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Round flue give better draw. Smoke rise and circles. When you are calculating a square flue area, for example, you use the largest diameter circle that would fit in it for the calculation. That is for straight flue.
For a throat, the concept is different, and a rectangular shape is best, along with a curve to provide a venturi effect.
Also I believe that the surface area for a circular flue is less than a square or rectangular for the same sized area, therefore there would be less friction or resistance for the flue to pass.
Also, rectangular chimneys would generally be made from brick which would take longer the heat up and draw properly than a round cylindrical steel/stainless flue.
Prevention is better than cure, - do it right the first time!
The more I learn, the more I realise how little I know
At this point, I will be attempting to build a rectangular throat with a venturi effect, much like the shape of a horn-loaded loudspeaker. Kebwi's 36" in Seattle is what I will use as a model. My initial thoughts are to make the rectangle with opposite short sides the same. The long sides would have a gentle slope for the side nearest the oven, and a more aggressively curved slope for the side nearest the outer arch. The thought here is that a curved venturi surface increases the speed of air traveling (like a wing) over it. This would help keep smoke/exhaust from the oven exiting the front of the oven.
Any engineers out there who could validate this reasoning?
For optimum airflow the transition should be the same width as the door and as deep as the diameter of the pipe. It should then be a square to round with as gentle a slope as possible in your space. That is the ideal from a purely airflow point of view, but obviously you can make concessions for space limitations. This is how I built my vent and it draws perfectly with no smoke out the front even on startup.
Give the smoke a reason to go up vs out. I have a rectangular (in one dimension) vent. But did sneaky things to make the smoke go up. I rounded the edges of the transition by cutting 45 degree angles as smoke does not like sharp turns. I made my outer brick arch 1 inch lower than the inner and kept the transistion sharp to keep the smoke in the flu. So far so good no smoke stains on the front of my oven. I love my oven.
I would try to cast mine next time. Sorry for bad typing I'm on my cell.
It seems smoke channel shape is very important for better gas flow.
Round channels provide the best gas flow, square second best and rectangular channels offer the poorest gas flow The further a rectangle retreats from a square the greater resistance to gas flow.