The mathematical modeling of air- and oxy-coal flames is a great challenge because of the complexity of the turbulence chemistry interactions. However, the different turbulence chemistry interaction models can give very different results. Therefore, an investigation of the effects of these interactions on air- and oxy-coal flames is needed, especially with both improved kinetic mechanisms and modified physical parameters. This work presents a numerical investigation of the effects of the interaction models on the characteristics of air-and oxy-coal confined swirling flames. These interaction models are two extended eddy-dissipation models (EDMs), the finite-rate and eddy-dissipation (FRED) model and the eddy dissipation concept (EDC) model. First, two important factors were considered in the oxy-coal combustion simulations, namely, improved global reaction mechanisms and modified physical parameters. Second, with these improvements and modifications, numerical simulations of air- and oxy-coal flames were carried out. The results showed that the flames focus on the horizontal center and propagate forward with a swirling closure shape and that the flame shapes belong to an intensively accelerated flame type II. Good predictions of the combustion efficiencies were obtained by these two combustion models. Superior predictions of both the exhausted flue gas mixture and the minor carbon monoxide concentration were obtained with the eddy dissipation-chemical equilibrium (EDC) model. However, both ignition delays and temperature fields were better predicted with the kinetic-controlled and mixed-is-burned (FRED) model.