## What I really did during Christmas and New Year Holidays

First of all a very happy new year to all the viewers of my blog article. This Christmas and new year 2021 eve have been different from any other holiday season so far in my life. I live in Ontario in Canada and unlike US, most of Canada went into a second lockdown from Dec 26 and that will continue till the end of Jan 2021. That means all public places including restaurants, bars, parks etc. closed and no new year fireworks either. Nothing much could be done outside. One of my friend who lives in Waterloo, Ontario has a huge backyard and he decided to make an ice skating ring for kids during holiday season. Being a designer himself he used 3DX design applications to create the model and asked for my help in simulation. So we got an exciting and novel project to execute during Holidays.

There are two aspects of simulation in skating ring, one is thermal and other is structural. Let’s see how simulation addressed each of these:

Thermal Requirement: The ambient temperature around new year has been between -1C and -3C in southern Ontario. At this temperature solidification of water into ice would be a concern. Standard ice skating ring practice recommends that ice bed should be atleast 6 inches thick so it can take load of person with skates. Few questions arise here:

1. How long will it take to solidify a 6 inches pool of water to ice at ambient temperature?
2. Can we save time by solidifying two layers of water, each of 3 inches thickness instead of a single 6inches layer?

The answer can be found by doing a transient thermal simulation that we did in Abaqus standalone 2021 release. The simulation was done on a rectangular cross section of ice bed so geometry was very simple. We used following scenario and properties.

Ambient Temperature -3C, initial water temperature 5C, water pool dimensions 15m x 9m x 6in, phase change temp range  -0.2C to 0.2C, Latent heat of water 333kJ/kg, specific heat of water 4220 J/kg/K, thermal conductivity of water 0.5 W/mK. We assumed wind speed to be 40km/hr and air convection coefficient calculated as 39W/m2 C using following formulation.

Results and conclusion: We rerun the simulation for different duration of time at 6inches and 3inches thickness respectively till we see top layer completely frozen below -0.2C and inside region reaches at least fusion temperature which is 0.2C. We found that 3inches thickness bed takes 3.7 days to solidify in this way while 6inches thickness bed takes 13.7 days. It makes perfect sense to complete the process in two or more layers instead of single layer.

Structural Requirement: Once ice bed is formed, temperature may go well below -3C as winter approaches. This will further expand the ice and cause stresses on surrounding wooden structure that supports the ice. Can wooden structure sustain the stresses caused by thermal expansion of ice? We got answer to this by performing structural simulation of outer wooden structure using DRD role of 3DExperience 2020 release which is now SFO role in 2021 release. We used data as follows:

Thermal expansion of ice taken as 60e-6/degree C. Accordingly a 10m long ice bed will expand by 6mm with a 10C drop in temperature. We used a quarter model because of symmetry and applied 3mm enforced displacement in both directions.

Results and conclusions: Wood can resist upto 70MPa stresses and the structure was loaded only upto 50MPa stresses. That means wood can resist thermal expansion of ice till -10C. We did not check for further lower temperatures as further drop is unlikely. It would have been nice to capture real time wind speed and temperature data from weather apps and link it to our thermal model. However, the data acquisition took too long to accommodate this factor.