HYDRAULIC CHARACTERISTICS OF SLIT-TYPE ENERGY DISSIPATERS*

WU Jian-hua, MA Fei, YAO Li

College of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing 210098, China, Email: jhwu@hhu.edu.cn

(Received September 19, 2012, Revised November 7, 2012)

HYDRAULIC CHARACTERISTICS OF SLIT-TYPE ENERGY DISSIPATERS*

WU Jian-hua, MA Fei, YAO Li

College of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing 210098, China, Email: jhwu@hhu.edu.cn

(Received September 19, 2012, Revised November 7, 2012)

Slit-Type Energy Dissipater (STED) has been a kind of important devices for energy dissipation. The flow through the STED is longitudinally extended and the velocity is decreased by means of the cross-section increase of the flow, which is closely related to geometric and hydraulic parameters of the STED. Therefore, it is necessary to investigate and control the hydraulic conditions through the STED, including the nappe section form, the conversion condition, and the effect of energy dissipation with the geometric and hydraulic parameters. In the present work, “I-type” and “T-type” nappe forms were experimentally classified, the conversion conditions of the nappe forms were empirically provided, and the effects of geometric parameters of the STED on energy dissipation were roughly analyzed. It is concluded that the contraction angle of the STED is a key factor influencing the hydraulic characteristics of the STED.

contraction angle, energy dissipation, fin, nappe form, shock wave, Slit-Type Energy Dissipater (STED)

Introduction

In recent 20 years, the rapid developments of large-scale hydropower projects with high dams have taken place in China[1,2]. It brings about tremendous pressures for the project constructions. The conventional approaches of energy dissipation and scour control have faced new challenge due to large unit discharge and deep gorge topography. In this aspect, Slit-Type Energy Dissipaters (STED) are proved to be of high efficiency on the basis of their geometric characteristics[3,4]. The flow is transversely contracted and longitudinally extended when it leaves the edge of the STED, and the energy dissipation ratio greatly increases making use of air entrainment, and violent turbulence of the flow[5]. Some of hydropower projects have used this kind of the STEDs in their release works, such as the Longyangxia, Lijiaxia, Geheyan, Manwan, and Shuibuya Projects in China[6,7], the Cabril Project in Portugal, and the Almendra Project in Spanin[8].

There are some investigations about the STEDs[9].Early in 1990, Li and Liu[10]proposed a hydraulic calculation method of the STEDs. Further investigations were conducted by Zhang and Wu[11], Yang[12], Dai and Ning[13], Boss and Hager[14], and Charles[15]. Considering the effect of flow aeration, Liu and Ni[16]suggested the estimation of the jet length with a reduction coefficient.

Liu and Qu[17]observed the section form of the nappe downstream of the STEDs in their physical model tests. It was noticed that, along the flow direction, there are three kinds of section forms of the nappe, i.e., rectangular compact section, spreading and breaking ones. The rectangular compact section appears at the position just leaving the edge of the energy dissipater, then the spreading form exists on the top due to the turbulence and air entrainment and in the low part due to the effect of the gravity, and further, the breaking one occurs and its mushroom type section is produced with the two-side drops on the top of the section. It should be reminded that those section forms occur only at various positions along the flow direction.

In fact, there are the changes of the nappe forms of the flow, which are related to the shock waves brought about by the STEDs. Meanwhile, there are also the fins beneath the nappe in certain conditions ofthe flow. Hence it is necessary to determine the nappe forms and the hydraulic characteristics of the flow for the designs of the STEDs.

The objectives of the present work are to investigate the nappe forms and the hydraulic characteristics of the flow through the STEDs by physical model experiments, and to establish the empirical expression of the conversions of the above-mentioned nappe forms.

1. Experimental set-up and methodology

1.1 Experimental set-up

The experiments were conducted at the highspeed flow laboratory at Hohai University (Nanjing, China). The experiment model was designed on the basis of a middle outlet with the scale of 1/40 for the Shannipo Hydropower Project. The working section of the STED, made from Perspex, is 0.15 m wide and 1.10 m long, and the bottom angle is –17.15oto the horizontal plane. The maximum available discharge is 135 l/s, and the water head (H) varies from 0.4 m to 1.6 m (see Fig.1).

Fig.1 Experimental set-up

Fig.2 Sketch of flow through STED

1.2 Experimental cases and methodology

Figure 2 is the sketch of the flow from a STED, in which Lj1and Lj2are the lower and upper surface lengths of the nappe, respectively, d is the approach flow depth, e=0.25m, is the vertical distance of the bottom to the measured plane, andβ= arctan(e/Lj1), is the fin plunging angle. Figure 3 shows the geometry of the STED, where B andb are the widths before and after the contraction section, respectively, and B=0.15m, b/B is the contraction ratio,θ=arctan[(B-b)/2L], is the contraction angle, L is the length of the contraction section.

Fig.3 Sketch of STED geometry

Table 1 Experimental cases and parameters of models

Table 1 lists the experimental cases and the geometric parameters of the STED model. There are two kinds of geometric variables, i.e., b and L. The cases were designed to investigate the influences of the geometric variables of the STED on the nappe form and the fin, as well as the hydraulic parameters. Cases M1, M2 and M3 keep b constant, and in cases M1, M4 and M5, L is the same. In the experiments, the Froude number varies from 2.02 to 3.49. The parameters H,Lj1, Lj2and d were directly measured by steel ruler.

2. Experimental results and discussions

2.1 Observation of flow

The flow upstream of the STED is the one of open channel with hydrostatic pressure distribution. Entering into the contraction section, the flow narrowed immediately and expanded vertically. The rapid shock waves are produced due to the effects of the sidewall contraction, and have significant effects on the flow.

Except the section forms along the flow described by Liu and Qu[17], it could be observed that, there are two kinds of nappe forms under the conditions of different STED geometry and Froude numbers, i.e.,“I-type” and “T-type” nappe sections (see Fig.4). Therapid shock waves are brought about by the contraction of the STED. The “I-type” nappe form appears at low Froude number, while the “T-type” nappe form occurs when the flow passes through STED with large Froude number. The type of the flow, obviously, is related to the STED geometry and Froude number, and there are the threshold values of the conversions of the types of flows.

Fig.4 Nappe forms

Meanwhile, the fins beneath the flow were observed in certain geometric and hydraulic conditions, and they should be noticed. The fins have high speed similar to the flow although they are thinner than the nappe body.

2.2 Fins

The fins beneath the flow are a kind of specific phenomena of the flow from the STED. In the present work, the bottom of the outlet of the STED was designed as –17.5o, and the boundary of the fins was expressed by the lower surface of the nappe measured in β. The range between –17.5º of the bottom and angle β was defined as the fins. From the experiments, the fins are thinner than the nappe body, and increase longitudinally the section of the flow.

Figures 5 and 6 are the variations of the lower surface measured for β and the range of the fin Δβ with the Froude number (Fr), respectively. Firstly, eitherβ or Δβ, varies linearly with Fr, but the variations in them are small. The maximum valueso, for the angles β and Δβof case M1, are only 3.3 from 2.31 to 3.49 of Fr. Secondly, as is shown in Table 1, the contraction angle (θ) is the key factor resulting in the fin, and if it is smaller than a certain value, there does not exist the fin, for example, θ＜8.84ofor case M3. The fins occur if θ≥11.31ofor case M2. The flow extends longitudinally, and then the lower surface angle ()β, and the range (βΔ) of the fins increase as θ increases (see Figs.5 and 6). Finally, both β and βΔ increase mainly with θ, and the increment of β (or)βΔ is about 4ofor the increase of each 3o. So, it is necessary to control the contraction angle to avoid the fins beneath the flow.

Fig.5 Variation of β with Fr

Fig.6 Variation of βΔ with Fr

2.3 Nappe form and conversion

As stated above, the nappe sections of the flow could be divided into two kinds of the forms, i.e., the“I-type” and “T-type” sections. The experiments demonstrated that the nappe form is related to the geometric parameters of the STED and the hydraulic parameters of the flow through the STED.

Fig.7 Variation Lj2/d with Fr at various contraction lengths

Fig.8 Variation Lj2/d with Fr at various contraction widths

Figures 7 and 8 exhibit the variations of the upper surface length (Lj2/d) of the nappe with the Froude number (Fr) at the various contraction lengths (L) and widths (b), respectively. It could be seen that Lj2/d increases approximately linearly with Fr for either lengths (L) or widths (b) of the contraction section. The effects of lengths (L) or widths (b) are all owed to the results of the contraction angle(θ). The shorter L or smaller b produces the larger Lj2/d for the same Fr . On the other hand, it could be observed that, there are the threshold values of the conversions of the nappe form of the flow for each geometric STED with the change of Fr, stood for by the dots with “T” (see Figs.7 and 8).

The threshold values, from Fig.7, are 2.31, 2.58 and 3.37 of (Fr )thres, respectively, for cases M1, M2 and M3. It means that the conversions of the nappe forms occur from the “I-type” to the “T-type” if the Froude numbers reach the magnitudes above mentioned. The nappe forms stay in the extent of the “I-type” when Fr＜(Fr)thres, and the nappe form of “T-type” appears if Fr＞(Fr)thres. The similar phenomena of the nappe form conversions appear for cases M1, M4 and M5 (see Fig.8). Those conversions of the nappe forms, naturally, owe to the effect of the rapid shock waves resulted from the contraction of the STEDs. The strong rapid shock waves will bring about “T-type” nappe form of the flow with the top crown of the nappe.

Meanwhile, the effects of the contraction length or width result in the changes of the contraction angle of the STED, and then the rapid shock waves. The small contraction angle decreases (Fr )thresfor either cases M1, M2 and M3 or cases M1, M4 and M5 (see Figs.7 and 8).

Figure 9 shows the variation of Lj2/d with (Fr )thresfor the comprehensive geometric parameters, including all the cases in Table 1. Regression analysis for the data presents the limit of the conversions of the nappe forms. Using the data of Fig.9, the best fitting is

where (Lj2/d )thresis the upper surface length corresponding to the threshold values of (Fr)thres. Thus, the chart of Lj2/d-Fr could be divided into two parts, i.e., the “T-type” nappe form zone above the limit and the “I-type” one below limit.

Fig.9 Conversion of nappe forms

2.4 Energy dissipation

To compare the effects of energy dissipation for various geometric and hydraulic parameters of the STEDs, the total energy (E) at the measured plane could be defined as

where z=0 for the measured plane,p/γ=0 due to the free surface flow, α≈1, g=9.81m3/s , and vis the average velocity of the flow. Thus, Eq.(2) could be rewritten as

Assume that for all the cases listed in Table 1, there are the similar section shapes of the flow at the measured plane, then v equals to approximately

where Q is the discharge, w the width of the flow,and ΔL=Lj2-Lj1the longitudinal length of the flow section. If the widths of the flows are roughly the same for two cases, then the effects of the energy dissipation (η) could be compared by

Figure 10 shows the variation of ΔL/d with Frfor the cases in Table 1. It could be seen that there are differences in various cases except M2 and M4, and the contraction angle is the key factor influencing ΔL/d , then the effectiveness of the energy dissipation. By making use of the data from Fig.10, it could be estimated that for cases M1 and M3,η= 0.51 and 0.43 at Fr=2.5 and 3.5, respectively.

Fig.10 Variations of /LdΔ with Fr

3. Conclusions

For the STED, it is the contraction angle that could bring about the rapid shock waves, and then produce two kinds of the nappe forms of the flow, i.e., the “I-type” and “T-type” nappe forms. Meanwhile, the fins beneath the nappe could appear if the coontraction angle is large enough, such as θ＞11.31. On the other hand, the contraction angle is also a key factor influencing the effects of the energy dissipation of the STED.

There exist the threshold values of the conversion of the nappe forms, which are related to (Fr )thresfor various geometric parameters of the STED. Equation (1) gives the empirical expression of those conversions suitable for the geometries of the STEDs in Table 1.

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10.1016/S1001-6058(11)60316-8

* Project supported by the National Natural Science Foundation of China (Grant No. 51179056).

Biography: WU Jian-hua (1958-), Male, Ph. D., Professor