The chimney is what produces draft in a wood burning fireplace. Heat rising up the chimney pulls air through the air controls through the combustion air ducts. The taller the chimney, the stronger the draft. If the chimney is too short it struggles to pull air in through the air controls. Symptoms of this includes a fireplace that struggles to burn or puffs smoke out the front when the doors are open, or if the fireplace dies out when the doors are closed.
If you add a set of elbows to offset around framing, it’s recommended that you add additional chimney height to compensate for the elbows.
A proper chimney system is as important as the fireplace.