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Flow Chocking Characteristics of Leak-Floor Flip Buckets

  • Shu-fang LiEmail author
  • Ji-wei Yang
Conference paper
Part of the Environmental Earth Sciences book series (EESCI)

Abstract

Leak-floor flip bucket is a new type of flip bucket recently proposed. It has the advantages of decreasing flow choking on the bucket in small flow regimes and improving energy dissipation by a typical long-narrow nappe. However, if the structure parameters are designed unreasonably, flow choking may also occur on the bucket if the impact location of the lower jet trajectory is too near to the base of the structure, and will threaten the safety of the dam. The purpose of this paper is to study the critical conditions when flow choking begins to disappear or appear on the leak-floor flip bucket, during the increasing and decreasing discharge regimes, respectively. Five leak-floor flip bucket models were conducted, and one circular-shaped flip bucket was prepared for comparison. The critical conditions were investigated under a systematic variation of the approach flow depth, gap width and gap length. It concludes that the critical Froude numbers are primarily influenced by the relative bucket height and the area ratio of the gap; empirical equations for the prediction of critical conditions are obtained and conformed to the test data reasonably.

Keywords

Leak-floor flip bucket Flow choking Critical condition Dissipater 

1 Introduction

Ski jumps are a major element of high dam spillways or tunnel outlet for its satisfactory energy dissipation, especially when the velocity is larger than about 15–20 m/s [1, 2]. Many types of flip buckets were designed as ski jump generators. After the traditional continuous circular-typed (CCT) flip bucket [3, 4, 5, 6], a series of different types of energy dissipaters such as slit-type flip bucket [7], triangular-shaped flip bucket [8, 9, 10] and deflector dissipaters [11] were proposed. However, a significant disadvantage of the mentioned bucket is the increased level of local flow choking, which is the breakdown of supercritical flow and a local hydraulic jump due to small approach Froude number and the presence of the bucket. When flow choking occurs, the water flow on the bucket is unstable, the jet trajectory impinges almost vertical and causes significant scour at the toe of the dissipater. Further, the choking makes the hydrodynamic and fluctuation pressures on the sidewalls much greater, thus flow choking must be carefully checked.

Leak-floor (LF) flip bucket has firstly been proposed by Deng [12] (Sichuan University, China) in 2009 to improve flow choking, energy dissipation and impact location. It is made up of a curved bed and two side walls, with a gap in the center axis of the bed, and that the length of the two beds which connect the two side walls can be designed to be the same or different, and the bed may be curved or distorted. As its plan view is like a swallowtail, it is also called the swallowtail-type flip bucket. Figure 1a gives a specific LF flip bucket with an equal side wall length proposed by Deng [12]. The LF flip bucket mainly has three advantages as a dissipater: (1) it can decrease flow choking on the bucket and reduce the incipient ski-jump discharge; (2) it makes the water jet diffuse in the longitudinal direction due to the existence of the gap, and reduces the pressure that effects on the side walls; and (3) by changing the length of the two side walls or the bed forms, it can adjust the jet direction into the downstream water flexibly, and adapt to complex terrain conditions to protect the banks of the downstream river.
Fig. 1

Schematic view of leak-floor flip bucket a proposed by Deng [12]; b the present research

The LF flip bucket has firstly been used in the right spillway tunnel of Jinping I hydropower project in China [13], and is also being used in the testing stage of Nam Ngiep II spillway [14]. In 2015, Deng [15] studied the flow pattern, the formation and the mechanism of the LF flip bucket based on experiments and numerical simulation. Until now, several questions have so far not been systematically addressed, such as flow choking characteristics, cavitations, energy dissipation, and so on. Although the flow choking characteristic is somewhat not as important as the other problems, the research on it will fill in the gaps in the systematic study of LF flip bucket. In this paper, the flow choking characteristics of LF flip bucket are experimentally investigated. As a preliminary research, this paper only considered a simple condition with equal side bucket length and an axis symmetric gap as shown in Fig. 1b.

2 Experimental Setup

The experiments were conducted in a rectangular channel as described by Wu et al. [16]. It involved a horizontal approach channel to simplify the research. It is 1.25 m long, 0.15 m wide and 0.38 m high. Water was pumped from a laboratory sump to a water tank and then entered the horizontal approach channel. The maximum pump capacity was 400 Ls−1, and the working head was about 1.50 m.

The discharge Q was measured by discharge measurement weir at the end of the tail water channel. The flow depth in the scope of 0.04 m ≤ ho ≤ 0.18 m was controlled by a radial sluice gate, which separates the pressure and the free-surface flow section at the inlet of the channel, approach Froude number Fr = vo/(gho)1/2 was generated by the jet box and the average approach flow velocity vo = Q/bho = q/ho (q is the unit discharge), was adjusted by the working head.

The test model, made of Perspex, including five LF flip buckets inserted at the end of the channel, and one circular-shaped bucket was tested for comparison. Figure 1b gives a schematic view of LF flip bucket, where the width B = 0.15 m, the side bucket radius R = 0.50 m and deflection angle β = 45° were fixed. The gap deflection angle θ and the gap width b was changed for θ = 0°, 15° and 30°; b = 0.03, 0.05 and 0.07 m, with the gap area ratio coefficient S = lb/BL changed accordingly. Table 1 lists the experimental cases and geometric parameters in this paper, in which case M1 is a CCT flip bucket, and cases M2 to M5 are LF flip buckets.
Table 1

Test program with basic parameter variation

Cases

b (m)

θ (°)

S

ho (m)

M1

0

0

0

0.04, 0.07, 0.10, 0.18

M2

0.05

30

0.11

M3

0.05

15

0.22

M4

0.05

0

0.33

M5

0.03

0

0.20

M6

0.07

0

0.47

3 Observations of Flow Choking

Figure 2 shows flow choking regimes for all the cases. From visual observations, several aspects can be derived: for the CCT flip bucket of case M1, a hydraulic jump occurs on the bucket, associated with significant air entrainment at the air-water interface, water depth on the bucket increasing dramatically and even part of the turbulent roller climbs over the side walls, the outlet flow flapping sharply, with a jet trajectory impinges almost vertical at the toe [2]. This situation must be avoided in practical engineering because it will endanger the hydraulic structure’s foundation; As for the LF flip bucket,  case M2 has almost the same flow choking regime as M1 except it is a little weaker, and has a small fin below the nappe because of the small gap on the bucket bed and a small part of water flow from the gap; as for case M3, when the gap deflection angle is decreased to θ = 15°, a fully developed hydraulic jump still exists on the bucket, but the surface turbulence is much weaker than M1 and M2, and the fin extends longitudinal along the gap; when decrease θ to 0° as is the case for M4 (Fig. 2d), there is only a little water block near the bucket outlet. If seen from the plan view (Fig. 3), it can be found that, shock waves intersect on the axis when the water flow direction changed by the gap; observations from Fig. 2e, f found that, when the gap width is decreased to b = 0.03 m, a slight surface hydraulic jump appears again; but if the gap width is enlarged to b = 0.07 m, the hydraulic jump is then replaced by shock waves once again. It can be obtained from the experiments that the shock wave height is decreased with the increasing of the gap width b.
Fig. 2

Flow choking a M1: b = 0 m, θ = 0°, Fr = 1.97; b M2: b = 0.05 m, θ = 30°, Fr = 1.91; c M3: b = 0.05 m, θ = 15°, Fr = 1.54; d M4: b = 0.05 m, θ = 0°, Fr = 1.22; e M5: b = 0.03 m, θ = 0°, Fr = 1.64; f M6: b = 0.07 m, θ = 0°, Fr = 1.11

Fig. 3

Plan view of shock waves for M4: ho = 0.04 m

In conclusion, the flow choking regimes of LF flip bucket can be divided into three types by visual observation: strong hydraulic jump (SHJ) (Fig. 2a, b), weak hydraulic jump (WHJ) (Fig. 2c, e) and shock wave (SW) flow choking (Fig. 2d, f). The first two situations need special consideration in hydraulic operation, but the last can be ignored. Table 2 lists all the flow choking cases in the experiments.
Table 2

Experimental observations of flow choking regimes

Cases

ho (m)

Flow choking types

M1

0.04–0.18

SHJ

M2

0.04–0.18

SHJ

M3

0.04–0.18

WHJ

M4

0.04–0.10

SW

0.18

WHJ

M5

0.04–0.18

WHJ

M6

0.04–0.18

SW

Similarly, as with the CCT flip bucket, flow choking also occurs in the decreasing discharge regime, and it is just the opposite process as the increasing discharge regime. As the decreasing discharge process is always less important [17] in the hydroelectric operation, it will not be discussed here.

4 Critical Flow Choking Froude Number

The flow choking characteristics can be defined by the critical Froude number Fcri, where i = 1 and 2 represent that flow choking completely disappeared in the increasing discharge regime and appeared in the decreasing discharge regime, respectively. From Heller’s [4] result it can be obtained that the relative bucket height w/ho is the main influence parameter of the flow choking characteristics for the CCT flip bucket, and it can be noted from Wu’s [16] experimental results that the outlet width, the contraction angle and the approach flow depth are important in the critical flow choking Froude number of the slit-type flip bucket. As for the LF flip bucket, the relative bucket height w/ho and the area ratio S = lb/LB are considered as the main parameters influencing the flow choking characteristics.

The critical Froude numbers Fcri were recorded during experiments. The experimental results were plotted as Fcri versus w/ho (Fig. 4a, b). It can be found that both Fcr1 and Fcr2 are increasing with w/ho, and Fcr1 is obviously larger than Fcr2. This is reasonable as w enhances the flow depth choked on the bucket and a larger momentum is needed to push the choked flow jump out of the bucket. Otherwise, the depth below the hydraulic jump increases with the flow depth ho and it is relatively easy to push the hydraulic jump out of the bucket. This is similar to the result of the CCT flip bucket proposed by Heller [4]. It can be obviously observed that the critical Froude numbers of the LF flip buckets are much smaller than the corresponding CCT flip buckets (Fig. 4). Figure 5a, b relate to Fcr1 and Fcr2 versus the gap area ratio parameter S for LF flip buckets of cases M2 to M6. Both Fcr1 and Fcr2 are decreased with S when w/ho are fixed.
Fig. 4

Critical Froude numbers versus w/ho: a increasing discharge regime; b decreasing discharge regime

Fig. 5

Critical Froude numbers versus S: a increasing discharge regime; b decreasing discharge regime

Considering all of the parameters above, a combined parameter K = (1−S) (w/ho) was proposed and Fig. 6a, b relate to Fcr1 and Fcr2 versus K, in which, the dashed line represents results of ho = 0.04 m, and the solid line represents ho = 0.07, 0.10 and 0.18 m. For ho = 0.04 m, the data can be expressed as:
Fig. 6

Critical Froude number versus K = (1−S)(w/ho): a Increasing discharge regime; b decreasing discharge regime

$$F_{cr1} = 1.63K - 0.93$$
(1)
$$F_{cr2} = 0.79K + 1.01$$
(2)
with the correlation coefficients R2 = 0.95 for Fcr1 and R2 = 0.92 for Fcr2.
For cases when ho = 0.07, 0.10 and 0.18 m, the critical Froude number can be expressed as:
$$F_{cr1} = 2.37K^{0.75}$$
(3)
$$F_{cr2} = 2.16K^{0.66}$$
(4)
with both correlation coefficients R2 = 0.97.

The limitations of the above equations are 0 ≤ S ≤ 0.5 for the bucket gap area ratio and 0.8 ≤ w/ho ≤ 4.1 for the relative bucket height.

Figure 7 is the comparisons of the calculated critical Froude number Fcric by Eqs. (1)–(4) with the experimental results; the dotted lines represent the ranges of 10% error. The results show that the error is mostly less than 10% and Eqs. (1)–(4) have high precision in the critical flow choking Froude number.
Fig. 7

Comparisons between the measured (x-axis) and calculated (y-axis) critical Froude number: a increasing discharge regime and Fcr1c is calculated by Eq. (1) and Eq. (3); b decreasing discharge regime and Fcr2c is calculated by Eqs. (2) and (4)

5 Discussions

Scale effects may exist when the approach flow depth is too small, such as when ho = 0.04 m, resulted in a different relationship of Fcri and K, thus Eqs. (1) and (2) actually have no practical meanings and just for reference only. Equations (3) and (4) can be expressed in a uniform format as:
$$F_{cri} = a_{i} \left( {\frac{w}{{h_{0} }}\left( {1 - S} \right)} \right)^{{b_{i} }}$$
(5)
where a1 = 2.37, b1 = 0.75 for Fcr1 and a2 = 2.16, b2 = 0.66 for Fcr2.

The experimental data of the CCT flip bucket was also included in Fig. 6 while considering S = 0. This represents that the critical flow choking Froude number, for both LF flip bucket and the CCT flip bucket, has the same tendency with Eq. (5).

From the experiments, it can be shown that the flow choking decreased with S but increased with w/ho. Besides, it also can be concluded that when S ≥ 0.33 and w/ho ≤ 0.81, or S ≥ 0.47 and w/ho ≤ 4.06, only slightly a weak shock wave appeared, and these situations are far-fetched to be called flow choking, can be considered as reasonable situations in practical engineering. In addition, the design standard suggested that 4 ≤ R/ho ≤ 10 for CCT flip bucket [18]. Then, considering from the aspect of avoiding flow choking, the LF flip bucket can be designed as S ≥ 0.33 and w/ho ≤ 0.81, or S ≥ 0.47 and w/ho ≤ 4.06. Additionally, the trajectory distance must be avoided being too close to cause scour at the toe of bucket.

6 Conclusions

Flow choking regimes and critical conditions of LF flip buckets are explored experimentally. The critical flow choking Froude numbers Fcr1 and Fcr2 are focused on and empirical equations to calculate them are obtained. Comparisons between the empirical equations and the test data showed that the paper’s equations are reasonable in critical flow choking prediction, both for LF and CCT flip buckets, and can be used for hydraulic design as a preliminary estimation. Furthermore, a preliminary design standard of S ≥ 0.33 and w/ho ≤ 0.81, or S ≥ 0.47 and w/ho ≤ 4.06 for LF flip bucket was proposed from the consideration of avoiding flow choking.

Notes

Acknowledgements

This research was financially supported by the National Science Foundation. Thanks to the guidance of Professor Jianhua Wu and Fei Ma in Hohai University. Thanks to the proposal of Professor Jiwei Yang in Hebei University of Engineering.

References

  1. 1.
    Grigoryan, K.A.: Calculation of the regime of submergence of a ski-jump bucket behind a deep outlet. Hydrotech. Constr. 18(7), 313–316 (1984).  https://doi.org/10.1007/BF01427682CrossRefGoogle Scholar
  2. 2.
    Juon, R., Hager, W.H.: Flip bucket without and with deflectors. J. Hydraul. Eng. ASCE 126(11), 837–845 (2000).  https://doi.org/10.1061/(ASCE)0733-9429(2000)126:11(837)CrossRefGoogle Scholar
  3. 3.
    Butakov, A.N.: Determination of the optimal height of the bucket lip of a ski-jump spillway. Hydrotech. Constr. 15(6), 335–341 (1981).  https://doi.org/10.1007/BF01432568CrossRefGoogle Scholar
  4. 4.
    Heller, V., Hager, W.H., Mior, H.E.: Ski jump hydraulics. J. Hydraul. Eng. ASCE 5, 347–355 (2005).  https://doi.org/10.1061/(ASCE)HY.1943-7900.0001178CrossRefGoogle Scholar
  5. 5.
    Khatsuria, R.M.: Discussion of “ski jump hydraulics” by Valentin Heller, Willi H. Hager and Hans-Erwin Minor. J. Hydraul. Eng. 131(5), 347–355 (2005).  https://doi.org/10.1061/(ASCE)0733-9429(2006)132:10(1115)CrossRefGoogle Scholar
  6. 6.
    Savic, L., Kuzmanovic, V., Milovanovic, B.: Ski jump design. Water Manag. 163(WM110), 523–527 (2010).  https://doi.org/10.1680/wama.900052CrossRefGoogle Scholar
  7. 7.
    Wu, J.H., Yao, L., Ma, F.: Hydraulics of a multiple slit-type energy dissipater. J. Hydrodyn. 26(1), 86–93 (2014).  https://doi.org/10.1016/S1001-6058(14)60010-XCrossRefGoogle Scholar
  8. 8.
    Steiner, R., Heller, R.V., Hager, W.H., et al.: Deflector ski jump hydraulics. J. Hydraul. Eng. 134(5), 562–571 (2008).  https://doi.org/10.1061/(ASCE)0733-9429(2008)134:5(562)CrossRefGoogle Scholar
  9. 9.
    Pfister, M., Hager, W.H.: Deflector-generated jets. J. Hydraul. Res. 47(4), 466–475 (2009).  https://doi.org/10.3826/jhr.2009.3525CrossRefGoogle Scholar
  10. 10.
    Pfister, M., Hager, W.H.: Deflector-jets affected by pre-aerated approach flow. J. Hydraul. Res. 1–11 (2012).  https://doi.org/10.1080/00221686.2012.657875
  11. 11.
    Lucas, J., Hager, W.H., Boes, R.M.: Deflector effect on chute flow. J. Hydraul. Eng. ASCE 139(4), 444–449 (2013).  https://doi.org/10.1061/(ASCE)HY.1943-7900.0000652CrossRefGoogle Scholar
  12. 12.
    Deng, J., Liu, S.J., Zhou, Z., et al.: A swallowtail—type of bucket. 2009.12.25, Application number: 200910263563.9. (in Chinese)Google Scholar
  13. 13.
    Wang, J.M., Duan, S.H., Zheng, J.: Key technical problems in the construction of Jinping I high arch dam. Technical Progress in the Dam Construction and Management, The Chinese Association of Dam, Sichuan China, 2012:11. (in Chinese)Google Scholar
  14. 14.
    Chen, X.M., Wang, Z.M., Wang, X.B., et al.: Key techniques in the Nam Ngiep II hydropower construction. Technical Progress of high dam construction and operation management, The Chinese Association of Dam, Guiyang, China, 2014.1016. (in Chinese)Google Scholar
  15. 15.
    Deng, J., Yang, Z.L., Tian, Z., et al.: A new type of leak-floor flip bucket. Sci. China Technol. Sci. 1–8 (2015).  https://doi.org/10.1007/s11431-015-5925-x
  16. 16.
    Wu, J.H., Wan, B., Ma, F.: Flow choking characteristics of slit-type energy dissipaters. J. Hydrodyn. 27(1), 159–162 (2015).  https://doi.org/10.1016/S1001-6058(15)60468-1CrossRefGoogle Scholar
  17. 17.
    Liu, Z.R., Jiang, Y.Y., Liu, G.C., et al.: Arc radius and critical jet flow discharges in the ski jump energy dissipaters. Proc. Energy Dissipation Eros. Control 441–448 (1980). (in Chinese)Google Scholar
  18. 18.
    Design specification for concrete gravity dams. Water Conservancy Industry Standard of the People’s Republic of China, SL319-2005. (in Chinese)Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  1. 1.College of Water Conservancy and Hydropower EngineeringHebei University of EngineeringHandanChina
  2. 2.College of Water Conservancy and Hydropower EngineeringHohai UniversityNanjingChina

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