This paper presents detailed numerical simulations of propeller wake dynamics, both with and without a duct, near a vertical wall. Using the arbitrary mesh interfaces (AMI) method and delayed detached-eddy simulation (DDES) models, the study analyzes vortex generation, evolution, and dissipation in the wake. The wake is divided into near wake, transition, far field, and near-wall regions, with the tip leakage vortex playing a crucial role in radial diffusion, maximum jet velocity formation, and wake-wall interactions. The introduction of a deceleration duct results in a more uniform and compact wake, with maximum axial velocity observed upstream at x = 0.3D for the ducted propeller, compared to x = 0.5D for the non-ducted case, where D is the propeller diameter. Wall effects modify vortex interactions, influencing tip leakage vortex formation at smaller wall distances (1D-2D) and vortex dissipation at larger distances. The wake spreads near the wall, forming a triangular low-speed zone, and jet spreading weakens as the wall distance increases, stabilizing at 4D. A wall distance of 1D is identified as the threshold for affecting maximum axial velocity.