A better understanding of two-phase flows with evaporation allows leading to an optimal design of evaporators. For that purpose, numerical simulations are very useful. In this paper, a numerical study has been carried out in order to model and simulate the combination of a two-phase flow with evaporation in a vertical tube. The VOF (volume-of-fluid) multiphase flow method and a phase-change model for the mass transfer have been used. For an accurate modeling, the effect of axial conduction has been also taken into account using a conjugate heat transfer model. Since thermal oscillations are undesirable as they can lead to the failure of the tube, flow instabilities have also been analyzed, using FFT (fast Fourier transforms), in order to comprehend their behavior and influence. A control study of the flow instabilities in the tube is also presented. For that purpose tube inlet temperature has been varied using a gain control parameter.