Bubble Plume Integral Model for Line-Source Diffusers in Ambient Stratification
Publication: Journal of Hydraulic Engineering
Volume 147, Issue 5
Abstract
We developed an integral plume model to simulate the behavior of bubble plumes generated from line-source geometry in stratified ambient reservoirs by adapting the double-plume integral model developed for point-sources to a line plume. The model, based on top-hat velocity and buoyancy profiles, uses an Eulerian integral modeling approach and predicts the hydrodynamic, chemical, and thermodynamic behavior of the bubbles using a discrete bubble model. Existing integral models for line-source bubble plumes consider only the upward motion of bubbles and entrained water. To accurately predict intrusion formation, mixing patterns, and efficiency of bubble plumes in stratified environments, the downward flow of plume fluid from the maximum extent of plume rise to the trap height should also be included. To solve this problem, we presented a derivation of a continuously peeling double-plume model for line plumes and calibrated the model peeling factor to data for trap height in two stratified reservoirs. We applied the calibrated model to predict the gas transfer and vertical fluxes of oxygen from an oxygenation system in Carvins Cove reservoir and compared the predictions of the double-plume model to that using a standard single-plume model. We showed that the amount and the vertical distribution of entrainment into the plume differs in the double-plume model compared to the single-plume; hence, the type of model (double-plume or single-plume) would affect the results of simulations in coupled reservoir circulation models.
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Data Availability Statement
Some or all data, models, or code generated or used during the study are available in a repository or online in accordance with funder data retention policies. Model simulation code and simulation results will be publicly available through the Gulf of Mexico Research Initiative Information & Data Cooperative (GRIIDC) at https://data.gulfresearchinitiative.org/10.7266/YTFWPAS8.
Acknowledgments
This research was made possible in part by a Grant from the Gulf of Mexico Research Initiative to the Center for Integrated Modeling and Assessment of the Gulf Ecosystem (C-IMAGE II). We are also grateful to the three anonymous reviewers for their constructive comments that helped to improve the manuscript.
References
Asaeda, T., and J. Imberger. 1993. “Structure of bubble plumes in linearly stratified environments.” J. Fluid Mech. 249: 35–57. https://doi.org/10.1017/S0022112093001065.
Bierlein, K. A., M. Rezvani, S. A. Socolofsky, L. D. Bryant, A. Wüest, and J. C. Little. 2017. “Increased sediment oxygen flux in lakes and reservoirs: The impact of hypolimnetic oxygenation.” Water Resour. Res. 53 (6): 4876–4890. https://doi.org/10.1002/2016WR019850.
Bombardelli, F., G. Buscaglia, C. Rehmann, L. Rincón, and M. García. 2007. “Modeling and scaling of aeration bubble plumes: A two-phase flow analysis.” J. Hydraul. Res. 45 (5): 617–630. https://doi.org/10.1080/00221686.2007.9521798.
Cederwall, K., and J. D. Ditmars. 1970. Analysis of air-bubble plumes. Pasadena, CA: California Institute of Technology.
Chen, S., C. Lei, C. C. Carey, P. A. Gantzer, and J. C. Little. 2017. “A coupled three-dimensional hydrodynamic model for predicting hypolimnetic oxygenation and epilimnetic mixing in a shallow eutrophic reservoir.” Water Resour. Res. 53 (1): 470–484. https://doi.org/10.1002/2016WR019279.
Choi, K., and J. H. Lee. 2007. “Distributed entrainment sink approach for modeling mixing and transport in the intermediate field.” J. Hydraul. Eng. 133 (7): 804–815. https://doi.org/10.1061/(ASCE)0733-9429(2007)133:7(804).
Crounse, B., E. Wannamaker, and E. Adams. 2007. “Integral model of a multiphase plume in quiescent stratification.” J. Hydraul. Eng. 133 (1): 70–76. https://doi.org/10.1061/(ASCE)0733-9429(2007)133:1(70).
Dissanayake, A. L., J. Gros, and S. A. Socolofsky. 2018. “Integral models for bubble, droplet, and multiphase plume dynamics in stratification and crossflow.” Environ. Fluid Mech. 18 (5): 1167–1202. https://doi.org/10.1007/s10652-018-9591-y.
Dissanayake, A. L., M. Rezvani, S. A. Socolofsky, K. A. Bierlein, and J. C. Little. 2016. “Integral model for bubble plumes from line-source geometry.” In Proc., Int. Symp. on Outfall Systems. New York: Springer.
Fanneløp, T., S. Hirschberg, and J. Küffer. 1991. “Surface current and recirculating cells generated by bubble curtains and jets.” J. Fluid Mech. 229: 629–657. https://doi.org/10.1017/S0022112091003208.
Fanneløp, T., and K. Sjoen. 1980. Hydrodynamics of underwater blowouts: Ship research. Trondheim, Norway: Institute of Norway, Marine Technology Centre.
Fanneløp, T., and D. Webber. 2003. “On buoyant plumes rising from area sources in a calm environment.” J. Fluid Mech. 497: 319–334. https://doi.org/10.1017/S0022112003006669.
Fox, D. G. 1970. “Forced plume in a stratified fluid.” J. Geophys. Res. 75 (33): 6818–6835. https://doi.org/10.1029/JC075i033p06818.
Gill, A. E. 1982. Vol. 30 of Atmosphere-ocean dynamics. New York: Academic Press.
Harleman, D. R. F., G. H. Jirka, and D. H. Evans. 1973. Experimental investigation of submerged multiport diffusers for condenser water discharges with application to the Northport electric generating station. Boston: Massachusetts Institute of Technology.
Horita, C. O., T. B. Bleninger, R. Morelissen, and J. L. B. de Carvalho. 2019. “Dynamic coupling of a near with a far field model for outfall discharges.” J. Appl. Water Eng. Res. 7 (4): 295–313. https://doi.org/10.1080/23249676.2019.1685413.
Hussain, N., and B. Narang. 1984. “Simplified analysis of air-bubble plumes in moderately stratified environments.” J. Heat Transfer 106 (3): 543–551. https://doi.org/10.1115/1.3246713.
Jirka, G. H. 2004. “Integral model for turbulent buoyant jets in unbounded stratified flows. Part I: Single round jet.” Environ. Fluid Mech. 4 (1): 1–56. https://doi.org/10.1023/A:1025583110842.
Jirka, G. H. 2006. “Integral model for turbulent buoyant jets in unbounded stratified flows. Part II: Plane jet dynamics resulting from multiport diffuser jets.” Environ. Fluid Mech. 6 (1): 43–100. https://doi.org/10.1007/s10652-005-4656-0.
Kaminski, E., S. Tait, and G. Carazzo. 2005. “Turbulent entrainment in jets with arbitrary buoyancy.” J. Fluid Mech. 526: 361–376. https://doi.org/10.1017/S0022112004003209.
Kobus, H. E. 1968. “Analysis of the flow induced by air-bubble systems.” In Proc., 11th Int. Conf. Coastal Engineering, 1016–1031. Reston, VA: ASCE.
Lee, J. H., and V. H. Chu. 2003. Vol. 1 of Turbulent jets and plumes: A Lagrangian approach. New York: Springer.
Lee, S. L., and H. W. Emmons. 1961. “A study of natural convection above a line fire.” J. Fluid Mech. 11 (3): 353–368. https://doi.org/10.1017/S0022112061000573.
Lemckert, C. J., and J. Imberger. 1993. “Energetic bubble plumes in arbitrary stratification.” J. Hydraul. Eng. 119 (6): 680–703. https://doi.org/10.1061/(ASCE)0733-9429(1993)119:6(680).
Lesser, G. R., J. V. Roelvink, J. A. T. M. Van Kester, and G. S. Stelling. 2004. “Development and validation of a three-dimensional morphological model.” Coastal Eng. 51 (8–9): 883–915. https://doi.org/10.1016/j.coastaleng.2004.07.014.
Liedtke, J., and M. Schatzmann. 1997. Dispersion from strongly buoyant sources. Hamburg, Germany: Univ. of Hamburg, Meteorological Institute.
McDougall, T. J. 1978. “Bubble plumes in stratified environments.” J. Fluid Mech. 85 (4): 655–672. https://doi.org/10.1017/S0022112078000841.
McGinnis, D., J. Little, and A. Wüest. 2001. “Hypolimnetic oxygenation: Coupling bubble-plume and reservoir models.” In Proc., Asian WATERQUAL. Fukuoka, Japan: International Water Association.
McGinnis, D., A. Lorke, A. Wüest, A. Stöckli, and J. Little. 2004. “Interaction between a bubble plume and the near field in a stratified lake.” Water Resour. Res. 40 (10): 1–11. https://doi.org/10.1029/2004WR003038.
Milgram, J. H. 1983. “Mean flow in round bubble plumes.” J. Fluid Mech. 133: 345–376. https://doi.org/10.1017/S0022112083001950.
Morelissen, R., T. van der Kaaij, and T. Bleninger. 2013. “Dynamic coupling of near field and far field models for simulating effluent discharges.” Water Sci. Technol. 67 (10): 2210–2220. https://doi.org/10.2166/wst.2013.081.
Morelissen, R., R. Vlijm, I. Hwang, R. L. Doneker, and A. S. Ramachandran. 2016. “Hydrodynamic modelling of large-scale cooling water outfalls with a dynamically coupled near-field–far-field modelling system.” J. Appl. Water Eng. Res. 4 (2): 138–151. https://doi.org/10.1080/23249676.2015.1099480.
Morton, B. R., G. I. Taylor, and J. S. Turner. 1956. “Turbulent gravitational convection from maintained and instantaneous sources.” Proc. R. Soc. London, Ser. A. 234 (1196): 1–23.
Nikiforakis, I. K., A. I. Stamou, and G. C. Christodoulou. 2017. “Integrated modeling of single port brine discharges into unstratified stagnant ambient.” Environ. Fluid Mech. 17 (1): 247–275. https://doi.org/10.1007/s10652-016-9473-0.
Priestley, C. H. B., and F. K. Ball. 1955. “Continuous convection from an isolated source of heat.” Q. J. R. Meteorol. Soc. 81 (348): 144–157. https://doi.org/10.1002/qj.49708134803.
Rezvani, M. 2016. “Bubble plumes in crossflows: Laboratory and field measurements of their fluid dynamic properties with application to lake aeration and management.” Ph.D. dissertation, Zachry Dept. of Civil Engineering, Texas A&M Univ.
Ricou, F. P., and D. Spalding. 1961. “Measurements of entrainment by axisymmetrical turbulent jets.” J. Fluid Mech. 11 (1): 21–32. https://doi.org/10.1017/S0022112061000834.
Rouse, H., C. S. Yih, and H. Humphreys. 1952. “Gravitational convection from a boundary source.” Tellus 4 (3): 201–210. https://doi.org/10.3402/tellusa.v4i3.8688.
Schladow, S. 1992. “Bubble plume dynamics in a stratified medium and the implications for water quality amelioration in lakes.” Water Resour. Res. 28 (2): 313–321. https://doi.org/10.1029/91WR02499.
Singleton, V. L., P. Gantzer, and J. C. Little. 2007. “Linear bubble plume model for hypolimnetic oxygenation: Full-scale validation and sensitivity analysis.” Water Resour. Res. 43 (2): 1–12. https://doi.org/10.1029/2005WR004836.
Singleton, V. L., F. J. Rueda, and J. C. Little. 2010. “A coupled bubble plume-reservoir model for hypolimnetic oxygenation.” Water Resour. Res. 46 (12): W12538. https://doi.org/10.1029/2009WR009012.
Socolofsky, S. A., and E. E. Adams. 2005. “Role of slip velocity in the behavior of stratified multiphase plumes.” J. Hydraul. Eng. 131 (4): 273–282. https://doi.org/10.1061/(ASCE)0733-9429(2005)131:4(273).
Socolofsky, S. A., T. Bhaumik, and D.-G. Seol. 2008. “Double-plume integral models for near-field mixing in multiphase plumes.” J. Hydraul. Eng. 134 (6): 772–783. https://doi.org/10.1061/(ASCE)0733-9429(2008)134:6(772).
Stamou, A. I., and I. K. Nikiforakis. 2013. “Integrated modelling of single port, steady-state thermal discharges in unstratified coastal waters.” Environ. Fluid Mech. 13 (4): 309–336. https://doi.org/10.1007/s10652-012-9266-z.
van Reeuwijk, M., and J. Craske. 2015. “Energy-consistent entrainment relations for jets and plumes.” J. Fluid Mech. 782: 333–355. https://doi.org/10.1017/jfm.2015.534.
Wüest, A., N. H. Brooks, and D. M. Imboden. 1992. “Bubble plume modeling for lake restoration.” Water Resour. Res. 28 (12): 3235–3250. https://doi.org/10.1029/92WR01681.
Yang, D., B. Chen, S. A. Socolofsky, M. Chamecki, and C. Meneveau. 2016. “Large-eddy simulation and parameterization of buoyant plume dynamics in stratified flow.” J. Fluid Mech. 794: 798–833. https://doi.org/10.1017/jfm.2016.191.
Yuan, L.-M., and G. Cox. 1995. “Entrainment of line thermal plumes.” Fire Saf. Sci. 2 (1): 200–209.
Zhang, X. Y., and E. E. Adams. 1999. “Prediction of near field plume characteristics using far field circulation model.” J. Hydraul. Eng. 125 (3): 233–241. https://doi.org/10.1061/(ASCE)0733-9429(1999)125:3(233).
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Journal of Hydraulic Engineering
Volume 147 • Issue 5 • May 2021
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© 2021 American Society of Civil Engineers.
History
Received: Jul 11, 2020
Accepted: Jan 22, 2021
Published online: Mar 12, 2021
Published in print: May 1, 2021
Discussion open until: Aug 12, 2021
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