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In this paper, the application of NACA airfoil pillar-shaped flumes and the influence of their wing lengths on flow measurement characteristics are discussed. The standard k-ε three-dimensional turbulence model and the volume of fluid (VOF) method were used for numerical simulation of the flow in six NACA airfoil pillar-shaped flumes with different wing lengths. In addition, to verify the accuracy of numerical simulations, the corresponding experiments were conducted. The Buckingham Pi theorem of dimensional analysis coupled with the incomplete self-similarity theory was applied to deduce the theoretical flow calculation formula of these flumes. Moreover, Froude number, velocity distribution, backwater height, critical submergence, and energy loss of the flume were analyzed, for which the experimental and numerical results are compared and further discussed. The results show that the backwater height is directly proportional to the wing length, while the head loss and critical submergence are inversely proportional to the wing length. Based on the results, in terms of backwater height, it is recommended to use the NACA airfoil pillar-shaped flume with a smaller wing length, while, in terms of head loss and critical submergence, the NACA airfoil pillar-shaped flume with a larger wing length should be used.

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Investigation of flow measurement mechanism and hydraulic characteristics of the NACA airfoil pillar-shaped flume with different wing lengths in a rectangular channel