The added damping generated by liquid sloshing in a tank has been utilized in a number of civil applications, including aviation, to reduce the vibration of the system. As part of a wider EU H2020 project called SLOWD (Sloshing Wing Dynamics), the presented study performed numerical simulations on the slosh-induced damping of liquid in tanks that were under free decay oscillations and embedded in an aircraft wing-like structure. A new open-source partitioned fluid–structure interaction software framework is presented and employed for the numerical simulations. Periodic sloshing waves and violent vertical fluid motions are observed in the study. These demonstrate the effects of slosh-induced damping under different excitation amplitudes of the structure and a varying number of baffled regions within the tank. Various sloshing patterns caused by different combinations of the excitation amplitude and compartment numbers lead to different induced dampings of the free decay motion. We observed a distinctly non-monotonic function on the slosh damping when the initial excitation amplitude is small (i.e., 0.25), with a 59% reduction when we increase the number of baffled compartments from one to four, and a 153% increase when moving from one to eight compartments. This is due to the change in the sloshing wave frequency, resulting in a significant change in the impact of the fluid between the tank ceiling and the wave crests. When the initial excitation amplitude is large (i.e., 1.0), there is no significant change in the slosh-induced damping when changing the number of compartments in the tank, for the range of parameters considered, due to the highly turbulent fluid motion. This work is expected to form the basis of further, more detailed studies within the context of the SLOWD project and its ever-expanding experimental data output.