[1] N. Rajaratnam, A.Mainali, C. Y. Hsung, Observations on flow in vertical dropshafts in urban 627
drainage systems, Journal of Environmental Engineering, 123(5) (1997), 486-491. 628
[2] S. C. Jain, Free-surface swirling flows in vertical drop shaft, Journal of Hydraulic 629 Engineering
,113(10) (1987): 1277-1289. 630
[3] D. L. Bagheri, and W. H. Hager, Energy dissipators, hydraulic structures design 631 manual, IAHR,
Balkema, Rotterdam, the Netherlands, (1995). 632
[4] R. Shemshi, and S. Kabiri-Samani, Swirling flow at vertical shaft spillways with circular 633 pianokey
inlets, Journal of Hydraulic Research, 55(2) (2017), 248-258. 634
[5] S.C. Jain, Tangential vortex-inlet, Journal of hydraulic engineering, 110(12) (1984), 1693- 635
1699. 636
[6] W. H. Hager, Vortex drop inlet for supercritical approaching flow, Journal of Hydraulic 637
Engineering, 116(8) (1990), 1048-1054. This preprint research paper has not been peer reviewed.
Electronic copy available at: https://ssrn.com/abstract=4329747 Preprint not peer reviewed 21 638
[7] M. C. Quick, Analysis of spiral vortex and vertical slot vortex drop shafts, Journal of 639
Hydraulic Engineering, 116(3) (1990), 309-325. 640
[8] X. L. Dong, K. L. Yang, X. L. Guo, Y. X. Guo, Hydraulic mechanism and application of 641
swirling device in morning glory shaft spillway, Journal of Hydraulic Engineering, (2011), 1. 642
Civil and Project Journal, 2022, 4(9), 52-71/ R. Aghamajidi
70
[9] A. Kasra, A. Khosrojerdi, H. Babazadeh, Cavitation Risk through the Bottom Outlet of the 643
Dam Using Numerical Solution of Ansys Model, JWSS-Isfahan University of Technology, 26(1) 644
(2022), 195-209. 645
[10] P. Wu, X. Wang, W. Lin, L. Bai, Acoustic characterization of cavitation intensity: A 646 review,
Ultrasonics Sonochemistry, 82 (2022), 105878. 647
[11] Z. P. Liu, X. L. Guo, Q. F. Xia, H. Fu, T. Wang, X. L. Dong, Experimental and numerical 648
investigation of flow in a newly developed vortex drop shaft spillway, Journal of Hydraulic 649
Engineering, 144(5) (2018), 04018014. 650 [
12] M. Haghbin, A. Sharafati, R. Aghamajidi, S. B. H. S. Asadollah, M. H. M. Noghani, M. L 651
Jalón, Determination of discharge coefficient of stepped morning glory spillway using a hybrid 652
data-driven method, Flow Measurement and Instrumentation, 85 (2022), 102161. 653
[13] M. Chitsazan, and H. R. Ghafouri, Optimization of Anti-vortex Blades Geometry in 654 Morning
Glory Spillways by Numerical simulation, Engineering, Environmental Science, 655 (2022).
https://doi.org/10.21203/rs.3.rs-1685709/v1. 656
[14-1] S. Radmanesh, A. Bazaee, R. Aghamajidi, Calculating the overflow coefficient of stepped 657
and non-Stepped morning glory spillway and investigating its behavior using anti vortex 658 blades,
Civil and Project Journal, 4(2) (2022). 659
[14-2] R. Aghamajidi,(2013) Computerized simulation of hydraulic behavior of shaft spillway vortex
breaker on crest and semi long stepped chamber throat, Technical Journal of Engineering and Applied
Sciences. Issu23. 3325-3332.
https://scholar.google.com/citations?view_op=view_citation&hl=en&user=u9WtUQs8WkUC&cstart=
20&pagesize=80&citation_for_view=u9WtUQs8WkUC:L8Ckcad2t8MC
[15] S. Esmaeilizadeh, T. Mirzavand, Effect of deflector and aeration on the discharge 660 coefficient
of submerged flow of morning glory spillways, Journal of Dam and Hydroelectric 661 Powerplant,
8(31) (2022), 62-74. 662
[16] S. T. Maynord, General Spillway Investigation; Hydraulic Model Investigation (No. 663
WES/TR/HL-85-1), (1985) 664
[17] USBR, Design of small dams, Water Resources Technical Publication Series, (1987). 665
[18] C. H. Zhao, D. Z. Zhu, S. K. Sun, Z. P. Liu, Experimental study of flow in a vortex drop 666
shaft, Journal of Hydraulic Engineering, 132(1) (2006), 61-68. 667
[19] C. A. Fattor, and J. D. Bacchiega, Design conditions for morning-glory spillways: 668 application
to potrerillos dam spillway, In Advances in Water Resources and Hydraulic 669 Engineering, Springer,
Berlin, Heidelberg. (2009), (2123-2128). 670
[20] G. Christodoulou, A. Mavrommatis, T. Papathanassiadis, Experimental study on the effect 671 of
piers and boundary proximity on the discharge capacity of a morning glory spillway, In 1st 672 IAHR
European Congress, Edinburgh, Scotland, (2010). 673
[21] L. Savic, R. Kapor, V. Kuzmanovic, B. Milovanovic, Shaft spillway with deflector 674
downstream of vertical bend, In Proceedings of the Institution of Civil Engineers-Water 675
Civil and Project Journal, 2022, 4(9), 52-71/ R. Aghamajidi
71
Management, 167(5) (2014), 269-278. This preprint research paper has not been peer reviewed.
Electronic copy available at: https://ssrn.com/abstract=4329747 Preprint not peer reviewed 22 676
[22] A. salehi, moghadam: (2023) Effect of the pipe bend of the morning glory spillway on the
cavitation number.
[23] A. Parsaie, S. Dehdar-Behbahani, A. H. Haghiabi, Numerical modeling of cavitation on 679
spillway’s flip bucket, Frontiers of Structural and Civil Engineering 10(4) (2016), 438-444. 680
[24] J. J. Cassidy, Irrotational flow over spillways of finite height, University of Missouri681
Columbia, (1965). 682
[25] M. Ikegawa, and K. Washizu, Finite element method applied to analysis of flow over a 683
spillway crest, International Journal for Numerical Methods in Engineering, 6(2) (1973), 179- 684 189.
685
[26] P. L. Betts, A variational principle in terms of stream function for free-surface flows and its 686
application to the finite element method, Computers & Fluids, 7(2) (1979), 145-153. 687
[27] B. M. Savage, and M. C. Johnson, Flow over ogee spillway: Physical and numerical model 688
case study, Journal of hydraulic engineering, 127(8) (2001), 640-649. 689
[28] N. R. Olsen, and H. M. Kjellesvig, Three-dimensional numerical flow modelling for 690
estimation of spillway capacity, Journal of Hydraulic Research, 36(5) (1998), 775-784. 691
[29] W. R. Fiedler, Performance of spillway structures using Hoover dam spillways as a 692
benchmark, In Hoover Dam: 75th Anniversary History Symposium Fluent User Manual, 693 Sheffield,
UK. (2010) (267-287) 694
[30] T. J. Alfatlawi, and H. I. Alshaikhli, Prediction the coefficient of discharge for stepped 695
morning glory spillway using ANN and MNLR approaches, International Journal of Civil and 696
Environmental Engineering, 37(2) (2015), 1701-8285. 697
[31] J. Liu, D. Nissim, J. Thomas, Equity valuation using multiples, Journal of Accounting 698
Research, 40(1) (2002), 135-172. 699
[32] H. T. Falvey, Cavitation in chutes and spillways, Denver: US Department of the Interior, 700
Bureau of Reclamation, (1990) 701
[33] R. Aghamajidi, H. M. Jahromi, H. Seghi, H. A. Kashkoi, Study effect of guide pier and 702
stepped chamber on flow regime of morning glory spill way, International Journal of Agriculture 703
and Crop Sciences (IJACS), 6(9) (2013), 493-500. 704
[34] A. Bordbar, H. Mousavi Jahromi, M. ShafaeiBajestan, H. Sedghi, Step effects investigation 705 on
the flow regime and cavitation in stepped morning glory spillways, World Applied Sciences 706
Journal, 10(9) (2010), 1024-1031. 707
[35] E. F. Kermani, G. A. Barani, M. Ghaeini-Hessaroeyeh, Investigation of cavitation damage 708
levels on spillways. World Applied Sciences Journal, 21(1) (2013), 73-78. 709
[36] F. Asadsangabi, N. Talebbeydokhti, M. Rahnavard. Two phase flow modeling in shaft710
spillways using volume of fluid (VOF) method. Iranian Journal of Science and Technology, 711
Transactions of Civil Engineering, 38(C1) (2014), 99. This preprint research paper has not been peer
Civil and Project Journal, 2022, 4(9), 52-71/ R. Aghamajidi
72
reviewed. Electronic copy available at: https://ssrn.com/abstract=4329747 Preprint not peer reviewed
23 712
[37] P. K. Swamee, S. K. Pathak, and M. Ghodsian, Viscosity and surface tension effects on 713
rectangular weirs, The ISH Journal of Hydraulic Engineering (2001) 7(2), 45-50. 714
[38] A. H. Azimi, N. Rajaratnam, D. Z. Zhu, “Water surface characteristics for submerged 715
rectangular sharp-crested weirs, Journal of Hydraulic Engineering, (2016) 142(5): 06016001-9. 716
[39] S.Salehi, and A. H. Azimi, Discharge characteristics of weir-orifice and weir-gate 717 structures,
Journal of Irrigation and Drainage Engineering, 145(11) (2019): 04019025. 718
[40] A. H. Azimi, and S. Salehi, Hydraulics of flow over full-cycle cosine and rectangular sharp719
crested weirs, Canadian Journal of Civil Engineering, 49(6) (2022), 954-968. 720
[41] S. Salehi, A. Mahmudi Moghadam, K. Esmaili, Flow regimes of submerged rectangular 721
sharp-crested weirs in sand bed channel, Sadhana, 48(6) (2022), 58. 722
[42] S. Salehi, A. H. Azimi, H, Hydraulics of sharp-crested weir culverts with downstream 723 ramps
in free-flow partially, and fully submerged-flow conditions. Irrigation Science, 39(2) 724 (2021): 191-
207. 725
[43] S. Salehi, A. Mostaani A. H. Azimi, Experimental and Numerical Investigations of Flow 726 over
and under Weir-Culverts with a Downstream Ramp. Journal of Irrigation and Drainage 727
Engineering, 147(7) (2022), pp.04021029. 728
[44] D. C. Wilcox, Reassessment of the scale-determining equation for advanced turbulence 729
models, AIAA journal, 26(11) (1988), 1299-1310. 730
[45] V. Yakhot, and L. Smith, The renormalization group, the ɛ-expansion and derivation of 731
turbulence models, Journal of scientific computing 7(1) (1992), 35-61. 732
[46] G. Mahtabi, and H. Arvanaghi, Experimental and numerical analysis of flow over a 733
rectangular full-width sharp-crested weir, Water Science and Engineering, 11(1) (2018), 75-80. 734
[47] B. Dargahi, Experimental study and 3D numerical simulations for a free-overflow 735 spillway,
Journal of Hydraulic Engineering, 132(9) (2006), 899-907. 736
[48] T. M. Salaheldin, J. Imran, M. H. Chaudhry, Numerical modeling of three-dimensional flow 737
field around circular piers, Journal of Hydraulic Engineering, 130(2) (2004), 91-100. 738
[49] P. J. Roache, Perspective: a method for uniform reporting of grid refinement studies, (1994). 739
[50] S. Salehi, and A. H. Azimi, Effects of spoiler and piggyback on local scour under single and 740
twin submerged pipes, Ocean Engineering, 261(2022), 112137.