# inordinatum

Physics and Mathematics of Disordered Systems

## Spatial studies

Étude spatiale No. IV, source: [1]

Visiting an exhibition of Paul Klee recently, I was quite intrigued (among many other exciting ideas in his paintings) by the aesthetic effect of slightly disordered geometric forms… Looking at his “Etudes spatiales” (“Spatial studies” – three examples, unfortunately in rather low resolution, can be found here, one of them shown on the right), I decided to play around a bit and try to generate something similar algorithmically.

After a few hours of tinkering around in Python, here’s the result (i.e. a random sample of the result):It certainly lacks the stringency of the original sketches, but hey, it’s animated 🙂

If you’re interested in the Python source, let me know!

Written by inordinatum

November 16, 2018 at 9:39 am

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## InnoCentive challenge on optimizing soft drink cans

Simulation of air convection during the cooling of a soft-drink can

Nature, arguably one of the most important academic journals in natural sciences, is as of late advertising an “open innovation platform” together with a company called InnoCentive. Their basic idea is to outsource scientific problems (with a certain bias towards chemistry) from enterprises to a broad pool of “solvers” (mostly from academia). The challenges promise a quite substantial cash award to the winner(s), and are not at all boring but rather quite appealing research problems.

So one day, I decided to take my chances and participate in one: Containers that keep beverages cold longer. This challenge required only a written solution, which should propose a modified drink container that keeps cold longer in a warm environment, while satisfying the following constraints:

1. The container should still feel cold on the outside
2. The container, when warm, should not take longer to cool down in a fridge

These constraints eliminate the most basic proposition one would first think of: better insulation. They also seem a bit contradictory (at least to a physicist who is used to simplifying problems to the most general case). On the other hand, I can well imagine that customers would like this!

The first question I had to answer myself for tackling that challenge is how a cold container actually warms up. The main mechanism is, of course, convection. This implies that the thermal conductivity of the container material (e.g. glass vs. aluminum, which are very different) does not have a big influence (for a more detailed discussion see this article). However, the object’s geometry is all the more important, since it influences the air flow velocity around it.

During some more literature research I found this article by Bhavnani and Bergles, who claim to have experimental evidence for a reduction of heat transfer through convection, when transverse ribbing is added to a surface. This sounds very promising, of course – reducing convection still keeps the cold feeling to the can surface. On the other hand putting the can horizontally in the fridge would make the ribbing vertical, which (according to them) enhances convection, and makes it cool down faster! But then this whole idea sounds also a bit strange, since obviously any kind of roughening or ribbing increases the surface area, so it would have to disrupt convective air flow massively in order to over-compensate for that.

I was about to write down a proposal on adding ribbing to a can as a purely theoretical idea, but then I decided to play around some more and see if I could do some computer simulations. After some tries with commercial software, I settled on the open-source Elmer finite element software by the Finnish CSC. It turned out to be easy to use and not overbloated; within a few days I was able to generate nice convection pictures like the one above, and obtain quantitative information on how long various can designs keep cold.

Needless to say, the simulations showed that a ribbed surface kept cold less than the flat one; I don’t know what Bhavnani and Bergles have measured in their paper but I cannot believe their results were correct. So, pressed for new ideas I put some rather mundane improvements in my proposal:

• Better insulating the can base (insulating rim, thicker air layer between can and table) turned out to prolong cold storage by approximately 12%
• Making the shape more aerodynamic (i.e. more bottle-like) further increased the time it keeps cold by about 7%

Unfortunately the total improvement of about 19% still falls short of the goal of this challenge (which was 30%). I submitted my proposal anyway – after all, it has some nice convection pictures in it, gives some improvements, and who knows if the other participants are any better 😉 If anybody is interested in more details on the Elmer implementation, or on the proposal itself, please let me know!

So finally I learned a lot on simulation convection and cooling/heating processes, which is quite nice. I would still like to understand better the interplay between surface area and convection: What is the optimal shape of a body in order to minimize convection? Is it just the surface-area-minimizing sphere, or is it better to make it more streamlined (i.e. narrower near the top) in order to have a “smoother” air flow? Can, in principle, the geometry of the resulting air flow lead to a larger surface having less heat transfer than a smaller one? It seems that these (quite basic questions) are not really answered in physics or engineering literature. But then, they are not that basic since they require information on the solution of the Navier-Stokes equations for the air flow around the object, which is notorious hard. If anybody has any insights on this, I’d be thrilled to know it!

Written by inordinatum

September 9, 2012 at 8:17 am

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