A smoke-free fireplace is not smoke-free. A fire can smoke, and smoke usually means fire.
But here’s the thing: smoke, especially black or grey smoke, is a sign of inefficiency in fires. Most of the smoke is unfueled material, which brings it high into the air. If you burn more efficiently, you create much less unapplied material and therefore less smoke. Of course, you will make the smoke less dirty, less filled with particles, both unpleasant and unhealthy.
Most modern smokeless fireplaces have very similar designs. The fireplace is a double wall design with gaps between the top and bottom walls and vents. The bottom of the pit is raised so oxygen can always reach the flame.
The air is drawn into the vents at the bottom and heated as it travels in the space between the double walls. When it leaves the top vent, it is hot enough to reignite and burn the particles in the smoke during a process called secondary combustion. This secondary combustion makes the fire hotter, more efficient, and generally less smoke efficient.
Interestingly, this is a self-enhancing cycle: if the fire burns hotter, the air circuit through the double walls will also get hotter and accelerate the cycle. As a result, the stove will become hotter, more efficient, and less smoke over time. Usually, when you first fire, you still have a lot of smoke until the fire gets hot enough to start a secondary burn.
This increased heat will also ultimately mean that you burn the fuel faster, even if you burn it more efficiently. It is fascinating that the fuel burns twice as fast as an effective smoke-free pit, and I also reach coal temperatures at a rate of more than a thousand degrees. Needless to say, this makes the smokeless fireplace awesome in cooking.