This article presents unsteady Reynolds averaged Navier-Stokes simulations (URANS) of a well-characterized aero-engine model combustor with finite-rate chemistry (FRC). The simulations give insight into the complex formation and destruction processes of soot at technically relevant conditions. It will be shown that a recently developed PAH (polycyclic aromatic hydrocarbons) and soot model is able to predict soot under complex combustion conditions at elevated pressure. Finite-rate chemistry is employed for the gas phase, a sectional approach for PAHs and a two-equation model for soot. Thus, feedback effects, such as the consumption of gaseous soot precursors by growth of soot and PAHs, are inherently captured accurately. In agreement with the experiment a precessing vortex core (PVC) is observed in the ethylene fueled combustor. This requires that the computational grid covers swirlers. The PVC intensifies mixing of fuel, primary air, and hot burned gas from the inner recirculation zone, thereby supporting flame stabilization and subsequently influencing soot. The numerical results (velocity components, temperature, and soot volume fraction) compare well with experimental data. Details of soot evolution and remaining differences to the experiment are analyzed.