Merging Effluent Discharge Plumes from Multiport Diffusers on a Sloping Beach
Author(s)
Anton Purnama
ABSTRACT
Multiport diffusers are the effective engineering devices installed at the marine outfall systems for the steady discharge of effluent streams from the modern coastal plants, such as municipal sewage treatment, power generation and seawater desalination. A far field mathematical model using a two-dimensional advection-diffusion equation is presented for continuous discharges of effluent streams from multiple outfalls on a uniformly sloping beach with a current parallel to the shoreline. The analytical solutions are illustrated graphically to replicate and capture the merging process of effluent plumes in shallow coastal waters, and then asymptotic approximation will be made to the maximum shoreline’s concentration to formulate effluent discharge plume dilution from a multiport diffuser.
Multiport diffusers are the effective engineering devices installed at the marine outfall systems for the steady discharge of effluent streams from the modern coastal plants, such as municipal sewage treatment, power generation and seawater desalination. A far field mathematical model using a two-dimensional advection-diffusion equation is presented for continuous discharges of effluent streams from multiple outfalls on a uniformly sloping beach with a current parallel to the shoreline. The analytical solutions are illustrated graphically to replicate and capture the merging process of effluent plumes in shallow coastal waters, and then asymptotic approximation will be made to the maximum shoreline’s concentration to formulate effluent discharge plume dilution from a multiport diffuser.
KEYWORDS
Effluent Discharge; Mathematical Model; Multiple Outfalls; Multiport Diffuser; Sloping Beach
Effluent Discharge; Mathematical Model; Multiple Outfalls; Multiport Diffuser; Sloping Beach
Cite this paper
A. Purnama, "Merging Effluent Discharge Plumes from Multiport Diffusers on a Sloping Beach," Applied Mathematics, Vol. 3 No. 1, 2012, pp. 24-29. doi: 10.4236/am.2012.31004.
A. Purnama, "Merging Effluent Discharge Plumes from Multiport Diffusers on a Sloping Beach," Applied Mathematics, Vol. 3 No. 1, 2012, pp. 24-29. doi: 10.4236/am.2012.31004.
References
[1] S. Lattemann and T. Hopner, “Environmental Impact and Impact Assessment of Seawater Desalination,” Desalination, Vol. 220, No. 1-3, 2008, pp. 1-15. doi:10.1016/j.desal.2007.03.009 [2] D. A. Roberts, E. L. Johnston and N. A. Knott, “Impacts of Desalination Plant Discharges on the Marine Environment: A Critical Review of Published Studies,” Water Research, Vol. 44, No. 18, 2010, pp. 5117-5128. doi:10.1016/j.watres.2010.04.036 [3] T. Bleninger and G. H. Jirka, “Modelling and Environmentally Sound Management of Brine Discharges from Desalination Plants,” Desalination, Vol. 221, No. 1-3, 2008, pp. 585-597. doi:10.1016/j.desal.2007.02.059 [4] G. H. Jirka, “Integral Model of Turbulent Buoyant Jets in Unbounded Stratified Flows. Part 2. Plane Jet Dynamics Resulting from Multiport Diffuser Jets,” Environmental Fluid Dynamics, Vol. 6, 2006, pp. 43-100. [5] P. J. W. Roberts and X. Tian, “New Experimental Techniques for Validation of Marine Discharge Models,” Environmental Modeling and Software, Vol. 19, No. 7-8, 2004, pp. 691-699. doi:10.1016/j.envsoft.2003.08.005 [6] A. Purnama, H. H. Al-Barwani, T. Bleninger and R. L. Doneker, “CORMIX Simulations of Brine Discharges from Barka Plants, Oman,” Desalination and Water Treatment, Vol. 32, 2011, pp. 329-338. doi:10.5004/dwt.2011.2718 [7] H. H. Al-Barwani and A. Purnama, “Re-Assessing the Impact of Desalination Plants Brine Discharges on Eroding Beaches,” Desalination, Vol. 204, No. 1-3, 2007, pp. 94-101. doi:10.1016/j.desal.2006.03.536 [8] H. H. Al-Barwani and A. Purnama, “Analytical Solutions for Brine Discharge Plumes on a Sloping Beach,” Desalination and Water Treatment, Vol. 11, 2009, pp. 2-6. doi:10.5004/dwt.2009.835 [9] A. Kay, “The Effect of Cross-stream Depth Variations upon Contaminant dispersion in a Vertically Well-Mixed Current,” Estuarine and Coastal Shelf Science, Vol. 24, No. 2, 1987, pp. 177-204. doi:10.1016/0272-7714(87)90064-3 [10] R. Smith, “Longitudinal Dispersion of Buoyant Contaminant in a Shallow Channel,” Journal of Fluid Mechanics, Vol. 78, No. 4, 1976, pp. 677-688. doi:10.1017/S0022112076002681 [11] D. W. Ostendorf, “Longshore Dispersion over a Flat Beach,” Journal of Geophysical Research, Vol. 87, No. C6, 1982, pp. 4241-4248. doi:10.1029/JC087iC06p04241 [12] G. M. Murphy, “Ordinary Differential Equations and Their Solutions,” D. Van Nostrand, London, 1960. [13] I. S. Gradshteyn and I. Ryzhik, “Tables of Integrals, Series and Products,” Academic Press, London, 1980. [14] A. Erdelyi, W. Magnus, F. Oberhettinger and F. G. Tricomi, “Tables of Integral Transforms,” Vol. 1, McGraw Hill, London, 1954.
[1] S. Lattemann and T. Hopner, “Environmental Impact and Impact Assessment of Seawater Desalination,” Desalination, Vol. 220, No. 1-3, 2008, pp. 1-15. doi:10.1016/j.desal.2007.03.009 [2] D. A. Roberts, E. L. Johnston and N. A. Knott, “Impacts of Desalination Plant Discharges on the Marine Environment: A Critical Review of Published Studies,” Water Research, Vol. 44, No. 18, 2010, pp. 5117-5128. doi:10.1016/j.watres.2010.04.036 [3] T. Bleninger and G. H. Jirka, “Modelling and Environmentally Sound Management of Brine Discharges from Desalination Plants,” Desalination, Vol. 221, No. 1-3, 2008, pp. 585-597. doi:10.1016/j.desal.2007.02.059 [4] G. H. Jirka, “Integral Model of Turbulent Buoyant Jets in Unbounded Stratified Flows. Part 2. Plane Jet Dynamics Resulting from Multiport Diffuser Jets,” Environmental Fluid Dynamics, Vol. 6, 2006, pp. 43-100. [5] P. J. W. Roberts and X. Tian, “New Experimental Techniques for Validation of Marine Discharge Models,” Environmental Modeling and Software, Vol. 19, No. 7-8, 2004, pp. 691-699. doi:10.1016/j.envsoft.2003.08.005 [6] A. Purnama, H. H. Al-Barwani, T. Bleninger and R. L. Doneker, “CORMIX Simulations of Brine Discharges from Barka Plants, Oman,” Desalination and Water Treatment, Vol. 32, 2011, pp. 329-338. doi:10.5004/dwt.2011.2718 [7] H. H. Al-Barwani and A. Purnama, “Re-Assessing the Impact of Desalination Plants Brine Discharges on Eroding Beaches,” Desalination, Vol. 204, No. 1-3, 2007, pp. 94-101. doi:10.1016/j.desal.2006.03.536 [8] H. H. Al-Barwani and A. Purnama, “Analytical Solutions for Brine Discharge Plumes on a Sloping Beach,” Desalination and Water Treatment, Vol. 11, 2009, pp. 2-6. doi:10.5004/dwt.2009.835 [9] A. Kay, “The Effect of Cross-stream Depth Variations upon Contaminant dispersion in a Vertically Well-Mixed Current,” Estuarine and Coastal Shelf Science, Vol. 24, No. 2, 1987, pp. 177-204. doi:10.1016/0272-7714(87)90064-3 [10] R. Smith, “Longitudinal Dispersion of Buoyant Contaminant in a Shallow Channel,” Journal of Fluid Mechanics, Vol. 78, No. 4, 1976, pp. 677-688. doi:10.1017/S0022112076002681 [11] D. W. Ostendorf, “Longshore Dispersion over a Flat Beach,” Journal of Geophysical Research, Vol. 87, No. C6, 1982, pp. 4241-4248. doi:10.1029/JC087iC06p04241 [12] G. M. Murphy, “Ordinary Differential Equations and Their Solutions,” D. Van Nostrand, London, 1960. [13] I. S. Gradshteyn and I. Ryzhik, “Tables of Integrals, Series and Products,” Academic Press, London, 1980. [14] A. Erdelyi, W. Magnus, F. Oberhettinger and F. G. Tricomi, “Tables of Integral Transforms,” Vol. 1, McGraw Hill, London, 1954.