Acoustic damping, a key element for the accurate prediction of combustion instabilities, is studied in this work through the combined analysis of the NPCC test bench. This gaseous nonreactive test bench, developed for the study of acoustic damping in a coupled-cavity configuration, is composed of a dome, a chamber and 3 injectors. It mimics the geometry of a LRE in a simplistic way. An acoustic modulation at three different frequencies-corresponding to acoustic modes of the system-is achieved using a perforated wheel. Large Eddy Simulation (LES) properly reproduces the experimental pressure signal for the 3 cases. Then, a Reduced Order Modeling (ROM) approach is presented with a modal expansion, which retrieves numerical results in a linear framework.