8th IAHR ISHS 2020 Santiago, Chile, May 12th to 15th 2020

DOI: 10.14264/uql.2020.590

A Triangle-Wedge Sidewall Design for the Surface Spillway Outlet on a High-Head : Experimental Investigations

W.R. Wei, J. Deng, Z. Tian and F. X. Zhang State Key Laboratory of Hydraulics and Mountain River Engineering University Chengdu, E-mail: [email protected] (corresponding author)

ABSTRACT

To improve the jet diffusion and energy dissipation for the surface spillway in high-head , an optimal design of the outlet structure is studied using scaled experimental model. A symmetrical pair of triangle-wedges is set at the surface spillway outlet to make lateral and vertical contractions at the end cross-sections of the channel. Due to the triangle-wedge shape, the contraction areas with the elevation increase are different for an identical cross-section, and this makes fully contributions to the incoming water head applicability, flow discharge capacity and jet longitudinal diffusion. Based on a series of model tests for different lengths, heights and contraction ratios of the triangle-wedge, the effects of design parameters on the impact pressure on the plunge pool are analyzed. With the increase of the contraction ratio, the mean impact pressure reduces and subsequently increases. An optimal design of contraction ratio can make fully contribution on the energy dissipation in plunge pool. With the increase of the triangle-wedge length, the jet impact gets greater gradually. The contraction effect of triangular-wedge structure on the jet impact is almost established. The deflection of the inclined surface with the increase of triangular-wedge height may improve the lateral contraction, but the reduction on jet impact is limited. The significant decrease of impact for different water discharge confirms the triangular-wedge structure can affect the initial jet shape. This optimal design of outlet sidewalls will give a new option for surface spillways in high-head dams.

Keywords: Outlet Sidewall, high-head dam, impact pressure, energy dissipation, experimental study.

1. INTRODUCTION

With the development of hydraulic technological evolution and hydropower energy consumption, a huge evolution of large reservoirs and high-head dams occurs, and the dam height reaches 300 m with unit flow discharge exceeding 300 m2/s. One of the most important issues for the dam safety is the downstream flood protection. As the water transfers from the reservoir level to the tail-water downstream, the large discharge and high-velocity of the releasing water flow results in massive energy dissipation downstream the dam. To reduce the downstream erosion and improve the foundation protection, the ski-jump energy dissipator combined with a concrete lining plunge pool is the common hydraulic structure design. This design has been applied to different high-arch dams such as Baserca Dam (Spain), Gebidem dam (Switzerland), Ertan dam (China), Jinping-I dam (China), Xiluodu dam (China). The outlet structures deflecting the ski-jump flow are of interest to remove floods with high-head and large discharge from the dam (Chanson 2015). The shape of jet footprint impacting on the plunge pool bottom is important affected by the specific design. The hydraulic characteristics have been obtained using different theoretical analysis and scale models. In high arch dams, surface spillway on the dam is an economical design, and the energy dissipation pattern is jet spreading in the air, plunging in the pool and impacting on the pool bottom (Beltaos and Rajaratnam 1973; Ervine and Falvey 1987). The dynamic pressure magnitude, frequency and fluctuations on the pool floor are the key parameters for the pool depth selection and other technical decisions. For design considerations, the issuance conditions decided by the surface spillway and the outlet shape should be considered. For example, the maximum dynamic pressure on the plunge pool floor is determined by falling height H, water energy head h0, flow discharge per unit width q, flow thickness B, aeration C, tail water depth Y, et al.

pm = f (H, h0, q, B, C, Y…) (1)

Bollaert and Schleiss (2003) summarized a plenty of different investigation data and showed that the relative mean dynamic pressure is a function of the ratio of tail water depth to equivalent jet thickness. Castillo (2006) proposed a family of curves in the function of this parameter by classifying the jet pattern on the basis of the ratio of falling height to jet break-up length. Moreover, different behaviors can be observed between circular and rectangular jets in the case of jet plunging phenomenon. The difference of jet radial diffusion among different jet cross-sectional shapes may result in a strong decrease of mean dynamic pressure for circular jets. Although many empirical relationships developed based on theoretical and model investigations for the estimations of jet impact on stilling basins, these expressions are only applicable to some project cases. Once the coupling effect of flow aeration and thickness is considered, the detailed mean and fluctuation pressure became much more complicated to give a reasonable estimation of jet impingement (Xu et al 2004, Wei et al. 2013). According to the energy dissipation processes, it is acknowledged that flow aeration and turbulence are the mainly governed factors, which highlights the complexity of the energy dissipation phenomenon (Xu, et al. 2002; Manso et al. 2007; Manso et al. 2009; Melo and Pinheiro 2008). Thus, it is urgent to find effective ways to control the water pattern at the outlet. In the present study, an optimal design of the outlet sidewall, the triangle-wedge structure, is conducted for a surface spillway on a high-head dam. Based on a series of scaled model tests, the effects of design parameters, including the length, height and contraction ratio of the triangle- wedge, on the impact pressure on the plunge pool are analyzed. The incoming water head applicability to the triangle-wedge contraction ratio is discussed compared with previous expressions. This optimal design will give a new option for surface spillway outlets and improve the dissipation performance in high-head dams.

Figure 1. Physical process of jet falling impact at a high-head dam (Photo of surface spillway flow discharge at the Jinping-I dam is taken by the authors).

2. DESIGN MOTIVATION

For a high arch dam built in a narrow valley, the principle design of the outlet is to contract the dissipator structure. There are two limitation conditions: 1) the transverse space for energy dissipation is not sufficient; 2) the channel length of surface spillway is too short and the flow velocity is relative low for well ski-jump jet generation. The previous investigation confirms that the jet diffusion along the flow direction can avoid the jets colliding and flood discharge atomization (Liu and Xu 2010). The typical flaring gate piers and slit-type buckets were proposed to give feasible ways as the contracted dissipator (Li et al. 2012). On the other hand, because the short channel length of surface spillway and the contraction structure design, the flow pattern may changes from the supercritical to subcritical flow, and the hydraulic jump occurs in the contracted area. The chocking phenomenon will decrease the flow discharge capacity and the increase the possible souring closed to the dam base. Thus, the optimal design of the surface spillway outlet, the triangle-wedge sidewall, is proposed to achieve a well longitudinal diffusion and energy dissipation performance for a high-head dam.

3. EXPERIMENTAL METHODS

The experimental tests are conducted in State Key Laboratory of Hydraulics and Mountain River Engineering (SCU), China. The surface spillway on an arch dam, triangular-wedge and plunge pool parts are made of polymethyl methacrylate. The falling height from the weir crest of surface spillway to the water surface in the plunge pool is H0 = 3.26 m. The tail water depth is Y = 0.64 m. The bottom angle of spillway is α = 33° with an elevation difference at the end of the surface spillway to the weir crest h = 0.32 m. The detailed design of triangular-wedge sidewalls is shown in Figure 2. From a certain point at the sidewall bottom, the inclined face make the channel get contracted, from the initial channel bottom width B1 to B2 at the end of the surface spillway. The thickness of the triangular-wedge is bottom width b, decreasing to zero at the triangular-wedge height hd with the elevation increase. The distance from the initial contraction point to the end of surface spillway is the triangular-wedge length Ld. In the present study, the initial channel width is a constant B1 = 0.157 m, and the contraction ratios of the triangular-wedge B2/B1 ranges from 0.14 – 0.74, with Ld = 0.09 m – 0.36 m and dd = 0.14 m – 0.26 m.

Figure 2. Photo of the experimental model.

Figure 3. Definition sketch of triangular-wedge structure.

Five flow discharge rate Q are tested with Q = 0.036 m3/s, 0.031 m3/s, 0.023 m3/s, 0.017 m3/s and 0.012 m3/s, and the relative energy head h0 = 0.229 m, 0.209 m, 0.172 m, 0.143 m and 0.114 m. The flow discharge per unit width ranges from q = 0.078 – 0.229 m2/s. The flow rate in the scale model is controlled according to the basic relationship between water depth and flow discharge of the specific model. A stabilization system is used to ensure the water depth in the reservoir with an error of ±1 mm. Thus, it is considered that no perturbation velocities occur into the reservoir during the experimental tests. The jet impact pressure on the plunge pool floor is measured using a series of piezo-resistive pressure sensors (CY201, Test, Inc., China) and an acquisition device (RS485-20, Test, Inc., China). The accuracy of the pressure sensor is 0.1% of the 100 kPa full scale. The

pressure measurement system is calibrated by hydrostatic operation before conducting each test to ensure measurement reliability. The pressure sensor is aligned vertically with the flume floor. In the present study, the floor thickness is only 1cm and the total distance from the piezo-resistive sensing element inside the sensor to the water-bottom interface is about 2 cm, which is significantly short. Thus, on the basis of the incoming jet velocities is relatively low in all experimental tests, the effect of type of connection type on pressure signal measurements can be neglected. An acquisition duration is set as T = 100 s at acquisition frequency F = 100 Hz during the pressure measurements. The measurement points are established both along the centerline and a half of the pool floor. The intervals are set as 0.5–2 cm and these smaller intervals are used to capture the main impact pressure near the jet axis. For the laboratory pressure result, the mean impact pressure coefficient Cp is calculated by the following expression,

Cp = (pm – Y ) / H0 (2) where pm is the maximum mean pressure results obtained from the time-series signal, as shown in Figure 4.

Figure 4. A typical time-series of pressure signal (P = 20.3 KPa).

Compared to the prototype surface spillway, the present model test can be considered as a Froude similarity criterion. The jet pattern and impact properties are similar between the prototype and scaled models. In terms of the scale effect, it is hart to extrapolate the free jet model results to prototype without scale effects, especially considering the effect of jet air-water mixture and break-up level. The scale effect on air-water properties of supercritical flow cannot be neglected regarding the surface tension and viscosity effects in high speed air-water flows (Pfister and Chanson 2014). Dimensional analyses indicate that free jet diffusion depends on the Reynolds number, Weber number, turbulent intensity et al. (Albertson et al. 1950; Chanson 2013). The limitations of dynamic similarity and physical modelling of jets are obtained from the previous investigations for the reduction 2 3 of scale effects (Chanson 2009; Heller 2011). The Weber number We =ρV0 B1/σ should exceed 10 , and the 5 Reynolds number Re = V0B1/ν should exceed 10 , where ρ is the water density and σ is the surface tension between air and water. The V0 is estimated from,

VgHh0002( ) (3)

In the present study, the minimum values of We and Re are 1.80 × 104 and 4.58 × 105, respectively, and these limits are respected. It should be noted that the mean pressure property Cp is used to represent the jet impact performance. Besides, the pressure fluctuation, which is affected by the jet air concentration and detailed bubble size properties, also affects the jet impact into the plunge pool. It is hard to avoid these scale effects of jet aeration because of the scaled model and the reduction of flow turbulence intensity. Thus, the present study focuses on the effects of triangular-wedge structure design on the energy dissipation.

4. RESULTS AND DISCUSSIONS

4.1. Effect of contraction ratio B2/B1

Figure 5(a) shows the effect of triangular-wedge contraction ratio B2/B1 on jet impact Cp on plunge pool floor 2 for h0 = 0.229 m and qw = 0.229 m /s. With the increase of B2/B1, the value of Cp decreases and subsequently increases. This phenomenon indicates that an optimized contraction ratio design of the triangular-wedge is required to obtain a sufficient reduction of jet impact. As the contraction ratio of the triangular-wedge structure change the cross-sectional shape of water flow, this makes different lateral contractions along the elevation, resulting in different contraction performance. For B2/B1 smaller than the optimized design, the contraction effect at the flow bottom is over-acted, and the lateral contracted flow is aggregated at the relative high elevation (in Figure 5(b)). More water is released from the top of free jet, resulting in high impact on the plunge pool. For B2/B1 larger than the optimized design, the lateral contraction of water flow is not sufficient. Under this situation, more water releases at the bottom of triangular-wedge area, little affected by the lateral deflecting constraint.

(a) (b)

Figure 5. (a) Effect of triangular-wedge contraction ratio B2/B1 on Cp; (b) Sketch flow pattern through the 2 triangular-wedge structure. (h0 = 0.229 m and qw = 0.229 m /s)

4.2. Effect of triangle-wedge length Ld and height hd

Figure 6(a) and 6(b) show the effects of triangular-wedge length and height on the jet impact on the plunge pool. With the increase of triangle-wedge length Ld, the mean impact pressure coefficient Cp gets increased, and this trend is independent of the contraction ratio and height of triangular-wedge structure. Because the triangular- wedge length determines the initial change point of the flow streamline, contracting laterally along the streamwise direction, the location close to upstream reduces the lateral contraction performance, resulting in a high jet impact effect on the plunge pool downstream. For the effect of triangular-wedge height hd, the Cp decreases slightly with hd for other identical conditions. As the hd gets about two times greater, the reduction of Cp is smaller than 15%. Thus, for identical length and thickness conditions, the contraction effect of triangular- wedge structure on the jet impact is almost established. The deflection of the triangular-wedge inclined surface may adjust the interior flow pattern and improve the streamwise diffusion, but the reduction on jet impact is limited.

(a) (b)

2 Figure 6. Effects of triangular-wedge (a) length Ld and (b) height hd on Cp (h0 = 0.229 m and qw = 0.229 m /s).

On the basis of jet pattern releasing from the surface spillway outlet with triangular-wedge structure, as shown in Figure 7, the jet gets deflected by the lateral contracted constraint, releasing as a thin and long ski-jump flows. Different parameters of the triangular-wedge structure change the contraction and deflection performance of the jet through the triangular-wedge part. A well diffusion of jet can result in a weak dynamic impact on the plunge pool and improve the safety and reliability of energy dissipation structures. Consequently, the optimal design can be conducted based on the three factors: 1) determination of an optimized contraction ratio (or the thickness) by B2/B1 variation; 2) determination of the triangular-wedge length to reduce the jet impact; 3) determination of the triangular-wedge height to further reduce the jet impact.

Figure 7. An optimal design of the triangular-wedge structure based on the jet pattern.

4.3. Flow discharge application

In Figure 8, the mean pressure coefficient Cp of jet impact increases with water discharge per unit width q. Compared with previous studies (Table 1) about the jet plunging impingement, including rectangular and circular jets, the present jet impingement generally results in a low impact pressure on the plunge pool floor. This is mainly because the lateral contraction effect of the triangular-wedge structure leads to a relative long jet shape in the air. This reduces the water discharge per unit width when the jet impinges the water surface in the plunge pool compared to the previous falling jets without the lateral contraction effect. The reduction effects are more obvious for small water discharges with low water head h0. This is mainly because more water can be contracted from the bottom of the triangular-wedge structure for lower water depths. Moreover, the decrease of Cp for circular jets indicates that this kind of cross-sectional shape may increase the radial diffusion compared to the rectangular jets. For some large flow discharge cases, the Cp properties are close to the circular jet impact performance, and this confirm that the triangular-wedge structure can reduce the jet impact on the plunge pool by affecting the jet shape releasing in the air and impingement diffusion downstream. The defection effects of the triangular-wedge structure change the flow pattern as the water flow discharges into the air and diffuse longitudinally. Due to the present experimental model study, detailed investigation about the performance in prototype and other hydraulic conditions should be further conducted in the further study.

Table 1. Previous studies on plunging jet impact with different analysis domains. References Flow conditions Jet type Year Hartung & Hausler Theoretical analysis Rectangular plunging jet 1973

3 Franzetti & Tanda H0 < 0.31 m, Q < 0.001 m /s, Y < 0.38 m Circular plunging jet 1987 3 Puertas H0 < 5.45 m, Q < 0.081 m /s, Y < 0.80 m Rectangular plunging jet 1994 3 Ervine et. al H0 < 2.63 m, Q < 0.063 m /s, Y < 0.50 m Rectangular plunging jet 1997

Figure 8. Relationship between the flow discharge and jet impact affected by the triangular-wedge structure.

5. CONCLUSIONS

In the present study, a triangular-wedge structure at the surface spillway outlet is proposed to improve the energy dissipation in a high-head dam. Based on a series of experimental tests, the effects of structure parameters on the mean impact pressure are analyzed for an optimal design. An optimized contraction ratio of the triangular-wedge is required to obtain a sufficient reduction of jet impact. The increase of triangular-wedge height leads to a slightly decrease of jet impact, but the reduction caused by the deflection of the triangular- wedge inclined surface limited. With the increase of the triangle-wedge length, the jet lateral contraction gets decreased gradually and the impact pressure increases. The effect of triangle-wedge length on the mean impact pressure coefficient is independent of its contraction ratio and height. The significant decrease of impact for different water discharge confirms the triangular-wedge structure can affect the initial jet shape as it releases in the air and impingement diffusion downstream. This optimal design of outlet sidewalls will give a new option for surface spillways in high-head dams. Due to the present experimental model study, detailed investigations about the performance in prototype and other hydraulic conditions should be conducted in the further study.

6. ACKNOWLEDGMENTS

The authors thank the financial support from the National Natural Science Foundation of China (grant No. 51979183) and the Key Program of the National Natural Science Foundation of China (grant No. 51939007).

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