Calculations of the structure of an upward polydisperse gas-liquid pipe flow are presented. The model is based on the Eulerian approach with account of the feedback effect of the bubbles on the average parameters and turbulence of the carrier phase. The turbulent kinetic energy of the fluid is calculated using the transport equations for the Reynolds stresses. The bubble dynamics are described with account for the variation of the mean bubble volume due to the coalescence and break-up of the bubbles. The comparison of the results with experimental data shows that the approach developed makes it possible to describe adequately turbulent gas-liquid flows over a wide range of variation of the gas volume fraction and the initial bubble size.Vertical bubbly flows are typical of chemical, nuclear, power and other branches of engineering. The information on the structure, the average and fluctuation parameters, and the cross-sectional distributions of bubbles in a channel (pipe) flow is necessary both from the fundamental and practical points of view.The complexity of the mathematical description of such flows is associated with the necessity to take into account a large number of factors of different physical nature, such as the carrier-phase turbulence, phase interaction, coalescence and fragmentation of the bubbles. A gas-liquid two-phase flow depends on the flow-rate parameters, geometry, flow regime, physical properties of the liquid and bubbles, and the bubble size [1-6]. As a rule, gas-liquid flows are polydisperse, since the bubbles usually are of different size [7-10]. When modeling these flows with account for the coalescence and break-up of the bubbles, the computational expenses are much higher than in calculating monodisperse bubbly flows. This is why different simplifying assumptions are widely used, the main of which is the monodispersity of the gas-liquid flow [1][2][3][4].To date, several methods of modeling of polydisperse two-phase flows with bubble coalescence and break-up have been developed. At the moment, one of the most informative methods of description of bubble dynamics is the Population Balance Model (PBM) [11]. This model, accomplished with the continuity and momentum equations, is widely used in the Eulerian methods [12][13][14].One of the PBM approaches is the calculation based on the decomposition of all bubbles into several classes with different size and (or) velocity [15] and modeling of each group on the basis of the multi-fluid approach. This is the MUSIG method, in which the inclusions with different sizes have the same velocity [8-10], or its modification H-MUSIG [15], in which the inclusions with different sizes have different velocities. The mass, momentum, and energy balance equations are solved for each "monodisperse" group with account of bubble coalescence and break-up, which results in the nonlinear increase in the computation time with increase in the number of the groups. In [16,17], a model is proposed and the evolution of the bubble size spectrum is modeled numerically. ...