Proceedings of the 7 th International Conference on HydroScience and Engineering Philadelphia, USA September 10-13, 2006 (ICHE 2006) ISBN:

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1 Proceedings of the 7 th International Conference on HydroScience and Engineering Philadelphia, USA September 10-13, 2006 (ICHE 2006) ISBN: Drexel University College of Engineering Drexel E-Repository and Archive (idea) Drexel University Libraries The following item is made available as a courtesy to scholars by the author(s) and Drexel University Library and may contain materials and content, including computer code and tags, artwor, text, graphics, images, and illustrations (Material) which may be protected by copyright law. Unless otherwise noted, the Material is made available for non profit and educational purposes, such as research, teaching and private study. For these limited purposes, you may reproduce (print, download or mae copies) the Material without prior permission. All copies must include any copyright notice originally included with the Material. You must see permission from the authors or copyright owners for all uses that are not allowed by fair use and other provisions of the U.S. Copyright Law. The responsibility for maing an independent legal assessment and securing any necessary permission rests with persons desiring to reproduce or use the Material. Please direct questions to archives@drexel.edu

2 AIR RAMPS LOCATION IN HIGH HEAD SPILLWAYS Gabriel Echávez 1 and Gerardo Ruiz ABSTRACT In high head spillways it is necessary to put ramp aerators to avoid damages due to cavitation. The location of the aerators is a critical decision in the spillway design. Too many of them increase costs and produces excessive flow aeration augmenting the depth flow. Since cavitation damages are due to the pressure and flow velocity close to the spillway surface, it is important to consider the boundary layer growth as the fluid goes down the slope of the spillway, and not the mean flow velocity as it is usually done. A convenient way to do this is to introduce V : the velocity at a distance (the roughness) from the surface. With this V a Thoma or Cavitation Number given by hp hv σ = (1) 2 V 2g in which h, pressure head at the point, and h, vapor pressure head of the water, is calculated p v along the spillway and it is compared with an Incipient Cavitation Index, obtained from prototypes with cavitation damages. In the zones in which the Cavitation Number is less than the Incipient Cavitation Index, there is danger of damages due to cavitation and it is necessary to protect them with aerators. From the location of the damages found in the dams of: El Infiernillo, Mexico; Chicoasen, Mexico; and Karum, Iran; an Incipient Cavitation Index of 1.5 is proposed. In the case of isolated irregularities, common in the spillway surfaces, it can be used a similar procedure, but substituting the V by Vb, in which Vb is the velocity at the height of the protuberance when it is against the flow, and to compare this values with Incipient Cavitation Indexes estimated from data found in the literature. Keywords: Spillway, aerator, cavitation, damages. 1. INTRODUCTION In high head spillways it is necessary to put ramp aerators to avoid damages due to cavitation. Pinto (1983,1986) and Arreguin (2005). The location of the aerators is a critical decision in the spillway design. Too many of them increase costs and produces excessive flow aeration augmenting the 1 Professor, Graduate Engineering School, Faculty of Engineering, National Autonomous University of Mexico, México, Alborada Pte. 412, México D.F., MÉXICO (echavez@servidor.unam.mx)

3 depth flow. An insufficient number of them will not protect adequately the spillway surface and may, eventually, become an obstacle to the flow that could even produce a catastrophic situation. Although the use of the aerator has become a common practice Echávez (2001), and many of them have been built and performed adequately for a number of years, there are still several questions in some aspects of their performance that need to be addressed, to reach better and more economical design and operation decisions. Two of these doubts are related to the proper location of the first aerator and the number of them, mainly when the spillway continues in an almost horizontal fashion after a steep slope, situation common in spillways in tunnel. In this paper a practical method to locate the first aerator, based in theoretical considerations and in observations and measurements done in laboratory and prototype, is presented. The method intends to substitute the rules of thumb -such as in spillways of less than 100 m of height, the aerators are not necessary that are used in normal practice- and also includes a criteria to determine the permissible height of isolated irregularities that can be allowed in the high head spillway surfaces. 2. METHOD PROPOSED TO LOCATE THE FIRST AERATOR Since cavitation damages are due to the pressure and flow velocity close to the spillway surface, it is important to consider the boundary layer growth as the fluid goes down the slope of the spillway, and not the mean flow velocity as it is usually done Levi et al (1988). A convenient way to do this is to introduce : the velocity at a distance (the roughness) from the surface. This velocity is V proportional to the shear velocity, V boundary layer thicness. With this, and it is related to the coefficient of local resistance and to the a Thoma or Cavitation Number given by V hp hv σ = (1) 2 V 2g in which h, pressure head at the point, and h, vapor pressure head of the water, is calculated p v along the spillway and it is compared with an Incipient Cavitation Index, obtained from prototypes with cavitation damages. In the zones in which the Cavitation Number is less than the Incipient Cavitation Index, there is danger of damages due to cavitation and it is necessary to protect them with aerators. Observe that the pressure head, h p, in each section, is calculated with the equation h p 2 d V = h p1 + (2) g r where d = water depth, perpendicular to the flow g = gravity acceleration h p1 = vertical projection of the water depth V = mean velocity at the section R = radius of curvature, being r positive, for concave curvature r negative, for convex curvature

4 r infinite, for rectilinear boundary Figure 1 is a drawing with the main variables involved, and in Figure 2, a graph of versus, x, plus experimental points obtained from the literature and from a recent measurement in prototype -described in the next chapter-, is shown. V 2 2gh Figure 1. Spillway profile and variables definition V 2gh V 1.68 = 2 gh log x x/ Arndt, Ippen Bauer Norris Arabutla Glanmaggie Equation (1) Aguamilpa dam Ai Figure 2. Dimensionless local velocity against x/

5 The equation of the curve on the graph, above the experimental values reported in the literature and measured in prototype, which is a conservative one used for design purposes, is V 1.68 = (3) 2 gh log x 3 MEASUREMENTS AND OBSERVATIONS IN PROTOTYPE 3.1 Velocity profile measured in prototype In Figure 2, the point depicted as a blac triangle was measured at the Aguamilpa Dam with a comb of three Prandtl tubes, shown in Figure 3, located at a distance from the spillway crown of 130 m, assuming a roughness = 12 mm. When the discharge per unit width was 425 m 2 s the velocity profile measured at that point is shown in Figure 4. Figure 3. Arrangement of Prandtl tubes to measure the velocity profile in prototype

6 Figure 4. Velocity profile measured in prototype 3.2 Determination of the Incipient Cavitation Index From the damages found in the dams of: El Infiernillo, Mexico, see Figure 5; Chicoasen, Mexico, see Figure 6; and Karun, Iran, Hopping and Mass (1987) it was found an Incipient Cavitation Index of 1.5. That is, for values of σ along the spillway greater than 1.5, as calculated with equations 1 and 2, there were not damages associated to cavitation due to the distributed roughness of the surface in any of the three dams abovementioned. For practical applications, it is recommended to use a value for this Incipient Index of 1.7, to be in the conservative side.

7 Left profile Right profile Figure 5. Main cavitation damage in tunnel No. 3 of El Infiernillo Dam Figure 6. Cast of the erosion due to cavitation, erosion depth in cm In Figures 7 and 8, as an example, graphs of the profile and the Cavitation Index along the operation and emergency spillways of Netzahualcoyotl Dam, show the regions that are at ris of damages due to cavitation, and that may need to be protected with aerators.

8 Figure 7. Figure Isolated irregularities In some cases isolated irregularities, common in the spillway surfaces, remain in regions with high water velocities; and the question arises if they need to be eliminated or reduced and how much it is necessary to do so.

9 Now, a similar procedure can be used, but substituting the V by Vb, in which Vb is the velocity at the height of the protuberance when it is against the flow, and is given by equation 4, and to compare this values with those given in Figure 9. V V b b = 0.68 log + 1 (4) Irregularity Characteristic Velocity Incipient Cavitation Index σ i b V b 2.4 V 1.1 V 1.5 V 1.4 b V b 1.4 b V b 1.6 Figure 9. Characteristic velocity and Incipient Cavitation Indexes for different isolated irregularities. 4 CONCLUSIONS In this wor, a procedure to estimate the exposed areas to cavitation that taes in consideration the surface roughness and the flow conditions near the floor and walls of the spillway is presented. The method is calibrated and validated with observations and data from several prototypes, already in operation, and with measurements of the water velocity, near the floor of the spillway, done in prototype. Finally, incipient cavitation indexes for surfaces of different roughness as well as for different isolated irregularities are proposed, and a more rational general design procedure, to decide whether it is necessary to put aerators or not, and to locate the first one is presented.

10 AKNOWLEDGMENTS This wor was realized in the Engineering Institute of the National Autonomous University of Mexico and in the Engineering and Architecture Faculty of the Juarez Autonomous University of the State of Durango, Mexico. The authors appreciate the material provided by the Federal Commission of Electricity of Mexico. REFERENCES Arreguín, F. (2005). Cavitación y aireación en obras de excedencia, AMH-IMTA, Mexico. Echávez, G. (2001). Aerator of the Trigomil Dam, Mexico, Water Power and Dam Construction, Wilmington, United Kingdom, Vol. 53, May, pp Hopping, P., and Mass, G. (1987). Cavitation Damage on the Karum Dam, Concrete Internacional, USA, pp Levi E., Rodríguez N., Echávez G., Civil Engineering Practice, 5-Volume Encyclopedia, Editors: Cheremisinoff P.N. Cheremisinoff N.P., Cheng S.L.; Capítulo: Solid Fluid Interaction, Vol. 2. Technomic Publishing Company Inc., Pennsylvania, USA, Pinto, N. (1986). Basic hydraulics of shooting flows over aerators, Proceedings Advancements in Aerodynamics, Fluid Mechanics, and Hydraulics, ASCE, June 3-6, Minneapolis, Minnesota, USA, pp Pinto, N. (1983). Noções básicas sobre cavitação e aeração em fluxos de alta velocidade, Notas de aula, Brazil.