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:
(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.
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!
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Continued: Here are some details on simulations.
elkemental Force 
Interesting! I recently discovered that mathematics can offer a lot of mental/creative freedom in the process of exploring a concept, but the continued emphasis on axioms, propositions and correct notation or proofs can sometimes induce a bit of anxiety that then makes going forward (or sharing one’s discoveries) almost impossible. I’ve been thinking a lot about Taleb’s Antifragile as a frame for responding to these two contradictory pressures. Your response really ties all this together very nicely; there is a point when we have to set aside the books and just do something.
I didn’t keep a copy of it, but I encountered a quote from Richard Feynman recently that essentially goes that the published results of discoveries follow a format that is efficient and tidy, and always omits the parts that went wrong, the misdirected work, and all the things that led from question to answer to achieve a real understanding of a problem.
I think we already know that we don’t completely trust theoretical ideas on their own, that we require tests and experiments before we purchase or try a new product. So it is always exciting to encounter great ideas that have been refined by trial and experiment (by someone with skin in the game, too!).
Thank you.
I vaguely recall that account of Feynman’s – perhaps it’s the same article / book / talk where he says that he always thinks in specific examples when he works on a seemingly ‘general’ and ‘theoretical’ solution. But I might also confuse with some historical accounts of Einstein’s years of struggling with General Relativity and how this was presented by different authors with hindsight, wrongly presented sometimes as a purely mathematical deduction whereas Einstein thought in terms of physics and followed many blind alleys , ‘tinkering-style’ and in a ‘messy’ way.
Both Einstein and Feynman had exposure to engineering and real-world problems which shaped their philosophy. What worries me is when I read that young people aspire at becoming ‘theoretical physicists’, motivated by popular physics books written by the rock stars in the field. I’ve often read statements like ‘… because I don’t want to do experiments’ or ‘… because I hate lab work…’ as if touching something in the real world is beyond them.
I am starting to become restless with lectures only. I think I might disappear from math for a while and take some physics courses again soon, because of the labs. That isn’t sexy these days (to be hands on), but then, I’m not a young person, either.
I finally launched the new blog this morning. (I hope.) I think the private setting is properly removed now.
I am curious :-) … but I still see your blog as ‘private’.
https://mathatmidlife.wordpress.com
I should have mentioned it has a different name and location. Sorry.
Thanks – honored to leave the first comment on a freshly minted blog ;-) (awaiting moderation)
BTW – I was already considering to write a more philosophical post also on this blog now and then – your new blog will finally nudge me ‘back’!! :-)
Hi Elke, I just did a little reading tour through some old posts and a bit at your not-for-comment website. It was nice to time travel for a while! Interesting that you mention your model that predated the ice storage. One of my instructors likes to tell stories during office hours of his past applications work. He commented once about the differences between the DIY approach of engineers creating a models (a kind of approach that suggests if you can make it, or find it in nature, then you can use it) and mathematicians who sweat all the details and obey every axiom; he seems to find both mindsets amusing and quite different from one another. Do you find there is much difference between the way you thought of your model when you first created it, and now, with another university degree and several years of tinkering in the field?
That’s a very good question, Michelle! I definitely thought about it in a more mathematical way in the beginning – e.g. I even tried to solve the heat equation analytically first. For me the difference between physics and engineering is like: Physics: Know how to derive anything from a few fundamental equations; engineering: know rules-of-thumb and numbers that really count in practice. Summary: “You cannot build a power plant just from knowing Maxwell’s equations”.
Nassim Taleb pointed out in Antifragile that many ‘innovations’ have in fact been done by tinkerers without advanced math knowledge – and ancient buildings still stand despite they did not have 3D software and simulations. These tinkerers rather made progress by trying out small changes that were more likely to result in an improvement but were associated with low risk. Highly optimized systems, on the other hand, are necessarily fragile. Every time I look at some history of engineering in more detail – I see that he was right (heat pumps or solar energy in middle Europe for example).
Of course we were fortunate: The existing cellar happened to be large enough for the building’s energy needs. But we did not fully rely only on the model and used a tinkerer’s approach: We started with a version 1 of the system with a heat pump whose power was much too low and we knew that: We still had the gas boiler as a secondary system. Then we built version 2, using a heat pump of proper sizing, but still having the gas boiler as a backup. Only after we did not use gas for two years, we cancelled our contract.
I don’t say, you don’t need simulations (as I am still using and refining that model myself) but I think there are so many input parameters that you can model and predict anything – if you don’t have any measurements to compare with. But if you have real-live data, you can replace part of your model by those data … and simulations with 1 minute intervalls by simple accounting for every months. You can also over-do the latter: simple accounting in advance (for prediction of peak ice for example), with neither simulations or measurements will not work … in this case because the hydraulic design and control logic is very important, and you cannot assess the impact of all the feedback loops in advance.