An evaluation method and system for the cavitation area of an impeller of a tubular pump device

Through CFD technology, the three-dimensional fixed cavitation value calculation of the flow pump device is carried out. Combined with the actual engineering, the impeller cavitation evaluation problem of the flow pump device under the multi-water operating conditions is solved, and efficient and accurate impeller cavitation area evaluation is achieved, which is suitable for engineering design and management.

CN116579091BActive Publication Date: 2025-07-18YANGZHOU UNIV
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Patent Information

Application Number
CN202310299227.X
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2023-03-24
Publication Date
2025-07-18
Estimated Expiration
2043-03-24

AI Technical Summary

Technical Problem

The prior art cannot effectively consider the impeller cavitation damage of the flow pump device under multi-water operating conditions, and the model test is long and expensive, so it cannot meet the evaluation needs of the impeller cavitation area.

Method used

The three-dimensional fixed cavitation numerical calculation is carried out by using CFD technology. Combined with the actual engineering, the gas phase volume fraction and cavitation proportion coefficient of the impeller under different water levels are simulated, and a comprehensive evaluation of the impeller cavitation area is carried out.

Benefits of technology

Simplifies the evaluation process, reduces costs, improves the accuracy and efficiency of evaluation, is suitable for engineering design and management, and avoids the limitations of hardware conditions.

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Abstract

The present invention belongs to the technical field of pumping station engineering, and discloses a method and system for evaluating the cavitation area of the impeller of a tubular pump device. Through CFD technology, simulation calculation is carried out on the tubular pump device. Combining with the actual engineering, considering the influence of the operation time factor on the cavitation area of the impeller blades of the tubular pump device under different water level conditions, a comprehensive evaluation is carried out, avoiding the disadvantages of long time consumption, high cost and inability to give the cavitation area of the impeller blades in the physical model test. This method takes into account the actual multi-water level operation of the pumping station, combines CFD technology to calculate the ratio of the cavitation area of the impeller blades under different water level conditions, and combines the operation time of the pump device at different water level conditions to evaluate the cavitation area of the impeller of the tubular pump device. The prediction result is more in line with the actual engineering. This method is simple, easy to operate, and easy to be mastered by engineering design and management personnel, and is not limited by hardware conditions such as testing equipment.
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Description

Technical Field

[0001] The present invention relates to the technical field of pumping station engineering, and particularly relates to a method and system for evaluating the cavitation area of an impeller of a tubular pump device. Background Art

[0002] Due to its characteristics of extremely low head and large flow rate, the tubular pump device is widely used in tubular pumping stations in plain areas. Cavitation, also known as vapor cavitation, is a phenomenon in which local low pressure (lower than the saturated vapor pressure of the liquid at that temperature) in the liquid flow passage causes the liquid to vaporize at that place, resulting in the explosive growth of a large number of micro-vapor bubbles. After the micro-vapor bubbles rapidly grow into large bubbles, they suddenly collapse with the liquid flow to a high-pressure place, generating an impact of up to several hundred atmospheric pressures on the wall surface of the flow passage and causing erosion of the wall surface material. The tubular pump device generally consists of four flow-through components: an inlet flow passage, an impeller, a guide vane body, and an outlet flow passage. The impeller component is prone to cavitation, which causes damage to the impeller, resulting in a decline in the hydraulic performance of the tubular pump device and even threatening the safe and stable operation of the tubular pump device. The main methods for evaluating the cavitation of the pump device impeller are model tests and numerical simulations. Model tests have the disadvantages of long test time and high cost and cannot meet the requirements of long-term operation at different water levels for evaluating the cavitation area of the pump device impeller. Currently, numerical simulations are used to numerically calculate the cavitation of the impeller and predict the cavitation area, but no prediction method for the cavitation area of the impeller is given. Cavitation occurs in the impeller and cavitation occurs after a certain time, and the actual operation of the pump device under different water level conditions is often ignored.

[0003] In order to effectively solve the above problems, the present invention proposes a method for evaluating the cavitation area of an impeller of a tubular pump device. This method combines numerical simulation with engineering practice, comprehensively considers the actual operation of the pump device under different water level conditions, can reasonably and effectively evaluate the area of cavitation damage to the impeller, and this method is simple and feasible and is easy for engineering designers and pumping station management units to master. Summary of the Invention

[0004] The purpose of this part is to outline some aspects of the embodiments of the present invention and briefly introduce some preferred embodiments. Some simplifications or omissions may be made in this part, as well as in the abstract and title of the present application, to avoid obscuring the purpose of this part, the abstract, and the title. However, such simplifications or omissions cannot be used to limit the scope of the present invention.

[0005] In view of the above existing problems, the present invention is proposed.

[0006] Therefore, the technical problem solved by the present invention is that the prior art cannot consider the external condition factors of multi-water level operation, and there are problems of complex operation, long time consumption, and limitation by the hardware conditions of the test equipment.

[0007] To solve the above technical problems, the present invention provides the following technical solutions:

[0008] In a first aspect, an embodiment of the present invention provides a method for evaluating the cavitation area of an impeller of a tubular pump device, including:

[0009] Performing three-dimensional steady cavitation numerical calculation on the tubular pump device;

[0010] Based on the numerical calculation results, predicting the cavitation area of the impeller of the tubular pump device under different water level conditions;

[0011] Performing ratio calculation according to the operation time and cavitation area under different water level conditions, and comprehensively evaluating the impeller cavitation of the tubular pump device.

[0012] As a preferred solution of the method for evaluating the cavitation area of the impeller of the tubular pump device according to the present invention, wherein: the three-dimensional steady cavitation numerical calculation includes:

[0013] Using computational fluid dynamics technology to simulate the entire fluid conditions of the tubular pump device.

[0014] As a preferred solution of the method for evaluating the cavitation area of the impeller of the tubular pump device according to the present invention, wherein: when the residual convergence accuracy of each physical quantity in the simulation is lower than 1.0×10 -5 , and the change in the detected head tends to be a fixed value, the numerical calculation of the pump device under the operation conditions of this water level meets the convergence requirements.

[0015] As a preferred solution of the method for evaluating the cavitation area of the impeller of the tubular pump device according to the present invention, wherein: according to the results of the three-dimensional steady cavitation numerical calculation of the pump device, determining the gas-phase volume fraction on the blade surface of the impeller under different water level conditions, and the gas-phase volume fraction is expressed as:

[0016]

[0017] wherein, C v is the gas-phase volume fraction, V a is the volume when the gas exists alone, and V t is the sum of the gas-phase and liquid-phase volumes.

[0018] As a preferred solution of the method for evaluating the cavitation area of the impeller of the tubular pump device according to the present invention, wherein: the area where the gas-phase volume fraction is above 0 is the area where cavitation occurs, and the area where the gas-phase volume fraction is above 0.8 is the area where cavitation erosion occurs.

[0019] As a preferred solution of the method for evaluating the cavitation area of the impeller of the tubular pump device according to the present invention, wherein: calculating the cavitation ratio coefficient k i , which is expressed as:

[0020]

[0021] Among them, i represents the i-th water level condition with a running time exceeding 22 hours, 1 ≤ i ≤ b and i is an integer, b is the total number of water level conditions with a running time exceeding 22 hours, S ki is the area of the cavitation region occurring on the surface of the impeller blades under the i-th water level condition with a running time exceeding 22 hours, S is the surface area of the impeller blades, k i is the cavitation ratio coefficient under the i-th water level condition with a running time exceeding 22 hours.

[0022] As a preferred scheme of the method for evaluating the cavitation area of the impeller of the tubular pump device according to the present invention, wherein: calculating the cavitation area of the impeller of the tubular pump device, expressed as:

[0023]

[0024] Among them, S ks is the estimated cavitation area of the impeller of the tubular pump device, t i is the running time of the i-th water level condition with a running time exceeding 22 hours, T is the sum of the running times of all water level conditions of the tubular pump device with a running time exceeding 22 hours, expressed as:

[0025]

[0026] In a second aspect, an embodiment of the present invention provides an evaluation system for the cavitation area of the impeller of a tubular pump device, including:

[0027] A calculation module for performing three-dimensional steady cavitation numerical calculation on the tubular pump device;

[0028] An estimation module for estimating the cavitation area of the impeller of the tubular pump device under different water level conditions based on the numerical calculation results;

[0029] An evaluation module for performing ratio calculation according to the running times and cavitation areas of different water level conditions, and comprehensively evaluating the cavitation of the impeller of the tubular pump device.

[0030] In a third aspect, an embodiment of the present invention provides a computing device, including:

[0031] A memory and a processor;

[0032] The memory is used to store computer-executable instructions, and the processor is used to execute the computer-executable instructions. When the one or more programs are executed by the one or more processors, the one or more processors implement the method for evaluating the cavitation area of the impeller of the tubular pump device as described in any embodiment of the present invention.

[0033] Fourthly, an embodiment of the present invention provides a computer-readable storage medium storing computer-executable instructions, which, when executed by a processor, implement the method for evaluating the cavitation area of the impeller of the tubular pump device.

[0034] Advantages of the present invention: The method and system for evaluating the cavitation area of the impeller of the tubular pump device provided by the present invention perform simulation calculations on the tubular pump device through CFD technology. Combining with the actual engineering situation, comprehensively considering the influence of the operation time factor on the cavitation area of the impeller blades of the tubular pump device under different water level conditions for comprehensive evaluation, avoiding the disadvantages of long time consumption, high cost and inability to give the cavitation area of the impeller blades in physical model tests. This method takes into account the actual multi-water-level operation of the pumping station, combines CFD technology to calculate the ratio of the cavitation area of the impeller blades under different water level conditions, and combines the operation time of the pump device at different water level conditions to evaluate the cavitation area of the impeller of the tubular pump device, and the prediction result is more in line with the actual engineering situation. This method is simple, easy to operate, and easy to be mastered by engineering design and management personnel, and is not limited by hardware conditions such as testing equipment. Description of the Drawings

[0035] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for the description of the embodiments will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts. Among them:

[0036] Figure 1 is the overall flowchart of the method for evaluating the cavitation area of the impeller of the tubular pump device according to an embodiment of the present invention;

[0037] Figure 2 is the system architecture diagram of the method for evaluating the cavitation area of the impeller of the tubular pump device according to an embodiment of the present invention;

[0038] Figure 3 is the gas-phase diagram of the impeller blade surface of the tubular pump device of the method for evaluating the cavitation area of the impeller of the tubular pump device according to an embodiment of the present invention. Detailed Embodiments

[0039] To make the above objects, features and advantages of the present invention more obvious and understandable, the following detailed description of the specific embodiments of the present invention will be made in conjunction with the drawings of the specification. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the scope of protection of the present invention.

[0040] In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention. However, the present invention may be practiced in other ways than those specifically described herein, and those skilled in the art can make similar extensions without departing from the spirit of the present invention. Therefore, the present invention is not limited by the specific embodiments disclosed below.

[0041] Secondly, the so-called "one embodiment" or "embodiment" herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation manner of the present invention. The appearances of "in one embodiment" in different places in this specification do not all refer to the same embodiment, nor are they separate or alternative embodiments that exclude each other with other embodiments.

[0042] The present invention is described in detail in conjunction with schematic diagrams. When describing the embodiments of the present invention in detail, for the convenience of explanation, the cross-sectional views showing the device structure will be enlarged locally in a non-general proportion, and the schematic diagrams are only examples and should not limit the scope of protection of the present invention herein. In addition, in actual production, three-dimensional spatial dimensions including length, width, and depth should be included.

[0043] Meanwhile, in the description of the present invention, it should be noted that the orientation or positional relationship indicated by terms such as "upper, lower, inner, and outer" is based on the orientation or positional relationship shown in the drawings, and is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be construed as a limitation to the present invention. In addition, the terms "first, second, or third" are only used for descriptive purposes and cannot be construed as indicating or implying relative importance.

[0044] Unless otherwise clearly defined and limited in the present invention, the terms "mounted, connected, and coupled" should be understood in a broad sense. For example, it may be a fixed connection, a detachable connection, or an integral connection; it may also be a mechanical connection, an electrical connection, or a direct connection, or may be indirectly connected through an intermediate medium, or may be the communication inside two elements. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific situations.

[0045] Embodiment 1

[0046] Referring to Figure 1 -2, which is an embodiment of the present invention. This embodiment provides a method for evaluating the cavitation area of the impeller of a tubular pump device, characterized by including:

[0047] S100: Perform three-dimensional steady cavitation numerical calculation on the tubular pump device;

[0048] Furthermore, the three-dimensional steady cavitation numerical calculation includes:

[0049] The entire fluid conditions of the tubular pump device are simulated using computational fluid dynamics technology.

[0050] When the residual convergence accuracy of each physical quantity in the simulation is lower than 1.0×10 -5 , and the change in the detected head tends to be a constant value, the numerical calculation of the pump device under the operating conditions of this water level meets the convergence requirements.

[0051] S200: Estimate the cavitation area of the impeller of the tubular pump device under different water level conditions based on the numerical calculation results;

[0052] Furthermore, according to the results of the three-dimensional steady cavitation numerical calculation of the pump device, determine the gas-phase volume fraction on the blade surface of the impeller under different water level conditions. The gas-phase volume fraction is expressed as:

[0053]

[0054] Among them, C v is the gas-phase volume fraction, V a is the volume when the gas exists alone, and V t is the sum of the gas-phase and liquid-phase volumes.

[0055] The area on the impeller blade surface where the gas-phase volume fraction is above 0 is the area where cavitation occurs. Based on the ultrasonic cavitation test, the cavitation rate of common materials for impellers (such as carbon structural steel, alloy structural steel, stainless steel, etc.) tends to be stable after 22 hours of high-intensity cavitation impact. Therefore, the area where the gas-phase volume fraction on the impeller blade surface is above 0.8 is the area where cavitation occurs.

[0056] S300: Perform a ratio calculation based on the operating time and cavitation area under different water level conditions to comprehensively evaluate the cavitation of the impeller of the tubular pump device.

[0057] Furthermore, calculate the cavitation ratio coefficient k i under different water level conditions, which is expressed as:

[0058]

[0059] Among them, i represents the i-th water level condition where the operating time exceeds 22 hours, 1 ≤ i ≤ b and i is an integer, b is the total number of water level conditions where the operating time exceeds 22 hours, S ki is the area of the cavitation-occurring area on the impeller blade surface under the i-th water level condition where the operating time exceeds 22 hours, S is the surface area of the impeller blade, and k i is the cavitation ratio coefficient under the i-th water level condition where the operating time exceeds 22 hours.

[0060] Furthermore, calculate the cavitation area of the impeller of the tubular pump device, which is expressed as:

[0061]

[0062] Among them, S ks is the estimated cavitation area of the impeller of the tubular pump device, and t i is the operating time of the i-th water level condition with an operating time exceeding 22 hours, and T is the sum of the operating times of all water level conditions of the tubular pump device with an operating time exceeding 22 hours, which is expressed as:

[0063]

[0064] The above is a schematic solution of an evaluation method for the cavitation area of the impeller of a tubular pump device in this embodiment. It should be noted that the technical solution of the evaluation system for the cavitation area of the impeller of the tubular pump device belongs to the same concept as the technical solution of the above evaluation method for the cavitation area of the impeller of the tubular pump device. For the details not described in detail in the technical solution of the evaluation system for the cavitation area of the impeller of the tubular pump device in this embodiment, reference can be made to the description of the technical solution of the above evaluation method for the cavitation area of the impeller of the tubular pump device.

[0065] Figure 2 is a structural schematic diagram of an evaluation system for the cavitation area of the impeller of a tubular pump device provided by the present invention. This embodiment is applicable to the situation of the evaluation method for the cavitation area of the impeller of the tubular pump device.

[0066] See Figure 2 , in this embodiment, the evaluation system for the cavitation area of the impeller of the tubular pump device includes:

[0067] Calculation module 101, performing three-dimensional steady cavitation numerical calculation on the tubular pump device;

[0068] Estimation module 201, estimating the cavitation area of the impeller of the tubular pump device under different water level conditions based on the numerical calculation results;

[0069] Evaluation module 301, performing ratio calculation according to the operating time and cavitation area under different water level conditions, and comprehensively evaluating the impeller cavitation of the tubular pump device.

[0070] This embodiment also provides a computing device, applicable to the situation of the evaluation method for the cavitation area of the impeller of the tubular pump device, including:

[0071] A memory and a processor; the memory is used to store computer-executable instructions, and the processor is used to execute the computer-executable instructions to implement the evaluation method for the cavitation area of the impeller of the tubular pump device as proposed in the above embodiment.

[0072] The computer device can be a terminal, which includes a processor, a memory, a communication interface, a display screen, and an input device connected via a system bus. Among them, the processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage medium. The communication interface of the computer device is used to communicate with external terminals in a wired or wireless manner, and the wireless manner can be achieved through WIFI, operator network, NFC (Near Field Communication), or other technologies. The display screen of the computer device can be a liquid crystal display screen or an electronic ink display screen. The input device of the computer device can be a touch layer covering the display screen, or buttons, trackballs, or touchpads provided on the outer shell of the computer device, or an external keyboard, touchpad, or mouse, etc.

[0073] This embodiment also provides a storage medium, on which a computer program is stored. When the program is executed by a processor, it implements the method for evaluating the cavitation area of the impeller of the tubular pump device as proposed in the above embodiment.

[0074] The storage medium proposed in this embodiment and the data storage method proposed in the above embodiment belong to the same inventive concept. Technical details not described in detail in this embodiment can be referred to the above embodiment, and this embodiment has the same beneficial effects as the above embodiment.

[0075] Embodiment 2

[0076] Refer to Figure 3 , which is an embodiment of the present invention. This embodiment provides that in order to verify the beneficial effects of the present invention, scientific demonstration is carried out through specific implementation methods and implementation effects.

[0077] In this embodiment, taking the shaft tubular pump device adopting the ZM25 model as an example, a three-dimensional mathematical model of the tubular pump device is constructed using a three-dimensional modeling software, and then the cavitation calculation of the shaft tubular pump device is carried out using CFD (Computational Fluid Dynamics) technology, and the turbulence model is SST k-ω. In the cavitation flow calculation, the liquid and gas phases are respectively set as water and water vapor at a normal temperature of 25°C, and the Rayleigh Plesset cavitation model is selected. The saturation pressure in the model is set to 3167.6 Pa. CFD calculations are carried out for three water level conditions, and the calculations all meet the requirement that the residual convergence accuracy of each physical quantity is lower than 1.0×10 -5 , and the head change tends to be stable. According to the cavitation calculation results of the 3 water level conditions shown in Table 1, the gas phase on the impeller blade surface of the tubular pump device is obtained as Figure 3 shown.

[0078] Table 1 Information Table of Different Water Level Conditions

[0079] Water level condition Head (m) Flow rate (L / s) Design operation time (hours / month) Condition 1 0.88 260 56 Condition 2 1.59 217 224 Condition 3 2.14 174 28

[0080] The area where the gas-phase volume fraction on the surface of the impeller blade is greater than 0.8 is determined as the cavitation-occurring area and its area is determined. The cavitation ratio coefficient is calculated through the cavitation ratio coefficient, and finally the estimated cavitation area of the impeller of the tubular pump device is calculated through the cavitation area formula. The calculation results are shown in Table 2

[0081] Table 2 Cavitation Ratio Coefficient and Estimated Cavitation Area of the Impeller under Different Water Level Conditions

[0082]

[0083] In this embodiment, the surface area of a single blade of the impeller of the tubular pump device is 267.4 mm 2 , and after running for 1 month according to the designed operation time, the finally estimated cavitation area of the impeller of the tubular pump device is 81 mm 2 . In this embodiment, the operation time under different water level conditions is greater than 22 hours. If there is a water level condition with an operation time less than 22 hours during the calculation process, it is considered that although cavitation occurs in this water level condition, no cavitation phenomenon occurs, and this water level condition is ignored for calculation to obtain the cavitation area of the impeller of the pump device for the reference of engineering designers and pump station management units to ensure the safe, stable and efficient operation of the tubular pump device.

[0084] In this embodiment, the selection and setting of various parameters such as the turbulence model, cavitation model, saturation pressure, etc. in the CFD numerical simulation are only used to illustrate the present invention. The specific settings should determine appropriate parameters for calculation according to the actual project.

[0085] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that the technical solutions of the present invention can be modified or equivalently replaced without departing from the spirit and scope of the technical solutions of the present invention, and they should all be covered by the scope of the claims of the present invention.

Claims

1. A method for evaluating the cavitation area of an impeller of a tubular pump device, characterized in that Comprising: Performing three-dimensional steady cavitation numerical calculation on the tubular pump device; According to the results of the three-dimensional steady cavitation numerical calculation of the pump device, determining the gas-phase volume fraction on the blade surface of the impeller under different water level conditions, and the gas-phase volume fraction is expressed as: Among them, C v is the gas-phase volume fraction, V a is the volume when the gas phase exists alone, and V t is the sum of the volumes of the gas phase and the liquid phase; Based on the numerical calculation results, predicting the cavitation area of the impeller of the tubular pump device under different water level conditions; the area where the gas-phase volume fraction is above 0 is the cavitation-occurring area, and the area where the gas-phase volume fraction is above 0.8 is the cavitation area; According to the operation time and cavitation area under different water level conditions, perform proportioning calculations to comprehensively evaluate the impeller cavitation of the tubular pump device; calculate the cavitation ratio coefficient k under different water level conditions i , which is expressed as: Among them, i represents the i-th water level condition with an operating time exceeding 22 hours, 1 ≤ i ≤ b and i is an integer, b is the total number of water level conditions with an operating time exceeding 22 hours, S ki is the area of the cavitation region occurring on the surface of the impeller blades under the i-th water level condition with an operating time exceeding 22 hours, S is the surface area of the impeller blades, k i is the cavitation ratio coefficient under the i-th water level condition with an operating time exceeding 22 hours; Calculating the cavitation area of the impeller of the tubular pump device, expressed as: Among them, S ks is the estimated cavitation area of the impeller of the tubular pump device, t i is the running time of the i-th water level condition with a running time exceeding 22 hours, and T is the sum of the running times of the water level conditions of the tubular pump device with running times exceeding 22 hours, expressed as:

2. The evaluation method for the cavitation area of the impeller of the tubular pump device according to claim 1, characterized in that: The three-dimensional steady cavitation numerical calculation includes: Using computational fluid dynamics technology to simulate the entire fluid conditions of the tubular pump device.

3. The method for evaluating the cavitation area of the impeller of the tubular pump device according to claim 2, characterized in that: When the residual convergence accuracy of each physical quantity in the simulation is lower than 1.0×10 -5 , and the change in the detected head tends to be a fixed value, the numerical calculation of the pump device under the operating conditions of this water level meets the convergence requirements.

4. An evaluation system for the cavitation area of the impeller of a tubular pump device, which is applied to the method according to any one of claims 1-3, and is characterized in that, Comprising: A calculation module (101) for performing three-dimensional steady cavitation numerical calculation on the tubular pump device; A prediction module (201) for predicting the cavitation area of the impeller of the tubular pump device under different water level conditions based on the numerical calculation results; An evaluation module (301) for performing a ratio calculation according to the operation time and cavitation area under different water level conditions to comprehensively evaluate the cavitation of the impeller of the tubular pump device.

5. A computing device, comprising: A memory and a processor; The memory is used to store computer-executable instructions, and the processor is used to execute the computer-executable instructions. When the computer-executable instructions are executed by the processor, the steps of the method for evaluating the cavitation area of the impeller of the tubular pump device according to any one of claims 1 to 3 are implemented.

6. A computer-readable storage medium storing computer-executable instructions, and when the computer-executable instructions are executed by a processor, the steps of the method for evaluating the cavitation area of the impeller of the tubular pump device according to any one of claims 1 to 3 are implemented.

Citation Information

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