Experience gained from previous jet noise studies with the unstructured large eddy simulation (LES) flow solver "Charles" are summarized and put to practice for the predic-tions of supersonic jets issued from a converging-diverging round nozzle. In this work, the nozzle geometry is explicitly included in the computational domain using an unstructured body-fitted mesh with 42 million cells. Three different operating conditions are consid- ered: isothermal ideally-expanded, heated ideally-expanded and heated over-expanded. Blind comparisons with the currently available experimental measurements carried out at United Technologies Research Center for the same nozzle and operating conditions are presented. The initial results show good agreement for both flow and sound field. In par- ticular, the spectra shape and levels are accurately captured in the simulations for both near-field and far-field noise. In these studies, sound radiation from the jet is computed using an efficient permeable formulation of the Ffowcs Williams-Hawkings equation in the frequency domain. Its implementation in Cascade's massively-parallel unstructured LES framework is reviewed and additional parametric studies of the far-field noise predictions are presented. As an additional step towards best practices for jet aeroacoustics with unstructured LES, guidelines and suggestions for the mesh design, numerical setup and acoustic post-processing steps are discussed.