Passive heat transfer techniques are considered to be one of the most important means to enhance heat transfer in heat exchangers that allow also reducing their size and manufacturing cost. Moreover, this passive technique can also be used to control the thermal instabilities caused by the two-phase flow in the evaporators. The thermal instabilities are undesirable because they can lead to a tube failure. For this purpose, a numerical study of the two-phase flow with evaporation in a vertical tube has been performed in this work. The volume of fluid (VOF) multiphase flow method has been used to model the water vapor–liquid two-phase flow in the tube. A phase-change model, for which source terms have been added in the continuity and energy equation, has been used to model the vaporization. The numerical simulation procedure was validated by comparing the obtained results with those given in the literature. The passive control technique used here is a ring element with square cross section, acting as a vortex generator, which is attached to the tube wall at various positions along the tube. Instabilities of temperature and void fraction at the tube wall have been analyzed using fast Fourier transforms (FFTs). The results show that the attachment of the control element has a significant influence on the value and distribution of the void fraction. Higher positions of the control element along the tube allow reducing the magnitude of void fraction oscillations.