Control of saline water intrusion by vane-like barrier

Transcription

1 Control of saline water intrusion by vane-like barrier M. Ifuku Department of Civil and Environmental Engineering, Ehime University, Japan. Abstract There have been many studies on density current in estuary such as a problem of mixed density current, salt wedge, and buoyant jet. The upstream intrusion of saline water has become a social problem for river environment and water resources. In view of taking water resources durably and preventing the ecology, artificial control methods for preventing the saline water intrusion are quired. Setting up a mound on a riverbed and using a bubble plume have been proposed and applied to real estuaries. However, these control methods have a few problems for the river improvement and the control effect. So, the author proposed an artificial control method with lateral depth-varied barrier, which does not need much labor and cost for maintenance and also examined its control effect numerically. 1 Introduction There have been many studies on density current in estuary such as a problem of mixed density current, salt wedge, buoyant jet. The upstream intrusion of saline water has became a social problem for river environment and water resources. In view of taking water resources durably and preventing the ecology, artificial control methods for preventing the saline water intrusion are required. Jirka and Arita[l] developed the control method of saline water intrusion with the weir near the river mouth, which is important to maintain the aqueous environment. It is, however, supposed that several problems may arise on the construction of wier of which flow ability is comparatively low. While, the bubble jet system is utilized for industrial and environmental processes such as the aeration to prevent the eutrophication in dam and

2 1 12 Coastal Engineering V1 reservoir and nuclear reactor cooling system, oil fence. It is vexy important to clarify the flow structure in air bubble and water CO-existing system. Komatsu et a1.[2] proposed the method that was able to control the saline water intrusion by using the bubble plume and its experiment has been done on site. This control method has an advantage that is able to prevent the saline water intrusion without decreasing the flow ability. However, author pointed out that the control efficiency was relatively low in cases of high salinity by carrying out two-dimensional analysis on basis of experiments by Komatsu et al.. So, it was indicated that in order to increase the control efficiency, it is necessary to increase the volume of air bubbles discharged from the aerator or to set up several aerators. Moreover, it is supposed that much labor and cost are necessary to maintain the equipment. So far, the prediction of saline water intrusion was carried out by two-dimensional numerical model. However, it would be possible to carry out the numerical analysis by using the three-dimensional model by developing the high-precise calculation technique with the rapid increase in a processing capacity of the computer. Li et a1.[3] investigated the three-dimensional structure of subtidal currents caused by tidal wave motion in estuary, and indicated that, under the influence of nonlinearity and significant depth variation across a shallow coastal plain estuary, the tidally induced subtidal flow is seaward in the channel with a core of high velocity centered between surface and mid-depth of the channel. However, the analysis of mixing with saline and fresh water has not been carried out. As mentioned above, subtidal flow structure and mixing characteristic of density current that was induced by lateral depth variation are gradually being clarified. In this paper, the artificial control method with lateral depth-varied barrier that does not need much labor and cost for maintenance is proposed and numerical analysis by three-dimensional numerical model is carried out to verify the control effect of proposed barrier and to obtain the fundamental data on maintenance of the aqueous environment. 2 Numerical analysis 2.1 Governing equation Momentum equations We have a left handed coordinate system with the X axis pointing upestuary, the z axis vertical upward with origin at the reference datum, and the y axis at right angles to X and z. Fluid is assumed to be imcompressive, the density is assumed to be dependent onlt to salinity and it is apllicable to Boussinesq approximation, the equation for the conservation of longitudinal, lateral and vertical momentum leads to

3 Coastal Engineering V DvlDt = -(llpo)(~~ld~) + (11~0) (d~xyldx + d-r,,ldy + d~zyldz) (2) DwlDt = -(~I~o)g-(llPo) (~pldz)+(llpo) (d-r,,ldx + d-r,,ldy + d.r,,/dz) (3) where, t is time, U, v and W are the velocity components ofx, y and z- axis, p 0 is the reference density of fluid, p is the density of fluid, p is the pressure, g is the gravitational acceleration. Moreover, T, T, T, T, T, T,,, T,,, T, and T,, are the Reynolds stress, respectively and are described in the notation of Cartesian tensors as follows: ~jilpo (v + vt) (d~jldxi + d ~ildx~) (4) where v is a kinematic viscosity. vt is the SGS(subgid-scale) diffusivity suggested by Smagorinsky[4] and given as follows: where c, is the Smagorinsky constant, A is the grid size[a = (Ax. Ay. AZ)'/~], Ax, Ay and Az are the longitudinal, lateral and vertical grid intervals, respectively. The continuity equation leads to Integrating of eq.(6) over water depth and substituting the kinematic boundary conditions, yields where 5 is the position of the bottom. the free water surface, zb is the z-coordinate of Salt content The equation of conservation of salt content leads to where S is the salinity, K,, K, and K, are the turbulent diffusivities. The turbulent diffusivities, K,, K, and K,, which depends on flow velocity are assumed to be expressed in the form suggested by Bear[5].

4 114 Coastal Engineering V1 where y,, yy and y, are the constant proportionality, a~ and a~ are the characteristic length. where cl is an empirical constant Equation of condition The equation of condition leads to: P/PO = 1 + PS, where p, is the density of saline water. 2.2 Initial and boundary conditions P = (p, - po)/ps The initial conditions are assumed to still water condition. At the downstream, upstream, bottom, free surface and lateral boundaries, the following boundary conditions are imposed: Downstream boundary The surface elevation,^, must be identified as ~(t) = a sin at (12) where a is the tidal amplitude, a is the angular frequency (a = 27r/T, T is the tidal period). Further, boundary conditions for longitudinal, lateral and vertical velocities are required. Because no velocity profiles are generally available duxing a tidal cycle, a through-condition is imposed and lateral and vertical velocities are set to zero. Finally, a condition for the conservation of salinity must be given. During a flood tide, the increase in salinity is dependent only on t. During an ebb tide, a condition is set to in a similar way to the condition for longitudinal velocity. S=SoG(t) (flood:u>o) G(t) = 1 - (1- sin &)S' (14) d2s/bx2 = 0 (ebb : U < 0) where So is the salinity of the sea, S' is a weighting coefficient Upstream boundary Once the discharge is given, the longitudinal velocity profile in the flume is assumed to be logarithmic and lateral and vertical velocities are set to zero.

5 Coastal Engineering V Then, a conservation of salinity is set in a similar way to the condition for the conservation of salinity at the downstream boundary during an ebb tide. where U< is longitudinal velosity at the free water surface Bottom boundary At the bottom z= zb, the conditions are: Free surface boundary At the free water surface z= <, the conditions are: where u ~, VC and we are longitudinal, lateral and vertical velocities of fluid at the free water surface Side boundaries There is no-normal flow on the sides of the flume. The nonslip condition is imposed for longitudinal and vertical velocities and a conservation of salinity is set in a similar way to the condition for the conservation of salinity at the bottom boundary. U = v = W = 0, ds/dy = 0 (18) Coordinate transformation In the physical domain, the water surface is a moving boundary because of tide or river discharge, and the bottom also changes in space. Further, the longitudinal and lateral area of interest will not in general be a rectangular parallelepiped, because of variations in the bottom and the free surface. To obtain a good representation of the flow, a good description of the form of the free surface and the bottom is necessary. For a numerical approach based on finite differences, however, a rectangular parallelepiped grid that is coincident with the boundaries is preferable. Therefore, the area of interest is modified by a simple transformation into a rectangle parallelepiped.

6 1 16 Coastal Engineering V1 3 Numerical results 3.1 Analysis based on experiment by Komatsu et al. At the downstream boundary, surface elevation was computed by the Airy wave theo~y with wave amplitude of 0.7 cm and wave period of 240 S. The discharge was set to 50 ml/s at the upstream boundary. The length, width and slope of flume were 20 m, 0.25 m and 0.005, respectively. The still water depth at the downstream boundary was m. A nonslip condition was imposed at the bottom. The longitudinal and lateral grid intervals were set to 0.05 m and m, respectively and the water depth was divided into 10 planes. The time increment was T/8000. At the downstream boundary, salinity was set to 3 and 5 L. The Smagorinsky constant in eq.(5) was set to 0.1 after Ifuku[G] and the constants of proportionality y,, yy and y, in eq.(9) were set to 0.1, and 0.003, respectively. The empirical constant, cl, in eq.(lo) was set to 50. The weighting factor, S', in eq.(14) was set to Configuration of barrier Figure 1 shows the typical barriers that are used in numerical analysis. The height of the barrier top is 3 cm. The vane-typed part that extends from the top to the side makes 30, 45 and 90 degrees with x-axis. In cases where the angle between the vane-typed part and x-axis is 30 degree (hereafter referred to as type-a30), the control effect of saline water intrusion is maximal. So, the results of type-a30 and type-x90 where the transverse section is the same are mainly examined. Figure 1 : Typical barrier's configurations that are used in numerical analysis 3.3 Vector map Figure 2 shows the vector map of type-a30 and x90 around the barrier at the phase that the upstream velocity is maximal (hereafter referred to as MFV). The salinity at the downstream boundary is 3 L and the broken line shows the position of barrier. Figs.2(a) and 2(b) show the results at the center of flume. Figs.2(c) and 2(d) show the results of 3 cm height from the bottom. In both types, the flow velocity is maximal near X= 5 m, and the maximum occurs at the depth of two third water depth. The amplitude of horizontal

7 Coastal Engineering V velocity near X= 5.25 m is almost equivalent to it at the top of barrier in cases of type-x90, though it is considerably small in cases of typea30. Furthermore, the vertical flow velocity increases near the top of barrier. The horizontal flow velocity at the downstream region and the upstream region of X= 6 m is almost same on both types. In addition, the vertical flow velocity increases near the top of barrier. Furthermore, the horizontal flow velocity at the downstream region and the upstream region of X= 6 m is almost same on both types. In the meantime, in cases of type-a30, the flow converges along the ridge of the barrier at the downstream, the flow diverges along the ridge of the barrier at the upstream. Though, in cases of typex90, the flow also converges at the downstream of the barrier, but the rate of convergence is smaller than type-a30. Furthermore, the longitudinal flow velocity at the upstream of the barrier is faster than typea30 except the wall. The effect of two and three-dimensional barriers on the flow velocity is significant at the upstream toe of slope of the barrier. It is supposed that the rate of distortion for such longitudinal and lateral flow velocity affects the mixing of the saline water. (a) type-a30 (b) type-x90 (c) typea30 (d) type-x90 Figure 2:Vector map around barrier. Broken line is the position of barrier's toe. Figure 3 shows the spatial distribution of lateral velocity at x=5 m in MFV. Figs.3(a) and 3(b) are the results of type-a30 and x90, respectively. The

8 l 18 Coastal Engineering V1 sign of flow velocity that is toward the center of flume from the left bank (y=o m) is positive, and both are viewed from the upstream. In Figure 3(a), a pair of circulation that flows from the channel to the shoal near the bottom and from the center of flume to the bank near the surface is generated. Though the flow direction near the bottom at y= 0.1 m does not change during a tidal cycle, the flow direction near the surface changes in flood and ebb tide. That is to say, the flow directs toward the bank in flood tide and toward the center of flume in ebb tide. Li carried out the numerical analysis with the flume whose transverse section is symmetric and indicated that the lateral velocity directs from the channel to the shoal in high water (hereafter referred to as HWS) and the reverse occurring in low water and the amplitude of flow velocity changes with time. It is supposed that the discrepancies between Li's and present results are induced by their bottom profile. In Figure 3(b), the flow directs from bank to the center of flume and maximum velocity occurs near the surface at y=0.05 and 0.2 m. In comparison with Figure 3(a), the amplitudes of flow velocity near the surface and bottom are approximately one third and one fifth, respectively and those are considerably small compared with Figure 3(a), the flow pattern is also different. (a) type-a30(interval:0.5 cm/s) (b) type-x90(interval:0.2 cm/s) Figure 3:Spatial distribution of transverse velocity(mfv). 3.4 Salinity around barrier in HWS Figure 4 shows the spatial distribution of isohalines in HWS which the length of saline water intrusion is maximum. Figures 4(a) and are the case of no barrier and type-a30, respectively. Furthermore, the salinity in the downstream boundary is 3 %, and those are the results at the center of flume. In Figure 4(a), the salinity of mixed water near the bottom is approximately 0.8 times the salinity of the downstream boundary and the stratification is significant. There is the mixed water whose salinity is approximately one third of downstream boundary near the surface. In Figure 4(b), vertical mixing with the vertical flow which is induced by barrier is remarkable and the mixed water with higher salinity extends to the surface in the convex. The intrusion length of isohaline, S/So=0.5, is short about 5 m in comparison with Figure 4(a). This is the reason why the barrier was set up. In the

9 Coastal Engineering V case of type-x90(not shown), the distribution of isohaline is almost similar to Figure 4(b) at the downstream of the barrier. However, the intrusion length of isohaline is longer than that in Figure 4(b) at the upstream. It is caused that velocity gradient and lateral velocity amplitude increase as shown Figures 2 and 3, as the result the horizontal mixing rate increases. (a) non-barrier(y=0.125 m) (b) type-a30(y=0.125 m) Figure 4:Isohaline around barrier(hws). 3.5 Time and depth averaged salinity Figure 5 shows the spatial distribution of time and depth averaged salinity at the center of flume and 2.5 cm from the left bank, respectively. In Figure 5, the darkened triangles are the toe of barrier. Moreover, the salinity at the downstream boundary is 3 %. The solid circle depicts experimental results by Komatsu et al.. The angle between the vane and the bank is 30 degrees. As shown Figure 5(a) which is the result at the center, in cases of non-barrier, salinity at the downstream and upstream toes of barrier is approximately 0.52 and While, in cases where several barriers are set up, salinity rapidly decreases at the upstream from x=3 m. Furthermore, salinity of type-a30, b30, c30 and d30 at x=3 m are approximately 0.61, 0.72, 0.68 and 0.68, respectively. But, those at x=5.35 m are two fifths or three fifths of those at x=3 m. In Figure 5(b), the distribution of salinity is similar to Figure 5(a) well and the control effect is highest in cases of type-a30. (a) y= m (b) y= m Figure 5:Time and depth averaged salinity(h,:top height of barrier).

10 120 Coastal Engineering V1 4 Conclusions Three-dimensional numerical model was developed for mixing and circulation in estuary and numerical analysis was conducted with changing tidal level. Furthermore, the control efficiency of barrier, which is set up to prevent the saline water intrusion was examined. The results obtained are as follows: (l)shear, lateral and vertical flow velocity increase and the water is mixed well around the barrier, because of the setting of barrier. As the result, saline water intrusion is controlled. (2)In eleven types of barrier, type-a30 is highest for the control of saline water intrusion. So, the control efficiency depends on the barrier's configulation. This is the reason why the upwelling flow changes by the difference of flow resistance. (3)The backwater by the barrier do not generate at the upstream, though the volume of the barrier occupies about 2 % of the whole water volume of the construction region. The salinity around the barrier decreases to two fifths or three fifths of that in cases of non-barrier. So, the proposed structure is useful to control the saline water intrusion. The control method for the saline water intrusion is proposed, the control effect is verified by numerical analysis. However, present analysis was carried out under the condition with the uniform bottom slope and constant width. It is necessary that in addition, many analyses are carried out for the application on site and then the fundamental data are accumulated. References [l] Jirka, G.H. and M.Arita. Density currents or density wedge boundary layer influence and control method,j.f.m., Vo1.177, pp , [2] Komatsu, T., S.Sun, T.Adachi, Y.Kawakami and K.Komesu. Study on the artificial control method for preventing salinity intrusion in a tidal estuay, Ann. J.Hydraul.Eng., JSCE, Vo1.40, pp , [3] Li, C., J. O'Donnel, A.Valle-Levinson, H.Li, K.-C.Wong and K.M.M. Lwiza. Tide induced mass-flux in shallow estuaries, Ocean wave measurement and analysis, Vo1.2, pp , [4] Smagorinsky, J. General circulation experiments with primitive equations, Monthly Weather Rev., 9(3), pp , [5] Bear J. Hydraulics of Groundwater, McGraw-Hill, pp , [6] Ifuku, M. Control of Saline Water Intrusion by Air Bubbles with Changing Tidal Range, Proc. of International Symposium on Stratified Flow, Vo1.2, pp , 2000.