Understanding and optimizing turbulence in combustion systems has a profound effect on combustion efficiency, emission reduction, and safety in applications ranging from industrial burners to propulsion systems in aerospace. This paper contributes to this pivotal field by investigating a real-scale low-swirl combustor utilizing a range of turbulence generation plates characterized by different blockage ratios and numbers of fractal pattern iterations. The work encompasses two states, namely nonreacting and premixed reacting modes, utilizing a large-eddy simulation method equipped with a dynamic Smagorinsky sub-grid model and adaptive mesh refinement for high accuracy. Verifying the robustness of the approach, the simulation aligns closely with experimental data, registering a maximum error of less than 0.9% in the swirl number. The research provides an insightful evaluation of the impact of four different fractal geometries on turbulence intensity, a vital element for attaining more complete combustion. Findings indicate a fractal with a 73% blockage ratio and four iteration levels enhances several key parameters including turbulence intensity, flow residence time, vorticity, and velocity gradient in the nonreacting mode. Conversely, a fractal with a 73% blockage ratio and three iteration levels shows the least progress in the reacting mode. Moreover, the paper delves into a comparative analysis of these two cases in the reacting mode, particularly observing the reaction zone. The appropriate fractal geometry unveiled significantly improves combustion efficiency, evidenced by an increased presence of the OH radical and a decrease in NO emission gas, thus demonstrating potential for wider application in enhancing combustion systems.