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Bubble flow can be simulated by the two-fluid model and the multi-fluid model based on the Eulerian method. In this paper, the gas phase was further divided into several groups of dispersed phases according to the diameter by using the Eulerian-Eulerian (E-E) multi-fluid model. The diameters of bubbles in each group were considered to be the same, and their distributions were reorganized according to a specific probability density function. The experimental data of two kinds of bubble flow with different characteristics were used to verify the model. With the help of the open-source CFD software, OpenFOAM-7.x (OpenFOAM-7.0, produced by OpenFOAM foundation, Reading, England), the influences of the group number, the probability distribution function, and the parameters of different bubble diameters on the calculation results were studied. Meanwhile, the numerical simulation results were compared with the two-fluid model and the experimental data. The results show that for the bubble flow with the unimodal distribution, both the multi-fluid model and the two-fluid model can obtain the distribution of gas volume fraction along the pipe radius. The calculation results of the multi-fluid model agree with the experimental data, while those of the two-fluid model differ greatly from the experimental data, which verifies the advantage of the multi-fluid model in calculating the distribution of gas volume fraction in the polydisperse bubble flow. Meanwhile, the multi-fluid model can be used to accurately predict the distribution of the parameters of each phase of the bubble flow if the reasonable bubble diameter distribution is provided and the appropriate interphase force calculation model is determined.

The purpose of the present study is to analyze the effect of different discrete representations of the continuous bubble size distribution function on the flow structure in a bubble column reactor. Poly- and monodisperse media were considered, such that the mathematical expectation of the bubble size in the polydisperse case was equal to the bubble size in the monodisperse case at the same volumetric bubble contents. For these computations the normalized variances of the velocity profiles of the carrier and the disperse phases, the volume fraction of the disperse phase, and the specific area of the interfacial surface were determined. The normalized variances were calculated from a reference scenario with a detailed resolution of the bubble size distribution function with ten bubble classes. It was shown that with increase of the average bubble sizes mono- and polydisperse approaches provide converging solutions. A modified hybrid discretization of the bubble size distribution function with four classes of bubbles was shown to predict the flow structure with normalized variance less than 5% over the entire computational domain for all monitored parameters.

The results of numerical simulation of the flow structure and heat transfer in a vertical polydispersed bubbly flow are presented. The mathematical model is based on the Euler approach taking into account the effect of bubbles on the mean characteristics and turbulence of the carrier phase. The polydispersed distribution of bubbles size in a two-phase flow is modeled by the method of delta approximation considering the process of bubble break-up and coalescence. Carrier phase (fluid) turbulence is predicted using the Reynolds stress transport model. The simulation results showed good agreement with the experimental data presented in the literature. The measured and predicted thermal-hydraulic parameter distribution indicates that in a turbulent bubbly flow, the wall friction increase is greater than heat transfer enhancement.

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 developedmakes 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.