The noise produced by rotating systems such as fans and turbo machines is of growing importance in the academic and engineering communities. The prediction and understanding of the physical mechanisms associated with noise generation are required in order to develop innovative solutions able to efficiently reduce radiated acoustics levels. The flow-induced noise generation mechanisms related to rotating devices are various and complex, and one of them is related to the blade tip flow. The tip flow noise, or tip leakage noise, is particularly important for free-tip configurations, for which the tip flow induced by the pressure gradient between the suction and pressure sides can be particularly intense. The experimental investigation of this mechanism is practically challenging. Consequently, a simplified non-rotating representative configuration has been proposed, and has been previously investigated experimentally. In this paper, transient, compressible, and time-explicit Computational Fluid Dynamics/Computational Aero-Acoustics (CFD/CAA) simulations of an airfoil tip leakage flow for this simplified geometry are performed using a Lattice Boltzmann Method (LBM) based approach. The studied configuration is a NACA 5510 airfoil profile at high Reynolds number flow conditions, for which a variable size gap is introduced between the airfoil and one of the end plates, modeling the tip gap encountered in free-tip fans. First, the simulation results are compared with experimental results to validate the numerical approach. Further investigation of the numerical results underlines the connection between the tip vortex structures and noise radiation, including a parametric study on the Angle of Attack (AoA) and the tip gap width.