Modelling and Environmentally Sound Management of Brine Discharges from Desalination Plants
3. T. Bleninger, G.H. Jirka / Desalination 221 (2008) 585–597 587 to be embedded in a sustainable concentrate management plan. Togeth er these technologies can be considered as concentrate management technologies. However, discharge designs are often not optimized regarding environmental impacts nor operational needs. In ad dition, regulations often lack clear guidance regarding the control of ambient standards or environmental impact stud- ies . Consequently it can be observed that the majority of discharges, especially in the Middle East North African (MENA) region, are surface discharges directly at the coastline (Fig. 2(a)) with very low mixing capacities. Similar design deficiencies also apply for intakes, that can be harmful to fish or othe r species. In addition, there is a potential for recirculation to the plant intake, reducing overall system efficiency espe- cially for larger plants or plant complexes. Scientifically validated and efficient plan- ning tools in the form of predictive models and expert system design guides are needed to assist desalination plant designers and plant managers in designing and operating the intake-treatment- outfall scheme so that environmental impacts on the marine environment can be controlled and Fig. 2. Discharge strategies for negatively buoyant effluent s . (a) Shoreline discharge via channel or weir, (b) sub- merged discharge via pipeline and nozzle or diffuser.
5. T. Bleninger, G.H. Jirka / Desalination 221 (2008) 585–597 589 by these authors themselv es and later by Roberts and Toms . In more recent experiments, Cipollina et al.  have investigated the 30°, 45° and 60° configuration. Unfortunately, their measurements were limited to the jet trajectory, and did not include dilution values that are critical for environmental impact evaluations. Further- more all studies predict only near-field (initial mixing until impingemen t with boundary) char- acteristics and do not include the intermediate field (boundary interaction and density current development) or far-field characteristics (den- sity currents and passive mixing and transport) of the brine. For the far-field related impacts the discharge region sea currents and salinity distri- butions need to be predic ted in addition. Further complexities to near and far-field regions are related to very shallo w water conditions (e.g. Arabian Gulf is only 40 m deep but some 250 km wide and 1000 km long) and extremely high evaporation rates. Although there are several massive develop- ments in this scientific area there are still sub- stantial deficits in the basic understanding and in practical implementation, especially for nega- tively buoyant effluents and their complex inter- actions with boundaries and their unknown interplay. Given the paucity of reliable experi- mental data (notably dilution measurements) for the entire negatively buoya nt jet including sloping bottom interaction, exis ting design recommenda- tions  are considered preliminary. To further corroborate them, a vigorous program of experi- mental studies using modern field-revolving techniques, such as laser induced fluorescence (LIF) and particle-image-v elocimetry (PIV), sup- ported by detailed computational fluid dynamics (CFD) modeling, is called for in several labora- tories. This appears to be crucial in view of ongoing design and siti ng activities for numerous new desalination plants all around the globe. A commonly used model for wastewater dis- charges is CORMIX (Cor nell Mixing Zone Expert System, see www.cormix.info) which is used worldwide in engineering and research projects especially for planning and design purposes belonging the near-field characteristics of mainly positive discharges into water bodies. Its major application area is for discharges from waste- water sources or from industrial treatment plants, including cooling water discharges. The model has been extensively validated and is equipped with a wide range of extensive pre- and post- processing routines for data preparation, result visualization and design recommendation [14,15]. Thus the model already allows for design purposes for positive buoyant effl uents from cogeneration plants with large coo ling water flows (approx. above 50 m 3 /s). Special preliminary extensions of CORMIX have been built for negative buoyant brine discharges under an EPRI (Electric Power Research Institute, USA) contract in the early 1990’s  and for sediment density currents from dredging operations under a U.S. Army Corps of Engineers contract . However, these versions have not undergone extensive valida- tion, do not contain appropriate pre- and post- processing, and are missing design optimization guidelines. Currently, no flexible and widely validated predictive tool exists to deal with the special geometrical aspects of such brine dis- charges, encompassing both the initial negatively- buoyant free jets and the final bottom-hugging density current plumes. In the following a preliminary parametric study of the submerged negatively buoyant jet discharging over a flat or sloping bottom and covering the entire range of angles form 0° to 90° above horizontal is given. The CORMIX submodel CorJet , a numerical jet integral model, is first compared to the limited existing experimental data on jet trajectory and dilutions, all for flat bottom. The mo del is then applied for the jet behavior over a variable bottom slope using the conditions at th e point of jet impinge- ment on the bottom slope as well as overall trajec- tory shape as key indicators for discharge design and siting strategies. Finally recommendations
13. T. Bleninger, G.H. Jirka / Desalination 221 (2008) 585–597 597 J. Hydraul. Eng., ASCE, November 2005, pp. 1017–1022.  G.H. Jirka, Integral model for turbulent buoyant jets in unbounded stratified flows, Part 2: plane jet dynamics resulting from multiport diffuser jets, Environ. Fluid Mech., 6 (2006) 43–100.  G.H. Jirka, Integral model for turbulent buoyant jets in unbounded stratified flows, Part 1: The single round jet, Environ. Fluid Mech., 4 (2004) 1–56.  G.H. Jirka, Optimal discharge configuration for brine effluents from desalination plants, J. Hydraul. Eng., submitted.  J.V. Del Bene, G.H. Jirka and J. Largier, Ocean brine disposal, Desalination, 97 (1–3) (1994) 365–372.  R.L. Doneker, J.D. Nash and G.H. Jirka, Pollutant transport and mixing zone simulation of sediments density currents, J. Hydrau l. Eng., ASCE, 130 (4).  S.J. Wright, Mean behavior of buoyant jets in a crossflow, J. Hydraul. Div., ASCE, 103 (HY5), 499–513, (5) (1977) 643–656.  G.H. Jirka and R.L. Doneker, Hydrodynamic classification of submerged single port dis- charges, J. Hydraul. Eng., 117 (1991) 1095–1112.  H. Zhang and R.E. Baddour, Maximum penetra- tion of vertical round dense jets at small and large Froude numbers, J. Hydraul. Eng., 124 (5) (1998) 550–553.  G. Abraham, Jets with negative buoyancy in homogeneous fluid, J. Hydraul. Res., 5 (4) (1967).  G.H. Jirka, R.L. Done ker and S.W. Hinton, User’s Manual for CORMIX: A Hydrodynamic Mixing Zone Model and Decision Support System for Pollutant Discharges into Surface Waters, U.S. Environmental Protection Agency, Tech. Rep., Environmental Research Lab, Athens, Georgia, USA, 1996.
2. 586 T. Bleninger, G.H. Jirka / Desalination 221 (2008) 585–597 substances can have a harmful impact on the local environment. Especially vulnerable are areas such as mangrove forest s, salt marshes, coral reefs, or generally, low energy intertidal areas, while exposed rocky coasts with high energy wave action may be less susceptible . Enclosed seas, like the gulf or the red-sea have limited water exchange capacities and are generally shallow and less energetic, thus more sensitive to effluent discharges. Potential impacts on local fisheries or tourism resources w ith considerable economic consequences are some of the conflict points that arise when planning desalination plants. In particular, increased plant capacities raise the impact concentrations of effluent constituents to levels that can beco me harmful to the marine environment. Genthner  notes that there is increased public concern and scien tific awareness on the environmental impact of desalination plants. For example, objections in the USA regarding envi- ronmental impacts have already become key issues for project permits, often considerably influencing plant commissioning and design . The necessity of sound environmental impact studies and public in volvement will further increase because severa l countries define new regulatory strategies on protection and conser- vation of the marine environment . From a regulatory viewpoint, many countries (e.g. USA or European Union countr ies) restrict the levels of aquatic pollutants both at the discharge point (“effluent standards”, e.g. chlorine, 7.5 μg/L, US-EPA) as well as within the receiving water (“ambient standards”). The former encourage source control principl es and treatment and recycling technologies. The latter demand for the consideration of the ambient response often associated with the concept of the “mixing zone”, an allocated impact zone in which the numerical water quality standards can be exceeded . In order to meet these regulations, optimized high efficiency mixing designs are needed for the brine effluent discharges (Fig. 2(b)), which need Fig. 1. Al Ghubrah desalination plant (largest in Oman, production capacity 191,000 m 3 /d): Brine waste discharge through an open channel at the beach into the Gulf of Oman (photo: H.H. Al-Barwani).
4. 588 T. Bleninger, G.H. Jirka / Desalination 221 (2008) 585–597 minimized. The preliminary results of the devel- opment of such tools are presented as follows. 2. State of the art — previous works The high salt concentration and the residual concentrations of added process chemicals of the discharge water may harmfully impact organisms near the outfall that cannot tolerate either high concentration levels or fl uctuations in levels of these substances. In general there is little sys- tematic information ava ilable on the impacts of desalination plants on th e marine environment. Even less data is available to quantify such impacts for regulatory or design purposes. This is similar to other disc harge regulations where specification of where in the water body the envi- ronmental quality standards apply are missing . Only an at least basic knowledge of the resulting concentration distributions allows for an impact assessment and design optimization. The concentration distribution depends on the siting of the outfall, the amount of mixing and the transport capacities of the prevailing currents. The former two are major design parameters, whereas the latter can only be influenced indi- rectly via an appropriate siting. Problem complexitites ar e related to the mixing calculation. Due to their high salinity, the dis- charges from desalination plants are more dense than seawater. Even brine with elevated temper- ature from plants with thermal desalination pro- cesses is significantly de nser than seawater. If discharged directly the effluent sinks to the bot- tom, and spreading horizontally following the slope of the sea bathymetry. Mixing is very low during that spreading proc ess thus causing poten- tial adverse impacts to benthic communities, besides the impacts on other biota, including plankton, fish, and mari ne mammals. The problem becomes even more comp lex for discharges from cogenerating plants consisting on a thermal elec- tric power plant and a desalination plant with thermal desalination technologies, where the desalination brine is gene rally blended with the cooling water discharge before entering the sea. In these cases (depending on the cooling water flow) the resulting plume may be always or intermittent positive buoyant or with neglectable density difference. Occurring density differences depend on salinity but also temperat ure differences and are dominating the mixing processes. Common tech- nological measures to reduce density differences and to control concentration distributions are outfalls with efficient mixing devices as shown in Fig. 2(b). High mixing efficiencies can be attained with submerged high-velocity discharges located offshore that pr oduce a negatively buoy- ant jet. Obviously, a surface discharge directly at the shoreline produces very little initial mixing and leads to high concentrations in the negatively buoyant plume that will progress at the bottom of the receiving water. In difference to buoyant discharges (i.e. treated domestic wastewater) there have been very few systematic studies of negative buoyant brine discharges and discharge configurations, let alon e any consistent design recommendation. The earliest study by Zeitoun et al.  exper- imentally investigated jets in stagnant fluids with angles of 30°, 45°, 60°, and 90° above the horizontal. Based on dilution measurements at the maximum rise level of the jet trajectory these authors concluded th at the 60° inclination provided the highest d ilution. This suggestion of an apparent “optimal angle of 60°” has been adopted in further experimental studies by Pincince and List , Roberts and Toms  and Roberts et al.  who investigated jet tra- jectories and mixing under both stagnant and flowing conditions. Based on these results, the 60° design has apparently “been adopted as the de facto standard”  for brine discharge installations. This is rather surprising given the considerable uncertaint y of the crude dilution measurement technique of Zeitoun et al.  with highly variable and erratic results as noted
12. 596 T. Bleninger, G.H. Jirka / Desalination 221 (2008) 585–597 offshore transport of the mixed effluent during weak ambient current co nditions, and the ability to locate in more sh allow water near-shore. However given the paucity of reliable exper- imental data (notably dilution measurements) for the entire negatively buoyant jet including sloping bottom interactio n, the above recom- mendations are considered preliminary. The summary of state of the art design methodolo- gies for brine discharges shows that there is a fur- ther need for more experi ments that describe the jet evolution and mixing in better resolution. To further corroborate them, a vigorous program of experimental studies using modern field-revolv- ing techniques, such as LIF and PIV, supported by detailed CFD modeling, is called for in sev- eral laboratories. This appears crucial in view of ongoing design and siting activities for numer- ous new desalination plants all around the globe. Furthermore a detailed study of the impinge- ment zone and the far-fi eld mixing is necessary. Even after strong initial jet mixing the heavy effluent generally sinks on the seabed and develops a density current. Depending on topo- graphical features (i.e. channels, submarine valleys or depressions) the density current is strongly limited in its spatial extents resulting in weak mixing and strong benthic impacts. In addition velocities at the sea-floor are small and vertical mixing inhibited by the strong density gradient. The extension of existing models prom- ises better capabilities for future brine discharge assessments. In addition alternativ e concentrate manage- ment technologies (e.g. recycling or substitution of substances, or treatment of effluents) need to be examined. A summary of experiments, design alternatives and technologi es could be given in a design manual for the standardization of concen- trate management tech nologies including opti- mized outfall-intake de signs for desalination plants to mitigate the im age of desalination tech- nologies being non-sustainable and expensive technologies regarding the natural sources. References  R. Einav, Checking todays brine discharges can help plan tomorrows plan ts, Desal. Wat. Reuse, 13 (1) (2003) 16–20.  S. Lattemann, and T. Höpner, Seawater desalina- tion: impacts of brine and chemical discharge on the marine environment, Desalination Publications, L’Aquila, Italy, 2003.  T. Höpner and J. Windelberg, Elements of envi- ronmental impact studies on coastal desalination plants, Desalination, 108 (1996) 11–18.  K. Genthner, Research and Development in Desalination – Current Activities and Demand, in Lecture Notes, DME Seminar, Berlin, June 2005.  Huntington Beach, Seawater Desalination Facil- ity, The City of Huntington Beach, California, 2006, http://www.ci.huntington-beach.ca.us/ citydepartments/planning/major/poseidon.cfm  WFD (Water Framework Directive), Official Publication of the European Community, L327, Brussels, 2000.  G.H. Jirka, T. Bleninger, R. Burrows and T. Larsen, Environmental Quality Standards in the EC-Water Framework Directive: Consequences for Water Pollution Control for Point Sources, European Water Management Online (EWMO), January 26, 2004.  T. Bleninger, G.H. Jirka and V. Weitbrecht, Optimal discharge configuration for brine effluents from desalination plants, Proc. DME (Deutsche Meer- wasserEntsalzung) — Congress, 04.-06.04.2006, Berlin, 2006.  M.A. Zeitoun, R.O. Reid, W.F. McHilhenny and T.M. Mitchell, Model studies of outfall systems for desalination plants. Pa rt III Numerical simula- tions and design considerations, Res. and Devel. Progress Rep. No. 804, Office of Saline Water, U.S. Dept. of Interior, Washington, DC, 1970.  A.B. Pincince and E.J. List, Disposal of brine into an estuary, J. Water Pollut. Control Fed., 45 (1973) 2335–2344.  P.J.W. Roberts and G. Toms, Inclined dense jets in flowing current, J. Hydraul. Eng., 113 (3) (1987) 232–341.  P.J.W. Roberts, A. Ferrier and G. Daviero, Mixing in inclined dense jets, J. Hydraul. Eng., 123 (8) (1997) 693–699.  A. Cipollina, A. Brucato, F. Grisafi and S. Nicosia, Bench scale investigation of inclined dense jets,
1. Desalination 221 (2008) 585–597 Presented at the conference on Desalination and the Envi ronment. Sponsored by the European Desalination Society and Center for Research and Technology Hellas (CERTH) , Sani Resort, Halkidiki, Greece, April 22–25, 2007. 0011-9164/06/$– See front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.desal.0000.00.000 Modelling and environmentally sound management of brine discharges from desalination plants Tobias Bleninger*, Gerhard H. Jirka Institut fuer Hydromechanik, Universitaet Ka rlsruhe, Kaiserstr. 12, 76131 Karlsruhe, Germany Tel. + 49 721 6083687; Fax + 49 721 6082202; email: email@example.com Received 21 January 2007; accepted 4 February 2007 Abstract Sea water desalination plants discha rge a concentrated brine effluent into coastal waters. Modern, large capacity plants require submerged discharges, in form of a negatively buoyant jet, that ensure a high dilution in order to minimize harmful impacts on the marine environment. Existing design practice favors a steep discharge angle of 60° above horizontal that is based on very limi ted laboratory data on dilutions at the level of maximum rise. However, examination of more r ecent laboratory data and the parametric applicat ion of CorJet, a jet integral model within the CORMIX expert system suggest that flatter discharge angles of about 30° to 45° above horizontal may have considerable design advantages. Thes e relate to better dilution levels at the impingement location, especially if bottom slope on port height are taken into account, better offshore transport of the mixed effluent during weak ambient curren t conditions, and the ability to locate in more shallow water near-shore. Keywords: Brine disposal; Negatively buoyant jets; Mixing; Density 1. Introduction Seawater desalination contributes positively to the environment (e.g. reducing exploitation of non-renewable drinking water sources) and to humanity, but at the sa me time may cause nega- tive local impacts on th e environment. Besides the impacts regarding energy consumption and land use, the major impact is related to the marine environment, especially to coastal water quality . Seawater desalination plants carry a number of waste products into the coastal ocean . The most direct product is a concentrated salt brine discharge (Fig. 1) that may also have an elevated turbidity and temperature (latter most notable for plants with thermal desalina- tion techniques such as multistage flash (MSF)). Other waste products relate to chemicals used for biofouling control (e.g. chlorine), scale control (antiscalants), foam reduc tion, and corrosion inhi- bition. Depending on the physical and ecological characteristics of the receiving waters, these *Corresponding author.
10. 594 T. Bleninger, G.H. Jirka / Desalination 221 (2008) 585–597 2.0 1.89 90° 1.5 z L M z max / L M = 1.77 x L M 1.0 0.5 0.5 1.0 1.5 2.0 2.5 3.0 3.5 Bottom slope 4.0 0° 20° 30° 0 –0.5 –1.0 –1.5 –2.0 –2.5 75° = θ θ B = 10° 1.47 60° 45° 30° 15° 0° 1.05 0.61 0.23 Fig. 6. Jet trajectories: Negatively buoyant jet behavior for complete range of discharge angles 0 °≤ q o ≤ 90 ° and with variable offshore slopes q B from 0 ° to 30 ° . A zero discharge height, h o = 0, is assumed .
11. T. Bleninger, G.H. Jirka / Desalination 221 (2008) 585–597 595 (2) Choose a discharge angle q o = 45 ° for weaker bottom slopes ( q B ≤ 15 ° ) or q o = 30 ° for stronger slopes. (see step (5) for consid- eration of port height.) (3) Evaluate jet geometry using Fig. 4(a) and 6, respectively. (4) Select the offshore location for the dis- charge in terms of a local water depth H ao (Fig. 3) that guarantees that the upper jet boundary Z max ≤ 0.75 H ao , in order to prevent dynamic surface interference. (5) Choose a port height h o = 0.5 to 1.0 m. (In a second iteration, the effect of the port height can be considered as an added slope angle when using Fig. 6 in steps (3) and (4)). (6) Evaluate the concentration of key effluent parameters at the impingement point using Fig. 7 and compare with applicable environ- mental criteria or regulations. If the dilution effect is insufficient, a design iteration is necessary. The above procedure and illustrations apply to a discharge into stationary, non-flowing ambi- ent conditions that are typically the most limiting for dilution. Detailed ap plication of the CorJet model is needed for case s of flowing environment, leading to more complex three-dimensional trajectories. Furthermore, in case of large volume discharges it may be nece ssary to distribute the flow over several ports, i.e. a multiport diffuser, a situation that can also be predicted by CorJet . The CorJet model can be used embedded within the CORMIX expert system  that allows for the prediction of not only the buoyant jet phase, but also of other mixing processes, such as the formation of the bottom density cur- rents, boundary interactions, and transitions to far-field mixing. A special version DCORMIX for brine discharges from desalination plants , or for sediment currents , that includes the dynamics of the downward propagating density current can be used for a complete environmental impact evaluation for th e near and intermediate field regions. 5. Conclusions Sea water desalination plants discharge a concentrated brine effluent into coastal waters. Modern, large capacity pl ants require submerged discharges, in form of a negatively buoyant jet, that ensure a high dilution in order to minimize harmful impacts on th e marine environment. Existing design practice fa vors a steep discharge angle of 60 ° above horizontal that is based on very limited laboratory da ta on dilutions at the level of maximum rise. However, examination of more recent laboratory data and the paramet- ric application of CorJet , a jet integral model within the CORMIX expe rt system, suggest that flatter discharge angles of about 30 ° to 45 ° above horizontal may have cons iderable design advan- tages. These relate to be tter dilution levels at the impingement location, especially if bottom slope on port height are taken into account, better θ B = 30° θ o 20° 10° 0° 2.0 1.5 1.0 0.5 0 0 30° 60° 90° S i F o Fig. 7. Bulk dilutions as a function of discharge angle q o : Negatively buoyant jet behavior for complete range of discharge angles 0° ≤ q o ≤ 90° and with variable off- shore slopes q B from 0° to 30°. A zero discharge height, h o = 0, is assumed .
7. T. Bleninger, G.H. Jirka / Desalination 221 (2008) 585–597 591 A related non-dimensional parameter is the jet densimetric Froude number F o (3) that is simply proportio nal to the length scale ratio, L M / L Q = ( p /4) − 1/4 F o . Thus, for high Froude number discharges, F o >> 1, L Q ceases to be a dynamically important pa rameter, as is well known for many other jet configurations . Detailed studies by Zhang and Baddour  for a vertical negatively buoyant jet have shown that the dilution at the maximum level becomes independent of Froude number when F o ≥ 10. For smaller Froude numb ers the initial dilution becomes lower. A high Froude number dis- charge, F o > 10, is assumed in the following so that L M is the unique length scale for displaying jet properties. The jet integral model CorJet  is used in this investigation. CorJet uses a flux conserving integral formulation with an entrainment closure approach that includes the different shear mech- anisms leading to tur bulent jet/plume entrain- ment. The model has been extensively validated for the five asymptotic self-similar stages of jet/plume flows as well as for a wide variety of non-equilibrium buoyant jet flows, in stagnant or flowing environments, with or without density stratification, respectivel y, generally with good comparison to experime ntal results . This prior validation also in cludes several types of negatively buoyant discharges with or without crossflow. Of the many jet integral models that can be found in the litera ture, CorJet is clearly the most thoroughly validated one. Available experimental data of the nega- tively buoyant jet for the conditions at the maxi- mum level of rise and CorJet predictions are summarized in Fig. 4 as a function of discharge angle q o . The geometric properties (Fig. 4(a)) relate to the point of the centerline trajectory maximum ( x max , z max ) as well as the maximum of the upper jet boundary ( Z max ), as defined in Fig. 3. Most of the experimental data reported concern Z max that is usually taken form visual (photo- graphic) observations. Th is involves consider- able judgment and erro r due to the type and amount of dye used, th e illumination level, and the sensitivity of the recording method. These parameters vary betw een experiments in an unknown manner. CorJet predictions (always with zero port height, h o = 0) are given using two criteria for the “vis ual boundary”, a local FU gD oo o / = ′ 4 CorJet CorJet Experiments Experiments        3 2 1 0 0.4 0.3 0.2 0.1 0 0 30° 60° 90° 0 30° 60° 90° θ o θ o Z max Z max x max Z max = 3% 25% C max C Z max X max Z max L M Z max L M x max L M S m F o Fig. 4. Jet properties at maximum level of rise. Com- parison of CorJet model with experimental data. (a) Geometric properties, (b) Minimum centerline dilu- tion, both as a function of discharge angle q o .
9. T. Bleninger, G.H. Jirka / Desalination 221 (2008) 585–597 593 between that for 60 ° by Roberts and Toms using a suction technique and by R oberts et al.  using an LIF visualization for dilution measurements. Unfortunately, the recent st udy of Cipollina et al.  did not include dilution measurements. In summary, the CorJet model appears rea- sonably validated with available experimental data sources. The inco nsistency among different experimental studies is la rger than the disagree- ment with the numerical model. Deficiencies in the experimental set-up (e.g. flat bottom with possible recirculation e ffects after impingement; limited tank sizes) and in the measurement tech- niques (e.g. ambiguities in visual determina- tions; incomplete suctio n sampling in view of jet fluctuations) are the so urce of these inconsis- tencies. Considering th e other validation cases (trajectories and dilutions ) for negatively buoy- ant jets with or without crossflow that have been reported in Jirka  it is therefore concluded that CorJet can be used as a tool for a prelimi- nary parametric study of negatively buoyant jet discharge configurations covering a wider range of possible site conditions. 4. Brine discharge design The CorJet model is applied over the entire range of discharge angles 0 °≤ q o ≤ 90 ° and for different offshore bathymetries, q B from 0 ° to 30 ° , in order to evaluate possible design improvements. Fig. 6 shows the normalized cen- terline trajectories, z / L M versus x / L M , and their intersections with the possible bottom slopes. The discharge range q o from 30 ° to 45 ° provides the largest offshore impingement location, x i / L M . The dilutions at the maximum rise level, S m / F o , have already been given in Fig. 4(b). CorJet predicts an optimal value of 45 ° , but a wide flat plateau between 30 ° and 60 ° . Impor- tant from the viewpoint of environmental impacts is the dilution at the impingement point (e.g. for exposure of benthic organisms). Fig. 7 gives the predicted bulk dilution as a use- ful measure for that impact. For a flat bottom (and with zero discharge height) the maximum dilution is attained in the range q o from 60 ° to 75 ° , for moderate slopes (10 ° to 20 ° ) the maxi- mum is found at about 45 ° to 60 ° , while for strong slopes (30 ° ) this shifts to a discharge angle between 30 ° to 45 ° . Rather flat plateau values apply in all of these cases. Note that increasing discharge heights h o have a qualitatively similar effect as increasing offshore slopes! These results, together with several other siting factors, lead to the conclusion that the discharge angle range of 30 ° to 45 ° appears preferable for negatively buoyant jet discharges located in a near-shore environment. This is for the following reasons: (1) It produces the highest dilutions at the point of maximum rise (Fig. 4(b)). (2) It provides high dilutions at the impingement point (Fig. 7) , especially so if suf- ficient offshore slope is given or, equivalently, if the discharge port is raised above the bottom. (3) It locates the jet impingement region further offshore (Fig. 6) and, because of the flatter impingement angle, provides more offshore momentum for the ensuing bottom density current. It provides considerab ly flatter trajectories (Fig. 6), thus allowing th e discharge to be located more near-shore in smalle r water depth (Fig. 3). Even under these simple conditions the follow- ing design procedure can already recommended for a discharge with given plant flowrate Q o and discharge density r o (hence, given g ′ o and J o ) located on an offshore slope with angle q B : (1) Choose a sufficiently high Froude number design, F o ≥ 10, with the recommended range F o = 20 to 25. (Note that higher values imply larger pumping head losses.) With U o = Q o /( D 2 p /4) in Eq. 3, the required port diameter is computed as as well as the values M o Eq. (1) and L M Eq. (2). SF io / DFg = () ′ ( ) ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ 4 12 25 // / / p Q ooo
6. 590 T. Bleninger, G.H. Jirka / Desalination 221 (2008) 585–597 are given for the subsequent modeling of the intermediate and far-fiel d regions and the brine discharge assessment. 3. Brine discharge model Fig. 3 shows the side view of a negatively buoyant jet discharging into a receiving water body with a local ambient water depth H ao and a sloping bottom with inclination angle q B . The port geometry is given by its diameter D , its height above bottom h o , and its inclination angle q o above the horizontal, pointing offshore. The receiving water is unstratified with a constant density r a and stagnant. The jet has a discharge velocity U o and density r o > r a . This gives the following flux variables, the volume flux (dis- charge) Q o , momentum flux M o , and buoyancy flux J o , respectively, Q o = U o D 2 p /4, M o = U o Q o , J o = g ′ o Q o (1) in which g ′ o = g ( r a − r o )/ r a < 0 is the buoyant acceleration. The turbulent jet that results from this high velocity discharge first rises to a maximum level and then falls downward under the influence of the negative buoyancy until it impinges on the sloping bottom. Impingement is a complex three-dimensional process, with forward, lateral, and partially reverse sp reading, until a density current is formed that propagates downslope. The geometric and mixing characteristics of the turbulent buoyant je t can be determined by two length scales, the discharge length scale L Q and the momentum ( jet/p lume transition) length scale L M [19,20] (2) ρ a H ao h o Discharge D U o , ρ o θ o θ B Z max z max x max Jet Density current Impingement g Maximum √ 2 b z θ Fig. 3. Schematic side view of negatively buoyant jet discharging into stagnant ambient with sloping bottom . LQM L M J Qoo / Moo // == 12 3 4 12 , / /
8. 592 T. Bleninger, G.H. Jirka / Desalination 221 (2008) 585–597 concentration level c / c max = 3 and 25%, respec- tively, where c max is the centerline concentration at the maximum level. The 25% value corresponds to a jet width where b is the 1/e = 37% jet width for the standard Gaussian profile . All the data sources [11–13,19,21] are in reasonable agreement with this ra nge of predictions, the only exception being Cipollina et al.’s  data for q o = 60 ° . The data by Roberts and Toms have been corrected for their reported port height h o . Also note that Zhang and Baddour gives a wide range Z max = 1.7 to 3.2 (not included in Fig. 4(a)) for a summary of several earlier investigations for the vertical ( q o = 90 ° ) jet that scatters widely about the model predictio ns . The only data reported on the centerline position of the trajectory maximum are the recent ones by Cipollina et al. , once again with reasonable agreement. (The dotted line for x max for q o → 0 ° indicates the fact that for small discharge angles the horizontal location of the jet boundary maximum Z max dif- fers greatly from that of z max ; Fig. 3). The normalized minimum (centerline) dilu- tion S m / F o at the maximum rise level are com- pared in Fig. 4(b). The CorJet prediction indicates a flat maximum S m / F o ≈ 0.28 to 0.29 over the angle range q o = 30 ° to 60 ° . For a verti- cal discharge, the predicted values S m / F o = 0.24 are in reasonable agreement with 0.23 reported by Abraham  and 0.19 by Roberts and Toms . For q o = 60 ° , however, Roberts and Tom’s data point shows a rather strong increase to S m / F o = 0.38, much more than is predicted by CorJet. Not included in Fig. 2(b) are the data by Zeitoun et al.  that would lie yet much higher ( S m / F o = 0.55, 0.42, and 0.36 for q o = 60 ° , 45 ° and 30 ° , respectively), but appear erroneous in hindsight as has b een commented in the introduction. The conditions at the impingement point for a discharge over flat bottom ( q B = 0 ° ) are sum- marized in Fig. 5. The location of impingement x i / L M (Fig. 5(a)) is well predicted by CorJet when compared to the data of Roberts et al.  and Cipollina et al. . Two predicted values for the dilution impingement dilutions are plotted in Fig. 5(b) the minimum dilution S i at the level z = 0 and the corresponding bulk (flux averaged) dilution . Since the impingement process represents an additional mixing mecha- nism, actual observed dilutions should probably lie between these limits. The observations shown in Fig. 5(b) generally support that expectation, even though there is considerable inconsistency 2 b 4 θ B = 0° θ o θ o θ B = 0° CorJet CorJet Experiments  Experiments    3 2 1 0 2.0 1.5 1.0 0.5 0 0 30° 60° 90° 0 30° 60° 90° S i S i S i F o x i L M S i F o Fig. 5. Jet properties at the impingement point for zero offshore slope ( q B = 0 ° ). (a) Location x i / L M , (b) Dilution levels, both as a function of discharge angle q o . SS ii ≅ 17 .
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