Numerical simulation and thrust performance optimization of water jet thruster

With the increasing use of water jet thrusters on ships, the demand for increasing their thrust performance and efficiency is also increasing. The impeller, as the core power component, is the key to the thrust of the water jet thruster. Therefore, to obtain a more energy-saving, low-carbon, and higher-thrust water jet thruster, this paper conducts an in-depth study on the impeller of the water jet thruster. The hexahedral grid is used to divide the internal flow field of the water jet thruster into structured grids, and the RANS equation and k-ε turbulence model are used to simulate the hydraulic performance of the original model, and then the blade of the impeller is optimized. Finally, compared with the original model, the simulation results of the optimization model show that the efficiency is increased by 4.8 %, and the thrust at the highest efficiency point is increased from 614 N to 1623 N. The optimized model greatly improves the efficiency and thrust of the water jet thruster, and the optimization effect is obvious.


Introduction
Water jet thruster is a new type of propulsion technology currently used on ships, which has many advantages such as high propulsion efficiency, simple operation, flexible direction change, and strong adaptability to changing working conditions.Therefore, water jet thruster has become the key research and development direction of underwater equipment in all countries in the world.[1][2][3][4] The thrust of the water jet thruster seriously affects the overall performance of the entire ship system, especially at high speed and low speed, the thrust is too small and even the entire propulsion system stops working.In severe cases, cavitation and huge noise will be produced, which will affect the performance and life of t he water jet thruster.
Bulten et al. [5] used commercial CFD software to numerically calculate the water jet thruster, and t he rotation area used the MRF method to calculate the thrust and moment, which was in good agreement with the test results, which verified the feasibility of the CFD method to predict the thrust of the w water j et thruster.Willem N [6] proposed that the pressure of the flow pipe and the tail of the flow pipe outside t he hull has a very large effect on the thrust when calculating thrust, but it is easy to overlook.The i ntroduction of this concept also explains the difference in the calculation results between the wall area division method and the velocity flow method.Sun et al. [7] studied the two methods of theoretical analysis and simulation calculation to predict the thrust of the water jet thruster and found that the calculation results of these two methods and the thrust characteristic curves of the data obtained from the supplier were in good agreement, and analyzed the advantages and disadvantages of these two methods.Ni et al. sorted out the research progress of water jet thrusters and found that the thrust of water-spray thrusters has a lot of research space, and by comparing axial flow impellers and oblique flow impellers, it is determined that the propulsion efficiency of axial flow impellers is higher.They also proposed that the water jet thruster can work at the optimal efficiency point or increase the nozzle diameter to make it thrust greater.[8][9][10][11] From the above analysis, it is found that scholars at home and abroad have rarely studied the thrust optimization of the impeller of the water jet thruster very systematically.[12][13] This paper takes the waterjet propeller as the research object to establish its internal fluid simulation.First, it explains the numerical simulation method used, then optimizes the waterjet propeller impeller, then summarizes the simulation results, and finally discusses the changes in performance and thrust.

Control equations
The water jet thruster is numerically calculated using the RANS equation, including the continuity equation and the momentum equation: where ρ is the fluid density; t is time; u represents velocity and p is the pressure on fluid microelements; u and   are laminar and turbulent viscosity coefficients, respectively.Using the k-ε turbulence model, the transport equation for the turbulent energy k and dissipation rate ε is as follows: where   is the viscosity coefficient of the turbulent vortex,   is the generic term of turbulent kinetic energy  caused by the average velocity gradient, and  1 ,  2 and   is constant.

Numerical calculation model
The research object of this paper is a small high-speed water jet thruster.Its flow passage area is shown in Figure 1, mainly including four parts: inlet, impeller, guide vane, and nozzle.Among them, the role of the impeller is to convert the rotating mechanical energy into the energy of the water flow, and the role of the guide vane is to reduce the axial velocity of the water flow and change the kinetic energy into pressure energy.The main parameters of the water jet propulsion are shown in Table 1.The boundary conditions of the model are defined as follows: the inlet of the water jet thruster is used as the pressure inlet calculated by simulation, and the value is 1 atm.The outlet of the nozzle is the flow outlet calculated by simulation.The speed of the impeller is 8500 r/min; The impeller is the rotating domain, and the rest part is the static domain.The Stage Average Velocity interface was set between the rotation domain and the stationary domain, and the rest adjacent regions were set as the static-static interface.
The whole calculation domain was divided into four parts: inlet, impeller, guide vane, and nozzle.The inlet and nozzle were meshed by ICEM, while the impeller and guide vane were meshed by Turbo Grid.A boundary layer mesh is used in the near wall area to locally encrypt the tip clearance area to ensure accurate simulation of the near wall flow.The meshes after division are shown in Figure 2. The number of meshes of the inlet is 1.2 million, the impeller is 1.02 million, the guide vane is 1.55 million, the nozzle is 550,000, and the total number of meshes is 4.32 million.The mesh quality is above 0.35, which meets the calculation requirements.

Simulation results of the original model
According to the above numerical method, the whole flow field and multi-flow condition of the water jet thruster are simulated numerically, and the four indexes of head, efficiency, power, and thrust are taken as the reference indexes of the water jet thruster.The simulation results are shown in Table 2.The thrust of the original model of the water jet thruster increases with the increase of flow rate, while the head decreases with the increase of flow rate, and the efficiency increases first and then decreases.And when the flow rate reaches 172.8 m 3 /h, the efficiency reaches a maximum of 73.75%.

Optimization of the original model and numerical calculation
The impeller is optimized by CFturbo.The axial flow pump blade is optimized by solving the differential equation of the circular arc airfoil cascade.The main impeller inlet and outlet placement angle and blade profile optimization.The optimization impeller is shown in Figure 3.The blade inlet placement angle is 6.6° lower than that of the original model, the blade outlet placement angle is 11.6° higher than that of the original model, and the overall blade wrap angle is reduced by 90.9°.The numerical simulation results of the optimization model are shown in Table 3.

Conclusion
Based on the RANS equation and k-ε turbulence model, numerical analysis was conducted on the original model and the original optimized simulation model of the water jet thruster.The main conclusions of the study are as follows: By reducing the blade inlet angle, increasing the blade outlet angle, and reducing the blade wrap angle, not only can the optimal operating point of the water jet thruster be moved to the right and the rated flow rate of the water jet thruster can be increased, but also improved waterjet efficiency and thrust.In addition, by taking the above measures, it was also found that the internal flow pressure drop of the water jet thruster and the high pressure condition at the blade edge under part flow conditions have also been greatly improved.With the flow rate increase, the pressure at the impeller decreases gradually, and the velocity at the outlet pipe increases gradually.
Compared with the original model, the efficiency of the optimized water jet thruster finally increased by 4.8 %, and the thrust at the highest efficiency point increased from 614 N to 1623 N. The optimized model greatly improves the efficiency and thrust of the water jet thruster, and the optimization effect is obvious.

Figure. 4
Figure.4The axial drawing and 3D drawing of the optimized impeller.Table3.Optimized model performance.

Figure 5 .
Figure 5. Optimized model performance.According to the calculation results, the optimal operating point of the optimization model shifts to the right and reaches the optimal operating point at 270 m 3 /h.Meanwhile, the efficiency is 78.55 % and the thrust generated is 1623 N.
To analyze the comparison of the flow field between the optimization and the original model of the water jet thruster, Figure6shows the pressure distribution cloud diagram and velocity distribution cloud diagram of the water jet thruster axial surface under different flow rates.The pressure of the original model and the optimization model both increased to the maximum at the impeller and gradually decreased as the fluid medium moved toward the nozzle.However, the velocity change of fluid medium in the original model and optimization model is not obvious in the inlet passage, and then starts to rise steeply at the impeller, and the velocity of fluid drops at the guide vane, and rises at the nozzle.Moreover, compared with the original model, the velocity of the optimization model at the guide vane decreases less.

Figure 6 .
Figure 6.Original model axial pressure and velocity distribution.

Figure 7 .Figure 8 .Figure 9 .
Figure 7. Optimized model axial pressure and velocity distribution.To analyze and compare the pressure of the internal flow field between the optimization and the original impeller, Figure8and Figure9shows the pressure distribution of the blade on the impeller.The blade pressure in both the original model and the optimization model increases with the increase of flow rate.When the flow rate is small, the blade edge of the original model generates a comparative pressure, while the high-pressure area of the blade edge of the optimization model is improved, which effectively

Table 2 .
Original model performance.