Analytical Model Study of Flow Through Trapezoidal, Half-Trapezoidal and Rectangular Channels with Submerged and Un-submerged Rigid Cylinders

• Main Author: Tamrakar, Swaraj
• Format: Others
• Published: OpenSIUC 2014
• Subjects: analytical; defects; momentum; superposition; velocity; wake
• Online Access: https://opensiuc.lib.siu.edu/theses/1380; https://opensiuc.lib.siu.edu/cgi/viewcontent.cgi?article=2394&context=theses

For this study, two analytical models were developed for predicting the depth-averaged velocity distribution (U) in trapezoidal, half-trapezoidal and rectangular channels with submerged and unsubmerged rigid cylinders. The first model uses linear superposition of momentum defects (MDS) and mass conservation, and is referred to as the MDS model. The second model uses linear superposition of velocity defects (VDS) and mass conservation, and is referred to as the VDS model. For implementing either the VDS or MDS model, a criterion is required for considering the wake created by an individual cylinder to be fully dissipated (i.e., a cutoff criterion). Also, implementing the MDS model requires numerical integration. Analyses were conducted to identify suitable cutoff criterion and an appropriate subinterval size for the numerical integration. Data from a physical model study conducted in a flume with a half-trapezoidal channel section was used to calibrate and validate the models. Data from a physical model study conducted in a rectangular channel section was also used to validate the model. Predicted values of U from the VDS and MDS models were within the range of ± 20 % of the trapezoidal channel section validation data. The models failed to accurately predict U for the rectangular channel section data. It is concluded that the models developed herein should be used only for half-trapezoidal channel sections. With respect to the trapezoidal channel section validation data, the MDS model yields a sum of squared errors that is 36% less than that yielded by the VDS model. Therefore, the MDS model is regarded as the best model overall for computing U in half-trapezoidal channel sections.