Acoustic damping plays a key role in the stability analysis of liquid rocket engines (LRE). Its characterization is a necessary step towards prediction of thermoacoustic instabilities. To our knowledge, current analysis of the damping is limited to experimental measurements in practical systems or theoretical models for simple configurations. This study presents large-eddy simulations (LES) of the NPCC setup, a cold-flow configuration representing a simplified LRE geometry, compared to experiments previously carried out at EM2C, to characterize the global acoustic damping of the rig. Steady-state simulations are first performed. Headlosses due to the injection plane and jet profiles are assessed. Then, simulations of the forcing of three eigenmodes give results in very good agreement with the experiment. It is found that the high forcing amplitudes reached in the experiment triggers a non-linear response of the rig. By imposing a lower modulation in the simulations, it is possible to stay in a linear framework. A low-order linear model for the pressure response using the acoustic damping as a key parameter is then compared to the LES and correctly predicts the transitory phase and the limit-cycle amplitude.