Predicting Manhole Mixing Using a Compartmental Model
Publication: Journal of Hydraulic Engineering
Volume 147, Issue 12
Abstract
Manholes in combined sewers may become surcharged during storm events, resulting in complex mixing conditions. Although manhole hydrodynamics are reasonably well understood, predicting mixing across a surcharged manhole remains a challenge. An analytical compartmental mixing model for manholes, based on jet theory, has been further developed and applied to generate cumulative residence time distributions (CRTDs), which describe mixing. The modeled CRTDs were compared with the experimentally derived CRTDs of over 850 manhole configurations to evaluate how well the new compartmental model represents physical processes. The model underpredicts short-circuiting in manholes with manhole diameter to pipe diameter ratios greater than 4.4 and consequently overestimates mixing. Otherwise, the modeled CRTDs show good agreement with the experimental CRTDs. The new compartmental model represents key manhole hydrodynamics that are not represented in current software modeling packages, which assume manholes are instantaneously well-mixed. The compartmental model provides good predictions of the experimental downstream concentration profiles, although with reduced peak concentrations in those manhole configurations where short-circuiting is not well-predicted. Despite this, the compartmental model still predicts concentrations downstream of a manhole in closer agreement with the recorded data than the complete instantaneously well-mixed assumption. As an analytical model requiring no inputs other than manhole geometry, the new compartmental model applies to a wide range of manhole configurations, is robust, and is useful for predicting manhole mixing in practical applications.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
Data and code used during this study are available in a repository online in accordance with funder data retention policies from Guymer, I., Stovin, V., O’Brien, R., Dennis, P., Saiyudthong, C., Lau, S.-T. D., and Sonnenwald, F. (2020). https://doi.org/10.15131/shef.data.13373039 and Sonnenwald, F., Mark, O., Stovin, V., and Guymer, I. (2021). https://doi.org/10.15131/shef.data.14160884.
Acknowledgments
This work was supported by the EPSRC (Grant No. EP/P012027/1).
References
Agelin-Chaab, M., and M. F. Tachie. 2011. “Characteristics of turbulent three-dimensional offset jets.” J. Fluids Eng. 133 (5): 051203. https://doi.org/10.1115/1.4004071.
Albertson, M. L., Y. B. Dai, R. A. Jensen, and H. Rouse. 1950. “Diffusion of submerged jets.” Trans. Am. Soc. Civ. Eng. 115 (1): 639–664. https://doi.org/10.1061/TACEAT.0006302.
Arao, S., and T. Kusada. 1999. “Effects of pipe bending angle on energy losses at two-way circular drop manholes.” In Proc., 8th Int. Conf. on Urban Storm Drainage, 2163–2168. London: International Water Association.
Beg, M. N. A., R. F. Carvalho, and J. Leandro. 2019. “Effect of manhole molds and inlet alignment on the hydraulics of circular manhole at changing surcharge.” Urban Water J. 16 (1): 33–44. https://doi.org/10.1080/1573062X.2019.1611887.
BSI (British Standards Institution). 1981. Methods of measurement of liquid flow in open channels. Part 4A: Method using thin-plate weirs. BS 3680-4A:1981. London: BSI.
BSI (British Standards Institution). 2003. Measurement of fluid flow by means of pressure differential devices inserted in circular cross-section conduits running full. Part 1: General principles and requirements. BS EN ISO 5167-1:2003. London: BSI.
Butler, D., C. J. Digman, C. Makropoulos, and J. W. Davies. 2018. Urban drainage. Boca Raton, FL: CRC Press.
Chapra, S. 1997. Surface water-quality modeling. New York: McGraw-Hill.
Danckwerts, P. V. 1953. “Continuous flow systems: Distribution of residence times.” Chem. Eng. Sci. 2 (1): 1–13. https://doi.org/10.1016/0009-2509(53)80001-1.
Dennis, P. 2000. “Longitudinal dispersion due to surcharged manholes.” Ph.D. thesis, Dept. of Civil and Structural Engineering, Univ. of Sheffield.
DHI A/S. 2019. MOUSE pollution transport reference manual. Hørsholm, Denmark: DHI A/S.
European Union Commission. 2000. “Directive 2000/60/EC of the European Parliament and of the Council of 23 October 2000 establishing a framework for community action in the field of water policy.” OJL 327 (1): 1–73.
Gauntner, J. W., J. N. B. Livingood, and P. Hrycak. 1970. Survey of literature on flow characteristics of a single turbulent jet impinging on a flat plate. NASA TN D-5652. Washington, DC: National Aeronautics and Space Administration.
Guymer, I., P. Dennis, R. O’Brien, and C. Saiyudthong. 2005. “Diameter and surcharge effects on solute transport across surcharged manholes.” J. Hydraul. Eng. 131 (4): 312–321. https://doi.org/10.1061/(ASCE)0733-9429(2005)131:4(312).
Guymer, I., and R. O’Brien. 2000. “Longitudinal dispersion due to surcharged manhole.” J. Hydraul. Eng. 126 (2): 137–149. https://doi.org/10.1061/(ASCE)0733-9429(2000)126:2(137).
Guymer, I., V. Stovin, R. O’Brien, P. Dennis, C. Saiyudthong, S.-T. D. Lau, and F. Sonnenwald. 2020. University of Sheffield experimental manhole traces and CRTDs. V1. Sheffield, UK: Univ. of Sheffield.
Guymer, I., and V. R. Stovin. 2011. “One-dimensional mixing model for surcharged manholes.” J. Hydraul. Eng. 137 (10): 1160–1172. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000422.
Habib, M. A., H. M. Badr, S. A. M. Said, I. Hussaini, and J. J. Al-Bagawi. 2005. “On the development of deadleg criterion.” J. Fluids Eng. 127 (1): 124–135. https://doi.org/10.1115/1.1852481.
Innovyze Inc. 2019. InfoWorks ICM 10.5 manual. Portland, OR: Innovyze.
Jimoh, M., I. Guymer, and V. Stovin. 2014. “Hydraulic threshold levels in square manholes with high length to pipe diameter ratio.” In Proc., 13th Int. Conf. on Urban Drainage. Beijing: International Association for Hydro-Environment Engineering and Research.
Lau, S.-T. D. 2008. “Scaling dispersion processes in surcharged manholes.” Ph.D. thesis, Dept. of Civil and Structural Engineering, Univ. of Sheffield.
Levenspiel, O. 1972. Chemical reaction engineering. New York: Wiley.
Mark, O., and M. Ilesanmi-Jimoh. 2017. “An analytical model for solute mixing in surcharged manholes.” Urban Water J. 14 (5): 443–451. https://doi.org/10.1080/1573062X.2016.1179335.
MathWorks Inc. 2020. MATLAB R2020a. Natick, MA: MathWorks.
O’Brien, R. 2000. “Dispersion due to surcharged manholes.” Ph.D. thesis, Dept. of Civil and Structural Engineering, Univ. of Sheffield.
Obropta, C. C., and J. S. Kardos. 2007. “Review of urban stormwater quality models: Deterministic, stochastic, and hybrid approaches.” JAWRA J. Am. Water Resour. Assoc. 43 (6): 1508–1523. https://doi.org/10.1111/j.1752-1688.2007.00124.x.
Pedersen, F. B., and O. Mark. 1990. “Head losses in storm sewer manholes: Submerged jet theory.” J. Hydraul. Eng. 116 (11): 1317–1328. https://doi.org/10.1061/(ASCE)0733-9429(1990)116:11(1317).
Rajaratnam, N. 1976. Turbulent jets. Amsterdam, Netherlands: Elsevier.
Rossman, L. A. 2015. Storm water management model user’s manual version 5.1. NTIS EPA-600/R-14/413b. Washington, DC: US EPA Office of Research and Development.
Rutherford, J. C. 1994. River mixing. Chichester, UK: Wiley.
Saiyudthong, C. 2004. “Effect of changes in pipe direction across surcharged manholes on dispersion and head loss.” Ph.D. thesis, Dept. of Civil and Structural Engineering, Univ. of Sheffield.
Skilling, J., and R. K. Bryan. 1984. “Maximum entropy image reconstruction-general algorithm.” Mon. Not. R. Astron. Soc. 211 (1): 111–124. https://doi.org/10.1093/mnras/211.1.111.
Sonnenwald, F. 2014. “Identifying the fundamental residence time distribution of urban drainage structures from solute transport data using maximum entropy deconvolution.” Ph.D. thesis, Dept. of Civil and Structural Engineering, Univ. of Sheffield.
Sonnenwald, F., O. Mark, V. Stovin, and I. Guymer. 2021. Code for a compartmental mixing model for describing mixing in manholes. V1. Sheffield, UK: Univ. of Sheffield.
Sonnenwald, F., V. Stovin, and I. Guymer. 2015. “Deconvolving smooth residence time distributions from raw solute transport data.” J. Hydrol. Eng. 20 (11): 04015022. https://doi.org/10.1061/(ASCE)HE.1943-5584.0001190.
Stovin, V., P. Bennett, and I. Guymer. 2013. “Absence of a hydraulic threshold in small-diameter surcharged manholes.” J. Hydraul. Eng. 139 (9): 984–994. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000758.
Stovin, V., I. Guymer, and S.-T. D. Lau. 2010. “Dimensionless method to characterize the mixing effects of surcharged manholes.” J. Hydraul. Eng. 136 (5): 318–327. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000183.
WRC. 2012. Sewers for adoption. Swindon, UK: WRC.
Young, P., A. Jakeman, and R. McMurtie. 1980. “An instrument variable method for model order identification.” Automatica 16 (3): 281–294. https://doi.org/10.1016/0005-1098(80)90037-0.
Information & Authors
Information
Published In
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Mar 26, 2021
Accepted: Aug 9, 2021
Published online: Sep 23, 2021
Published in print: Dec 1, 2021
Discussion open until: Feb 23, 2022
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.
Cited by
- Fred Sonnenwald, Joe Shuttleworth, Olivia Bailey, Margaret Williams, James Frankland, Becky Rhead, Ole Mark, Matthew J. Wade, Ian Guymer, Quantifying Mixing in Sewer Networks for Source Localization, Journal of Environmental Engineering, 10.1061/JOEEDU.EEENG-7134, 149, 5, (2023).