Real scale investigation of interaction between a supercritical flow and a bottom sill. 1: physical aspects and time-averaged pressures on sill

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1 Real scale investigation of interaction between a supercritical flow and a bottom sill. 1: physical aspects and time-averaged pressures on sill D. Borsani, E. Larcan, S. Mambretti & E. Orsi Dipartimento di Ingegneria Idraulica, Ambientale e del Rilevamento, Politecnico di Milano, Italy. Abstract Results of field scale experiments concerning the interactions between a supercritical flow and a vertical bottom sill are presented. Experiments are performed in a channel (width B = 5.01 m) downstream of the weir of Sernio (Adda River, Northern Italy) using a vertical sill with adjustable height s (0.5 m, 0.6 m and 0.7 m). Significant cinematic and geometric parameters of flow have been measured for different discharge regimes. The fluctuating local pressure on the upstream face of the sill have been recorded by means of sensors, connected to a digital acquisition system. The experimental tests show that, in accordance with previous laboratory experiments of Guadagnini, Larcan, Orsi [l], the type of forced hydraulic jump is a function of both the supercritical flow Froude number Fr, and the ratio, s/hl, between sill height S and depth of approaching supercritical flow hl. Classification of forced jump, derived under laboratory conditions, is also recognized at the field scale.due to scale effects, some differences are recognized and discussed. 1. Introduction The possibility of using tests carried out on laboratory models for the study of real scale structures is very important and useful in many practical problems. The experience here shown have two main aims: (i) to analyse real flow pattern and (ii) to control the scale effect on the distribution of time-averaged pressures

2 3 16 Fluid Structure Interaction generated by a supercritical flow on a transversal bottom sill [l], [2], [3], [4], [5], W], [71. Given the availability of a real plant, a series of tests similar to those already developed at a laboratory scale has been organised. [l], [3]. As evident, real scale operations have some advantages (a wider experimental field) but also limitations due to the difficulties in measuring some geometrical or cinematic parameters, for instance water depth h,, which affects the degree of spread of experimental data in dimensionless correlations and the resulting interpretation. 2. Experimental equipment Experiments have been carried out in a channel downstream of the weir of Sernio (Adda River, Northern Italy). The channel has a width B = 5.01 m and average slope of 1.7 %. An artificial reservoir supplies the discharge through a mobile gate. The hydraulic head H of the reservoir ranges between 6 m and 9 m and can be considered constant during each test. The sill used to force the hydraulic jump has been positioned at a distance of m from the gate. Three different sill heights have been used: s = 0.7 m, S = 0.6 m and s = 0.5 m. Figure 1 depicts a sketch of the experimental set-up. The sill is a wooden plane supported by a reticular structure fixed to the channel walls. l 1 ~ldh8=5.0l m/ I Gate l B 7 Figure 1 - Experimental set-up Piezo-resistive pressure transducers (Sensit M ) have been installed on the upstream face of the sill in order to record the temporal behaviour of the pressure values. Eight transducers have been installed on the 0.7 m sill, seven on the 0.6 m and six on the 0.5 m ones. The lowest sensor is always positioned at 2.5 cm from the channel floor. The remaining sensors are distributed almost equally along the vertical, depending on the presence of the support structure.

3 Fluid Structure Interaction 3 17 generated by a supercritical flow on a transversal bottom sill [l], [2], [3], [4], [5], H, [71. Given the availability of a real plant, a series of tests similar to those already developed at a laboratory scale has been organised. [l], [3]. As evident, real scale operations have some advantages (a wider experimental field) but also limitations due to the difficulties in measuring some geometrical or cinematic parameters, for instance water depth h,, which affects the degree of spread of experimental data in dimensionless correlations and the resulting interpretation. 2. Experimental equipment Experiments have been carried out in a channel downstream of the weir of Sernio (Adda River, Northern Italy). The channel has a width B = 5.01 m and average slope of 1.7 %. An artificial reservoir supplies the discharge through a mobile gate. The hydraulic head H of the reservoir ranges between 6 m and 9 m and can be considered constant during each test. The sill used to force the hydraulic jump has been positioned at a distance of m from the gate. Three different sill heights have been used: S = 0.7 m, S = 0.6 m and s = 0.5 m. Figure 1 depicts a sketch of the experimental set-up. The sill is a wooden plane supported by a reticular structure fixed to the channel walls. l / 5" 7, Width B = 5.01 m / : Hydraulic jump Figure 1 - Experimental set-up Piezo-resistive pressure transducers (Sensit M ) have been installed on the upstream face of the sill in order to record the temporal behaviour of the pressure values. Eight transducers have been installed on the 0.7 m sill, seven on the 0.6 m and six on the 0.5 m ones. The lowest sensor is always positioned at 2.5 cm from the channel floor. The remaining sensors are distributed almost equally along the vertical, depending on the presence of the support structure.

4 3 18 Fluid Structure Interaction For each test the following parameters have been measured: the hydraulic head H, the opening a of the gate, the depth hl of the upstream supercritical flow, the hydraulic depth h, on the sill. Depth hl of table 1 (for the difficulties of a direct measure) has been calculated by means of a classical finite-differences code with Strickler coefficient k, = 40 rnk/r starting from the vena contracts downstream of the gate. The procedure of pressure acquisition was controlled by computer codes built up with the software LAB-VIEW. On the basis of laboratory tests a sampling frequency f = 100 Hz and a total sampling time T = 1 hour have been adopted. Thus, the number of data for each series of pressure values is equal to Experimental tests Parameters of the experimental tests have been reported in table 1. Dimensionless quantities Frl and s/hl have been computed in order to allow the positioning of the experimental tests in plane (Frl, s/hl) to evaluate the flow region for each test [l], [2], [3], [8], [9] [10]. Table 1 - Experimental tests - S Test H a Q hl Frl s/hl ~low7 [m1 [m1 [m1 [m3/sl [m1 region 0,7 A a The classification of forced jump of Guadagnini et al. [l], which was derived under laboratory conditions is proved to be robust also at the field scale;

5 Fluid Structure Interaction 3 19 three regions have been defined: region a (characterized by the presence of a free or forced-jump), P (the stream forms a jet that directly strikes the sill and the maximum flow depth is located downstream of the sill itself), and y(the water surface of the supercritical jet remains continuous around the sill with negligible air trapping). The type of forced hydraulic jump is a function of both the Froude number Fr, and the ratio s/hl between sill height s and depth of approaching supercritical flow hl. In the real scale experiments it has been possible to reproduce also y flow patterns. The latter were not analysed during the laboratory tests, due to limitations of the experimental set-up. Figure 2 depicts experimental tests organized on the plane (Fr,, s/hl), together with the limits of the three flow regions. Figure 2 - Flow regions and experimental data. 4. Pressure distribution and comparison with laboratory data Figures 3, 4 and 5 show the time averaged distribution of the piezometric head ~, ~ on / y the central vertical axis of the three tested sills. At a first glance it is possible to observe a more or less evident S-shaped distribution. These results have been compared against those of a previous laboratory study, with a geometrical scale reduction of about 1 : 10. Laboratory results [l] led to the following interpolating expressions:

6 320 Fluid Structure Interaction where V, = %, h, is the average velocity of the upstream supercritical flow and 1 S p* =-I, p,, dy is the mean weighted pressure on the vertical axis of the S upstream face of the sill and p,, is the local time-averaged pressure at location y. Fig. 3 - Local time-averaged piezometric head for s = 0.70 m Fig. 4 - Local time-averaged piezometric head for s = 0.60 m

7 Fluid Structure Interaction 32 1 Fig. 5 -Local time-averaged piezometric head for s = 0.50 m Figures 6,7 and 8 show the distribution of dimensionless time-averaged pressure along the vertical axis of the sill. A possible explanation of the discrepancies observed might be due to the fact that experimental points are related to flow conditions very close to the y region.. A U B c A - D * E X F x G Theoret. Fig. 6 - Time-averaged dimensionless pressures for s = 0.70 m

8 322 Fluid Structure Interaction p. X A 0 H I L Theoret. Fig. 7 - Time-averaged dimensionless pressures for s = 0.60 m X R A S l = Theoret Fig. 8 - Time-averaged dimensionless pressures for s = 0.50 m A critical analysis of figures 6-8 shows that the maximum percentage difference between predicted (by means of eq. (1)) and observed values of p, 1 p* reaches ~15+20%, when only tests in a and P regions are considered (discrepancies between experiments and predictions at the laboratory scale were of the order of

9 Fluid Structure Interaction 323 +lo%).taking into account also results into or near y region, the maximum percentage difference may reach +30%. 5. Conclusions Time-averaged pressure on central axis of a sill interacting with a supercritical flow is studied. This study was performed at real scale and follows a long series of laboratory tests. One of its aims was to evaluate the possibility of understanding the general features of the phenomenon by means of the equation derived from the laboratory-scale model (approximately at a geometrical scale 1:lO). Tests confirm the dependence of pressure distribution from few parameters (or, in other words, from characteristic flow region of occurrence). The comparison with the interpolating curve already proposed is rather good, considering that in the new test series it was possible to reach the y flow region. The following step of this research will consist in finding a more general function to describe the time-averaged pressure values in dependence of geometric and cinematic parameters. Acknowledgements The work was supported by the Chizzolini foundation - Milano, and by AEM - Milano. The Authors whish to thank in particular engineers Fontana and De Campo. References Guadagnini, A., Larcan, E., Orsi, E. Flow Conditions and Pressure Distributions Over Sills. L'Energia Elettrica, No. 3, 1998 Cigada, A., Guadagnini, A., Orsi, E. Statistical Characteristic of Pressure Fluctuations Over Sills in Stilling Basins. L'Energia Elettrica, Vol. 73, No. 6, 1996 Borsani, D., Larcan, E., Orsi, E. Statistics of pressure fluctuations on a transversal sill due to supercritical flow. 3rd International Conference on Hydroscience and Engineering, Berlin, Germany, 31St August - 31d September l998 Borsani, D., Larcan, E., Mambretti, S., Orsi, E. Pressure fluctuation on structures: experimental data analysis. Advances in Fluid Mechanics Ill, Montreal, Canada, 24~ - 26" May 2000 Borsani, D., Larcan, E., Mambretti, S., Orsi, E.: Hydraulic Jump at a Positive Step: Statistics of Pressure Fluctuations XXIX IAHR Congress, Beijing, China, 17' - 21St September Hager, W.H.: Discussion on "Drag on vertical sill forced jump" J. Hydraulic Research, IAHR Vol. 30, n. 2, 1992, p

10 324 Fluid Structure Interaction [7] Karki, K.S. Supercritical flow over sills J. Hydraulic Division, ASCE, 1976, Vol. 102, n. HY10, p [8] Ohtsu, I., Yasuda, Y., Hashiba, H. Incipient jump conditions for flows over a vertical sill J. Hydraulic Engineering, ASCE Vol. 122, n. 8, p , l996 [9] Rajaratnam N., Murahari, V. A contribution to forced hydraulic jump " J. Hydraulic Research, IAHR Vol. 9, n. 2, 1971, p [l01 Borsani, D., Larcan, E., Mambretti, S., Orsi, E. Real Scale Investigation of Interaction between a Supercritical Flow and a Bottom Sill. 2: Statistical Analysis of Pressure Fluctuations on Sill. Fluid Structure Interaction 2001, Halkidiki, Greece, 26" - 28" September 2001