Longitudinal Dispersion in Unsteady Pipe Flows
Publication: Journal of Hydraulic Engineering
Volume 147, Issue 9
Abstract
Temporal concentration profiles resulting from an injected pulse of fluorescent tracer were recorded at multiple locations along a pipe during controlled unsteady flow conditions. A linear temporal change in discharge over durations of 5, 10, or 60 s for both accelerating and decelerating flow conditions was studied. Tests were performed for flows that changed within the turbulent range, between Reynolds numbers of 6,500 and 47,000, and for laminar to turbulent flows, between Reynolds numbers of 2,700 and 47,000. Analysis of the data shows the limitations of employing steady-state routing of temporal concentration profiles in unsteady flow. Employing a flow weighted time routing approach, using tracer mean velocity and dispersion coefficients, provides accurate predictions of mixing in unsteady flow. For decelerating flows, longitudinal dispersion coefficients were lower than for the equivalent mean steady discharge. Previously unreported disaggregation of the tracer cloud was observed during all experiments accelerating from laminar to turbulent conditions.
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Data Availability Statement
The data, models, and code generated or used during the study are available in a repository online in accordance with funder data retention policies, see Hart et al. (2021), https://doi.org/10.15131/shef.data.14135591.
Acknowledgments
Many thanks go to Mr. Ian Baylis who provided the technical support for all the laboratory studies conducted at the University of Warwick. This work was supported by the EPSRC Grant No. EP/P012027/1.
References
Basha, H. A., and L. N. Malaeb. 2007. “Eulerian–Lagrangian method for constituent transport in water distribution networks.” J. Hydraul. Eng. 133 (10): 1155–1166. https://doi.org/10.1061/(ASCE)0733-9429(2007)133:10(1155).
Buchberger, S. G., J. T. Carter, Y. Lee, and T. G. Schade. 2003. Random demands, travel times and water quality in deadends. Denver: American Water Works Association Research Foundation.
Chatwin, P. C. 1970. “Approach to normality of concentration distribution of a solute in a solvent flowing along a straight pipe.” J. Fluid Mech. 43 (2): 321–352. https://doi.org/10.1017/S0022112070002409.
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.
Fernandez-Sempere, J., R. Font-Montesinos, and O. Espejo-Alcaraz. 1995. “Residence time distribution for unsteady-state systems.” Chem. Eng. Sci. 50 (2): 223–230. https://doi.org/10.1016/0009-2509(94)00230-O.
Fischer, H. B., J. E. List, C. R. Koh, J. Imberger, and N. H. Brooks. 1979. Mixing in inland and coastal waters. Amsterdam, Netherlands: Elsevier.
Greenblatt, D., and E. A. Moss. 2004. “Rapid temporal acceleration of a turbulent pipe flow.” J. Fluid Mech. 514: 65–75. https://doi.org/10.1017/S0022112004000114.
Hart, J., I. Guymer, A. E. Jones, and V. R. Stovin. 2013. “Longitudinal dispersion coefficients within turbulent and transitional pipe flow.” In Experimental and computational solutions of hydraulic problems, GeoPlanet: Earth and planetary sciences, edited by P. Rowinski. Berlin: Springer.
Hart, J., I. Guymer, F. Sonnenwald, and V. Stovin. 2016. “Residence time distributions for turbulent, critical, and laminar pipe flow.” J. Hydraul. Eng. 142 (9): 04016024. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001146.
Hart, J., F. Sonnenwald, and I. Guymer. 2021. Temporal concentration profiles in steady and unsteady pipe flow. Sheffield, UK: Univ. of Sheffield Online Research Data. https://doi.org/10.15131/shef.data.14135591.
He, S., and J. D. Jackson. 2000. “A study of turbulence under conditions of transient flow in a pipe.” J. Fluid Mech. 408: 1–38. https://doi.org/10.1017/S0022112099007016.
Holland, J. F., J. F. Martin, T. Granata, V. Bouchard, M. Quigley, and L. Brown. 2004. “Effects of wetland depth and flow rate on residence time distribution characteristics.” Ecol. Eng. 23 (3): 189–203. https://doi.org/10.1016/j.ecoleng.2004.09.003.
Kurokawa, J., and M. Morikawa. 1986. “Accelerated and decelerated flows in a circular pipe.” Jpn. Soc. Mech. Eng. 29 (249): 758–765. https://doi.org/10.1299/jsme1958.29.758.
Leclerc, J., S. Claudel, H. Lintz, O. Potier, and B. Antoine. 2000. “Theoretical interpretation of residence-time distribution measurements in industrial processes.” Oil Gas Sci. Technol. 55 (2): 159–169. https://doi.org/10.2516/ogst:2000009.
Levenspiel, O. 1972. Chemical reaction engineering. New York: Wiley.
Nauman, E. 1969. “Residence time distribution theory for unsteady stirred tank reactors.” Chem. Eng. Sci. 24 (9): 1461–1470. https://doi.org/10.1016/0009-2509(69)85074-8.
Piazza, S., E. J. M. Blokker, G. Freni, V. Puleo, and M. Sambito. 2020. “Impact of diffusion and dispersion of contaminants in water distribution networks modelling and monitoring.” Water Supply 20 (1): 46–58. https://doi.org/10.2166/ws.2019.131.
Romero-Gomez, P., and C. Y. Choi. 2011. “Axial dispersion coefficients in laminar flows of water-distribution systems.” J. Hydraul. Eng. 137 (11): 1500–1508. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000432.
Taylor, G. I. 1953. “Dispersion of soluble matter in solvent flowing slowly through a tube.” Proc. R. Soc. London, Ser. A 219 (1137): 186–203. https://doi.org/10.1098/rspa.1953.0139.
Taylor, G. I. 1954. “The dispersion of matter in turbulent flow through a pipe.” Proc. R. Soc. London, Ser. A 223 (1155): 446–468. https://doi.org/10.1098/rspa.1954.0130.
Wahl, M. D., L. C. Brown, A. O. Soboyejo, and B. Dong. 2012. “Quantifying the hydraulic performance of treatment wetlands using reliability functions.” Ecol. Eng. 47 (Oct): 120–125. https://doi.org/10.1016/j.ecoleng.2012.06.009.
Werner, T. M., and R. H. Kadlec. 1996. “Application of residence time distributions to stormwater treatment systems.” Ecol. Eng. 7 (3): 213–234. https://doi.org/10.1016/0925-8574(96)00013-4.
Young, P., A. Jakeman, and R. McMurtrie. 1980. “An instrumental variable method for model order identification.” Automatica 16 (3): 281–294. https://doi.org/10.1016/0005-1098(80)90037-0.
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Published In
Journal of Hydraulic Engineering
Volume 147 • Issue 9 • September 2021
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Aug 27, 2020
Accepted: Apr 22, 2021
Published online: Jul 8, 2021
Published in print: Sep 1, 2021
Discussion open until: Dec 8, 2021
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