A comprehensive numerical study is conducted to explore the dynamic behaviors of a flame stabilized by a triangular bluff body in a straight chamber. The formulation accommodates the complete set of conservation equations with turbulence closure achieved by a large eddy simulation (LES) technique. A G-equation-based level-set flamelet approach is employed to model the interactions between premixed combustion and turbulence. Both non-reacting and reacting flows are treated, with special attention given to the effect of inlet boundary conditions on the flame evolution. The flow around the bluff body consists of boundary layers, separated shear layers, a recirculation zone and a wake. Their mutual coupling, as well as interactions with acoustic motion and flame oscillation are analyzed in detail. The physical processes responsible for driving combustion instabilities and the mechanism of energy transfer from chemical reactions in the flame zone to acoustic oscillations in the bulk of the chamber are investigated systematically. Intensive resonance is found to occur between shear-layer instabilities and chamber acoustic waves, when the acoustically reflecting inlet boundary condition is enforced. The resulting complex interplay among acoustic motion, vortex shedding, and unsteady heat release forms a feedback loop and excites combustion instabilities with large flow oscillations.