Numerical and Experimental Analysis of the Pressurized Wave Front in a Circular Pipe
Publication: Journal of Hydraulic Engineering
Volume 140, Issue 3
Abstract
This paper focuses on pressurized wavefront behavior and an analysis of trapped air pockets. Flow behavior, trapped air-pocket pressure, and different pressurized wavefront shapes in addition to their propagation conditions were investigated to improve modeling of mixed flows with trapped air pockets in stormwater systems. Pipe slopes, inflow, and reservoir water-levels were considered in an experimental analysis of the initiation, propagation of the wavefront, and flow behavior. Results show that the formation, propagation, and stability of the wavefront shape are highly dependent on the reservoir water-level and pipe slope. Pressurized wavefronts take on different shapes depending on manhole water level, pipe slope, and air pressure. The shape of the pressurized wavefront is sharper when the initial pipe depth is set between 0.5 and 0.85. With low inflow, the pipe-filling phase is progressive and is accompanied by undulations with stronger curvature and short length on the free-surface flow zone. For mild slopes with low flow-rates, the pipe-filling process is achieved through progressive undulations with trapped air pockets. A two-phase numerical model is developed, combining the method of characteristics (MOCs) for solving the free-surface flow conditions, the rigid column for the pressurized flow conditions, and the ideal gas law. Numerical results are achieved by applying of the continuity equation taking into account any type of flow regime in the interface vicinities. The four equations that consider the direction of wavefront propagation and the type of pressurized or depressurized wavefront are then taken into account. In these equations, a minimum distance between the moving wavefront and the considered cross section on the fixed grid is imposed. Compliance with this minimum distance allows avoiding numerical instabilities that may affect the stability of the model. Good agreement is obtained between numerical and experimental results. This agreement demonstrates that pressure variations due to pressurized waves combined with trapped air-pockets can be reproduced by implementing the numerical model as a shock-fitting approach.
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Acknowledgments
The writers express their gratitude to the Natural Sciences and Engineering Research Council (NSERC) of Canada and Canada Foundation for Innovation (CFI) for their financial support to the research reported in this paper.
References
Aimable, R., and Zech, Y. (2003). “Experimental results on transient and intermittent flows in a sewer pipe model.” Proc., Int. Association for Hydro-Environment Engineering and Research (IAHR) Congress, International Association for Hydraulic Research, Delft, The Netherlands, 377–384.
American_Gas_Association. (1978). “Orifice metering of natural gas.” American National Standards Institute (ANSI)/American Petroleum Institute (API) 2530, New York.
Arai, K., and Yamamoto, K. (2003). “Transient analysis of mixed free surface-pressurized flows with modified slot model (part 1: Computational model and experiment).” Proc., ASME FEDSM’03, 4th ASME-JSME Joint Fluids Engineering Conf., Honolulu, Hawaii.
Baines, W. D. (1991). “Air cavities as gravity currents on slope.” J. Hydraul. Eng., 1600–1615.
Benjamin, T. B. (1968). “Gravity currents and related phenomena.” J. Fluid Mech., 31(2), 209–248.
Bousso, S., Daynou, M., and Musandji, F. (2013). “Numerical modeling of mixed flows in storm water systems: Critical review of literature.” J. Hydraul. Eng., 385–396.
Bousso, S., Daynou, M., and Musandji, F. (2014). “Mixed flows with depressurizing wavefront in circular pipe.” J. Irrig. Drain. Eng., 04013007.
Cardle, J. A., and Song, C. S. S. (1988). “Mathematical modeling of unsteady flow in storm sewers.” Int. J. Eng. Fluid Mech., 1(4), 495–518.
Cunge, J. A., and Wegner, M. (1964). “Numerical integration of Barre de Saint-Venant’s flow equations by means of implicit scheme of finite differences.” Houille Blanche, 19(1), 33–39.
De Martino, G., Fontana, N., and Giugni, M. (2008). “Transient flow caused by air expulsion through an orifice.” J. Hydraul. Eng., 1395–1399.
Fuamba, M. (2002). “Contribution on transient flow modelling in storm sewers.” J. Hydraul. Res., 40(6), 685–693.
Gardner, G. C., and Crow, I. G. (1970). “Motion of large bubbles in horizontal channels.” J. Fluid Mech., 43(2), 247–255.
Glauser, S., and Wickenhauser, M. (2009). “Bubble movement in downward-inclined pipes.” J. Hydraul. Eng., 1012–1015.
Gomez, M., and Achiaga, V. (2001). “Mixed flow modelling produced by pressure fronts from upstream and downstream extremes.” Proc., Urban Drainage Modeling, ASCE, Reston, VA, 461–470.
Guinot, V. (2003). Godunov-type schemes: An introduction for engineers, Elsevier, Amsterdam, Netherlands.
Guizani, M., Vasconcelos, J. G., Wright, S. J., and Maalel, K. (2006). “Investigation of rapid filling of empty pipes.” CHI intelligent modeling of urban water systems, monograph 14, W. James, K. N. Irvine, E. A. Mc Bean, and R. E. Pitt, eds., Guelph, ON, Canada.
Guo, Q. (1991). “Dropshaft hydrodynamics under transient conditions.” J. Hydraul. Eng., 1042–1055.
Guo, Q., and Song, C. C. S. (1990). “Surging in urban storm drainage systems.” J. Hydraul. Eng., 1523–1539.
Izquierdo, J., Fuertes, V. S., Cabrera, E., Iglesias, P. L., and Garcia-Serra, J. (1999). “Pipeline start-up with entrapped air.” J. Hydraul. Res., 37(5), 579–590.
Lee, N. H., and Martin, C. S. (1999). “Experimental and analytical investigation of entrapped air in a horizontal pipe.” Proc., 3rd ASME/JSME Joint Fluids Engineering Conf., ASME/JSME Joint Fluids Engineering, San Francisco, CA, 1–8.
León, A. S., Ghidaoui, M. S., Schmidt, A. R., and Garcia, M. H. (2010). “A robust two-equation model for transient-mixed flows.” J. Hydraul. Res., 48(1), 44–56.
Li, J., and McCorquodale, A. (1999). “Modeling mixed flow in storm sewers.” J. Hydraul. Eng., 1170–1180.
Li, J., and McCorquodale, A. (2001). “Modeling the transition from gravity to pressurized flows in sewers.” Proc., Urban Drainage Modeling, ASCE, Reston, VA, 134–145.
Martin, C. S. (1976). “Entrapped air in pipelines.” Proc., Int Conf. on Pressures Surges, H. S. Stephens, A. L. King, and C. A. Stapleton, eds., British Hydromechanics Research Association, London, 15–28.
Nathan, J. L., Rollin, H. H., and Nelson, E. J. (2011). “Theoretical determination of sequent depths in closed conduits.” J. Irrig. Drain. Eng., 801–810.
Politano, M., Odgaard, A. J., and Klecan, W. (2007). “Case study: Numerical evaluation of hydraulic transients in a combined sewer overflow tunnel system.” J. Hydraul. Eng., 1103–1110.
Pozos, O. P. O., Sanchez, A. S. A., Rodal, E. A. R. E. A., and Fairuzov, Y. V. F. Y. V. (2010). “Effects of water-air mixtures on hydraulic transients.” Can. J. Civ. Eng., 37(9), 1189–1200.
Sanders, B. F., and Bradford, S. F. (2011). “Network implementation of the two-component pressure approach for transient flow in storm sewers.” J. Hydraul. Eng., 158–172.
Song, C. C. S., Cardle, J. A., and Leung, K. S. (1983). “Transient mixed-flow models for storm sewers.” J. Hydraul. Eng., 1487–1504.
Tran, P. D. (2011). “Propagation of pressure waves in two-component bubbly flow in horizontal pipes.” J. Hydraul. Eng., 668–678.
Trindade, B., and Vasconcelos, J. (2013). “Modeling of water pipeline filling events accounting for air phase interactions.” J. Hydraul. Eng., 921–934.
Vasconcelos, J. G., and Leite, G. M. (2012). “Pressure surges following sudden air pocket entrapment in stormwater tunnels.” J. Hydraul. Eng., 1081–1089.
Vasconcelos, J. G., and Marwell, D. T. B. (2011). “Innovative simulation of unsteady low-pressure flows in water mains.” J. Hydraul. Eng., 1490–1499.
Vasconcelos, J. G., and Wright, S. J. (2005). “Experimental investigation of surges in a stormwater storage tunnel.” J. Hydraul. Eng., 853–861.
Vasconcelos, J. G., and Wright, S. J. (2007). “Comparison between the two-component pressure approach and current transient flow solvers.” J. Hydraul. Res., 45(2), 178–187.
Vasconcelos, J. G., and Wright, S. J. (2009). “Investigation of rapid filling of poorly ventilated stormwater storage tunnels.” J. Hydraul. Res., 47(5), 547–558.
Vasconcelos, J. G., and Wright, S. J. (2011). “Geysering generated by large air pockets released through water-filled ventilation shafts.” J. Hydraul. Eng., 543–555.
Wiggert, D. C. (1972). “Transient flow in free-surface, pressurized systems.” J. Hydraul. Div., 98(1), 11–27.
Wright, S. J., Lewis, J. W., and Vasconcelos, J. G. (2011a). “Geysering in rapidly filling storm-water tunnels.” J. Hydraul. Eng., 112–115.
Wright, S. J., Lewis, J. W., and Vasconcelos, J. G. (2011b). “Physical processes resulting in geysers in rapidly filling storm-water tunnels.” J. Irrig. Drain. Eng., 199–202.
Yen, B. C. (1986). “Hydraulics of sewers.” Chapter 1, Advances in hydroscience, urban storm drainage, Academic, London, 1–122.
Zhou, F., Hicks, F., and Steffler, P. (2004). “Analysis of effects of air pocket on hydraulic failure of urban drainage infrastructure.” Can. J. Civ. Eng., 31(1), 86–94.
Zhou, F., Hicks, F. E., and Steffler, P. M. (2002a). “Observations of air-water interaction in a rapidly filling horizontal pipe.” J. Hydraul. Eng., 635–639.
Zhou, F., Hicks, F. E., and Steffler, P. M. (2002b). “Transient flow in a rapidly filling horizontal pipe containing trapped air.” J. Hydraul. Eng., 625–634.
Zukoski, E. (1966). “Influence of viscosity, surface tension, and inclination angle on motion of long bubbles in closed tubes.” J. Fluid Mech., 25(4), 821–837.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 140 • Issue 3 • March 2014
Pages: 300 - 312
Copyright
© 2013 American Society of Civil Engineers.
History
Received: Sep 24, 2012
Accepted: Sep 16, 2013
Published online: Sep 18, 2013
Discussion open until: Feb 18, 2014
Published in print: Mar 1, 2014
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