The Collector Size Paradox

Recently I presented the usual update of our system’s and measurement data documentation.The PDF document contains consolidated numbers for each year and month of operations:

Total output heating energy (incl. hot tap water), electrical input energy (incl. brine pump) and its ratio – the performance factor. Seasons always start at Sept.1, except the first season that started at Nov. 2011. For ‘special experiments’ that had an impact on the results see the text and the PDF linked above.

It is finally time to tackle the fundamental questions:

What id the impact of the size of the solar/air collector?

or

What is the typical output power of the collector?

In 2014 the Chief Engineer had rebuilt the collector so that you can toggle between 12m2 instead of 24m

TOP: Full collector – hydraulics as in seasons 2012, 2013. Active again since Sept. 2017. BOTTOM: Half of the collector, used in seasons 201414, 15, and 16.

Do we have data for seasons we can compare in a reasonable way – seasons that (mainly) differ by collector area?

We disregard seasons 2014 and 2016 – we had to get rid of a nearly 100 years old roof truss and only heated the ground floor with the heat pump.

Attic rebuild project – point of maximum destruction – generation of fuel for the wood stove.

Season 2014 was atypical anyway because of the Ice Storage Challenge experiment.

Then seasonal heating energy should be comparable – so we don’t consider the cold seasons 2012 and 2016.

Remaining warm seasons: 2013 – where the full collector was used – and 2015 (half collector). The whole house was heated with the heat pump; heating and energies and ambient energies were similar – and performance factors were basically identical. So we checked the numbers for the ice months Dec/Feb/Jan. Here a difference can be spotted, but it is far less dramatic than expected. For half the collector:

  • Collector harvest is about 10% lower
  • Performance factor is lower by about 0,2
  • Brine inlet temperature for the heat pump is about 1,5K lower

The upper half of the collector is used, as indicated by hoarfrost.

It was counter-intuitive, and I scrutinized Data Kraken to check it for bugs.

But actually we forgot that we had predicted that years ago: Simulations show the trend correctly, and it suffices to do some basic theoretical calculations. You only need to know how to represent a heat exchanger’s power in two different ways:

Power is either determined by the temperature of the fluid when it enters and exits the exchanger tubes …

[1]   T_brine_outlet – T_brine_inlet * flow_rate * specific_heat

… but power can also be calculated from the heat energy flow from brine to air – over the surface area of the tubes:

[2]   delta_T_brine_air * Exchange_area * some_coefficient

Delta T is an average over the whole exchanger length (actually a logarithmic average but using an arithmetic average is good enough for typical parameters). Some_coefficient is a parameter that characterized heat transfer for area or per length of a tube, so Exchange_area * Some_coefficient could also be called the total heat transfer coefficient.

If several heat exchangers are connected in series their powers are not independent as they share common temperatures of the fluid at the intersection points:

The brine circuit connecting heat pump, collector and the underground water/ice storage tank. The three ‘interesting’ temperatures before/after the heat pump, collector and tank can be calculated from the current power of the heat pump, ambient air temperature, and tank temperature.

When the heat pump is off in ‘collector regeneration mode’ the collector and the heat exchanger in the tank necessarily transfer heat at the same power  per equation [1] – as one’s brine inlet temperature is the other one’s outlet temperature, the flow rate is the same, and also specific heat (whose temperature dependence can be ignored).

But powers can also be expressed by [2]: Each exchanger has a different area, a different heat transfer coefficient, and different mean temperature difference to the ambient medium.

So there are three equations…

  • Power for each exchanger as defined by [1]
  • 2 equations of type [2], one with specific parameters for collector and air, the other for the heat exchanger in the tank.

… and from those the three unknowns can be calculated: Brine inlet temperatures, brine outlet temperature, and harvesting power. All is simple and linear, it is not a big surprise that collector harvesting power is proportional temperature difference between air and tank. The warmer the air, the more you harvest.

The combination of coefficient factors is the ratio of the product of total coefficients and their sum, like: \frac{f_1 * f_2}{f_1 + f_2} – the inverse of the sum of inverses.

This formula shows what one might you have guessed intuitively: If one of the factors is much bigger than the other – if one of the heat exchangers is already much ‘better’ than the others, then it does not help to make the better one even better. In the denominator, the smaller number in the sum can be neglected before and after optimization, the superior properties always cancel out, and the ‘bad’ component fully determines performance. (If one of the ‘factors’ is zero, total power is zero.) Examples for ‘bad’ exchangers: If the heat exchanger tubes in the tank are much too short or if a flat plat collector is used instead of an unglazed collector.

On the other hand, if you make a formerly ‘worse’ exchanger much better, the ratio will change significantly. If both exchangers have properties of the same order of magnitude – which is what we deign our systems for – optimizing one will change things for the better, but never linearly, as effects always cancel out to some extent (You increase numbers in both parts if the fraction).

So there is no ‘rated performance’ in kW or kW per area you could attach to a collector. Its effective performance also depends on the properties of the heat exchanger in the tank.

But there is a subtle consequence to consider: The smaller collector can deliver the same energy and thus ‘has’ twice the power per area. However, air temperature is given, and [2] must hold: In order to achieve this, the delta T between brine and air necessarily has to increase. So brine will be a bit colder and thus the heat pump’s Coefficient of Performance will be a bit lower. Over a full season including the warm periods of heating hot water only the effect is less pronounced – but we see a more significant change in performance data and brine inlet temperature for the ice months in the respective seasons.

Same Procedure as Every Autumn: New Data for the Heat Pump System

October – time for updating documentation of the heat pump system again! Consolidated data are available in this PDF document.

In the last season there were no special experiments – like last year’s Ice Storage Challenge or using the wood stove. Winter was rather mild, so we needed only ~16.700kWh for space heating plus hot water heating. In the coldest season so far – 2012/13 – the equivalent energy value was ~19.700kWh. The house is located in Eastern Austria, has been built in the 1920s, and has 185m2 floor space since the last major renovation.

(More cross-cultural info:  I use thousands dots and decimal commas).

The seasonal performance factor was about 4,6 [kWh/kWh] – thus the electrical input energy was about 16.700kWh / 4,6 ~ 3.600kWh.

Note: Hot water heating is included and we use flat radiators requiring a higher water supply temperature than the floor heating loops in the new part of the house.

Heating season 2015/2016: Performance data for the 'ice-storage-/solar-powered' heat pump system

Red: Heating energy ‘produced’ by the heat pump – for space heating and hot water heating. Yellow: Electrical input energy. Green: Performance Factor = Ratio of these energies.

The difference of 16.700kWh – 3.600kWh = 13.100kWh was provided by ambient energy, extracted from our heat source – a combination of underground water/ice tank and an unglazed ribbed pipe solar/air collector.

The solar/air collector has delivered the greater part of the ambient energy, about 10.500kWh:

Heating season 2015/2016: Energy harvested from air by the collector versus heating-energy

Energy needed for heating per day (heat pump output) versus energy from the solar/air collector – the main part of the heat pump’s input energy. Negative collector energies indicate passive cooling periods in summer.

Peak Ice was 7 cubic meters, after one cold spell of weather in January:

Heating season 2015/2016: Temperature of ambient air, water tank (heat source) and volume of water frozen in the tank.

Ice is formed in the water tank when the energy from the collector is not sufficient to power the heat pump alone, when ambient air temperatures are close to 0°C.

Last autumn’s analysis on economics is still valid: Natural gas is three times as cheap as electricity but with a performance factor well above three heating costs with this system are lower than they would be with a gas boiler.

Is there anything that changed gradually during all these years and which does not primarily depend on climate? We reduced energy for hot tap water heating – having tweaked water heating schedule gradually: Water is heated up once per day and as late as possible, to avoid cooling off the hot storage tank during the night.

We have now started the fifth heating season. This marks also the fifth anniversary of the day we switched on the first ‘test’ version 1.0 of the system, one year before version 2.0.

It’s been about seven years since first numerical simulations, four years since I have been asked if I was serious in trading in IT security for heat pumps, and one year since I tweeted:

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 Air 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.

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.

Art from Plastic and Wood

After the musings on Life, the Universe and Everything you deserve a break – and a post with not too much verbiage.

I am borrowing some images from a series of posts the Chief Engineer is currently running on our German blog. (My job job title is Science Officer, but we don’t have a Captain). One of the regular followers of this blog recently discovered that and even honored our blog with the first comment in English.

This is a client’s project. In this case the building has just been built, and the design of water tank and the solar collector for the heat pump had been taken into account in an early stage of the project.

The general concept is the same as shown in earlier posts (schematic here). The water tank serving as the heat pump’s heat source is placed directly underneath the garage, and the solar collector is put on top of it – as a railing to the ‘terrace’.

This is to become the pillars that will support the heat exchanger in the water tank:

Carefully designed to allow for transporting by a small car:

… if you temporarily remove the back seat:

This is the future water tank  / ‘ice storage’ and the supporting construction. The tank will also be used as a cistern.

Here the heat exchanger tubes have finally been mounted: The same type of ribbed pipes are used that also form the solar collector.

Since the Chief Engineer would have been a carpenter or artist working with wood in an alternative universe, the supporting construction for the solar collector is mainly made from wood.

The larch wood laths with the plastic brackets that will hold the collector tubes:

The German post has been titled with The Coronation of a Garage:

The top and bottom wooden cross-bars are mounted to metal pickets. Then the vertical wooden laths are attached to the horizontal ones and the tubes are clipped on to them – laths are placed in front or behind the tubes alternately.

If somebody from the geek / IT / security world clicked on this and managed to scroll down here – there is nerdy stuff included. Actually, we click Refresh on the control system’s web portal all the time right now. But I will keep my promise and stick to the more palpable stuff – in this post!

Measurement Data for Our Heat Pump System – Finally Translated Documentation

In an earlier post  I said

Although we have very innovative, and if I may say so, geeky / nerdy customers it is rather unlikely that we will plan heat pump systems in Australia via sending checklists or doing ‘remote support’ in the same way we work in IT projects.

OK – now we really got a question from a non-German speaker in a remote place who tried to make sense of our mostly German documents. Thus finally I really got started and translated the documentation of measurement data and systems parameters for our heat pump system.

That work sucked all the creativity and research capabilities out of me – so In this post I try to mix some of the diagrams presented in that document with replies to some FAQs.

We had a very warm winter and early spring here in Austria – this was the solar collector last month:

Solar-Collector-March-2014

Solar Collector in March 2014. Beauty is in the eye of the beholder.

It is also reflected in the long-term measurements of ambient temperatures:

Ambient Temperature 2014-04, measurement data heat pump system LEO_2, punktwissen

Ambient air temperature in Zagersdorf, Eastern Austria. ‘Maximum’, ‘average’, and ‘minimum’ refers to one day, respectively.

Although I find that the collector is quite a cool decoration / replacement for a fence the typical question by visitors is (in addition to the question: Where can we install this so that nobody sees it?)

Can I use flat plate collectors?

Not really if the system should work in a performant way. Actually, those unglazed collectors have been picked deliberately, not because they are cheaper and lighter.

This system should replace any other fossil fuel powered system – we haven’t switched on our gas heater in two years now. Thus it has to harvest energy when it is really cold. Flat solar plate collectors are optimized for harvesting energy from solar radiation in summer; they are designed for minimum losses via convection of air.

Unglazed collectors are typically used for heating swimming pools as you can live with rather high convective losses here. But the highly efficient convective heat transfer is to our advantage in winter – then you gain energy even in the night if the temperature of the air is just a few degrees above the temperature of the brine flowing through the collector.

In summer you have more energy than you need anyway, so we don’t care about ‘convective losses’. Rather on the contrary: we are happy that we dont’ have to worry about high temperature making the brine decompose.

In addition the system is used for passive cooling in summer – that is, the temperature of the water tank (the ‘heat source’, then ‘cold source’) must not exceed a reasonable temperate which is well below the room temperature. This is also in line with the fact that there is a maximum heat source temperature the heat pump can deal with, specified by the manufacturer (about 20°C).

Energy Harvested by the Collector 2014-04, measurement data heat pump system LEO_2, punktwissen

Energy harvested by the collector. The total heating demand of the building is about 18.000 kWh per year, incl. hot water. Nearly all the energy needed is delivered to the water tank via the collector (and a minor part directly from ground). Collector power becomes negative if the system operates in cooling mode.

Can you explain BRIEFLY how the system works?

It is all about using a large tank of water as energy storage: The heat pump extracts heat and cools the water, then freezes it. Either the collector transfers heat to the tank in winter, or the floor heating system delivers heat to it in summer when the heater is actually a cooler.

Energy Stored in the Water Tank 2014-04, measurement data heat pump system LEO_2, punktwissen

Energy stored in the Water Tank. The 25m3 water tank corresponds to 430 kWh sensible heat – extracted when cooling water – and 2.300 kWh latent heat – extracted when freezing.

Anything else is the details of hydraulics and control – this is a screenshot of the online monitoring system (a slightly different way to present the hydraulic design shown in the earlier post)

Online Diagram, Hydraulic-Setup. Heat pump system punktwissen.

Online monitoring diagram – sketch of the heat pump system showing measurement data. The water tank and the solar collector are the combined heat source of the heat pump. The heat pump works either in ‘space heating mode’ or ‘hot water heating mode’ and diverts the heating water to either circuit. Buffer storages are important for efficient control as the heat pump always operates at its maximum power.

Regarding the hydraulic design a question that comes up very often is about hot water heating:

You heat hot water indirectly by using a tank at 50°C? I don’t believe you that this is sufficient.

Believe me, it is. My very own very long and very hot showering – elementary showering as I call it – is a worst case test. The heat exchanger in this hygienic storage tank has an effective area of nearly 6m2 – that’s rather large, and this is crucial for a heat-pump-powered system.

The operating temperature of the heat pump should be kept as low as possible in order to obtain high coefficients of performance. Thus the temperature difference between tap water and heating water is rather low, and in order to compensate for that and still get reasonable heating powers the area of the heat exchanger should be big. The effective heating power of this heat exchanger is 12kW.

What’s the performance?

We proudly present:

 Monthly Performance Data 2014-04, measurement data heat pump system LEO_2, punktwissen

Heating Energy: Space heating and hot water. Total Electrical Energy: Heat pump, brine pump, heating circuit pump. Monthly Coefficient of Performance: Ratio of heating energy and electrical energy. The dotted line indicates the performance factor for the whole period covered in the diagram.

Solar-Collector-April-2014

Solar Collector in April 2014