On the rEvolution of Doorways

Dipping once again this week into my list of topics, I chose a particularly old one: revolving doors. Ever since my stay at Mass. General Hospital, I've been curious how efficient revolving doors are at keeping heat in or out, compared with sliding doors. Last time, aside from the disadvantage of chemo effects, I attempted to do a detailed simulation of the motion of particles through the doorway, which never panned out. This time, I took a much simpler approach using an approximation for the rate of heat flow between two reservoirs:

where Q is the heat energy transferred in a time Δt through a surface of area A. The temperature difference ΔT between the two reservoirs is spread over a distance Δx, and the thermal conductivity k is a property of the air, which we can look up. The idea with a revolving door is that the inside and outside are never in direct contact: The air moves from outside, to a segment of the door, then to the inside. I wasn't sure how to get the distance, since it will change with time as the air moves, but I went with a guess of 20 cm. For the dimensions of the door, I found an architecture page that gave some example measurements. I went for a 3-segment door. For each person who enters, the door will turn 120°, so we can try a few different rates.

Along with the heat transferred, we need to know the current temperature in each section of the door. That will be a simple scale factor, the heat capacity. Since the change in energy/temperature is proportional to the current energy/temperature, we'll get an exponential relationship in time, where the door section will approach the in/outdoor temperature, but never quite make it.

I put together a simulation with some values more suited to my current Florida environment: 20°C (68°F) inside and 35°C (95°F) outside. First, we can look at the temperature in each section of the door as it rotates with 1 person every 30 seconds:

I was surprised how consistent the temperature stayed – In total it's only about half a degree C in variation. To get a visualization of what was going on, I made an animation from the same run:

I find it really interesting that the oscillations are consistent enough that the door segments return to their original uniform temperature about every 1.5 minutes. I did not expect such a clean result.

Turning to the comparison with the sliding door, we can consider having direct contact between the inside and outside temperatures for the same time it takes for a person to go through the revolving door. We can add up the energy transfer over time for different rates of entry for both the sliding and revolving door. Below I've plotted the results on a log-log scale:

According to this model, the revolving door is only more efficient if more than 120 people per hour are going in/out. However, I suspect this could change drastically with the choice of the temperature spreading distance I mentioned earlier. A more reliable result may be that all the revolving door cases lose nearly the same amount of energy. I've often scoffed at airports that have motorized continuously rotating doors, on the belief that they were wasting power pumping air between the inside and outside, but perhaps I owe those architects an apology!