Considering the increasingly stringent targets for aircraft emissions, computational fluid dynamics (CFD) is becoming a viable tool for improving future aero-engine combustors. However, predicting pollutant formation remains challenging. In particular, directly solving the evolution of soot particles is numerically expensive. To reduce the computational cost but retain detailed physical modeling, quadrature-based moments methods can be efficiently employed to approximate the particle number density function (NDF). An example is the recently developed split-based extended quadrature method of moments (S-EQMOM), which enables a continuous description of the soot particles' NDF, essential to consider particle oxidation accurately. This model has shown promising results in laminar premixed flames up to turbulent laboratory scale configurations. However, the application to large-scale applications are still scarce. In this work, the S-EQMOM model is applied to the Rolls-Royce BR710 aero-engine combustor to investigate the soot evolution process in practically relevant configurations. For this, the soot model is embedded into a high-fidelity simulation framework, consisting of large eddy simulation for the turbulent flow and mixing and the flamelet-generated manifold method for chemistry reduction. An additional transport equation for polycyclic aromatic hydrocarbons is solved to model their slow chemistry and the transition from the gaseous phase to the solid phase. Simulations are performed for different operating conditions (idle, approach, climb, takeoff) to validate the model using experimental data. Subsequently, the results are analyzed to provide insights into the complex interactions of hydrodynamics, mixing, chemistry, and soot formation.