Evaluation and Analysis of Flow over Arced Weirs Using Traditional and Response Surface Methodologies
Publication: Journal of Hydraulic Engineering
Volume 143, Issue 11
Abstract
This paper experimentally studies the hydraulic characteristics of arced weirs located in a reservoir. The accuracy and ability of the response surface methodology (RSM), especially central composite design (CCD), to describe the hydraulic performance of this type of weir is validated using experimental data. The discharge coefficient of arced weirs is presented as a function of headwater ratio () and magnification ratio () using both traditional and response surface methodologies. The results indicate that like the traditional methodology, RSM-CCD introduces an acceptable model to determine the discharge coefficient of the arced weirs, but it requires a much lower number of experiments. The results show that the discharge coefficient of an arced weir decreases by increasing and [or arc angle ()]. In addition, compared to a linear weir, the efficiency of an arced weir can increase up to 50%. Finally, based on the experimental results, a method is introduced for designing the in-reservoir arced weirs.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The authors would like to express their appreciation to the Applied Research Office of the Iran Water Resources Management Company (IWRMC) for partial support of this study through project RIV4-91042. The authors would like to thank Younes Sangsefidi (Ph.D. Candidate at the School of Electrical Engineering and Computer Science, Washington State University, Pullman, Washington) and Seyyed Mohammad Mousavi (Biotechnology Group, Chemical Engineering Department, TMU, Tehran, Iran) for their help in writing and RSM, respectively. The authors also are grateful to Stat-Ease, Minneapolis, Minnesota, for the provision of the Design-Expert package.
References
Ahmadi, M., Vahabzadeh, F., Bonakdarpour, B., Mofarrah, E., and 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.” J. Hazard. Mater., 123(1–3), 187–195.
Amiri, F., Mousavi, S. M., Yaghmaei, S., and Barati, M. (2012). “Bioleaching kinetics of a spent refinery catalyst using Aspergillus niger at optimal conditions.” Biochem. Eng. J., 67, 208–217.
Anderson, R. M., and Tullis, B. P. (2012). “Comparison of piano key and rectangular labyrinth weir hydraulics.” J. Hydraul. Eng., 358–361.
Antony, J. (2003). Design of experiments for engineers and scientists, Butterworth-Heinemann, New York.
ASCE. (2000). Hydraulic modeling: Concepts and practice, Reston, VA.
Bezerra, M. A., Santelli, R. E., Oliveira, E. P., Villar, L. S., and Escaleira, L. A. (2008). “Response surface methodology (RSM) as a tool for optimization in analytical chemistry.” Talanta, 76(5), 965–977.
Box, G. B. P., and Wilson, K. B. (1951). “On experimental attainment of optimum conditions.” J. R. Stat. Soc., 13(1), 1–45.
Bradley, N. (2007). “The response surface methodology.” M.S. thesis, Indiana Univ. of South Bend, South Bend, IN.
Christensen, N. A. (2013). “Flow characteristics of arced labyrinth weirs.” M.S. thesis, Utah State Univ., Logan, UT.
Crookston, B. M. (2010). “Labyrinth weirs.” Ph.D. thesis, Utah State Univ., Logan, UT.
Crookston, B. M., and Tullis, B. P. (2012a). “Arced labyrinth weirs.” J. Hydraul. Eng., 555–562.
Crookston, B. M., and Tullis, B. P. (2012b). “Discharge efficiency of reservoir-application-specific labyrinth weirs.” J. Hydraul. Eng., 555–562.
Crookston, B. M., and Tullis, B. P. (2013a). “Hydraulic design and analysis of labyrinth weirs. I: Discharge relationships.” J. Irrig. Drain. Eng., 363–370.
Crookston, B. M., and Tullis, B. P. (2013b). “Hydraulic design and analysis of labyrinth weirs. II: Nappe aeration, instability, and vibration.” J. Irrig. Drain. Eng., 371–377.
Design-Expert version 7.0.0 [Computer software]. Stat-Ease, Inc., Minneapolis.
Dey, S. (2014). Fluvial hydrodynamics: Hydrodynamic and sediment transport phenomena, Springer, Berlin.
Erpicum, S., et al. (2016). “Scale effects in physical piano key weirs models.” J. Hydraul. Res., 54(6), 692–698.
French, R. H. (1986). Open channel hydraulic, McGraw-Hill, New York.
Ghodsian, M. (2009). “Stage-discharge relationship for a triangular labyrinth spillway.” Proc. Inst. Civil Eng. Water Manage., 162(3), 173–178.
Ghodsian, M., Amanian, N., and Marashi, S. A. (2002). “Discharge coefficient of semicircular labyrinth weir.” Amirkabir J. Sci. Technol., 13(49), 76–83 (in Persian).
Hager, W. H. (1987). “Lateral outflow over side weirs.” J. Hydraul. Eng., 491–504.
Hager, W. H., and Schwalt, M. (1994). “Broad-crested weir.” J. Irrig. Drain. Eng., 13–26.
Hashemi, M., Razavi, S. H., Shojaosadati, S. A., Mousavi, S. M., Khajeh, K., and Safari, M. (2010). “Development of a solid-state fermentation process for production of an alpha amylase with potentially interesting properties.” J. Biosci. Bioeng., 110(3), 333–337.
Heller, V. (2011). “Scale effects in physical hydraulic engineering models.” J. Hydraul. Res., 49(3), 293–306.
Henderson, F. M. (1966). Open channel flow, Prentice-Hall, Englewood Cliffs, NJ.
Ilaiyaraja, N., Likhith, K. R., Sharath Babu, G. R., and Khanum, F. (2015). “Optimisation of extraction of bioactive compounds from Feronia limonia (wood apple) fruit using response surface methodology.” Food Chem., 173, 348–354.
Karami, H., Karimi, S., Rahmanimanesh, M., and Farzin, S. (2017). “Predicting discharge coefficient of triangular labyrinth weir using support vector regression, support vector regression-firefly, response surface methodology and principal component analysis.” Flow Meas. Instrum., 55, 75–81.
Khode, B. V., Tembhurkar, A. R., Porey, P. D., and Ingle, R. N. (2012). “Experimental studies on flow over labyrinth weir.” J. Irrig. Drain. Eng., 548–552.
Kline, S., and McClintock, F. (1953). “Describing uncertainties in single sample experiments.” Mech. Eng., 75(1), 3–8.
Kumar, S., Ahmad, Z., Mansoor, T., and Himanshu, S. K. (2012). “Discharge characteristics of sharp crested weir of curved plan-form.” Res. J. Eng. Sci., 1(4), 16–20.
Liu, R. S., and Tang, Y. J. (2010). “Tuber melanosporum fermentation medium optimization by Plackett-Burman design coupled with Draper-Lin small composite design and desirability function.” Bioresour. Technol., 101(9), 3139–3146.
Liu, Y., Liu, L., Liang, L., Liu, X., and Li, J. (2015). “Thermodynamic optimization of the recuperative heat exchanger for Joule-Thomson cryocoolers using response surface methodology.” Int. J. Refrig., 60, 155–165.
Mohammadi, R., Mohammadifar, M. A., Mortazavian, A. M., Rouhi, M., Ghasemi, J. B., and Delshadian, Z. (2016). “Extraction optimization of pepsin-soluble collagen from eggshell membrane by response surface methodology.” Food Chem., 190, 186–193.
Montgomery, D. C. (2012). Design and analysis of experiments, 8th Ed., Wiley, Hoboken, NJ.
Oehlert, G. W. (2000). Design and analysis of experiments: Response surface design, W.H. Freeman, Co., New York.
Pfister, M., Battisacco, G., Cesare, D., and Schleiss, A. (2013). “Scale effects related to the rating curve of cylindrically crested piano key weirs.” Labyrinth and piano key weirs II, CRC Press, London, 73–82.
Sangsefidi, Y., Mehraein, M., and Ghodsian, M. (2014). “Experimental investigation on the hydraulic performance of arced weirs.” Modares J. Civil Eng., 15(2), 51–63 (in Persian).
Sangsefidi, Y., Mehraein, M., and Ghodsian, M. (2015). “Numerical simulation of flow over labyrinth spillways.” Scientia Iranica Trans. A, 22(5), 1779–1787.
Savage, B. M., Crookston, B. M., and Paxson, G. S. (2016). “Physical and numerical modeling of large headwater ratios for a 15° labyrinth spillway.” J. Hydraul. Eng., 04016046.
Taylor, G. (1968). “The performance of labyrinth spillways.” Ph.D. thesis, Univ. of Nottingham, Nottingham, U.K.
Tullis, J. P., Amanian, N., and Waldron, D. (1995). “Design of labyrinth weir spillways.” J. Hydraul. Eng., 247–255.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 143 • Issue 11 • November 2017
Copyright
©2017 American Society of Civil Engineers.
History
Received: Dec 10, 2016
Accepted: May 24, 2017
Published online: Sep 8, 2017
Published in print: Nov 1, 2017
Discussion open until: Feb 8, 2018
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.