FLUCTUATING PRESSURES AT THE BOTTOM OF A PLUNGE POOL

Transcription

1 FLUCTUATING PRESSURES AT THE BOTTOM OF A PLUNGE POOL Nadia Ursino*, Paolo Salandin** & Luigi Da Deo* * Deartment of Engineering I.M.A.GE. University of Padova ITALY ** Hydraulic Institute Faculty of Engineering University of Ancona ITALY ** via Brecce Bianche, Ancona - ITALY hone: int fax: int sala@ocsi.unian.it ABSTRACT The aer describes the results of a laboratory set of exeriments made to investigate the ressure fluctuation field on beneath of a lunge ool subected to et imingement. As an examle this henomenon takes commonly lace in the case of the dro structure, where the elevation reduces with a take off and iminging ortion. When the downstream bottom is nearly horizontal and made of concrete or rock, there is no significant scour, and the dro is followed by a stilling basin where the hydraulic um takes lace. The relevance of the toic is related to the structural design of the linings of the dissiation basin downstream barrages or check dams. Nevertheless the knowledge of the stresses at the basis of lunge ool dissiation basins can be useful to redict a localized erosion rocess. With reference to the secific case of the rototye of a dam sillway and downstream energy dissiation basin, we discuss the effect of a variable water cushion deth on the reduction of the severe ressure fluctuations that take lace at the bottom of the stilling basin. The exeriments are made on a 1:40 laboratory model, recording the dynamic behavior of ressure fluctuations in a set of different ositions on beneath the lunge ool. The exerimental results resented in dimensionless form, give a better understanding of the fluctuating ressure reduction that can be obtained increasing the cushion deth. Keywords: lunge ool, ressure fluctuations, dissiation structures. INTRODUCTION The whole energy dissiation rocess in the assage from the reservoir ustream a dam to the tailwater, involves from a general oint of view several asects, each one ascribed to a different henomena [Novak et al., 2001]: the downhill sillway surface, the free-falling et, the imact into the ool, the hydraulic um in the dissiation basin and the outflow into the river. A large ortion of energy dissiation is related to the aeration/disintegration of lunging et and to the henomena that take lace in the downstream dissiation basin. So that a better understanding of these dissiation rocesses is of rimary interest not only for large dams, but also for smaller check dams and, more generally, for dro structures. The dro structures are those where the elevation reduces with a take off and iminging ortion: the aroach flow lunges into a water cushion and the energy is dissiated for air resistance before the imingement, imact, wall et deviation and hydraulic um. The et entrains a considerable amount of air as it enters the water cushion and forms two counter rotating macro vortices which diameter is of the same order as the ool deth. The imact structures that receive and deflect the et dissiate the excess energy by et diffusion [e.g. Hager, 1995]. In corresondence to the hydraulic um, the incoming flow is converted into turbulence which is contained initially into large eddies and then is assed down the energy cascade and is finally dissiated by the smaller eddies [e.g. Raaratnam, 1995]. Both energy

2 dissiation rocesses are associated with the origin of severe ressure fluctuations at the bottom of the stilling basin. Ervine et al. [1997] consider the effect of a falling et and the air entrainment on the lunge ool ressure fluctuations and the same toic was recently discussed by Melo [2002]. The literature works on dynamic ressures and the ultimate scour are discussed by Castillo [2002], while Jia et al. [2001] simulate comutationally the scouring rocess due to a two dimensional lane iminging et in a lunge ool. An exerimental work similar to those resented in our aer is reorted by Puertas and Dolz [2002]. They measure the dynamic ressure increment at the oint of imact of the et, demonstrating that an effective cushion enlarges the area of noticeable ressures as a consequence of the sreading of the et. The exerimental analysis here roosed considers the fluctuating ressure at the base of the dissiation basin of a rototye dam and its modifications, in terms of maximum values, for different deth of the water cushion within the basin. Our goal is to reach a better understanding of the two maor hysical mechanisms involved in the energy dissiation rocess: i) the imact at the imingement oint of a falling et and ii) the turbulence henomena under the hydraulic um occurring downstream. Nevertheless to infer from the analysis of the dynamic ressure measurements a quantitative criterion for the design of the stilling basin is of extreme imortance. In fact, severe ressure fluctuations linked to the dissiative henomena may be resonsible for the failure of high head dissiation structure and of smaller check dams structures. So that our exeriments are oriented to the design of the lining of dissiation basins, by evaluating conventionally the aroriate thickness of the rotection concrete slabs. It follows a criterion, combining laboratory observation with a theoretical analysis, rogressively develoed on the base of measurements and statistical evaluation of turbulent ressure fluctuation at the bottom of the hydraulic um. The criterion is based on the time instantaneous ressure differences, assuming that the ulsating ressure at the bottom of the stilling basing roagates with negligible delay through the oint seal of the slabs, allowing extreme ressure differences from the uer to the lower surface of the slabs. This way, the total force related to the ressure acting on both sides of the slab may exceed the weight of the slab and the anchor resistance. As an examle, Fiorotto and Rinaldo [1992] develoed a design criterion based on the ulift due to the severe ressure fluctuations associated to the dissiative henomena in the hydraulic um. This criterion rovides an equivalent thickness s of the slab as a function ' of the maximum ulift force F max. + Being h' = max( med ) and h' = min( med ), the resectively the maximum and the minimum measured ressure fluctuation around the mean ressure med, and γ and γ c the secific weight of water and concrete resectively, the equivalent thickness according with the design criterion roosed by Fiorotto and Rinaldo is: + lx l l y h' h' ' x F s = Ω,, = max. (1) y I x I y γ c γ ( γ c γ ) lxl y In eqn. (1) y is the deth of the incident flow, while l, l are the slab dimensions and I, I y the fluctuating ressure correlation lengths, in the longitudinal and transversal direction resectively. The dimensionless coefficient Ω, related to the instantaneous satial distribution of the fluctuating ressures, may be determined by direct measurement in hydraulic models of the maximum ulift or by using the exression rovided by Bellin and Fiorotto [1995] in case of normal distributed force and ressure. If the slab is anchored, the x y x

3 dynamic behavior of the whole system (the slab and the anchor) can be evaluated as in Fiorotto and Salandin [2000]. Nevertheless in this context the resence of a lunging et in a water cushion was never considered and, more general in literature, a generic design criterion for the otimum cushion deth to reduce the dissiation basin floor stresses, still lack. DESCRIPTION OF THE PHYSICAL MODEL AND OF THE MONITORING APPARATUS The exerimental setu was develoed on the hysical model of sillway and stilling basin of the Sa Stria dam, under constraction on the Monti Nieddu river in southern Sardinia (Italy). The original 1:40 model was realized ensuring the Froude similarity to verify the erformance of the dam outlet works and of the dissiation basin. In the rototye the sillway crest, divided in 4 stretch each 11.5 m long by the resence of 3 iers, is at m a.s.l. and it ensures the evacuation of the design flood (570 m 3 /s) with m a.s.l. of the ustream reservoir level. The chute ends with a horizontal ski um at m a.s.l. and the dissiation basin is limited about 200 m downstream by a barrage with a sillway m long and crest at m a.s.l.: this barrage realizes a cushion deth large enough to localize the dissiative henomena for all exected discharges. In our exeriments we substitute the barrage with a series of removable stologs each of 4 cm of height (see Figure 1 and 2), to gain the ossibility of realize different deth of water cushion in the dissiation basin. In the area affected by the et imingement 21 oenings were rovided at the bottom to evaluate the dynamic ressure behavior. The ta diameter was set of 2 mm, according with revious studies of Fiorotto and Rinaldo [1992], which show that further increasing in the ta diameter reduces the magnitude of measured fluctuating ressure. Figure 1. Exerimental setu. General lanimetric view of the Sa Stria dam model.

4 Figure 2. Exerimental setu. Sa Stria dam model stilling basin, longitudinal rofile. The fluctuating ressure was measured by means of 5 AEP LAB TP14 ressure transducers, calibrated in the range of 0-1 bar and characterized by an accuracy of 0.05% in the entire range. The ressure transducers were connected to the tas by a rigid tube of 4 mm diameter and the connections were equied with a bleed valve to allow the removal of any air entraed during oeration. The comuter was linked to the transducers by a 16-channel analog-digital board (Data Translation 2801 A) and samling was accomlished by a Global Lab rogram. Since several reliminary tests indicate that the iminging et affects uniformly the area monitored by ressure tas and no relevant differences in the dynamic ressure behavior are manifest in the transversal direction, the ressure fluctuations recordings were limited to the longitudinal axis of the stilling basin corresonding to the tas number 3, 8, 13, 18 and 21 (see Figures 1 and 2). Moreover, since the sectra analyses demonstrated that the dominant frequencies of ressure fluctuations were less than Hz, a samling rate of 200 Hz was adoted according to the Nyquist theorem. The ressure fluctuations were recorded for the Q =39.5 and the Q =56.3 l/s discharge values increasing the height of the cushion deth by change the number of stologs at the end of dissiation basin. The duration of every exeriment was 60 minutes: this duration was chosen balancing the comuter disk sace with the requirement of a recording time large enough to define the statistics of the measured signal. RESULTS AND DISCUSSION As reviously stated, in our exeriments we considered two different values of the water discharge, Q = 39.5 l/s and Q = l/s, while the fluctuating ressures are measured along the longitudinal axis of the stilling basin corresonding to the cells numbered as 3, 8, 13, 18 and 21 in Figure 1. In the following we will refer with med, i the time average of ressure measured at cell i and with its variance. var( i ) In order to evaluate the satial distribution of the fluctuating ressure on the base of the time continuous ressure measurements along the axes of the stilling basin, the following arameters have been estimated.

5 1) The maximum, minimum and mean ressure relative to the five location of the cells and to different water cushion deths. The mean downstream ressure value is estimated on measurements taken at cell number 21. In fact, we assume that = med,21. The water level measured on the sillway crest of the model is h = 8.31 cm and h = 6.71 cm corresonding to the two water discharge Q = 56.3 l/s and Q = l/s. With resect to the symbols indicated in Figure 2, H* = Δz + h hv. 2) The maximum ositive and negative dimensionless ressure fluctuation are defined as + C = + h' and = h'. The absolute values of + and are lotted as a C function of the cells osition xi within the stilling basin in Figure 3 for Q = l/s and in Figure 4 for Q = 39.5 l/s. The deth of the corresonding water cushion is resumed by the dimensionless arameter. 3) The dimensionless variance of ressure fluctuation var( i ). In Figure 5 this quantity is lotted as a function of xi for Q = l/s (left) and for Q = l/s (right). 4) The satial correlation structure of the ressure fluctuation relative to cell number 3 for different water cushion deths, evaluated as ( ) var( ) C C 3 med,3 med, var 3, with =3, 8, 13, 18 and 21. For sake of simlicity we indicated with the symbol < z >, the time average of the quantity z over all the recording time. In Figure 6 are lotted as a function of the horizontal distance from the beginning of the stilling basin the correlation structures relative to the larger discharge Q = l/s (on the left) and those relative to the smaller discharge Q = 39.5 l/s (on the right) C Q 56.3 l s C Figure 3. Case of water discharge Q = l/s. Satial distribution of the maximum (left) and minimum (right) dimensionless ressure fluctuation for different water cushion deth. In the legend is indicated the corresondence between symbols and mean dimensionless cushion deth. Figure 3 and Figure 4 demonstrate the existence of a limit water cushion deth, above which no relevant further reduction of the extreme ressure fluctuation is detectable. In the cases 0.00

6 examined, such limit deth seems to be around = When the water cushion is close to the this limit value and Q = l/s (squared symbols in Figure 3) the extreme ressure fluctuation caused by the et imingement and by the hydraulic um are about the same order of magnitude. For shallower water cushions the maor ressure fluctuations are due to the et imingement C Q 39.5 l s C Figure 4. Case of water discharge Q = l/s. Satial distribution of the maximum (left) and minimum(right) dimensionless ressure fluctuation for different water cushion deth. In the legend is indicated the corresondence between symbols and mean dimensionless cushion deth h C v C Q 56.3 l s Q 39.5 l s Figure 5. Satial distribution of the variance of the dimensionless ressure fluctuation for different water cushion deth. Case of water discharge Q = l/s (left) and Q = 39.5 l/s (right).

7 In Figure 4, it is manifest that the maximum ositive ressure fluctuation for a ratio = 0.13 and Q = l/s was measured in the ta number 18 while the general behavior indicates that the maximum ressure fluctuations were measured at ta 3, in the osition where the et lunges in the ool. Because of the extreme ressure fluctuations have a small robability of occurrence, this fact can be related to the duration of exeriments limited to 60 minutes, so that a longer acquisition time may gives a more robust statistics on the extreme ressure fluctuations. Nevertheless this fact not affects the general satial behavior of the fluctuating ressures confirmed also by the analysis of the variances reorted in Figure 5. The variance of the ressure fluctuations is an index of the stress on the bottom of the stilling basin. Once more, Figure 5 shows how the maor art of the stress is caused by the et imingement whereas the stress caused by the hydraulic um is less than half of the one caused by the et. The area under the evaluated correlation oints is a measure of the longitudinal correlation length I x of the ressure fluctuations. As the water cushion deth increases, the diffusion of the iminging et revails on henomena related to the et deflection. So that the fluctuations of ressure with statistically comarable behavior interest a more extended area, leading to a larger correlation length. This fact can be recognized from the Figures 6 for both the discharges here considered med 3 med (var( 3 )) ((var( )) med 3 med (var( 3 )) ((var( )) Q 56.3 l s Q 39.5 l s x cm Figure 6. Longitudinal correlation structure of the ressure fluctuation referred to the first cell, for different water cushion deth. Case of water discharge Q = 56.3 l/s (left) and Q = 39.5 l/s (right). CONCLUSIONS From a design oint of view the results obtained demonstrate that the deth of the water cushion influences the thickness of the dissiation basin linings through the reduction of the ressure fluctuation as the water cushion deth increases u to a certain limit value. As well, the water deth is connected to the lanimetric critical dimension of the slabs if this kind of lining is adoted through its influence on the correlation structure and thus on the integral scale. Further research would be necessary in order to define guidelines for engineering design that quantify in the more general case the otimum cushion deth and the relative attenuation on the dissiation rocesses that take lace within the lunge ool stilling basin

8 ACKNOWLEDGEMENTS This aer is a sin-off of the roect COFIN 2000 Fenomeni localizzati in corrisondenza a manufatti in alveo of the University of Padova and of the roect CNR-GNDCI Interazione tra manufatti e fenomeni di iena nei corsi d acqua of the University of Ancona. REFERENCES Ervine, D.A., H.T. Falvey, and W. Withers, Pressure fluctuation on lunge ool floors, Journal of hydraulic Research, Vol. 35, 2, , Castillo E. L.G., Parametric analysis of the ultimate scour and mean dynamic ressures at lunge ools, in Rock Scour, A.J. Schleiss and E. Bollaert Editors, , Balkema Pub., The Netherland, Bellin A. and V. Fiorotto, Direct dynamic measurement on slabs in sillway stilling basins, Journal of Hydraulics Engineering, ASCE, Vol 121(10), Fiorotto V. and A. Rinaldo, Fluctuating ulift and linings design in sillway stilling basins, Journal of Hydraulic Engineering, ASCE, 118(4), Fiorotto V. and P. Salandin, Design of anchored slabs in sillway stilling basins, Journal of Hydraulic Engineering, ASCE, 127(7), Hager, W.H., Dro structures and lunge ools, in Energy dissiators, D.L.Visher and W.H. Hager Editors, , Balkema Pub., The Netherland, Jia Y., T. Kitamura, S.S.Y. Wang, Simulation of scour rocess in lunging ool of loose bed material, J. Hydr., Engrg., ASCE, Vol 127 (3), Melo J.F., Reduction of lunge ool floor dynamic ressure due to et air entraitment, in Rock Scour, A.J. Schleiss and E. Bollaert Editors, , Balkema Pub., The Netherland, Novak P., A.I.B. Moffat, C. Nallury and R. Narayanan, Hydraulic structures, Son Press, New York, Puertas J. and J. Dolz, Pressure fields due to the iningement of free falling ets on a riverbed, in Rock Scour, A.J. Schleiss and E. Bollaert Editors, , Balkema Pub., The Netherland, Raaratnam N., Almanac of energy dissiation mechanisms, in Energy dissiators, D.L.Visher and W.H. Hager Editors,.23-41, Balkema Pub., The Netherland, 1995.