CN114492247A - Impeller high-efficiency low-vibration optimization method based on standard function of Euler lift of blade - Google Patents

Abstract

The invention discloses an impeller high-efficiency and low-vibration optimization method based on the Euler lift density function of the blade. Data sampling is carried out through the central experimental design method to obtain multiple sets of data of the maximum value of the thickness distribution and the wrap angle value of different flow surfaces of the blade; Other geometric parameters and performance parameters of the pump, create multiple vane pump geometric models, and perform steady and unsteady value simulations for each vane pump geometric model; The Euler head standard function is extracted from the distribution of the density function of the pull head, and the relationship between the Euler head standard function and the impeller axial force and vibration force level is analyzed. The multi-objective optimization method is used to optimize the impeller efficiency and the Euler head standard function. Constraints, a high-efficiency and low-vibration vane pump impeller model is obtained. The method of the invention can improve the impeller efficiency of the vane pump and reduce the axial force vibration of the impeller.

Description

High-efficiency and low-vibration optimization method of impeller based on standard function of blade Euler lift

technical field

The invention relates to the field of fluid machinery blade optimization, and proposes an impeller high-efficiency and low-vibration optimization method based on the Euler lift standard function of the blade.

Background technique

Vane pump refers to a kind of power equipment commonly used in industrial production and modern manufacturing. The vane pump uses the rotation of the impeller to convert electrical energy into mechanical energy. Common types are mainly axial flow pump, mixed flow pump and centrifugal pump. Different types of vane pumps are used in various specific applications. In industrial and agricultural applications, it is used in irrigation, drainage and large-scale power plant circulating water systems; in new energy utilization, it is used in industries such as nuclear pumps and seawater pumps. In actual production, different pump types are selected according to the specific rotational speed determined by the design parameters. The production efficiency of the pump is mainly determined by the working performance of the impeller. By optimizing the design of the impeller structure, the efficiency of the impeller can be improved. When the vane pump is working, the non-uniform flow structure generated inside the flow channel will not only destroy the flow performance, but also lead to the increase of the flow-induced vibration force between the impeller channels and the increase of the axial force vibration of the blade surface, which will further cause the loss of energy. and waste, affecting the stability and safety of equipment work. Therefore, the efficient operation and axial force vibration suppression of the vane pump is of great significance for engineering applications.

At present, research methods such as entropy change method, velocity slip coefficient method and Euler head analysis method are commonly used to qualitatively describe the impeller flow state distribution and influence during fluid flow. Generally, the size and direction of the outlet speed of the impeller in the vane pump are analyzed, and the dynamic and static interference performance between the impeller and the guide vane or volute is optimized, thereby optimizing the working performance of the pump. However, most of the existing analysis and research are only based on the qualitative analysis of the vane pump. The existing technology lacks the multi-objective optimization analysis technology to predict the impeller efficiency and vibration performance of the vane pump only through the constant value simulation calculation. The optimization design method is cumbersome and the optimization Analytical methods are complex.

SUMMARY OF THE INVENTION

The purpose of the present invention is to overcome the deficiencies of the above-mentioned background technology, and proposes a high-efficiency and low-vibration optimization method for the impeller based on the Euler lift standard function of the blade. According to the performance analysis of the Euler lift density function, the characteristic optimization using the Euler lift standard function The vibration performance of the impeller in the fluid machinery can effectively reduce the influence of the uneven flow structure. The efficiency and vibration performance of the impeller optimized according to the method of the present invention are greatly improved.

The present invention is achieved through the following technical solutions:

An impeller high-efficiency and low-vibration optimization method based on the standard function of the Euler lift of the blade, comprising the following steps:

Step 1: Given the maximum thickness range and wrap angle range of the different flow surfaces of the impeller to be designed, the data sampling is performed by the central experimental design method, and multiple sets of the maximum thickness distribution and wrap angle values of the different flow surfaces of the blade are obtained. Combined with other geometric parameters and performance parameters of the vane pump, multiple vane pump geometric models are created, and steady and unsteady values are simulated for each vane pump geometric model;

Step 2: (1) For the non-constant value simulation, extract the vibration information of the axial force of the impeller in the low frequency range of 10-430 Hz, and perform fast Fourier transform to extract the vibration force level;

(2) For the constant value simulation, the impeller efficiency, impeller head and impeller Euler head corresponding to the geometric model of each vane pump are obtained; the obtained Euler head of multiple blades is processed by data processing, and the Euler head is calculated by formula (1). Pull head density function Equal

Among them, Euler(j, i) represents the value of the j-th point on the i-th Euler head curve; m and n respectively represent the m-th point in the flow direction from the impeller inlet to the impeller outlet on an Euler head curve and n data points; k represents the number of data points selected in the flow direction from the impeller inlet to the impeller outlet, k=n-m; x and y represent the xth in the span direction from the hub face to the rim face, respectively and y Euler head curves; l represents the number of Euler head curves selected in the spanwise direction from the hub surface to the rim surface, l=y-x; a represents the a-th Euler head density point in the flow direction, a =∑j/(k+1); b represents the bth Euler lift density point in the spanwise direction, b=∑i/(l+1).

Then, for each impeller, the corresponding Euler head standard function Dispersion is calculated by formula (2),

Dispersion=σ[Equal(a,b)] (2)

Step 3: perform linear fitting on the Euler head standard function Dispersion corresponding to the plurality of impeller geometric models and the impeller axial force and vibration force level, and calculate the fitting error R ² of all data;

Step 4: When R ² is greater than the set threshold, it indicates that the number of fitting samples and fitting criteria for a single factor are satisfied, and step 5 is performed; when R ² is not greater than the set threshold, repeat steps 1 to 3;

Step 5: Select a multi-objective optimization model, take the Euler head standard function and impeller efficiency as the optimization objectives,

Constrained as the impeller lift, input the maximum thickness range and wrap angle range of different flow surfaces of the impeller blade into the multi-objective optimization model, and perform multi-objective optimization to obtain the optimization results of the maximum thickness and wrap angle of the different flow surfaces of the impeller blade. , based on the optimization result, the optimized impeller can be obtained.

Further, in the second step, for the non-constant value simulation, the axial force time-domain pulsation information under rated operating conditions is obtained, and the FFT fast Fourier transform is performed on the axial force time-domain pulsation data to obtain the axial force frequency. Using the formula (3), extract the axial force frequency domain pulsation data from 10 to 430 Hz to obtain the vibration force level

L _F =20lg(F/F ₀ ) (3)

Among them, F ₀ is the reference value of the vibration force level, and F ₀ =1 μN.

Further, the Euler head of the impeller in the second step represents the flow state distribution of the fluid when the fluid flows in the impeller channel, and the calculation formula is shown in formula (4),

Among them, V _θ represents the circumferential component of the absolute velocity at a certain position in the flow field, U represents the circumferential velocity at a certain position in the flow field, and g is the acceleration of gravity.

Further, the set threshold value in the fourth step is 0.9.

Beneficial effects of the present invention:

The invention proposes the Euler head density function of the impeller based on the Euler head, and aims to obtain the impeller efficiency and the impeller Euler head through numerical simulation calculation under steady conditions, analyze the Euler head density function, and extract the standard function for prediction and calculation. Improve the vibration performance of the impeller of the vane pump. The multi-objective optimal design of the impeller of the vane pump is simply and effectively carried out, and the high-efficiency and low-vibration vane design method is obtained, which makes the optimization purpose more clear, and the optimization analysis is simpler and more reliable. The optimally designed vane pump impeller of the present invention effectively reduces the influence caused by the uneven flow structure, and on the basis of reducing the computational workload of non-constant value simulation, the impeller efficiency and vibration performance are greatly improved.

Description of drawings

FIG. 1 is a schematic flowchart of an optimization method of an embodiment.

Fig. 2 is the Euler head curve of the initial model impeller flow domain.

Fig. 3 is the distribution diagram of the Euler lift density function of the initial model.

Fig. 4 is the frequency domain diagram of axial force pulsation of the initial model impeller.

Figure 5 shows the fitting relationship between the Euler lift standard function and the axial force and vibration performance.

Figure 6 is a graph showing the Euler head of the optimized model impeller.

Fig. 7 is the distribution diagram of the Euler lift density function of the optimization model.

Fig. 8 is the frequency domain diagram of the axial force pulsation of the impeller of the optimized model.

Detailed ways

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

As shown in Figure 1, the impeller high-efficiency and low-vibration optimization method based on the standard function of blade Euler lift of the present invention includes the following steps:

Step 1: Given the maximum thickness range and wrap angle range of the different flow surfaces of the impeller to be designed, the data sampling is performed by the central experimental design method, and multiple sets of the maximum thickness distribution and wrap angle values of the different flow surfaces of the blade are obtained. Combined with other geometric parameters and performance parameters of the vane pump, multiple vane pump geometric models are created, and steady and unsteady values are simulated for each vane pump geometric model.

Step 2: (1) For the non-constant value simulation, obtain the time-domain pulsation information of the impeller axial force under rated operating conditions, perform FFT fast Fourier transform on the axial force time-domain pulsation data, and obtain the axial force frequency-domain pulsation data; using the formula (1) to extract the axial force frequency domain pulsation data of 10-430Hz to obtain the vibration force level;

L _F =20lg(F/F ₀ ) (1)

Among them, F ₀ is the reference value of the vibration force level, and F ₀ =1 μN.

(2) For the constant value simulation, the impeller efficiency, impeller head and impeller Euler head Euler corresponding to each vane pump geometric model are obtained; the impeller Euler head Euler characterizes the flow state distribution of the fluid when the fluid flows in the impeller channel, and the calculation formula Such as formula (2):

Among them, V _θ represents the circumferential component of the absolute velocity at a certain position in the flow field, U represents the circumferential velocity at a certain position in the flow field, and g is the acceleration of gravity.

Each set of impeller models has a set of impeller Euler head data that characterizes the flow state performance on the meridian surface, that is, from the impeller inlet to the impeller outlet, and from the impeller hub to the rim.

The obtained Euler lifts of multiple blades are processed to obtain the Euler lift density function Equal, which represents the Euler lift density distribution of the selected research range, and Equal is calculated by formula (3).

Among them, Euler(j, i) represents the value of the j-th point on the i-th Euler head curve; m and n respectively represent the m-th point in the flow direction from the impeller inlet to the impeller outlet on an Euler head curve and n data points; k represents the number of data points selected in the flow direction from the impeller inlet to the impeller outlet, k=n-m; x and y represent the xth in the span direction from the hub face to the rim face, respectively and y Euler head curves; l represents the number of Euler head curves selected in the spanwise direction from the hub surface to the rim surface, l=y-x; a represents the a-th Euler head density point in the flow direction, a =∑j/(k+1); b represents the bth Euler lift density point in the spanwise direction, b=∑i/(l+1).

Then, for each impeller, the corresponding Euler head standard function Dispersion is calculated by the following formula. The Euler head standard function Dispersion of the impeller describes the degree of Euler head dispersion on the meridian plane of the impeller.

Dispersion=σ[Equal(a,b)] (4)

Step 3: perform linear fitting on the Euler head standard function Dispersion corresponding to the plurality of impeller geometric models and the impeller axial force and vibration force level, and calculate the fitting error R ² of all data;

Step 4: Take R ² to get the set threshold value of 0.9. When R ² is greater than the set threshold value, it indicates that the number of fitting samples and fitting criteria for single factor are satisfied, and step 5 is executed; when R ² is not greater than the set threshold value, Repeat steps one to three;

Step 5: Select the multi-objective optimization model, take the Euler head standard function and the impeller efficiency at this time as the optimization objective, and constrain the impeller head as the impeller head, and input the maximum thickness range and wrap angle range of the different flow surfaces of the impeller blades. The objective optimization model is used for multi-objective optimization, and the optimization results of the maximum thickness and wrap angle of the different flow surfaces of the impeller blades are obtained. Based on the optimization results, the optimized impeller can be obtained.

The method of the present invention is applied in the design of a specific pump below to illustrate the advantages of the method of the present invention.

Taking the design and optimization of an axial flow pump model as an example, referring to Figures 2 to 8, the specific implementation process is as follows:

Step 1: For the steady flow state calculation of hydraulic components, complete the hydraulic full basin model of the impeller, volute and gap flow channel in UG, and the overall number of grids is about 5.5 million. ANSYS CFX software is used for numerical simulation calculation. In the steady flow state calculation, the impeller part is the rotating area, the other parts are the static area, and the dynamic and static areas are connected to each other through the interface surface. The inlet adopts the velocity inlet, the outlet adopts the pressure outlet, the solid boundary adopts the no-slip wall condition, and the near-wall region adopts the enhanced wall function.

Through the numerical simulation calculation of the overall model, the performance parameters under the rated working conditions at the rated flow rate of 1300m3/h and the rotational speed of 1200rpm are obtained: impeller head, impeller efficiency and impeller Euler head. The design geometric parameters of the axial flow pump are shown in Table 1.

Table 1 Geometry parameters of axial flow pump

parameter value Outer diameter of impeller, D₂ 400mm Hub diameter, d_h 200mm Number of impeller blades 7 Number of guide vanes 9 Rated speed, n 1200rpm Rated flow, Q_d 1300m³/h

The numerical simulation results of the original model are analyzed by the following steps, as shown in Figures 1, 2 and 3, the impeller efficiency is 86.73%, and the vibration force level is 165.05.

The wrap angle value and the maximum thickness of the three-layer flow surface of the blade are selected as input variables, and the sample of the six input parameters is amplified by the experimental design method Central Composite Design (CCD), and the design exploration will be based on the input variables. The number of automatically selects the design type. The central combinatorial design method is the most commonly used experimental design method because it automatically switches between G-Optimality and VIF-Optimality if the number of input variables is 5.

When using the center combination design test method, the hub wrap angle is distributed in 48-64°, the S1 flow wrap angle is distributed in 40-60°, the rim wrap angle is distributed in 36-52°, the maximum thickness of the hub is distributed in 34-46mm, S1 The maximum thickness of the flow surface is 65-83mm, and the maximum thickness of the rim is 94-130mm. When fitting a three-level response surface to a single factor, at least 3 sets of samples are required. Export the impeller efficiency and impeller Euler head data of 20 sets of blades. The number of derived samples satisfies the fit criteria based on the number of factors in the response surface fit to the Euler head density function in the following steps.

Step 2: (1) Perform unsteady flow state calculation on the blade model, monitor the axial force pulsation in the unsteady calculation, take the steady flow state calculation result as the initial condition, and set the time step as the impeller rotation. 1° elapsed time. In order to ensure the accurate and stable pressure pulsation law, the time taken for one rotation of the impeller to be one cycle is used to obtain the time-domain pulsation information of the axial force under the rated working condition, and the time-domain signal within 10 cycles after the calculation is stabilized is used as a fast Fourier transform. The frequency domain information is obtained after Lie transform.

FFT Fourier transform is performed on the axial force time-domain pulsation data, the axial frequency is 20Hz, and the one-fold blade frequency is 140Hz, as shown in Figure 4, which is the axial force vibration frequency domain diagram of the impeller, using the vibration force level formula ( 1) Analyze the vibration data in the frequency domain of the axial force, extract the low-frequency vibration force level of 10-430 Hz, and the reference value F ₀ =1 μN.

(2) Carry out steady flow state calculation for the blade model, and perform image processing and density function analysis on the Euler head data of the blade watershed. Taking the impeller meridian plane as the research object, 30 data points are uniformly extracted in the spanwise direction, and 30 data points are uniformly extracted in the flow direction.

After the static pressure data distribution is processed by formula (2), the Euler head distribution curve is obtained as shown in Figure 2. Perform density function analysis on the fluid in the impeller area, where Euler(j, i) represents the value of the jth point on the ith Euler head curve; m and n respectively represent an Euler head curve from the impeller inlet to the impeller outlet The m and nth data points in the flow direction between the impeller inlet and the impeller outlet; k represents the number of data points selected in the flow direction between the impeller inlet and the impeller outlet, k=n-m, the value is 2; x and y respectively represent from the hub The x and y Euler head curves in the span direction from the hub face to the rim face; l represents the number of Euler head curves selected in the span direction from the hub face to the rim face, l=y-x, the value is 2; a represents the a-th Euler head density point in the flow direction, a=∑j/(k+1), and the value is 10; b represents the b-th Euler head density point in the spanwise direction, b=∑i /(l+1), the value is 10.

Equal represents the Euler head density distribution of the fluid in the impeller part. The distribution law of the fluid in this area is directly fed back by the vibration performance of the impeller. The larger the Equal value, the more irregular the fluid energy change in the study area, and the worse the stability of energy exchange. The density function analysis for the original model is shown in Figure 3. Dispersion is the Euler head standard function, which represents the degree of dispersion of the Euler head density function in the overall study area, and is expressed by the standard deviation of the Euler head density function in the overall study area.

Step 3: Describe the relationship between the Euler head density function of the impeller in the steady simulation calculation and the axial force pulsation performance under the unsteady simulation calculation. The physical meaning of Equal calculated in the second step is the Euler head distribution density of the impeller meridian surface, indicating that The stability and uniformity of energy conversion during blade loading are improved. When the Euler head density function is larger, it indicates that the static pressure energy changes disorderly during the impeller loading process, and there is a sudden change in energy caused by flow structures such as low-speed vortices. The complex and chaotic flow structure is also the cause of the abnormal pulsation of axial force vibration. The blade frequency pulsation amplitude of the axial force reflects the fluid flow induced vibration caused by the blade when the impeller is working, and the overall vibration in the low frequency band reflects the impeller flow. The influence of the complex flow structure on the surface excitation force of the impeller. Therefore, taking the vibration force level in the low frequency band (10-430 Hz) as the criterion for the vibration performance of the impeller axial force, the response fitting relationship of the sample group is obtained as follows.

Y=34.797X+133.42

Among them, X represents the standard function of Euler lift extracted from the meridian surface of the impeller blade, and Y represents the vibration force level. In summary, the Euler head density function can be used as a parameter to measure the axial force and vibration performance of the blade. The data of this sample group are shown in Table 2.

Table 2 Impeller performance sample group data

Step 4: According to the fitting image and fitting result in Step 3, it can be obtained that R ² =0.9249>0.9, and the response distribution image is shown in Figure 5 . Analysis of the fit graph can evaluate the accuracy of the response surface, the predicted value and the observed value are in good agreement, and the goodness of fit is high, that is, the impeller data in Table 2 can be used as a reliable sample for analysis and optimization.

Step 5: According to steps 1 to 4, set the impeller efficiency and the Euler head standard function as the optimization goals. The higher the impeller efficiency is, the smaller the Euler head standard function is, and the better the impeller performance is. The impeller head is set to 11.5m as the constraint The multi-objective optimization method selects NSGA-II; according to the selection of the optimization variables of the sample group, the multi-objective optimization sets the wrap angle value and the maximum thickness distribution of the three-layer flow surface of the blade as the optimization variables, and the specific selections are as follows:

The input parameters are distributed within a certain range, the hub wrap angle is distributed in 41.38～60.62°, the S1 flow wrap angle is distributed in 44.22～60°, the rim wrap angle is distributed in 33.38～48.62°, and the maximum thickness of the hub is distributed in 36.53～43.47mm , the maximum thickness of the S1 flow surface is 65-83mm, and the maximum thickness of the rim is 94-130mm. In NSGA-II optimization, the population size was 16 (multiple of 4), and the number of iterations was 20. A total of 320 sets of leaf fitting results were obtained, and numerical simulations were carried out to verify the optimization results.

The comparison between the optimization results and the simulation results is shown in Table 3, and the error analysis is as follows.

Table 3 Analysis of optimization results and numerical simulation verification results

Impeller head (m) Dispersion Impeller efficiency Optimization Results 11.398 0.406 89.928% Simulation results 11.411 0.400 90.116% Error Analysis 0.11% 1.50% 0.21%

The error analysis is less than 2%, which meets the error requirements, indicating that the optimization results are reliable. The comparison between the optimized model and the original model is shown in Figures 6, 7, 8 and Figures 2, 3, and 4. The impeller efficiency is optimized by 3.39%; the Euler lift standard function is reduced by 0.4713, and optimized by 54.09%. The vibration force level of the optimized model is 148.84, which is 9.79% optimized compared with the original model vibration force level. It can be seen from Figure 8 of the impeller axial force spectrum that the vibration performance of the impeller axial force has been significantly improved; from the Euler lift density function distribution of the impeller, it can be seen that the density function distribution of the optimized model is more uniform than the original model. To sum up, the result is determined as the final optimization result, and the Euler head density function and standard function analysis of the impeller have guiding significance for optimizing the vibration performance of the impeller.

Claims (4)

1. an impeller high-efficiency and low-vibration optimization method based on blade Euler lift standard function, is characterized in that: comprise the following steps: Step 1: Given the maximum thickness range and wrap angle range of the different flow surfaces of the impeller to be designed, the data sampling is performed by the central experimental design method, and multiple sets of the maximum thickness distribution and wrap angle values of the different flow surfaces of the blade are obtained. Combined with other geometric parameters and performance parameters of the vane pump, multiple vane pump geometric models are created, and steady and unsteady values are simulated for each vane pump geometric model; Step 2: (1) For the non-constant value simulation, extract the vibration information of the axial force of the impeller in the low frequency range of 10-430 Hz, and perform the fast Fourier transform to extract the vibration force level; (2) For the constant value simulation, the impeller efficiency, impeller head and impeller Euler head corresponding to the geometric model of each vane pump are obtained; the obtained Euler head of multiple blades is processed by data processing, and the Euler head is calculated by formula (1). Pull head density function Equal

Among them, Euler(j, i) represents the value of the j-th point on the i-th Euler head curve; m and n respectively represent the m-th point in the flow direction from the impeller inlet to the impeller outlet on an Euler head curve and n data points; k represents the number of data points selected in the flow direction from the impeller inlet to the impeller outlet, k=n-m; x and y represent the xth in the span direction from the hub face to the rim face, respectively and y Euler head curves; l represents the number of Euler head curves selected in the spanwise direction from the hub surface to the rim surface, l=y-x; a represents the a-th Euler head density point in the flow direction, a =∑j/(k+1); b represents the bth Euler lift density point in the spanwise direction, b=∑i/(l+1). Then, for each impeller, the corresponding Euler head standard function Dispersion is calculated by formula (2), Dispersion=σ[Equal(a,b)] (2) Step 3: perform linear fitting on the Euler head standard function Dispersion corresponding to the plurality of impeller geometric models and the impeller axial force and vibration force level, and calculate the fitting error R ² of all data; Step 4: When R ² is greater than the set threshold, it indicates that the number of fitting samples and fitting criteria for a single factor are satisfied, and step 5 is performed; when R ² is not greater than the set threshold, repeat steps 1 to 3; Step 5: Select the multi-objective optimization model, take the Euler head standard function and the impeller efficiency at this time as the optimization objective, and constrain the impeller head as the impeller head, and input the maximum thickness range and wrap angle range of the different flow surfaces of the impeller blades. The objective optimization model is used for multi-objective optimization, and the optimization results of the maximum thickness and wrap angle of the different flow surfaces of the impeller blades are obtained. Based on the optimization results, the optimized impeller can be obtained. 2. The impeller high-efficiency and low-vibration optimization method based on blade Euler lift standard function according to claim 1, characterized in that: in the step 2, for non-constant value simulation, when obtaining the axial force under rated operating conditions To obtain the axial force frequency domain pulsation data, use the formula (3) to extract the axial force frequency domain pulsation data from 10 Hz to 430 Hz to obtain the vibration force level L _F =20lg(F/F ₀ ) (3) Among them, F ₀ is the reference value of the vibration force level, and F ₀ =1 μN. 3. the impeller high-efficiency and low-vibration optimization method based on blade Euler lift standard function according to claim 1, is characterized in that: the impeller Euler Euler head Euler in described step 2 characterizes the flow state of fluid when flowing in impeller flow channel distribution, the calculation formula is shown in formula (4),

Among them, V _θ represents the circumferential component of the absolute velocity at a certain position in the flow field, U represents the circumferential velocity at a certain position in the flow field, and g is the acceleration of gravity. 4 . The high-efficiency and low-vibration impeller optimization method based on the Euler lift standard function according to claim 1 , wherein the set threshold value in the step 4 is 0.9. 5 .

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