A method for analyzing the influence of centrifugal pump blade error on flow field

Abstract

The application discloses a kind of methods for analyzing the influence of centrifugal pump blade error on flow field, including calculating the airfoil coordinate of centrifugal pump blade after considering machining error, calculating the pressure and velocity values corresponding to the discrete points of the center section of centrifugal pump flow field according to the airfoil coordinate, constructing PCE proxy model using the pressure and velocity values corresponding to the discrete points of the center section of centrifugal pump flow field and the random variables of machining error, extracting random variables using Sobol to obtain random variable matrix, inputting random variable matrix into PCE proxy model, and calculating the estimation of the influence of random variables on flow field using Monte Carlo algorithm.The application uses PCE model to describe the complex nonlinear relationship between centrifugal pump pressure, velocity field and airfoil machining error uncertainty, and then performs sensitivity analysis on the quantized uncertainty parameters to obtain the influence of machining error on centrifugal pump pressure and velocity field.

Description

Technical Field

[0001] This invention belongs to the field of error-induced flow field analysis, and particularly relates to a method for analyzing the influence of centrifugal pump blade errors on the flow field. Background Technology

[0002] Airworthiness regulations for aircraft engines stipulate that the expected probability of a hazardous engine consequence occurring does not exceed the defined minimum probability (1e-7 to 1e-9 times per engine flight hour). In the design of aircraft engines and related products, any potential factors that could jeopardize engine safety must be thoroughly studied to ensure the flight safety of the aircraft platform and passengers. The primary function of the aviation fuel centrifugal pump is to pre-pressurize fuel from the aircraft's fuel tanks before supplying it to the engine combustion chamber to generate thrust; its performance stability is crucial to ensuring the safe and reliable operation of aircraft engines.

[0003] Aero engines operate under highly variable flight conditions, including start-up, idle, subsonic cruise, and supersonic speeds across their entire flight envelope. Under these varying conditions, the inlet pressure, speed, and temperature of the fuel pump change constantly. In these harsh environments, the actual operating conditions of the fuel centrifugal pump face significant uncertainty, often deviating from its original design parameters. Furthermore, the blades of the fuel centrifugal pump exhibit diverse three-dimensional structures, including bends, twists, and sweeps. Machining these complex geometric blades presents extremely high challenges. Random errors are unavoidable in the machining of centrifugal pump blades due to factors such as tool geometry errors, tool trajectory accuracy errors, and machining deformation caused by residual stress.

[0004] Uncertainties arising from operating conditions and manufacturing errors can cause deviations in the performance of fuel centrifugal pumps, posing a potential threat to engine safety. Current centrifugal pump design primarily employs traditional deterministic design methods, which struggle to quantify the impact of manufacturing errors and operating condition uncertainties on the overall performance of the fuel centrifugal pump. As the performance and robustness requirements of centrifugal pumps continue to increase, the impact of manufacturing errors and operating condition uncertainties on fuel pump performance can no longer be ignored.

[0005] Therefore, to address the uncertainty problem of blade machining error in fuel centrifugal pumps, this invention provides a method for quantifying the impact of blade machining error uncertainty based on KL decomposition, PCE surrogate model, and Sobol sensitivity analysis, thus offering a new quantitative method for analyzing the internal flow field error of fuel centrifugal pumps. Summary of the Invention

[0006] The purpose of this invention is to provide a method for analyzing the influence of centrifugal pump blade errors on the flow field, so as to solve the problem that the flow field error caused by the uncertainty of the machining error of aviation fuel centrifugal pump blades cannot be quantified.

[0007] This invention employs the following technical solution: a method for analyzing the influence of centrifugal pump blade errors on the flow field, comprising:

[0008] Step 1: Calculate the airfoil coordinates of the centrifugal pump blades after considering manufacturing errors;

[0009] Step 2: Calculate the pressure and velocity values ​​corresponding to discrete points at the center section of the centrifugal pump flow field based on the airfoil coordinates;

[0010] Step 3: Construct a PCE surrogate model using the pressure and velocity values ​​corresponding to discrete points at the center section of the centrifugal pump flow field and the random variables of machining errors;

[0011] Step 4: Use Sobol to extract random variables and obtain a random variable matrix;

[0012] Step 5: Input the random variable matrix into the PCE surrogate model and use the Monte Carlo algorithm to calculate the estimate of the influence of random variables on the flow field.

[0013] Furthermore, the method for calculating the airfoil coordinates in step 1 is as follows:

[0014]

[0015] In the formula, ξ is the average airfoil coordinate at the curvilinear coordinate s; i Let be a random variable representing processing error; is the unit normal vector of the airfoil surface; d is the dimension of the random variable;

[0016] in,

[0017] In the formula, λ i ω represents the eigenvalues ​​of the covariance kernel; l represents the eigenvalue length; ω represents the eigenvalues ​​of the kernel. i The weight of the i-th feature value;

[0018] in,

[0019] In the formula, φ i It is the characteristic function of the covariance kernel; a = s max / 2,

[0020] Where, ω i The calculation method is as follows:

[0021] The dimension d of the random variable is calculated as follows:

[0022]

[0023] In the formula, the value of d constrains the range of i, i∈[1,2,…,d].

[0024] Furthermore, the method for calculating the estimator of the main index of the influence of random variables on the flow field in step 5 is as follows:

[0025]

[0026] In the formula, N is the number of random variable samples required for the quasi-Monte Carlo estimator, j is the j-th random variable sample group, which is generally taken as 30,000 to 50,000; A and B are both random variable groups sampled by Sobol sampling. To construct a random vector group y by replacing the i-th column of random vector group B with the i-th column of random variable group A, A These are the pressure and velocity values ​​corresponding to discrete points on the central cross-section of the centrifugal pump flow field, obtained from the PCE model, when the input is a set of random variables A. When the input is a set of random variables At that time, the pressure and velocity values ​​corresponding to discrete points of the central section of the centrifugal pump flow field obtained from the PCE model; Let y be the matrix A The mean.

[0027] Furthermore, the method for calculating the estimate of the total index of the influence of random variables on the flow field in step 5 is as follows:

[0028]

[0029] In the formula, N is the number of random variable samples required for the quasi-Monte Carlo estimator, j is the j-th random variable sample group, which is generally taken as 30,000 to 50,000; A and B are both random variable groups sampled by Sobol sampling. To construct a random vector group y by replacing the i-th column of random vector group B with the i-th column of random variable group A, A Let y be the pressure and velocity values ​​corresponding to discrete points on the central cross-section of the centrifugal pump flow field obtained from the PCE model when the input is a set of random variables A. B These are the pressure and velocity values ​​corresponding to discrete points on the central cross-section of the centrifugal pump flow field, obtained from the PCE model, when the input is a set of random variables B. When the input is a set of random variables At that time, the pressure and velocity values ​​corresponding to discrete points of the central section of the centrifugal pump flow field obtained from the PCE model; Let y be the matrix A The mean.

[0030] The beneficial effects of this invention are:

[0031] This invention utilizes KL blade profile decomposition to effectively quantify the processing error of blade profiles and reduces the processing error of high-dimensional blades to the superposition of random vector perturbations at key locations. The vector densification processing of the blade inlet wedge shape accurately fits the actual processing accuracy at the inlet of the blade profile.

[0032] This invention utilizes the PCE model to describe the complex nonlinear relationship between the pressure and velocity fields of a centrifugal pump and the uncertainty of blade machining errors. Then, it performs sensitivity analysis on the quantified uncertainty parameters to obtain the influence law of machining errors on the pressure and velocity fields of the centrifugal pump, providing a new method for the design, manufacturing and optimization of centrifugal pump structures.

[0033] This invention is highly operable, has high simulation accuracy, short calculation time, and low implementation cost. It eliminates the need for traditional experimental verification methods used to address uncertainties in processing and significantly improves the design and optimization efficiency of centrifugal pumps.

[0034] This invention is based on the Karhuben-Loève method for calculating the machining error of centrifugal pump blades. It can characterize the overall airfoil error using very few random variables, making it extremely simple and easy to use in the field of error analysis. Attached Figure Description

[0035] Figure 1 The direction of the blade machining error disturbance vector in Embodiment 1 of the present invention;

[0036] Figure 2 Example 1ω of the present invention i The solution diagram;

[0037] Figure 3 This refers to 50 samples of the blade-shaped machining error in Embodiment 1 of the present invention;

[0038] Figure 4 This refers to the fluid domain of the fuel centrifugal pump in Embodiment 1 of the present invention;

[0039] Figure 5 (a) shows the pressure field proxy model prediction results for some working conditions in Embodiment 1 of the present invention;

[0040] Figure 5 (b) shows the velocity field proxy model prediction results for some working conditions in Embodiment 1 of the present invention;

[0041] Figure 6 Sensitivity analysis based on centrifugal pump pressure reconstruction under multiple operating conditions in Embodiment 1 of the present invention;

[0042] Figure 7 This is a sensitivity analysis of centrifugal pump velocity field reconstruction under multiple operating conditions in Embodiment 1 of the present invention. Detailed Implementation

[0043] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0044] The structures, proportions, sizes, etc., shown in the accompanying drawings of this specification are only for the purpose of assisting those skilled in the art in understanding and reading the content disclosed in the specification, and are not intended to limit the conditions under which the present invention can be implemented. Therefore, they have no substantial technical significance. Any modifications to the structure, changes in the proportions, or adjustments to the size, without affecting the effects and objectives that the present invention can produce, should still fall within the scope of the technical content disclosed in the present invention.

[0045] The manufacturing technology and quality of centrifugal pump blades directly affect the pump's output, efficiency, stability, reliability, and service life. Therefore, in the manufacturing process of aviation fuel centrifugal pump impeller blades, five-axis CNC machining is typically used to ensure manufacturing quality. However, during machining, the cutting force, clamping force, and gravity can cause deformation, disrupting the correct relative position between the tool and the blade, leading to machining errors. These machining errors randomly fluctuate along the blade's normal direction. Figure 1 As shown.

[0046] This invention discloses a method for analyzing the influence of centrifugal pump blade errors on the flow field, comprising the following five steps.

[0047] Step 1: Calculate the airfoil coordinates of the centrifugal pump blades after considering manufacturing errors based on the Karhuben-Loève model.

[0048] The method for calculating airfoil coordinates is as follows:

[0049]

[0050] In the formula, ξ is the average airfoil coordinate at the curvilinear coordinate s; i Let be a random variable representing processing error; is the unit normal vector of the airfoil surface; d is the dimension of the random variable;

[0051] in,

[0052] In the formula, λ i ω represents the eigenvalues ​​of the covariance kernel; l is the eigenvalue length; ω i The weight of the i-th feature value;

[0053] in,

[0054] In the formula, φ i It is the characteristic function of the covariance kernel; a = s max / 2,

[0055] Where, ω i The calculation method is as follows:

[0056] The dimension d of the random variable is calculated as follows:

[0057]

[0058] In the formula, the value of d constrains the range of i, i∈[1,2,…,d].

[0059] Based on the quantification of processing error obtained through KL decomposition, uncertainty analysis is performed by combining chaotic polynomial expansion.

[0060] Step 2: Calculate the pressure and velocity values ​​corresponding to discrete points on the central section of the centrifugal pump flow field based on the airfoil coordinates.

[0061] This invention uses computational fluid dynamics software to calculate the pressure and velocity values ​​corresponding to discrete points on the central cross section of the centrifugal pump flow field, including but not limited to ANSYS FLUENT, CFX, or Pumplinx.

[0062] Step 3: Construct a PCE surrogate model using the pressure and velocity values ​​corresponding to discrete points at the center section of the centrifugal pump flow field and the random variables of machining errors.

[0063] Step 4: Use Sobol to extract random variables and obtain the random variable matrix.

[0064] A 2n-dimensional matrix with N random variable samples is drawn using a Sobol sequence. The first n columns are used as matrix A, and the last n columns are used as matrix B. Then, the i-th column of matrix B is replaced with the i-th column of matrix A to construct... The matrix i∈[1,2,…,d], where d is the dimension of the random variable.

[0065] Let y A(j)j＝1，…，N y B(j)j＝1，…，N and Represents A, B and The output value is then input into the PCE proxy model.

[0066] Step 5: Input the random variable matrix into the PCE surrogate model and use the Monte Carlo algorithm to calculate the estimate of the influence of random variables on the flow field.

[0067] The quasi-Monte Carlo estimator of the main indicator is calculated as follows:

[0068]

[0069] In the formula, N is the number of random variable samples required for the quasi-Monte Carlo estimator, j is the j-th random variable sample group, which is generally taken as 30,000 to 50,000; A and B are both random variable groups sampled by Sobol sampling. To construct a random vector group y by replacing the i-th column of random vector group B with the i-th column of random variable group A, A These are the pressure and velocity values ​​corresponding to discrete points on the central cross-section of the centrifugal pump flow field, obtained from the PCE model, when the input is a set of random variables A. When the input is a set of random variables At that time, the pressure and velocity values ​​corresponding to discrete points of the central section of the centrifugal pump flow field obtained from the PCE model; Let y be the matrix A The mean.

[0070] The quasi-Monte Carlo estimator of the overall index is calculated as follows:

[0071]

[0072] In the formula, N is the number of random variable samples required for the quasi-Monte Carlo estimator, j is the j-th random variable sample group, which is generally taken as 30,000 to 50,000; A and B are both random variable groups sampled by Sobol sampling. To construct a random vector group y by replacing the i-th column of random vector group B with the i-th column of random variable group A, A Let y be the pressure and velocity values ​​corresponding to discrete points on the central cross-section of the centrifugal pump flow field obtained from the PCE model when the input is a set of random variables A. B These are the pressure and velocity values ​​corresponding to discrete points on the central cross-section of the centrifugal pump flow field, obtained from the PCE model, when the input is a set of random variables B. When the input is a set of random variables At that time, the pressure and velocity values ​​corresponding to discrete points of the central section of the centrifugal pump flow field obtained from the PCE model; Let y be the matrix A The mean.

[0073] Example 1

[0074] Based on KL expansion calculations, it is found that each flow surface profile under uncertainty is composed of three eigenvalues ​​ξ. i The (i = 1, 2, 3) control, namely the hydrofoil shape on the middle surface, consists of three parameters that together quantify the blade error of the centrifugal pump.

[0075] Figure 2 The process of solving for the eigenvalues ​​is illustrated by using the values ​​on the left side of the equation as the ordinate, ω. i The x-coordinate represents the value of ω when the left side of the equation equals 0. i For specific solutions.

[0076] Figure 3The figure shows 50 samples of the impeller profile of the intermediate flow surface when the machining error is 0.6 mm. As can be seen from the figure, the method of quantifying the blade machining error by superimposing random disturbance vectors along the blade profile is consistent with the actual machining situation. In particular, the vector densification processing at the leading edge of the blade makes the blade inlet radius transition smoothly, which can increase the accuracy of error quantification.

[0077] Table 1 shows the specific data of 50 sets of random quantities obtained from KL expansion. During centrifugal pump operation, in addition to impeller machining errors, uncertainties in operating conditions also exist during the pump's operation. In this embodiment, 1% uncertainty in operating conditions is used as the quantification error, and 11-dimensional uncertainty parameters are input to explore the feedback of the flow field and performance within the centrifugal pump under uncertainty.

[0078] Table 1. Blade machining error under design conditions

[0079]

[0080]

[0081] Based on the specific processing error quantities of the 50 sets of random quantities in Table 1, and simultaneously constructing a model using 3D modeling software, the 3D model derived from a set of data is as follows: Figure 4 As shown.

[0082] A surrogate model for the centrifugal pump's head and efficiency was constructed using the LAR-PCE surrogate model and stored in the numerical software. The pressure and velocity field prediction results for some operating conditions are shown below. Figure 5 As shown.

[0083] Figure 6 Sensitivity analysis of centrifugal pump pressure coefficient field reconstruction under multiple operating conditions is presented in the figure. It can be seen that operating condition uncertainty has a greater impact on the internal flow field of the centrifugal pump than manufacturing uncertainty. Uncertainty in blade geometry parameters affects the blade inlet and mid-section. Rotational speed and flow rate fluctuations have significant sensitivity to the entire flow field. Under low-flow-rate conditions, rotational speed fluctuation is the main parameter causing changes in the internal flow field. Under both design and high-flow-rate conditions, blade manufacturing errors and operational uncertainties have similar effects on the centrifugal pump pressure coefficient field, with relatively small impacts on the pressure field distribution.

[0084] Figure 7 Sensitivity analysis of centrifugal pump velocity coefficient field reconstruction under multiple operating conditions is presented in the figure. It can be seen that both operating condition uncertainties and manufacturing uncertainties affect the centrifugal pump velocity coefficient field, with the impact concentrated in the lower left corner of the mid-section and the left side of the blade tongue region. Under low-flow conditions, rotational speed fluctuations are the main parameter causing changes in the velocity coefficient field. Under design and high-flow conditions, the uncertainty of blade manufacturing errors has a relatively small impact on the centrifugal pump velocity coefficient field.

[0085] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for analyzing the effect of centrifugal pump blade errors on the flow field, characterized in that, include: Step 1: Calculate the airfoil coordinates of the centrifugal pump blades after considering manufacturing errors. The calculation method for the airfoil coordinates is as follows: ， In the formula, Curve coordinates The average airfoil coordinates at the location; Let be a random variable representing processing error; is the unit normal vector of the airfoil surface; d is the dimension of the random variable; in, , In the formula, These are the eigenvalues ​​of the covariance kernel; The characteristic length; For the first The weights of each feature value; in, , In the formula, It is the characteristic function of the covariance kernel; , in, The calculation method is as follows: ; The dimension d of the random variable is calculated as follows: ， In the formula, the value of d constrains... Scope ; Step 2: Calculate the pressure and velocity values ​​corresponding to discrete points at the center section of the centrifugal pump flow field based on the airfoil coordinates; Step 3: Construct a PCE surrogate model using the pressure and velocity values ​​corresponding to discrete points at the center section of the centrifugal pump flow field and the random variables of machining errors; Step 4: Use Sobol to extract random variables and obtain a random variable matrix; Step 5: Input the random variable matrix into the PCE surrogate model and use the Monte Carlo algorithm to calculate the estimate of the influence of random variables on the flow field.

2. The method for analyzing the influence of centrifugal pump blade errors on the flow field according to claim 1, characterized in that, The method for calculating the estimators of the main indices of the influence of random variables on the flow field in step 5 is as follows: ， In the formula, N is the number of random variable samples required for the quasi-Monte Carlo estimator, and j is the j-th random variable sample. , All are random variable sets sampled from Sobol. To use a set of random variables The Column replacement random vector group Constructed random vector group, When the input is a set of random variables At that time, the pressure and velocity values ​​corresponding to discrete points at the center section of the centrifugal pump flow field obtained from the PCE model are... When the input is a set of random variables At that time, the pressure and velocity values ​​corresponding to discrete points of the central section of the centrifugal pump flow field obtained from the PCE model; For matrix The mean.

3. The method for analyzing the influence of centrifugal pump blade errors on the flow field according to claim 1, characterized in that, The method for calculating the estimate of the total index of the influence of random variables on the flow field in step 5 is as follows: In the formula, N is the number of random variable samples required for the quasi-Monte Carlo estimator, and j is the j-th random variable sample. , All are random variable sets sampled from Sobol. To use a set of random variables The Column replacement random vector group Constructed random vector group, When the input is a set of random variables At that time, the pressure and velocity values ​​corresponding to discrete points at the center section of the centrifugal pump flow field obtained from the PCE model are... When the input is a set of random variables At that time, the pressure and velocity values ​​corresponding to discrete points at the center section of the centrifugal pump flow field obtained from the PCE model are... When the input is a set of random variables At that time, the pressure and velocity values ​​corresponding to discrete points of the central section of the centrifugal pump flow field obtained from the PCE model; For matrix The mean.

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