SPREADING OF VERTICAL DENSE JETS ON A SLOPING BOTTOM: CONCENTRATION MEASUREMENTS

Transcription

1 Proceedings of the 13 th International Conference on Environmental Science and Technology Athens, Greece, 5-7 September 2013 SPREADING OF VERTICAL DENSE JETS ON A SLOPING BOTTOM: CONCENTRATION MEASUREMENTS I. K. NIKIFORAKIS*, G. C. CHRISTODOULOU*, and A. I. STAMOU* * Department of Water Resources and Environmental Engineering, School of Civil Engineering, National Technical University of Athens, Heroon Polytechniou 5, Athens, Greece. giannisnikiforakis@gmail.com EXTENDED ABSTRACT Seawater desalination plants discharge large quantities of brine effluents into coastal waters. Usually, these effluents are disposed in the form of dense jets through submerged diffusers. It is a common practice to design these diffusers inclined upwards so as to increase the jet s trajectory and consequent dilution, thus minimizing harmful impacts on the marine environment. Although considerable experimental and theoretical research has been carried out on the characteristics of dense jets, the flow behaviour after impingement on the bottom has received little attention, despite its significance for the subsequent development of the gravity current. Previous studies concerning the spreading of dense jets on horizontal and sloping bottoms focus on the geometrical characteristics of spreading without studying the concentration field. This paper presents detailed concentration measurements vertically and transversally in the body region of gravity currents formed after the impingement of vertical dense jets on a 5º sloping bottom. The dense jets consisted of salt water solution and were issued into a tank filled with fresh water through specially made small pipes at a distance about 48 cm from the bottom. The measurements were carried out using microconductivity probes accompanied by a portable salinity, concentration and temperature meter. The results showed that in the vicinity of the falling jet, large concentration fluctuations appear indicating high turbulent intensity of the flow. The fluctuations decay with distance from the impingement point due to turbulence collapse under the influence of density stratification. Concentration values at measurement locations were correlated to (a) the source value, showing an approximately linear variation of normalized dilution with normalized distance from the source, (b) the jet concentration just before impingement, showing dilution to be nearly constant at each location and independent of the initial jet Froude number. The bottom slope does not seem to have an appreciable effect on the dilution field within the density current, in the vicinity of the impingement point. Keywords: dense jets, gravity currents, sloping bottom, concentration measurements 1. INTRODUCTION Worldwide, many semi-arid or arid coastal areas encounter the problem of water scarcity. One solution to this problem is sea water desalination. Despite the benefits of this process for water supply, the constant discharge of large quantities of brine into the sea may cause harmful effects on marine flora and fauna. Such effects can be mitigated by discharging the brine effluents through submerged diffusers as inclined upward jets to increase their trajectory and consequent dilution.

2 The trajectory of an inclined brine (dense) jet after its discharge into the sea can be divided into three parts. In the first part, the jet moves upwards, due to its initial momentum and discharge orientation, until it reaches a terminal height. At the terminal height the vertical component of jet momentum becomes equal to zero and the jet starts to move downwards due to buoyancy; this is the second part. The third part consists of the jet impingement on the sea bed and its consequent spreading as a density (gravity) current. Although there is a considerable amount of research concerning the dilution and geometrical characteristics of dense jets before their impingement on the bottom (Zeitoun et al.,1970; Roberts et al., 1997; Cipollina et al., 2005; Kikkert et al., 2007; Papakonstantis et al., 2011 a,b), the study of the characteristics of density currents developed after impingement has received little attention. Early studies by Sharp (1969 a, b) reported on the bottom spreading of vertical jets impinging on a horizontal bottom. Papakontantis and Christodoulou (2010) and Christodoulou et al. (2011, 2012) focused on the geometrical characteristics of spreading of dense jets on horizontal and sloping bottoms without studying the concentration field. Roberts et al. (1997) studied the concentration field of laterally confined density currents arising from the impingement of inclined jets on a horizontal plane. Cavalleti and Davies (2003) dealt with the impact region of plane (2-D) dense jets, whereas Abessi et al. (2012) conducted limited concentration measurements at the impact region and end of mixing zone of dense horizontal surface discharges issuing from a rectangular source. This work presents concentration measurements vertically and transversally in the body region of density currents formed after the impingement of dense jets on a 5º sloping bottom. The dense jets, consisting of saltwater, were issued vertically downwards to the bottom. The selection of vertical instead of inclined discharge is due to two basic reasons: (a) the impingement point of vertical jets is a priori defined with accuracy, in contrast to the impingement point of inclined jets, which should be estimated by using experimental techniques, (b) the behaviour of vertical jets can serve as a first step towards understanding the concentration field of the developed current without the interference of the falling parcels that detach from the inclined jets around their terminal height (see Kikkert et al., 2007; Papakonstantis et al., 2011a). 2. EXPERIMENTS The experiments were conducted in the Applied Hydraulics Laboratory of the National Technical University of Athens, in a tank 3.0 m long, 1.5 m wide and 0.9 m deep. In the tank, a Perspex bottom slab was introduced at an angle of φ=5 ο to the horizontal. Round pipes of diameter D=0.8 and 1.6 cm, were used to discharge the jet vertically downwards (Figure 1a). The distance between the discharge point and the inclined bottom was approximately H=48 cm. The tank was initially filled up with tap water and the jet effluent was salt water solution, coloured with blue dye, of density % higher than the ambient. The densities of the salt water solution (ρ ο) and the tank water (ρ a<ρ ο) were calculated from their salinity (ppt) and temperature ( o C) values measured by a portable instrument (YSI Model 30). These densities were generally in good agreement with the densities measured by a hydrometer and by weighting (KERN Model EMB ) a known volume of sample contained in a calibrated flask. The flow rate of the salt water effluent was measured by means of a Venturi meter combined with a differential manometer and a volumetric cylinder. Concentration measurements concerning salinity were performed in the body region of the developed density current by using a Microscale Conductivity and Temperature Instrument (MSCTI) manufactured by Precision

3 Measurement Engineering, USA (Model 125). More details about MSCTI technical characteristics and its calibration process can be found in the work of Papakonstantis et al. (2011b). (a) (b) Figure 1. (a) The experimental tank, (b) Measurement locations. A total of 51 experiments were carried out. Table 1 lists the main parameters of the experiments, where Δρ/ρ a denotes the relative density difference (ρ o-ρ a)/ρ a and F o the initial densimetric Froude number; F o= U o/(dgδρ/ρ o) 1/2 with U o being the exit flow velocity and g the gravitational acceleration. Table 1: Summary of experimental conditions Number of Location experiments x y Qo Δρ/ρo Fo - (cm) (cm) (cm 3 /s) (%) - 3 A , 16.72, B , 16.65, B , B , 4.46, 19.21, B , 16.91, C , C , C , C , 17.85, D , 16.79, D , 17.31, E , , , All vertical jets were turbulent, with initial Reynolds number ranging from 3273 to The measurement locations are shown in Figure 1b as well as the coordinate system used. The coordinate system was 2D-Cartesian, with its origin at the jet impingement point (location A1), the x-axis pointing downslope and the y-axis normal to x axis. The coordinates of the measurement locations are shown in Table 1. Concentration measurements were performed on the vertical at five points with heights h=1, 2, 3, 4 and 6 cm above the bottom, starting from the closest to the bottom point. The duration of sampling at every point was 30 s at a frequency of 100 Hz. This duration was selected due to the turbulent character of flow, after trial experiments showing that this duration was adequate for measuring the time average concentration (C m). In most cases the

4 vertical profile was nearly linear up to the height of 3 cm, in agreement with similar observations by Roberts et al. (1997). However, due to the finite tank width the density current returned to the x axis after its impingement to the tank side walls, affecting the measurements at the points with h >3 cm. 3. RESULTS The variation of salinity concentration (ppt) with time (s) at measurement locations, at h=1cm and for F o 23 is shown in Figure 2. It is observed that adjacent to the impingement point (locations A2, B1, B2, B-1, B-2) the flow is highly turbulent and instantaneous concentration (C i) may be much higher than the mean values (C m). At greater distances, turbulent fluctuations seem to decay and the flow tends to relaminarize due to the influence of density stratification, as also observed by Roberts et al. (1997). Figure 2. Variation of salinity with time at the measurement locations, at h=1cm and for F o 23. For each experiment the source concentration (C o) is shown. The aforementioned concentration fluctuation due to the turbulent character of flow can be described by the turbulence intensity defined as the coefficient of variation (CV) of the root mean square deviation (RMS) of concentration, given by Eq.1. RMS CV= C, m RMS= C -C 2 i m n-1 (1) where n stands for the size of the sample (30s x 100Hz=3000 values). The variation of CV with F o at h=1 and 2 cm at the measurement locations is shown in Figure 3.

5 Figure 3. Variation of CV with F o at downslope locations for (a) h=1cm and (c) h=2 cm and at transverse and upslope locations for (b) h=1cm and (d) h=2 cm. Figure 4. Variation of S m with F o at downslope locations for (a) h=1cm and (c) h=2 cm and at transverse and upslope locations for (b) h=1cm and (d) h=2 cm. Figure 4 shows the variation of dilution (S m), given by Eq.2, with F o at each location and at h=1 and 2 cm, C o S m= C m C C a a (2)

6 where C o and C a is the source and ambient concentration of salinity. 4. DISCUSSION As seen in Table 1, the experiments form two groups, (a) with low F o values between 3.14 and 4.46 and (b) with moderate to high F o between and The criterion for the selection of these F o values was the ratio of H/l M, where l M is a length scale equal to M o 3/4 /B o 1/2, with M o and B o being the jet s initial specific fluxes of momentum and buoyancy, respectively. According to Papanicolaou and List (1988) a vertical buoyant jet behaves like a pure jet for H/l M<1 and like a plume for H/l M>5. This ratio for the investigated F o values was between 7.15 and for 3.14<F o<4.46 and between 2.55 and 4.33 for 14.71<F o< Therefore, for the small F o values the dense jet has turned completely into a plume before reaching the bottom, whereas this was not the case in the experiments with high F o. From Figure 3, it can be observed that for both groups of jet discharges and at both heights (h=1 and 2 cm) CV seems to decrease, despite the scatter, as the distance from the impingement point increases. The variation of CV seems to be independent of F o. Moreover (Figure 4), S m seems to increase slightly with the distance from the impingement point and as F o increases. S m and the straight line distance L of each measurement location from the source can be expressed in dimensionless form by dividing by F o and DF o, respectively, following Roberts et al. (1997). Figure 5 (a, b) depicts the correlation of these two normalised parameters at h=1 cm and 2 cm. It is seen that both correlations are approximately linear, which is in agreement with the results of Abessi et al. (2012). Figure 5. Variation of normalized dilution at (a) h=1 cm and (b) h=2 cm with distance L. So far, total dilution (S m) at each location has been calculated as the ratio of the measured concentration and the source concentration. Local dilution (S i) due only to spreading on the bottom can be estimated by dividing the measured concentration to the concentration at the impingement point or at a small height above the impingement point. The mean jet concentration (C imp) at h=4 cm above the bottom was calculated by employing Eq. 3 (List and Imberger, 1973; Papanicolaou and List, 1988), considering that height adequate to avoid interaction with the developed density current, as it was slightly greater than the current thickness at locations adjacent to the impingement point (locations A2, B1, B-1). The calculation of the impingement concentration at h=4cm was preferred rather than its measurement to avoid interference of the vertical probe with the free development of the jet.

7 1/ R H 4.0 o H 4.0 C imp=c a+ Co Ca 1 1 z o R p zo (3) where R o is the initial Richardson number, R p=0.63 is the Richardson number for the pure plume and z o=3.28d. The results show that S i is nearly constant at each location and almost independent of F o. The average values of S i at each location are listed in Table 2. According to Table 2, S i values at 2 cm are 19-85% higher than those at 1 cm. As also observed in Table 2, dilution at both heights increases as the distance from the impingement point increases. Moreover, as seen in Table 3, the ratio of dilution values at upslope and downslope locations at equal distances from the impact point is close to unity. Therefore, the bottom slope does not seem to have an appreciable effect on the dilution field within the density current, in the vicinity of the impingement point. Table 2: Average values of S i at measurement heights Location S i Location S i 1 cm 2 cm 1 cm 2 cm A C B C B C B D B D C E Table 3: Ratio of dilution S i of upslope and downslope locations Compared locations Ratio of S i at 1cm Ratio of S i at 2cm B1/B B2/B C1/C C2/C CONCLUSIONS The performance of concentration measurements in the body region of density currents formed after the impingement of vertical dense jets on a 5º sloping bottom showed that in the vicinity of the falling jet, large concentration fluctuations appear due to the high turbulent character of the flow. These fluctuations seem to decay with distance due to turbulence collapse under the influence of density stratification. Concentration values at measurement locations were correlated to (a) the source value, showing an approximate linear variation of normalized dilution with normalized distance from the source, (b) the mean jet concentration at a small height above the impingement point, showing dilution to be nearly constant at each location and independent of the initial jet Froude number. The bottom slope does not seem to have an appreciable effect on the dilution field within the density current, in the vicinity of the impingement point.

8 ACKNOWLEDGEMENTS This research has been co-financed by the European Union (European Social Fund ESF) and Greek national funds through the Operational Program Education and Lifelong Learning of the National Strategic Reference Framework (NSRF) Research Funding Program: Heracleitus II. Investing in knowledge society through the European Social Fund. REFERENCES 1. Abessi O., Saeedi M., Bleninger T. and Davidson M. (2012), Surface discharge of negatively buoyant effluent in unstratified stagnant water, J. of Hydro-Environment Res., 6, Cavalletti A. and Davies P.A. (2003), Impact of vertical, turbulent, planar, negatively buoyant jet with rigid horizontal bottom boundary, J. Hydraul. Eng., ASCE, 129(1), Christodoulou G.C., Nikiforakis I.K. and Papakonstantis I.G. (2011), Spreading of a negatively buoyant jet on a sloping bottom, Proc. of the 7th. Symp. on Stratified Flows, Rome, Italy. 4. Christodoulou G.C., Nikiforakis I.K. and Papakonstantis I.G. (2012), Spreading of a dense jet on a sloping bottom, Proc. of the joint 12 th Conference of the Hellenic Hydrotechnical Assosiation and 8 th Conference of the Greek Committee of Water Resources Management, October 2012, Patra, Greece (in Greek). 5. Cipollina A., Brucato A., Grisafi F. and Nicosia S. (2005), Benchscale investigation of inclined dense jets, J. Hydraul. Eng., ASCE, 131 (11), List E.J. and Imberger J. (1973), Turbulent entrainment in buoyant jets, J. Hydraul. Div., ASCE, 99, Kikkert G.A., Davidson M.J. and Nokes R.I. (2007), Inclined negatively buoyant discharges, J. Hydraul. Eng., ASCE, 133 (5), Papakonstantis I.G. and Christodoulou G.C. (2010), Spreading of round dense jets impinging on a horizontal bottom, J. Hydro-Environment Res., 4, Papakonstantis I.G., Christodoulou G.C. and Papanicolaou P.N. (2011a), Inclined negatively buoyant jets 1: geometrical characteristics, J. Hydraul. Res., 49(1), Papakonstantis I.G., Christodoulou G.C. and Papanicolaou P.N. (2011b), Inclined negatively buoyant jets 2: concentration measurements, J. Hydraul. Res., 49(1), Papanicolaou P. and List J. (1988), Investigations of round vertical turbulent buoyant jets, J. Fluid Mech., 195, Roberts P.J.W., Ferrier A. and Daviero G. (1997), Mixing of inclined dense jets, J. Hydraul. Eng., ASCE, 123(8), Sharp J.J. (1969a), Spread of buoyant jets at the free surface, J. Hydraul. Div., ASCE, 95(3), Sharp J.J. (1969b), Spread of buoyant jets at the free surface-ii, J. Hydraul. Div., ASCE, 95(5), Zeitoun M.A., McIlhenny W.F. and Reid R.O. (1970), Conceptual designs of outfall systems for desalting plants, Research and Development Progress Report No 550, Office of Saline Water, US Dept. of Interior, Washington, DC, USA, p. 139.