A method for representing blade frequency amplitude of unsteady pressure fluctuation of a centrifugal pump based on steady calculation

Abstract

This invention discloses a method for characterizing the unsteady pressure pulsation blade frequency amplitude of a centrifugal pump based on steady-state calculations. The method includes: establishing a fluid domain for the centrifugal pump; performing steady-state CFD simulation calculations on the established fluid domain; extracting the steady-state pressure field based on the steady-state calculations; generating a pressure spatial distribution sequence based on the steady-state pressure field and making it dimensionless; performing a fast Fourier transform on the dimensionless pressure spatial distribution sequence at a spatial scale; and finally, forming a quantitative index for the unsteady pressure pulsation blade frequency based on the spatial fast Fourier transform results. This invention eliminates the need for time-consuming unsteady calculations and expensive experimental testing, saving computational resources and manpower. The steady-state index proposed in this invention can serve as an important basis for comparing pressure pulsation characteristics during the optimization process of low-pulsation centrifugal pumps, significantly shortening the optimization design cycle of low-pulsation centrifugal pumps.

Description

Technical Field

[0001] This invention relates to the field of fluid machinery, and in particular to a method for characterizing the amplitude of unsteady pressure pulsation blade frequency in centrifugal pumps based on steady-state calculations, which is applicable to centrifugal pump design optimization, vibration and noise prediction, and reliability assessment. Background Technology

[0002] During the operation of a centrifugal pump, the dynamic and static interference between the impeller and the volute causes unsteady pressure pulsations in the flow field. Among these pulsations, the pressure pulsation amplitude at the blade passage 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 levels of the equipment.

[0003] Traditional methods for obtaining the characteristics of unsteady pressure pulsations mainly include unsteady numerical simulation and experimental testing. While both can provide relatively accurate results, they also have significant drawbacks. Unsteady numerical simulation requires substantial computational resources and time, while experimental testing is relatively expensive and time-consuming. Therefore, in practical applications, these traditional methods often fail to meet the demands of rapid design iteration and cost control.

[0004] To address the aforementioned issues, there is an urgent need to develop an efficient and highly accurate method for characterizing leaf frequency amplitude, which can significantly shorten the time required to obtain results while ensuring accuracy. Summary of the Invention

[0005] To address the technical problems of large computational load and long computation time for unsteady pressure pulsation index in the design and optimization of existing low-pulsation centrifugal pumps, this invention provides a characterization method for the blade frequency amplitude of unsteady pressure pulsation in centrifugal pumps based on steady-state calculations. This method only requires steady-state CFD simulation calculations to evaluate the pressure pulsation blade frequency characteristics of centrifugal pumps, which is convenient, fast, and provides reliable results.

[0006] The objective of this invention is achieved through the following steps:

[0007] A method for characterizing the impeller frequency amplitude of unsteady pressure pulsation in a centrifugal pump based on steady-state calculations includes the following steps:

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

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

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

[0011] Step 4: Generate a spatial distribution sequence of pressure based on the steady-state pressure field and perform dimensionless transformation;

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

[0013] Step Six: Based on the spatial fast Fourier transform results from Step Five, a quantitative index for unsteady pressure pulsation blade frequency is generated.

[0014] Furthermore, step four specifically includes:

[0015] (4-1) Generate the coordinates (m) of the impeller outlet monitoring point s ,n s ), where s is the discrete spatial index. To ensure no energy leakage at the leaf frequency, we take 0 ≤ s ≤ 360k⁻¹, and s ∈ Z, where k takes the values ​​1, 2, 3, ..., i.e., the number of sampling points N = 360k, and the sampling frequency F s =k, unit is 1 / °;

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

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

[0018] (4-4) According to the following formula, x(m) s ,n s After removing the mean and dimensionless transformation, the spatially distributed pressure coefficient sequence x(s) is obtained:

[0019]

[0020] Where ρ is the density of the pumped liquid, u o denoted as circumferential velocity at the impeller outlet.

[0021] Furthermore, m s and n s Calculated using the following formula:

[0022]

[0023] Among them, R m R is the radius of the circle containing the monitoring point. m The reference range is 1.01R. o ≤R m ≤1.11R o α is the polar coordinate angle of the monitoring point.

[0024] Furthermore, step five includes the following sub-steps:

[0025] (5-1) Define the spatial axis frequency f according to the principle that a fluctuation occurs once in one period. sp and through Calculate the frequency resolution Δf;

[0026] (5-2) The spatially distributed pressure coefficient sequence x(s) is subjected to a fast Fourier transform on a spatial scale using the following formula to obtain the spatial frequency domain pressure coefficient sequence X(f):

[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 value of pi.

[0029] (5-3) The modulus of the complex number X(f) is calculated by the following formula and normalized by half the number of sampling points of the spatially distributed pressure coefficient sequence to obtain |X(f)|. nor :

[0030]

[0031] (5-4) With f*Δf as the x-coordinate, |X(f)| nor Plot the spatial spectrum of the pressure signal using the vertical axis as the ordinate; where the horizontal axis ranges from 0 to 1.

[0032] Furthermore, step six specifically includes:

[0033] Based on the spatial spectrum diagram drawn in step (5-4), the frequency through which the space blade passes is denoted as f. c =num×f sp num represents the number of impeller blades. The steady index Ste, representing the amplitude of the unsteady pressure pulsation blade frequency in a centrifugal pump, is calculated using the following formula:

[0034]

[0035] Furthermore, step three specifically includes:

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

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

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

[0039] Furthermore, step two includes:

[0040] (2-1) Inspect the fluid domain to ensure that there are no fragments or broken surfaces, and name the fluid domain;

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

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

[0043] (2-4) Perform CFD steady-state simulation calculations.

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

[0045] This invention, based on steady-state CFD numerical simulation, extracts the steady-state pressure field structure of the dynamic-static interference region of a centrifugal pump. The resulting characterization method can accurately represent the unsteady pressure pulsation characteristics. This method eliminates the need for time-consuming unsteady calculations and costly experimental testing, saving computational resources and manpower. The steady-state indices proposed in this invention can serve as an important basis for comparing pressure pulsation characteristics during the optimization process of low-pulsation centrifugal pumps, significantly shortening the optimization design cycle of low-pulsation centrifugal pumps. Attached Figure Description

[0046] Figure 1 This is a basic flowchart of the method for characterizing the amplitude of unsteady pressure pulsation blade frequency in a centrifugal pump based on steady-state calculation, as described in this invention.

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

[0048] Figure 3 This is a schematic diagram showing the location of the impeller outlet monitoring point in an embodiment of the present invention.

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

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

[0051] Figure 6 This is a spatial spectrum obtained by the spatial scale fast Fourier transform in an embodiment of the present invention.

[0052] Figure 7 The geometric models of the three impellers used to verify the accuracy of the method proposed in this invention are shown in the left figure, the middle figure, and the right figure. The number of blades is 6, the number of blades is 7, and the number of blades is 8.

[0053] Figure 8 This is a correlation fitting graph used in embodiments of the present invention to verify the steady-state index obtained by the proposed method and the pressure pulsation blade frequency amplitude obtained by unsteady calculation. The left graph shows the correlation between the steady-state index obtained by the proposed method and the unsteady calculation.d The fitting results under the operating conditions, with the middle figure showing the results at 1.2Q. d The fitting results under the operating conditions are shown in the right figure at 1.4Q. d Fitting results under operating conditions. Detailed Implementation

[0054] The present invention will be described in detail below with reference to the accompanying drawings and preferred embodiments. The purpose and effects of the present invention will become clearer. It should be understood that the specific embodiments described herein are merely for explaining the present invention and are not intended to limit the present invention.

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

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

[0057] The specific process for establishing the fluid domain of a centrifugal pump is as follows:

[0058] Based on design requirements, use 3D modeling software to complete the basic geometric structure modeling of the centrifugal pump's fluid domain, such as... Figure 2 As shown, the model includes the inlet pipe, impeller, guide vanes, volute, and outlet pipe, serving as the watershed model for subsequent analysis.

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

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

[0061] (2-1) Inspect the watershed for any broken sections or surfaces, and name the watershed.

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

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

[0064] (2-4) For rated operating condition 1.0Q d Perform CFD steady-state simulation calculations.

[0065] S03, Extraction of steady-state pressure field based on steady-state calculation.

[0066] The specific process for extracting the steady-state pressure field is as follows:

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

[0068] (3-2) Establish the plane containing the surface where the impeller span = 0.5 and the mid-section of the volute;

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

[0070] S04 generates a spatial distribution sequence of pressure based on the steady-state pressure field and performs dimensionless transformation.

[0071] The specific process of generating and dimensionlessly converting the spatial distribution sequence of pressure is as follows:

[0072] (4-1) Generate the coordinates (m) of the impeller outlet monitoring point s ,n s ), where s is the discrete spatial index. To ensure no energy leakage at the leaf frequency, we take 0 ≤ s ≤ 360k⁻¹, and s ∈ Z, where k takes the values ​​1, 2, 3, ..., i.e., the number of sampling points N = 360k, and the sampling frequency F s = k(1 / °);

[0073] Where, m s and n s Calculated using the following formula:

[0074]

[0075] In the above formula, R m R is the radius of the circle containing the monitoring point. m The reference range 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 of the circle containing the exit monitoring point is... m =130mm, preferably, take k=1, then 0≤s≤359, and s∈Z, the polar coordinate angle of the monitoring point The calculated coordinates of the exit monitoring points are shown in Table 1, and the locations of the exit monitoring points are as follows: Figure 3 As shown. In this embodiment, the spatial sampling period T = 1°, and the spatial sampling frequency F s =1 (1 / °), number of sampling points N = 360.

[0077] Table 1 Coordinates of the Impeller Outlet Monitoring Points

[0078]

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

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

[0081] (4-4) According to the following formula, x(m) s ,n s After removing the mean and dimensionless transformation, the spatially distributed pressure coefficient sequence x(s) is obtained:

[0082]

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

[0084] Table 2 Pressure and pressure coefficient at each monitoring point

[0085]

[0086] S05, Perform a Fast Fourier Transform on the spatial scale for the spatially distributed pressure coefficient sequence x(s). The specific process is as follows:

[0087] (5-1) Define the spatial axis frequency f according to the principle that a fluctuation occurs once in one period. sp and through Calculate the frequency resolution Δf;

[0088] In this embodiment, spatial axis frequency

[0089] (5-2) The spatially distributed pressure coefficient sequence x(s) is subjected to a fast Fourier transform on a spatial scale using the following formula to obtain the spatial frequency domain pressure coefficient sequence X(f):

[0090]

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

[0092] (5-3) The modulus of the complex number X(f) is calculated by the following formula, and then normalized by half the number of sampling points of the spatially distributed pressure coefficient sequence to obtain |X(f)|. nor :

[0093]

[0094] (5-4) With f*Δf as the x-coordinate, |X(f)| nor Plot the spatial spectrum of the pressure signal using the vertical axis as the ordinate; where the horizontal axis ranges from 0 to 1. In this embodiment, the x-axis range is 0 ≤ f * Δf ≤ 0.5, and the unit is (1 / °). The fast Fourier transform process in this embodiment is as follows: Figure 5 As shown, the obtained spatial spectrum is as follows: Figure 6 As shown.

[0095] S06, based on the transformation results, forms a quantitative index of unsteady pressure pulsation blade frequency.

[0096] Based on the spatial spectrum diagram drawn in step (5-4), the frequency through which the space blade passes is denoted as f. c =num×f sp num represents the number of impeller blades. The steady index Ste, representing the amplitude of the unsteady pressure pulsation blade frequency in a centrifugal pump, is calculated using the following formula:

[0097]

[0098] In this embodiment, the centrifugal pump used has 7 blades, i.e., num = 7, then f c =7 × 0.00278 = 0.01946, therefore

[0099] On a workstation with 64 cores, calculating a steady-state operating condition using the method proposed in this invention takes approximately 3 hours, while calculating a non-steady-state operating condition using traditional methods takes about 3 days. Therefore, this method significantly reduces computation time and is a rapid method for characterizing the amplitude of non-steady-state pressure fluctuations.

[0100] To verify the accuracy of this invention, the calculation results of the unsteady index Ste proposed in this embodiment and the pressure pulsation blade frequency amplitude obtained from unsteady simulation calculations were compared. ( R represents the radius of the circle where the impeller outlet is located. m Correlation analysis was performed on the average value of the unsteady pressure pulsation blade frequency amplitude at 30 monitoring points evenly distributed around the circumference of 130 mm. The validation model used in this embodiment consisted of three impellers with 6, 7, and 8 blades (e.g.,...). Figure 7 As shown), the method proposed in this invention was used to obtain the product at 1.0q. d 1.2q d and 1.4q d The unsteady indexes under three operating conditions are calculated, and then the unsteady pressure pulsation frequency amplitude is calculated. Figure 8 This is a correlation fitting graph showing the relationship between the steady-state index obtained using the method proposed in this invention and the pressure pulsation blade frequency amplitude obtained from unsteady calculations in this embodiment of the invention.

[0101] In 1.0q d 1.2Q d and 1.4Q dThe correlation coefficient is calculated under the three operating conditions as follows:

[0102]

[0103] Where, σ Ste and They represent Ste and Standard deviation; E[Ste] and They represent Ste and The mathematical expectation.

[0104] Table 3 shows the correlation analysis results of the steady index and unsteady pressure pulsation amplitude obtained by the method proposed in this invention for the three impellers under various operating conditions.

[0105] Table 3. Results of Correlation Analysis

[0106]

[0107] As shown in Table 3, when the flow rate is 1.0Q d 1.2q d and 1.4q d At that time, Ste and The correlation coefficients between them were 0.98698, 0.99938, and 0.99864, respectively, indicating that under the same working conditions, Ste and It exhibits a highly linear relationship. Furthermore, through cross-analysis of the three operating conditions, the correlation coefficient of the nine sets of data was 0.98141, further illustrating the strong linear relationship between Ste and... It maintains a high linear relationship under different operating conditions. Therefore, the characterization quantity Ste obtained by the calculation method proposed in this invention can effectively characterize the amplitude of unsteady pressure pulsation blade frequency.

[0108] It will be understood by those skilled in the art that the above descriptions are merely preferred examples of the invention and are not intended to limit the invention. Although the invention has been described in detail with reference to the foregoing examples, those skilled in the art can still modify the technical solutions described in the foregoing examples or make equivalent substitutions for some of the technical features. All modifications and equivalent substitutions made within the spirit and principles of the invention should be included within the scope of protection of the invention.

Claims

1. A method for characterizing the impeller frequency amplitude of unsteady pressure pulsation in a centrifugal pump based on steady-state calculations, characterized in that, Includes the following steps: Step 1: Establish the fluid domain of the centrifugal pump; Step 2: Perform steady-state CFD simulation calculations on the established fluid domain; Step 3: Extract the steady-state pressure field based on steady-state calculations; Step 4: Generate a spatial distribution sequence of pressure based on the steady-state pressure field and perform dimensionless transformation; Step 5: Perform a Fast Fourier Transform on the spatial scale of the dimensionless pressure spatial distribution sequence obtained in Step 4; Step 5 includes the following sub-steps: (5-1) Define spatial axis frequency based on the principle that a fluctuation occurs once in one period. and through Calculate frequency resolution ;in, N represents the sampling frequency, and N represents the number of sampling points; (5-2) The pressure coefficient sequence of spatial distribution is obtained by the following formula. Performing a Fast Fourier Transform on a spatial scale yields the pressure coefficient sequence in the spatial frequency domain. : ； in, For discrete frequency indexing, and , The imaginary unit, Pi; (5-3) Calculate complex numbers using the following formula The modulus is obtained by normalizing half the number of sampling points of the spatially distributed pressure coefficient sequence. : ； (5-4) with The x-axis is... Plot the spatial spectrum of the pressure signal using the vertical axis as the ordinate; where the horizontal axis ranges from 0 to 1. ; Step Six: Based on the spatial fast Fourier transform results from Step Five, a quantitative index of unsteady pressure pulsation blade frequency is generated.

2. The method for characterizing the impeller frequency amplitude of unsteady pressure pulsation in a centrifugal pump based on steady-state calculation according to claim 1, characterized in that, Step four specifically includes: (4-1) Generate the coordinates of the impeller outlet monitoring point , For discrete spatial indexing, to ensure no energy leakage at the leaf frequency, we take... and ,in That is, the number of sampling points sampling frequency ; (4-2) Set the coordinates of the monitoring points Import into post-processing software; (4-3) Export the pressure data of each monitoring point ; (4-4) According to the following formula, After removing the mean and dimensionless transformation, the spatially distributed pressure coefficient sequence is obtained. : ； in, The density of the pumped liquid, denoted as circumferential velocity at the impeller outlet.

3. The method for characterizing the impeller frequency amplitude of unsteady pressure pulsation in a centrifugal pump based on steady-state calculation according to claim 2, characterized in that, and Calculated using the following formula: ； in, The radius of the circle containing the monitoring point. The reference range is ; The polar coordinate angle of the monitoring point. .

4. The method for characterizing the impeller frequency amplitude of unsteady pressure pulsation in a centrifugal pump based on steady-state calculation according to claim 3, characterized in that, Step six specifically includes: Based on the spatial spectrum diagram drawn in step (5-4), the spatial blades are denoted by their frequencies as follows: , Given the number of impeller blades, calculate the steady index of the unsteady pressure pulsation blade frequency amplitude of the centrifugal pump according to the following formula. : 。 5. The method for characterizing the impeller frequency amplitude of unsteady pressure pulsation in a centrifugal pump based on steady-state calculation according to claim 1, characterized in that, Step three specifically includes: (3-1) Import the calculation results of steady CFD simulation into the post-processing software; (3-2) Establish the intermediate cross-section of the impeller and volute; (3-3) Generate a steady-state pressure field on the cross section.

6. The method for characterizing the impeller frequency amplitude of unsteady pressure pulsation in a centrifugal pump based on steady-state calculation according to claim 1, characterized in that, Step two includes: (2-1) Inspect the fluid domain to ensure that there are no flakes or broken surfaces, and name the fluid domain; (2-2) Use mesh generation software to mesh the fluid domains of each part of the centrifugal pump; (2-3) Import the mesh into the CFD simulation software and set the boundary conditions and solution method in the CFD simulation software; (2-4) Perform CFD steady-state simulation calculations.

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