The objective of this work was to improve the modelling of boiling bubbly flows.We focused on the modelling of the polydisperse aspect of a bubble population, i.e. the fact that bubbles have different sizes and different velocities. The multi-size aspect of a bubble pupolation can originate from various mechanisms. For the bubbly flows we are interested in, bubble coalescence, bubble break-up, phase change kinematics and/or gas compressibility inside the bubbles can be mentionned. Since, bubble velocity depends on bubble size, the bubble size spectrum also leads to a bubble velocity spectrum. An averaged model especially dedicated to dispersed flows is introduced in this thesis. Closure of averaged inter- phase transfer terms are written in a polydisperse framework, i.e. using a distribution function of the bubble sizes and velocities. A quadratic law and a cubic law are here proposed for the modelling of the size distribution function, whose evolution in space and time is then obtained with the use of the moment method. Our averaged model has been implemented in the NEPTUNE_CFD computation code in order to simulate the DEBORA experiment. The ability of our model to deal with sub-cooled boiling flows has therefore been evaluated.