The effect of the energy head and the inlet and outlet key width on discharge coefficient of Piano key weir

Document Type : Original Article

Authors

1 M.Sc Graduated of Water Structure, Department of Water Science and Engineering, Campus of Agriculture and Natural Resources, Razi University, Kermanshah, Iran

2 ssistant Professor, Department of Water Science and Engineering, Campus of Agriculture and Natural Resources, Razi University, Kermanshah, Iran.

Abstract

Introduction

Piano key weir is a form of nonlinear weir designed to improve the discharge capacity of spillway structures. Due to the increase in effective length, they can be used in dam spillways or water regulation structures. It is modified form of labyrinth weir which easy to place on the existing spillway or newly constructed dam with less base area. There is no standard method available for PK weir design, and the amount of published information is insufficient for the design of PK weir. A large number of geometric and hydraulic parameters affect the discharge capacity of PK weir, and their effect on the hydraulic performance of the weir can be investigated with a numerical model or laboratory data. Simulation of flow over PKW using FLOW-3D software and the effect of the turbulence model on the accuracy of the numerical model is one of the goals of this study. Also, in this research, the effect of the ratio of the inlet key width to the outlet key width (Wi/Wo) and the effect of the energy head on the discharge capacity are investigated.

Methodology
Laboratory data from Anderson (2011) were used to validate the numerical model. The total length and height of the weir are 4.848 and 0.197 m respectively, the floor slope in inlet and outlet key are 1:1.8, and number of keys is 4. The inlet and outlet key width are 0.116 and 0.925 m respectively, and the Wi/Wo ratio is 1.25. Selection of boundary conditions for the numerical model is one of the most basic stages of simulation. In order to define the boundary conditions, in the inflow point (Xmin) volume flow rate, in the sides of the weir (Ymin, Ymax) and bed (Zmin) wall condition, on the upper border (Zmax) symmetry condition and in the outflow section of the weir, outflow condition was used.

Results and discussion
The numerical model results were compared with the laboratory data. The results showed that if the second order scheme and RNG k-ε turbulence model are used in the numerical model, the simulation accuracy of the flow over PKW increases. Also, the results show that increasing the He/P decreases the discharge coefficient. So that the discharge coefficient for He/P=0.92 decreases by about 50% compared to He/P=0.24. With the increase of the water depth on the weir, the interference of the flow takes place at the breaking point of the weir cycles, and as a result, the discharge coefficient decreases. Another factor affecting the flow coefficient of the piano key is the ratio of the inlet key width to the outlet key width. By increasing the Wi/Wo, the flow coefficient has increased, and then it becomes maximum at Wi/Wo=1.5.

Conclusions
In this research, the simulation of the flow over piano key and labyrinth weir was done using a numerical model. The results showed that for a fixed depth, the piano key weir passes more discharge than the labyrinth weir, and the ratio of flow through the piano key weir to the labyrinth weir is about 1.08. In other words, at a constant depth, the piano key weir passes 8% more flow. In this research, the effect of head energy on the discharge coefficient of the piano key weir was also investigated. The results show that increasing the He/P decreases the discharge coefficient. The results showed that if the Wi/Wo equal to 1.5, the highest discharge coefficient occurs for the piano key weir.


Keywords

Main Subjects

References

Anderson, R. M. (2011). Piano key weir head discharge relationships. M.S. thesis, Utah State Univercity.
Anderson, R.M., & Tullis, B.P. (2012). Comparison of piano key and rectangular labyrinth weir. Journal of Hydraulic Engineering, 138, 358- 361. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000509
Bremer, F.L., & Oertel, M. (2017). Numerical investigation of wall thickness influence on Piano Key Weir discharge coefficients: A preliminary study. Labyrinth and Piano Key Weirs III, CRC Press, London. https://www.taylorfrancis.com/chapters/edit/10.1201/9781315169064-14
Chahartaghi, M.K., Nazari, S., & Mahmoodian Shooshtari, M. (2019). Experimental and numerical simulation of arced trapezoidal piano key weirs. Flow Measurement and Instrumentation, 68, 1-16. https://doi.org/10.1016/j.flowmeasinst.2019.101576
Crookston, B. M., Anderson, R. M., & Tullis, B. P. (2018). Free-flow discharge estimation method for Piano Key weir geometries. Journal of Hydroenvironment Research. 19, 160-167. https://doi.org/10.1016/j.jher.2017.10.003
Dabling, M. R., & Tullis, B. P. (2012). Piano key weir submergence in channel application. Journal of Hydraulic Engineering, 138(7), 661-666. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000563
Falvey, H. T. (2003). Hydraulic design of labyrinth weirs. ASCE Press, USA. http://ndl.ethernet.edu.et/bitstream/123456789/61317/1/1081.pdf
Flow Science, Inc. (2014). FLOW-3D user’s manual version 11.0. Santa Fe, Mexico. https://www.flow3d.com/wp-content/uploads/2020/10/FLOW-3D_HYDRO_installation_instructions.pdf
Gharibvand, R., Heidarnejad, M., Kashkouli, H.A., Hasoonizadeh, H., & Kamanbedast A. A. (2020). Numerical Analysis of Flow Hydraulic in Trapezoidal Labyrinths and Piano Key Weirs. Journal of Water and Soil Science, 24(1), 45-56. https://doi.org/10.47176/jwss.24.1.38092 [In Persian]
Heidarpoor, M., Mousavi, F., & Roshani-Zarmehri, R. (2006). Labyrinth weir with rectangular and U-shape plan-forms, Journal of Science and Technology of Agriculture and Natural Resources. 10(3), 1-11. https://www.sid.ir/paper/440089/fa#downloadbottom [In Persian]
Henderson, F. M. (1966). Open channel flow, Channel controls. MacMillan. United State of America. https://heidarpour.iut.ac.ir/sites/heidarpour.iut.ac.ir/files//u32/open-henderson.pdf
Karimi, M., Jalili-Ghazizadeh, M., saneie, M., & Attari, J. (2020). Experimental study of piano key side weir with oblique keys. Amirkabir Journal of Civil Engineering, 52(7), 1671-1684. https://doi.org/10.22060/CEEJ.2019.15599.5970 [In Persian]
Machiels, O., Pirotton, M., Pierre, A., Dewals, B., & Erpicum, S. (2014). Experimental parametric study and design of Piano Key Weirs. Journal of Hydraulic Research. 52(3), 326-335. https://doi.org/10.1080/00221686.2013.875070
Ouamane, A., & Lempérière, F. (2006). Design of a new economic shape of weir. Proc. Int. Symp. Dams in the Societies of the 21st Century, Barcelona, Spain.                                  https://www.scirp.org/reference/referencespapers?referenceid=3431226
Riberio, M., Pfister, M., Schleiss, A. J., & Boillat, J. L. (2012). Hydraulic design of A-type Piano key weirs. Journal of Hydraulic Research, 50(4), 400-408. https://doi.org/10.1080/00221686.2012.695041
Safarzadeh, A & khayyatrostami, S. (2016) Laboratory evaluation of height effects on hydraulics of submerged piano key weirs. Journal of Iranian Dam and Hydroelectric Powerplant, 2(7), 1-12. https://doi.org/20.1001.1.23225882.1394.2.7.2.1 [In Persian]
Safarzadeh, A., & Noroozi, B. (2014) Three dimensional hydrodynamics of arced piano key spillways. Journal of Hydraulic, 9(3), 61-79. https://doi.org/10.30482/JHYD.2014.10176 [In Persian]
Safarzadeh, A., Khayat Rostami, S., & Khayat Rostami, B. (2019). Investigation on the effects of water head on discharge distribution and streamlines pattern over the Asymmetric Piano key weirs. Journal of Hydraulic, 14(1), 1-17. https://doi.org/10.30482/JHYD.2019.101685.1253 [In Persian]
Yousif, A.A. (2020) Experimental investigation on hydraulic performance of non-rectangular piano key weir (PKW). International Journal of Advanced Science and Technology, 29(8), 4467-4480. https://www.researchgate.net/publication/342550937
Anderson, R. M. (2011). Piano key weir head discharge relationships. M.S. thesis, Utah State Univercity.
Anderson, R.M., & Tullis, B.P. (2012). Comparison of piano key and rectangular labyrinth weir. Journal of Hydraulic Engineering, 138, 358- 361. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000509
Bremer, F.L., & Oertel, M. (2017). Numerical investigation of wall thickness influence on Piano Key Weir discharge coefficients: A preliminary study. Labyrinth and Piano Key Weirs III, CRC Press, London. https://www.taylorfrancis.com/chapters/edit/10.1201/9781315169064-14
Chahartaghi, M.K., Nazari, S., & Mahmoodian Shooshtari, M. (2019). Experimental and numerical simulation of arced trapezoidal piano key weirs. Flow Measurement and Instrumentation, 68, 1-16. https://doi.org/10.1016/j.flowmeasinst.2019.101576
Crookston, B. M., Anderson, R. M., & Tullis, B. P. (2018). Free-flow discharge estimation method for Piano Key weir geometries. Journal of Hydroenvironment Research. 19, 160-167. https://doi.org/10.1016/j.jher.2017.10.003
Dabling, M. R., & Tullis, B. P. (2012). Piano key weir submergence in channel application. Journal of Hydraulic Engineering, 138(7), 661-666. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000563
Falvey, H. T. (2003). Hydraulic design of labyrinth weirs. ASCE Press, USA. http://ndl.ethernet.edu.et/bitstream/123456789/61317/1/1081.pdf
Flow Science, Inc. (2014). FLOW-3D user’s manual version 11.0. Santa Fe, Mexico. https://www.flow3d.com/wp-content/uploads/2020/10/FLOW-3D_HYDRO_installation_instructions.pdf
Gharibvand, R., Heidarnejad, M., Kashkouli, H.A., Hasoonizadeh, H., & Kamanbedast A. A. (2020). Numerical Analysis of Flow Hydraulic in Trapezoidal Labyrinths and Piano Key Weirs. Journal of Water and Soil Science, 24(1), 45-56. https://doi.org/10.47176/jwss.24.1.38092 [In Persian]
Heidarpoor, M., Mousavi, F., & Roshani-Zarmehri, R. (2006). Labyrinth weir with rectangular and U-shape plan-forms, Journal of Science and Technology of Agriculture and Natural Resources. 10(3), 1-11. https://www.sid.ir/paper/440089/fa#downloadbottom [In Persian]
Henderson, F. M. (1966). Open channel flow, Channel controls. MacMillan. United State of America. https://heidarpour.iut.ac.ir/sites/heidarpour.iut.ac.ir/files//u32/open-henderson.pdf
Karimi, M., Jalili-Ghazizadeh, M., saneie, M., & Attari, J. (2020). Experimental study of piano key side weir with oblique keys. Amirkabir Journal of Civil Engineering, 52(7), 1671-1684. https://doi.org/10.22060/CEEJ.2019.15599.5970 [In Persian]
Machiels, O., Pirotton, M., Pierre, A., Dewals, B., & Erpicum, S. (2014). Experimental parametric study and design of Piano Key Weirs. Journal of Hydraulic Research. 52(3), 326-335. https://doi.org/10.1080/00221686.2013.875070
Ouamane, A., & Lempérière, F. (2006). Design of a new economic shape of weir. Proc. Int. Symp. Dams in the Societies of the 21st Century, Barcelona, Spain.                                  https://www.scirp.org/reference/referencespapers?referenceid=3431226
Riberio, M., Pfister, M., Schleiss, A. J., & Boillat, J. L. (2012). Hydraulic design of A-type Piano key weirs. Journal of Hydraulic Research, 50(4), 400-408. https://doi.org/10.1080/00221686.2012.695041
Safarzadeh, A & khayyatrostami, S. (2016) Laboratory evaluation of height effects on hydraulics of submerged piano key weirs. Journal of Iranian Dam and Hydroelectric Powerplant, 2(7), 1-12. https://doi.org/20.1001.1.23225882.1394.2.7.2.1 [In Persian]
Safarzadeh, A., & Noroozi, B. (2014) Three dimensional hydrodynamics of arced piano key spillways. Journal of Hydraulic, 9(3), 61-79. https://doi.org/10.30482/JHYD.2014.10176 [In Persian]
Safarzadeh, A., Khayat Rostami, S., & Khayat Rostami, B. (2019). Investigation on the effects of water head on discharge distribution and streamlines pattern over the Asymmetric Piano key weirs. Journal of Hydraulic, 14(1), 1-17. https://doi.org/10.30482/JHYD.2019.101685.1253 [In Persian]
Yousif, A.A. (2020) Experimental investigation on hydraulic performance of non-rectangular piano key weir (PKW). International Journal of Advanced Science and Technology, 29(8), 4467-4480. https://www.researchgate.net/publication/342550937
 
Advanced Technologies in Water Efficiency
Volume 3, Issue 4
December 2023
Pages 1-17

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History

  • Receive Date: 29 September 2023
  • Revise Date: 08 December 2023
  • Accept Date: 27 December 2023

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