CFD Based Model to Identify the Minimum Length of a Gradual Rectangular Expansion Operated under Supercritical Flow

Abstract

Computational Fluid Dynamics (CFD) has been used to derive a mathematical model to relate the length of a gradual expansion (Le) with the others of hydraulic and geometric parameters of the flow in rectangular channels under supercritical flow conditions. Five models with different length of expansion 30 cm, 50 cm, 75 cm, 100 cm, and 125 cm were simulated in the CFD v18.2 software and verified by experimental data which have been measured into a laboratory flume. All models of CFD software were processed depending on k – epsilon viscous models while the mesh was built by adapting the multi-zone method. Five values of inlet velocity of flow were applied in the runs of the program to each model of 1.5 m/s, 1.6 m/s, 1.7 m/s, 1.8 m/s, and 2 m/s. Depths of water along the channel were measured in multi-section, before expansion, within expansion and after expansion. The results of CFD analysis showed that the minimum length of expansion to maintain the flow within supercritical regime was 0.35 m and the ratio of (Le/W) equal to 1.167. The results of the non-dimensional relationship were compared with the experimental results and the comparison showed a significant correlation where the highest percentage difference was 13.8 %. The coefficient of determination for this equation was 0.973.