Research on Resonance Mechanism and Collaborative Optimization of Double-cavity Self-Excited Oscillating Pulse Cavitation Jet Nozzle

: The peak value and pulsation amplitude of the self-excited oscillating pulse cavitation jet nozzle are important indexes to evaluate the jet performance. It is of great significance in theory and engineering practice to predict the peak value of the self-excited oscillating pulse cavitation jet nozzle accurately. In order to investigate the evolution mechanism of the inner and outer flow field of a double-cavity self-excited oscillation pulse cavitation jet nozzle, a simulation model of the jet impact test of the nozzle was established. Before entrance rounded corners, former cavity cavity diameter, cavity cavity length, before the cavity under the nozzle diameter, cavity, the cavity cavity after entry the rounded, lumen diameter, cavity length and cavity after cavity under the nozzle diameter as design variables, and strike force to combat force peak pulse amplitude as the target variable, the orthogonal experiment method, back propagation neural network combined with non dominated sorting genetic algorithm, The collaborative optimization design method of self-excited oscillating pulse cavitation jet nozzle was determined. Based on the collaborative optimization results, the 3D printing technology was used to manufacture the visualization test model of the flow field of the self-excited oscillating pulse cavitation jet nozzle, and the experimental verification was carried out. The results show that when the inlet pressure is 2MPa, the main and secondary order of the influences of various factors on the jet performance of the nozzle is the nozzle diameter under the front cavity, the diameter of the back cavity, the diameter of the front cavity, the length of the front cavity, the nozzle diameter under the back cavity, the cavity distance, the fillet of the back cavity, the fillet of the front cavity and the length of the back cavity. Compared with the optimal result of orthogonal test, the amplitude of impact pulsation and the peak value of impact force are increased by 14.61% and 2.42% respectively. The optimal structure of the nozzle determined by collaborative optimization can produce obvious pulse cavitation jet, and the cavitation region of the nozzle cavity contracts periodically with time. The higher the inlet pressure, the higher the cavitation intensity and the higher the content of hollow bubble. This study can promote the development of jet performance calculation of self-excited oscillation pulse cavitation jet nozzles, and provide support for the design of self-excited oscillation pulse cavitation jet nozzles.


Introduction
Water jet technology began in the first half of the 19th century, and is one of the representative application technologies in the field of fluid engineering [1].When water jet is in contact with the surface of the acted solid material, it will produce a great instantaneous impact force due to the stagnation pressure. Its most obvious advantage is cold operation, and it is widely used in the fields of hydraulic mining, cleaning, surface treatment and cutting in the world at present [2,3]. 1 Pulsed cavitation jet nozzles belong to self-excited oscillating jet nozzles, which can transform continuous single-phase water jet into two-phase high-frequency pulsed cavitation jet [4,5]. By making full use of the cumulative output characteristics of self-excited oscillating jet, the premature fracturing of the jet into droplets is *Correspondence: xiaomingbingbing@163.com 1 Hebei Provincial Key Laboratory of Heavy Machinery Fluid Power Transmission and Control, Yanshan University, Qinghuangdao066004, China 2 Key Laboratory of Fire Emergency Rescue Equipment, Ministry of Emergency Management, Shanghai200032, China effectively suppressed and the striking performance of the jet is improved. The transient energy generated by high-frequency hydraulic impact and the micro-jet generated by cavitation collapse are used to achieve the purposes of cleaning, rock breaking and surface treatment [6,7].At present, each performance index of pulsed cavitation jet is obviously better than that of continuous jet, and has been widely used in oil drilling [8], coal mining [9], equipment cleaning [10], metal surface strengthening [11] and other fields.
Typical pulsed cavitation jet nozzles mainly include organ pipe nozzles and Helmholtz oscillating cavity nozzles [12,13].They are continuous jet can be made into discrete pulse jet cavitation, the effective use of the broken jet high-frequency transient energy, reduce the jet energy losses as a result of the interaction with air medium [14,15], but the above two kinds of the nozzle structure parameters must match the inlet flow rate, pressure fluid parameters, such as to achieve the best effect of jet, The cavitation efficiency and jet impact performance of the nozzle are obviously reduced when the medium of low pressure and large flow or high pressure and small flow flows into the nozzle, which has certain limitations in practical engineering application. Therefore, we need to further explore and study the resonance mechanism of self-excited oscillating jet nozzles in order to further improve their jet performance.
In conclusion, pulse cavitation jet can only be generated by self-excited oscillating nozzles under specific structure and state parameters, and the generation and evolution mechanism of the phenomenon of pulse cavitation jet is very complex, and relevant issues need to be further explored and studied. Based on this, this paper will carry out the research on the resonance mechanism and multi-objective collaborative optimization of the double-cavity self-excited oscillation pulsed cavitation jet nozzle, in order to develop a self-excited oscillation pulsed cavitation jet nozzle with better jet performance and meet the major needs of the country and the market.

Geometric Modeling
The geometric model of the double-cavity self-excited oscillating pulse cavitation jet nozzle is shown in Fig. 1.The inlet parameters include upper nozzle diameter d 1 , upper flow passage length l 1 and the rounded corner of the front cavity inlet R 1 . The parameters of the middle segment include the diameter of the front cavity D 1 , the length of the front cavity L 1 , the Angle of the collision wall of the front cavityα 1 , the diameter of the nozzle under the front cavity D 2 , the distance of the cavity L 2 , the rounded corner of the rear cavity inlet R2, the diameter of the rear cavity D 2 , the length of the rear cavity L 2 and the Angle of the collision wall of the rear cavity α 2 .The outlet parameters include the length of the lower runner L 3 and the diameter of the nozzle under the rear cavity D 3 .Under the action of inlet pressure, the steady water jet enters the nozzle cavity and self-excitation occurs, and the continuous water jet is transformed into a pulse cavitation water jet. The structural parameters and fluid motion parameters of the nozzle are the main factors affecting the performance of the jet, and the structural parameters have a great influence on the peak value of the nozzle's striking force and the amplitude of the pulsation of the striking force. It is found that the rounded corner R 1 at the inlet of the front cavity, the diameter of the front cavity D 1 , the length of the front cavity L 1 , the diameter of the nozzle under the front cavity D 2 , the cavity distance L 2 , the rounded corner R2 at the inlet of the back cavity, the diameter of the back cavity D 2 , the length of the back cavity L 2 and the diameter of the nozzle under the back cavity D 3 are important parameters that need to be prioritized in the optimization design, which directly determine the jet performance. In order to deeply study the jet performance and flow field characteristics of self-excited oscillating pulse cavitation jet nozzles, it is necessary to carry out near-wall jet impingement simulation research. According to its geometric model features, the axisymmetric model is adopted to establish the simulation computing domain model as shown in Fig.  2.The jet and the external air medium interact and develop together, so the area of the static air domain outside the nozzle should not be too small to affect the development and evolution of the jet, but should not be too large to reduce the numerical calculation efficiency. The study found that it is more reasonable when the width of the air domain of the outflow field is 30mm and the length is 80mm.The same target width of 30mm can reflect the impact performance of pulse cavitation jet in more detail and accurately.

Parameter Setting
For the evolution mechanism of the inner and outer flow field of the self-excited oscillating pulse cavitation jet nozzle, it is assumed that water is an incompressible fluid and the influence of temperature on the flow field is ignored, that is, the fluid flow is an isothermal flow. On non-flooded conditions pulsed cavitation jet flow characteristics is analyzed, found that the jet is air -steam -water complex multiphase flow problem, and contains cavitation and cavitation factors such as vortex and turbulence vortex, therefore the simulation model for jet flow field calculation to solve critical, is directly related to the correctness of the simulation results.
In this paper, the Mixture multiphase flow model, Realizer k-ε turbulence model, Schnerr and Sauer cavitation model were used to simulate the flow state inside and outside the nozzle. The inlet boundary condition is the pressure inlet and the outlet boundary condition is the pressure outlet. PISO algorithm is used in the pressure-velocity coupling mode, and second-order upwind mode is used in the pressure-momentum discrete mode. The convergence tolerance criterion is 10 -4 . In order to ensure the accuracy of numerical calculation, a double precision solver is used to solve the problem.

Mesh Partitioning and Verification of Irrelevance
In the simulation calculation, because the nozzle cavity has the characteristics of small size, high jet velocity and involves cavitation phase transition, turbulent vortex and other factors, the mesh of the nozzle domain is refined and encryption processing, and the wall boundary layer thickness is controlled to increase the reliability of the simulation results.
According to the mesh division criteria determined above, the mesh refinement and encryption processing are carried out step by step until the simulation results no longer show significant changes, so as to reduce the errors of the simulation results caused by the grid quality problems and increase the reliability of the simulation. In grid independence verification, only the number of grids is changed while the other simulation conditions remain unchanged, and the pulsation amplitude and peak value of hitting force borne by the target in the outflow field are taken as the evaluation indexes of grid independence. In grid independence verification, the first group of grids was taken as the benchmark grid to calculate the deviation values of simulation results under different grid numbers. The results are shown in Table 1. Can be seen from the table, when the grid number is 26148, continue to increase the number of grid on the simulation results of peak force pulse amplitude and force no longer obvious, the influence of the deviation is below 1%, the results of simulation in the thought that the grid has meet the requirement of independence, and ultimately divided the nozzle of the overall and local grid model is shown in figure 3.

Orthogonal Test
It is found that the structural parameters of the self-excited oscillation pulse cavitation jet nozzle directly affect its jet performance. In order to determine the value of each structural parameter when the jet performance is better, and to analyze the influence law of key structural parameters on its jet performance, the orthogonal test method is adopted to design the simulation scheme. According to the control variable method theory, the main structural parameters that affect the performance of the jet and the matching scheme among different parameters are simulated and studied, keeping the inlet pressure and ambient pressure unchanged.
The peak value of striking force and pulsation amplitude of self-excited oscillating pulse cavitation jet nozzle are important indexes to evaluate its jet performance. Convenient to express, this paper use A, B, C, D, E, F, G, H, I and other symbols represent Rounded corner of front cavity entrance R1, the diameter of the front cavity D1, the length of the front cavity L1, the diameter of the nozzle under the front cavity d2, the cavity distance l2, Rounded corner at entrance of posterior cavityR2, the diameter of the back cavity d2, the length of the back cavity L2 and the diameter of the nozzle under the back cavity d3 structure parameters, such as nozzle diameter. J and K respectively represent the amplitude of the pulsation F  and the peak value of the striking force F m . The factors selected in this simulation are shown in Table  2.The specific scheme is shown in Table 3.The simulation results are shown in Table 4.    Fig. 4 shows the curve of jet impact force borne by target surface in Test 2, and Fig. 5 shows the curve of jet impact force borne by target surface in Test 7.Analysis found that due to the double cavity before and after the self-excited oscillation pulsed cavitation jet nozzle cavity cavitation vortex in the development of evolution is not synchronized, this leads to a degree of polymerization of cavitation flow field of pulse jet, jet speed and cavitation content in a certain degree of difference, the jet action formed on the surface of the target changes to the size of the force waveform. As can be seen from the figure, when the front and rear resonators alternately release energy, the peak value of striking force is small, but the difference of striking force waveform is small, and the jet striking force is relatively stable. When the front and rear resonators release energy at the same time, both the amplitude and peak value of the striking force on the target surface are large. Because the cavitation vortex development and evolution of the front and rear resonators are not completely synchronized, the magnitude of the striking force and the amplitude of the pulsation in the front and rear periods vary to a certain extent.

Analysis of Orthogonal Test Results
It is found that the amplitude and peak value of the average striking force are sufficient to represent the jet performance. Therefore, 20 stable jet pulsation periods were selected for analysis in each group of simulation, and the average striking force pulsation amplitude of 20 jet pulsation periods of the double-cavity nozzle was selected as the evaluation index of pulse cavitation performance. The average peak value of 20 jet pulsation periods of the double-cavity nozzle was selected as the evaluation index of the striking performance.
According to the orthogonal test scheme and simulation results, the nozzle multi-objective orthogonal test matrix analysis model is established, as shown in Table 5. The matching scheme of the structural parameters of the nozzle jet was preliminarily studied when the two evaluation indexes of the average striking force pulsation amplitude ΔF and the average striking force peak F m were optimized comprehensively.
Based on the data in Tab. 2, 3 and 4, the pulsation amplitude of nozzle jet impact force and the comprehensive weight of peak impact force were calculated and analyzed, and the two indexes were finally integrated to achieve a better effect. The calculated results are shown in Table 6.The following conclusions can be drawn from the analysis in Table 6: (1) x  represents the arithmetic average value of the total weight values of all levels of the structural factors of the double-cavity nozzle. After calculation, can be obtained. The results show that the influence on the comprehensive performance index of the self-excited oscillating cavity pulse cavitation jet nozzle from strong to weak is the diameter of the nozzle under the front cavity, the diameter of the back cavity, the diameter of the front cavity, the length of the front cavity, the diameter of the nozzle under the back cavity, the cavity distance, the fillet of the back cavity inlet, the fillet of the front cavity inlet and the length of the back cavity.
(2) By comprehensive analysis of the total weight values in Table 6, it can be seen that when the optimal synthesis of the peak value of the jet force and the amplitude of the pulsation of the jet generated by the self-excited oscillation pulse cavitation jet nozzle of the double-cavity under various structural parameters, the optimal matching scheme of the structural parameters of the double-cavity nozzle is R 1 of 1mm, D 1 of 26mm, L 1 of 10mm, D 2 of 6mm, L 2 of 8mm and R 2 of 2mm.D 2 was 30mm, L 2 was 8mm and D 3 was 6.6mm. The results of matrix analysis were shown in Table 7.

Analysis of resonance mechanism
The analysis shows that the cavitation vortex evolution of the double-cavity nozzle can be roughly divided into two typical states. One is the completely asynchronous state of the cavitation vortex movement in the front and rear resonators as shown in simulation test 2. The front and rear resonators alternately gather and release energy, as shown in Fig. 6. The other is that cavitation vortex movement in front and rear resonators is in a synchronous state as shown in simulation test 7. The front and rear resonators gather and release energy at the same time, as shown in Fig.  7. Under these two typical flow field evolution processes, high frequency and high speed pulse cavitation jet can be formed at the outlet of the self-excited oscillating pulse nozzle. Fig. 6 shows the evolution process of cavitation vortex in Experiment 2. At t=0.0027s, when the high-speed jet flows into the resonator, cavitation takes the lead at the fillet corner of the front cavity entrance under the comprehensive action of nozzle structural parameters, fluid motion parameters and environmental factors. When t = 0.003 s to 0.005 s, due to the resonance cavity fluid boundary layer has strong shearing action, the discrete vortex in the jet is selective amplification, eventually formed in the collision near the wall and flow channel wall cavitation vortex structure, large scale with cavitation constant motion of the vortices and growth, finally under the impact scores of jet downstream development evolution. With the passage of time, cavitation vortices in the front and rear resonators develop towards their limit states at t=0.120s, and finally the cavitation vortices in the front cavity reach their limit states first and begin to approach the middle passage and release the accumulated energy. At t=0.124s, the energy is released in the front cavity and away from the middle flow passage. At this time, the cavitation vortex in the back cavity develops to its limit state and begins to approach the middle flow passage and releases energy. When t=0.128s, the resonator completes the energy release process before and after the cavity, and the cavitation vortex continues to develop and evolve and enters the energy accumulation stage again. Since the front cavity has entered the energy gathering stage earlier than the back cavity, at t=0.130s, the cavitation vortex in the front cavity develops to the limit state again and enters the energy release stage. Finally, the evolution and development process of the flow field is similar to that at t=0.120s, and it begins to enter the next cycle. Fig. 7 shows the evolution process of cavitation vortex in Experiment 7. When t=0.002s~0.011s, cavitation occurs at the fillet corner of the inlet of the front resonator of the nozzle, and the cavitation moves with the backward resonator under the entanglement of the jet. When t=0.151s, the cavitation vortex in the front and rear resonators develops and evolves together and reaches its limit state at the same time. The cavitation vortex in the front and rear resonators almost approaches the middle passage at the same time and enters the energy release stage. When t=0.154s, the front and rear resonators complete the energy release process and the cavitation vortex begins to break away from the intermediate flow channel. It can be seen that the front and rear resonators almost complete the energy release process at the same time. When t=0.156s, the cavitation vortex develops and evolves again, and the front and rear cavies enter the stage of energy accumulation. When t=0.160s, cavitation vortexes in the front and rear resonators reach their limit states and begin to contact with the intermediate flow channel and release energy, finally forming high-frequency pulse cavitation jet.  Fig. 8 is the axial velocity distribution nephogram of the flow field at different times in Simulation 2, and Fig. 9 is the axial velocity distribution nephogram of the flow field at different times in Simulation 7. It can be seen from Fig. 8 that the length of the core area of the efflux velocity in the flow field at t=0.120s energy release stage is longer, while the length of the core area of the efflux velocity in the energy gathering stage is shorter. When t=0.124s, the nozzle instantly releases a large amount of energy, and a large number of cavitation bubbles are ejected with the jet, so the width of the velocity core area at the lower flow passage is the widest. When t=0.128s, the high speed segment of the jet is inhibited in the resonant cavity due to the damping effect of the nozzle cavity, and the pulse cavitation jet appears periodic convergence and dispersion in the outflow field with the evolution and development of the cavitation vortex. From figure 9 you can see, from the energy release to the energy accumulation phase, the nozzle jet core length decreases, has finally been completely inhibit within the cavity, due to the cavity before and after the release of energy at the same time, the outflow field appear obvious pulsed cavitation jet phenomenon, with the continuous jet axial velocity decreases with the increase of distance away from the nozzle exit is different, The pulsed cavitation jet also has a high strike velocity at the target surface, as shown in Fig. 9b).
By comparative analysis of Experiment 2 and Experiment 7, it can be found that the pulse cavitation intensity of the jet is stronger, the degree of polymerization of the jet in the outflow field is higher and the impact performance of the jet is better than that of the front and rear resonators when the energy is released alternately.    Fig. 11 is the radial velocity distribution nephogram of the flow field at different times in Simulation 7. In the internal flow field, due to the sudden expansion and contraction of the flow channel, there exists a large local radial velocity region of the flow field. Flow field, because the submerged jet diffusion effect on both sides to the speed of the diffusion area gradually, compared with energy release phase test 2 is greater than 7 flow field of radial velocity test, and this is because the cavity before and after the alternation of release energy when jet atomization characteristic is better, before and after the cavity at the same time release energy when jet polymerization degree is better. The maximum radial velocity of the flow field exists at the target surface, and the larger the value is, the greater the striking force of the jet will be. It can be seen that when the front and rear resonators release energy at the same time, the striking force of the jet will be stronger. Synthetic analysis shows that the jet has better pulse cavitation effect, larger impact force and higher degree of jet polymerization when energy is released simultaneously by front and rear resonators. Fig. 12 is the distribution nephogram of turbulent kinetic energy in the flow field at different times in Experiment 2, and Fig. 13 is the distribution nephogram of turbulent kinetic energy in the flow field at different times in Experiment 7. There is a large amount of turbulent kinetic energy in the shear layer region on both sides of the middle flow channel in the resonator, which is due to the large number of disturbed vortices in the shear layer region. During the energy release stage, the jet flow has completely penetrated the outflow field, and the turbulence intensity at the nozzle outlet is relatively high because of the drastic velocity change at the nozzle outlet. The intensity of turbulent kinetic energy at the interface area between the jet and the air is also high, which is due to the collapse of the hollow bubbles of the jet resulting in the crushing effect, and the collapse of a large number of cavities directly causes the jet atomization. In addition, due to the blocking effect of the target face, there exists a region of high turbulent kinetic energy near the target face. By comparative analysis of Experiment 2 and Experiment 7, it is found that the turbulence kinetic energy intensity of the flow field is higher when the energy is released alternately by the front and rear resonators, and the jet energy loss is greater, and the atomization degree of the flow field is higher, which is consistent with the velocity distribution cloud map of the flow field. 20

Research on Cooperative Optimization
The method was combined with Back Propagation (BP) neural network Algorithm and improved non-dominated Sorting Genetic Algorithm (NSGA-Ⅱ).
A multi-objective collaborative optimization scheme with excellent equalization, high speed and high accuracy can be established to study the collaborative optimization of self-excited oscillating pulse cavitation jet nozzles.

BP neural network algorithm
BP neural network is a kind of using the method of calculating error backward propagation training out of the multilayer feedforward network [16], training process, input parameters are passed, the results of the calculation error reverse relay feedback, using the input sample data training qualified unit, the multilayer neural network input parameters and establish accurate multidimensional mapping relationship between the output value, Qualified network units possess memory and prediction capabilities [18,19].
BP neural network consists of input factor layer, output target layer and hidden structure layer [20].In this paper, the number of input factor layer nodes is the key structural parameters of the self-excited oscillation pulse cavitation jet nozzle, so the number of input factor layer nodes of the nozzle is 9.The number of nodes in the output target layer is 2, which are respectively the pulsation amplitude and peak value of the striking force acted on the target surface by the jet of the nozzle. The number of nodes in the hidden structure layer is 9.The main calculation process of BP neural network algorithm is divided into creating neural network, training neural network and prediction neural network. In this paper, BP neural network program was written based on Matlab. Newff function was used to create neural network units. Tansig function was used as node transfer function in the hidden structure layer, and Purelin function was used as node transfer function in the output target layer. The Levenber-Marquardt training algorithm was adopted to train the neural network training function. The network training times were 3000 times, the network training rate was 0.01, and the expected error of the network was 1×10 -6 . The SIM function was used to predict the neural network after the training and verify whether the neural network met the accuracy requirements [21].

Non-dominated sorting genetic algorithm
Genetic algorithm realizes global parallel optimization by simulating the survival of the fittest among biological populations. It adopts the mechanism of selection, crossover and mutation to simulate the evolution of organisms in nature, which has the advantages of accuracy and efficiency. In this paper, the non-dominated sorting genetic algorithm (NSGA-II) was used to realize the multi-variable and multi-objective global optimization of the structural parameters of self-excitation oscillation pulse cavitation jet nozzles. The NSGA-Ⅱ algorithm was proposed by Kalyanmoy Deb [22,23].The convergence rate is reduced from O(MN3)(M is the number of target, and N is the number of population) to O(MN2) by fast iteration combined with the crowding calculation method, which greatly improves the calculation efficiency.
In order to make up for the shortcoming that genetic algorithm is easy to fall into the local optimal solution, this paper combines BP neural network and NSGA-Ⅱ algorithm, uses the excellent multi-dimensional function mapping ability of BP neural network to calculate the individual fitness of NSGA-zero algorithm, and then uses the NSGA-II algorithm to conduct population optimization and find out the individual with the optimal fitness [24].

Collaborative optimization design scheme
The structural design parameters and target values of the nozzle in the simulation (amplitude and peak value of striking force pulsation) were taken as the training data of the BP network unit, so that the BP network unit could establish the nonlinear mapping relationship between the input variables and the output targets, and had the ability of memory and prediction. Combining BP neural network algorithm and NSGA-Ⅱ algorithm, the optimal matching scheme of nozzle structure parameters is determined through global optimization, which can not only avoid the occurrence of local optimal solution, but also reduce the global search time and improve the computational efficiency. The overall optimization scheme flow is shown in Figure 14.
Firstly, model parameters x (key structural parameters) and y (amplitude and peak value of cracking force pulsation) and variable optimization interval of collaborative optimization were determined according to the research basis and simulation results. Then, according to the numerical simulation results of the self-excited oscillating pulse cavitation jet nozzle above, the corresponding BP neural network training and test databases are established respectively. Using the advantages of BP neural network and NSGA-Ⅱ algorithm to build a multi-variable multi-objective collaborative optimization algorithm program. The qualified BP neural network was trained and modified based on the experimental database, and the population was optimized by using the non-dominated sorting genetic algorithm. The optimal solution set of Pareto was obtained, that is, the solution set of the optimal matching scheme of nozzle structural parameters.

Simulation scheme design Simulation solution calculation
Simulation results processing

Optimized design variable
The variables x and y are determined The optimization range is determined

Construction of BP neural network
Accuracy test Whether to meet the precision requirement

Initial population
The NSGA-Ⅱ algorithm is constructed

Individual fitness
Generate the first subgroup Iterative algebra Gen=2 The combination of parents and children

Analysis of collaborative optimization results
All the arrays of simulation results are out of order to establish a BP neural network training and testing database, and to conduct data testing and analysis [25,26]. The test results of BP neural network are shown in Fig. 15. The degree of fit between the predicted value and the simulated value is as high as 99.99%, which indicates that the trained neural network meets the required computational accuracy requirements. The optimization interval of each design variable in the genetic algorithm is determined according to the optimization range of structural parameters in the simulation study, as shown in Table 8 below. The initial population number of the non-dominated sorting genetic algorithm of the collaborative optimization algorithm was set as 3000, and the number of iterations was set as 300. The solution set of the optimal structural parameter matching scheme of the nozzle was taken the amplitude of the pulsation of the striking force as the abscissor and the peak of the striking force as the ordinate, and the optimal solution set of the Pareto solution set of the single-cavity nozzle was searched by the collaborative optimization, as shown in Fig. 16. The 300 groups of configuration schemes searched by the collaborative optimization algorithm were rounded and 5 groups of compromise configuration schemes were selected, as shown in Table 9. Simulation analysis was carried out for the five structural configuration schemes again. In the simulation results, the striking force waveform on the target surface is shown in Fig. 12. Data such as the pulsation amplitude of the striking force and the peak value of the striking force were extracted and compared with the predicted value of the collaborative optimization, as shown in Table 10.Through simulation and verification, it is found that the amplitude and peak value of the cracking force generated by the configuration scheme of the structural parameters obtained by the collaborative optimization are greatly improved compared with the results of the orthogonal test optimization. In the nozzle configuration scheme optimized by orthogonal test, the maximum striking force pulsation amplitude is 57.35N and the maximum striking force peak is 353.89N; in the collaborative optimization scheme, the maximum striking force pulsation amplitude is 65.73N and the maximum striking force peak is 362.47N.The amplitude of the impact pulsation and the peak of the impact force of the jet increased by 14.61% and 2.42%.It shows that collaborative optimization has better global optimization function.
The variation trend of the pulsation amplitude and peak value of the cracking force in the simulation results of the structure matching scheme obtained by collaborative optimization is basically consistent with the variation trend of the predicted value in Figure 11. The simulation results prove that the reliability of the collaborative optimization method is within an acceptable range. Here, the error of the collaborative optimization method is mainly caused by the accumulation of errors of BP neural network and NSGA-II algorithm. Meanwhile, due to the relatively few training data, the interaction between various structural parameters cannot be reflected comprehensively and in detail. However, the error of the collaborative optimization method is within an acceptable range compared with that of the above uniform discretized value optimization which cannot accurately determine the optimal value of each structure in the continuous domain. The comprehensive analysis shows that the collaborative optimization method in this paper has a high accuracy, and the collaborative optimization design scheme meets the expected requirements.

Visualization Test of Flow Field
In order to verify the actual optimization effect of collaborative optimization design and the rationality of the above work, a visualization test model of the nozzle flow field was made by 3D printing in equal proportion to observe the movement state of the cavitation vortex in the resonator of the nozzle under the state of low-pressure jet flow, so as to determine whether it can effectively generate pulse cavitation jet.

Test Platform
The pump station of WHPS-32 water hydraulic test system was selected as the power source in this test to provide constant inlet pressures of 0.5MPa and 3MPa for the flow field visualization test of self-excited oscillation pulse cavitation jet nozzle. The flow field visualization test device of self-excited oscillation pulse cavitation jet nozzle is shown in Fig.  13 [27,28].
The test system is composed of two parts: the pump station of the water hydraulic test system and the visualization test bed of the nozzle flow field. Water hydraulic pump test system from motor 1, Torque tachometer 2, water pump 3, pressure gage 4, force sensor 5, low pressure cut-off valve 6, three four-way solenoid valve 7, quick change connector 8, flow control valve 9, two position two way valve10, Three-way valves 11, flow sensor 12, graded filter 13, temperature sensor 14, filling water filter 15, liquid level gauge 16, water tank 17 and other components; The starting and stopping of the system, as well as the flow and pressure provided by the system, can be adjusted through the control panel on the pump station of the water hydraulic test system. The nozzle flow field visualization test bed is composed of connector, nozzle, camera, image acquisition, processing system, water collecting hood, reservoir, bracket, motor, water pump, cut-off valve, pressure reducing valve, flow sensor and other units; The flow field information of the nozzle can be recorded by adjusting the camera. The water collecting cover can prevent the jet from splashing and concentrate the water jet into the reservoir at the same time. Electric motors, pumps and other equipment return the water from the reservoir to the water tank in the water hydraulic test system pump station for recycling of water resources. The water hydraulic test system, the pump station and the nozzle flow visualization test rig, cooperate with the adjustment to complete the visualization test of the nozzle flow field.

Test Model
The processing is carried out by 3D section printing and then bonding and sealing. The material is transparent resin, and the inside of the nozzle resonator is manually polished [29,30]. In order to save research and development costs, a matching scheme of the optimal solution set obtained by nozzle collaborative optimization was selected in this paper to carry out flow field visualization test model processing. Structural parameters of the nozzle test model are shown in Table 11.

Testing Program
In this paper, the flow field visualization test of the self-excited oscillation pulse cavitation jet nozzle was carried out to record the development and evolution process of the jet flow field of the nozzle under different inlet pressure conditions. The test was conducted according to the following steps: (1) According to Fig. 13, a visualization test rig for flow field of self-excited oscillating pulse cavitation jet nozzle was built, and stress devices such as nozzle and water collecting hood were fixed to prevent droplets from splashing into the test room.
(2) Adjust the pump station of the water hydraulic test system, check whether the buttons of the control panel are reset, and then start the power switch of the pump station.
(3) The control panel of the pump station of the water hydraulic test system was adjusted to set the system pressure to 0.5MPa, and the camera was adjusted to record the development and evolution process of the cavitation vortex in the resonant cavity under the corresponding working conditions.
(4) The control panel of the pump station of the water hydraulic test system is adjusted to set the system pressure to 3MPa, and the camera is adjusted to record the development and evolution process of the cavitation vortex in the resonator cavity under the corresponding working conditions. (5) Turn off the power supply of the pump station of the water hydraulic test system, remove the test equipment and put it back in place, and clean the laboratory.

Analysis of Test Results
Visualization test of flow field of self-excited oscillating pulse cavitation jet nozzle was completed according to the above operation process. Fig. 14 shows the evolution process of flow field in the nozzle under inlet pressure of 0.5MPa, and Fig. 15 shows the evolution process of flow field in the nozzle under inlet pressure of 3MPa.It can be seen from the figure that the cavitation intensity in the nozzle resonator is low under the inlet pressure of 0.5MPa, the area of cavitation vortex is relatively small in the stage of cavitation aggregation, and the content of hollow bubbles in the jet is also low. Cavitation phenomenon is obvious in the nozzle resonator under the condition of 3MPa inlet pressure. The cavity is almost full of cavitation in the stage of cavitation aggregation, and a large number of cavitation is full in the stage of cavitation collapse, and the jet is ejected in the state of aggregation at the same time. The research shows that the higher the inlet pressure is within the specified pressure range, the higher the cavitation intensity in the resonant cavity of the nozzle will be, and the higher the hollow bubble content of the pulsed cavitation jet will be, which is consistent with the conclusion drawn from the previous simulation study.  Through the self-excited oscillation pulsed cavitation jet nozzle flow field visualization experiment, observed the low pressure inlet swirl nozzle inside the cavity under the condition of cavitation has obvious cyclical movement process, the resonant cavity cavitation area do periodic shrink over time, cavitation energy phase vortex expanded, clamp block, on the formation fluid cavitation energy release phase vortex narrowed, instantaneous release energy savings, A large number of cavitation jets move together with the pulse jet and are ejected out of the nozzle outlet to form the pulse cavitation jet. It is found that the higher the inlet pressure in the specified pressure range, the higher the cavitation intensity in the resonant cavity, and the higher the cavitation content of the flow beam in the outflow field. This part proves that the optimal matching scheme of nozzle structural parameters obtained by collaborative optimization can produce effective pulsed cavitation jet, and verifies the rationality of its actual optimization effect and the previous work.

Conclusions
(1) Matrix analysis method by orthogonal experiment, the paper analyzes the self-excited oscillation pulsed cavitation jet nozzle structure and key parameters of regularity of influence on the properties of the jet on the jet performance influence from strong to weak structural parameters for the former in turn after the cavity under the nozzle diameter, cavity cavity diameter, cavity cavity diameter, before the cavity cavity length, cavity after the nozzle diameter, cavity, the cavity before entry the rounded, cavity cavity after entry rounded corners and cavity length.
(2) BP neural network algorithm and non-dominated sorting genetic algorithm were used to establish the self-excited oscillation nozzle collaborative optimization method, and the optimal structural parameter matching scheme of the nozzle was obtained. Compared with the optimal results of orthogonal test, the collaborative optimization results increased the amplitude of the pulsation of the blow force by 14.61% and the peak value of the blow force by 2.42%.
(3) The visualization test results of the flow field of the self-excited oscillating pulse cavitation jet nozzle show that the optimal structure of the nozzle determined by the collaborative optimization can generate obvious pulse cavitation jet, and the cavitation region of the nozzle cavity contracts periodically with time. The higher the inlet pressure, the higher the cavitation intensity and the higher the content of hollow bubble. The results obtained by the collaborative optimization scheme of the nozzle are in good agreement with the measured results of the experimental model, which verifies the rationality of the optimization results and the correctness of the work done.
Authors' contributions XMY conceived the research and wrote the manuscript; NW and WDW conducted experiments; LJZ and YZ revised the manuscript. All authors read and approved the final manuscript.

Authors' information
Xiaoming Yuan, born in 1985, is an associate professor and master supervisor of Hebei Provincial