Method for representing unsteady pressure pulsation blade frequency amplitude of centrifugal pump based on steady calculation

Abstract

The characterization method comprises the steps that a fluid domain of the centrifugal pump is established, steady CFD simulation calculation is conducted on the established fluid domain, and a steady-state pressure field is extracted based on steady calculation; then generating a pressure space distribution sequence on the basis of the steady-state pressure field and carrying out dimensionless operation; fast Fourier transform on the spatial scale is carried out on the dimensionless pressure spatial distribution sequence; and finally, forming an unsteady pressure pulsation blade frequency quantitative index based on a spatial fast Fourier transform result. According to the method, time-consuming unsteady calculation and expensive experimental tests are not needed, and calculation resources, manpower and material resources are saved. The steady index provided by the invention can be used as an important basis for pressure pulsation characteristic comparison in the optimization process of the low-pulsation centrifugal pump, and the optimization design period of the low-pulsation centrifugal pump is greatly shortened.

Description

Technical Field

[0001] The present invention relates to the field of fluid machinery, and in particular to a method for characterizing the amplitude of the blade frequency of an unsteady pressure pulsation of a centrifugal pump based on steady calculation, which is suitable for centrifugal pump design optimization, vibration noise prediction and reliability evaluation. Background Art

[0002] During the operation of a centrifugal pump, the dynamic and static interference between the impeller and the volute will cause unsteady pressure pulsation in the flow field, among which the pressure pulsation amplitude of the blade passing frequency (referred to as "blade frequency") is a key indicator. It not only directly affects the working performance of the centrifugal pump, but also has a significant impact on the vibration and noise level of the equipment.

[0003] Traditional methods for obtaining unsteady pressure pulsation characteristics mainly include unsteady numerical simulation and experimental testing. Although both methods can provide relatively accurate results, they also have obvious disadvantages. Unsteady numerical simulation requires a lot of computing resources and time, and the cost of experimental testing is relatively high and the cycle is long. Therefore, in practical applications, these traditional methods often fail to meet the needs of rapid design iteration and cost control.

[0004] In order to solve the above problems, it is urgent to develop an efficient and high-precision leaf frequency amplitude characterization method to significantly shorten the time to obtain results while ensuring the accuracy of the results. Summary of the invention

[0005] In order to solve the technical problems of large amount of calculation and long calculation time of unsteady pressure pulsation index in the design optimization process of existing low-pulsation centrifugal pumps, the present invention provides a characterization method for the unsteady pressure pulsation blade frequency amplitude of a centrifugal pump based on steady calculation. This method only needs to use steady CFD simulation calculation to judge the pressure pulsation blade frequency characteristics of the centrifugal pump, which is convenient, fast and reliable.

[0006] The object of the present invention is achieved by following steps:

[0007] A method for characterizing the amplitude of blade frequency of unsteady pressure pulsation of a centrifugal pump based on steady calculation comprises the following steps:

[0008] Step 1: Establish the fluid domain of the centrifugal pump;

[0009] Step 2: Perform steady CFD simulation calculation on the established fluid domain;

[0010] Step 3: Extract the steady-state pressure field based on steady-state calculation;

[0011] Step 4: Generate the pressure space distribution sequence based on the steady-state pressure field and make it dimensionless;

[0012] Step 5: Perform a fast Fourier transform on the dimensionless pressure spatial distribution sequence obtained in Step 4 in terms of spatial scale;

[0013] Step 6: Based on the results of the spatial fast Fourier transform in Step 5, form an unsteady pressure pulsation blade frequency quantization index.

[0014] Further, Step 4 specifically includes:

[0015] (4-1) Generate the coordinates (m s , n s ) of the monitoring points at the impeller outlet, where s is the discrete space index. To ensure that the energy at the blade frequency does not leak, take 0 ≤ s ≤ 360k - 1 and s ∈ Z, where k takes 1, 2, or 3…, that is, the number of sampling points N = 360k, and the sampling frequency F s = k, with the unit of 1 / °;

[0016] (4-2) Import the coordinates (m s , n s ) of the monitoring points into the post-processing software;

[0017] (4-3) Export the pressure data x(m s , n s ) of each monitoring point;

[0018] (4-4) De-mean and dimensionless x(m s , n s ) according to the following formula to obtain the pressure coefficient sequence x(s) of the spatial distribution:

[0019]

[0020] where ρ is the density of the pumped liquid, and u o is the circumferential linear velocity at the impeller outlet.

[0021] Further, m s and n s are calculated by the following formula:

[0022]

[0023] where R m is the radius of the circle where the monitoring point is located, and the reference range of R m is 1.01R o ≤ R m ≤ 1.11R o ; α is the polar coordinate angle of the monitoring point,

[0024] Further, Step 5 includes the following sub-steps:

[0025] (5-1) Define the spatial axis frequency f according to the principle of fluctuating once per cycle sp , and calculate the frequency resolution Δf through ;

[0026] (5-2) Perform a fast Fourier transform on the pressure coefficient sequence x(s) distributed in space in terms of spatial scale through the following formula to obtain the pressure coefficient sequence X(f) in the spatial frequency domain:

[0027]

[0028] where f is the discrete frequency index, 0 ≤ f ≤ N - 1, and f ∈ Z; i is the imaginary unit, and π is the pi;

[0029] (5-3) Calculate the modulus of the complex number X(f) through the following formula and normalize it by half of the number of sampling points of the pressure coefficient sequence distributed in space to obtain |X(f)| nor :

[0030]

[0031] (5-4) Use f*Δf as the abscissa and |X(f)| nor as the ordinate to plot the spatial frequency spectrum of the spatial Fourier transform of the pressure signal; where the abscissa range is taken as

[0032] Further, the specific steps of step six include:

[0033] Based on the spatial frequency spectrum plot in step (5-4), record the spatial blade passing frequency as f c = num×f sp , num is the number of impeller blades, and calculate the steady index Ste of the unsteady pressure pulsation blade frequency amplitude of the centrifugal pump according to the following formula:

[0034]

[0035] Further, the specific steps of step three include:

[0036] (3-1) Import the calculation results of the steady CFD simulation into the post-processing software;

[0037] (3-2) Establish the middle section of the impeller and the volute;

[0038] (3-3) Generate the steady pressure field on the section.

[0039] Further, step two includes:

[0040] (2-1) Check the fluid domain to ensure that there are no patches and broken surfaces in the fluid domain, and name the fluid domain;

[0041] (2-2) Use grid generation software to mesh each part of the fluid domain of the centrifugal pump;

[0042] (2-3) Import the mesh into the CFD simulation software and set the boundary conditions and solution methods in the CFD simulation software;

[0043] (2-4) Conduct a CFD steady-state simulation calculation.

[0044] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0045] Based on the steady-state CFD numerical simulation calculation, the present invention extracts the steady-state pressure field structure in the dynamic and static interference region of the centrifugal pump, and the obtained characterization method can accurately represent the unsteady pressure pulsation characteristics. This method does not require time-consuming unsteady calculations and expensive experimental tests, saving computational resources and manpower and material resources. The steady-state index proposed by the present invention can be used as an important basis for comparing the pressure pulsation characteristics during the optimization process of low-pulsation centrifugal pumps, greatly shortening the optimization design cycle of low-pulsation centrifugal pumps. Brief Description of the Drawings

[0046] Figure 1 It is the basic flowchart of the characterization method for the unsteady pressure pulsation blade frequency amplitude of the centrifugal pump based on steady-state calculation of the present invention.

[0047] Figure 2 It is the schematic diagram of the fluid domain of the centrifugal pump established in the embodiment of the present invention.

[0048] Figure 3 It is the schematic diagram of the position of the monitoring point at the impeller outlet in the embodiment of the present invention.

[0049] Figure 4 It is the schematic diagram of the steady-state pressure field structure extracted in the embodiment of the present invention.

[0050] Figure 5 It is the schematic diagram of the principle of spatial scale fast Fourier transform in the embodiment of the present invention.

[0051] Figure 6 It is the spatial frequency spectrum diagram obtained by the spatial scale fast Fourier transform in the embodiment of the present invention.

[0052] Figure 7 It is the geometric models of three impellers used to verify the accuracy of the method proposed by the present invention in the embodiment of the present invention, where the number of blades in the left figure is 6, the number of blades in the middle figure is 7, and the number of blades in the right figure is 8.

[0053] Figure 8 It is the correlation fitting diagram of the steady-state index obtained by the method proposed by the present invention and the pressure pulsation blade frequency amplitude obtained by unsteady calculation in the embodiment of the present invention, where the left figure is at 1.0Qd The fitting results under the working conditions, the middle figure is at 1.2Q d The fitting results under the working conditions, the right figure is at 1.4Q d The fitting results under the working conditions. Specific implementation manners

[0054] The present invention will be described in detail below according to the accompanying drawings and preferred embodiments. The objectives and effects of the present invention will become more apparent. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0055] As Figure 1 shown, the method for characterizing the unsteady pressure pulsation blade frequency amplitude of a centrifugal pump based on steady calculation of the present invention includes the following steps:

[0056] S01, establish the fluid domain of the centrifugal pump.

[0057] The specific process of establishing the fluid domain of the centrifugal pump is:

[0058] According to the design requirements, use 3D modeling software to complete the basic geometric structure modeling of the fluid domain of the centrifugal pump, as Figure 2 shown, including the inlet pipe, impeller, diffuser, volute and outlet pipe, as the basin model for subsequent analysis.

[0059] S02, perform steady-state CFD simulation calculations on the established fluid domain.

[0060] The specific process of the steady-state CFD simulation calculation is:

[0061] (2-1) Check the basin, there are no patches and broken surfaces, and name the basin;

[0062] (2-2) Use grid generation software to mesh each part of the fluid domain of the centrifugal pump;

[0063] (2-3) Set the boundary conditions and solution methods in the CFD simulation software;

[0064] (2-4) Perform CFD steady-state simulation calculations on the rated working condition 1.0Q d

[0065] S03, extract the steady-state pressure field based on the steady calculation.

[0066] The specific process of extracting the steady-state pressure field is:

[0067] (3-1) Import the calculation results of the steady-state CFD simulation into the flow field post-processing software;

[0068] (3-2) Establish the plane where the surface where the impeller span = 0.5 is located and the middle section of the volute are located;​

[0069] (3-3) Generate the steady-state pressure field on the above-mentioned cross-section. The steady-state pressure field obtained in this embodiment is as Figure 4 shown.

[0070] S04, generate a sequence of pressure spatial distributions based on the steady-state pressure field and perform non-dimensionalization.

[0071] The specific process of generating the sequence of pressure spatial distributions and performing non-dimensionalization is as follows:

[0072] (4-1) Generate the coordinates (m s , n s ) of the monitoring points at the impeller outlet. s is the discrete space index. To ensure that the energy at the blade passing frequency does not leak, take 0 ≤ s ≤ 360k - 1 and s ∈ Z, where k takes 1, 2, or 3..., that is, the number of sampling points N = 360k, and the sampling frequency F s = k (1 / °);

[0073] Among them, m s and n s are calculated by the following formula:

[0074]

[0075] In the above formula, R m is the radius of the circle where the monitoring point is located. The reference range of R m is 1.01R o ≤ R m ≤ 1.11R o ; α is the polar coordinate angle of the monitoring point

[0076] In this embodiment, the radius R m of the circle where the outlet monitoring point is located is 130 mm. Preferably, take k = 1, then 0 ≤ s ≤ 359 and s ∈ Z. The polar coordinate angle of the monitoring point is calculated, and the coordinates of the outlet monitoring points are shown in Table 1. The positions of the outlet monitoring points are as Figure 3 shown. In this embodiment, the spatial sampling period T = 1°, the spatial sampling frequency F s = 1 (1 / °), and the number of sampling points N = 360.

[0077] Table 1 Coordinates of the impeller outlet monitoring points

[0078]

[0079] (4-2) Import the coordinates (m s , n s ) of the monitoring points into the flow field post-processing software;

[0080] (4-3) Export the pressure data x(m s ,n s ) of each monitoring point;

[0081] (4-4) De-mean and non-dimensionalize x(m s ,n s ) according to the following formula to obtain the pressure coefficient sequence x(s) of spatial distribution:

[0082]

[0083] where ρ = 998.2 kg / m 3 , u o = 37.35 m / s, and the results are shown in Table 2.

[0084] Table 2 Pressures and pressure coefficients of each monitoring point

[0085]

[0086] For S05, perform a fast Fourier transform on the pressure coefficient sequence x(s) of spatial distribution in terms of spatial scale. The specific process is as follows:

[0087] (5-1) Define the spatial axis frequency f sp according to the principle of one fluctuation per period, and calculate the frequency resolution Δf through ;

[0088] In this embodiment, the spatial axis frequency

[0089] (5-2) Perform a fast Fourier transform on the pressure coefficient sequence x(s) of spatial distribution in terms of spatial scale through the following formula to obtain the pressure coefficient sequence X(f) in spatial frequency domain:

[0090]

[0091] where f is the discrete frequency index, 0 ≤ f ≤ 359, and f ∈ Z; i is the imaginary unit, and π is the pi;

[0092] (5-3) Calculate the modulus of the complex number X(f) through the following formula and normalize it by half of the number of sampling points of the pressure coefficient sequence of spatial distribution to obtain |X(f)| nor :

[0093]

[0094] (5-4) Use f*Δf as the abscissa and |X(f)| nor as the ordinate to plot the spatial frequency spectrum diagram of the spatial Fourier transform of the pressure signal; where the abscissa range is taken as In this embodiment, the abscissa range is taken as 0 ≤ f*Δf ≤ 0.5, unit: (1 / °). The fast Fourier transform process of this embodiment is as follows Figure 5 shown, and the obtained spatial frequency spectrum diagram is as Figure 6 shown.

[0095] S06. Based on the transformation result, a non-steady pressure pulsation blade frequency quantization index is formed.

[0096] Based on the spatial frequency spectrum diagram drawn in step (5-4), the spatial blade passing frequency is denoted as f c = num×f sp , where num is the number of impeller blades. The steady index Ste of the non-steady pressure pulsation blade frequency amplitude of the centrifugal pump is calculated according to the following formula:

[0097]

[0098] In this embodiment, the number of blades of the centrifugal pump used is 7, that is, num = 7, then f c = 7×0.00278 = 0.01946. Therefore

[0099] Using the method proposed by the present invention to perform a steady calculation for one working condition on a workstation with 64 cores takes about 3 hours, while using the traditional method to calculate an unsteady working condition takes about 3 days. Therefore, this method significantly reduces the calculation time and is a fast characterization method for the non-steady pressure pulsation amplitude.

[0100] To verify the accuracy of the present invention, the non-steady index calculation result Ste proposed in this embodiment and the pressure pulsation blade frequency amplitude obtained from the non-steady simulation calculation ( represents the average value of the non-steady pressure pulsation blade frequency amplitude of 30 monitoring points evenly distributed circumferentially with the radius R m = 130 mm of the circle where the impeller outlet is located) are subjected to correlation analysis. The verification models used in this embodiment are three impellers with 6, 7, and 8 blades (as Figure 7 shown), and the non-steady index calculation results obtained by using the method proposed by the present invention at 1.0q d , 1.2q d and 1.4q d under three working conditions are calculated respectively, and then their non-steady pressure pulsation blade frequency amplitudes are calculated. Figure 8 This is the correlation fitting diagram between the steady index obtained by using the method proposed by the present invention in the embodiment of the present invention and the pressure pulsation blade frequency amplitude obtained from the non-steady calculation.

[0101] At 1.0q d , 1.2Q d and 1.4Q dUnder the three working conditions, the calculation method of the correlation coefficient is as follows:

[0102]

[0103] where σ Ste and respectively represent the standard deviations of Ste and ; E[Ste] and respectively represent the mathematical expectations of Ste and .

[0104] Table 3 shows the correlation analysis results of the steady-state indexes and the unsteady pressure pulsation amplitudes obtained by using the method proposed in the present invention for the three impellers under each working condition.

[0105] Table 3 Correlation Analysis Results Table

[0106]

[0107] As can be seen from Table 3, when the flow rates are 1.0Q d , 1.2q d and 1.4q d , the correlation coefficients between Ste and are 0.98698, 0.99938 and 0.99864 respectively, which indicates that under the same working conditions, Ste and show a high degree of linear relationship. In addition, through the cross-analysis of the three operating conditions, the correlation coefficient of the nine groups of data is 0.98141, further indicating that Ste and also maintain a high linear relationship under different operating conditions. Therefore, the characterization quantity Ste obtained by the calculation method proposed in the present invention can effectively characterize the unsteady pressure pulsation blade frequency amplitude.

[0108] Those of ordinary skill in the art can understand that the above are only preferred examples of the invention and are not used to limit the invention. Although the invention has been described in detail with reference to the foregoing examples, for those skilled in the art, they can still modify the technical solutions recorded in the foregoing examples, or perform equivalent replacements for some of the technical features. Any modifications, equivalent replacements, etc. made within the spirit and principle of the invention shall be included within the protection scope of the invention.

Claims

1. A method for characterizing the amplitude of blade frequency of unsteady pressure pulsation of a centrifugal pump based on steady calculation, characterized in that: The steps include: Step 1: Establish the fluid domain of the centrifugal pump; Step 2: Perform steady CFD simulation calculation on the established fluid domain; Step 3: Extract the steady-state pressure field based on steady-state calculation; Step 4: Generate the pressure space distribution sequence based on the steady-state pressure field and make it dimensionless; Step 5: Perform fast Fourier transform on the spatial scale of the dimensionless pressure spatial distribution sequence obtained in step 4; Step 6: Based on the spatial fast Fourier transform result of step 5, a quantitative index of the blade frequency of unsteady pressure pulsation is formed.

2. The method for characterizing the amplitude of blade frequency of unsteady pressure pulsation of a centrifugal pump based on steady calculation according to claim 1 is characterized in that: The step 4 specifically includes: (4-1) Generate the coordinates of the impeller outlet monitoring point (m s ,n s ), s is the discrete space index. In order to ensure that the energy at the leaf frequency is not leaked, 0≤s≤360k-1 is taken, and s∈Z, where k is 1, 2 or 3..., that is, the number of sampling points N = 360k, the sampling frequency F s =k, unit is 1 / °; (4-2) The coordinates of the monitoring points (m s ,n s ) into post-processing software; (4-3) Export the pressure data x(m) of each monitoring point s ,n s ); (4-4) According to the following formula, x(m s ,n s ) is removed from the mean and dimensionless to obtain the spatially distributed pressure coefficient sequence x(s): Where ρ is the density of the pumped liquid, u o is the circumferential velocity of the impeller outlet.

3. The method for characterizing the blade frequency amplitude of a centrifugal pump with unsteady pressure pulsation based on steady calculation according to claim 2 is characterized in that: m s and n s Calculated by the following formula: Among them, R m is the radius of the circle where the monitoring point is located, R m The reference range is 1.01R o ≤R m ≤1.11R o ; α is the polar coordinate angle of the monitoring point, 4. The method for characterizing the amplitude of blade frequency of unsteady pressure pulsation of a centrifugal pump based on steady calculation according to claim 3 is characterized in that: The step five includes the following sub-steps: (5-1) Define the spatial axial frequency f based on the principle that one wave occurs in one cycle sp and through Calculate the frequency resolution Δf; (5-2) The spatially distributed pressure coefficient sequence x(s) is subjected to a fast Fourier transform on a spatial scale by the following formula to obtain the pressure coefficient sequence X(f) in the spatial frequency domain: Where f is a discrete frequency index, 0≤f≤N-1, and f∈Z; i is the imaginary unit, π is the circumference of a circle; (5-3) The modulus of the complex number X(f) is calculated by the following formula and normalized to half the number of sampling points of the spatially distributed pressure coefficient sequence to obtain |X(f)| nor : (5-4) With f*Δf as the horizontal coordinate, |X(f)| nor As the vertical axis, draw the spatial spectrum of the pressure signal spatial Fourier transform; the horizontal axis range is 5. The method for characterizing the amplitude of blade frequency of unsteady pressure pulsation of a centrifugal pump based on steady calculation according to claim 4 is characterized in that: The step six specifically includes: Based on the spatial spectrum diagram drawn in step (5-4), the spatial blade passing frequency is recorded as f c =num×f sp , num is the number of impeller blades, and the steady index Ste of the blade frequency amplitude of the centrifugal pump's unsteady pressure pulsation is calculated according to the following formula:

6. The method for characterizing the amplitude of blade frequency of unsteady pressure pulsation of a centrifugal pump based on steady calculation according to claim 1 is characterized in that: The step three specifically includes: (3-1) Import the calculation results of steady-state CFD simulation into the post-processing software; (3-2) Establish the middle section of the impeller and volute; (3-3) Generate a steady-state pressure field on the cross section.

7. The method for characterizing the amplitude of blade frequency of unsteady pressure pulsation of a centrifugal pump based on steady calculation according to claim 1 is characterized in that: The second step comprises: (2-1) Check the fluid domain to ensure that there are no fragments or broken surfaces in the fluid domain, and name the fluid domain; (2-2) Use mesh generation software to mesh each fluid domain of the centrifugal pump; (2-3) Importing the mesh into the CFD simulation software, and setting the boundary conditions and solution method in the CFD simulation software; (2-4) Perform CFD steady-state simulation calculations.

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