Mr. Bubble Was Confused. A Cliffhanger.

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:

Level sensor: The old way

So a multitude of prototypes had been evaluated …

Level sensors: The precursors

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:

blubber-messrohr-3

Mr. Bubble is fine and sane, as long as ice is growing monotonously: Ice grows from the heat exchanger tubes into the water, and 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!

>> Next episode.

Where to Find What?

I have confessed on this blog that I have Mr. Monk DVDs for a reason. We like to categorize, tag, painstakingly re-organize, and re-use. This is reflected in our Innovations in Agriculture …

The Seedbank: Left-over squared timber met the chopsaw.

The Nursery: Rebirth of copper tubes and newspapers.

… as well as in my periodical Raking The Virtual Zen Garden: Updating collections of web resources, especially those related to the heat pump system.

Here is a list of lists, sorted by increasing order of compactification:

But thanks to algorithms, we get helpful advice on presentation from social media platforms: Facebook, for example, encouraged me to tag products in the following photo, so here we go:

“Hand-crafted, artisanal, mobile nursery from recycled metal and wood, for holding biodegradable nursery pots.” Produced without crowd-funding and not submitted to contests concerned with The Intersection of Science, Art, and Innovation.

Ice Storage Hierarchy of Needs

Data Kraken – the tentacled tangled pieces of software for data analysis – has a secret theoretical sibling, an older one: Before we built our heat source from a cellar, I developed numerical simulations of the future heat pump system. Today this simulation tool comprises e.g. a model of our control system, real-live weather data, energy balances of all storage tanks, and a solution to the heat equation for the ground surrounding the water/ice tank.

I can model the change of the tank temperature and  ‘peak ice’ in a heating season. But the point of these simulations is rather to find out to which parameters the system’s performance reacts particularly sensitive: In a worst case scenario will the storage tank be large enough?

A seemingly fascinating aspect was how peak ice ‘reacts’ to input parameters: It is quite sensitive to the properties of ground and the solar/air collector. If you made either the ground or the collector just ‘a bit worse’, ice seems to grow out of proportion. Taking a step back I realized that I could have come to that conclusion using simple energy accounting instead of differential equations – once I had long-term data for the average energy harvesting power of the collector and ground. Caveat: The simple calculation only works if these estimates are reliable for a chosen system – and this depends e.g. on hydraulic design, control logic, the shape of the tank, and the heat transfer properties of ground and collector.

For the operations of the combined tank+collector source the critical months are the ice months Dec/Jan/Feb when air temperature does not allow harvesting all energy from air. Before and after that period, the solar/air collector is nearly the only source anyway. As I emphasized on this blog again and again, even during the ice months, the collector is still the main source and delivers most of the ambient energy the heat pump needs (if properly sized) in a typical winter. The rest has to come from energy stored in the ground surrounding the tank or from freezing water.

I am finally succumbing to trends of edutainment and storytelling in science communications – here is an infographic:

Ambient energy needed in Dec/Jan/Fec - approximate contributions of collector, ground, ice

(Add analogies to psychology here.)

Using some typical numbers, I am illustrating 4 scenarios in the figure below, for a  system with these parameters:

  • A cuboid tank of about 23 m3
  • Required ambient energy for the three ice months is ~7000kWh
    (about 9330kWh of heating energy at a performance factor of 4)
  • ‘Standard’ scenario: The collector delivers 75% of the ambient energy, ground delivers about 18%.
  • Worse’ scenarios: Either collector or/and ground energy is reduced by 25% compared to the standard.

Contributions of the three sources add up to the total ambient energy needed – this is yet another way of combining different energies in one balance.

Contributions to ambient energy in ice months - scenarios.

Ambient energy needed by the heat pump in  Dec+Jan+Feb,  as delivered by the three different sources. Latent ‘ice’ energy is also translated to the percentage of water in the tank that would be frozen.

Neither collector nor ground energy change much in relation to the base line. But latent energy has to fill in the gap: As the total collector energy is much higher than the total latent energy content of the tank, an increase in the gap is large in relation to the base ice energy.

If collector and ground would both ‘underdeliver’ by 25% the tank in this scenario would be frozen completely instead of only 23%.

The ice energy is just the peak of the total ambient energy iceberg.

You could call this system an air-geothermal-ice heat pump then!

____________________________

Continued: Here are some details on simulations.

Frozen Herbs and Latent Energy Storage

… having studied one subject, we immediately have a great deal of direct and precise knowledge … of another.

Richard Feynman

Feynman referred to different phenomena that can be described by equations of the same appearance: Learning how to calculate the distribution of electrical charges gives you the skills to simulate also the flow of heat.

But I extend this to even more down-to-earth analogies – such as the design of a carton of frozen herbs resembling our water-tight underground tank.

(This is not a product placement.)

No, just being a container for frozen stuff is too obvious a connection!

Maybe it is the reclosable lid covering part of the top surface?

Lid of underground water/ice storage tank.

No, too obvious again!

Or it is the intriguing ice structures that grow on the surface: in opened frozen herb boxes long forgotten in the refrigerator – or on a gigantic ice cube in your tank:

Ice Storage Challenge of 2015 - freezing 15m3 of water after having turned off the solar/air collector.

The box of herbs only reveals its secret when dismantled carefully. The Chief Engineer minimizes its volume as a dedicated waste separating citizen:

… not just tramping it down (… although that sometimes helps if some sensors do not co-operate).

He removes the flaps glued to the corners:

And there is was, plain plane and simple:

The Chief Engineer had used exactly this folding technique to cover the walls and floor of the former root cellar with a single piece of pond liner – avoiding to cut and glue the plastic sheet.

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 / air collector and an underground water / ice tank plus the surrounding ground. The collector allows to replenish the energy stored in the tank quickly, even in winter: Air temperature just needs to be some degrees warmer than the cold brine. 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 visualized 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 / air collector: The critical months in our climate are Dec-Jan-Feb: Before and after, the 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 collector provides for 75-80% of the ambient energy needed to drive the heat pump.(*)

(*) Edit: This post written in 2017 show how much energy is stored / exchanged by each component. An overview of essential numbers is given here; emphasis on the volume of ice – which is compared to simulations here.

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.

More information on the system (technical data, sizing) and measurement data since 2012 can be found in this documentation – updated every few months.

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

Economics of the Solar Collector

In the previous post I gave an overview of our recently compiled data for the heat pump system.

The figure below, showing the seasonal performance factor and daily energy balances, gave rise to an interesting question:

In February the solar collector was off for research purposes, and the performance factor was just a bit lower than in January. Does the small increase in performance – and the related modest decrease in costs of electrical energy – justify the investment of installing a solar collector?

Monthly Performance Factor, Heat Pump System

Monthly heating energy provided by the heat pump – total of both space heating and hot water, related electrical input energy, and the ratio = monthly performance factor. The SPF is in kWh/kWh.

Daily energy balances, heat pump system, season 2014-2015

Daily energies: 1) Heating energy delivered by the heat pump. Heating energy = electrical energy + ambient energy from the tank. 2) Energy supplied by the collector to the water tank, turned off during the Ice Storage Challenge. Negative collector energies indicate cooling of the water tank by the collector during summer nights. 200 kWh peak in January: due to the warm winter storm ‘Felix’.

Depending on desired pay-back time, it might not – but this is the ‘wrong question’ to ask. Without the solar collector, the performance factor would not have been higher than 4 before it was turned off; so you must not compare just these two months without taking into account the history of energy storage in the whole season.

Bringing up the schematic again; the components active in space heating mode plus collector are highlighted:

Space heating with solar collector on, heat pump system punktwissen.

(1) Off-the-shelf heat pump. (2) Energy-efficient brine pump. (3) Underground water tank, can also be used as a cistern. (4) Ribbed pipe unglazed solar collector (5) 3-way valve: Diverting brine to flow through the collector, depending on ambient temperature. (6) Hot water is heated indirectly using a large heat exchanger in the tank. (7) Buffer tank with a heat exchanger for cooling. (8) Heating circuit pump and mixer, for controlling the supply temperature. (9) 3-way valve for switching to cooling mode. (10) 3-way valve for toggling between room heating and hot water heating.

The combination of solar collector and tank is ‘the heat source’, but the primary energy source is ambient air. The unglazed collector allows for extracting energy from it efficiently. Without the tank this system would resemble an air heat pump system – albeit with a quiet heat exchanger instead of a ventilator. You would need the emergency heating element much more often in a typical middle European winter, resulting in a lower seasonal performance factor. We built this system also because it is more economical than a noisy and higher-maintenance air heat pump system in the long run.

Our measurements over three years show that about 75%-80% of the energy extracted from the tank by the heat pump is delivered to it by the solar collector in the same period (see section ‘Ambient Energy’ in monthly and yearly overviews). The remaining energy is from surrounding ground or freezing water. The water tank is a buffer for periods of a few very cold days or weeks. So the solar collector is an essential component – not an option.

In Oct, Nov, and March typically all the energy needed for heating is harvested by the solar collector in the same month. In ‘Ice Months’  Dec, Jan, Feb freezing of water provides for the difference. The ice cube is melted again in the remaining months, by the surplus of solar / air energy – in summer delivered indirectly via ground.

The winter 2014/2015 had been unusually mild, so we had hardly created any ice before February. The collector had managed to replenish the energy quickly, even in December and January. The plot of daily energies over time show that the energy harvested by the collector in these months is only a bit lower than the heating energy consumed by the house! So the energy in the tank was filled to the brim before we turned the collector off on February 1. Had the winter been harsher we might have had 10 m3 of ice already on that day, and we might have needed 140kWh per day of heating energy, rather than 75kWh. We would have encountered  the phenomena noted during the Ice Storage Challenge earlier.

This post has been written by Elke Stangl, on her blog. Just adding this in case the post gets stolen in its entirety again, as it happened to other posts tagged with ‘Solar’ recently.

Heat Pump System Data: Three Seasons 2012 – 2015

We have updated the documentation of monthly and seasonal measurement data – now including also the full season September 2014 to August 2015.

The overall Seasonal Performance Factor was 4,4 – despite the slightly lower numbers in February and March, when was the solar collector was off during the Ice Storage Challenge.

Edit: I have learned from a question that the SPF is also calculated in BTU/Wh. ‘Our’ SPF uses the same units in nominator and denominator, so 4,4 is in Wh/Wh. The conversion factor is about 3,4 (note that I use a decimal comma BTW), so our SPF [kWh/kWh] is equivalent to an SPF [BTU/Wh] ~ 15.

Monthly Performance Factor, Heat Pump System

Monthly heating energy provided by the heat pump – total of both space heating and hot water water, related electrical input energy, and the ratio = monthly performance factor. The SPF is in kWh/kWh.

The SPF determines economics of heating with a heat pump.

It’s time to compare costs again, based on current minimum prices of electricity and natural gas in our region in Austria (published by regulator e-control):

  • We need about 20.000 kWh (*) of heating energy per year.
  • Assuming a nearly perfect gas boiler with an efficiency of 95%, we would need about 21.050 kWh of gas.
  • Cost of natural gas incl. taxes, grid fees: ~ 0,0600 € / kWh
  • Yearly energy costs for heating with gas would be: € 1.260
  • Given an SPF of 4,4 for the heat pump, 20.000 kWh heating energy demands translate to 4.545 kWh of electrical energy.
  • Costs of electricity incl. taxes, grid: ~ 0,167 € / kWh
  • Yearly energy costs for heating with the heat pump: € 760
  • Yearly savings with the heat pump: € 500 or 40% of the costs of gas.

(*) As indicated in the PDF, In the past year only the ground floor was heated by the heat pump. So we needed only 13.300 kWh. In the first floor we got rid of the remainders of the old roof truss. The season 2012/2013 was more typical, requiring about 19.700 kWh.

The last winter was not too extreme – we needed 100 kWh maximum heating energy per day. The collector was capable of harvesting about 50 kWh / day:

Daily energy balances, heat pump system, season 2014-2015

Daily energies: 1) Heating energy delivered by the heat pump. Heating energy = electrical energy + ambient energy from the tank. 2) Energy supplied by the collector to the water tank, turned off during the Ice Storage Challenge. Negative collector energies indicate cooling of the water tank by the collector during summer nights. 200 kWh peak in January: due to the warm winter storm ‘Felix’.

Ice formation in this season was mainly triggered by turning off the solar collector deliberately. As soon as we turn the collector on again in March the ice was melted quickly, and the temperature increased to the set value of 8°C – a value picked deliberately to prepare for cooling in summer:

Temperatures and ice formation, heat pump system, season 2014-2015

Daily averages of the air temperature and the temperature in the water tank plus volume of ice created by extracting heat from the heat source (water tank).

Further reading / about the system:
I am maintaining a list of answers to Frequently Asked Questions here.