In this paper, the numerical findings of a high fidelity CFD model will be compared with the experimental data of a test campaign devoted at characterizing the performance of a technically premixed industrial burner regarding the thermoacoustic instabilities. The data are retrieved at relevant gas turbine conditions in a test bench where the flame tube can change its length during the test execution allowing its fundamental acoustic frequencies to be modified and, in case, triggered. Mimicking the test configuration, several Large-Eddy Simulations are performed with different lengths of the flame tube in order to verify the ability of the numerical model to reproduce the excited dominant frequency and the corresponding limit cycle amplitude measurements. The numerical model demonstrates the ability to correctly reproduce the frequency triggered during the test and to reach different limit cycle amplitudes along different flame tube lengths in agreement with the tests, as well. However, it is found that the amplitude of the acoustic pressure fluctuation during the limit cycle is generally under-predicted. Despite this, the proposed approach demonstrates to be a robust tool for the characterization of a given design, allowing to dramatically reduce the computational cost of the analysis, at least in the early design phase. Since the numerical model can correctly reproduce the behavior of the investigated design, a deep post-processing of the solutions is performed to shed light on the physical mechanisms sustaining the thermo-acoustic instability. Among the numerical techniques employed at this purpose, the Phase-Locked Average and the Extended-POD are applied trying to correlate the fluctuations of the different quantities inside the premixed channel of the burner and the primary zone as well.