# 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:

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, 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.

# The Stages of Blogging – an Empirical Study

… with sample size 1.

Last year, at the 4-years anniversary, I presented a quantitative analysis – in line with the editorial policy I had silently established: My blogging had turned from quasi-philosophical ramblings on science, work, and life to no-nonsense number crunching.

But the comment threads on my recent posts exhibit my subconsciousness spilling over. So at this anniversary, I give myself permission to incoherent reminiscences. I have even amended the tagline with this blog’s historical title:

Theory and Practice of Trying to Combine Just Anything.

Anecdotal evidence shows that many people start a blog, or another blog, when they are in a personal or professional transition. I had been there before: My first outburst of online writing on my personal websites predated quitting my corporate job and starting our business. The creative well ran dry, after I had taken the decision and had taken action – in the aftermath of that legendary journey.

I resurrected the old websites and I started this blog when I was in a professional no-man’s-land: Having officially left IT security, still struggling with saying No to project requests, working on our pilot heat pump system in stealth mode, and having enrolled in another degree program in renewable energies.

The pseudonymous phase: Trying out the new platform, not yet adding much About Me information. Playing. In the old times, I had a separate domain with proper name for that (subversiv.at). This WordPress blog was again a new blank sheet of paper, and I took the other sites offline temporarily, to celebrate this moment.

The discovery of a new community: The WordPress community was distinct from all other professional communities and social circles I was part of. It seems that new bloggers always flock together in groups, perhaps WordPress’ algorithms facilitate that. I participated with glee in silly blogging award ceremonies. However, I missed my old communities, and I even joined Facebook to re-unite with some of them. Living in separate worlds, sometimes colliding in unexpected ways, was intriguing.

Echoes of the past: I write about Difficult Things That I Handled In the Past – despite or because I have resolved those issues long before. This makes all my Life / Work / Everything collections a bit negative and gloomy. I blogged about my leaving academia, and my mixed memories of being part of The Corporate World. It is especially the difficult topics that let me play with geeky humor and twisted sarcasm.

The self-referential aspect: Online writing has always been an interesting experiment: Writing about technology and life, but also using technology. As philosophers of the web have pointed out, the internet or the medium in general modifies the message. I play with websites’ structure and layout, and I watch how my online content is impacted by seemingly cosmetic details of presentation.

Series of posts – find our favorite topic: I’ve never participated in blogging challenges, like one article a day. But I can understand that such blogging goals help to keep going. I ran a series on quantum field theory, but of course my expertise was Weird Internet Poetry … yet another demonstration of self-referentiality.

The unexpected positive consequences of weird websites – perhaps called ‘authentic’ today. They are a first class filter. Only people who share your sense of humor with contact you – and sense of humor is the single best criterion to find out if you will work well with somebody.

Writing about other people’s Big Ideas versus your own quaint microcosmos. I have written book reviews, and featured my favorite thinkersideas. I focussed on those fields in physics that are most popular (in popular science). My blog’s views had their all-time-high. But there are thousands of people writing about those Big Things. Whatever you are going to write about, there is one writer who cannot only write better, but who is also more of a subject matter expert, like a scientist working also as a science writer. This is an aspect of my empirical rule about your life being clichÃ©. The remaining uncharted territory was my own small corner of the world.

Skin in the Game versus fence-sitting. Lots of people have opinions on many things on the internet. The preferred publication is a link to an article plus a one-liner of an opinion. Some people might really know something about the things they have opinions on. A minority has Skin in the Game, that is: Will feel the consequences of being wrong, personally and financially. I decided to focus on blogging about topics that fulfill these criteria: I have 1) related education and theoretical knowledge, 2) practical hands-on experience, 3) Skin in the Game. Priorities in reverse order.

The revolutionary experiment: Blogging without the motivational trigger of upcoming change. Now I have lacked the primary blogging impulse for a while. I am contented and combine anything in practice since a while. But I don’t have to explain anything to anybody anymore – including myself. I resorted to playing with data – harping on engineering details. I turn technical questions I get into articles, and I spend a lot of time on ‘curating’: creating list of links and overview pages. I have developed the software for my personal websites from scratch, and turned from creating content to structure for a while.

Leaving your comfort zone: I do edit, re-write, and scrutinize blog postings here relentlessly. I delete more content again than I finally publish, and I – as a text-only Courier New person – spend considerable time on illustrations. This is as much as I want to leave my comfort zone, and it is another ongoing experiment – just as the original stream-of-consciousness writing was.

But perhaps I will write a post like this one now and then.

# 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 andÂ  ‘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:

Using some typical numbers, I am illustrating 4 scenarios in the figure below, for aÂ  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.

Ambient energy needed by the heat pump inÂ  Dec+Jan+Feb,Â  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.

# 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?

or

What’s the contribution of ground?

or

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):

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:

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.

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 0Â°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 8Â°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.

# Frozen Herbs and Latent Energy Storage

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

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.

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

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

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:

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.

# On Photovoltaic Generators and Scattering Cross Sections

Subtitle:Â Dimensional Analysis again.

Our photovoltaic generator has about 5 kW rated ‘peak’ power – 18 panels with 265W each.

South-east oriented part of our generator – 10 panels. The remaining 8 are oriented south-west.

Peak output power is obtained under so-called standard testing condition – 1 kWp (kilo Watt peak) is equivalent to:

• a panel temperature of 25Â°C (as efficiency depends on temperature)
• an incident angle of sunlight relative to zenith of about 48Â°C – equivalent to an air mass of 1,5. This determines the spectrum of the electromagnetic radiation.
• an irradiance of solar energy of 1kW per square meter.

Simulated spectra for different air masses (Wikimedia, User Solar Gate). For AM 1 the path of sunlight is shortest and thus absorption is lowest.

The last condition can be rephrased as: We get 1 kW output per kW/m2Â  input. 1 kWp is thus defined as:

1 kWp = 1 kW / (1 kW/m2)

Canceling kW, you end up with 1 kWp being equivalent to an area of 1 m2.

Why is this a useful unit?

Solar radiation generates electron-hole pairs in solar cells, operated as photodiodes in reverse bias. Only if the incoming photon has exactly the right energy, solar energy is used efficiently. If the photon isÂ not energetic enough – too ‘red’ – it is lost and converted to heat. If the photon is too blueÂ  – too ‘ultraviolet’ – it generates electrical charges, but the greater part of its energy is wasted as the probability of two photons hitting at the same time is rare. Thus commercial solar panels have an efficiency of less than 20% today. (This does not yet say anything about economics as the total incoming energy is ‘free’.)

The less efficient solar panels are, the more of them you need to obtain a certain target output power. A perfect generator would deliver 1 kW output with a size ofÂ 1 m2 at standard test conditions. The kWp rating is equivalent to the area of an ideal generator that would generate the same output power, and it helps with evaluating if your rooftop area is large enough.

Our 4,77 kW generator uses 18 panels, about 1,61 m2 each – so 29 m2 in total. Panels’ efficiencyÂ  is then about 4,77 / 29 = 16,4% – a number you can also find in the datasheet.

There is no rated power comparable to that for solar thermal collectors, so I wonder why the unit has been defined in this way. Speculating wildly: Physicists working on solar cells usually have a background in solid state physics, and the design of the kWp rating is equivalent to a familiar concept: Scattering cross section.

An atom can be modeled as a little oscillator, driven by the incident electromagnetic energy. It re-radiates absorbed energy in all directions. Although this can be fully understood only in quantum mechanical terms, simple classical models are successful in explaining some macroscopic parameters, like the index of refraction. The scattering strength of an atom is expressed as:

[ Power scattered ] / [ Incident power of the beam / m2 ]

… the same sort of ratio as discussed above! Power cancels out and the result is an area, imagined as a ‘cross-section’. The atom acts as if it were an opaque disk of a certain area that ‘cuts out’ a respective part of the incident beam and re-radiates it.

The same concept is used for describing interactions between all kinds of particles (not only photons) – the scattering cross section determines the probability that an interaction will occur:

Particles’ scattering strengths are represented by red disks (area = cross section). The probability of a scattering event going to happen is equal to the ratio of the sum of all red disk areas and the total (blue+red) area. (Wikimedia, User FerdiBf)