A centrifugal pump drag reduction optimization design method based on response surface method

Abstract

The application discloses a centrifugal pump drag reduction optimization design method based on a response surface method, relates to the technical field of hydraulic design optimization of fluid machinery, and comprises the following steps: first, the arrangement area of a groove is determined; the groove depth, width, spacing and arrangement length are non-dimensionalized and given constraint conditions; a response surface test design is adopted to generate four-factor three-level samples and to perform CFD numerical simulation; the torque of the upper cover plate, the lower cover plate and the blade in the impeller area and the efficiency of the centrifugal pump are taken as evaluation indexes; a second-order polynomial response surface model of the torque and the efficiency is respectively established and the significance and fitting reliability of the model are verified; multi-objective optimization is performed to realize the minimization of the torque and the maximization of the efficiency, and the optimal non-dimensional parameter combination is obtained; and the accuracy and implementability of the optimization result are verified through CFD recalculation. The method is used to replace the absolute size with the non-dimensional parameter, and the migration of the optimization conclusion to different pump types and scales is improved.

Description

Technical Field

[0001] This invention relates to the field of hydraulic design optimization technology for fluid machinery (pumps), and in particular to a centrifugal pump drag reduction optimization design method based on response surface methodology. Background Technology

[0002] As a widely used type of general-purpose hydraulic machinery, centrifugal pumps are extensively used in many important fields such as vehicle engineering, aerospace, and marine engineering. With increasingly complex application scenarios and a continuously expanding range of applications, modern engineering practices are placing ever higher demands on pump performance, particularly in terms of efficiency, stability, and energy conservation, which present significant challenges.

[0003] Centrifugal pumps operate continuously in water supply and circulation scenarios, where hydraulic losses directly translate into energy consumption. Existing designs often suffer from low efficiency due to impeller inlet impact, uneven diffusion in the impeller passages, and insufficient volute matching, leading to separation and secondary flow, accompanied by noise, vibration, and cavitation risks. Drag reduction design requires optimization under multi-parameter coupled constraints. Traditional empirical trial-and-error or iterative simulation is costly and struggles to balance multiple objectives. Response surface methodology (CSDM) can establish a surrogate model of dimensionless parameters and drag reduction results using a small number of samples, quickly assessing sensitivity and interactions, and performing local optimization under constraints. This significantly reduces CFD and experimental counts, improves optimization efficiency and result transferability, thereby achieving a low-drag, high-efficiency design applicable to multiple pump types.

[0004] Given that existing centrifugal pumps, while meeting design flow and head requirements, generally suffer from problems such as strong wake, large near-wall shear loss, and additional hydraulic losses induced by pressure pulsation and local separation in the blade trailing edge region, resulting in limited pump efficiency improvement, high energy consumption, and potentially increased noise and vibration as well as deterioration in operational stability; at the same time, traditional drag reduction designs often rely on empirical selection or local correction of a single geometric dimension, lacking a unified dimensionless parameter system, making it difficult to achieve effective transfer between different pump types and scales, and requiring a large number of calculation samples, long iteration cycles, and high experimental and simulation costs. Summary of the Invention

[0005] The purpose of this invention is to provide a centrifugal pump drag reduction optimization design method based on response surface methodology. By establishing a dimensionless parameterized description and response surface proxy model for multiple pump types, rapid and multi-objective drag reduction optimization of groove structures can be achieved with a small sample size, thereby reducing hydraulic loss at the blade trailing edge, improving hydraulic efficiency, and providing a reusable optimization process and parameter range basis for low-resistance and high-efficiency design of different pump types.

[0006] To achieve the above objectives, this invention provides a centrifugal pump drag reduction optimization design method based on response surface methodology, comprising the following steps:

[0007] S1. Determine the arrangement area of ​​the grooves, and characterize the groove depth, groove width, groove spacing, and arrangement length respectively through dimensionless methods. , , , And given dimensionless constraints, where , ,and and When the values ​​are similar, the drag reduction effect is better;

[0008] S2. Using Box-Behnken response surface methodology, 29 sets of samples were generated for a four-factor, three-level experiment. CFD numerical simulations were performed on each sample to extract the torque of the upper and lower cover plates and blades in the impeller region. and the centrifugal pump efficiency under corresponding operating conditions. As an evaluation indicator;

[0009] S3, Based on step S2, establish respectively and The second-order polynomial response surface model was constructed, and the significance and fitting reliability of the model were verified by analysis of variance and residual test.

[0010] S4. Draw three-dimensional response surfaces and contour plots for pairwise variable combinations, for observation. , , , The coupling effect of torque loss and efficiency;

[0011] S5. Under the conditions of variable range and performance constraints, perform multi-objective optimization to achieve torque minimization and efficiency maximization, obtain the optimal dimensionless parameter combination, and verify the accuracy and feasibility of the optimization results through CFD recalculation.

[0012] Preferably, in step S11, the groove depth is extracted based on the key geometric features of the groove structure. Groove width Spacing between adjacent grooves and the length of the groove arrangement Four design variables were used, and each was dimensionless to obtain a dimensionless depth parameter. Dimensionless width parameter Dimensionless spacing parameters and dimensionless length parameter ;

[0013] S12. Combining pump type dimensions and blade trailing edge structure constraints, the value range and level setting principles for each dimensionless variable are given, among which, , ;

[0014] S13. Considering the mechanism of the groove's effect on the near-wall shear layer, introduce the following into the parameter settings and constraints: and Similar range constraints are used to guide the optimization search to a more effective drag reduction region.

[0015] Preferably, the dimensions of each dimensionless parameter in S11 are defined as follows:

[0016] ;

[0017] ;

[0018] ;

[0019] ;

[0020] in, The coefficient of friction of the wall surface; for The dynamic viscosity of water is 0.001003 Pa·s; The viscosity coefficient, m 2 / s; Let be the blade length, in meters (m).

[0021] Preferably, the arrangement length of the groove in S12 is a dimensionless length parameter. The effective area is located in the trailing edge of the blade, preferably within the posterior 33% of the blade length, i.e. .

[0022] Preferably, the content of S2 is as follows:

[0023] S21. Determine the variable definitions, design method, and sample size for the response surface methodology. The variables defined include: , , , Four dimensionless design variables; the preferred design method is... Experimental design methods;

[0024] S22. Simulate the sample of the response surface methodology to obtain drag reduction evaluation indicators, including the torque of the upper and lower cover plates and blades in the impeller region. Centrifugal pump efficiency .

[0025] Preferably, the content of S3 is as follows:

[0026] S31. Based on the CFD sample simulation results, establish a system... , , , A second-order polynomial response surface model with drag reduction and performance evaluation indicators as dependent variables, using them as independent variables;

[0027] S32. Perform significance testing and goodness-of-fit evaluation on the second-order polynomial response surface model. Validation methods include analysis of variance (ANOVA) and coefficient of determination R-squared. 2 Residual analysis and missing fit test;

[0028] S33. Using the verification method in step S32, a reliable surrogate model that can be used for optimization is obtained.

[0029] Preferably, the performance constraints in step S5 include constraints on the range of values ​​for dimensionless variables.

[0030] Preferably, the following steps in step S5 involve verifying the accuracy and feasibility of the optimization results through CFD recalculation:

[0031] The optimal dimensionless parameter combination obtained by multi-objective optimization was re-verified by CFD calculation prototype test. The error between the response surface prediction value and the verification result was compared, and the accuracy and feasibility of the optimization result were finally confirmed.

[0032] Therefore, the centrifugal pump drag reduction optimization design method based on response surface methodology described above has the following beneficial effects:

[0033] (1) By using the groove geometry features , , , The dimensionless form of the parameterized description decouples the optimization variables from the pump type scale, which significantly improves the transferability and reusability of the method in pump types with different diameters, specific speeds and structures.

[0034] (2) Response surface methodology is used to obtain samples with high information content, improve sample effectiveness under the same sample quantity conditions, reduce inefficient calculation caused by blind scanning, and reduce the time cost of CFD calculation.

[0035] (3) By constructing and verifying the second-order response surface model, the main effects, interactions and optimal ranges of each dimensionless variable on drag reduction and performance can be clearly identified, providing interpretable and traceable parameter basis for engineering design;

[0036] (4) Under constraints, multi-objective optimization can be performed to achieve better drag reduction and efficiency improvement while ensuring performance requirements such as head. The credibility and engineering feasibility of the optimization scheme can be ensured through final CFD verification, reducing development cycle and cost, and providing a general technical route for low-resistance and high-efficiency design of various pump types.

[0037] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0038] Figure 1 is a flowchart of an embodiment of the centrifugal pump drag reduction optimization design method based on response surface methodology according to the present invention;

[0039] Figure 2 is a schematic diagram of a three-dimensional model of the centrifugal pump impeller flow channel according to an embodiment of the present invention;

[0040] Figure 3 is a schematic diagram of the arrangement of the trailing edge grooves on the pressure surface of the blade in the embodiment of the present invention, wherein (a) is a three-dimensional model of the groove arrangement position; and (b) is a schematic diagram of the groove structure parameters.

[0041] Figure 4 shows the main factors and response values ​​of the embodiment of the present invention, including torque. The fitting analysis results are shown in the following figures: (a) shows the fitting analysis results of groove width and groove depth; (b) shows the fitting analysis results of groove spacing and groove depth; (c) shows the fitting analysis results of groove length and groove depth; (d) shows the fitting analysis results of groove spacing and groove width; (e) shows the fitting analysis results of groove length and groove width; and (f) shows the fitting analysis results of groove length and groove spacing.

[0042] Figure 5 illustrates the efficiency of the main factors and response values ​​in the embodiments of the present invention. The fitting analysis results are shown in the following figures: (a) shows the fitting analysis results of groove width and groove depth; (b) shows the fitting analysis results of groove spacing and groove depth; (c) shows the fitting analysis results of groove length and groove depth; (d) shows the fitting analysis results of groove spacing and groove width; (e) shows the fitting analysis results of groove length and groove width; and (f) shows the fitting analysis results of groove length and groove spacing.

[0043] Figure 6 shows the main response value torque in the embodiment of the present invention. Relative to the four-variable response surface plot, where (a) is (a) is the residual normal probability plot; (b) is The residuals are shown in the schematic diagram as a function of sample order; (c) is... The variation of the residual predicted values; (d) is A comparison chart of actual and predicted residual values;

[0044] Figure 7 illustrates the response efficiency of the main embodiments of the present invention. Relative to the four-variable response surface plot, where (a) is (a) is the residual normal probability plot; (b) is The residuals are shown in the schematic diagram as a function of sample order; (c) is... The variation of the residual predicted values; (d) is A comparison chart of actual and predicted residual values;

[0045] Figure Labels

[0046] 1. Volute; 2. Inlet extension section; 3. Outlet extension section; 4. Impeller; 5. Pressure surface; 6. Suction surface. Detailed Implementation

[0047] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0048] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0049] Example

[0050] Please see Figure 1 This invention provides a centrifugal pump drag reduction optimization design method based on response surface methodology, comprising the following steps:

[0051] S1. Determine the arrangement area of ​​the grooves, and characterize the groove depth, groove width, groove spacing, and arrangement length respectively through dimensionless methods. , , , And given dimensionless constraints, where , ,and and When the values ​​are similar, the drag reduction effect is better.

[0052] Extract the groove depth based on the key geometric features of the groove structure. Groove width Spacing between adjacent grooves and the length of the groove arrangement Four design variables were used, and each was dimensionless to obtain a dimensionless depth parameter. Dimensionless width parameter Dimensionless spacing parameters and dimensionless length parameter Its definition is as follows:

[0053] ;

[0054] ;

[0055] ;

[0056] ;

[0057] in, The coefficient of friction of the wall surface; for The dynamic viscosity of water is 0.001003 Pa·s; The viscosity coefficient, m 2 / s; Let be the blade length, in meters (m).

[0058] Based on this, and considering the constraints of pump dimensions and blade trailing edge structure, the value range and level setting principles for each dimensionless variable are given. Preferably, , Simultaneously, considering the mechanism of the groove's effect on the near-wall shear layer, when and Similar values ​​are generally more conducive to forming a stable flow reconfiguration, therefore, they are introduced into parameter settings and constraints. and Similar range constraints are used to guide the optimization search to a more effective drag reduction region. This applies to the arrangement length of the groove. The present invention limits its effective area to the trailing edge of the blade, preferably within the posterior 33% length of the blade. This allows for a more direct effect on the formation and shedding of the trailing edge and wake, thereby achieving a more significant drag reduction effect.

[0059] S2. Using Box-Behnken response surface methodology, 29 sets of samples were generated for a four-factor, three-level experiment. CFD numerical simulations were performed on each sample to extract the torque of the upper and lower cover plates and blades in four regions of the impeller. and the centrifugal pump efficiency under corresponding operating conditions. As an evaluation indicator.

[0060] S3, Based on step S2, establish respectively and The second-order polynomial response surface model was derived, and the significance and reliability of the model were verified by analysis of variance and residual test.

[0061] Response surface methodology includes: variable definition, design methodology, and sample size determination. Variables defined include... , , , Four dimensionless design variables were used. The Box-Behnken experimental design method was preferred to balance the fitting accuracy of main effects, interaction effects and quadratic terms with a small sample size. A total of 29 experimental design samples with four variables and three levels were selected to ensure that the samples are evenly distributed in the design space and have sufficient information, reduce the proportion of inefficient or redundant samples, and provide a high-quality data foundation for the subsequent construction of surrogate models.

[0062] The CFD sample simulation involves simulating the sample designed for response surface methodology to obtain drag reduction evaluation indicators, including the torque on the upper and lower cover plates and blades in impeller region 4. Centrifugal pump efficiency .

[0063] The construction and validation of response surface models include: establishing a model based on CFD sample simulation results. , , , A second-order polynomial response surface model was developed, with drag reduction and performance evaluation indicators as dependent variables. The model was then subjected to significance testing and goodness-of-fit evaluation. Model validation was preferably performed using analysis of variance (ANOVA) and the coefficient of determination R-squared. 2 Methods such as residual analysis and missing fit test are used to determine the significance of each coefficient and the model's ability to interpret sample data, thereby obtaining a reliable surrogate model that can be used for optimization solutions.

[0064] S4. Draw three-dimensional response surfaces and contour plots for pairwise variable combinations, for observation. , , , The coupling effect of torque loss and efficiency.

[0065] S5. Under the conditions of variable range and performance constraints, perform multi-objective optimization to minimize torque and maximize efficiency, obtain the optimal dimensionless parameter combination, and verify the accuracy and feasibility of the optimization results through CFD recalculation. This includes: objective function, constraint conditions, and algorithm verification.

[0066] The objective function can be set to a multi-objective form, minimizing resistance and maximizing efficiency improvement, depending on application requirements. Constraints include range constraints for dimensionless variables. Analysis of variance is used to test the significance of the regression equation.

[0067] The optimal solution verification involves: re-performing the optimal dimensionless parameter combination obtained from the multi-objective optimization solution using a CFD prototype test, comparing the error between the response surface prediction and the verification results, and confirming the reliability and feasibility of the optimized solution.

[0068] Example 1

[0069] Determination of Response Objectives and Numerical Calculation Setup for the Reference Pump Model

[0070] like Figure 2 The three-dimensional model of the centrifugal pump impeller 4 includes a volute 1, with an inlet extension 2 connected to the center of the volute 1 and an outlet extension 3 connected to one side. The impeller 4 is mounted on the volute 1, and the blades of the impeller 4 include a pressure surface 5 and a suction surface 6. The rated operating flow rate, speed, and medium parameters are determined, using a reference impeller 4 as a comparison. A computational domain is established and a mesh is generated: local refinement is performed on the blade region of the impeller 4, and a boundary layer mesh is set to ensure near-wall resolution; the mesh is checked for independence to ensure head... ,efficiency The result satisfies the preset error limit as the mesh density changes. Its expression is as follows:

[0071] ;

[0072] in, For total export pressure, ; Total import pressure, ; For fluid density, ; It is the acceleration due to gravity. ; For the height difference between import and export, ;

[0073] ;

[0074] ;

[0075] ;

[0076] ;

[0077] ;

[0078] in, For volumetric efficiency, For water conservancy efficiency, Power loss due to friction of the four discs in the impeller; specific speed 32; Q is the pump flow rate. ; The impeller's angular velocity is 4. ; The impeller rotates at speed 4. ; The outlet speed of impeller 4 is... .

[0079] Setting up the numerical model and boundary conditions: When performing transient numerical simulations, the following methods are used: The turbulence model equations are solved for the computational domain of the model pump. A velocity inlet is selected for the inlet boundary conditions, while a free-flow outlet is selected for the outlet boundary conditions. The inlet section, the volute 1 region, and the outlet extension 3 are set as static computational domains, while the impeller 4 region is set as a rotating computational domain. This invention does not consider wall roughness in the model pump; that is, the wall surface is smooth but without slippage. Two dynamic-static interfaces are set in the computational domain of the flow field within the model pump, located at the boundary between the computational domain of the inlet extension 2 and the impeller 4 computational domain, and at the boundary between the impeller 4 outlet computational domain and the volute 1 inlet computational domain, respectively.

[0080] Based on existing research on centrifugal pump performance, this invention selects a design scheme for a groove structure on the blade surface at the high-speed, high-shear-stress blade outlet position: a flow-oriented groove structure is arranged on the trailing edge of the blade pressure surface 5. The specific arrangement of the groove structure is as follows... Figure 3 As shown in (a) of the diagram.

[0081] Target response value: Torque and efficiency .

[0082] In satisfying , , and similar, Under the premise of groove depth Take 0.2mm, 0.3mm, and 0.4mm, corresponding to... The groove widths are 6.28, 9.72, and 12.96 respectively. Take 0.2mm, 0.3mm, and 0.4mm, corresponding to... The groove spacings are 6.28, 9.72, and 12.96 respectively. Take 0.6mm, 0.7mm, and 0.8mm, corresponding to... The values ​​are 19.44, 22.68, and 2592 respectively, representing the groove length. Take 22mm, 28.5mm, and 35mm as the corresponding values. Take 10%, 13%, and 16%.

[0083] CFD sample simulation is a numerical simulation of the samples obtained from response surface experimental design. The CFD simulation takes the internal flow of the centrifugal pump under standard operating conditions as the object, and the impeller 4 and stationary components are calculated using rotation-stationary coupling. The torque of the upper and lower cover plates and blades in the impeller 4 region is obtained by analyzing and calculating the CFD simulation results. And the efficiency under the corresponding working conditions. There are two evaluation indicators.

[0084] The response surface methodology was constructed based on evaluation indices obtained from CFD simulations; torque was used as a metric for each index. With efficiency A second-order polynomial response surface model was established for the response values, and an analysis of variance was performed on the second-order polynomial model to verify the significance and fit reliability of the response surface model.

[0085] The experimental design for generating the DOE is shown in Table 1:

[0086] Table 1 DOE Experimental Design

[0087]

[0088] Specifically, the dimensionless depth parameter will be... Dimensionless width parameter Dimensionless spacing parameters and dimensionless length parameter Torque and efficiency The response relationship was fitted using a second-order regression, and residual analysis was performed on the fitting results to test the normality, independence, and homoscedasticity of the model. The resulting second-order polynomial model formula is as follows:

[0089] ;

[0090] .

[0091] Torque and efficiency The fitting results are shown in Tables 2 and 3. The multiple correlation coefficient R of the model is... 2 A value close to 1 indicates that the model can explain the variation of the experimental data well, the fitting effect is relatively ideal, and the experimental error is small; the coefficient of variation (CV%) is used to measure the stability of the experiment, and the lower the value, the more reliable the experimental results; the adjusted coefficient of determination (Adjusted R) is... 2 ) and prediction coefficient (Predicted R) 2The difference is less than 0.2, indicating that there is no overfitting; the signal-to-noise ratio (AdeqPrecision) reflects the ratio between the effective signal and the noise. When it is greater than 4, the model is feasible. All indicators show that the model has good predictive ability and reliability.

[0092] Table 2 Torque Fitting effect

[0093]

[0094] Table 3 Efficiency Fitting effect

[0095]

[0096] Furthermore, it visually reveals the effects of variable coupling, such as Figure 4 , Figure 5 As shown, under the condition that the remaining variables are fixed at the central level, the following are established respectively: and A three-dimensional response surface plot relative to a two-variable combination is used to analyze interactions and determine the optimization interval.

[0097] More specifically, a fitting analysis was conducted on the factors and response values ​​in the experimental design. Figure 6 , Figure 7 The response values ​​of torque are shown respectively. With efficiency Residual analysis of the fitting results of the second-order regression model, for and The regression models established by the two response quantities basically satisfy the statistical assumptions of classical linear regression. First, from... Figure 6 (a) Figure 7 The normal probability plot (a) shows that the residual points are approximately distributed along a straight line, and the residuals approximately follow a normal distribution; secondly, Figure 6 (b) Figure 7 In (b) of the sample, the residuals do not show significant periodic fluctuations with the sample order, indicating that the error term is independent of the sample order and has no serial correlation; Figure 6 (c) Figure 7 (c) The residuals in the model vary with the experimental sequence and predicted values. The point set distribution is uniform, without obvious diffusion trends, clustering areas, or periodic fluctuations, indicating that the model has good linear fit and homogeneity of variance. Furthermore, Figure 6 (d) Figure 7The comparison plot (d) of actual and predicted values ​​shows that the experimental data points are closely distributed along the diagonal, reflecting a high degree of consistency between the model's predicted values ​​and the actual measured values. This indicates that the model's explanatory and predictive abilities are both within the ideal range. In summary, the established Box-Behnken quadratic regression equation can accurately characterize the dimensionless groove parameters. , , , With torque and efficiency The inherent relationship between them provides a reliable response surface surrogate model for subsequent multi-objective optimization solutions.

[0098] The optimal solution verification is based on the optimization results obtained from multi-objective optimization; CFD numerical simulation is performed on the optimal solution to be verified to obtain the evaluation index of the optimal solution, including the torque of the upper and lower cover plates and blades in the four regions of the impeller. And efficiency The multi-objective optimization prediction results of the optimal solution to be verified were compared and analyzed with the results obtained from CFD simulation. The errors of both were within 1%, thus completing the verification of the optimal solution.

[0099] Therefore, this invention employs the aforementioned centrifugal pump drag reduction optimization design method based on response surface methodology. Addressing the problem of difficult cross-pump type transfer of dimensional parameters and the reliance on extensive simulation trial-and-error in centrifugal pump blade trailing edge drag reduction design, it proposes a response surface optimization method centered on dimensionless groove parameters. This is achieved by dimensionlessly transforming the groove depth, width, spacing, and length into... , , , CFD calculations were performed on 29 samples across four factors and three levels within a unified dimensionless design space. A quadratic regression response surface was established, and residual analysis was used to evaluate the reliability of the model. Finally, the response surface plot was used to visually reveal the multivariate effect on torque. With efficiency The coupling law is described. This method replaces absolute dimensions with dimensionless parameters, improving the transferability of optimization conclusions to different pump types and sizes, and providing quantifiable and reusable engineering basis for the design of low-resistance and high-efficiency pumps.

[0100] Finally, 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 preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A centrifugal pump drag reduction optimization design method based on response surface methodology, characterized in that, Includes the following steps: S1. Determine the arrangement area of ​​the grooves, and characterize the groove depth, groove width, groove spacing, and arrangement length respectively through dimensionless methods. , , , And given dimensionless constraints, where , ; Specifically, it includes: S11. Extract the groove depth based on the key geometric features of the groove structure. Groove width Spacing between adjacent grooves and the length of the groove arrangement Four design variables were used, and each was dimensionless to obtain a dimensionless depth parameter. Dimensionless width parameter Dimensionless spacing parameters and dimensionless length parameter The definitions of each dimensionless parameter are as follows: ； ； ； ； in, The coefficient of friction of the wall surface; for The dynamic viscosity of water is 0.001003 Pa·s; The viscosity coefficient, m 2 / s; The blade length is in meters (m). S12. Combining pump type dimensions and blade trailing edge structure constraints, the value range and level setting principles for each dimensionless variable are given, among which, , ; S13. Considering the mechanism of the groove's effect on the near-wall shear layer, introduce the following into the parameter settings and constraints: and Similar range constraints are used to guide the optimization search to a more effective drag reduction region; S2. Response surface methodology was used to generate samples for a four-factor, three-level experiment. CFD numerical simulations were performed on each sample to extract the torque of the upper and lower cover plates and blades in the impeller region. and the centrifugal pump efficiency under corresponding operating conditions. As an evaluation indicator; S3, Based on step S2, establish respectively and A second-order polynomial response surface model was constructed, and the significance and reliability of the model were verified through analysis of variance and residual tests. Based on CFD sample simulation results, a model was established... , , , A second-order polynomial response surface model with drag reduction and performance evaluation indicators as dependent variables, using them as independent variables; S4. Draw three-dimensional response surfaces and contour plots for pairwise variable combinations, for observation. , , , The coupling effect of torque loss and efficiency; S5. Perform multi-objective optimization under variable range and performance constraints to achieve torque minimization and efficiency maximization, obtain the optimal combination of dimensionless parameters, and verify the accuracy and feasibility of the optimization results through CFD recalculation; among which the performance constraints include the range constraints of the dimensionless variables.

2. The centrifugal pump drag reduction optimization design method based on response surface methodology according to claim 1, characterized in that: The arrangement length of the groove is defined in S12, a dimensionless length parameter. The effective area is located at the trailing edge of the blade, specifically within the posterior 33% of the blade length. .

3. The centrifugal pump drag reduction optimization design method based on response surface methodology according to claim 2, characterized in that, The content of S2 is as follows: S21. Determine the variable definitions, design method, and sample size for the response surface methodology. The variables defined include: , , , Four dimensionless design variables; the design method adopted is Experimental design methods; S22. Simulate the sample of the response surface methodology to obtain drag reduction evaluation indicators, including the torque of the upper and lower cover plates and blades in the impeller region. Centrifugal pump efficiency .

4. The centrifugal pump drag reduction optimization design method based on response surface methodology according to claim 3, characterized in that, The content of S3 is as follows: S31. Based on the CFD sample simulation results, establish a system... , , , A second-order polynomial response surface model with drag reduction and performance evaluation indicators as dependent variables, using them as independent variables; S32. Perform significance testing and goodness-of-fit evaluation on the second-order polynomial response surface model. Validation methods include analysis of variance and adjusted coefficient of determination R0. 2 Residual analysis and missing fit test; S33. Using the verification method in step S32, obtain a reliable surrogate model for optimization solution.

5. The centrifugal pump drag reduction optimization design method based on response surface methodology according to claim 1, characterized in that, The following steps in step S5 involve verifying the accuracy and feasibility of the optimization results through CFD recalculation: The optimal dimensionless parameter combination obtained by multi-objective optimization was re-verified by CFD calculation prototype test. The error between the response surface prediction value and the verification result was compared, and the accuracy and feasibility of the optimization result were finally confirmed.

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