In the present study, a recently developed improved Self-Adaptive Turbulence Eddy Simulation (SATES) turbulence model (marked as SATES-Mixed), is validated for the simulation of complex multiple swirling turbulent flows. The new SATES-Mixed method aims to enhance both the performances in the wall region as well as the free shear layer region. For comparisons, the Large Eddy Simulation (LES) with WALE and Smagorinsky sub-grid model is also conducted with the same numerical setups. Compared with the original widely used SATES model, the SATES-Mixed model inherits the low grid sensitivity and high accuracy for free turbulence while improving the calculation accuracy in the near-wall regions. Therefore, the prediction ability of the SATES-Mixed model is validated in challenging complex swirling flows encountered in multi-stage swirl combustion chambers. Good overall agreement between SATES-Mixed and experiments is observed with relatively coarse mesh, which is even better than the LES-WALE results. The SATES-Mixed model accurately captures the typical single-vortex tube PVC evolution characteristics in a double swirling combustor (GTMC) and effectively models the complex interactions between single/double vortex tubes in a three-stage swirling combustor, including their intertwined twisting motions and mutually evolving processes.