This paper is the second part of a global work investigating the physics of premixed flame propagation in several kinds of long pipes. It focuses on the potential of CFD for modelling such cases and on the key issues for being able to address generic cases. Four tests among the database detailed in the first part are selected. In each case, the pipe is straight, open at one end and closed at the other where ignition is triggered. The pipe is filled with a stoichiometric methane/air mixture at rest. Varied parameters are the inner pipe diameter and the pipe material. CFD computations, based on a URANS framework were carried out and enabled to recover several physical trends, such as the role of acoustics and boundary layer turbulence on the flame dynamics. Although most overpressure peaks orders of magnitude of the measured overpressure signals can be predicted numerically, the computed flames are quicker than the measured ones. It could be explained by the chosen turbulent model, the k-ω SST model, known to be adapted for wall-bounded flows but producing too much turbulence for accelerating flows. The criterion for the near wall cells (y + <200) might be too loose as well.