**E**ff**ect of the Area Contraction Ratio on the Hydraulic Characteristics of the Toothed Internal Energy Dissipaters**

#### **Ting Zhang 1, Rui-xia Hao 1,\*, Xiu-qing Zheng <sup>1</sup> and Ze Zhang <sup>2</sup>**


#### Received: 16 May 2019; Accepted: 3 July 2019; Published: 9 July 2019

**Abstract:** Toothed internal energy dissipaters (TIED) are a new type of internal energy dissipaters, which combines the internal energy dissipaters of sudden reduction and sudden enlargement forms with the open-flow energy dissipation together. In order to provide a design basis for an optimized body type of the TIED, the effect of the area contraction ratio (ε) on the hydraulic characteristics, including over-current capability, energy dissipation rate, time-averaged pressure, pulsating pressure, time-averaged velocity, and pulsating velocity, were studied using the methods of a physical model test and theoretical analysis. The main results are as follows. The over-current capability mainly depends on ε, and the larger ε is, the larger the flow coefficient is. The energy dissipation rate is proportional to the quadratic of Re and inversely proportional to ε. The changes of the time-averaged pressure coefficients under each flow are similar along the test pipe, and the differences of the time-averaged pressure coefficient between the inlet of the TIED and the outlet of the TIED decrease with the increase of ε. The peaks of the pulsating pressure coefficient appear at 1.3 D after the TIED and are inversely proportional to ε. When the flow is 18 l/s and ε increases from 0.375 to 0.625, the maximum of time-averaged velocity coefficient on the line of *Z*/*D* = 0.42 reduces from 2.53 to 1.17, and that on the line of *Z*/*D* = 0 decreases from 2.99 to 1.74. The maximum values of pulsating velocity on the line of *Z*/*D* = 0.42 appear at 1.57*D* and those of *Z*/*D* = 0 appear at 2.72*D*, when the flow is 18 l/s. The maximum values of pulsating velocity decrease with the increase of ε. Finally, two empirical expressions, related to the flow coefficient and energy loss coefficient, are separately presented.

**Keywords:** toothed internal energy dissipaters (TIED); area contraction ratio; over-current capability; energy dissipation rate; time-averaged pressure; pulsating pressure; time-averaged velocity; pulsating velocity

#### **1. Introduction**

The internal energy dissipater effectively reduces the downstream flow speed, smoothly connects the downstream flow, and avoids the erosion of the river channel by a traditional energy dissipater in a water conservancy project with high water head and high flow. This is because it converts the large area effect of high-speed water flow into a local energy dissipation effect. The most common form of internal energy dissipation is the energy dissipaters with sudden reduction and sudden enlargement. The energy dissipaters with the sudden reduction and sudden enlargement forms are a pressure energy dissipation method that uses the sectional contraction water flow to adjust and dissipate excess energy [1], and its hydraulic characteristics are mainly affected by the geometric size of energy dissipaters.

The common energy dissipaters with sudden reduction and sudden enlargement forms were divided into orifice plates and plugs (thick plates) according to their thickness along the flow direction [2], and many researchers investigated their hydraulic characteristics and influencing factors. It was found that the contraction ratio was an important factor affecting the hydraulic characteristics of the plug [3], and the shape and thickness of the plug also had a great influence on the flow characteristics [4]. The affecting factors of head loss coefficient for orifice plate, such as relative thickness, area contraction ratio (ε), and Reynolds (*Re*), were studied by Wu [5], who proved that relative thickness and ε of orifice plate were important geometric factors affecting the head loss coefficient. Some researchers mainly focused on the energy dissipation rate and over-current capability of internal energy dissipaters with different body types and area contraction ratios. The energy dissipation ratios of single and two-stage plug energy dissipaters were obtained by the combination of a physical model and numerical simulation [6]. The energy dissipation ratio of a plug, with the combination of the vertical jet, straight curved hole plugs, and horizontal hole plugs was designed and analyzed [7]. The change of pressure was also one of the hydraulic characteristics concerned. The study concluded that the pressure pulsation decreased with the reduced cross-sectional area for the orifices plate [8]. The numerical simulation of pressure field for the thin and thick plates was conducted, and the change law of the sectional pressure drop was analyzed [9]. The distribution of wall pressure coefficient for the orifice dissipaters was discussed [10]. The distribution characteristics of mean flow velocity and pulsating velocity for the orifice plate or the plug were obtained by the simulated or measured flow fields [11,12]. Meantime, scholars have also studied the cavitation characteristics of orifice plates and plugs. The cavitation characteristics of orifice plates and plugs, the cavitation mechanism, and influencing factors of orifice dissipaters were studied by Ai [13]. Additionally, cavitation numbers decreased with the increase of ε for the internal energy dissipaters with the sudden enlargement and reduction forms in the work of Zhou [14] and Zhang [15]. To sum up, the area contraction ratio (ε) of internal energy dissipation with sudden enlargement and reduction was an important geometric factor to decide its hydraulic characteristics.

On the basis of previous studies, new internal energy dissipaters called toothed internal energy dissipaters (TIED) were proposed by our research team [16], which combines the internal energy dissipaters of the sudden reduction forms and sudden enlargement with the open-flow energy dissipation. The flow characters affecting the body factors of the TIED were discussed, and the reasonable body factors of the TIED were preliminary optimized [17–19]. In previous works, the body shape of internal energy dissipater was the key to analyze the variation of the hydraulic characteristics, and the area contraction ratio was the most critical body geometry parameter influencing the hydraulic characteristic of the TIED.

In order to study the effect of the area contraction ratio (ε) on the hydraulic characteristics of TIED, it is necessary to confirm the length, height, and angle of piers. Some researchers mainly focused on the length and height of the plug and TIED. The effect of the length of the plug [20] and piers [21] on the head loss coefficient was analyzed via numerical simulation. It was found that the head loss coefficient decreased sharply and then increased with the increase of their length, and its turning point was a length of 0.5*D*. When their length increased to 0.9*D*, the local head loss tended to be stable. The effect of the pier's height on the hydraulic characteristics of the toothed internal energy dissipate (TIED) was studied via a physical model test [22]. The results showed that the energy dissipating effect was better when the height of the piers (*h*) was no greater than 0.25*D*, and the flow coefficient was larger when the height of piers (*h*) was equal to 0.25*D*. According to the results, the length and height of piers was initially chosen to be 13.5 cm (0.9*D*) and 3.75 cm (0.25*D*), respectively.

In this paper, five different types of the TIED with four toothed piers (the length of each toothed piers is 0.9*D*), which have different area contraction ratios (ε), were designed and used to experimentally study the effect of the area contraction ratio (ε) on hydraulic characteristics.

#### **2. Model Experiment**

The test device consists of a flat water tank, a pipeline, an electromagnetic flow meter, a test section, and a valve. The test pipe is made of organic glass to observe the flow regime easily. The inner diameter (*D*) of the test pipe is 15 cm, and its total length is 370 cm. Figure 1 shows the layout of the test device.

(**b**) The photo of test pipe

**Figure 1.** Layout of test pipe.

The TIED is located 143.5 cm away from the inlet of the test pipe, and its length (*L*) is 13.5 cm. For the TIED, the number of the piers (*n*) is 4, and the height of the piers (*h*) is 3.75 cm. The area contraction ratio (ε) can be defined as: <sup>ε</sup> = *<sup>A</sup>*0/*<sup>A</sup>* = <sup>1</sup><sup>−</sup> <sup>θ</sup> <sup>90</sup>◦ <sup>4</sup>*Dh*−4*h*<sup>2</sup> *<sup>D</sup>*<sup>2</sup> . In equation, *A*<sup>0</sup> is the cross-sectional area of TIED, *A* is the cross-sectional area of test pipe, and θ is the angle of the piers. In order to study the effect of area contraction ratio (ε) on hydraulic characteristics of the TIED, five types of TIED were experimentally studied via the physical model. The cross-sectional areas of the TIED are displayed in Figure 2.

**Figure 2.** Cross-sectional areas of toothed internal energy dissipaters (TIED).

During the test, the upstream head (*H*) was kept constant, the flow was constant in the test pipe, the indoor temperature was 20 ◦C, and the range of flow was between 18 l/s and 42 l/s. In order to analyze the same flow condition, the flow of each group was about 6 l/s increased sequentially, and the flow measurement error of each experimental flow group was ±0.2 l/s.

The flow (*Q*) through the test pipe and the transient pressure (*pi*) along the bottom of the test pipe were measured for each test group. The center point at the inlet of the TIED is the origin of the coordinate, the direction of water flow is positive for the X axis, and the direction for vertical upwards is the positive *Z* axis. *Q* was measured using an intelligent electromagnetic flow meter, and its measured accuracy was ±0.5%.

*pi* was measured with a digital pressure sensor, and its measured accuracy was 0.1%, and its measuring frequency 100 HZ. Figure 3a shows the relative position of the pressure measuring points.

**Figure 3.** The distribution of measuring points along the test pipe.

When *Q* was 18 l/s, the transient flow velocity (*u*) was measured by the DOP3010 flow velocity meter for different ε. The sampling frequency of the DOP3010 flow meter was 1MHz and its resolution was 0.01 mm. The angle between the measuring probe of u and the pipe wall was 70◦, and their gap was filled with coupling medium to make the measurement of *u* more precise. Taking the measuring point of 1\* as an example, it is possible to obtain the value of u for measuring points at intervals of 1 cm on the line of a. *Z*/*D* = 0 is at the central axis of the test pipe and *Z*/*D* = 0.42 is 1.2 cm away from the upper side of test pipe. The measured value of u is stable in the position of *Z*/*D* = 0.42 and *Z*/*D* = 0 for every measuring point. The relative position of the measuring point is shown in Figure 3b.

#### **3. Analysis of the Flow Characteristics A**ff**ected by the Area Contraction Ratio**

#### *3.1. Over-Current Capability*

The flow coefficient (μ*c*) reflects the over-current capability of the test pipe, written as:

$$
\mu\_{\rm c} = \frac{Q}{A\sqrt{2g\Delta H}},
\tag{1}
$$

where Δ*H* is the head loss between the fifth and fourteenth measuring point.

Δ*H* is calculated by the following equation:

$$
\Delta H = (z\_{14} + \frac{\overline{p\_{14}}}{\rho \mathcal{g}} + \frac{v\_{14}^2}{2\mathcal{g}}) - (z\_5 + \frac{\overline{p\_5}}{\rho \mathcal{g}} + \frac{v\_5^2}{2\mathcal{g}}) = h\_w = \xi \frac{v^2}{2g'} \tag{2}
$$

where *z*<sup>14</sup> and *z*<sup>5</sup> are the position head for the measuring points of 14 and 5, respectively, and the position head of *z*<sup>14</sup> is equal to that of *z*5; *p*<sup>14</sup> and *p*<sup>5</sup> are the time-averaged pressure for the measuring points of 14 and 5, respectively; *v*<sup>14</sup> and *v*<sup>5</sup> are the average flow velocity for the measuring points of 14 and 5, respectively, and their value are equal to *v*; *v* is the averaged velocity of the test pipe; *hw* is the head loss between the front and back of TIED; ξ is the head loss coefficient, and the sum of the resistance coefficient (λ) along the pipe and the local head loss coefficient (ζ).

Combining Equations (1) and (2) together, we can obtain:

$$
\mu\_{\mathfrak{c}} = \frac{1}{\sqrt{\xi}'} \tag{3}
$$

The influencing factors of λ are the flow regime and the roughness of the pipe wall, and the roughness of the pipe wall is affected by the geometric parameters of the TIED. When the water flow is laminar, λ is only affected by *Re*. When the water flow is turbulent and in the transition zone, λ is determined by the roughness of the pipe wall and *Re*. When the water flow is turbulent in the square zone of resistance, λ is determined by the roughness of the pipe wall and not affected by *Re*. When *Re* is between 1.5 <sup>×</sup> <sup>10</sup><sup>5</sup> and 3.5 <sup>×</sup> <sup>10</sup>5, the water flow is located in the square area of turbulent resistance, <sup>ξ</sup> is determined by the body type of the TIED, the wall roughness of the TIED, and the wall roughness of the testing pipe.

Figure 4 shows the change of the flow coefficients (μ*c*) with ε for different *Re*. μ*<sup>c</sup>* is little affected by *Re* and its relative errors are within 2% for the same <sup>ε</sup> when *Re* is between 1.5 <sup>×</sup> 105 and 3.5 <sup>×</sup> 105. For the same *Re*, μ*<sup>c</sup>* increases from 0.4 to 0.9 with the increase of ε, so ε is the main influencing factor of over-current capability.

**Figure 4.** Relationship of the flow coefficient (μ*c*) and area contraction ratio (ε).

In order to eliminate the error of μ*<sup>c</sup>* caused by the *Re* in the experiment, the averaged value (μ*c*) of μ*<sup>c</sup>* for different ε is acquired in the testing flow range, and the relationship between μ*<sup>c</sup>* and ε is presented in Figure 5. It indicates that μ*<sup>c</sup>* increases with the addition of ε, and the empirical formula of μ*<sup>c</sup>* is presented as:

$$
\mu\_{\varepsilon} = 0.1213 e^{3.1948\varepsilon} \text{ (0.375 } \le \varepsilon \le 0.625\text{)}.\tag{4}
$$

**Figure 5.** Relationship between the measured or calculated values of the averaged flow coefficient (μ*c*) and the area contraction ratio (ε).

The calculated values of μ*<sup>c</sup>* obtained by Equation (4) and the measured values of μ*<sup>c</sup>* are shown in Figure 5. Comparing the calculated values with the measured values for the same ε, their errors are smaller than 5% and within the range of allowable error. Therefore, Equation (4) can calculate the flow coefficient of the TIED in the testing flow range.

#### *3.2. Energy Dissipation Rate*

The energy dissipation rate (η) can represent the energy dissipation effect of the TIED. The higher the energy dissipation rate, the better the energy dissipation effect. It can be expressed as:

$$
\eta = \frac{h\_w}{H} = \xi \frac{v^2}{2gH'} \tag{5}
$$

where *hw* is the head loss between the front and back of TIED, *H* is the total test head, ξ is the head loss coefficient, and *v* is the average velocity of test pipe.

Figure 6 shows the variation trend of η with ε in the condition of different *Re*. η increases with *Re* for the same ε and decreases exponentially with ε for the same *Re*.

**Figure 6.** Relationship of the energy dissipation rate (η) and area contraction ratio (ε).

Because of the constant total head in the test, Equation (6) can be transformed as follows, aiming to analyze the change of η:

$$
\eta = = \xi \frac{Q^2}{2gA^2H} \tag{6}
$$

In Equation (6), when ε is constant; ξ, *g*, *A*, and *H* are constant and η is proportional to the square of *Q*; when *Q* is constant, η is proportional to ε. Therefore, the value of η can be calculated by ξ in the case of a known *Q*.

In order to eliminate the influence of *Re* on ξ, the average value (ξ) is obtained by taking an average of ξ in the testing flow range, and the change of ξ with the increase of ε is shown in Figure 7. ξ decreases from 5.9 to 1.2 when ε is between 0.375 and 0.625. The empirical formula of ξ can be expressed as follows:

$$
\xi = 59.766e^{-6.198\varepsilon} \text{ (0.375 } \le \varepsilon \le 0.625\text{)}.\tag{7}
$$

The calculated values of ξ are obtained by Equation (7), and the measured values of ξ are obtained with the help of the model test. Both of them are presented in Figure 7. Comparing the calculated values of ξ with the measured values, the errors are less than 5%. Thus, this formula can calculate ξ for the TIED in the testing flow range. Moreover, it can obtain η to substitute ξ into Equation (6) in a certain flow.

**Figure 7.** Relationship between the measured or calculated averaged value of the head loss coefficient (ξ) and the area contraction ratio (ε).

#### *3.3. The Variation of the Time-Averaged Pressure along the Test Pipe*

When *Q* increases in the pipeline, *Re* becomes larger, the frictional head loss and local head loss also become greater, and the reduced amplitude of the time-averaged pressure (*pi*) decreases sharply along the test pipe. The time-averaged pressure coefficient (α) is introduced to express *pi* better, established as:

$$\alpha = \frac{\overline{p\_i} - \overline{p\_{\text{min}}}}{\rho \upsilon^2 / 2},$$

where *pi* is the time-averaged pressure for each measuring point; *p*min is the smallest value of the time average pressure among the measuring points along the test pipe; and its position pressure in the test is at 0.2*D*. Figure 8a shows the change of α along the test pipe. It can be seen that the time-averaged pressure coefficients are less affected by *Q* and have similar change trends along the test pipe. The reason is that the difference of α between the two measured points is equal to the head loss coefficient, and the effect of *Re* on the value of α can be neglected, and it was only affected by the energy dissipater. In order to reduce the error caused by the changes of *Re*, the average value (α) is obtained to study α better in the range of *Q*. The relationship between α and ε is shown in Figure 8b, and the changes of α with the increase of ε for the inlet or outlet of the TIED are presented in Figure 9.

**Figure 8.** Distribution of time-averaged pressure coefficient (α) and the mean of time-averaged pressure coefficient (α) along the test pipe.

**Figure 9.** Relationship between the mean of time-averaged pressure coefficient (α) and the area contraction ratio (ε).

As shown in Figures 8 and 9, α drop sharply at the inlet of the TIED, then gradually increases and tends to remain nearly constant in the place of 4*D* after the inlet of the TIED. The reason is that the sudden changes of the flow velocity, caused by the sudden change of the flow cross-section through the TIED, lead to changes of α. For different types of TIED, α decreases from 9.8 to 2.8 before the inlet of the TIED and falls from 3.9 to 1.6 after the outlet of the TIED with the increase of ε from 0.375 to 0.46, and the minimum of α along the test pipe increases with the increase of ε. For different types of the TIED, α in the outlet and inlet of the TIED both decrease with the increase of ε, and their differences drop from 8.2 to 1.8 when ε grows from 0.375 to 0.625. The change of α within and near the TIED is mainly due to the increase of the head loss coefficient, which is caused by the change of cross-sectional area.

When *Q* is constant, the smaller ε is, the larger α in the front of the TIED is. Thus, the larger enough value of *p*<sup>6</sup> − *p*min should be provided. Additionally, the value of *p*<sup>6</sup> is constant when *Q* is constant. Therefore, the value of *p*min will be negative with the decrease of ε. When ε is constant, α is constant. The larger *Q* is, the smaller *pi* becomes, so the value of *p*min will be negative with the increase of *Q*. In the testing range flow, when the flow is about 42 l/s and ε is equal to 0.375 and 0.46, the value of *p*min is negative. The air will enter the pipe when the value of time-averaged pressure is negative, and then cavitations are likely where the flow velocity becomes small.

#### *3.4. Variation of Pulsating Pressure*

The size of the pulsating pressure can be represented by the root mean square of the pulsating pressure (σ) in the Equation (9):

$$
\sigma = \sqrt{\frac{1}{N} \Sigma\_{i=1}^{N} (p\_i - \overline{p})^2},
\tag{9}
$$

where *N* is the measuring times of the pressure and *pi* is the instant pressure at the measuring points. The pulsation of pressure is caused by the mixing of particles in each layer of turbulence. If air enters the pipe, the stronger the pressure pulsation, the more likely it is for cavitations to occur.

The pulsating pressure coefficient (*Cp*) can be acquired to express σ, written as:

$$\mathcal{C}\_p = \frac{\sigma/\gamma}{v^2/2g} = \frac{\sigma/\gamma}{Q^2/2gA}. \tag{10}$$

Figure 10 presents the change of *Cp* along the test pipe. The variation trend of *Cp* is similar for different ε and *Q*, and the peaks of *Cp* appear at 1.3*D* after the outlet of the TIED, because the TIED increases the turbulence of water flow, resulting in the enhancement of pulsating intensity near the outlet of the TIED.

**Figure 10.** Distribution of pulsating pressure coefficient along for the typical body type of the TIED.

Table 1 shows the greatest peak of *Cp* for each test group. It is clear that the peaks of *Cp* decrease with the increase of *Q* and ε, because *Cp* is inversely proportional to the square of *Q* from Equation (10) and the changing rate of pressure decreases with the increase of ε. When ε increases from 0.375 to 0.625, the averaged peak of *Cp* (*Cp*max) decreases from 0.747 to 0.306 in the range of the testing flow. When *Q* is constant, the larger ε is, the smaller *Cp* is, and the larger σ is, indicating that the smaller ε is, the larger the pressure pulsation is.


**Table 1.** Peaks and average values of pulsating pressure coefficient for each test group.

#### *3.5. Change of the Time-Averaged Velocity*

The water flow in the test pipe is a turbulent flow within the test flow range, and the transient velocity of the water flow (*ui*) can be divided into two parts: the time-averaged velocity (*u*) and the pulsating velocity (*u* ). The time-averaged velocity coefficient (β) is introduced to describe the characteristic of *u*, written as:

$$
\beta = \overline{\mathfrak{u}}/v.\tag{11}
$$

*u* is logarithmic distribution along the radial direction in the pipe. The value of *u* at the center is greater than that at the side wall, and *u* in a different position of the pipe is affected by its position and sectional geometry parameters when *Q* is constant.

*Z*/*D* = 0 is at the central axis of the test pipe and *Z*/*D* = 0.42 is 1.2 cm away from the upper side of the test pipe. When *Q* is 18 l/s, the variation of β along the line of *Z*/*D* = 0 and *Z*/*D* = 0.42 for different ε is shown in Figure 11. It is clear that the change trends of β along the pipe are similar for each TIED. The values of β have little changes in the inlet and outlet sections of the test pipe, suddenly increasing at the entrance of the TIED, and then dropping sharply at the outlet of the TIED, because of the same flow cross section in the inlet and outlet sections in the test pipe and sudden changes near the TIED

causing a sharp change of *v*. Further, the value of β on the line of *Z*/*D* = 0.42 reduced slightly before the inlet of the TIED. The value of β on the line of *Z*/*D* = 0 is larger than that on the line of *Z*/*D* = 0.42 for each measuring point. The values of β at the inlet and outlet sections of the test pipe are little affected by ε at the inlet and outlet sections of the test pipe, less than 1 on the line of *Z*/*D* = 0.42 and greater than 1 on the line of *Z*/*D* = 0. The main reason is that the inlet and outlet sections of the test pipe are far away from the TIED and *u* is the logarithmic distribution along the radial direction in these sections. The maximum value of β is located inside the TIED. When ε increases from 0.375 to 0.625, the maximum of β near the side wall reduces from 2.53 to 1.17 on the line of *Z*/*D* = 0.42 and decreases from 2.99 to 1.74 on the line of *Z*/*D* = 0.42.

**Figure 11.** Changes of the time-averaged velocity along the test pipe.

According to the comprehensive analysis, the maximum value of *u* appears on the central axis of the pipe when *X* is constant. When *Z* is constant, the changed region of *u* is located inside and near the TIED, and its maximum value appears inside the TIED. That is caused by the sudden decrease of the cross-sectional area for the TIED. The larger ε is, the smaller the reduced amplitude of the cross-sectional area, and the smaller β is, the smaller the maximum of *u*.

#### *3.6. Change of the Pulsating Velocity*

The pulsating strength (σ*u*) is used to represent the fluctuating strength of the velocity for different measuring points and is denoted by the root mean square of the pulsating velocity (σ*u*):

$$
\sigma\_u = \sqrt{\frac{1}{N\_2} \Sigma\_{i=1}^N \left( u\_i - \overline{u} \right)^2},
\tag{12}
$$

where *N*<sup>2</sup> is the measured times of the velocity.

Introducing the turbulent strength (*Tu*), and defined as:

$$T\_u = \sigma\_u / v.\tag{13}$$

The change of *Tu* along the test pipe for different ε is illustrated in Figure 12 when *Q* is 18 l/s. It is shown that the variation of *Tu* is similar for the different ε, and the maximum value of *Tu* on the line of *Z*/*D* = 0.42 and *Z*/*D* = 0 appears at 1.57*D* and 2.72*D* away from the inlet of the TIED, respectively. ε has little effect on *Tu* in the constant section of *u* and has a great effect on the abrupt section of *u*. When ε increases from 0.375 to 0.625, the maximum value of *Tu* on the line of *Z*/*D* = 0.42 reduces from 0.68 to 0.21 and decreases from 0.56 to 0.13 on the line of *Z*/*D* = 0.

As shown in Figure 12, *Tu* in the side wall is larger than that in the central axis when *X* is constant, which is mainly due to the diffusion of turbulent energy and the interference of the edge wall roughness causing the larger turbulence intensity at this position. The maximum value of *Tu* appears after the

outlet of the TIED and decreases with the increase of ε when *Z* is constant because of the convection of turbulent energy, resulting in downstream movement of the interference wave.

**Figure 12.** Distribution of turbulent strength along the test pipe.

#### **4. Conclusions**

In order to gain insight into the optimized body type parameters of the TIED, the effects of the area contraction ratio (ε) on the hydraulic characteristics of the TIED were discussed using the methods of a physical model test and theoretical analysis in this paper. In the testing flow range, the main conclusions are as follows.

During the test, the flow was basically in the square area of turbulent resistance when Re changed from 1.5 <sup>×</sup> <sup>10</sup><sup>5</sup> to 3.5 <sup>×</sup> 105, and the Re had little effect on the flow characteristics. The energy dissipation rate (η) was proportional to the head loss coefficient (ξ). The flow characteristics were mainly affected by the body type of the TIED. The over-current capability (μ*c*) and the energy dissipation rate (η) can be characterized by μ*<sup>c</sup>* and ξ, respectively. They mainly depended on ε. With the increase of <sup>ε</sup>, <sup>μ</sup>*<sup>c</sup>* increased exponentially (μ*<sup>c</sup>* = 0.1213*e*3.1948ε(0.375 <sup>≤</sup> <sup>ε</sup> <sup>≤</sup> 0.625)) and <sup>ξ</sup> decreased exponentially (<sup>ξ</sup> = 59.766*e*−6.198<sup>ε</sup> (0.375 <sup>≤</sup> <sup>ε</sup> <sup>≤</sup> 0.625)).

The transient pressure of turbulent flow was composed of time-averaged pressure and pulsating pressure. The change trends of time-averaged pressure coefficients (α) only depended on ε; the differences of the averaged α between the inlet and outlet of the TIED decreased from 8.2 to 1.8 when ε increased from 0.375 to 0.625 in the range of the testing flow; when the flow was about 42 l/s and ε was equal to 0.375 or 0.46, the minimum of time-averaged pressure along the pipe was negative. The pulsating pressure coefficient (Cp) was determined by *Re* and ε, and its peaks appeared at 1.3D after the outlet of the TIED; the averaged peaks in the range of the testing flow decreased from 0.747 to 0.306 when ε increased from 0.375 to 0.625. Negative pressure and larger peaks of pulsating pressure coefficient were more prone to cavitations behind the outlet of TIED.

The transient velocity of turbulent flow was divided into time-averaged velocity and pulsating velocity, which can be represented by time-averaged flow velocity coefficients (β) and turbulent strength (*Tu*), respectively. When *X* was constant, the maximum of β appeared on the line of *Z*/*D* =0 in pipe, and β near the side wall was larger than that on the line of *Z*/*D* =0 in pipe due to the diffusion of turbulent energy and the interference of the wall roughness. When *Z* was constant, the maximum value of β appeared inside the TIED for different ε, decreasing with the increase of ε. Moreover, the maximum value of *Tu* appeared after the outlet of the TIED and decreased with the increase of ε because of the convection of turbulent energy. Therefore, the smaller ε is, the more likely it is that cavitations occur near the pipe wall behind the outlet of the TIED.

Comprehensive analysis of over-current capability, energy dissipation rate, and the distribution of flow velocity and pressure showed that the optimized body type parameter (ε) of the TIED in the test was 0.5 when flow in the pipe was about 42 l/s.

**Author Contributions:** T.Z., designed and performed the model test, and wrote the preliminary manuscript paper; Z.Z., conducted preparation of experiment and preliminary analysis the data of model test; R.H. and X.Z., provided guidance for model test and also further improved the concept, structure, contents and writing of the preliminary manuscript paper.

**Funding:** This work was supported by the Natural Science Foundation of Shanxi Province (Grand No: 2013011037-4) and National Natural Science Foundation of China (Grant No.51109155).

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


22. Wang, H. Experimental Research about Tooth Block Height Effect on Inner Energy Dissipaters of Tooth Block. Master's Thesis, Taiyuan University of Technology, Taiyuan, China, October 2015.

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## *Article* **Physical Modeling of Ski-Jump Spillway to Evaluate Dynamic Pressure**

#### **Mehdi Karami Moghadam 1, Ata Amini 2,\*, Marlinda Abdul Malek 3, Thamer Mohammad <sup>4</sup> and Hasan Hoseini <sup>5</sup>**


Received: 18 June 2019; Accepted: 11 July 2019; Published: 15 August 2019

**Abstract:** The effects of changes in the angle of pool impact plate, plunging depth, and discharge upon the dynamic pressure caused by ski-jump buckets were investigated in the laboratory. Four impact plate angles and four plunging depths were used. Discharges of 67, 86, 161, and 184 L/s were chosen. For any discharge, plunging depth and impact plate angle were regulated, and dynamic pressures were measured by a transducer. The results showed that with the increase in the ratio of drop length of the jet to its break-up length (H/Lb), and with an increase in the impact plate angle, the mean dynamic pressure coefficient decreased. An inspection of the plunging depth (Y) ratio to the initial thickness of the jet (Bj) revealed that when Y/Bj > 3, the plunging depth of the downstream pool reduced dynamic pressure. At the angle of 60◦, the dynamic pressure coefficient due to increasing in plunging depth varied from 34% to 95%.

**Keywords:** jet falling; energy dissipation; surface disturbances; pressure fluctuations; water jet; physical modeling

#### **1. Introduction**

Owing to dynamic pressures resulting from the flow in hydraulic structures, the river bed is frequently affected with scouring [1,2]. To dissipate the flow energy and to avoid this scouring, dissipater structures such as a spillway with a fillip bucket, which is applied at the end of chute spillway, are used [3]. The flow in the structure is thrown into the air by a ski-jump and goes down after dissipation of part of the energy. Steiner et al. [4] conducted experiments on triangular jets, and compared parameters such as dynamic pressure over the bucket, as well as energy dissipation between triangular and circular buckets. Their results indicated that the relative energy dissipation hinges on the deflection angle and jet falling height from the take-off lip to tail water level. Jorabloo et al. [5] simulated the ski-jump stream outlet through the Fluent model and compared the model output with the results of the physical model. They concluded that pressure distribution, as well as jet trajectory in the two models, are close to each other. Turbulent jet into the flow was numerically analyzed by Mahmoud et al. [6], along with studying the recirculation bubbles in the flow. Their results show that the size and power of the recirculation bubbles increase with the enlargement of the nozzle size. Furthermore, the bubbles disappeared as the Froude number was reduced. Chakravarti et al. [7] have investigated the static and dynamic scouring caused by submerged circular vertical jets. They verified that the depth of dynamic scouring is greater than that of static scouring. Artificial neural

network (ANN) was employed by Noori and Hooshyripor [8] based on the major effects of the input parameters on the downstream scouring of the fillip bucket. Their results showed that the Log–Sigmaid model had good performance in the modeling of the depth of scouring. The smooth particle hydrodynamics technique was adopted to study pressure distribution on the steps of a stepped spillway by Husain et al. [9]. Their results showed good consistency with the laboratory observations. Distribution of hydrostatic and non-hydrostatic pressure in shallow waters was investigated by Arico and Re [10]. Dividing the whole pressure into dynamic and hydrostatic components, they solved a hydrostatic and a non-hydrostatic problem sequentially in a fractional time step procedure. Simpiger and Bhalera [11] developed an equation for measuring the jet length according to the jet trajectory. They compared the obtained length with the observation values in a physical model and used the equation to calculate the jet trajectory length in the prototype. Aminoroayaie Yamini et al. [12] investigated the pressure fluctuations and the effect of the entering flow on the fillip bucket bed of Gotvand Dam in Iran. The results show that when the depth and discharge of the entering flow increases and Froude number decreases, the mean dynamic pressure declines and pressure fluctuations grow. They observed that the average pressure was at a maximum at the bucket entry, and was at a minimum at the end part of it. Wu et al. [13] studied the energy dissipation in a fillip bucket of slot-type, both numerically and in the laboratory, and suggested equations to estimate the energy dissipation value. The results showed that as the flow drops in downstream submerged or unsubmerged pools, the resulting dynamical pressure was transformed to the bottom and sidewalls.

Understanding the jet features is crucial in designing the pool and determining the plunging rate. Notwithstanding the research carried out in this regard, it seems that realizing the precise mechanism of ski-jet impacting on the pool requires more studies. In this research, the effects of the main variables upon changes in dynamical pressure and jet break-up length were investigated using the laboratory model of the spillway and the fillip bucket of a dam constructed in Iran. Comprehensive data, as well as the analyses presented in this study, can be used by researchers and engineers.

#### **2. Materials and Methods**

#### *2.1. Mechanism and E*ff*ective Parameters*

The effective parameters in jet break-up include fluid properties, the environment features, and the jet outlet conditions. A schematic drawing of regions and parameters in a jet break-up is depicted in Figure 1.

**Figure 1.** Features of falling jet and its development (adapted from Ervine et al. [14]).

As shown in Figure 1, there are three flow regimes to be considered before the vertical jet impacts the water surface. Region A is composed of three sub-regions: A1, A2, and A3. In subregion A1, when the flow exits the nozzle, the surface tension resists disturbance, meaning the jet surface remains flat and glass-like. In subregion A2, roughness (waves) grows at the water surface. As for subregion A3, surface waves turn into circumferential vortices. Region B is where surface disturbances (ε) increase with the square root of the fall distance (ε∝ <sup>√</sup> X), where X is the distance from the beginning of the jet. The air penetrates the jet perpendicular to its trajectory. The distance from the jet beginning up to the end of region B is called break-up length (Lb). Very intense surface disturbances enter the jet in region C, whereby the flow gets out of continuity mode. In region C, the flow is not of continuous mass and the flow masses are quite distinct. Surface tension and turbulence determine the distance of Lb, where the jet breaking-up occurs and causes the jet impacts with less energy (Ervine et al. [14]). The jet along its direction may be either core or non-core. In Figure 1, up till region B, the core jet exists, and in region C, there is the non-core situation. In case the plunging is sufficient, the non-core jet expands to the sides as vortices.

#### *2.2. Dimensional Analysis*

The parameters governing the dynamic pressure resulting from impacting the fillip bucket jet on the plunge pool floor are expressible as in Equation (1) [15]:

$$\mathbf{f}(\mathbf{q}, \rho\_{\mathbf{w}}, \Delta \mathbf{P}\_{\text{max}}, \mathbf{g}, \mathbf{B}\_{\text{f}}, \mathbf{Y}, \mathbf{H}, \mathbf{R}, \mathbf{x}, \mathbf{q}, \mu, \mathbf{H}, \mathbf{L}\_{\text{b}}) = \mathbf{0}. \tag{1}$$

In Equation (1), q stands for discharge per unit width, ρ<sup>w</sup> is water density, ΔPmax represents the maximum pressure head, g is the gravitational acceleration, Bj designates impingement jet thickness, Y is tail water depth, H is the drop height, R is radius of fillip bucket, α signifies the angle of impact plate with horizon, ϕ is the take-off angle of jet with horizon, μ stands for water dynamic viscosity, H is the jet length, and Lb is the jet break-up length. The dimensionless parameters may be represented, through dimensional analysis, as Equation (2) [15]:

$$\text{f}(\text{Re}, \text{Fr}, \frac{\Delta \text{P}\_{\text{max}}}{\text{Y}}, \frac{\text{H}}{\text{Y}}, \frac{\text{R}}{\text{Y}}, \frac{\text{B}}{\text{Y}}, \text{x}, \text{q.}, \frac{\text{H}}{\text{Y}}, \frac{\text{L}\_{\text{b}}}{\text{Y}}) = 0,\tag{2}$$

where Re stands for Reynold's number and Fr is Froude number. By removing the fixed parameters, the average dynamic pressure coefficient (Cp) is obtained as follows:

$$\mathbf{C\_P} = \frac{\mathbf{H\_m} - \mathbf{Y}}{\frac{\mathbf{U\_j^2}}{\frac{\mathbf{Y}}{2\mathbf{g}}}} = \mathbf{f}(\alpha, \frac{\mathbf{H}}{\mathbf{L\_b}}, \frac{\mathbf{Y}}{\mathbf{B\_j}}),\tag{3}$$

where Hm is the average of observed dynamic pressures, and Uj designates the jet velocity at the impingement moment. The break-up length is calculated from Equations (4) and (5) [16]:

$$\frac{\mathbf{L\_b}}{\mathbf{B\_i}\mathbf{F}\mathbf{r\_i}^2} = \frac{0.85}{(1.07\mathbf{T\_u}\mathbf{F}\mathbf{r\_i}^2)^{0.82}}\tag{4}$$

$$T\_{\mathbf{u}} = \frac{\text{RMS}(\mathbf{u}')}{\overline{\mathbf{u}}},\tag{5}$$

where Bi, Tu, and Fri are initial thickness, turbulence intensity, and initial Froude number of the jet, respectively. RMS (u') is the root mean square of the values of the velocity fluctuations in the cross section and in the direction of the falling jet axis, and u is the average jet velocity. ¯

#### *2.3. The Experiments and Models*

The experiments of the present research were conducted in the hydraulic laboratory of Chamran University, Ahwaz, Iran. The laboratory models of the spillway and fillip bucket were scaled down of Balarood Dam spillway, located 27 km north of Andimeshk, Khouzestan Province. Balarood dam is constructed on the Balarood River and is of the earthy type with clay core. It is 75.5 m in height and 1070 m crest length, and has a reservoir volume of 131 MCM. The laboratory model of the spillway was scaled down with a scale of 1:40 based on the principle of dynamic simulation, and with due regard to the flume and discharge conditions in the laboratory. The dimensions of the flume were 0.5 m width, 9 m length, and 2 m height. Four discharges of 67, 86, 161, and 184 L/s were taken corresponding with the real discharges of 674.85, 870, 1622.2, and 1857.2 m3/s in the prototype, respectively. The latter discharges correspond to those with the return periods of 2, 100, 1000, and 5000 years. The four downstream water depths used in the plunge pool were 0, 15, 30, and 45 cm. Also, angles of 0◦, 30◦, 60◦, and 90◦ were chosen for the impact plate in the plunge pool. Taking these variables into account, a total of 64 experiments were carried out.

#### *2.4. Experiments' Setup*

During the experiments, the flow was established by a pump using a circulation system. To minimize turbulence, stilling reservoir and honeycomb were utilized before the flow reaches the experiment area. At the beginning of each experiment, the required discharge was regulated via a gate valve and a rectangular weir installed at the end of the flume. Figure 2 shows a schema of the ski-jump jet (Figure 2a) plus parts of the physical model (Figure 2b). A Plexiglass 0.5 m × 0.5 m square plate was employed in designing the impact plate on which the jet arising from the fillip bucket was to be impinged. A total of 37 pores, each with a diameter of 2 mm, was set on the impact plate in order for connection of the piezometer tubes. The impact plate was placed on a metal system movable in a vertical direction in order to set particular water depth at the position of jet impingement. Also, the impact plate was able to rotate around the horizontal axis to create various angles with the horizon. By moving and rotating, the impact plate angle (α) and the plunging depth (Y) were adjusted as in Figure 2a. Finally, the flow was discharged through the return channel system into the primary reservoir.

**Figure 2.** (**a**) Ski-jump, plunging depth, and angle of impact plate; (**b**) jet trajectory of ski-jump and impinge on impact plate.

#### *2.5. Measurement of Dynamic Pressure*

Piezometers were used to observe the fluctuations of the dynamic pressures on the impingement place. Those connected to the impact plate were stretched out from the bottom of the reservoir wall and moved to the dial board, as shown in Figure 3. After the flow exhausted from the bucket and the jet impinged on the impact plate, the dynamic pressures were measured. To demonstrate the dynamic pressures, two of the 37 piezometers, showing the highest pressures, were linked to a transducer. The transducer converts the dynamic pressure of the piezometers into electrical signals and transmitted to the amplifiers by the particular cables. For 10 min, 50 data of dynamic pressures per second were taken. The accuracy of the transducer was ±1 mm for the laboratory model corresponding to 0.04 m for the prototype (Balarood dam). The data obtained by the transducer were translated into the computer via Data Translation Scope, DT9800. This software recorded the sent information and presented them as graphs of pressure fluctuations versus time. For further analysis of the data, the output file of the software was provided to be used in MS Excel spreadsheet programs.

**Figure 3.** The 37 piezometers connected to impact plate for observation of dynamic pressure fluctuations.

#### **3. Results and Discussion**

#### *3.1. Mean Dynamic Pressure Coe*ffi*cient*

The mean dynamic pressure coefficient (Cp) was used in the quantitative study of dynamic pressures (Equation (3)). Table 1 contains the mean values of dynamic pressure coefficients at various impact plate angles, plunging depths, and flow discharges.


**Table 1.** Values of mean dynamic pressure coefficients obtained in this research

#### 3.1.1. Effect of Plunging Depth

Figure 4 shows the mean values of dynamic pressure coefficients measured at the place of jet impingement on the impact plate for different discharges and angles versus the ratio of plunging depth to the jet width (Y/Bj).

(**b**)

**Figure 4.** *Cont*.

**Figure 4.** Variations of mean dynamic pressure coefficient versus the plunging depth ratio in discharges of (**a**) 67; (**b**) 86; (**c**) 161; and (**d**) 184 L/s.

Figure 4 reveals that for all discharges, when the plunging depth of the pool is zero (Y/Bj = 0), the mean dynamic pressure coefficient attains its maximum value at 0◦, and its minimum value corresponds to 90◦. The reason is that in the case of α = 0, the jet impingement is centralized at just one point. By increasing the jet angle, part of the jet is tangent with the impact plate, so the coefficient reduces. Figure 4 also shows that once the plunging depth increases (increment of Y/Bj), the value of Cp is at first constant or has no significant reduction, whereas from a certain depth, this coefficient decreases. This occurrence may be argued on the basis of the jet features so that with an increase in the plunging depth, the jet would be of developed type. As regards to the developed jets, they generate more spectral energy at moderate frequencies (100–200 Hz) and low frequencies (less than 20 Hz) compared with the core jets. This is owing to the formation of greater vortices with fewer frequencies in the situation of developed jets [17,18]. The percentage reduction of the mean dynamic pressure coefficient due to the increase in plunging depth is variable from 34% for the 60◦ and discharge of 161 L/s to 95% for the same angle and with a discharge of 67 L/s.

The impingement of the core jet on the bottom of the downstream pool is a result of the plunge pool being shallow or ineffectiveness of its depth. When the plunge depth is sufficient, the jet impacts the bottom in the non-core or developed nature. In the case of non-core, the dynamic pressure on the bottom decreases, and consequently so does Cp. As seen in Figure 4, the value of Cp falls in the decline mode for the range of 2 < Y/Bj < 4. Therefore, the boundary between the two jet areas, with the core and developed, is within this range. From the region of Y/Bj > 3, the plunge value of the downstream pool would be in effect as a result of the jet not impacting in the core state on the impact plate. In accordance with Figure 4a,c, increasing the water depth on the impact plate along with formation of the developed jet brings the diagrams close to each other, which is an indication of the reduction in the effect of impact plate angle. Furthermore, with the increases in discharge, the values of mean dynamic pressure coefficients increase. Figure 5 illustrates the relation between mean dynamic pressure coefficients and submerge ratio in previous studies compared with the data of this research.

**Figure 5.** Comparison between correlation of Y/Bj and Cp in present research and previous works (reported by Castillo [19]).

Figure 5 shows that in previous research, in agreement with current research, the Cp value decreases from a certain plunge depth onwards. Converting core jet to developed jet, in most investigations, occurs when the ratio of Y/Bj is close to 4. This bound is commonly obtained in this research and some previous works such as Ervine et al. [14] and Castillo [20], and differs, to a degree, from the results of Cola [21] and Albertson et al. [22]. This dissimilarity arises from differences in drop height, jet thickness, and jet shape (aerated and non-aerated, rectangular and circular).

#### 3.1.2. Effect of Jet Impact Angle

Figure 6 shows the diagram of Cp versus the impact plate angles in non-plunging depth.

Figure 6 confirms that as the impact plate angle increases, the Cp coefficient decreases. This decrement for the range between 0◦ and 60◦ occurs sharper relative to the range between 60◦ and 90◦. An increase in the impact plate angle contributes to a decrease in discharges of 67, 86, 161, and 184 L/s, as almost 74%, 60%, 53%, and 51%, respectively. So, the effect of impact plate angle on the decrease of Cp is more in the lower discharges, and this coefficient increases along with increases in discharge. Hence, it is suggested that in executive works, the maximum discharges of the project design probability maximum flood (PMF) be used for the most critical situations being considered in applying dynamic pressures.

Figure 6 shows the diagram of Cp versus the impact plate angles in non-plunging depth.

**Figure 6.** Mean dynamic pressure coefficient versus angle of impact plate.

#### *3.2. Distribution of Dynamic Pressure on Impact Plate*

To study dynamic pressure distribution on 0.5 × 0.5 m impact plate in different angles, the changes in Cp values at different radial distances from the impact axis are shown in Figure 7. The figure concerns the discharge of 184 L/s and 0◦ (with the greatest Cp value) for plunging depths of 0, 15, 30, and 45 cm.

Figure 7a shows the mean dynamic pressure coefficient in the non-plunging depths state. The coefficient value at the center of impact is 0.85, and it decreases away from the center. As seen in Figure 7b, compared with the non-depth case, an increase in the water depth of 15 cm does not have a significant effect on the reduction of Cp values. In fact, the plunging is still of low influence in this stage. At 30 cm depth (Figure 7c), the mean dynamic pressure coefficient is affected by a perceptible decrease. This result indicated that in this situation, the plunging depth was effective in decreasing dynamic pressure. Also, in Figure 7d, in which the plunging depth attained 45 cm, the decline in Cp values was negligible. Thus, the favorable thickness of the plunging depth for the decrease of Cp value happened at the 30 cm depth. An overall consideration of Figure 7 indicated that most dynamic pressures were made in longitudinal distances between 20 and 25 cm, and in transversal distances between 20 and 30 cm. In the cases in which the plunge depth was not so effective, the highest pressure occurred at the center of the impact plate. Any increase in plunging depth causes the center of the effective pressure on the bottom is inclined toward the sides. This may be related to the vortices and turbulent flows created at a slight distance from the point of impact in the direction of the jet central axis [19].

**Figure 7.** *Cont*.

**Figure 7.** Variations of mean dynamic pressure coefficient at radial distances from falling jet axis for discharge 184 L/s at 0◦ in plunging depths of (**a**) 0; (**b**) 15 cm; (**c**) 30; and (**d**) 45 cm.

#### *3.3. Mean Dynamic Pressure Coe*ffi*cient and Break-Up Length*

Experiments were carried out at various depths in the plunge pool to study alterations in the hydrodynamic pressure attributable to variations of the ratio of jet drop length to its break-up length (H/Lb). The results are given in Figure 8.

Figure 8 shows that as the impact plate angle relative to the horizontal increases, the value of Cp decreases in all depth situations in the plunge pool. The Cp values at different angles would come close to each other along with an increment in plunging depth. The reason behind this is that when the plunging depth increases, the energy dissipation caused by vortices grows too. Therefore, the effect of the jet impact angle upon dynamic pressure diminishes. Figure 8 confirms that as the H/Lb increases, the coefficient Cp decreases. If the plunging depth is zero or has a low value, the graphs are mostly linear, and the increase in plunging depths causes the graphs to be drawn exponentially. With decreasing plunging depth, the jet drop length increases and motivates the air penetration into the jet, which in turn brings about energy dissipation. As the plunging depth increases, the jet length, H, would shrink and vortices are produced. Consequently, the energy dissipation of the jet would be affected mainly by the vortices, as a result of which the decreasing trend of the coefficient Cp lessens. Enlargement of H means the extension of the jet drop length and the increase of air entry into the jet subsequently. Thus, it causes more dissipation of energy and decrease in Cp values. Moreover, with a decrease in the break-up length, Lb, the jet would be converted from the core to non-core occasion faster, whence a lower dynamic pressure would be exerted [19].

$$\mathbf{(a)}\ \mathbf{Y} = 0 \text{ cm}$$

(**b**) Y = 15 cm

**Figure 8.** *Cont*.

**Figure 8.** Mean dynamic pressure coefficient versus break-up length at different impact plate angles and plunging depths: (**a**) Y = 0 cm; (**b**) Y = 15 cm; (**c**) Y = 30 cm; and (**d**) Y = 45 cm.

#### **4. Conclusions**

In this research, a laboratory model was used to investigate the effect of impingement of a jet after take-off from the fillip buckets. The variables of take-off discharge, jet impact angle, and the downstream plunging depth were simulated. The experiments were carried out both without and with plunging depths of 15, 30, and 45 cm. The most important results obtained from this research are as follows:


**Author Contributions:** M.K.M. and H.H. collected the data and revised original draft preparation, A.A.; provided critical comments in planning this paper, writing and editing the paper, T.M.; M.A.M. read and approved the final manuscript and M.A.M. funded the APC.

**Funding:** This research received no external funding.

**Acknowledgments:** The authors acknowledge Shahid Chamran University of Ahvaz, Iran, for their technical supports.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## *Article* **E**ff**ects of Spur Dikes on Water Flow Diversity and Fish Aggregation**

#### **Tingjie Huang 1,2, Yan Lu 1,\* and Huaixiang Liu <sup>1</sup>**


Received: 1 August 2019; Accepted: 29 August 2019; Published: 31 August 2019

**Abstract:** As a typical waterway modification, the spur dike narrows the water cross section, which increases the flow velocity and flushes the riverbed. Meanwhile, it also protects ecological diversity and improves river habitat. Different types of spur dikes could greatly impact the interaction between flow structure and local geomorphology, which in turn affects the evolution of river aquatic habitats. Four different types of spur dikes—including rock-fill, permeable, w-shaped rock-fill, and w-shaped permeable—were evaluated using flume experiments for spur dike hydrodynamics and fish aggregation effects. Based on Shannon's entropy, an index for calculating water flow diversity is proposed. Additionally, the impact of the different spur dikes on water flow diversity and the relationship between water flow diversity and fish aggregation effects were studied. The water flow diversity index around the spur dike varied from 1.13 to 2.96. The average aggregation rate of test fish around the spur dike was 5% to 28%, and the attraction effect increased with increasing water flow diversity. Furthermore, we plotted the relationship between water flow diversity index and average fish aggregation rate. A fish hydroacoustic study conducted on the Laohutan fish-bone dike in the Dongliu reach of downstream Yangtze River showed that the fish aggregation effect of the permeable spur dike was greater than the rock-fill spur dike. These research results could provide theoretical support for habitat heterogeneity research and ecologically optimal design of spur dikes.

**Keywords:** water flow diversity; permeable spur dike; fish aggregation effect; channel regulation

#### **1. Introduction**

Shipping is one of the important functions of rivers. Meanwhile, waterway remediation is an important means to improve waterway conditions. As a typical waterway modification, the spur dike narrows the water cross section, which increases flow velocity and flushes the riverbed. However, it affects the local river habitat as well by changing the interaction between water flow and sediment, and local geomorphology within the range of influence of the spur dike.

Recently, many researchers and engineers have studied the ecological effects of spur dikes through model tests, numerical simulations and on-site observations. The results show that spur dikes can enhance river habitat heterogeneity and improve the suitability of fish habitats under low and medium water flows. The tributary area behind the spur dike provides a habitat for plankton and benthic animals, and it also provides a good living environment and shelter for juveniles with a particular fish-aggregation effect [1–7]. The improvement of habitat quality can provide more living space for aquatic organisms [8,9]. Concurrently, a low-speed zone, or even still water zone, is formed behind the spur dike due to its blocking effect. Consequently, it is easy for fine sand and silt to accumulate, making the environment unstable and not conducive to benthic organism survival [10]. Furthermore, the still water area is not suitable fish habitat [11]. To increase quantity and quality of the habitat around the spur dike and strengthen its ecological effect, new layouts of dikes or permeable ecological spur dike are proposed. While retaining the effects of narrowing the water cross section to increase the flow velocity and flush the riverbed, the new spur dike has interrelated and complementary diverse flows, refuges and bait effects. In particular, the diverse flows encourage various plankton and benthic animals to remain as food for fish. The shelter formed by the proposed structure could be used by small animals such as juveniles to avoid predation and should become an excellent micro-habitat. The spur dike of new layouts such as notched spur dikes, J-Hook, cross vane and double cross vane were proposed and applied in the Upper Mississippi River restoration and the Austrian Danube River [12–15]. Presently, there are a variety of ecological spur dikes such as the fish nest ecological, the deflector ecological, the four-side six-edge permeable, the square ecological, the open-hole trapezoidal ecological, and the open-hole semi-circular ecological spur dike in China. Great parts of them have already been applied in channel regulation projects along the Yangtze River and Xijiang River [3,16–19].

The impacts of spur dikes on habitats has mainly been assessed by calculating and comparing the weighted available area (WUA) or the suitable habitat area, under different combinations of water flow and dike type. Additionally, the weighted available area (WUA) or the suitable habitat area is simulated using a habitat model (e.g., PHABSIM- the Physical Habitat Simulation System, [20,21]), which is based on the preference of aquatic organisms for habitat factors such as water depth, flow velocity, and sediment quality. However, fish use of habitats is not only determined by flow velocity, water depth, or sediment quality, but also closely related to water flow turbulence. Turbulence is common in rivers, rough terrain, plants in the river, stone blocks and artificial structures such as spur dikes, which can cause turbulence in the water flow. However, turbulence is not always correlated with velocity—particularly in pools and around roughness elements [22,23]. Fish will adjust their swimming mode and frequency of fishtail swing to conserve energy from the turbulent water flow. Furthermore, the turbulent water flow can reduce the probability of fish being preyed upon. Moreover, the turbulent kinetic energy can better reflect on the fish aggregation status than the flow velocity. Therefore, some scholars have suggested incorporating turbulence into fish habitat assessment management [11,24–32]. Turbulence and its relationship with fish swimming and shoaling are complex, so the effects of turbulence are generally not considered in the habitat models. Some scholars have suggested that turbulence could be described with vorticity or vortex scale to analyze the complexity of water flow. However, the vortex is three-dimensional, time-dependent, and the scale varies greatly. Even when using a two-dimensional vortex, it is difficult to describe the complexity of water flow. Furthermore, it is difficult to extrapolate laboratory results to the field [4,30,33,34]. Generally, there is a lack of a clear calculation method for water flow diversity using physical mechanisms that accurately reflect the impact of spur dikes on water flow diversity and its relationship to fish aggregation.

W-Weir is a habitat enhancement structure applied in middle and small rivers. It is a submerged closure dam and its symmetry plane coincides with the centerline of the river [35]. It is w-shaped along the direction of the water flow. The angle between the first section of the dike and the flume is 20–30◦. W-Weir can lower the water surface gradient along the river and decreases flow velocity nearshore, which improves the stability of the riverbank. Two back flow areas and two pools are formed downstream of W-Weir, where rapid flow and slow alternates, and step-pool morphology is generated. It provides habitat and spawning ground for fish and other dwellers. Based on the ecological mechanism of W-Weir, a w-shaped spur dike was proposed by Lu Y. et al. (2018) [36]. Its layout is similar to W-Weir, but not cover the whole cross section river. The w-shaped permeable spur dike is stacked with permeable frames of four sides and six edges, each with a length of 1.0 m and a section diameter of 0.1 m × 0.1 m, which is widely used in the Yangtze river waterway training as revetment. The w-shaped permeable spur dike is applied in the ecological conservation area in Lianhuazhougang within Dongliu reach, which is part of the waterway Project 645—the process of dredging the Yangtze to increase the depth of the waterway between Wuhan to Anqing to 6 m, and to 4.5 m from Wuhan to Yichang.

To determine the influence of different types of spur dikes on water flow diversity and the relationship between water flow diversity and fish aggregation, we therefore used flume experiments in rock-fill, permeable, w-shaped rock-fill, and w-shaped permeable spur dikes. The flow velocity, turbulent kinetic energy and fish distribution around the spur dike were measured. Subsequently, a water flow diversity index was proposed, and its relationship with the average fish aggregation rate was determined. A fish hydroacoustic study was carried out on Laohutan fish-bone dike in the Dongliu reach of the Yangtze River to investigate the fish aggregation effects of rock-fill and permeable spur dikes in the field.

#### **2. Experiments**

#### *2.1. Experimental Design*

The flume experiments were carried out at the Basic Theory Sediment Laboratory of the Tiexinqiao Test Base, Nanjing Hydraulic Research Institute. The test setup is shown in Figure 1. The flume is 42 m long, 2 m wide and 1 m deep, and flow velocity is controlled by a rectangular thin-walled weir with a maximum flow velocity of 0.60 m3/s. There are two 1 m energy-dissipating walls at the flume water inlet used to smooth the water flow. Nets are placed at the second wall position and at 32 m from the beginning of the flume inlet. The test section is 10 m long and located in the middle of the flume.

The test was divided into two groups. The first group consisted of a rock-fill spur dike and a permeable spur dike (Figure 1a,c). The rock-fill spur dike was made with 80 mm particle sized gravel with a porosity of about 10% (proportion of void volume with spur dike to the volume of spur dike, the same below). The permeable spur dike was stacked with permeable frames of four sides and six edges each with a length of 20 cm and a section diameter of 2 cm × 2 cm with porosity of about 80%. The permeable frame spur dike was placed 5 m upstream of the rock-fill spur dike on the left side, both of them were perpendicular to the side wall of the flume. The spur dike is 0.55 m long and 0.50 m high. Its relative length is 0.28 (ratio of length of spur dike to width of flume). The second group consisted of a w-shaped rock-fill spur dike and a w-shaped permeable spur dike (Figure 1b,c). It is w-shaped along the direction of the water flow, and the spur dike root to the spur dike head is composed of four straight-line dikes, each with an 80 cm axis length. The w-shaped permeable spur dike is located 5 m upstream of the w-shaped rock-fill spur dike and on the left side of the flume. The angle between the first section of the dike and the flume is 30◦, and the angle between adjacent dikes is 60◦. The straight-line distance from the starting point of the spur dike root to the spur dike head is 1.2 m (relative length is 0.60, ratio of the straight-line distance from the starting point of the spur dike root to the spur dike head to width of flume), and the height of the spur dike is 0.35 m.

The flow velocity was measured with an acoustic doppler velocimetry system (Sontek ADV, Sontek, Inc., San Diego California, CA, USA). The data acquisition frequency was 25 Hz and processed by winADV (a post-processing software, developed by the USA Department of the Interior). After removing data with a correlation coefficient lower than 70 and a signal-to-noise ratio less than 20, the average flow velocity and the three-dimensional pulsation flow square root at each measurement point were obtained.

The crucian, which are sensitive to changes in water flow, were selected as the test fish. The fish had a body length of about 15 cm and were caught from a natural reservoir. Initially, they were kept in a2m × 1.2 m × 0.9 m (length × width × depth) pool for three days, with regular feeding and the water changed regularly. Feeding was curtailed one day before the test. The fish distribution during the test was recorded by a high-definition camera mounted about 3 m above the spur dike. The camera resolution was 1920 × 1280 pixels, 25 frames per second.

**Figure 1.** Test layout: (**a**) experimental layout of the rock-fill spur dike and the permeable spur dike, (**b**) test layout of the w-shaped rock-fill spur dike and the w-shaped permeable spur dike and (**c**) pictures of spur dikes. The unit in the figure is m. The grid points around the spur dike are the measurement points.

#### *2.2. Experimental Procedure*

For all experiments, the test flow discharge of the rock-fill and permeable spur dikes was 0.12, 0.18 and 0.24 m3/s, and the water depth was 0.60 m. The test flow discharge of the w-shaped rock-fill and w-shaped permeable spur dikes was 0.18 and 0.20 m3/s, and the water depths were 0.35 and 0.40 m, respectively. Flow conditions of all experiment were listed in Table 1. The flow velocity of the water layer 5 cm from the bottom was measured as the representative flow velocity of the corresponding point. A total of 900 data measurements were made at each point. The measurement range of the rock-fill and permeable spur dikes is as follows: 1.0 m upstream from the dike axis and 1.80 m downstream of the dike in the direction of water flow. The streamwise direction starts from the side of the dike root, from 0.1 to 1.6 m, and the measurement interval is 0.1 m. The measurement range of the w-shaped rock-fill and w-shaped permeable spur dikes is from 1.8 m upstream to 2.0 m downstream from the dike along the direction of water flow. The streamwise direction is from 0.1 to 1.6 m, and the measurement interval is 0.1 m, as shown in Figure 1.

The water flow conditions for the fish aggregation test and the spur dike setup were the same as the hydrodynamic test. For each test, after the water level and flow velocity were adjusted to working conditions, 25 fish were placed near the net at the tail of the flume. The camera was used to record the aggregation status of the test fish around the spur dike. After the test, the fish were removed and separated. It should be noted that different fish groupings were used in each test. Each test started at 9:30 a.m. and ended at 15:30 p.m. on the same day. During the test, no one was close to the flume, and the test fish distribution was observed on the video recorder through the camera.


**Table 1.** Test conditions and water flow diversity.

#### *2.3. Data Processing*

#### (1) Flow data process:

The flow velocity of each point was calculated using the recorded average flow velocity. The calculation formula is as follows

$$
\mathcal{U} = \sqrt{\overline{\mu}^2 + \overline{\upsilon}^2 + \overline{w}^2},
\tag{1}
$$

where *u*, *v*, and *w* are the average flow velocity in the streamwise, transverse, and vertical directions of the measurement point, respectively.

The turbulent kinetic energy can be calculated by the following formula:

$$k = \frac{1}{2} (\overline{u'u'} + \overline{v'v'} + \overline{w'w'}),\tag{2}$$

where *u* , *v* , and *w* are streamwise, transverse, and vertical pulsating flow velocity. *u* = *u* − *u*, *v* = *v* − *v*, *w* = *w* − *w* are the difference between the instantaneous flow velocity and the average flow velocity. *u*, *v*, and *w* are instantaneous flow velocity in the streamwise, transverse, and vertical directions.

(2) Flow data standardized:

When the test group is different, the numerical values of the hydrodynamic parameters are quite different, and the flow velocity and the turbulent kinetic energy are inconsistent, making comparisons difficult. Therefore, the data was standardized. The standardization of dispersion (min–max standardization) preserves the data trend and "compresses" the data to 0–1, facilitating the comparison of multiple datasets, so this method was used to normalize the flow velocity and turbulent kinetic energy data. The calculation for standardization of dispersion can be expressed by:

$$y\_i = \frac{X\_i - X\_{\text{min}}}{X\_{\text{max}} - X\_{\text{min}}} \, ^\prime \tag{3}$$

where *yi* is the standardized data, *Xmin, Xmax, Xi* are the minimum, maximum and *i-th* data respectively.

(3) Fish aggregative data process:

At the beginning of the test, the fish were adapting to the conditions, so their positions changed greatly. Therefore, only the fish data from 10:00 a.m. to 15:00 p.m. were used in the actual analysis. A sample was taken every 30 min, and each sample was 5 min long. A picture was taken at every 10 s to record the frequency and position of the test fish. To eliminate influence of flow conditions and spur dike size on laboratory test data and on-site observation data, the average aggregation rate (*AAR*) was used to express the attraction effect of the spur dike on test fish [37]. This index indicates the ratio of

the amount of gathered fish around the spur dike to the total number of test fish after setting each spur dike and is calculated by the following formula:

$$AAR(\%) = \frac{\sum\_{i=1}^{n} N\_i}{nN} \times 100\%,\tag{4}$$

where *Ni* is the number of fish gathered around the spur dike of the *i-th* observation, *N* is the total number of test fish, and *n* is the number of observations.

#### **3. Results and Discussion**

#### *3.1. Mean Flow Characteristic*

Table 1 shows the range of average flow velocity and turbulent kinetic energy around different types of spur dikes in the two different test groups. As listed in Table 1, mean flow velocity of different spur dikes at the same statistical area within a test is almost the same, but the max-min range is different, as that of the rock-fill spur dike is larger than the permeable spur dike. Both mean turbulent kinetic energy and the max-min range of the rock-fill spur dike are larger than that of the permeable spur dikes of the same statistical area within a test, especially for the w-shaped spur dikes. Generally speaking, spur dikes extend max-min range of velocity and turbulent kinetic energy, especially the rock-fill and the w-shaped rock-fill spur dikes.

Figure 2 shows the flow velocity and turbulent kinetic energy distribution around the rock-fill spur dike and permeable spur dike at a discharge of 0.18 m3/s and average depth of 0.60 m. Figure 3 shows the flow velocity and turbulent kinetic energy distribution around the w-shaped rock-fill spur dike and w-shaped permeable spur dike at a discharge of 0.20 m3/s and average depth of 0.40 m. Four types of spur dike are submerged in water.

When water flows through the rock-fill spur dike (Figure 2b), the flow velocity on the water-facing side of the dike body gradually decreases due to water-blocking by the dike body. The upstream is restricted and moves towards another side of the flume. After passing the head of the spur dike, the narrowest main flow cross-section will be formed due to inertia (A-A in Figure 2b). Then, the main flow diffuses gradually along the flume. Meanwhile, a very small flow velocity region is formed on the backwater side. The flow boundary lay behind the spur dike sperate from the groin when flow is passing the groin head. Eddies are formed downstream of the separated point and move forward one by one. The moving eddies collide, break and merge with each other, and the corresponding turbulent kinetic energy is large. However, the turbulent kinetic energy in other areas is low, and in the vicinity of the dike body it is almost zero.

The permeable spur dike can divert flow and narrow flow area as well as rock-fill spur dike. At the same time, as the permeable spur dike had good water permeability, the narrowest main flow cross-section moves down (B-B in Figure 2a), the flow mixing area with high turbulent kinetic energy move towards the main flow. Flow velocity and turbulent kinetic energy in the vicinity of the dike body was low—but not zero. The zone with low flow velocity and low turbulence was diminished compared with the rock-fill spur dike. The gradient of flow velocity and turbulent kinetic energy is lower than that of the rock-fill spur dike, as the disturbance on flow of permeable spur dike is reduced.

The w-shaped spur dike preserves the water flow characteristics of the spur dike, but there are differences as well—mainly in the vicinity of the dike. Oblique dikes (1, 2, 3, 4 in Figure 2b) of the w-shaped rock-fill spur dike are inclined, which causes large flow velocity at the two junctions on the lower side of the dike (area around A and B in Figure 3b). After flow passes over the first two straight-line dike (1 and 2 in Figure 3b), flow from two directions come across and mix in the downstream area of the spur dike (area around D in Figure 3b), where flow velocity and turbulent kinetic energy are very high (area around D in Figure 3d). A similar area around E (in Figure 3b) is affected by flow around the groin head as well as the mix effect of flow from dike 3 and dike 4 (in Figure 3b), which makes flow velocity and turbulent kinetic energy small.

The w-shaped permeable spur dike has a similar diversion function as the w-shaped rock-fill spur dike, which causes flow to come across and mix around the two junctions on the lower side of the dike (the area around A and B in Figure 3a). However, as the w-shaped permeable spur dike has large porosity, flow velocity of the main flow (the area around F in Figure 3a) is smaller than that of the w-shaped rock-fill spur dike, and opposite in the vicinity of the dike (the area around A, B, D, F in Figure 3a). Frames of w-shaped permeable spur dike have excellent energy dissipation capacity. Flow run through those frames would generating high level turbulent kinetic energy in the vicinity areas downstream of the w-shaped dike (D, E, and C in Figure 3c).

**Figure 2.** Hydrodynamic distribution of permeable spur dike and rock-fill spur dike (flow velocity is 0.18 m3/s, water depth is 0.60 m; flow direction is from left to right, distance unit in the figure is m, same as below); (**a**) Average flow velocity distribution of permeable spur dike; (**b**) Average flow velocity distribution of rock-fill spur dike; (**c**) The turbulent kinetic energy distribution of permeable spur dike; (**d**) The turbulent kinetic energy distribution of rock-fill spur dike .

**Figure 3.** Hydrodynamic distribution of w-shaped permeable spur dike and rock-fill spur dike and aggregation of test fish (flow velocity is 0.20 m3/s, water depth is 0.40 m). (**a**) Average flow velocity distribution of w-shaped permeable spur dike; (**b**) Average flow velocity distribution of w-shaped rock-fill spur dike; (**c**) The turbulent kinetic energy distribution of w-shaped permeable spur dike; (**d**) The turbulent kinetic energy distribution of w-shaped rock-fill spur dike.

#### *3.2. Water Flow Diversity*

Entropy is a measure of system disorder, which is an extensive property of a thermodynamics system. In 1948, Shannon introduced the notion of entropy to information theory in order to measure the quantity of information contained in a message [38]. Entropy is a fundamental concept linking together information theory and statistical physics [39]. For a set of possible events {*x*1, *x*2, ... , *xn*} whose probabilities of occurrence are *p*1, *p*2, ... , *pn*. The information entropy or Shannon's entropy is expressed by:

$$H = -\sum\_{i=1}^{n} P\_i \ln P\_i. \tag{5}$$

The more uncertain and heterogeneous the possible event, the greater Shannon's entropy; the more certain and homogeneous the possible event, the smaller Shannon's entropy. For only one type in the data set, Shannon's entropy equals zero. Therefore, high Shannon's entropy stands for high diversity, low Shannon's entropy for low. The Shannon's entropy equation provides a way to quantifies the randomness of probability laws and is a measure of heterogeneity commonly applied in the fields of statistical physics, information theory, ecology [39,40].

The spur dike is a permanent disturbance for a river flow system at reach scale. In order to eliminate the disturbance, the river flow regime is changed and spatial distribution, range of mean velocity and turbulent kinetic energy are modified (analyzed in Section 3.1), which can be used to describe flow diversity around the spur dike. Mean velocity and turbulent kinetic energy are important parameters reflecting the engineer effect, structure stability as well as the habitat quality. Based on Shannon's entropy, we devised a water flow diversity index *HF*, to measure the diversity of water flow around the spur dike. It is defined as the product of the regional flow velocity diversity index *HV* and the turbulent kinetic energy diversity index *Hk*, which can be expressed by:

$$H\_{\rm F} = H\_{\rm V} \times H\_{\rm k\nu} \tag{6}$$

*Water* **2019**, *11*, 1822

$$H\_V = -\sum\_{i=1}^{n} P\_{Vi} \ln P\_{Vi} \tag{7}$$

$$H\_k = -\sum\_{i=1}^n P\_{ki} \ln P\_{ki} \tag{8}$$

where *n* is the level of flow velocity and turbulent kinetic energy. *n* is 10, meaning that the measured flow velocity and turbulent kinetic energy are divided into 10 levels after standardization, which is from 0.1 to 1.0. *PVi* and *Pki* are the ratios of i-th flow velocity and turbulent kinetic energy to the total area of the studied area, respectively. According to Equation (6), for the present study, HF reaches a maximum when *PVi* = *Pki* = 0.1, and HFmax = ln(10) <sup>2</sup> = 5.30. Namely, the more uniform the area ratio of flow velocity and turbulent kinetic energy, the larger the HF, indicating a higher water flow diversity around the spur dike. The area ratio of some level(s) of the flow velocity (turbulent kinetic energy) is not zero—however, it is extremely small, making it impossible to provide an effective habitat for fish. Therefore, the flow velocity and turbulent kinetic energy with an area ratio of less than 5% was excluded in actual calculations. Additionally, gaps among gravels of flume experiments are too small to use for fish, so this area was excluded in the statistics when calculating the water flow diversity index.

According to Equations (6)–(8), the water flow diversity index HF around the spur dikes for each working condition were calculated and the results are shown in Table 1. Under the different waterflow conditions, the values and distribution of flow velocity and turbulent kinetic energy are different. However, the water flow diversity index calculated after the nondimensionalization fluctuates within a certain range, which means the water flow diversity around a particular spur dike structure can be represented by a constant, such as the rock-fill spur dike, where the mean HF is 1.19 ± 0.05. According to the analysis above, the larger the constant—the higher the diversity of the water flow. Based on our calculations, the water flow diversity index around the four spur dikes ranged from 1.13 to 2.896, in the order (from high to low): w-shaped permeable > w-shaped rock-fill > permeable > rock-fill spur dike. The regional ratio of standardized velocity and standardized turbulent kinetic energy of different spur dikes is shown in Figure 4. Flow conditions are the same as discussed in Section 3.1. Under the same water flow conditions, the flow velocity and turbulent kinetic energy around the rock-fill spur dike was higher than that of the permeable spur dike, but the area of particularly large flow velocity and turbulent kinetic energy is small, and the area of slow flow zone is large, which makes small parts of standardized velocity and turbulent kinetic energy account for most of the area. The rock-fill spur dike, with a standardized velocity of 0.8, 0.9 and 1.0 accounts for 70% of the area, and the standardized turbulent kinetic energy of 0.2 takes up 67% of the area. The flow velocity and turbulent kinetic energy area ratios around the rock-fill spur dike are quite different at each level, while those around the permeable spur dike are relatively uniform. The corresponding water flow diversity index value is relatively high as well. For the w-shaped spur dike, its structural design increases the complexity of the water flow in the adjacent area of the dike (refer to the analysis above). As shown in Figure 4, subsequently, the corresponding water flow diversity index increases as well.

**Figure 4.** Regional ratio of velocity and turbulent kinetic energy (flow condition is the same as Figures 2 and 3).

#### *3.3. Relationships between Fish Aggregation and Water Flow Diversity Index*

The aggregation of the test fish around the rock-fill spur dike and permeable spur dike at discharge of 0.18 m3/s are shown in Figure 5, and the gathering of the test fish around the w-shaped rock-fill spur dike and the w-shaped permeable spur dike at discharge of 0.20 m3/s are shown in Figure 6. Overall, the test fish mainly gathered in the slow-flow area on the back side of the spur dike where flow velocity are nearly the lowest (Figures 2, 3, 5 and 6). For spur dikes of the same shape, the average aggregation rate of the test fish around the permeable spur dike was higher, and the aggregation range larger than that of the rock-fill spur dike. The test fish in the w-shaped spur dike would gather in the slow-flow area on the back side of the dike, but gathered in the slow-flow area on the water-facing side of the dike as well—especially for the W-shaped permeable spur dike. This can be explained by the following: the water-blocking effect of the rock-fill spur dike reduces flow velocity on the back side of the dike to extremely low levels, and the flow velocity and turbulent kinetic energy in the water flow mixing zone vary greatly. Additionally, the test fish need to use more energy if they want to stay, and the drastic change of the water flow environment makes it difficult for them to maintain their stability as well. However, the volume velocity of the slow-flow zone on the backwater side of the permeable spur dike is not zero—and there is a certain pulsation. In the water flow mixing zone behind the spur dike, flow velocity and turbulent kinetic energy vary only slightly so fish can gain power from the turbulence to reduce their own energy loss. Additionally, compared with the rock-fill spur dike, the structural design of the w-shaped rock-fill spur dike makes water flow around the spur dike more complex. The flow velocity and the turbulent kinetic energy gradient around the w-shaped permeable spur dike are lower than that of the w-shaped rock-fill spur dike as permeability of the permeable spur dike, which is easier for fish to maintain their stability. Besides, compared with the rock-fill spur dikes, cavity within the permeable spur dikes provides refuge for fish, which is an important factor for fish gathering and is widely applied in artificial reef design.

**Figure 5.** Aggregation of test fish of permeable spur dike and rock-fill spur dike (flow velocity is 0.18 m3/s, water depth is 0.60 m; "◦" represents fish location, flow direction is from left to right, distance unit in the figure is m, same as below). (**a**) Test fish distribution of permeable spur dike; (**b**) Test fish distribution of rock-fill spur dike.

**Figure 6.** Aggregation of test fish of w-shaped permeable and rock-fill spur dikes (flow velocity is 0.20 m3/s, water depth is 0.40 m). (**a**) Test fish distribution of w-shaped permeable spur dike; (**b**) Test fish distribution of w-shaped rock-fill spur dike.

Test fish average aggregation rate around the spur dike of each test was listed in Table 1. The average aggregation rate of the test fish around the w-shaped permeable spur dike was the highest (about 28%), while around the rock-fill spur dike it was the lowest (about 14%). Figure 7 shows the relationship between the test fish average aggregation rate and the water flow diversity index. It is not difficult to conclude that for a certain type of spur dike under different flow conditions, fish average aggregation rate increases with water flow diversity index—except for one group. For different types of spur dikes, average aggregation rate of all test increases with average water flow diversity index. In other way, the aggregation effect of the spur dike is enhanced with an increase in water flow diversity. A relation curve between average aggregation rate and water flow diversity index was plotted with a linear fitting method using experiment data. However, fish movement is random, turbulent flow and its relationship with complex correlations between water flow diversity index and average the fish aggregation is not very high.

**Figure 7.** Relationship between water flow diversity and average aggregation rate.

At present, before a newly designed structure applied in channel regulation or river restoration, a series of flume experiments and numerical studies have to be conducted to research flow characteristics (mean and turbulent), geomorphologic changes, habitat suitability, which would cost a lot of time and money. Although new layouts or structures of the spur dike were proposed and applied, it's still difficult to quantified parameters of flow diversity around spur dikes. Studies have demonstrated the importance of turbulence on fish swimming [30,41] and habitat selection [11,26,27,32]. However, fish movement is random, different fish have their own habits, and the complexity of turbulence and mechanisms of fish assemblage in a turbulent environment is still not clear, all these factors increase the difficulty of quantified research on fish responses to turbulent flow. The new relationship between structure and water flow complexity, average aggregation rate of test fish and water flow complexity in our research can provide a tool and a new method to determine which type of structure to be chosen and how to optimize the structure.

However, flow characteristic of spur dikes is affected not only by layouts and made-up elements, but also by parameters of spur dikes (such as length, height, porosity), their relative relations with flow (like ratio of height of spur dike to depth), which may change water flow diversity. Besides, as mention above, different fish (including different species and a specie of different age) have different habits. More research needs to be conducted—especially quantitative studies on flow characteristics and flow diversity of different spur dikes and studies on the relationship between more fish (different species, a specie of different life stage) aggregation and turbulent flow characteristics.

#### **4. Hydroacoustic Investigation of Laohutan Fish-Bone Dike, the Dongliu Reach and the Yangtze River**

#### *4.1. Project Background and Investigation Techniques*

The Dongliu reach is located between Jiujiang and Anqing in the downstream part of the Yangtze River (Figure 8). The waterway is complex and variable in the dry season with poor navigation conditions. It has always been one of the key shallow waterways of the Yangtze River. To limit the development of Donggang, control the width of the left-hand rectification line of Laohutan, increase the flow velocity of the left-hand of Laohutan, and improve the water depth of the left-hand waterway, the Yangtze River Waterway Bureau built a fish-bone dike at the head of Laohutan. The project began in November, 2012 and was completed in April, 2014. The fish-bone dike consists of a 1050 m ridge dike and two thorn dikes (342 and 521 m, respectively). The first 100 m in front of the right side of the thorn dike is a four-side six-edge permeable dike, and the other part is a rock-fill structure. Two investigations were carried out for the water flow during the season, using the flow of the Datong Station which can be used to represent the flow of the Dongliu reach as it is located 120 km downstream, with no large tributaries in between. During the dry season in 7 December 2016 the flow at the Dantong station was 13,022 m3/s and the flood flow there on 8 August 2017 was 46,190 m3/s.

**Figure 8.** Fish-bone dike Project at Laohutan of the Dongliu reach Waterway.

A BioSonics-DT-X-Digital Scientific Echosounder (BioSonics, Inc., Seattle, WA, USA) was used to investigate the distribution of fish around the fish-bone dike. Its transducer has an operational frequency of 208 khz and split-beam of 6.5◦. The investigation time was from 9:00 a.m. to 16:00 p.m. The transducer of the Biosonics DT-X echo detector (BioSonics, Inc., Seattle, WA, USA) was fixed to the trimaran and the trimaran was tied to the fishing boat's head by a rope. The transducer was about 0.4 m into the water and inclined at 45◦ to the water surface. Multiple navigation measurements were conducted around the fish-bone dike to cover as much of the dike as possible. Hydroacoustic data acquisition was performed using BioSonics Acquisition 6.0 software (BioSonics, Inc., Seattle, WA, USA). The pulse frequency of the transducer was 8 pps, the pulse width was 0.5 ms, the data acquisition threshold was −130 dB, and the data acquisition distance was 1–30 m. Using a Garmin GPS 17x HVS, GPS data was synchronously collected and stored as well. The instrument was calibrated in the field

using a 36 mm tungsten carbide standard ball prior to measurement. Hydroacoustic data collected from on-site observations were analyzed using BioSonics Visual Analyzer 4.3 (BioSonics, Inc., Seattle, WA, USA) to identify fish location and to record fish frequency of occurrence. The data analysis started from the 1 m position of the beam and synchronously outputted the monomer echo recognition result. The single echo recognition parameters were as follows: the echo threshold was −60 dB, the correlation coefficient was 0.90, the minimum pulse width coefficient was 0.75, the maximum pulse width coefficient was 3, the termination pulse width was −12 dB and the time-varying gain (TVG) was 40 lgR.

Field velocity in large river are usually measured with ADCP (Acoustic Doppler Current Profilers, produced by Teledyne RD Instruments, Poway California, CA, USA), and Vector Current Meter (point measure) (Nortek AS, Rud, Norway). Flow turbulent characteristics can be derived from the measured data of ADV (Nortek AS, Rud, Norway), or ADCP (Teledyne RD Instruments, Poway California, CA, USA) measure data [42,43], but the velocity measured devices need to be held still for a certain period. It means the devices must be fastened to a holder that can be fixed on the riverbed. According to the physical model research results, velocity around heads of the fish-bone is about 1.5 m/s, and D-shaped mattress and four-side six-edge permeable frames were placed around the dike to protect the structure [44]—which makes it difficult and dangerous to set a holder to fix ADCP and ADV. Besides, flow characteristic of rock-fill spur dike and permeable were measured and analyzed using experiment data. Flow around the rock-fill dikes and the permeable in Dongliu reach were not measured.

#### *4.2. Results*

During on-site observation, it was difficult to accurately determine the total fish *nN* due to the ship's disturbance and limited measurement coverage. Therefore, the total number of fish observed was taken as the total fish *nN*. The permeable spur dike area was 200 m × 300 m and surrounded by the 100 m of water-permeable dike facing the water side, the 100 m in front of the dike head, and the 200 m backwater side of the dike. The counting range of the rock-fill dike was the left-hand area of the fish-bone dike. The habitat selection of fish is affected by many factors, including hydrological, hydraulic, biological and the life stage of the fish. In our research, permeable spur dike and rock-fill spur dike are adjacent, and flow discharge, sediment size, temperature, fish composition are almost the same. The difference is the range and spatial distribution of velocity and turbulence, mainly caused by makeup of the spur dike, which affect fish aggregation of the spur dike. In other words—the fish aggregation rate in the Dongliu reach is comparable.

During water flow in the dry season on 7 December 2016, there were 65 fish observed in the fish-bone dike, including eight fish in the rock-fill spur dike and 17 fish in the permeable spur dike. The corresponding average aggregation rates were 12% and 26%, respectively. During flood flow on 8 August 2017, there were 69 fish observed in the fish-bone dike, including 11 fish in the rock-fill spur dike and 19 fish in the permeable spur dike. The corresponding average aggregation rates were 16% and 28%. Thus, it can be concluded that fish aggregation was better in the permeable spur dike than the rock-fill spur dike.

The permeable spur provides more heterogeneous flow environment than rock-fill spur dike (analyzed above), which is attractive for different fish (different species and a species of different life stage). Flow velocity in downstream of Yangtze River is very fast, which make it difficult for plankton and macroinvertebrate survive as their weak swimming ability. The flow velocity behind the permeable spur dike is slow but not almost still as where of the rock-fill spur dike, which provides a stable habitat for plankton and macroinvertebrate, increases feeding potential for fish. Besides, cavities with the permeable spur dike provide refuge for fish larvae and other small dwellers from rapid flow and predators [3,45,46]. In some degree, the permeable spur dikes work as an artificial reef applied to increase reef fish habitat quantity and quality, protect marine life, reduce user conflicts, and so on [47]. The artificial reef-like permeable spur dike makes it more attractive for fish than the rock-filled spur dike and has a greater fish aggregative rate.

In this section, hydraulic parameters were not measured for the complex flow environment. But Hydraulic characteristics are a key factor affecting habitat use of fish, and a link between results of flume experiments and field. Systematically monitors and analysis on hydraulic distribution, geomorphic change, dwellers (plankton, macroinvertebrate and fish) diversity around the permeable and rock-fill spur dikes in Laohutan, Dongliu are necessary in the future.

#### **5. Conclusions**

Rock-fill, permeable, w-shaped rock-fill, and w-shaped permeable spur dikes were selected for flume experiments to investigate their influence on water flow diversity and the relationship between water flow diversity and fish aggregation. Additionally, a fish hydroacoustic study was conducted on the Laohutan fish-bone dike in the Dongliu reach of the Yangtze River to investigate fish aggregation effects around rock-fill and permeable spur dikes in the field.

(1) Based on Shannon's entropy theory, a water flow diversity index, HF was proposed to calculate water flow diversity.

(2) The water flow diversity index values of different types of spur dikes under different flow condition were calculated, reflecting the degree of water flow diversity around the different spur dikes. The water flow diversity index values of the four different types of spur dikes are 1.13–2.96, and from high to low are: w-shaped permeable > w-shaped rock-fill > permeable > rock-fill spur dike.

(3) The test fish gathered in the backwater side slow-flow area of the spur dike, and the average aggregation rate was 5% to 28%. The attraction effect of the spur dike to fish increases with an increasing water flow diversity. The relationship between water flow diversity index and average fish aggregation rate was plotted, which provides a new method to assess the environmental effects of spur dikes.

(4) The permeable spur dike had a better fish aggregation effect than the rock-fill spur dike in the field at Laohutan fish-bone dike of the Dongliu reach Waterway in dry and flood seasons.

(5) The permeable spur dike works as a river training structure as well as an artificial reef: it alters hydrodynamic conditions, the sediment transport regime, and at the same time generates more heterogeneous flow than rock-fill spur dike, providing shelter for fish and other small organism, increasing fish habitat quantity and quality and reducing conflicts of river training and river protection.

The research results of this paper could provide theoretical support for the evaluation and analysis of habitat water flow diversity, as well as ecologically optimal design of spur dikes.

These results derive from some certain types of spur dikes among different river training structures and a limited number of individuals—all of the same species. Future works should expand this work with more river training structures and fish across different species and life stages.

**Author Contributions:** Flume experiments, T.H.; hydroacoustic investigation, Y.L., T.H., H.L.; writing-original draft preparation, T.H.; writing-review and editing, Y.L., H.L.; supervision, Y.L.

**Funding:** This research was funded by the National Key Research and Development Program of China (Grant No. 2016YFC0402108) and Hydraulic Science and Technology Program of Jiangsu Province, China (No. 2017044 and 2018038).

**Acknowledgments:** We are particularly grateful to Dingan Zhang, Yi Liu and Weixu Wang for assisting on experiments and the hydroacoustic investigation.

**Conflicts of Interest:** The authors declare no conflict of interest.

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