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

Document Type : Research Paper


Assist. Prof., Dept. of Civil Engineering, Faculty of Engineering, Higher Education Complex of Bam, Kerman, Iran


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.


Ahmadi, M., Vahabzadeh, F., Bonakdarpour, B., Mofarrah, E. & Mehranian, M. 2005. Application of the central composite design and response surface methodology to the advanced treatment of olive oil processing wastewater using Fenton's peroxidation. Journal of Hazardous Materials, 123, 187-195.
Amiri, F., Mousavi, S., Yaghmaei, S. & Barati, M. 2012. Bioleaching kinetics of a spent refinery catalyst using Aspergillus niger at optimal conditions. Biochemical Engineering Journal, 67, 208-217.
Crispino, G., Contestabile, P., Vicinanza, D. & Gisonni, C. 2021. Energy head dissipation and flow pressures in vortex drop shafts. Water, 13, 165.
Daggett, L. & Keulegan, G. 1974. Similitude conditions in free-surface vortex formations (flow tests using cylindrical tanks with adjustable vanes). Journal of the Hydraulics Division, 100(11), Nov 1974.
Granata, F., De Marinis, G. & Gargano, R. 2014. Flow-improving elements in circular drop manholes. Journal of Hydraulic Research, 52, 347-355.
Granata, F., De Marinis, G., Gargano, R. & Hager, W. H. 2011. Hydraulics of circular drop manholes. Journal of Irrigation and Drainage Engineering, 137, 102-111.
Hager, W. H. 1990. Vortex drop inlet for supercritical approaching flow. Journal of Hydraulic Engineering, 116, 1048-1054.
Hager, W. H. 2010. Wastewater hydraulics: theory and practice, Springer Heidelberg Dordrecht London New York.
Hajiahmadi, A., Ghaeini-Hessaroeyeh, M. & Khanjani, M. J. 2021. Experimental evaluation of vertical shaft efficiency in vortex flow energy dissipation. International Journal of Civil Engineering, 19, 1445-1455.
Jain, A. K., Garde, R. J. & Ranga Raju, K. G. 1978. Vortex formation at vertical pipe intakes. Journal of the Hydraulics Division, 104, 1429-1445.
Jain, S. C. 1984. Tangential vortex-inlet. Journal of Hydraulic Engineering, 110, 1693-1699.
Liu, Z. P., Guo, X. L., Xia, Q. F., Fu, H., Wang, T. & Dong, X. L. 2018. Experimental and numerical investigation of flow in a newly developed vortex drop shaft spillway. Journal of Hydraulic Engineering, 144, 04018014.
Ma, Y., Zhu, D. Z. & Rajaratnam, N. 2016. Air entrainment in a tall plunging flow dropshaft. Journal of Hydraulic Engineering, 142, 04016038.
Mahmoudi-Rad, M. & Khanjani, M. J. 2019. Energy dissipation of flow in the vortex structure: experimental investigation. Journal of Pipeline Systems Engineering and Practice, 10, 04019027.
Mahmoudi Rad, M. & Khanjani, M. J. 2020. Experimental study of air flow in a vortex structure using full factorial method. Journal of Water and Wastewater, 31(4), 57-70. (In Persian)
Montgomery, D. C. 2017. Design and analysis of experiments, John Wiley & Sons. New York. USA.
Pfister, M., Crispino, G., Fuchsmann, T., Ribi, J. M. & Gisonni, C. 2018. Multiple inflow branches at supercritical-type vortex drop shaft. Journal of Hydraulic Engineering, 144, 05018008.
Sangsefidi, Y., Mehraein, M., Ghodsian, M. & Motalebizadeh, M. R. 2017. Evaluation and analysis of flow over arced weirs using traditional and response surface methodologies. Journal of Hydraulic Engineering, 143, 04017048.
Yang, Z., Yin, J., Lu, Y., Liu, Z., Yang, H. & Xu, G. 2021. Three-dimensional flow of a vortex drop shaft spillway with an elliptical tangential inlet. Water, 13, 504.
Yu, D. & Lee, J. H. 2009. Hydraulics of tangential vortex intake for urban drainage. Journal of Hydraulic Engineering, 135, 164-174.
Zhao, C. H., Zhu, D. Z., Sun, S. K. & Liu, Z. P. 2006. Experimental study of flow in a vortex drop shaft. Journal of Hydraulic Engineering, 132, 61-68.