Investigation on the Effects of Distance-to-Diameter Ratio of piers on the Hydraulic Characteristics in a 90° Open Channel Bend

Xi  Shi; Tingting  Song; Hui  Chen; Hu  Tao; Yuanshun  Huo

doi:10.6180/jase.202602_29(2).0014

Investigation on the Effects of Distance-to-Diameter Ratio of piers on the Hydraulic Characteristics in a 90° Open Channel Bend

Xi Shi¹, Tingting Song¹, Hui Chen², Hu Tao¹, and Yuanshun Huo¹This email address is being protected from spambots. You need JavaScript enabled to view it.

¹College of Civil Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China

²State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, Tianjin 300354, China

Received: October 24, 2024
Accepted: April 25, 2025
Publication Date: June 7, 2025

Copyright The Author(s). This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cited.

Download Citation: ||https://doi.org/10.6180/jase.202602_29(2).0014

To investigate the influence of pier spacing on the flow structure in curved channels, a three-dimensional 90^◦ bend model was established. The simulation employed the PISO algorithm coupled with the RNGk −ε turbulence model, along with the Volume of Fluid (VOF) method for free-surface tracking. The flow char acteristics under different spacing-to-diameter ratios (s/d = 2, 3, 5) were analyzed. The results indicate that: (1) Along the flow direction, the longitudinal velocity (V^*_u) decreases while the transverse velocity (V^*_u) increases, and they are complementary to each other. At the convex and concave banks: V^∗_us/d=2 > V^∗_us/d=3 > V^∗_us/d=5, V^∗_vs/d=2 < V^∗_vs/d=3 < V^∗_vs/d=5. (2) Active circulation structures exist in low-velocity areas where flow velocity interacts with circulation patterns. As s/d increases, water flow superposition weakens leading to gradual separation and formation of complete vortex structures. This reduction in water flow turbulence and vortex formation helps mitigate erosion effects on bridge piers. (3) With increasing spacing-to-diameter ratio, K_s/d=5 > K_s/d=3 > K_s/d=2, is observed on both sides of convex and concave regions but opposite along the central axis. Relative turbulent kinetic energy exhibits an inverted "W" shape along the water depth direction on both sides of convex and concave regions while displaying an inverted " S " shape along the central axis.

Keywords: Bend flow characteristics; circular end bridge piers; span-to-diameter ratio; bend circulation; turbulent kinetic energy

[1] M.Asadollahi, M. Vaghefi, and M.Akbari, (2020) “Ef fect of the position of perpendicular pier groups in a sharp bend on flow and scour patterns: numerical simulation" Journal of the Brazilian Society of Mechanical Sci ences and Engineering 42(8): DOI: 10.1007/s40430-020 02503-2.
[2] M. Vaghefi, S. Moradi, and C. A. Chooplou, (2021) “Numerical Study of Bed Topography Variations Owing to Placement of Triad Series of Vertical Bridge Piers Installed in a 180-degree Bend with Different Relative Radii Using SSIIM Numerical Model" Iranian Journal of Science and Technology, Transactions of Civil Engineering 45(3): 1–18. DOI: 10.1007/s40996-020-00559-7.
[3] F. Sedighi, M. aghefi, and E. Zarei, (2022) “Experimen tal investigation of flow pattern at 180° bend with rigid bed in effect of twin convergent bridge piers" Journal of Engineering and Applied Science 69(1): 1–19. DOI: 10.1186/s44147-022-00110-7.
[4] K. Lahsaei, M. Vaghefi, and C. A. Chooplou, (2022) “Numerical simulationI of flow pattern at a divergent pier in a bend with different relative curvature radII using ansys fluent" Engineering Review 42(3): 63–85.
[5] M.Rasaei, S. Nazari, and S. Eslamian, (2020) “Experi mental investigation of local scouring around the bridge piers located at a 90° convergent river bend" Sadhana 45(1): DOI: 10.1007/s12046-020-1314-7.
[6] W. Wei, P. Li, S. Shao, and y. Liu, (2016) “Study on Effects of T-Spur-Dikes on Flow Characteristics in 90° Bend Channel by Large Eddy Simulation" Journal of System Simulation 28(06): 1419–1425. DOI: 10.16182/ j.cnki.joss.2016.06.024.
[7] A.Thair J. and H. Ameer Hashim, (2024) “A Review of Studying the Flow Characteristics in Branching Open Channels" International Journal of Heat and Tech nology 42(2): DOI: 10.18280/IJHT.420222.
[8] L. Bin, X. Haijue, B. Yuchuan, and L. Jun, (2024) “Experiment on the Hydrodynamic Characteristics of Plunging Flows in Bedrock Canyon Bends" Journal of Geophysical Research. Earth Surface 129(7): e2023JF007387–e2023JF007387. DOI: 10.1029/2023JF007387.
[9] A. Baranwal and B. S. Das, (2024) “Scouring around bridge pier: a comprehensive analysis of scour depth pre dictive equations for clear-water and live-bed scouring conditions" AQUA—Water Infrastructure, Ecosys tems and Society 73(3): 424–452. DOI: 10.2166/aqua.2024.235.
[10] M.R.Bharadwaj, L. K. Gupta, M. Pandey, and M. Va lyrakis, (2025) “Countermeasures for local scour around the bridge pier: a review" Acta Geophysica 73(1): 701 728. DOI: 10.1007/s11600-024-01361-z.
[11] L. K. Gupta, M. Pandey, and P. A. Raj, (2023) “Nu merical simulation of local scour around the pier with and without airfoil collar (AFC) using FLOW-3D" Environ mental Fluid Mechanics: DOI: 10.1007/s10652-023 09932-2.
[12] W. Kai, W. Jiahua, Z. Cheng, and W. Guangqian, (2009) “Effect to Discharge Capacity of Channel from Bridges Distribution——A Case Study of South-North Water Transfer Midline Project" Journal of Basic Sci ence and Engineering: DOI: 10.1109/MILCOM.2009. 5379889.
[13] A.-A. Beheshti, B. Ataie-Ashtiani, and H. Dasht peyma, (2017) “Numerical simulations of turbulent flow around side-by-side circular piles with different spacing ratios" International Journal of River Basin Man agement 15(2): 227–238. DOI: 10.1080/15715124.2017.1280811.
[14] M. Yilmaz, A. M. Yanmaz, and M. Koken, (2017) “Clear-water scour evolution at dual bridge piers" Cana dian Journal of Civil Engineering 44(4): 298–307. DOI: 10.1139/cjce-2016-0053.
[15] X. Shi, C.-b. Tan, L. Gong, and H. Tao, (2024) “Anal ysis of water and flow field characteristics of river diag onal bridge" Sediment Research 49(02): 64–71. DOI: 10.16239/j.cnki.0468-155x.2024.02.009.
[16] C. Gao, C. Cai, and Z. Zhang, (2021) “Study on wa ter blocking performance of semicircular-end bridge piers in plain rivers" Water Resources and Hydropower Engineering 52(S2): 269–274. DOI: 10.13928/j.cnki. wrahe.2021.S2.061.
[17] Z. Zhou, C. Zeng, J. Zhou, L. Wang, and S. Ding, (2020) “Numerical investigation on distribution charac teristics of velocities at equal-width open-channel conflu ences" Hydro-Science and Engineering (01): 32–39.
[18] S. Liu and W. Liao, (2019) “Differential model of total f low and principle of minimum energy dissipation for laminar flow in open channel" Engineering Journal of Wuhan University 52(09): 753–757+801. DOI: 10.14188/j.1671-8844.2019-09-001.
[19] D.Ran,W.Wang,X.Hu,andL.Shi,(2018)“Analyzing hydraulic performance of trapezoidal cutthroat flumes." Advances in Water Science 29(02): 236–244. DOI: 10.14042/j.cnki.32.1309.2018.02.011.
[20] C.-w. Hu, M.-h. Yu, and G. Qu, (2025) “Study on the evolution process of secondary flows in a sharply curved bend under different inflow conditions" Engineering Mechanics 42(01): 259–274.
[21] W. Wang, W. Liao, and L. Qi, (2020) “Experiment of turbulent characteristics of flow in wide-and-narrow chan nels" Advances in Water Science 31(03): 394–403. DOI: 10.14042/j.cnki.32.1309.2020.03.009.