Staged pressurized oxy-coal combustion (SPOC) is nowadays a promising technology to be used for low-cost, low-emission, high-efficiency power generation. The objective of this thesis is to compliment the experiments ongoing at the Washington University, St. Louis (WUSTL) by means of numerical simulations, thereby providing better understanding of the fluid flow, turbulence, combustion characteristics, particle dynamics and heat transfer. Carbon dioxide (CO2) is injected alongside the coal, for its carriage. A small amount of methane (CH4) is also injected alongside the coal to maintain a steady flame. The simulations are performed for a 3D geometry with the following energy source distribution: out of 100 kW in a lab-scale reactor, 10 kW originates from CH4 and 90 kW comes from coal combustion. Steady and unsteady Reynolds-averaged Navier-Stokes (RANS) simulations are performed resulting in an asymmetric flame shape. Two causes of the flame asymmetry are hypothesized: (i) influence of coal injection and (ii) onset of a shearlayer instability due to the density variation of different gases and velocity differences of various streams in a shear layer, where mixing occurs. An impact of coal on flame symmetry is shown. In addition, a benchmark at which the further increase of coal would result in flame asymmetry has been found. The present simulations also demonstrated an occurrence of vortex shedding when the flow passes over a disk (bluff body) in a reactor, used to stabilize the flame, constituting a potential reason for periodic flame oscillations observed. An aerodynamic investigation of a flow past this bluff body is conducted for various Reynolds numbers (Re), with the bluff body height determining the characteristic length scale. Consequently, various regimes of flow are identified as Re increases. Particularly, an onset of the vortex shedding is noticed when Re > 3000. Spectral analysis is further conducted to identify the frequencies at which the flame oscillations occur, which is aimed at guiding an eventual redesign of this bluff body. It is shown that coal injection is the major contributor to the flame oscillations, as hypothesized. A non-uniform coal distribution in the burner region is found, which, in turn, creates a non-steady coal feed and ultimately results in the flame oscillations. It is subsequently demonstrated that an increase in the coal carrier (CO2) concentration provides a better feeding of coal (continuous coal injection into the burner region), ultimately resulting in a more symmetric shape of the flame front. iii ACKNOWLEDGEMENTS I would like to thank everyone who has contributed, directly or indirectly, to my activities at West Virginia University, in general, and to completing this thesis, in particular. Specifically, my heart felt gratitude goes to Dr. Akkerman, my research advisor, who has entrusted the responsibility to work on a research field as interesting as this one. Furthermore, my heart felt gratitude goes to Ozioma Ozor, who has remained a permanent source of encouragement...