Intense axial vibration of the paste and the reversed flow make damage to the transportation system and lag the transport progress. This paper analyzed the axial vibration of the paste by building the vibration model according to the working situations of the system. The amount of the reversed flow share is then estimated based on the formed axial vibration model. The estimation of the reversed flow is carried out by counting the amount of the decompressed paste in certain time, which is being relative to the displacement in a single process of the vibration in numerical. The estimation of the reversed flow share of coal slime paste under certain transportation conditions was given and compared with the result based on the wave velocity method. It is evident that the introduction of axial vibration model into the study of the pipeline transportation system is feasible and reasonable, which also supplements the theoretical foundation for the analysis of dense paste vibrations in pipeline transportation system and its impacts on the system.
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