Experimental Study of Flow Energy Residual in a Vortex Drop Structure Using Full Factorial Method

One of the basic needs in urban wastewater and drainage systems is the connection of shallow ducts to deep underground tunnels. This connection is usually made through a vortex drop structure. In order to form a vortex flow, in addition to preventing the fluid from falling, a significant part of its energy is lost due to the friction of the walls. In the present study, by constructing a physical model, the residual energy head in the structure (ratio of specific energy at the output (E2) to specific energy at the input of the structure, (E1)) has been studied. Using dimensional analysis of dimensionless factors of Froude number (Fr), the ratio of total fall height to shaft diameter (L⁄D) and the ratio of sump depth to shaft diameter (Hs ⁄D) were determined as factors affecting the residual energy head in the structure. Using experimental observations, the accuracy and capability of the full factorial method to describe the residual flow energy in the structure were evaluated. The results showed that the residual energy head for the Froude number corresponding to the design flow discharge at Fr=2.18 is closest to the limit value of 1. On the other hand, for all L/D operating levels, the residual energy head values are close to 1. Moreover, the smallest difference between the values of the residual energy head and the limit value was 1 for Hs/D values between 1 and 2, indicating suitable range for the practical purpose. In addition, a polynomial equation as a function of Fr, L⁄D and Hs ⁄D was expressed to accurately estimate the residual energy head in the vortex, drop structure using regression analysis.