Ignition in annular multi-burner combustors is marked by a succession of four phases, ending with a characteristic flame expansion from burner to burner, often referred to as light-round. During this last phase, flame propagation is prone to substantial change depending on the boundary and operating conditions. With realistic aero-engine conditions in mind, wall heat transfers can be enhanced during ignition in cold wall conditions, which aid an understanding of the main governing mechanisms of flame propagation. From a modeling perspective, several works have outlined the need for detailed descriptions of the liquid phase, turbulent combustion and wall heat transfer, which are all included in the present work for the first time. Large-Eddy Simulations of light-round are performed in the annular MICCA-Spray combustor with cold walls, Lagrangian particle tracking, a dynamic closure for the sub-grid scale flame surface wrinkling as well as a custom tabulated wall model. The predicted light-round duration from the simulation is found to be in good agreement with experimental data. It is shown that the expansion of burnt gases induces a flow acceleration in azimuthal direction, known as thrust effect, which constitutes the main driving mechanism of flame propagation. Droplet accumulations in the wake of swirling jets are generated ahead of the propagating flame fronts, which in turn cause a characteristic sawtooth propagation mode of the leading point. A cooling effect of the combustor walls on burnt gases is particularly pronounced downstream, diminishing the generated thrust. The main governing mechanisms are investigated by means of a mathematical model for the absolute turbulent flame speed to quantify their relative impact on flame propagation. Finally, a priori estimations are provided for the flame propagation speed based on different models and boundary conditions, which are directly plugged into the model.