While Lowen says you can leave out the grills I don't agree,, they provide a place for the unburned sweep to stay with air beneath to burn more completely, and when they are burnt they fall to the bottom to be scooped out easily.
The burner in the afterburner is a pipe or tube burner which is nothing more than a pipe with holes drilled in it to provide a long line of flames to the inner tube. I suggest googling Charles A Hones, a manufacturer of burners specific to burnout ovens and heating equipment. Request a catalog, they make pipe burners with their "buzzer" style air intake which will work well and they also make the gas jets Lowen refers to to dry wet sweeps, also highly necessary.
The end of the afterburner at the front end is open to the room, it provides air intake to the afterburner and provides necessary air to combust the unburnt smoke. The back end of the afterburner has a blower with a nozzle aimed up to induce a draft to exhaust the burnt smoke to the chimney.
Make sure the doors close pretty tightly to minimize air leakage because if the gaps are too large this thing will smoke because the air will leak out of the burn chamber and not pass thru the afterburner. Gasketing would serve you well here.
I've seen these things work and for jewelry sweeps they are very effective.