Turbulent flame acceleration process has been studied in a two-dimensional valveless pulsed detonation combustor (PDC) using Schlieren flow visualization, ionization probes, and companion high-frequency pressure instrumentation. Experiments were conducted using near stoichiometric propane-air mixtures in a 76.2mm x 76.2mm, 1.68m long modular detonation tube with the windowed combustor under multicyclic conditions within the PDC operating in a valveless mode. The effect of the presence of the obstacle was investigated at various stages of the flame acceleration process in aerodynamically confined environment. Amplification of the leading shock waves through the interaction of the obstacle enhances the flame acceleration process owing to the reduction of post-shock induction time and the hydrodynamic instabilities at the baroclinic interface. The internal configuration of the combustor including the obstacle plays a major role of the flame acceleration due to the shock amplification pattern. Sequences of schlieren images also show the flow drifting and blowdown processes confirming that the gasdynamic valves are successfully operative in the valveless PDC.