Transverse galloping is a type of flow-induced vibration (FIV) that leads to critical design considerations for engineering structures. A purely nonlinear energy sink (NES) composed of a ball free to rotate in a circular track experimentally mitigated the galloping of a square in a previous study. The current study introduces a model for simulating the dynamics of the square prism coupled with a ball-in-track (BIT) NES and predicting the system behaviour at high flow speeds beyond the limits of the previously presented experiments. Numerical simulations employ the fitting of experimental data as inputs to define parameters. Wind tunnel static experiments provide the galloping force coefficient [[EQUATION]] relative to the prism angle of attack. Additionally, free rotation tests allow evaluating the ball damping coefficient [[EQUATION]] as a function of its mass and the NES track radius. The result of the rotation tests provides a critical angular speed beyond which the ball damping increases non-linearly. We point out the damping variation as an advantage of the BIT-NES; less damping at low angular velocities helps the ball start its rotation, while relatively large damping at higher speeds dissipates more energy from the vibrating system. Numerical results exhibit four response modes for the NES; oscillatory at low flow speeds, intermittent within a small range of higher flow speeds, rotational at higher flow speeds, and ineffective regime at flow speeds out of the NES effective range. Modelling the primary mass as a parametric excitation source for the NES provides an analytical estimation of the boundary between the oscillatory and intermittent regimes. Furthermore, we advance an analytical analysis of the power flow across the integrated prism-NES system to explain the NES behaviour and predict the limit of its effective range.