Underwater cavitation jet observation experiment device and method based on triangular reflector

Through the underwater cavitation jet observation experimental device based on a triangular reflector, the problem of observation of the impact surface of the cavitation jet is solved, and the simultaneous observation of the free jet area and the impact area is realized, which improves the accuracy and clarity of the experiment and meets the experimental requirements of different target distances.

CN120394418APending Publication Date: 2025-08-01烟台哈尔滨工程大学研究院 +2
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Patent Information

Application Number
CN202510429414.4
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2025-04-08
Publication Date
2025-08-01

AI Technical Summary

Technical Problem

Existing high-speed cavitation jet photography experiments are difficult to observe the impact surface of the cavitation jet, especially the simultaneous observation of the free jet area and the impact area.

Method used

The underwater cavitation jet observation experimental device based on a triangular mirror is adopted, including a jet control device, an impact observation device, a light source assembly and a high-speed camera. The triangular mirror realizes simultaneous observation of the free jet area and the impact area through a triangular mirror. The sliding table device and the driving component are combined to accurately locate the target distance, and the zoom light source assembly is used to adjust the light angle and intensity, the solenoid valve controls the water flow release time, and the pressure sensor monitors the jet pressure.

Benefits of technology

The simultaneous observation of the free jet area and impact area of the cavitation jet is achieved, which improves the accuracy and clarity of the experiment, meets the experimental requirements of different target distances, and ensures the accuracy of the test and the convenience of the equipment maintenance.

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Abstract

The invention relates to the technical field of cleaning equipment, in particular to an underwater cavitation jet observation experiment device and method based on a triangular reflector, and the device comprises a jet control device, an impact observation device, a plurality of light source assemblies and a high-speed camera. The spraying control device comprises a nozzle, and external high-pressure water flow is sprayed out downwards from the nozzle after passing through the pump pipe; the impact observation device comprises a clamping device. The clamping device comprises a triangular prism reflector and a support used for placing the triangular prism reflector. A shot picture of the high-speed camera can simultaneously comprise a free jet flow area and a jet flow impact area reflected by the triangular prism reflector. According to the double-angle free cavitation jet flow observation device, the three-edged reflector is utilized, cavitation flow evolution of a free jet flow area of cavitation jet flow and a jet flow impact area reflected by the three-edged reflector can be observed at the same time, and double-angle free cavitation jet flow observation is achieved.
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Description

Technical Field

[0001] The present invention relates to the technical field of cleaning equipment, and particularly to an underwater cavitation jet observation experimental device and method based on a triangular prism mirror. Background Art

[0002] Cavitation cleaning is an advanced cleaning technology that uses the cavitation phenomenon to remove dirt, impurities, and pollutants on the surface of objects. In recent years, with the increasingly strict environmental protection standards and requirements, traditional cleaning methods (such as chemical cleaning) face challenges in terms of environmental friendliness and safety. As a physical cleaning method, cavitation cleaning uses water or other liquid media, reducing the dependence on chemical cleaning agents, thus meeting the requirements of sustainable development. This technology can effectively remove oil stains, dust, oxides, and other attachments, and at the same time achieve high-efficiency cleaning in a short time, improving production efficiency and reducing labor costs. However, the current cavitation cleaning technology still has some limitations. Therefore, observing the morphology of cavitation jets is of great significance for the application of cavitation cleaning. By studying its dynamic behavior and characteristics, researchers can optimize the design of cleaning equipment and improve the cleaning effect. Different cavitation morphologies with different behaviors may correspond to different cleaning effects. Therefore, the best operating parameters (such as flow rate, pressure, and temperature) can be determined through observation and analysis to achieve more effective cleaning.

[0003] Existing high-speed photography observation studies on the morphology of cavitation jets mainly focus on the frontal observation of cavitation jets (free jet region), while the observation of the impact surface (impact region) is rarely involved. The observation of the cavitation jet impact surface helps to understand the correlation between the cavitation evolution characteristics and cavitation erosion characteristics on the impact surface, which is of great significance for understanding and optimizing the cavitation cleaning process. However, it is currently difficult to observe the cavitation jet impact surface in high-speed photography experiments of cavitation jets, especially the simultaneous observation of the free jet region and the impact region. Summary of the Invention

[0004] Technical Objective: In order to overcome the deficiencies in the prior art, the present invention provides an underwater cavitation jet observation experimental device and method based on a triangular prism mirror, realizing the simultaneous observation of the free jet region and the impact region.

[0005] Technical solution: To achieve the above object, the present invention discloses an underwater cavitation jet observation experimental device based on a triangular prism reflector, including a jet control device for generating a jet of water, an impact observation device arranged below the jet control device, a plurality of light source components for providing illumination for the experiment, and a high-speed camera for photographing the experimental process; the jet control device includes a nozzle, and the external high-pressure water jet is ejected downward from the nozzle after passing through the pump pipe; the impact observation device includes a clamping device, and the clamping device includes a triangular prism reflector and a bracket for placing the triangular prism reflector; the shooting screen of the high-speed camera can simultaneously include the free jet area and the jet impact area reflected by the triangular prism reflector.

[0006] Further, it also includes a frame, a transparent water tank is arranged inside the frame, and the impact observation device is arranged inside the transparent water tank; a drainage system is arranged at the bottom of the frame.

[0007] Further, the jet control device is slidably connected to the top of the frame through a slide table device; the slide table device includes a slider and a drive component for driving the slider to move.

[0008] Further, a connecting pipe is also arranged between the nozzle and the pump pipe, and the connecting pipe moves synchronously with the slider through a mounting base; a pressure sensor is also arranged at one end of the connecting pipe close to the nozzle, and a solenoid valve is arranged at the other end.

[0009] Further, the impact observation device also includes an impact table, and the impact table includes an impact frame and a substrate arranged on the impact frame, and the bracket is arranged on the substrate and its position is adjustable.

[0010] Further, the impact observation device also includes a modular base, and the impact table is fixedly installed on the modular base.

[0011] Further, an opening one is arranged on the top wall of the bracket, an opening two is arranged on the observation side, an inclined part is arranged inside the bracket, and the triangular prism reflector is clamped in the space surrounded by the inclined part and the side wall of the bracket; the clamping device also includes a limiting plate for restricting the movement of the triangular prism reflector; a glass plate is also arranged between the triangular prism reflector and the limiting plate, and an acrylic film is also arranged between the glass plate and the triangular prism reflector.

[0012] Further, the light source component includes a variable-focus light source, and the variable-focus light source is connected to the frame through an adjustable-distance bracket.

[0013] Further, the adjustable-distance bracket includes a first rod and a second rod. One end of the first rod is hinged to the second rod, and the other end is provided with a clamping end for clamping the variable-focus light source. The other end of the second rod is hinged to the frame.

[0014] An experimental method for observing underwater cavitating jets based on a triangular prism reflector includes the following steps:

[0015] S1: Install the impact observation device at the bottom inside the transparent water tank, and adjust the bracket through the limit groove and the limit block to fix it at the desired position.

[0016] S2: Start the driving component to adjust the position of the slider, and then adjust the position of the mounting base so that the jet control device moves to the experimental target distance.

[0017] S3: Adjust the position of the high-speed camera so that its picture can simultaneously include the free jet region A and the jet impact region B reflected by the triangular prism reflector.

[0018] S4: Run the pump set. After reaching the predetermined pressure, open the solenoid valve. The external high-pressure water flow passes through the pump pipe and the connecting pipe in sequence and then sprays downward from the nozzle. During this process, the pressure sensor monitors the pressure fluctuation in real time.

[0019] S5: After the spraying pressure is stable, turn on the variable-focus light source, adjust the position of the adjustable-distance bracket to achieve the best illumination angle for different target distance experimental conditions, and adjust the focal length of the variable-focus light source to achieve light concentration in the local observation area.

[0020] S6: Start the high-speed camera to take pictures.

[0021] S7: After the recording is completed, turn off the high-speed camera, the solenoid valve and the variable-focus light source in sequence, and the drainage system drains the water in the transparent water tank.

[0022] The present invention has at least the following beneficial effects:

[0023] 1. The present invention utilizes the triangular prism reflector in the experimental observation of underwater cavitating jets, and can simultaneously observe the free jet region of the cavitating jet and the cavitation flow evolution in the jet impact region reflected by the triangular prism reflector, realizing the observation of double-angle free cavitating jets.

[0024] 2. By setting the sliding table device and controlling the movement of the slider by the driving component, the target distance is accurately positioned to meet the experimental requirements of different target distances; by setting the impact observation device and adjusting and positioning the position of the bracket through the limit groove and the limit block, combined with the variable-focus light source assembly, the illumination angle adjustment for different experimental target distances is realized and the light concentration effect at a lower power is achieved, ensuring the clarity of high-speed photography.

[0025] 3. The release time of the water flow is controlled by a solenoid valve to accurately control the test time. The accuracy of the injection pressure is controlled by a pressure sensor to ensure the test effect. After the experiment, the water in the transparent water tank can be completely emptied through the drain outlet of the water tank, which is convenient for the maintenance of the transparent water tank. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 It is a schematic diagram of the overall structure of this experimental device;

[0027] Figure 2 It is a schematic diagram of the free jet region and the jet impact region;

[0028] Figure 3 It is a schematic diagram of the structure of the sliding table device and the injection control device;

[0029] Figure 4 It is a schematic diagram of the structure of the impact observation device;

[0030] Figure 5 It is a schematic diagram of the cooperation structure of the bracket and the substrate;

[0031] Figure 6 It is a schematic diagram of the structure of the limit block;

[0032] Figure 7 It is a schematic diagram of the structure of the light source assembly;

[0033] In the figure, 10, frame; 11, drainage system; 20, sliding table device; 21, slider; 22, drive assembly; 30, injection control device; 31, nozzle; 32, connecting pipe; 33, pump pipe; 34, mounting base; 35, solenoid valve; 36, pressure sensor; 40, light source assembly; 41, variable-focus light source; 42, adjustable-distance bracket; 43, first support rod; 44, second support rod; 45, clamping end; 46, mounting seat; 47, mounting chute; 50, impact observation device; 60, high-speed camera; 70, clamping device; 71, bracket; 72, triangular prism reflector; 73, limiting plate; 74, opening one; 75, opening two; 76, inclined part; 80, impact table; 81, substrate; 82, limiting groove; 83, impact frame; 84, limit block; 90, modular base. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0034] The following Figure 1 to Figure 7 describe the principles and features of the present invention. The examples given are only used to explain the present invention and are not intended to limit the scope of the present invention.

[0035] An underwater cavitation jet double-angle observation experimental device with a triangular prism mirror assembly, comprising a frame 10, a sliding table device 20, a jet control device 30, a light source assembly 40, an impact observation device 50, and a high-speed camera 60. The jet control device 30 is connected to the top of the frame 10 through the sliding table device 20 and is used to generate a jet of water; the impact observation device 50 is arranged inside the frame 10 and below the jet control device 30; several groups of light source assemblies 40 are arranged and are used to provide illumination for the experiment; the high-speed camera 60 is placed on one side of the frame 10 and is used to photograph the experimental process, and the side where the high-speed camera 60 is placed is defined as the observation side.

[0036] A transparent water tank is arranged inside the frame 10, and the impact observation device 50 is arranged inside the transparent water tank. Cavitation impacts during the experiment will generate vibrations. To prevent damage to the transparent water tank, shock absorption measures should be set between the transparent water tank and the frame 10, such as setting rubber pads, springs, etc. To meet the convenience of operation during cavitation jet experiments and the drainage requirements after the experiment, a drainage system 11 is arranged at the bottom of the water tank frame 10. The upper drainage port of the drainage system 11 is connected to the internal transparent water tank, and a drainage hose is connected to the lower part, through which water can be discharged. In this embodiment, the drainage hose uses PVC parts, the inner diameter of the hose is 50 mm, and bonding and plastic welding are used for fixation and watertightness during installation.

[0037] As Figure 3 shown, the sliding table device 20 is arranged vertically on the cross beam at the top of the frame 10. Specifically, the sliding table device 20 is arranged on a support fixedly connected to the cross beam at the top of the frame 10. The sliding table device 20 includes a slider 21 and a driving component 22 for driving the slider 21 to move. In one embodiment, the driving component 22 and the slider 21 are of a lead screw structure. Specifically, the driving component 22 includes a stepping motor, the output end of the stepping motor is connected to the lead screw, the lead screw is threadedly connected to the slider 21, and when the stepping motor rotates, it can drive the slider 21 to reciprocate vertically, thereby adjusting the height of the slider 21 to accurately control the target distance, and the slider 21 realizes stable movement through a guide rod.

[0038] As Figures 1 to 3 shown, the jet control device 30 is slidably connected to the top of the frame 10 through the sliding table device 20. Specifically, the jet control device 30 includes a nozzle 31, a connecting pipe 32, a pump pipe 33, an installation base 34, an electromagnetic valve 35, and a pressure sensor 36. The connecting pipe 32 is arranged between the nozzle 31 and the pump pipe 33, and different models of nozzles 31 can be replaced to meet different experimental requirements. The installation base 34 is arranged on the slider 21 and moves synchronously with it, and the connecting pipe 32 is installed on the installation base 34 and also moves synchronously with the slider 21. Specifically, as Figure 3As shown, the mounting base 34 fixes the connecting pipe 32 in a clamped connection manner. The pressure sensor 36 is arranged at one end of the connecting pipe 32 close to the nozzle 31, and pressure sensors 36 of different specifications and models can be replaced to achieve pressure monitoring for different experiments. The solenoid valve 35 is arranged at the other end of the connecting pipe 32 and is used to control the water inlet of the pump pipe 33. The external high-pressure water flow is sprayed downward from the nozzle 31 after passing through the pump pipe 33 and the connecting pipe 32 in sequence. In one embodiment, the distance between the pressure sensor 36 and the nozzle 31 is 80 mm.

[0039] As Figure 1 and Figure 7 As shown, the light source assembly 40 is detachably connected to the observation side of the frame 10 by bolts. The light source assembly 40 includes a variable-focus light source 41 and an adjustable-distance bracket 42. The variable-focus light source 41 is connected to the frame 10 through the adjustable-distance bracket 42. The adjustable-distance bracket 42 includes a first support rod 43 and a second support rod 44. One end of the first support rod 43 is hinged to the second support rod 44, and the other end is provided with a clamping end 45 for clamping the variable-focus light source 41. The other end of the second support rod 44 is hinged to the frame 10. Specifically, an installation chute 47 is provided on the first support rod 43 or the second support rod 44. The first support rod 43 and the second support rod 44 are connected by a wing screw and a wing nut, and the free angle adjustment in the horizontal plane is realized by using the installation chute 47. The second support rod 44 is hinged to the frame 10 through a mounting seat 46, and the same installation chute 47 is provided on the mounting seat 46. The installation chute 47 can be an arc structure, and the free angle adjustment in the vertical plane is realized by using the installation chute 47. The best illumination angle and illumination intensity are obtained by adjusting the angle of the adjustable-distance bracket 42 and the focal length of the variable-focus light source 41.

[0040] As Figure 1 and Figures 4 to 6 As shown, the impact observation device 50 includes a clamping device 70, an impact table 80, and a modular base 90. The impact table 80 is fixedly installed on the modular base 90 by bolts, and the clamping device 70 is fixedly installed on the impact table 80. The modular base 90 is made of PP material, and several screw holes are provided on the base to replace different modules to carry out different experiments.

[0041] The clamping device 70 includes a bracket 71, a prism reflector 72, and a limiting plate 73. The bracket 71 is used to place the prism reflector 72, and the limiting plate 73 is used to fix the prism reflector 72 on the bracket 71 to prevent it from moving under impact and vibration. Specifically, the prism reflector 72 is a right-angle prism. The top wall of the bracket 71 is provided with an opening 1 74, and the observation side is provided with an opening 2 75. The bracket 71 is provided with an inclined portion 76 that matches the inclined surface of the right-angle prism. The prism reflector 72 is clamped into the space enclosed by the inclined portion 76 and the side wall of the bracket 71. One of the right-angled surfaces of the prism reflector 72 faces the opening 1 74 and is flush with the top of the bracket 71, while the other right-angled surface faces the opening 2 75 and abuts against the inner surface of the opening 2 75. The limiting plate 73 is provided on the upper wall of the bracket 71 to limit the prism reflector 72 within the bracket 71. To prevent cavitation damage to the prism 72, in one embodiment, a transparent glass plate is provided between the prism 72 and the limiting plate 73 to protect the prism 72. Since the transparent glass plate will vibrate when impacted by the jet, an acrylic film is provided between the prism 72 and the transparent glass plate to prevent wear and tear caused by direct contact. In one embodiment, the prism 72 is made of K9 glass.

[0042] like Figure 2 As shown, after being ejected downward from nozzle 31, the external high-pressure water stream reaches the surface of the transparent glass plate, forming an impact surface, defined as jet impact area B. The area between nozzle 31 and the impact surface is defined as free jet area A. The image of jet impact area B is reflected to the observation side by prism reflector 72. With the observation experimental device of the present invention, the image captured by high-speed camera 60 can simultaneously include free jet area A and jet impact area B reflected by prism reflector 72.

[0043] The impact platform 80 includes a base plate 81, which is provided with a number of limiting grooves 82 and limiting blocks 84 for limiting the position of the bracket 71. The base plate 81 is detachably connected to the upper surface of the impact frame 83. The limiting grooves 82 and limiting blocks 84 allow the position of the bracket 71 to be adjusted and fixed. Specifically, the limiting blocks 84 are trapezoidal blocks that snap into the limiting grooves 82 to secure the bracket 71 in the front and back direction of the observation side. The limiting grooves 82 on the base plate 81 are arranged in pairs on the left and right sides of the bracket 71. By installing screws or other existing methods, the bracket 71 can be fixed in the left and right direction of the observation side. By adjusting the position of the bracket 71, the observation requirements at different locations can be met.

[0044] In this experimental device, the driving component 22, the solenoid valve 35, and the high-speed camera 60 are all electrically connected to a control system such as a computer. By controlling the switch through the computer and setting the control program, the driving component 22 can be autonomously driven to drive the slider 21 to adjust the target distance. After the solenoid valve 35 is opened, the high-speed camera 60 enters the shooting countdown, and after the shooting time ends, the solenoid valve 35 automatically closes to complete the experimental record.

[0045] In an embodiment of the present invention, an underwater cavitating jet double-angle observation experimental method with a triangular prism mirror assembly is also disclosed, including the following steps:

[0046] S1: Install the impact observation device 50 at the bottom inside the transparent water tank, and adjust the bracket 71 through the limit groove 82 and the limit block 84 to fix it at the required position;

[0047] S2: Start the driving component 22 to adjust the position of the slider 21, and then adjust the position of the mounting base 34, so that the jet control device 30 moves to the experimental target distance;

[0048] S3: Adjust the position of the high-speed camera 60 so that its picture can simultaneously include the free jet region A and the jet impact region B reflected by the triangular prism mirror 72;

[0049] S4: Run the pump set. After reaching the predetermined pressure, open the solenoid valve 35. The external high-pressure water flow passes through the pump pipe 33 and the connecting pipe 32 in sequence and then is ejected downward by the nozzle 31. During this process, the pressure sensor 36 monitors the pressure fluctuation in real time;

[0050] S5: After the injection pressure is stable, turn on the variable-focus light source 41, adjust the position of the adjustable-distance bracket 42 to achieve the best illumination angle for different target-distance experimental conditions, and adjust the focal length of the variable-focus light source 41 to concentrate the light source on the local observation area;

[0051] S6: Start the high-speed camera 60 for shooting;

[0052] S7: After the recording is completed, turn off the high-speed camera 60, the solenoid valve 35, and the variable-focus light source 41 in sequence, and the drainage system 11 drains the water in the transparent water tank.

[0053] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. An underwater cavitation jet observation experimental device based on a triangular prism reflector, characterized in that It includes a jet control device (30) for generating a jet of water, an impact observation device (50) arranged below the jet control device (30), a number of light source components (40) for providing illumination for the experiment, and a high-speed camera (60) for photographing the experimental process; The jet control device (30) includes a nozzle (31), and the external high-pressure water jet is ejected downward by the nozzle (31) after passing through the pump pipe (33); the impact observation device (50) includes a clamping device (70), and the clamping device (70) includes a triangular prism reflector (72) and a bracket (71) for placing the triangular prism reflector (72); the photographed image of the high-speed camera (60) can simultaneously include the free jet region and the jet impact region reflected by the triangular prism reflector (72).

2. The underwater cavitation jet observation experimental device based on a triangular prism reflector according to claim 1, characterized in that, It further includes a frame (10), a transparent water tank is arranged inside the frame (10), and the impact observation device (50) is arranged inside the transparent water tank; a drainage system (11) is arranged at the bottom of the frame (10).

3. The underwater cavitation jet observation experimental device based on a triangular prism reflector according to claim 2, characterized in that The jet control device (30) is slidably connected to the top of the frame (10) through a slide table device (20); the slide table device (20) includes a slider (21) and a drive assembly (22) for driving the slider (21) to move.

4. The underwater cavitation jet observation experimental device based on a triangular prism reflector according to claim 3, wherein A connecting pipe (32) is further arranged between the nozzle (31) and the pump pipe (33), and the connecting pipe (32) moves synchronously with the slider (21) through a mounting base (34); a pressure sensor (36) is arranged at one end of the connecting pipe (32) close to the nozzle (31), and a solenoid valve (35) is arranged at the other end.

5. The underwater cavitation jet observation experimental device based on a triangular prism reflector according to claim 1, characterized in that, The impact observation device (50) further includes an impact table (80), and the impact table (80) includes an impact frame (83) and a substrate (81) arranged on the impact frame (83), and the bracket (71) is arranged on the substrate (81) and its position is adjustable.

6. The underwater cavitation jet observation experimental device based on a triangular prism reflector according to claim 5, characterized in that The impact observation device (50) further includes a modular base (90), and the impact table (80) is fixedly installed on the modular base (90).

7. The underwater cavitation jet observation experimental device based on a triangular prism reflector according to claim 1, characterized in that, An opening one (74) is arranged on the top wall of the bracket (71), an opening two (75) is arranged on the observation side, and an inclined part (76) is arranged inside the bracket (71), and the triangular prism reflector (72) is clamped in the space surrounded by the inclined part (76) and the side wall of the bracket (71); The clamping device (70) further includes a limiting plate (73) for restricting the movement of the triangular prism reflector (72); a glass plate is further arranged between the triangular prism reflector (72) and the limiting plate (73), and an acrylic film is further arranged between the glass plate and the triangular prism reflector (72).

8. The underwater cavitating jet observation experimental device based on a triangular prism reflector according to claim 2, characterized in that, The light source component (40) includes a variable-focus light source (41), and the variable-focus light source (41) is connected to the frame (10) through an adjustable-distance bracket (42).

9. The underwater cavitation jet observation experimental device based on a triangular prism reflector according to claim 8, characterized in that, The adjustable-distance bracket (42) includes a first rod (43) and a second rod (44). One end of the first rod (43) is hinged to the second rod (44), and the other end is provided with a clamping end (45) for clamping the variable-focus light source (41). The other end of the second rod (44) is hinged to the frame (10).

10. An experimental method based on the experimental device according to any one of claims 1 to 9, characterized in that, The steps include: S1: Install the impact observation device (50) at the inner bottom of the transparent water tank, and adjust the bracket (71) through the limit groove (82) and the limit block (84) to fix it at the required position; S2: Start the drive assembly (22) to adjust the position of the slider (21), and then adjust the position of the mounting base (34) so that the jet control device (30) moves to the experimental target distance; S3: Adjust the position of the high-speed camera (60) so that its picture can simultaneously include the free jet region A and the jet impact region B reflected by the triangular prism (72); S4: Operate the pump set. After reaching the predetermined pressure, open the solenoid valve (35). The external high-pressure water flow passes through the pump pipe (33) and the connecting pipe (32) in sequence and then sprays downward from the nozzle (31). During this process, the pressure sensor (36) monitors the pressure fluctuation in real time; S5: After the jet pressure is stable, turn on the variable-focus light source (41), adjust the position of the adjustable-distance bracket (42) to achieve the best illumination angle for different target-distance experimental conditions, and adjust the focal length of the variable-focus light source (41) to concentrate the light source on the local observation area; S6: Start the high-speed camera (60) to take pictures; S7: After the recording is completed, turn off the high-speed camera (60), the solenoid valve (35) and the variable-focus light source (41) in sequence, and the drainage system (11) drains the water in the transparent water tank.

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