into snow flakes. Simply sublime desublimation?

Here is an elegant demo of Boiling water freezing in midair in the cold:

The science experiment took its toll: About 50 hobbyist scientists scalded themselves, ignoring the empirical rule about spraying any kind of liquid and wind direction:

“I accidentally threw all the BOILING water against the wind and burnt myself.”

Can it really be desublimation of water vapor? The reverse of this process, sublimation, is well known to science fiction fans:

Special effects supervisor Alex Weldon was charged with devising a way to realistically recreate the look of pools of steaming milky water that had been at the location. He concocted similar liquid with evaporated milk and white poster paint, mixed with water and poured into the set’s pools. Steam bubbling to the top was created with dry ice and steam machines, passed into the water via hidden tubing.

(Source: Star Trek online encyclopedia Memory Alpha on planet Vulcan.)

Dry ice is solid carbon dioxide, and it is the combination of temperature and atmospheric pressure on planet earth that allow for the sublimation of CO2. The phase diagram shows that at an air pressure of 1 bar and room temperature (about 293 K = 20°C) only solid and gaseous CO2 can exist:

Carbon dioxide p-T phase diagramIf a chunk of dry ice is taken out of the refrigerator and thrown onto the disco’s dance floor it will heat up a bit, and cross the line between the solid and gas areas in the diagram.

Sublimation of dry ice (Wikimedia, public domain)On the contrary, the phase diagram of water shows that at 1 bar (= 100 kPa) the direct transition from vapor to ice is the is not an option. Following the red horizontal 1-bar-line you need to cross the green realm of the liquid phase:

Phase diagram of water (Wikimedia, User cmglee)You would need to do the experiment in an atmosphere less than 1/100 as dense to sublimate ice or desublimate vapor.

But experiments show that the green area seems to be traversed in the fraction of a second – and boiling water seems to cool down much faster than colder water!

It seems paradoxical as more heat energy need to be removed from boiling water (or vapor!) to cool it down to 0°C. The heat of vaporization is about 2.300 kJ/kg whereas the specific heat of water is only 4 kJ/kgK.

I believe that the sudden freezing  is due to the much more efficient heat transfer between the ambient air and vapor / tiny droplets versus the smaller heat flow from larger droplets to the air.

Mixing water vapor with air will provide for the best exposure of the wildly shaking water molecules to the slower air molecules. If not-yet-vaporized water droplets are thrown into the air, I blame the faster freezing on water’s surface tension decreasing with increasing temperature:

Temperature dependence surface tension of waterSurface tension indicates the work it takes to create or maintain a surface between different phases or substances. The internal pressure inside a water droplet is proportional to surface tension and inverse proportional to its radius. This follows from the work against air pressure needed to increase the size of a droplet. Assuming that droplets of different sizes will be created with similar internal pressures, the average size of droplets will be smaller for higher temperatures.

A cup of water at 90°C will be dispersed into a larger number of smaller droplets and thus a bigger surface exposed to air than a cup at 70°C. The liquid with the lower surface tension will evaporate more quickly.

One more twist: If droplets are created in mid air, as precipitates from condensation or desublimation, it takes work to create their surfaces – proportional to surface tension and area. On the other hand, you gain energy from  these processes – proportional to volume. If the surface tension is lower but the area is larger the total volume is the same – and thus the net effect in terms of energy balance might be the same. But arguments based on energy balance only don’t take into account the dynamic nature of this process, far off thermodynamic equilibrium: The theoretical energy gain can only be cashed in (within the time frame we are interested in it) if condensation or freezing or desublimation is actually initiated – which in turn depends in the shape and area of the surface and on nuclei for droplets.

Heat transfer is of course more efficient for a larger temperature differences between air and water; perhaps that’s why the trend started in Siberia:

I have for sure not discussed any phenomenon involved here. Even hot water kept in a vessel can cool down and freeze faster than initially cooler water: This is called the Mpemba effect, a phenomenon known to our ancestors and rediscovered by the scientific community in the 1960s – after a curious African student refused to believe that his teachers called his observations on making ice cream ‘impossible’. The effect is surprisingly difficult to explain!

In 2013 an Mpemba effect contest had been held and the paper quoted at the top of this post was the winner (out of 22.000 submissions!). Physical chemist Nikola Bregovic emphasizes the impact of heat transfer and convection: Hot water is cooled faster due to more efficient heat transfer to the environment. Stirring the liquid will disturb convective flows inside the vessel and can prevent the Mpemba effect.

The  effect could also be due to different spontaneous freezing temperatures of supercooled water. Ice crystals can start to grow instantly at a temperature below the theoretical freezing point:

Various parameters and processes – such as living organisms in the water or heating water to higher temperatures before! –  might destroy or create nucleation sites for ice crystals. Supercooling of vapor might also allow for a jump over the green liquid area in the phase diagram, and thus for deposition of ice from vapor even at normal pressures.

Quoting Bregovic again:

I did not expect to find that water could behave in such a different manner under so similar conditions. Once again this small, simple molecule amazes and intrigues us with it’s magic.
Ice in our underground water tank, growing at the top layer of heat exchanger tubes. These are only covered with water if a bulk of ice underneath will make the water level rise.

We Want Ice!

We haven’t seen much of it this winter yet.

I am talking both about the ice you would expect in winter and about the one created from extracting heat from a water tank – our heat pump system‘s heat source.

This winter does again disappoint; it seems we will not be able to generate Pannonia‘s largest ice cube in this season. This plot shows the growth of ice in the past three seasons, since the system went live in autumn 2012:

Energy stored in the water tank, January 2015The tank of water can be considered a buffer that stores energy harvested by the solar collector; in addition some energy is directly harvested from the surrounding ground.

The water tank temperature is 20°C maximum. This is the maximum heat source temperature the heat pump can deal with, so the solar collector is hardly used in summer. Heat provided by ground is sufficient to provide the energy which is extracted from the tank on heating hot water.

This is the energy stored in the tank over time:

Energy stored in the water tank-2015-01The specific heat of water is 1,16kWh per m3  – cooling down the 25m3 tank from 20°C to 0°C provides about 580kWh. Currently we need about 70kWh per day for space heating and hot water heating; the maximum in this season was about 100kWh per day so far. We had not seen ice before December in the past three seasons: Water does not freeze as long as as the energy provided by the solar collector replenishes the energy in the tank quickly enough.

The ice formation curves in the first figure show that the blue peaks always follow a cold spell of weather –  a negative peak in the (green) ambient temperature. As soon as there is a positive peak the ice is quickly melted again. This year the latest green positive peak was quite pronounced – about 12°C average daily temperature; maximum temperatures were about 20°C in some regions in Austria.

But we try harder now to create a gigantic ice cube: On rebuilding the solar collector last summer a new feature has been added for research purposes – the effectively utilized area of the collector can be changed by letting brine only flow through a subset of the tubes.

Currently we use only the upper half of the area. There is hoarfrost on the pipes which are in use – as they are colder as energy is extracted from the flowing brine by the heat pump and / or by the water tank:

Solar collector in winter, half of the area used

If this is still not sufficient to challenge the system we might turn off the collector permanently in February. 100kWh heating energy per day translates to 75kWh to be extracted by the heat pump (given a performance coefficient of about 4). The tank containing about 2.000 kWh would then be exhausted and completely frozen in 27 days.

Solar collector in winter, half the area used, closeup


Further information:

Other plots and key performance data for each month and each season are detailed in our documentation of measurement data – this file contains two full seasons as per the writing of this blog post.

In the unlikely case somebody stumbles upon this post when searching for historical weather data for Austria: The English Annals page show the data in a format that is difficult to work with (you need an outdated browser), but CSV files can be downloaded from the German page with historical data. Pick daily data (Tagesauswertung) for the greatest level of detail.