# Optimal Design and Fish-Passing Performance Analysis of a Fish-Friendly Axial Flow Pump
## 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]. [PERSON] et al. [8; 9] found that negative pressure caused more damage to fish than positive pressure. [PERSON] [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\(\cdot\)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]. [PERSON] 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]. [PERSON]'s team [17; 18] designed a spiral centrifugal single-blade runner to reduce the pressure gradient and velocity gradient on the runner blade. [PERSON]'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. [PERSON] [23] and [PERSON] [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. [PERSON]'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. [PERSON] 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 [PERSON] and [PERSON] [29; 30] of Wuhan University obtained the transient flow data of a three-dimensional tubular turbine by IB-LBM.