Flow Chocking Characteristics of Leak-Floor Flip Buckets
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 Dissipater1 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.
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 ≤ h_{o} ≤ 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 = v_{o}/(gh_{o})^{1/2} was generated by the jet box and the average approach flow velocity v_{o} = Q/bh_{o} = q/h_{o} (q is the unit discharge), was adjusted by the working head.
Test program with basic parameter variation
Cases | b (m) | θ (°) | S | h_{o} (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
Experimental observations of flow choking regimes
Cases | h_{o} (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 F_{cri}, 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/h_{o} 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/h_{o} and the area ratio S = lb/LB are considered as the main parameters influencing the flow choking characteristics.
The limitations of the above equations are 0 ≤ S ≤ 0.5 for the bucket gap area ratio and 0.8 ≤ w/h_{o} ≤ 4.1 for the relative bucket height.
5 Discussions
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/h_{o}. Besides, it also can be concluded that when S ≥ 0.33 and w/h_{o} ≤ 0.81, or S ≥ 0.47 and w/h_{o} ≤ 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/h_{o} ≤ 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/h_{o} ≤ 0.81, or S ≥ 0.47 and w/h_{o} ≤ 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 F_{cr1} and F_{cr2} 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/h_{o} ≤ 0.81, or S ≥ 0.47 and w/h_{o} ≤ 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.
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