Optimal Design and Fish-Passing Performance Analysis of a Fish-Friendly Axial Flow Pump

Abstract

In this paper, the parameters of a prototype runner of an axial flow pump are optimized by using the immersion boundary–lattice Boltzmann numerical method based on a large-eddy simulation (LES-IB-LBM). A fish-friendly axial flow pump with a leading-edge thickness of 11.4 mm and blade cutting angle of 18° is proposed. Through experiments, the living conditions of many kinds of fish in extremely positive and negative pressure environments are explored, and the probability of damage caused by pump to fish is analyzed by taking −40 kPa as the low-pressure damage threshold. The flow passage of the fish-friendly axial flow pump effectively guides the fish to low-risk areas, reducing the risk of friction, shear, and impact damage to the fish. The total impact mortality ratio of runners before and after the axial flow pump optimization is close to 7:1.

1. Introduction

Because of its characteristics of a large transmission flow and low transport head, the axial flow pump is used in the water network and water system on a large scale, undertaking important missions such as interbasin water transfer, flood control and drainage, drought resistance, and disaster reduction [1]. Dense pumping stations have a particularly great impact on the reproduction and spawning of migratory fish, and the extinction of fish stocks caused by the failure to lay eggs significantly affects the entire ecosystem [2]. According to the fish ladder that has been used in all kinds of dam water control projects, their actual operation effect is ineffective [3].

The probability of fish injury is closely related to the shape of key flow channels of hydraulic machinery [4,5]. Fish may be subjected to mechanical, pressure, shear, and cavitation erosion damage [6,7]. Shao et al. [8,9] found that negative pressure caused more damage to fish than positive pressure. Cada [10] found that the pressure threshold of a fish’s swim bladder was 0.3 times the atmospheric pressure, and that of a fish’s closed swim bladder was 0.6 times the atmospheric pressure. When the pressure in the pressure channel is lower than −50 kPa, about half an atmosphere, fish are vulnerable to damage [5]. When the internal pressure drop rate of the turbine is greater than 3.5 MPa·s⁻¹, the fish body is damaged by a pressure gradient [11]. High shear strain rates have been found near the blades, guide blades, runners, and draft pipes of large axial-flow propeller turbines [12]. Neitzel et al. [13,14] pointed out that the safe threshold of shear strain rate for fish damaged by the fluid shear force and turbulence is 500 s⁻¹.

The design theory of the axial flow pump is determined by its three-dimensional unsteady flow characteristics and high specific speed characteristics. The binary design theory is usually used in the design, mainly the plane in-line cascade design theory [15]. In the era when computational fluid dynamics is widely used, numerical calculation can achieve more detailed and in-depth information extraction in the exploration of the internal flow law of hydraulic machinery [16].

Alden’s team [17,18] designed a spiral centrifugal single-blade runner to reduce the pressure gradient and velocity gradient on the runner blade. Voith’s team [19,20] put forward a new design concept that could reduce the damage rate of mechanical fish, including reducing the gap in the flow channel, reasonably arranging the position of fixed guide vane and movable guide vane, and so on. Alstom [21,22] also designed a runner with minimum clearance from the same point of view as the Voith team. David [23] and Li [24] studied a kind of upward-flow hydraulic turbine, which removed the draft tube structure. This significantly increased the amount of dissolved air in the current, improved the drastic change in pressure, and reduced the damage caused by the fish passing through the machine. Zhang’s team from Jiangsu University in China and Bosman Water management Co., Ltd. in the Netherlands used the blade impact model [25] to predict the damage of fish passing through the pump. They also designed axial flow pump runners with low impact and no impact damage. Pan et al. [26] combined the Lagrangian tracking method with computational fluid dynamics to discuss the motion behavior and damage mechanism of fish passing through an axial flow pump.

The lattice Boltzmann method is a particle-based solver, and the calculation depends on a set of automatically generated octree-structured lattices [27,28], which avoids the error-prone unstructured mesh reconstruction. Scholars such as Cheng and Li [29,30] of Wuhan University obtained the transient flow data of a three-dimensional tubular turbine by IB-LBM. The calculation showed that when simulating the load rejection and increasing the load conditions of the cross-flow turbine, the velocity change, pressure change characteristics, and the increase and decrease law of the axial force obtained by IB-LBM accorded with the conventional conditions and could achieve better transient-flow simulation results. Li [31,32] of Xi’an University of Technology calculated the motion of thin-scale salmon in a tubular turbine by using the submerged boundary–lattice Boltzmann coupling method and analyzed the pressure and pressure gradient damage suffered by the fish passing through the inner passage of the turbine. The results showed that the IB-LBM method could simulate the spatial location and damage of fish in the hydraulic turbine.

At present, the research on fish-friendly hydraulic machinery is still in the early stage of exploration and lacks more reliable analysis and research methods. In past research, streamlines or particles were generally used to replace the real fish flow for numerical simulation. Some scholars use the overlapping grid or DEM method, which generally has a low success rate or low efficiency, and the results obtained are difficult to truly represent the problems found in the simulation calculation.

In this paper, firstly, according to the different adaptations of different fish to water pressure, the corresponding evaluation index of fish pressure damage is designed through experiments. The geometric structure optimization design is carried out based on the pressure damage evaluation index and the axial flow pump design theory. At the same time, the LES-IB-LBM method is creatively introduced to simulate the fish body passing through the axial flow pump and the damage degree more accurately.

2. Experiment

2.1. Experimental Device and Experimental Fish

Figure 1 is a three-dimensional model of a pressure damage analysis test device for fish.

The set of test devices consisted of three steel cylindrical pressure tanks. The main test equipment was a visual steel tank (T2) located in the middle, a high-pressure steel tank (T1) connected on one side of the tank, and a vacuum steel tank (T3) on the other side. The high-pressure steel tank and vacuum steel tank were used to quickly control the internal pressure of the system, so the two steel tanks were externally connected with a high-power air compressor and a high-power vacuum pump, respectively. The tank size was customized according to the size of the test site, and the motor power met the maximum test requirements. The visual steel tank was designed as an uplift steel tank, which held about 1 ton of water for the test fish in the experiment. A toughened glass window was arranged at a height of 1.5 m in front of the tank, and the pressure resistance of the glass was above the test pressure range.

Pressure monitoring devices were arranged on each steel tank, including a pressure gauge on T1, a vacuum gauge on T3, and two high-range vacuum pressure gauges on T2, which could monitor both positive and negative pressure. The measuring range of the pressure gauge used was 1.6 MPa, the scale value was 0.05 MPa, the measuring range of the vacuum gauge was −0.1 MPa, the scale value was 0.002 MPa, the measuring range of the vacuum pressure gauge was from −0.1 to 0.9 MPa, the scale value was 0.02 MPa, and each range was within the pressure range involved in the test.

In this paper, three common freshwater fish species, cultured crucian carp, wild crucian carp, and yellow catfish, were selected in the pressure damage experiment. The average body length was 120 mm. The different kinds of fish used in the experiment are shown in Figure 2.

2.2. Experimental Scheme

Before the start of the experiment, we turned on the thermostat and fresh-air device to keep the oxygen supply. The experimental fish were reared in an environment with a pH value of 7 ± 5% and a water temperature of 15 ± 1 °C for more than 24 h to remove the fish with poor vital signs. Each experiment used 100 fish. The positive pressure threshold were 340 kPa and 680 kPa, and the negative pressure threshold were −20 kPa, −40 kPa, and −80 kPa.

During the positive pressure test, we ensured that the valve connected to the T1 air compressor was open and the other valves were closed. At that time, we started the air compressor, and when the T1 pressure rose to the set value, we closed the valve first, and then closed the air compressor. Slowly, we put the test fish into T2, locked the top cover bolt, opened the valve connecting T1 and T2, and at the same time, we observed the reaction of the fish in the visual window and recorded the pressurization time; when T2 was pressurized to a given pressure value, we ensured that the pressure change rate of each group was the same, we closed the valve for three minutes and slowly opened the vent valve to make T2 fully return to atmospheric pressure. Then, we took out the experimental fish and put them in a designated flume for culture. During the negative pressure test, we made sure that the valve connected to the vacuum pump T3 was open and the other valves were closed. At that time, we started the vacuum pump, and when the vacuum meter connected by T3 reached the set vacuum value, we first closed the valve and then closed the vacuum pump. The rest of the process was the same as the barotropic experiment.

At the end of the experiment, all experimental fish were cultured for seven days, and the control group was set up at the same time. The control group was put into T2 and stayed airtight for three minutes, but there was no pressure change, so as to reduce the uncertainty of the experiment. In the process of fish culture, the survival of fish was observed, the number of abnormal fish affecting vital signs such as eyeball congestion, being unable to keep balance, and the number of dead fish were counted, and the mortality and survival rate of fish were calculated. The related process and results of the experiment are shown in

Table 1. Setting of pressure threshold and damage of fish in the positive pressure experiment.

Experimental Label	Fish Species	Pressure Threshold (Mpa)	Increase Pressure Time (s)	Increase Pressure Rate (kPa·s−1)	The Number of Abnormal Fish	The Number of Dead Fish	The Proportion of Dead Fish (%)	The Proportion of Surviving Fish (%)
0C	Cultured crucian carp	0.101	0	0	3	0	0	100
0W	Wild crucian carp				6	18	18	82
0Y	Yellow catfish				0	3	3	97
1C	Cultured crucian carp	0.34	24	13.6	18	20	20	80
1W	Wild crucian carp				6	18	18	82
1Y	Yellow catfish				0	4	4	96
2C	Cultured crucian carp	0.68	48	13.6	17	72	72	28
2W	Wild crucian carp				3	19	19	81
2Y	Yellow catfish				1	8	8	92

and

Table 2. Setting of pressure threshold and damage of fish in the negative pressure experiment.

Experimental Label	Fish Species	Pressure Threshold(Mpa)	Increase Pressure Time (s)	Increase Pressure Rate (kPa·s−1)	The Number of Abnormal Fish	The Number of Dead Fish	The Proportion of Dead Fish (%)	The Proportion of Surviving Fish (%)
0C	Cultured crucian carp	0.101	0	0	3	0	0	100
0W	Wild crucian carp				6	18	18	82
0Y	Yellow catfish				0	3	3	97
3C	Cultured crucian carp	−0.02	6	3.33	12	76	76	24
3W	Wild crucian carp				6	6	6	94
3Y	Yellow catfish				2	13	13	87
4C	Cultured crucian carp	−0.04	12	3.33	0	100	100	0
4W	Wild crucian carp				1	19	19	81
4Y	Yellow catfish				6	37	37	63
5C	Cultured crucian carp	−0.08	24	3.33	0	100	100	0
5W	Wild crucian carp				18	78	78	22
5Y	Yellow catfish				15	70	70	30

.

2.3. Experimental Results and Analysis

In this experiment, a set of devices suitable for internal pressure simulation of hydraulic machinery was constructed. The device mainly included a pressure tank, an air compressor, a vacuum pump, a pressure monitoring device, a number of valves, and connecting pipes. It was found that the two kinds of crucian carp showed the movement characteristics or trend of resisting the change in pressure when the external pressure changed. Qualitatively, wild crucian carp is more sensitive and flexible than cultured fish. Different fish species have different abilities to withstand positive and negative pressure. Whether positive pressure or negative pressure, the survival ability of wild crucian carp is stronger than cultured crucian carp. Excluding the effect of the experimental culture environment on fish bodies in the control group and based on a survival ratio of 80%, the negative pressure survival threshold of wild crucian carp and yellow catfish should be determined as −40 kPa. If the stay time is less than 2 min in a pressure environment higher than −40 kPa, both kinds of fish can exhibit a healthy survival. The survival rate of cultured crucian carp under negative pressure was significantly lower than that of other fish. Therefore, this paper established −40 kPa as the low-pressure damage threshold, which was used as a reference to analyze the probability of fish damage caused by the hydraulic turbine.

Through the anatomy of two kinds of crucian carp and yellow catfish, it was found that the body damage of positive and negative pressure was mainly concentrated in the swim bladder, eyeball, fin junction, skin, and so on. The injured or dead fish had congestion on the surface of the eyeball, body surface, and fin junction, and the rupture of the swim bladder of most fish could be observed under strong negative pressure. We found that the rupture and shrinkage of the swim bladder was the direct cause of fish death on the spot, and other complications caused by positive and negative pressure were the key factors to determine the final mortality of the experimental fish.

3. Numerical Simulation Method and Main Parameters of the Model

3.1. IB-LBM Method

In this paper, the submerged boundary–lattice Boltzmann method (IB-LBM) was used to study the trajectory and damage of fish passing through an axial flow pump. The immersed boundary method (IBM) is also essentially a boundary-handling format. The basic idea of the IBM is to approximate the boundary of an object by a set of marked points close to the mesh. These marked points affect the fluid only through the force field, and an interpolation template is introduced to transfer information between the mesh points and the marked points. This makes the implementation of complex boundaries relatively simple. The combination of IBM and LBM, proposed by Feng and Michaelides, is called the immersed boundary–lattice Boltzmann method (IB-LBM).

By discretizing the Boltzmann equation in several dimensions such as velocity, physical space, and time, the basic form of the lattice Boltzmann equation can be obtained as:

$$f_i(x+c_i\Delta t,t+\Delta t)=f_i(x,t)+{\omega }_i(x,t)$$

(1)

where the distribution function and equilibrium distribution function are finite discrete terms.

Because the original collision operator of the Boltzmann equation is extremely complex, the linearized BGK collision model proposed by Bhatnagar, Gross, and Krook based on the H theorem has been proved to be an effective collision operator to simulate a Navier–Stokes behavior. Formula (2) is the mathematical expression of the discrete Bhatnagar–Gross–Krook (BGK) operator:

$${\omega }_i(f)=-\frac{f_i-f_i{}^{eq}}{\tau }\Delta t$$

(2)

where $\tau$ is the relaxation time, which determines the rate at which particle swarm $f_i(x,t)$ relaxes to equilibrium state $f_i{}^{eq}$.

Boltzmann’s H theorem holds that the distribution function changes with time. The H (the function representing the change) of the system always decreases, and when H gradually decreases to the minimum and no longer changes, the whole system will enter the equilibrium state. This process is irreversible. As a result, the lattice BGK equation (LBGK) has important application significance and can be derived as:

$$f_i(x+c_i\Delta t,t+\Delta t)-f_i(x,t)=-\frac{\Delta t}{\tau }(f_i(x,t)-f_i{}^{eq}(x,t))$$

(3)

Because the BGK operator in the LBGK equation contains a relaxation time that represents the relaxation rate of the equilibrium function, it is also called the single relaxation model. The collision and flow processes of solving the lattice Boltzmann model are based on the Cartesian mesh system of geometric objects. In order to better adapt to the object boundary to represent the computing domain, the octree algorithm (OA) is usually used as the basic algorithm to generate the 3D lattice model. The octree algorithm is a top-down algorithm with strong scalability and can dynamically generate lattice models for different uses according to the needs of users. The generation rules of the octree determine that once its structure is generated, the child lattice of any lattice in the tree can only be zero or eight, and there can be no other cases. Thus, its logical structure is a tree structure that may have eight bifurcations in any lattice.

3.2. Large-Eddy Simulation

In order to realize the large-eddy simulation, it is necessary to filter the turbulent vortices of different scales:

$${\varphi }_{\alpha }=\overline{{\varphi }_{\alpha }}+{\varphi }_{\alpha }\prime$$

(4)

where ${\varphi }_{\alpha }$ are original instantaneous variables before filtering, $\overline{{\varphi }_{\alpha }}$ are solvable scale variables after filtering, ${\varphi }_{\alpha }\prime$ are unsolvable scale variables after filtering.

The filtering behavior expressed by Formula (4) is realized by the integration process:

$$\overline{{\varphi }_{\alpha }}(x,t)={\displaystyle \int {}_V{\varphi }_{\alpha }(x^{\ast },t)}{G}_{\alpha }(x-x^{\ast }){dx}^{\ast }$$

(5)

where $\overline{{\varphi }_{\alpha }}(x,t)$ is the solvable scale variable obtained by filtering the position of $t$ time $x$ in space, and $x^{\ast }$ are the coordinate values of positions other than the current point $x$ in space

The filtered LES-LBGK equation is obtained by filtering the integral process Formula (1) of Formula (5):

$$\overline{f_i}(x+c_i\Delta t,t+\Delta t)-\overline{f_i}(x,t)=-\frac{\Delta t}{\overline{\tau }}\left(\overline{f_i}(x,t)-\overline{f_i{}^{eq}}(x,t)\right)$$

(6)

where the distribution function $f_i$ is replaced by $\overline{f_i}$ above the filter scale, and in the collision operator, the relaxation time $\tau$ is replaced by a $\overline{\tau }$ term.

3.3. Model’s Geometric Structure and Parameters

The model used in the calculation was a three-dimensional model of the full flow channel of the axial flow pump, including the inlet channel, the runner section, the diversion mechanism section, and the outlet channel. The main parameters for the design and operation of the axial flow pump are shown in

Table 3. Main parameters of the wheel model.

Parameter	Value
Rated head Hr (m)	6.0
Rated speed nr (r·min−1)	300
Rated discharge Qr (m3·s−1)	8.0
Runner diameter D1 (mm)	1475
Number of runner blades Nb	3
Number of guide vanes Ngv	5

.

The geometric structure and components of the axial flow pump are shown in Figure 3.

3.4. Computational Domain Discretization and Boundary Conditions

In this paper, for the three-dimensional calculation of the axial flow pump, the maximum discrete velocity number scheme of D3Q27 and the octree lattice structure were used to organize the lattice scale refinement scheme in different regions of the fluid domain. Specifically, the division of the lattice structure realized the construction of the whole channel lattice model by setting the scale for each part of the original geometric structure or drawing the geometric inclusion structure to set the analytical scale and far-field scale for the corresponding region. Schemes of different mesh sizes are shown in Figure 4.

In this paper, the time step was calculated by the combination of the Coulomb number and local lattice scale, which was generated dynamically by the algorithm. The Coulomb number is a parameter that characterizes whether the calculation conforms to the CFL condition, usually between 0.2 and 1. In order to ensure the robustness of the calculation, the Coulomb number was set to 0.4. The unsteady calculation of the axial flow pump was carried out by using several schemes with different analytical scales, and the irrelevant verification curve in Figure 4 was obtained. Because different lattice scales were used in the runner region and other regions, the runner efficiency and the whole machine efficiency were selected as the evaluation index of the lattice independence verification.

According to the results of the irrelevance verification, the final selected mesh total scheme was not less than 560 W at any time step, so as to meet the lattice independence requirements. Under this scheme, the global lattice scale was 0.025. In the local refinement lattice scale, the runner and wake had a 0.00625–0.0125 adaptive refinement. The result of meshing is shown in Figure 5.

In the setting of boundary conditions, the inlet boundary was set as the mass flow inlet, and the numerical value was converted according to the designed flow rate. The pressure outlet boundary was set to atmospheric pressure. The wall boundary was added with the nonequilibrium strengthening wall function, in which the forced motion was added to the runner rotor structure. The motion characteristic parameters were converted into a function of time according to the rated speed. The coupling calculation of the immersion boundary method was used.

The axial flow pump model was based on the axial flow pump used at the Datao second pumping station in China. We simulated the efficiency of the axial flow pump under different flow conditions and compared it with the pump characteristic curve. The comparison between the calculated results and the actual efficiency is shown in Figure 6. The numerical simulation results were consistent with the changing trend of the characteristic curve. Therefore, the numerical calculation method in this paper was reliable.

3.5. Evaluation Method of the Blade Impact Probability

The high incidence area of the impact between fish and runner is the leading edge of runner blades. A large number of studies have shown that the impact probability of the blade leading edge is related to the fish body length, orientation, swimming speed, and local fluid velocity. There is a certain relationship between the leading-edge thickness of the runner blade and the blade impact speed [33,34,35,36]. This complex relationship in axial flow pump can be expressed by the following formula:

$$P_{impact}=\frac{t_{fish}}{t_{blade}}=\min \left(1,\frac{h_{fish}{L}_{fish}{A}_b{N}_b{n}_r}{60Q_r}\right)$$

(7)

where $P_{impact}$ is the probability of impact between the fish and the blade, $t_{fish}$ is the time for the fish to pass through the leading edge of the blade, $t_{blade}$ is the time for the blade to walk through a leaf spacing, $h_{fish}$ is the correction coefficient of the effective length of the fish, which is related to the ratio of length to width of the fish, and is determined by the species of fish. The min function indicates that the calculated value should be less than 1.

The plate impact experiment of EPRI shows that the death probability of fish is directly related to the leading-edge thickness and impact velocity of the blade.

$$C_{dead}=\left(p\ln \left(\frac{L_{fish}}{d}\right)+q\right)\left(v_s-4.8\right)$$

(8)

where $C_{dead}$ is the fish’s impact death index, which characterizes the death probability of fish when they are hit by a plate. $\frac{L_{fish}}{d}$ is the ratio of the length of the fish body to the thickness of the leading edge of the blade. $v_s$ is the impact velocity. $p$ and $q$ are undetermined coefficients, respectively, and their value is affected by $\frac{L_{fish}}{d}$. The specific values of $p$ and $q$ are shown in

Table 4. The relationship between the values of p, q, and L_fish/d.

Lfish/d	p	q
0–2	0.0531	0.0202
2–10	0.0829	−0.0021
10–25	0.0327	0.1146

.

According to the formula, the impact velocity will directly increase the impact death probability, and the impact velocity below 4.8 m·s⁻¹ will not lead to fish death. When the threshold is exceeded, the death index increases exponentially with the increase in the impact velocity, and the magnification is the growth value of the impact velocity.

4. Optimal Design and Hydraulic Performance Analysis of a Fish-Friendly Axial Flow Pump

4.1. Optimal Design of the Leading-Edge Thickness of Blade

Previous studies have shown that the part of the runner structure that causes cutting damage to fish is located at the leading edge of the blade. The leading-edge structure of the blade is used to reduce the de-flow of the blade facing the incoming flow and reduce the hydraulic loss. From a fish-friendly point of view, increasing the thickness of the leading edge of the blade can avoid direct cutting when it hits the fish. However, the thickness of the leading edge of the blade is not better when bigger. On the one hand, the greater thickness increases the possibility of de-flow and hydraulic loss, on the other hand, it also increases the probability of hitting fish. Therefore, the choice of the leading-edge thickness of the blade needs to be analyzed.

Three runner schemes with different blade leading-edge thicknesses were designed for the prototype axial flow pump, as shown in Figure 7.

We used the comparative analysis method to comprehensively analyze the operation characteristics and flow field characteristics of the axial flow pump under different blade leading-edge thickness schemes and determine the better blade leading-edge thickness.

According to

Table 5. Operating parameters of axial flow pump with different leading-edge thickness of blade.

Leading-Edge Thickness of Blade	Discharge	Head	Average Pressure at Inlet and Outlet of Runner			Shaft Power	Runner Efficiency	Machine Efficiency
Thk (mm)	Q (m3·s−1)	H (m)	P1 (kPa)	P0 (kPa)	ΔP (kPa)	N (kw)	H (%)	H (%)
5.6	8.01	6.01	−44.5	14.3	58.8	523.4	90.12	75.68
11.4	8.02	5.91	−45.9	11.9	57.9	518.8	89.38	74.50
17.4	8.02	5.83	−47.3	9.8	57.1	514.8	88.87	73.59

, the head of the axial flow pump decreases with the increase in the leading-edge thickness of the blade. This shows that the mechanical energy obtained per unit fluid mass was reduced. The inlet and outlet pressure of the blade decreased by about 1.5 kPa with the thickening of the leading edge of the blade, and the decrease in the total pressure at the outlet was slightly larger than that at the entrance. On the one hand, this shows that the internal hydraulic loss of the runner increases with the thickening of the leading edge of the blade; on the other hand, for the pressure difference between the front and rear of the impeller shifts, although increasing the leading-edge thickness makes the suction chamber obtain a lower negative pressure and improve the suction lift, the lower negative pressure also increases the possibility of pressure damage to the upstream fish body. With the increase in the blade leading-edge thickness, the shaft power, runner efficiency, and machine efficiency decreases to a certain extent.

The cross-section pressure distribution of the axial flow pump under different blade leading-edge thickness schemes is shown in Figure 8. As can be seen from the pressure distribution map, with the thickening of the leading edge of the blade, the area lower than −40 kPa gradually increases. Too large a negative pressure area causes irreversible negative pressure damage to the fish. From the velocity distribution map, it can be seen that in the case of 5.6 mm, the velocity gradient at the leading edge of the blade and the guide vane region change gently, and the smooth iso velocity lines can be clearly observed in both X-sections. The velocity distribution in the guide vane region of the 11.4 mm and 17.4 mm thicknesses is more chaotic, which is caused by the increase in the thickness of the leading edge of the blade aggravating the flow separation. In the velocity cloud image of the 11.4 mm thickness, a smaller vortex core is derived from the guide vane region, and the vortex core basically disappears in the outlet bend section. The velocity cloud image of the 17.4 mm thickness shows that a large-scale vortex is formed in the guide vane region, which still exists in the outlet channel.

As shown in Figure 9, the surface pressure distribution of the runner blade shows that the effect of the increase in the leading-edge thickness on the blade surface pressure is consistent with the values read in the external characteristic table. When the thickness of the leading edge of the blade increases, the positive pressure decreases slightly for the blade working face. For the suction surface, the proportion of negative pressure less than −80 kPa decreases at first and then increases. This is because when the thickness of the leading edge of the blade increases, the nonuniform thickness distribution can reduce the axial vortex between the blades and improve the flow pattern. However, the excessive thickness of the leading edge leads to an excessive gradient of the thickness in the middle of the blade and the thickness of the trailing edge, and the fluid in this area is weakened by the constraint of the blade, resulting in flow separation.

The hydraulic performance of the axial flow pump with three blade leading edge thickness schemes was comprehensively compared, and the fish-passing characteristics of the pressure performance were properly considered. Based on the analysis results of the visual data such as the operation efficiency of the axial flow pump, the negative pressure level of the pump suction chamber, the velocity and pressure distribution characteristics of the runner and guide vane, and the streamline of the outlet passage, it was obtained that it could reduce the damage probability of fish. The best compromise scheme with less performance sacrifice was the scheme with a blade leading-edge thickness of 11.4 mm. The following takes this scheme as the benchmark and continue to carry out the next link of the optimization design.

4.2. Optimal Design of Leading-Edge Guiding Characteristics of the Blade

When the runner rotates, the linear velocity of the leading edge of the blade is proportional to the radius. When the speed of the runner is constant, the position of the fish entering and leaving the runner is closer to the hub side, and the impact velocity is smaller. Therefore, the effective way to reduce the impact speed of fish is to make the fish enter the flow channel from the inside of the runner as far as possible. For the runner, the cutting blade can make the entrance of the runner have a certain radial velocity, so that the position of the fish entering the runner is closer to the hub side, thus reducing the death rate in the event of an impact.

Aiming at an axial flow pump whose blade leading-edge thickness was 11.4 mm, the leading edge of the blade was obliquely cut to different degrees, and three kinds of runners with different blade cutting degrees were designed. The angles between the leading edge and the radial direction of runner blades in different schemes were 6°, 12°, and 18°.

When the blade angle becomes larger, the total area of the blade decreases, the throat area at the entrance of the blade increases slightly, the length of the airfoil bone line on the hub side increases, and the length of the flange wing bone line decreases.

As the output power of the runner changes with the change in the total area of the blade, it brings an unnecessary characteristic offset to the runner. To keep the output power of the runner stable, other control parameters should be considered at the same time to avoid great changes in the effective work area of the blade. To control the blade area, the cutting blade was properly extended to both sides of the inlet and outlet on the axial projection, and the gap between the total blade area of each scheme was narrowed. Finally, the total leaf area difference of each scheme was controlled within 0.01 m² (about 0.4% of the total area). The appearance after cutting and the adjusted results are shown in Figure 10.

According to

Table 6. Operating parameters of axial flow pump with different blade cutting angles.

Blade Cutting Angles	Discharge	Head	Average Pressure at Inlet and Outlet of Runner			Shaft Power	Runner Efficiency	Machine Efficiency
Ang (°)	Q (m3·s−1)	H (m)	P1 (kPa)	P0 (kPa)	ΔP (kPa)	N (kw)	η (%)	η (%)
6	8.02	5.91	−45.9	11.9	57.9	518.8	89.38	74.50
12	8.01	5.95	−46.0	12.2	58.3	529.6	88.20	72.62
18	8.02	5.90	−44.8	12.8	57.6	523.0	88.33	71.38

, We used the comparative analysis method to comprehensively analyze the operation characteristics and flow field characteristics of the axial flow pump under different blade cutting angles and determine the better blade cutting angle.

After the blade was cut at different degrees, the head of the axial flow pump increased at first and then decreased. This showed that the hydraulic loss in the runner before and after blade cutting was not linearly coordinated with the design’s cutting angle. With the increase in blade cutting angle, the blade inlet pressure first decreased and then increased, and the outlet pressure increased gradually, but the range of change was not more than 1.2 kPa, and the total pressure difference between the inlet and outlet of each scheme changed little. In terms of output power and efficiency, the runner with a blade cutting angle of 12° had the highest output shaft power and the lowest runner efficiency, but the overall efficiency was slightly higher than that of 18° runners. The results showed that there were more significant differences in different parts of the internal flow field.

As shown in Figure 11, the negative pressure area below −40 kPa increases at first and then decreases with the increase in blade cutting angle. The excessively high negative pressure area in the suction chamber increases the negative pressure injury time of fish, which is not conducive to the passage of fish. From the velocity distribution map, it can be seen that the leading edge of the cutting blade has a negative effect on the downstream flow pattern, and the fluid enters the state of separation from the mainstream earlier, which widens the downstream area surrounded by the velocity gradient line.

As shown in Figure 12, the main difference in the pressure distribution before and after the runner blade is the flatness of the isoline of the runner working face, and the isoline inflection point of the runner pressure distribution after cutting is close to 120°. On the suction surface of the blade, the area where the negative pressure of the suction surface of the blade with a cutting angle of 12° is less than −80 kPa is slightly larger than that of the other two schemes. The hydraulic loss of the impeller with a cutting angle of 12° decreases, the hydraulic loss of the guide vane increases, and the overall working efficiency obviously decreases. The work capacity of the blade with a cutting angle of 12° becomes stronger, which reduces the hydraulic loss of the impeller, but because the structure of the guide vane remains unchanged, the hydraulic loss of the guide vane region increases, and the overall working efficiency still decreases.

The purpose of blade cutting is to reduce the probability of the fish hitting the leading edge of the blade and to make the fish move towards one side of the hub and reduce its linear speed. In terms of the operation efficiency of the axial flow pump and the flow pattern of the outlet channel, the scheme of a cutting angle Ang = 12° has a slight advantage. But in contrast, the negative pressure level of the suction chamber and the velocity gradient at the back end of the runner in the Ang = 18° scheme are better, and the runner efficiency is better. Although the efficiency of the whole machine is slightly lower than the former, it is more in line with the design value of this paper to sacrifice a small part of the efficiency for the viability of fish. Therefore, the Ang = 18° scheme was chosen in this section.

5. Fish-Passing Performance Analysis of the Fish-Friendly Axial Flow Pump

5.1. Analysis of the Behavior Trajectory of Fish through the Axial Flow Pump

For the modeling of real fish, the balance between the simplification of the model and the calculation effect should be considered. First of all, the connection gaps of fins, tails, and organs on the surface of fish bodies should be ignored. Secondly, the fish body model should be convenient for computer recognition and calculation, that is, the complexity of the surface modeling of the fish body should be simplified, and the modeling of the fish body should be based on the surface composed of a simple conic curve.

According to the above modeling requirements, this paper established a fish body model with a 150 mm body length and other fish body models with only tail and belly shapes. Through trial calculation, it was found that the computational efficiency of the OB fish was lower than that of the SP fish under the lattice model, which could restore the best analytical scale of the fish’s surface shape. The effects of the two forms on the flow field and fish surface calculation results were not obvious. Therefore, the SP fish with a higher computational efficiency was selected as the fish body model object for subsequent calculations in this paper.

After entering the channel, the fish passed through the inlet channel, runner, guide vane, outlet channel, and other areas one by one. Due to the continuous work done by the pump blade, the kinetic energy of the flow body increased sharply, which made the movement trend of fish very easily affected by the fluid in the pump. Therefore, the change in the flow field characteristics caused by the change in the pump structure was bound to affect the trajectory of the fish. This section combines the LES-IB-LBM method to explore the influence of the change in flow field characteristics on the passage of fish.

When simulating the fish body passing through the fish-friendly axial flow pump, a total of three fish were placed at different radial positions at a certain section of the intake passage of the axial flow pump at the initial time, and the motion trajectories of the fish passing through the runner area of the axial flow pump and the water guide mechanism were calculated. The difference between the fish-friendly pump and the prototype pump affecting the passage trajectory of the fish body before and after the optimization design was analyzed. The fish model and its passage process are shown in Figure 13.

The speed and posture of the three fish in the fish-friendly pump were different. The three fish changed direction once at the three moments caught. The change in direction of the small yellow croaker was mainly due to its proximity to the curved surface of the hub, while the small red fish and the small blue fish had a very obvious movement to the hub side in the radial position. All three fish no longer maintained the circular motion of equal angular velocity, which made the outermost red fish, which should have had a higher linear velocity, lag significantly behind the other two fish near the inside after entering the runner.

After the fish body entered the water guide mechanism, what was different from the compact and consistent motion posture in the runner was that with the increase in motion space, the increase in motion speed, and the possible influence of dynamic and static interference, the motion trend of the three fish was basically inconsistent. The three fish always moved near the hub side, still keeping the blue fish in the lead, the red fish lagging. The movement distance of the three fish ensured that their different walls collided head-on.

5.2. Comparative Analysis on the Mortality of Fish Subjected to Blade Impact

The impact death probability of fish consists of two parts: impact probability and death index. The impact probability can be determined directly by the parameters of the fish body and runner. In order to obtain the death index, the impact velocity $v_s\left(r,{\alpha }_1,{\alpha }_2\right)$ should be calculated first. ${\alpha }_1$ can be exported at different radii r by runner design software. The scatter relationship between the two is shown in Figure 14.

In this paper, the polynomial function was used to fit the $r-{\alpha }_1$ data of the runner blade of the fish-friendly axial flow pump. The calculation equation obtained from the fitting model was:

$${\alpha }_1=-22.34943+0.79326r-0.00181r^2+1.18296\times {10}^{-6}{r}^3$$

(9)

The distribution curve of the impact death index of the runner blade of the axial flow pump before and after optimization is shown in Figure 15.

The optimized axial flow pump runner was close to the runner without damage. The calculation and verification of the original data points before fitting showed that when the radius of the impact point was 723.43 mm, the impact velocity was 4.807 m·s⁻¹ and the death index was less than 0.0015. When the radius was less than 716.8 mm, the impact velocity was less than 4.8 m·s⁻¹. Thus, there is no need to discuss the specific value of the blade impact probability as the fish would not be killed by hitting the leading edge of the blade. The impact death rate can be obtained by the integral of the impact death index for the radius r. Therefore, the yellow and blue shadow area in the figure can be used to roughly estimate the total impact mortality ratio of the axial flow pump runner before and after optimization, and the ratio before and after optimization was close to 7:1.

5.3. Comparative Analysis of Fish Subjected to Pressure and Shear Damage

From the point of view of the variation in the average pressure of the fish body with the motion path in Figure 16, the lowest negative pressure in the inlet section of the fish-friendly axial flow pump was higher than −40 kPa when the runner pressure was −59.2 kPa. The inlet passage of the prototype pump was at a pressure lower than −40 kPa, and the lowest negative pressure was −64.7 kPa. The average and maximum negative pressures of the fish friend pump were higher than those of the prototype pump. The maximum positive pressure on the front of the blade on the path of the fish was 11.8 kPa, which was significantly lower than that of the prototype axial flow pump at 43.8 kPa. This showed that the level of pressure gradient caused by the pressure change in the fish body in the fish-friendly pump was lower, so it was less vulnerable to pressure gradient damage. This means that the degree of negative pressure damage to the passing fish body was reduced, and it was more beneficial for the fish to pass through the axial flow pump.

Literature studies show that the main evaluation index of shear damage of fish in a strong shear environment is the shear strain rate. When the shear strain rate is less than 500 s⁻¹, it is considered that the fish will not be subjected to shear damage. Figure 16 shows the change in the average shear strain rate on the body surface as a fish passes through the axial flow pump. Both the prototype pump and the fish-friendly pump reach the maximum shear strain rate at the front of the runner. As far as the situation seen in the diagram is concerned, when the fish body passes through the prototype axial flow pump and the fish-friendly axial flow pump, it does not reach the damage threshold of 500 s⁻¹, so it will not be subjected to shear damage. The actual situation still needs to be analyzed by the distribution of the shear strain rate on the fish surface.

Thus, it can be seen that changing the blade thickness and cutting angle can effectively reduce the impact damage to fish. This is consistent with Amral’s view [37] that the non-right angle between the leading edge of the blade and the trajectory of the fish can reduce the strike speed or damage rate. The pressure injury of fish is mainly negative pressure injury, and Shao et al. [7,8] also reached a similar conclusion. Therefore, the impact damage caused by blades should be given priority in the design of fish-friendly hydraulic machinery. Klopries [38], based on CFD streamline assessment of Kaplan turbines, also found that collision is the most serious cause of fish death. Secondly, the negative pressure and pressure gradient need to be considered, while the priority of shear stress injury is slightly lower.

6. Conclusions

In this paper, taking the ordinary axial flow pump as the research object, a fish-friendly axial flow pump was designed, which greatly reduced the mortality of fish passing through the axial flow pump and ensured the high hydraulic performance of the pump.

The main contents and related achievements of the full text are summarized as follows:

(1)

By using the experimental device simulating the internal pressure of hydraulic machinery, the survival conditions of different fish species under different pressure thresholds were obtained, and the damage situation and damage mechanism of fish were studied. The survival threshold of wild crucian carp and yellow catfish was −40 kPa. Other fish species should not be subjected to negative pressure. Therefore, this paper established −40 kPa as the low-pressure damage threshold. At the same time, the experimental data can enrich a database for evaluating fish pressure damage, which is of guiding significance for the optimal design of axial flow pumps.

(2)

The runner design method of the axial flow pump was applied, and a fish-friendly axial flow pump was designed according to the blade impact model. The structure of the runner of the axial flow pump was designed under the guidance of the variables in the blade impact model, and a fish-friendly runner with a high hydraulic performance and low impact mortality was obtained based on the damage of hydraulic performance, pressure, and shear rate. This new type of runner can provide the optimization idea of geometric parameters for a subsequent optimization design of hydraulic machinery.

(3)

Based on the efficient boundary calculation ability of the LES-IB-LBM method for moving objects, the upstream trajectories of three fish in the axial flow pump were simulated. This method could efficiently and accurately simulate the process of fish passing through the axial flow pump. The ratio of total impact mortality of the axial flow pump before and after optimization was close to 7:1. The average negative pressure on the fish surface through the profish axial flow pump was higher than that of the prototype axial flow pump. In the process of pumping station unit design, more attention should be paid to the influence of the blade shape on fish trajectory so as to reduce the death rate caused by impacts. The LES-IB-LBM method can also be extended in follow-up numerical simulation work.