Students at Univ. of California at San Diego carried out experiments on combustion and flame in weightlessness while riding on a NASA plane flying parabolic trajectories:

• Weightless Flames: How Fires Burn in Space | Fire in Zero-G – Space.com
• MAE UCSD Team accepted into NASA’s Microgravity University program – UCSD Mechanical and Aerospace Engineering

This article describes the odd behavior of flames in microgravity:  Strange Flames on the ISS – NASA Science. This video, seen also in this earlier post, is about the “strange, cool-burning form of fire”: