A calibrated delayed detached eddy simulation of a sub-scale cold-gas dual-bell nozzle flow at high Reynolds number and in sea-level mode is carried out at nozzle pressure ratio NPR = 45.7. In this regime the over-expanded flow exhibits a symmetric and controlled flow separation at the inflection point, that is the junction between the two bells, leading to the generation of a low content of aerodynamic side loads with respect to conventional bell nozzles. The nozzle wall-pressure signature is analyzed in the frequency domain and compared with the experimental data available in the literature for the same geometry and flow conditions. The Fourier spectra in time and space (azimuthal wavenumber) show the presence of a persistent tone associated to the symmetric shock movement. Asymmetric modes are only slightly excited by the shock and the turbulent structures. The low mean value of the side-loads magnitude is in good agreement with the experiments and confirms that the inflection point dampens the aero-acoustic interaction between the separation-shock and the detached shear layer.