This pic just shows the combustion "core" before the barrel was installed over the heat riser. I included this just to give a little context and scale for the next picture (showing the barrel in place). Note that the black flue pipe with a 90 degree elbow is where the gases leave the "stove" portion of the stove and enter the "bench" thermal mass portion of the stove.
This shows the stove with barrels in place and cob starting to take shape around the combustion unit. Notice that the flue leading to the bench has another 90 degree adapter added -- this brought the flue pipe down to the level of the bottom of the heat riser. The round black "cap" visible next to the bucket is for access to clean-out the "transition area" where the gases from the barrel are directed into the flue pipe and light ash can collect from the combustion area.
This is a top-down view of the "transition area" -- the clean-out access is on the left. Notice that the sides of this chamber are being built up so that they narrow in toward the flue pipe. It is hard to tell from this picture, but the walls are also being gradually built closer together as they get taller -- to eventually close the top with a "dome" of cob. Also, the cob on the bottom of this chamber is dug out "below grade" a bit to create an ash-collection pit.
Here is a side-view of the "transition area" at the same stage during construction as the top-down view in the previous picture. The cob walls were built up around the flue cap, which acted as its own "form" for the clean-out opening.
Yet another view at roughly the same stage during construction. As you can see, there is plenty of area for the gas to flow unrestricted from the gap between heat-riser insulation and barrel to the flue.
Clean-out cap cleaned up and with a handle...
This shows the "transition area" completely enclosed with cob. The top of the chamber was reinforced with some stiff metal "hardware cloth" material. If I had more carefully tapered the sides in, I think it could have been done as a cob dome -- but it was easy to drop in some material for support and cob over a flat "roof".