Pump performance curve correction method based on similarity principle

Abstract

The application discloses a water pump performance curve correction method based on a similarity principle, relates to the technical field of water pump working condition analysis, and comprises the following steps: acquiring a conversion working condition point corresponding to a model pump test working condition point converted to a prototype pump and a theoretical performance curve of the prototype pump; confirming a similarity parabola passing through the field measured working condition point and mapping the similarity parabola to the theoretical performance curve of the prototype pump to obtain an intersection point as a similarity working condition point of the field measured working condition point according to a similarity parabola relationship and field measured working condition point data; obtaining a corresponding point under a theoretical rotating speed according to the similarity relationship and combining the working condition point on the theoretical curve of the prototype pump; replacing the theoretical rotating speed with a measured rotating speed, converting to a corresponding point under a rated rotating speed, and fitting to obtain an actual flow-head curve; and acquiring a theoretical efficiency value and an optimal efficiency value corresponding to the similarity working condition point to obtain an actual flow-efficiency curve, so that the actual performance curve of the prototype pump can be efficiently and accurately corrected.

Description

Technical Field

[0001] This application relates to the technical field of pump operating condition analysis, and in particular to a method for correcting pump performance curves based on the principle of similarity. Background Technology

[0002] Currently, large water pumps are increasingly used in my country's water resource allocation projects, and the stable operation of pumping stations plays a very important role in ensuring water supply security. In order to ensure that large water pumps operate efficiently under the premise of safety, it is necessary to accurately analyze the operating conditions of water pumps with a wide range of speed regulation, which requires that the actual performance curve of the prototype pump must be accurate enough.

[0003] Typically, the performance curve of a large water pump prototype is obtained by theoretically converting the performance of a model pump. This theoretical performance curve is provided to the user by the manufacturer. The actual performance curve of the prototype pump after installation and operation often deviates from this theoretical performance curve. In order to quickly and accurately understand the actual operating conditions of the water pump, it is necessary to correct the performance curve of the prototype pump based on on-site measured data. However, due to the limitations of on-site conditions such as influent water level and outlet water level, it is impossible to obtain all operating points on the actual curve through on-site testing. Therefore, the performance of the prototype pump can be corrected by a small number of measured operating points to obtain the complete actual performance of the prototype pump.

[0004] In related technologies, when multiple pumps operate simultaneously in a pumping station, the pump efficiency decreases significantly, indicating a large discrepancy between actual performance and theoretical conversion values. The substantial deviation between the actual performance curve and the theoretical conversion curve necessitates a scheme to effectively correct the actual performance curve of the prototype pump, thereby providing support for quickly and accurately understanding the actual operating conditions of the pump. Summary of the Invention

[0005] The purpose of this application is to provide a method for correcting the performance curve of a water pump based on the principle of similarity, which can efficiently and accurately correct the actual performance curve of the water pump.

[0006] To achieve the above objectives, this application provides the following solution: This application provides a pump performance curve correction method based on the similarity principle, including: obtaining the converted operating point of the prototype pump from the test operating point of the model pump and the theoretical performance curve of the prototype pump at its rated speed; obtaining the field-measured operating point and operating point data of the prototype pump, wherein the operating point data includes the pump's flow rate, head, speed, and efficiency; arbitrarily selecting a field-measured operating point of the prototype pump, and based on the similarity parabolic relationship and the field-measured operating point data, confirming the similarity parabola passing through the measured operating point, mapping the similarity parabola to the theoretical performance curve of the prototype pump, and obtaining the intersection point as the phase curve of the selected field-measured operating point. Similar operating point; based on the similarity principle, the theoretical speed is obtained, and the corresponding operating point at the theoretical speed is obtained through the conversion of the operating point at the rated speed of the prototype pump. The theoretical speed is transformed into the actual speed of the field-measured operating point, and the actual flow-head curve of the prototype pump at the rated speed is obtained. The theoretical efficiency value and the optimal efficiency value on the theoretical performance curve corresponding to the similar operating point are obtained. Based on the operating point data, the theoretical efficiency value and the optimal efficiency value, and combined with the principle that the efficiency of the similar operating point is consistent with the respective optimal efficiency, the actual flow-efficiency curve of the prototype pump at the rated speed is obtained.

[0007] For example, the expression for the similar parabola is as follows: in, H Indicates head (unit: meters). Q Flow rate (unit: m³) 3 / s), K is a constant, representing the shape coefficient of the similar parabola passing through the origin, and all the similar working points fall on the similar parabola.

[0008] For example, the correction to obtain the actual flow-head curve of the prototype pump at rated speed specifically includes the following steps: confirming the speed relationship between the similar operating point and the measured operating point according to the flow similarity law or the head similarity law, and calculating the theoretical speed; according to the flow similarity law, the head similarity law, the rated speed, and the theoretical speed, it is stipulated that the actual performance curve and the theoretical performance curve of the prototype pump have similar shapes, and obtaining the flow rate and head at the corresponding operating point of the theoretical speed by converting the test operating point of the model pump to the corresponding operating point of the prototype pump; transforming the theoretical speed into the actual speed of the measured operating point on site, it is stipulated that the actual performance curve and the theoretical performance curve of the prototype pump have similar shapes, and obtaining the flow rate and head at the corresponding operating point of the rated speed of the prototype pump according to the flow similarity law, the head similarity law, the rated speed, and the actual speed; fitting the above operating points, and correcting to obtain the actual flow-head curve of the prototype pump at rated speed.

[0009] For example, the process of calculating the theoretical rotational speed is as follows: ,or, in, Indicates the theoretical rotational speed. This represents the flow rate at the measured operating point (unit: m³). 3 / s), The measured head (in meters) indicates the actual head at the operating point. This indicates the rated speed (in r / min). Theoretical flow rate (in m³) for similar operating conditions 3 / s), The theoretical head (in meters) represents the similar operating conditions. The flow rate and head at each operating point on the performance curve under the measured speed are calculated as follows: The flow rate and head at each operating point under the corrected rated speed are calculated as follows: Among them, the proportionality coefficient or , This represents the flow rate at the i-th operating point on the theoretical performance curve at rated speed (in m³ / s). 3 / s), This represents the head (in meters) at the i-th operating point on the theoretical performance curve at rated speed, where i is the operating point number.

[0010] For example, the measured operating point data also includes the measured efficiency of the water pump. The correction to obtain the actual flow-efficiency curve specifically includes the following steps: based on the principle that the rate of decrease of the efficiency of similar operating points on the performance curve at different speeds relative to their respective optimal efficiencies is consistent, the optimal efficiency on the performance curve where the measured operating point is located is calculated according to the measured efficiency, the theoretical efficiency of similar operating points, and the theoretical optimal efficiency; the exponent in the Modi correction formula is calculated; the actual optimal efficiency at the rated speed is calculated; and the efficiency of the actual non-optimal efficiency point at the rated speed is calculated to obtain the actual flow-efficiency curve.

[0011] For example, the optimal efficiency on the performance curve where the measured operating point is located is calculated as follows: in, This indicates the pump efficiency at the measured operating point. This represents the efficiency value corresponding to the similar operating point at rated speed on the theoretical flow-efficiency curve, i.e., the flow rate is... The corresponding efficiency is obtained by interpolating the efficiency curve. This represents the optimal efficiency value on the theoretical flow-efficiency curve.

[0012] For example, the Modi formula is shown below: The calculation of the exponent in the Modi correction formula is as follows: in, This represents the exponent in Modi's correction formula. This represents the measured flow rate (unit: m³). 3 / s), Theoretical flow rate (in m³) for similar operating conditions 3 / s).

[0013] For example, the calculation of the actual optimal efficiency at the rated speed is as follows: in, This represents the actual optimal efficiency at rated speed. This indicates the measured rotational speed (in r / min). This indicates the rated speed (in r / min).

[0014] For example, the efficiency at the actual non-optimal efficiency point under rated speed is calculated as follows: in, This represents the efficiency at the i-th operating point on the theoretical flow-efficiency curve at rated speed.

[0015] For example, the field measured operating point data comes from 3 to 8 measured operating points obtained from the field operation monitoring of the prototype pump. The measured operating points are distributed near the high efficiency zone of the prototype pump. When there are multiple measured operating points, all points on the correction curve corresponding to each measured operating point are first calculated. Then, the average of each point on the correction curve is taken according to the number of measured operating points. The data of each measured operating point is fitted to form the corrected actual flow-head curve and the actual flow-efficiency curve.

[0016] According to the specific embodiments provided in this application, the following technical effects are disclosed: This application provides a pump performance curve correction method based on the principle of similarity. Based on physical similarity principles such as flow similarity law and head similarity law, the method performs similarity transformation on the theoretical curve based on physical similarity relationships. This can more accurately restore the real characteristics of the prototype pump in the actual operating environment, solving the problem that it is impossible to obtain the full-condition performance curve on site. Using a small number of easily obtainable measurement points, the performance curve of the full operating range can be deduced through the principle of similarity, reducing the engineering difficulty and cost of performance testing and verification. The application also establishes a framework for the correction of flow-head characteristics and flow-efficiency characteristics, ensuring that the final head curve and efficiency curve are physically and logically self-consistent. This provides a reliable and consistent data foundation for the overall operation optimization of the pumping station, and supports the safe, efficient and economical operation of the pumping station. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 This is a flowchart of the pump performance curve correction method based on the similarity principle in the embodiments of this application.

[0019] Figure 2 This is a schematic diagram of a similar parabola for the water pump in an embodiment of this application.

[0020] Figure 3 This is a schematic diagram of the measured operating points and similar operating points in the embodiments of this application. Figure 4 This is a schematic diagram showing the results of a water pump performance calibration example in this application. Detailed Implementation

[0021] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of this application.

[0022] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0023] Currently, theoretically, the necessary condition for two water pumps (such as a prototype pump and a model pump) to be dynamically similar is that four dimensionless similarity criteria numbers are equal: the Euler number, Reynolds number, Froude number, and Strouhal number. However, simultaneously satisfying the condition of equal numbers for all four similarity criteria is extremely demanding. For a steadily operating water pump, the Strouhal number has no effect; the Euler number characterizes the pressure at each point and is not a similarity condition but a result of similarity; since the flow inside the pump is pressure flow without free surfaces, the influence of gravity on the flow can be ignored. Therefore, the forces that play a major role in the flow inside the pump are inertial forces and viscous forces, and the similarity criterion for these two forces is the Reynolds number Re. To ensure that the Reynolds number Re of the model pump and the prototype pump are the same, relevant experiments show that when the Reynolds number Re > 10... 5 At this point, the fluid is already in the square-resistance region (i.e., the automatic simulation region), where changes in liquid velocity have a negligible effect on the drag coefficient. Even if the Reynolds number of the model pump differs from that of the prototype pump, the influence of viscous forces can still be ignored. Since the Reynolds number Re for liquid flow within the pump is generally greater than 10... 5 Therefore, the dynamic similarity condition can be automatically satisfied for water pumps. Thus, pump similarity only requires ensuring geometric and kinematic similarity. For radial flow fluid machinery, the specifications for model acceptance tests stipulate a Reynolds number Re ≥ 4106 and a nominal impeller diameter ≥ 0.25m.

[0024] like Figure 1 As shown in the figure, this application provides a method for correcting the performance curve of a water pump based on the similarity principle, including the following steps: S110. Obtain the converted operating point from the test operating point of the model pump to the corresponding operating point of the prototype pump, as well as the theoretical performance curve of the prototype pump at its rated speed; obtain the actual measured operating point and operating point data of the prototype pump on site, including the pump's flow rate, head, speed, and efficiency.

[0025] S120. Randomly select a field-measured operating point of the prototype pump. Based on the similar parabolic relationship and the operating point data, confirm the similar parabola passing through the field-measured operating point. Map the similar parabola to the theoretical performance curve of the prototype pump and obtain the intersection point as the similar operating point.

[0026] S130. Based on the similarity principle, the theoretical speed is obtained. By converting the operating point at the rated speed of the prototype pump, the corresponding operating point at the theoretical speed is obtained. The theoretical speed is transformed into the actual speed at the field measured operating point, and the actual flow-head curve of the prototype pump at the rated speed is obtained after correction.

[0027] S140. Obtain the theoretical efficiency value and the optimal efficiency value on the theoretical performance curve corresponding to similar operating points. Based on the operating point data, the theoretical efficiency value and the optimal efficiency value, and in accordance with the principle that the efficiency of similar operating points decreases in a consistent manner relative to their respective optimal efficiencies, the actual flow-efficiency curve of the prototype pump at rated speed is obtained.

[0028] The pump performance curve correction method based on similarity principles in this application, based on physical similarity principles such as flow similarity law and head similarity law, performs similarity transformation on theoretical curves based on physical similarity relationships. This can more accurately restore the true characteristics of the prototype pump in the actual operating environment, solving the problem that full-condition performance curves cannot be obtained on-site. Using a small number of easily obtainable measurement points, performance curves for the entire operating range can be deduced through similarity principles, reducing the engineering difficulty and cost of performance testing and verification. A framework for the correction of flow-head and flow-efficiency characteristics is established, ensuring that the final head and efficiency curves are physically and logically self-consistent. This provides a reliable and consistent data foundation for the overall operation optimization of the pumping station, supporting the safe, efficient, and economical operation of the pumping station.

[0029] For example, in step S110, the theoretical performance curves of the model pump include the theoretical flow-head curve and the theoretical flow-efficiency curve. Performance similarity relationships include at least: flow similarity law, head similarity law, and similar parabolic relationship. In some embodiments, the performance similarity relationships also include the impeller mechanical power similarity law. In this application, performance similarity relationships are the basis for theoretical calculations. The performance similarity relationships in this application are analyzed and described below.

[0030] The flow similarity law states that two geometrically similar water pumps, under conditions of similar motion, will have similar flow rates. With the nominal diameter of the pump impeller D It is proportional to the cube of the value and increases with the rotational speed. n and volumetric efficiency It is directly proportional to the first power, and its expression is as follows: (1) Without considering the scale effect, we can let The above formula can be simplified to: (2) in, This indicates the flow rate of the prototype pump (in cubic meters per second). 3 / s), This indicates the flow rate of the model pump (in cubic meters per second). 3 / s), This indicates the rotational speed of the prototype pump (in r / min). This indicates the rotational speed of the model pump (in r / min). This indicates the nominal diameter of the impeller of the prototype pump (in meters). This indicates the nominal diameter of the impeller of the model pump (in meters). This indicates the volumetric efficiency of the prototype pump. This indicates the volumetric efficiency of the model pump.

[0031] The head similarity law states that two geometrically similar water pumps, under similar motion conditions, will have similar heads. H With the nominal diameter of the pump impeller D and rotational speed n It is directly proportional to the square of the power and is related to hydraulic efficiency. It is directly proportional to the first power of the acceleration due to gravity. g It is inversely proportional to the first power. As shown in the following formula: (3) Without considering the scale effect, the above equation can be simplified to: (4) in, This indicates the head of the prototype pump (in meters). This indicates the head of the model pump (in meters). This represents the gravitational acceleration at the location of the prototype pump (in m / s²). 2 ), This represents the gravitational acceleration at the location of the model pump (in m / s²). 2 ), This indicates the hydraulic efficiency of the prototype pump. This represents the hydraulic efficiency of the model pump; the acceleration due to gravity is determined based on geographical location, and the calculation formula is: ,in, Latitude (unit: radians) Elevation (in meters).

[0032] The impeller mechanical power is the mechanical power transmitted between the impeller and the connecting flange of the main shaft. When considering the scale effect, the expression for the impeller mechanical power similarity law shows that for two geometrically similar water pumps, under similar motion conditions, their impeller mechanical power... With the nominal diameter of the pump impeller D It is proportional to the fifth power and the speed. n It is proportional to the cube of the fluid density. It is directly proportional to the first power and is related to hydraulic efficiency. It is inversely proportional to the first power of , and its expression is as follows: (5) Wherein, fluid density is temperature θ(Units are °C) and absolute pressure p A function (unit: Pa).

[0033] This shows that the determination of turbine mechanical power is closely related to the determination of hydraulic efficiency. For hydraulically similar operating points A and B, at Reynolds number... , and The relative hydraulic losses, calculated using the scale effect, have the following relationship: (6) (7) In the formula, the reference Reynolds number is used. =7×106, For the Reynolds number is The relative hydraulic loss at the operating point, calculated using scale effects. Replace the subscripts with those representing the prototype and model pumps. , The alternatives are: (8) If the optimal efficiency points of the prototype and model are taken from two similar operating conditions, then... , Therefore, the relative hydraulic loss satisfies the following equation: (9) Reynolds number , nominal diameter Circular velocity at the point , Rotational speed (r / min), kinematic viscosity coefficient It can be expressed by the following formula: For example, when only the speed of the same pump changes, it is assumed that the speed is from the rated speed. Change to any speed (between 0.6) ~1.2 Between), we can adjust equations (2), (4), and (9) in the above equations as follows: In the formula, H Indicates head (unit: meters). Q Flow rate (unit: m³) 3 / s), These represent the flow rate, head, and optimal hydraulic efficiency at any given rotational speed, respectively. 、 , These represent the corresponding data at the rated speed. The operating point satisfying equations (10) and (11) is ( Q , H )and( , () represents similar operating conditions.

[0034] For example, such as Figure 2 The diagram shows a similar parabola of a water pump, where A1, A2, A3, etc., represent operating points. If A1(Q1, H1), A2(Q2, H2), A3(Q3, H3), ..., A(Q, H) are similar operating points, then from equations (10) and (11), we have: (13) (14) Based on equations (13) and (14) above, we get: (15) Based on this, the expression for the relationship between similar parabolas can be obtained as follows: (16) in, H Indicates head (unit: meters). Q Flow rate (unit: m³) 3 / s), K is a constant representing the shape coefficient of the similar parabola passing through the origin. All similar operating points lie on this similar parabola. It is stipulated that the actual performance curve and theoretical performance curve of the prototype pump have similar shapes. After obtaining the measured operating points and their data through field testing, the similar parabola passing through the measured operating points can be identified based on the similar parabola relationship and the operating point data. The similar parabola is then mapped to the theoretical performance curve, and the intersection point is taken as the similar operating point.

[0035] The above content analyzes and introduces the performance similarity relationship. The following describes the calculation and correction process: Based on the flow similarity law and the head similarity law, the correspondence between the measured operating point and the similar operating point is confirmed. Through the above analysis process, it can be confirmed that the flow similarity law and the head similarity law are transformed into equations (10) and (11). It can be seen from this that the change in rotational speed will be clearly reflected in the change in flow rate and head. Therefore, based on the principle of similarity and the principle of similarity in the shape of flow-head curves, calculation and correction are performed. When correcting the flow-head performance curve of the prototype pump, it is assumed that the actual performance curve of the prototype pump and the theoretical (converted) performance curve of the prototype pump have similar shapes. Based on this assumption, the actual performance curve of the measured point at the measured rotational speed must be the same as the theoretical performance curve at a certain theoretical rotational speed, and the theoretical performance curve of the prototype pump at the rated rotational speed (obtained by model conversion) is known. Find the measured point (measured operating point) A ( Q A ，H A The intersection of the similar parabola and the theoretical performance curve at the rated speed is obtained by using the similarity relationship to find the theoretical speed. Then, based on the points on the theoretical curve of the prototype pump, the corresponding points at the theoretical speed are found, which are all the points on the actual performance curve at the measured speed. Finally, the actual performance curve at the measured speed is converted to the rated speed to obtain the corrected actual flow-head curve (i.e., the Q~H curve).

[0036] like Figure 3 As shown, this is a schematic diagram of the measured operating point and the similar operating point on the theoretical performance curve. It can be seen from the figure that the similar parabola will pass through the actual performance curve and the theoretical performance curve, and will pass through the intersection points A and T on the two respectively. Therefore, first confirm the measured point A and the similar parabola, and the similar operating point T can be confirmed based on the intersection point.

[0037] Based on the correspondence, the theoretical flow rate-head curve is transformed using a similarity transformation to obtain the actual flow rate-head curve. This process includes the following steps: S131. Based on the flow similarity law or head similarity law, confirm the speed relationship between the similar operating point and the measured operating point, and calculate the theoretical speed.

[0038] S132. Based on the flow similarity law, head similarity law, rated speed, and theoretical speed, it is stipulated that the actual performance curve and theoretical performance curve of the prototype pump have similar shapes. The flow rate and head at the corresponding operating point of the theoretical speed are obtained by converting the test operating point of the model pump to the corresponding operating point of the prototype pump.

[0039] S133. The theoretical speed is transformed into the actual speed at the field measured operating point. It is stipulated that the actual performance curve and the theoretical performance curve of the prototype pump have similar shapes. Based on the flow similarity law, the head similarity law, the rated speed, and the actual speed, the flow rate and head of the prototype pump at the corresponding operating point at the rated speed are obtained. The above operating points are fitted and corrected to obtain the actual flow rate-head curve of the prototype pump at the rated speed.

[0040] It should be noted that the above method is based on the premise that the actual performance curve of the water pump has a similar shape to the theoretical curve. If the actual performance curve is not similar to the theoretical curve, the actual curve can only be obtained through field testing or analysis of accumulated operational data.

[0041] Specifically, assume the measured operating point A data of the prototype pump includes: flow rate, head, speed, and pump efficiency. The operating point T on the theoretical (converted) performance curve of the measured operating point A and the prototype pump at its rated speed is a similar operating point (point T is obtained by finding the intersection of the similar parabola passing through point A and the theoretical curve at the prototype pump's rated speed). Then, in step S131, the theoretical speed corresponding to the measured operating point A is as follows: ， or ， (17) in, Indicates the theoretical rotational speed. This represents the flow rate at the measured operating point (unit: m³). 3 / s), The measured head (in meters) indicates the actual head at the operating point. This indicates the rated speed (in r / min). Theoretical flow rate (in m³) for similar operating conditions 3 / s), This represents the theoretical head (in meters) at the similar operating point. The data points are from the theoretical curve of the prototype pump at rated speed. The flow rate and head at each operating point on the actual performance curve at the measured speed are calculated from the known data (derived from data obtained by laboratory testing of the model pump), as shown below: (18) (19) in, Represents the proportionality coefficient. This represents the flow rate at the i-th operating point on the theoretical performance curve at rated speed (in m³ / s). 3 / s), This represents the head (in meters) at the i-th operating point on the theoretical performance curve at rated speed, where i is the operating point number (its value is between 1 and N).

[0042] Combining equations (17)-(19) above, the final actual operating point data can be calculated. The process of converting the flow rate and head of the operating point on the corrected curve at rated speed is shown below: (20) in, This represents the flow rate at the i-th operating point on the theoretical performance curve at rated speed (in m³ / s). 3 / s), This represents the head (in meters) at the i-th operating point on the theoretical performance curve at rated speed, where i is the operating point number (its value is between 1 and N). This indicates the rated speed of the water pump. The various operating points on the corrected curve are then obtained. This allows us to obtain the corrected actual flow-head curve by fitting various operating points.

[0043] For step S140 above, the corrected actual flow-efficiency curve includes the following steps: S141. Based on the principle that the rate of decrease of efficiency at similar operating points on the performance curves at different speeds is consistent with their respective optimal efficiencies, the optimal efficiency on the performance curve where the measured operating point is located is calculated according to the measured efficiency, the theoretical efficiency of similar operating points, and the theoretical optimal efficiency.

[0044] S142. Calculate the exponent in the Modified Modi formula.

[0045] S143. Calculate the actual optimal efficiency of the water pump at its rated speed.

[0046] S144. Calculate the efficiency at the actual non-optimal efficiency point under the rated speed of the water pump to obtain the actual flow-efficiency curve.

[0047] The efficiency of the prototype pump consists of hydraulic efficiency and mechanical efficiency (mainly caused by friction losses from shaft seals and bearings). The mechanical efficiency remains constant when the rotational speed changes. Therefore, during variable-speed operation, only the change in hydraulic efficiency is considered. In this application, pump efficiency refers to the hydraulic efficiency of the pump. It is assumed that the rate of decrease of efficiency relative to the optimal efficiency at similar operating points on the performance curve at different speeds is the same. Based on the efficiency of measured point A and the efficiency of the similar operating point T on the theoretical curve corresponding to measured point A at rated speed... and the optimal efficiency on the theoretical curve at rated speed. This allows us to obtain the optimal efficiency on the performance curve where the measured point A is located. Then, based on the efficiency curve at the measured speed (non-rated speed) and the efficiency correction formula, the efficiency curve at the actual rated speed (i.e., Q~η curve).

[0048] Specifically, for step S141 above, the optimal efficiency on the performance curve where the measured operating point A is located is determined. Assuming the speed is changed (speed is...). (At time) The efficiency value at the non-optimal efficiency point relative to the optimal efficiency after speed change The rate of descent and the efficiency at the non-optimal efficiency point at rated speed Relative to optimal efficiency If the rates of descent are the same, then: (twenty one) If a speed change is performed, the efficiency value at the highest efficiency point after the speed change is: (twenty two) Where, in the formula, The efficiency is the optimal point on the performance curve at the measured operating point A, where the theoretical rotational speed is... The theoretical rotational speed is When the efficiency is not optimal, the efficiency at the measured operating point A is taken. That is, take = ; Theoretical rated speed Minimize efficiency; Theoretical rated speed The efficiency corresponding to the operating point similar to the measured operating point A, i.e., the flow rate is The efficiency corresponding to the time is obtained by interpolation of the efficiency curve.

[0049] Equation (22) above can be rewritten to obtain: (twenty three) For step S142 above, calculate the exponent in the Moody's correction formula, which is as follows: (twenty four) Calculating the index based on the formula We can obtain: (25) Rewriting it, we get the final calculation formula as follows: (26) in, This represents the exponent in Modi's correction formula. This represents the measured flow rate (unit: m³). 3 / s), Theoretical flow rate (in m³) for similar operating conditions 3 / s).

[0050] For step S143 above, the actual optimal efficiency of the water pump at its rated speed is calculated. Based on the above equation (24), the calculation process is as follows: (27) After replacement and rewriting, we get: (28) in, This represents the actual optimal efficiency at rated speed. This indicates the measured rotational speed (in r / min). This indicates the rated speed (in r / min).

[0051] For step S144 above, calculate the efficiency at the actual non-optimal efficiency point under the rated speed of the water pump. Referring to equation (22) above, we obtain the following equation: (29) Rewriting the above expression, we finally obtain the following expression: (30) in, This represents the efficiency at the i-th operating point on the theoretical flow-efficiency curve at rated speed.

[0052] The above calculation method can confirm the efficiency at the actual non-optimal efficiency point under the rated speed of the water pump. This is used to confirm the actual flow-efficiency curve in order to complete the calibration process.

[0053] For example, the operating point data comes from 3 to 8 measured operating points obtained from on-site monitoring of the prototype pump. These measured operating points are distributed near the high-efficiency zone of the prototype pump. When there are multiple measured operating points (i can be multiple values ​​from 1 to N, and i is greater than 1), the above steps can be followed to first calculate all points on the correction curve corresponding to each measured point, and then the average of each point on the correction curve can be taken according to the number of measured operating points. The data of each measured operating point is fitted to form the corrected actual flow-head curve and the actual flow-efficiency curve.

[0054] Through the above calculation process, the actual flow-head curve and the actual flow-efficiency curve at rated speed were corrected, providing a reliable and consistent data foundation for the overall operation optimization of the pumping station and supporting the safe, efficient and economical operation of the pumping station.

[0055] The following is a specific example to illustrate this: Taking a pumping station of a water resources allocation project as an example, the prototype pump of the pumping station was tested on-site at the factory. The measured values ​​of five operating points near the high efficiency zone of the prototype pump were obtained, as shown in Table 1. Table 1 is the on-site measured data table of the prototype pump of a pumping station of a water resources allocation project.

[0056] Table 1 like Figure 4 As shown, this is a schematic diagram of the results of a pump performance calibration example. The actual flow-head curve after calibration shifts slightly to the upper right compared to the theoretical curve of the prototype pump, indicating that the actual flow rate of the prototype pump is slightly larger than the theoretical value at the same head, while the efficiency change is not significant. Table 2 is a comparison table of the measured values ​​and calibration values ​​of the prototype pump at a certain pumping station.

[0057] Table 2 As can be seen from Table 2, when the water pump is at its rated speed, under the same head, the maximum deviation between the flow correction value and the measured value is -1.25%. The above examples demonstrate that the method described in this application, after correcting the water pump, results in a relatively accurate flow-head curve with a small deviation.

[0058] According to the pump performance curve correction method based on similarity principle provided in the embodiments of this application, the theoretical curve is transformed based on physical similarity principles such as flow similarity law and head similarity law. This can more accurately restore the real characteristics of the prototype pump in the actual operating environment, solve the problem that the full-condition performance curve cannot be obtained on site, and use a small number of easily obtainable measurement points to deduce the performance curve of the full-condition range through similarity principle, reducing the engineering difficulty and cost of performance testing and verification. A framework for the correction of flow-head characteristics and flow-efficiency characteristics is established to ensure that the final head curve and efficiency curve are physically and logically self-consistent, providing a reliable and consistent data foundation for the overall operation optimization of the pumping station, and supporting the safe, efficient and economical operation of the pumping station.

[0059] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above methods.

[0060] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0061] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for correcting the performance curve of a water pump based on the principle of similarity, characterized in that, The pump performance curve correction method based on the similarity principle includes: Obtain the converted operating point from the test operating point of the model pump to the corresponding operating point of the prototype pump, as well as the theoretical performance curve of the prototype pump at its rated speed; obtain the actual measured operating point and operating point data of the prototype pump on site, including the pump's flow rate, head, speed, and efficiency. Arbitrarily select a field-measured operating point of a prototype pump, and based on the similar parabolic relationship and the field-measured operating point data, confirm the similar parabola passing through the field-measured operating point. Map the similar parabola to the theoretical performance curve of the prototype pump, and obtain the intersection point as the similar operating point of the selected field-measured operating point. The theoretical speed is obtained based on the similarity principle. The corresponding operating point under the theoretical speed is obtained by converting the operating point at the rated speed of the prototype pump. The theoretical speed is transformed into the actual speed at the field measured operating point. The actual flow-head curve of the prototype pump at the rated speed is obtained by correction. The theoretical efficiency value and the optimal efficiency value on the theoretical performance curve corresponding to the similar operating points are obtained. Based on the operating point data, the theoretical efficiency value and the optimal efficiency value, and in accordance with the principle that the efficiency of the similar operating points decreases in a consistent manner relative to their respective optimal efficiencies, the actual flow-efficiency curve of the prototype pump at rated speed is obtained.

2. The pump performance curve correction method based on the similarity principle according to claim 1, characterized in that, The expression for the similar parabolic curve is as follows: in, H Indicates head (unit: meters). Q Flow rate (unit: m³) 3 / s), K is a constant, representing the shape coefficient of the similar parabola passing through the origin, and all the similar working points fall on the similar parabola.

3. The pump performance curve correction method based on the similarity principle according to claim 1, characterized in that, The correction process yields the actual flow-head curve of the prototype pump at its rated speed, specifically including the following steps: The rotational speed relationship between the similar operating point and the measured operating point is determined based on the flow similarity law or the head similarity law, and the theoretical rotational speed is calculated. Based on the flow similarity law, head similarity law, rated speed, and theoretical speed, it is stipulated that the actual performance curve and theoretical performance curve of the prototype pump have similar shapes. The flow rate and head at the corresponding operating point of the theoretical speed are obtained by converting the test operating point of the model pump to the corresponding operating point of the prototype pump. The theoretical speed is transformed into the actual speed at the field measured operating point. It is stipulated that the actual performance curve and the theoretical performance curve of the prototype pump have similar shapes. Based on the flow similarity law, the head similarity law, the rated speed, and the actual speed, the flow rate and head of the prototype pump at the corresponding operating point at the rated speed are obtained. The operating point is fitted and corrected to obtain the actual flow rate-head curve of the prototype pump at the rated speed.

4. The pump performance curve correction method based on the similarity principle according to claim 3, characterized in that, The process of calculating the theoretical rotational speed is shown below: ,or, in, Indicates the theoretical rotational speed. This represents the flow rate at the measured operating point (unit: m³). 3 / s), The measured head (in meters) indicates the actual head at the operating point. This indicates the rated speed (in r / min). Theoretical flow rate (in m³) for similar operating conditions 3 / s), The theoretical head (in meters) represents the similar operating conditions. The flow rate and head at each operating point on the performance curve under the measured speed are calculated as follows: The flow rate and head at each operating point under the corrected rated speed are calculated as follows: Among them, the proportionality coefficient or , This represents the flow rate at the i-th operating point on the theoretical performance curve at rated speed (in m³ / s). 3 / s), This represents the head (in meters) at the i-th operating point on the theoretical performance curve at rated speed, where i is the operating point number.

5. The pump performance curve correction method based on the similarity principle according to claim 1, characterized in that, The measured operating point data also includes the measured efficiency of the water pump. The calibration to obtain the actual flow rate-efficiency curve specifically includes the following steps: Based on the principle that the rate of decrease of efficiency at similar operating points on the performance curves at different speeds is consistent with their respective optimal efficiencies, the optimal efficiency on the performance curve where the measured operating point is located is calculated according to the measured efficiency, the theoretical efficiency at similar operating points, and the theoretical optimal efficiency. Calculate the exponents in Modi's correction formula; Calculate the actual optimal efficiency at rated speed; Calculate the efficiency at the actual non-optimal efficiency point under rated speed to obtain the actual flow-efficiency curve.

6. The pump performance curve correction method based on the similarity principle according to claim 5, characterized in that, The optimal efficiency on the performance curve at the measured operating point is calculated as follows: in, This indicates the pump efficiency at the measured operating point. This represents the efficiency value corresponding to the similar operating point at rated speed on the theoretical flow-efficiency curve, i.e., the flow rate is... The corresponding efficiency is obtained by interpolating the efficiency curve. This represents the optimal efficiency value on the theoretical flow-efficiency curve.

7. The pump performance curve correction method based on the similarity principle according to claim 5, characterized in that, Modi's formula is shown below: The calculation of the exponent in the Modi correction formula is as follows: in, This represents the exponent in Modi's correction formula. This represents the measured flow rate (unit: m³). 3 / s), Theoretical flow rate (in m³) for similar operating conditions 3 / s).

8. The method for correcting the performance curve of a water pump based on the similarity principle according to claim 5, characterized in that, The calculation of the actual optimal efficiency at rated speed is as follows: in, This represents the actual optimal efficiency at rated speed. This indicates the measured rotational speed (in r / min). This indicates the rated speed (in r / min).

9. The pump performance curve correction method based on the similarity principle according to claim 8, characterized in that, The efficiency at the actual non-optimal efficiency point under rated speed is calculated as follows: in, This represents the efficiency at the i-th operating point on the theoretical flow-efficiency curve at rated speed.

10. The method for correcting the performance curve of a water pump based on the similarity principle according to any one of claims 1 to 9, characterized in that, The field-measured operating point data comes from 3 to 8 measured operating points obtained from the on-site operation monitoring of the prototype pump. These measured operating points are distributed near the high-efficiency zone of the prototype pump. When there are multiple measured operating points, all points on the correction curve corresponding to each measured operating point are first calculated. Then, the average of each point on the correction curve is taken according to the number of measured operating points. The data of each measured operating point is fitted to form the corrected actual flow-head curve and the actual flow-efficiency curve.

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