S.M.Borghei
Assoc. Prof. of Civil Engng., Sharif Univ. of Tech., Azadi ave., Tehran, Iran
Fax: (98-21) 8731059, E-mail: mahmood@sina.sharif.ac.ir
Member: IAHR, ASCE, IHA(Iranian Hydr. Assoc.)
A.A.Etminani
MSc. Graduate Student, Sharif Univ. of Tech
Abstract: Plunge pool is one of the main structures of dissipating energy in high head dams. Different geometric shapes of them have been designed and are in operation in many parts of the world which are mainly optimized by hydraulic models. Although many experimental results for evaluation of hydrodynamic pressure in this kind of hydraulic structure are available but, the effect of pool width on the hydrodynamic pressures are unknown. This paper examines the effect of pool width using experimental results. The experimental data of more than 130 tests for circular vertical Jet for different diameter, discharge, pool depth and pool width have been analyzed. The result show that by decreasing width, from 10 to 5 times the impact Jet diameter, the hydrodynamic pressures on bed does not change much while, the pressure on the walls shows reduction. In fact due to large circulation of water due to impact jet and the existence of wall jet, negative pressure occurs. The negative pressure also happens at the point where the impact jet in the pool changes direction and becomes a wall jet.
Keywords: plunge pool, variable pool dimension, hydrodynamic pressure, falling jet, hydraulic model
Plunge pools are among the hydraulic structures, which are very popular for high head dams. The costs of a long chute spillway and stilling basin, forces engineers to the alternative of ski jump or, falling type spillway and plunge pool (Visher and Hager, 1995). The pool can be natural or artificial. The natural plunge pool should be far enough from the dam in order that the scouring does not endanger the structure (Gijs and Hoffman, 1998). While the use of natural plunge pool requires certain topography and geology of the site, sometimes, in the absence of a natural pool artificial pools using concrete walls and slabs are still more economical than the chute and stilling basin.
On the other hand design of concrete apron and reinforced pool walls should be some how that the hydrodynamic pressures do not damage the basin, as it happened for Malpaso dam in Mexico (Novak, 1984). In case of natural pool the equilibrium scour depth for design is required but, for artificial pool the hydrodynamic pressures in the pool are important. Beside the pressures, the behavior of eddies and turbulence flow, which is a very difficult job to find, is very important. Design of plunge pools requires great experience and high knowledge of hydraulics and hydrodynamic pressure phenomenon. For example one of the main sources of energy dissipation for the jet is the stage of its disintegration in the air and its effect on the impact jet (Ervin and Falvey, 1987).
On the other hand, the most important part of a falling jet would be its behavior at the point of impact and in the pool. Therefore the characteristics of the jet at the point of impact to the pool and its depth are important. Among these parameters the jet impact diameter(Dj), jet velocity(Uj) and plunge pool depth(y) are the most important ones. The relationship of nondimensional parameters of y/Dj and pool depth Froude number (Uj/Ögy) together with the hydrodynamic pressure coefficient (Cp=(Hm¨Cy)/(Uj2/2g) where Hm is the measured mean pressure head), show the hydrodynamic pressure due to the falling jet and pool characteristics.
Usually results from physical models direct engineer to the final design of pool geometry. Hence, use of experimental data and laboratory work for this field is inevitable. Hausler (1973) showed that maximum pressure coefficient for a circular jet happens at y/Dj=2.5 and, hence, introduced a formula for the pressure variation. Castillo et al. (1991) and Armengon and Ervin (1991) studied the effect of rectangular vertical jets on the plunge pool. Rae (1994) used both circular and rectangular jets for his tests. Also, using pressure transducers to measure pressure fluctuations, he worked on instantaneous pressures with stochastic methods. Also, Ervin et al (1997) have studied the pressure fluctuation field on a plunge pool floor subjected to jet impingement. Their result include both mean and fluctuating components of pressure and, have demonstrated an example for the practical situations.
However, not much literature on the effect of pool width on the hydrodynamic pressure exists. Liu Peiqing et al. (1997) have discussed the existence of wall jet and, hence, the design length of the pool but, there is no mention of the pressure variations on the wall. This paper presents the experimental results of this effect.
The pool model was made of Plexiglas with dimensions of 120-cm in the direction of outflow (longitudinal direction), variable width (B) of 60 to 120-cm (transverse direction), an outlet control weir height (w) of 15 and 25-cm. Three different falling jet diameter (D) 5.5, 7 and 10-cm have been used at different discharge (Q) from 5 to 30 lit/s and pool depth (y, which was dependent of Q and w). Overall 133 tests were carried out to find the pressure fluctuations on the plunge pool bed and wall. The pressures were measured using piezometers, which were connected to the bed and walls. In the center of bed, for an area of 20 by 20-cm, the pressures were measured at a distance of 5-cm and beyond that at intervals of 10-cm to each side of the center the pressures were measured. Also, on the wall, the measured pressures were at a distance of 10 cm from the bed with increments of 10 cm to each side.
The results of pool pressure variations are presented in two groups, hydrodynamic pressures on bed and, hydrodynamic pressures on wall due to vertical falling jet. It is necessary to mention that, although the piezometers can not measure the instantaneous variations of pressure but, for measuring mean maximum and mean minimum pressure, piezometers are reliable and have good accuracy.
Hydrodynamic pressures on the bed
Pressure fluctuations on the pool bed were measured in two directions perpendicular to each other. A sample of the maximum measured pressure (using piezometers) is shown in longitudinal and transverse directions due to variable width in Fig. 1. As it was expected the maximum pressure happens in the direction of center of impact jet and radially decreases. The range of influence of the jet at the center, is similar for different widths (60 to 120 cm) while other variables were kept constant. At about 30-cm each side from the center the pressure fluctuation is negligible. Also, before the hydrodynamic effect diminishes completely, a negative pressure is observed for all tests at a certain area. The effect was seen in all results while, for this figure the negative (or minimum) pressure happens at about 10-cm to both sides of the center. This is due to the wall jet effect, which has a high velocity near and tangential to bed.
Hydrodynamic pressures on the wall
A sample of the variation of hydrodynamic pressure on the plunge pool wall due to falling jet is shown in Fig. 2. The effect of narrowing the pool is to decrease the pressure and push it into negative region. The negative pressure on the wall is due to the wall jet. The circulation, which starts from the bed, has more effect on the wall if the pool width is smaller. On the other hand, for larger distance from the impact point the fluctuations becomes smaller and positive, that is since the strength of circulation and hence the negative pressure effect diminishes. Also, as it is in the figure, the minimum pressure does not happen in the center of the wall but, in the neighbourhood of the center line on both sides. This again shows the diversion of the jet to the side which, is more stronger for narrower plunge pool.
Fig. 3 shows the variation of pressures (dynamic and total) to water depth versus B/Dj. As it is seen, by increasing B/Dj, the hydrodynamic pressure increases from negative to positive. At almost (B/Dj)=10 the pressure becomes positive and, the wall jet has lost its strength and influence and, only a small fluctuation of water surface exist. Fig. 4 also shows the variation of pressures on a horizontal line on the wall which is maximum at the center (or close to center) and decreasing to the sides. The figure shows that at about 3 times the impact jet diameter to each side of the center of jet, its effect becomes minimal.
The experimental results of variation of pressure in plunge pool due to pool size show;
l By decreasing the pool width, from 10 to 5 times the impact jet diameter, no significant changes in pressure on bed is observed.
l While the direction of the vertical jet on pool bed changes, the jet direction is changed to a wall jet which introduces negative pressures on the bed.
l For the slender pool the wall jet continues as a circulating flow and, therefore, it has its effect as negative pressure on the walls.
Acknowledgements
The support of Sharif University of Technology during this study is acknowledged.
References
[1] Armengon, J., and Ervine, D.A., ¡°Mean and fluctuating pressure field in full width free nappe stilling basin.¡±, Twenty fourth IAHR Congress, Vol. D Models and Control System for Hydraulic Engineering, Madrid 1991, PP D2161¨CD269.
[2] Castillo, L.G., Dolz, J., and Polo,J., ¡°Analysis of data to characterize dynamic actions in hydraulic energy.¡±, Twenty fourth IAHR Congress, Vol. D Models and Control System for Hydraulic Engineering, Madrid 1991, PP D271¨CD280.
[3] Ervin, D.A., and Falvey, H.T., ¡°Behavior of turbulent water jets in the atmosphere and in plunge pools.¡±, Proc. of the Inst. of Civil Engng., Part 2, Vol 83, 1987, PP 295-314.
[4] Ervine, D.A., Falvey, H.T., and Withers, W.J., ¡°Pressure fluctuations on plunge pool floors.¡±, J. of Hydraulic Research, 1997 Vol. 35, No.2, PP 257¨C279.
[5] Gijs .J.C.M., Hoffman ¡°Jet scour in equilibrium phase.¡±, Journal of Hydraulic Engineering, ASCE, Apr. 1998, PP 430¨C437.
[6] Hausler, E., ¡°Scours stilling basins and downstream protection under free over-fall jets at dams.¡±, 11th International Committe of Large Dams( ICOLD), Madrid 1973, PP 39-53.
[7] Liu Peiqing, Gao Jizhang, Li Zhongyi, and Li Yongmei, ¡°Mechanism of energy dissipation and hydraulic design for plunge pools downstream of large dams.¡±, Energy and Water Sustainable Development Proceeding 1997, 27th Congress of the International Association of Hydraulic Research (IAHR) Part D, PP 417¨C422.
[8] Novak. P., ¡°Development in Hydraulic Engineering.¡±, Vol.1 and 2, Elsevier Applied Science Ltd., 1984.
[9] Rae, P., J., ¡°Force and pressure measurement in spillway plunge pools.¡±, ASCE National Conference on Hydraulic Engineering, Buffalo, NY 1994, Vol. 1, PP 553 ¨C557.
[10] Visher, D.L., and Hager, W.H., ¡°Energy dissipators.¡±, Hyd. Stru. Design Manual, IAHR, A.A. Balkama, Roterdom, 1995, Chap. 2.
