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Concurrent flame spread over a thin solid material in a low-speed flow duct in microgravity is numerically studied using a three-dimensional transient CFD code. The height of the flow duct is the main parameter in this study. The preliminary results show that there exists a quenching flow duct height below which the flame fails to spread. For cases far from the quenching height, the flame reaches a steady spreading state before the sample is consumed. The flame spread rate and the pyrolysis length at steady state first increases then decreases when the flow duct height increases. Near the quenching height, a flame oscillation is observed throughout the flame spreading process. As it spreads downstream, the flame goes through periodic lateral separation and merging while accelerating and decelerating. This flame oscillation phenomenon is suspected to be due to thermo-diffusive instability. Detailed profiles of the gas and solid phases, including the heat flux distributions on the sample surfaces, interactions between the flame and the walls of the flow ducts, and the flow profiles are examined to elucidate the underlying physics of the observed phenomena.