Ensemble Kalman filtering turbulence model assimilation method based on full-field similarity criterion

Abstract

The invention discloses an ensemble Kalman filtering turbulence model assimilation method based on a full-field similarity criterion, and the method comprises the steps: carrying out the sensitivity analysis of a coefficient of a candidate turbulence model, and obtaining a sensitivity coefficient and a value range to be subjected to Latin hypercube sampling, namely, a sampling interval; a model constant sample combination is extracted in a sampling interval through a directional Latin hypercube sampling method, and a target flow field result is obtained through calculation; a data assimilation algorithm based on an ensemble Kalman filtering algorithm is adopted for the target flow field result and the model constant sample combination, after an optimized model constant combination is obtained, cyclic updating and convergence verification are conducted on the model constant combination, and an optimal model parameter combination is obtained; and finally, performing high-similarity simulation on the internal flow field of the fuel assembly in the pressurized water reactor core through the improved turbulence model. According to the method, an objective evaluation standard of full physical field similarity can be provided for a data assimilation method, the convergence speed of the algorithm is remarkably improved, the robustness of the algorithm is enhanced, and the calculation overhead of the algorithm is reduced.

Description

Technical Field

[0001] The present invention relates to a technology in the field of nuclear reactor simulation, in particular to an ensemble Kalman filter turbulence model assimilation method based on the full-field similarity criterion for inversion of turbulence model constants of secondary flow in a rod bundle channel. Background Art

[0002] The standard turbulence model is often used to numerically simulate the internal flow phenomena of existing complex nuclear reactor systems. However, there is an unacceptable engineering error between the prediction results of this model and the experimental results, which leads to design obstacles for nuclear reactor systems. The existing ensemble Kalman filter (EnKF) algorithm can calibrate the model constants of the existing turbulence model and improve the prediction ability of the turbulence model. However, the existing EnKF technology uses a random sampling method, which has a large computational overhead, and has problems such as constant overshoot, low algorithm robustness, and unreasonable evaluation basis for data assimilation effect. Summary of the invention

[0003] Aiming at the problems that the prediction results of the reactor internal flow field by the existing turbulence model are too different from the experimental results, the accuracy of the existing data assimilation results is low, and the computational cost in the data assimilation process is high, the present invention proposes an ensemble Kalman filter turbulence model assimilation method based on the full-field similarity criterion. By using the similarity between the field data of the experimentally observed physical quantity and the field data of the numerical simulation predicted value as the criterion of the data assimilation effect of the nonlinear k-ε turbulence model, an objective evaluation standard of the full physical field similarity is provided for the data assimilation method, which significantly improves the convergence speed of the algorithm, enhances the robustness of the algorithm, and reduces the computational cost of the algorithm.

[0004] The present invention is achieved through the following technical solutions:

[0005] The invention relates to an ensemble Kalman filter turbulence model assimilation method based on a full-field similarity criterion. The method performs sensitivity analysis on coefficients of a candidate turbulence model to obtain sensitive coefficients and their value ranges to be sampled by Latin hypercube, i.e., sampling intervals. A model constant sample combination is extracted in the sampling interval by a directional Latin hypercube sampling method to calculate a target flow field result. A data assimilation algorithm based on an ensemble Kalman filter algorithm is used for the target flow field result and the model constant sample combination to obtain an optimized model constant combination. The model constant combination is then cyclically updated and converged for verification to obtain an optimal model parameter combination. Finally, an internal flow field of a fuel assembly in a pressurized water reactor core is simulated with high similarity by an improved turbulence model.

[0006] The sensitivity analysis mentioned above refers to: calculating each model constant θ i The sensitivity coefficient According to the sensitivity coefficient S i The absolute value of the model constant θ is used to determinei Is it sensitive, where: i = 1…n, step size Δ = 0.05θ i .

[0007] The Latin hypercube sampling method is implemented by, but not limited to, the technology described in MCKAY MD, BECKMAN RJ, CONOVER WJ. Comparison of Three Methods for Selecting Values ​​of Input Variables in the Analysis of Output from a Computer Code ([J / OL]. Technometrics, 1979, 21(2): 239-245. DOI: 10.1080 / 00401706.1979.10489755.).

[0008] The target flow field result is obtained by performing numerical simulation of the flow field under the same working condition according to each set of model constants in the model constant sample combination, that is, physical quantities such as velocity and pressure in the flow field in the same region after reaching a steady state.

[0009] The cyclic update means that when the residual ε of the combination of two adjacent rounds of model constant samples is equal to or greater than 0.001, the data assimilation algorithm based on the ensemble Kalman filter algorithm is re-executed.

[0010] The convergence verification refers to: substituting the model constant sample combination into the same working condition example for verification, applying the flow field similarity to determine whether the result is similar to the experimental result, and when the similarity meets the requirements, it means that the constant combination recommended by the algorithm is applicable under the working condition.

[0011] The similarity mentioned above uses the correlation constant to evaluate the similarity between the flow field predicted by the combination of model constants recommended by data assimilation and the experimental results, specifically: Where: the function ρ is the average value of the sum of the cosine values ​​of the angle α between the predicted velocity field x and the velocity vector direction of each measuring point in the PIV flow field y.

[0012] The improved turbulence model refers to: substituting the optimal model parameter combination into the cubic nonlinear k-ε turbulence model.

[0013] The high similarity simulation means that, taking the correlation index ρ as the standard, the correlation between the internal flow field of the fuel assembly calculated by the improved turbulence model and the experimental flow field is significantly higher than the correlation between the calculated flow field of the original turbulence model and the experimental flow field.

[0014] The data assimilation algorithm based on the ensemble Kalman filter algorithm specifically includes:

[0015] a) According to the model constant sample combination given by the directional sampling method and the corresponding calculation, the target flow field, that is, the system state space variable in: u, v represent the velocity components in the x and y directions on the cross section, and Θ is a combination of sensitive parameters.

[0016] b) Calculate the simulated covariance matrix, calculate the experimental error matrix, calculate the Kalman gain, update the set members, convergence judgment and iterative update, where: the simulated covariance matrix C t It refers to: the autocovariance matrix of the target flow field obtained by calculating the combination of model constant samples and the corresponding calculation; the experimental error matrix R refers to: the uncertainty σ of each velocity measurement point given by the PIV experiment PIV , for each velocity measurement point, randomly select a point with a mean of 0 and a variance of σ PIV The error of the normal distribution forms the error matrix r. The experimental error matrix R is the autocovariance matrix of the matrix r; Kalman gain in: C t is a priori set The covariance matrix of .

[0017] The simulated covariance matrix is ​​preferably further corrected by a local correction method based on the spatial correlation length obtained by PIV experimental measurement, specifically: in: is the Hadamard product, P ρ Denotes the covariance matrix C t The weight of the elements in r decreases as the geometric distance increases. i,j is a function of the geometric distance between two points, and d0 is the flow field correlation length.

[0018] c) Take the disturbance Compute the posterior set Due to the nonlinear characteristics of turbulence phenomena and models, one prediction step and multiple update steps are required in the same assimilation round.

[0019] d) Convergence determination: Where: y ob is the experimental measurement value, is the velocity field generated during the assimilation process. When the result does not converge, the calculation of the update phase in step c is repeated.

[0020] The present invention relates to a system for realizing the above method, comprising: a turbulence model screening unit, a model constant sensitivity analysis unit, a directional sampling unit, a numerical simulation unit, a data assimilation unit and a field similarity verification unit, wherein: the turbulence model screening unit performs analysis according to the numerical simulation results of different turbulence models to obtain the optimal turbulence model; the model constant sensitivity analysis unit performs sorting processing on the sensitivity coefficients of the turbulence model constants according to the correlation coefficients to obtain the most sensitive n model constants and form a sensitive model constant vector and its sampling direction and sampling interval; the directional sampling unit performs Latin hypercube sampling according to the sensitive model constant vector and its sampling direction and sampling interval to obtain a sensitive model constant set; the numerical simulation unit performs flow field numerical simulation according to the sensitive model constant set to obtain a simulated flow field; the data assimilation unit performs data assimilation according to the experimentally observed flow field and the simulated flow field to obtain a calibrated sensitive model constant vector; the field similarity verification unit performs field similarity analysis on the calibrated simulated flow field and the experimentally observed flow field obtained by the numerical simulation of the flow field based on the calibrated sensitive model constant vector to obtain the similarity between the calibrated simulated flow field and the experimentally observed flow field. Technical Effects

[0021] The present invention uses sensitivity analysis of turbulence model constants and directional sampling methods to improve the existing data assimilation process; uses a local correction method to improve the existing ensemble Kalman filter algorithm; and uses the cosine similarity between the simulated physical vector field (such as the velocity field) and the experimental physical vector field in the target area to judge the similarity between the two fields. Compared with the prior art, the present invention reduces the numerical simulation calculations required for a round of data assimilation from 100 times to 20 times through sensitivity analysis of turbulence model constants and directional sampling methods. In the assimilation strategy, a multiple iteration method is used to avoid constant overshoot in the optimized turbulence parameters. In the ensemble Kalman filter algorithm, a local correction method is used to improve the calculation stability. The cosine similarity between the simulated physical vector field (such as the velocity field) and the experimental physical vector field in the target area is used as a convergence criterion and optimization criterion to improve the reliability of the optimization criterion. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 It is a flow chart of the present invention;

[0023] Figure 2 It is the flow chart of the ensemble Kalman filter algorithm;

[0024] Figure 3 It is a schematic diagram of the iterative residuals of the modified algorithm and the original algorithm;

[0025] Figure 4 It is a schematic diagram of the test section and the positioning grid;

[0026] In the figure: (a) is a diagram of the PIV experimental device, (b) is a schematic diagram of the 5×5 rod bundle structure, (c) is a cross-section of the fuel assembly, (d) is a top view of the mixing grid with a split-flow mixing wing, and (e) is a schematic diagram of the mixing wing structure;

[0027] Figure 5 Schematic diagram of the rod bundle geometric model;

[0028] In the figure: (a) left view, (b) top view, (c) subchannel top view;

[0029] Figure 6 This is a schematic diagram of sensitivity analysis of turbulence model constants;

[0030] In the figure: Z = 16D h , Y = 0.5P, (a) C ε1 , (b) C ε2 , (c) C' μ , (d)σ e ;

[0031] Figure 7 It is a schematic diagram of the directional sampling method and its effect;

[0032] In the figure: (a) the change of velocity distribution with sampling method, (b) the three-dimensional effect of directional sampling, (c) the two-dimensional effect of directional sampling, (d) the change of model constant residual with assimilation rounds;

[0033] Figure 8 It is a schematic diagram of correlation indicators;

[0034] Fig. 9 It is a schematic diagram of the secondary flow in the sub-channel;

[0035] In the figure: (a) is the experimental flow field, (b) is the flow field predicted by the original model, and (c) is the flow field predicted by the optimized model. DETAILED DESCRIPTION

[0036] like Figure 1 As shown, a method for assimilating an ensemble Kalman filter turbulence model based on a full-field similarity criterion involved in this embodiment includes:

[0037] Step 1) Conduct applicability research on the turbulence model and determine the selected turbulence model;

[0038] Step 2) For the important model constants contained in the selected turbulence model, m sensitive constants are selected in combination with experimental observations to form a sensitive constant set Θ = {θ1, θ2, …, θ m} T ;

[0039] Step 3) Sensitivity analysis: Perform sensitivity analysis on the constants involved in the selected turbulence model and calculate the sensitivity coefficient of the correlation coefficient to the model constant. Select S i The largest first m constants form the sensitive constant vector θ m×1 ; According to the sensitivity coefficient S i Determine the directional sampling direction and interval of each sensitive constant, and directionally extract N groups of sensitive constants to form a sample set;

[0040] Step 4) Numerical simulation: Set the turbulence model sensitivity constant according to the sample set and perform N CFD numerical simulations to obtain the predicted value vector x l×1 ; Step 5) From the model prediction value x, the experimental observation value y exp Starting from the sensitive constant sample set θ, the ensemble Kalman filter algorithm is executed to obtain the calibrated turbulence model constant θ';

[0041] Step 6) Determine whether the optimized turbulence model constant θ' converges, that is, satisfies: ε max =max{(θ'-θ) / θ}<0.001, go to step 7), otherwise repeat step 3), where: ε max is the model constant iterative residual, and max is the maximum value operator;

[0042] Step 7) Let θ = θ', substitute back to the turbulence model in step 4 to perform CFD calculation and obtain the optimized target physical quantity

[0043] Step 8) Compare the experimental measurement result y with the target physical quantity When the optimization result is judged to be acceptable, the function ρ is the sum of the model prediction value x and the experimental observation value y exp The correlation coefficient When it is greater than 0.8, output the optimization model constant θ', otherwise return to step 1) and re-carry out data assimilation, where: U CFD is the time-averaged velocity field in numerical simulation, U EXP is the time-averaged velocity field during experimental observation.

[0044] After specific actual experiments, data assimilation research was carried out on the secondary flow experimental data downstream of a 5×5 rod bundle based on a mixing grid with split-flow mixing wings. The experiment was carried out in the MEdium Scale Hydraulic (MESH) test loop of Shanghai Jiao Tong University. Figure 4 As shown, the length of the 5×5 rod bundle is 1100 mm, the rod diameter D is 9.5 mm, the rod spacing P is 12.6 mm, and the sub-channel hydraulic diameter D h The internal dimension of the test section channel is 66.1×66.1mm. Figure 1(c), the height of the mixing wing is 9.5 mm, the inclination angle is 30°, and the detailed dimensions of the mixing wing are shown in Figure 1 d. Take the plane on the grid as the Z=0 plane and the center of the center rod as the origin of the coordinate system. Figure 4 (b) and (c) are the laboratory coordinate systems. The mainstream velocity in the test condition is 1 m / s. The secondary flow at the cross sections Z = 1Dh, 4Dh, 8Dh and 16Dh downstream of the grid was measured using PIV. The uncertainty of the time-averaged velocity relative to the mainstream velocity was within 0.4%.

[0045] The commercial CFD software STAR-CCM+ was used for modeling and numerical simulation. The geometric model includes two parts: rod bundle and hybrid grid. Figure 5 As shown in (a)(b), the simulation coordinate system is consistent with the experimental coordinate system, the origin of the calculation domain is the center of the central rod, the Z=0 plane is the plane on the grid, and the calculation domain ranges from Z=-10Dh to Z=20Dh. The mesh is a polyhedral mesh, the inlet and outlet parts are stretched meshes, the wall is set to 5 layers of prisms, and the total number of meshes is 32.91 million. The inlet boundary condition is the fully developed flow inside the rod bundle, and the outlet boundary is set to a pressure outlet. Figure 2 As shown in (b), subchannel 7 and Y = 0.5P are selected as the application and evaluation area of ​​the data assimilation method.

[0046] Previous studies have compared the calculation results of the nonlinear eddy viscosity model and the Reynolds stress model. Studies have shown that the nonlinear eddy viscosity model cannot predict the evolution characteristics of the lateral vortex structure. However, the model has a wide range of application value in engineering, so this study selects the model as a candidate model for data assimilation. The standard model equation is as follows, and its model constants are shown in Table 1.

[0047] The equation of the nonlinear eddy viscosity model is specifically: in:

[0048] Table 1 Original coefficients of nonlinear eddy viscosity model

[0049] Table

[0050] Select Figure 5 Subchannel No. 7 selected by the green box in the middle is used as the geometric domain for data assimilation. The above data assimilation strategies and algorithms are applied and evaluated, including parameter sensitivity analysis, application of directional sampling method and covariance matrix correction method, and evaluation of the recommended model constant combination for data assimilation.

[0051] The sensitivity analysis of the nonlinear eddy viscosity model constants is carried out, and the analysis range is shown in Table 2:

[0052] Table 2 Nonlinear eddy viscosity model constant sensitivity analysis range

[0053] For the model constant θ i Calculate sensitivity coefficients Where: step size Δ = 0.05θ i The analysis shows that the constant C ε1 ,C ε2 , C' μ The sensitivity coefficients of are much larger than other constants, which are 0.780625, -0.77229, and -1.62774 respectively. The velocity distribution at z = 16Dh, y = 0.5P varies with the model constants as shown in Figure 6 As shown, except for the constant C ε1 ,C ε2 , C μ Except for this, the influence of other constants on the velocity distribution is not significant. Therefore, the above three constants are selected to form a sensitive constant set Θ = {θ1, θ2, …, θ m} T The above key model constants are calibrated using data assimilation methods.

[0054] C ε1 ,C ε2 , C μ The recommended value range of is shown in Table 3.

[0055] Table 3 C ε1 ,C ε2 ,C μ The recommended data assimilation range

[0056] Apply Latin hypercube sampling to the model constant C ε1 ,C ε2 , C μ Combination sampling was performed to obtain N = 20 groups of model constant combinations. The model constant combinations were introduced into STAR-CCM+ software for numerical simulation to obtain the predicted flow field. The predicted flow field was combined with the experimental data for data assimilation to obtain the recommended values ​​of the model constants.

[0057] like Figure 7 As shown in (a), compared with the existing random sampling method, the numerical simulation results of the model constant combination obtained by the directional sampling method envelop the experimental results, which can significantly improve the efficiency and accuracy of data assimilation. Figure 7As shown in (b), the recommended values ​​of the model constant combination quickly approach their convergence values. In the first round of data assimilation, the numerical changes of the model constant combination are the most significant, indicating that the directional sampling method effectively improves the convergence speed of data assimilation. Figure 7 (c) shows that the most critical model constant C ε1 ,C ε2 With the increase of assimilation rounds, the same trend of change is shown. Figure 7 (d) shows the relative percentage change of the recommended values ​​and convergence values ​​of the defined model constants. As the number of assimilation rounds increases, it quickly approaches the convergence value.

[0058] The improved model constant C ε1 ,C ε2 ,C μ Substitute the cubic nonlinear k-ε turbulence model to simulate the internal flow field of the fuel assembly in the core of the pressurized water reactor. Next, check whether the simulated flow field is highly similar to the experimental observation flow field. The test standard is the correlation index ρ x,y .

[0059] A single subchannel in the internal flow field of a 5×5 fuel bundle assembly was selected, and the correlation constant was used to evaluate the similarity between the flow field predicted by the combination of model constants recommended by data assimilation and the experimental results, and the optimal combination of model constants for cross-sectional flow field data assimilation was obtained. Where: the function ρ is the average value of the sum of the cosine values ​​of the angle α between the predicted velocity field x and the velocity vector direction of each measuring point in the PIV flow field y.

[0060] like Figure 8 As shown in the figure, the correlation index was only 0.6342 before assimilation, with a standard deviation of 0.5596. After assimilation, it increased to 0.92345, and the standard deviation decreased to 0.1847, indicating that the consistency between the vector direction of the velocity field in the sub-channel and the experimental observation increased significantly after assimilation.

[0061] Taking the normalized vorticity as the benchmark, the sub-channel secondary flow prediction results of the original model constant vector and the data assimilation recommended constant vector are compared, such as Fig. 9 As shown, the optimized turbulence model can effectively predict the secondary flow structure of the sub-channel on the z=16Dh cross section, while the original model cannot predict the secondary flow structure.

[0062] Therefore, the data assimilation method can effectively support the optimization of turbulence model constants for secondary flow in rod bundle channel. The turbulence model with optimized model constants can give a simulated flow field with high similarity to the experimental observation flow field.

[0063] Table 4 Model constant vectors recommended for data assimilation

[0064] The above-mentioned specific implementation can be partially adjusted in different ways by those skilled in the art without departing from the principle and purpose of the present invention. The protection scope of the present invention shall be based on the claims and shall not be limited by the above-mentioned specific implementation. Each implementation scheme within its scope shall be subject to the constraints of the present invention.

Claims

1. A method for assimilating turbulence models using an ensemble Kalman filter based on a full-field similarity criterion, characterized in that: The sensitivity analysis of the coefficients of the candidate turbulence model is performed to obtain the sensitive coefficients and their value ranges to be sampled by Latin hypercube, i.e., the sampling interval. Through the directional Latin hypercube sampling method, the model constant sample combination is extracted in the sampling interval, and the target flow field result is calculated; the data assimilation algorithm based on the ensemble Kalman filter algorithm is used for the target flow field result and the model constant sample combination, and after the optimized model constant combination is obtained, the model constant combination is cyclically updated and convergence verified to obtain the optimal model parameter combination, and finally the internal flow field of the fuel assembly in the core of the pressurized water reactor is simulated with high similarity through the improved turbulence model; The sensitivity analysis mentioned above refers to: calculating each model constant θ i The sensitivity coefficient According to the sensitivity coefficient S i The absolute value of the model constant θ is used to determine i Is it sensitive, where: i = 1…n, step size Δ = 0.05θ i .

2. The method for assimilating turbulence models using an ensemble Kalman filter based on a full-field similarity criterion according to claim 1, characterized in that: The cyclic update means: when the residual ε of the combination of two adjacent rounds of model constant samples is equal to or greater than 0.001, the data assimilation algorithm based on the ensemble Kalman filter algorithm is re-executed; The convergence verification refers to: substituting the model constant sample combination into the same working condition example for verification, applying the flow field similarity to determine whether the result is similar to the experimental result, and when the similarity meets the requirements, it means that the constant combination recommended by the algorithm is applicable under the working condition.

3. The method for assimilating turbulence models using an ensemble Kalman filter based on a full-field similarity criterion according to claim 1, characterized in that: The similarity mentioned above uses the correlation constant to evaluate the similarity between the flow field predicted by the combination of model constants recommended by data assimilation and the experimental results, specifically: Where: the function ρ is the average value of the sum of the cosine values ​​of the angle α between the predicted velocity field x and the velocity vector direction of each measuring point in the PIV flow field y.

4. The method for assimilating turbulence models using an ensemble Kalman filter based on a full-field similarity criterion according to claim 1, characterized in that: The data assimilation algorithm based on the ensemble Kalman filter algorithm includes: a calculation and prediction stage of a turbulence model, an updating stage of model parameters, and a data assimilation algorithm based on the ensemble Kalman filter algorithm that finally outputs an optimized model constant combination.

5. The method for assimilating turbulence models using an ensemble Kalman filter based on a full-field similarity criterion according to claim 1 or 4, characterized in that: The data assimilation algorithm based on the ensemble Kalman filter algorithm specifically includes: a) According to the model constant sample combination given by the directional sampling method and the corresponding calculation, the target flow field, that is, the system state space variable in: u, v represent the velocity components in the x and y directions on the cross section, Θ is a combination of sensitive parameters; b) Calculate the simulated covariance matrix, calculate the experimental error matrix, calculate the Kalman gain, update the set members, convergence judgment and iterative update, where: the simulated covariance matrix C t It refers to: the autocovariance matrix of the target flow field obtained by calculating the combination of model constant samples and the corresponding calculation; the experimental error matrix R refers to: the uncertainty σ of each velocity measurement point given by the PIV experiment PIV , for each velocity measurement point, randomly select a point with a mean of 0 and a variance of σ PIV The error of the normal distribution forms the error matrix r. The experimental error matrix R is the autocovariance matrix of the matrix r; Kalman gain in: C t is a priori set The covariance matrix of c) Take the disturbance Compute the posterior set Due to the nonlinear characteristics of turbulence phenomena and models, one prediction step and multiple update steps are required in the same assimilation round; d) Convergence determination: Where: y ob is the experimental measurement value, is the velocity field generated during the assimilation process. When the result does not converge, the calculation of the update phase in step c is repeated.

6. The method for assimilating turbulence models using an ensemble Kalman filter based on a full-field similarity criterion according to claim 5, characterized in that: The simulated covariance matrix is ​​corrected by a local correction method based on the spatial correlation length obtained by PIV experimental measurement, specifically: in: is the Hadamard product, P ρ Denotes the covariance matrix C t The weight of the elements in r decreases as the geometric distance increases. i,j is a function of the geometric distance between two points, and d0 is the flow field correlation length.

7. A ensemble Kalman filter turbulence model assimilation system based on full-field similarity criterion for implementing any of the methods described in claims 1-6, characterized in that: include: Turbulence model screening unit, model constant sensitivity analysis unit, directional sampling unit, numerical simulation unit, data assimilation unit and field similarity verification unit, wherein: the turbulence model screening unit analyzes the numerical simulation results of different turbulence models to obtain the optimal turbulence model; the model constant sensitivity analysis unit sorts the sensitivity coefficients of the turbulence model constants according to the correlation coefficients to obtain the most sensitive n model constants and compose the sensitive model constant vector and its sampling direction and sampling interval; the directional sampling unit performs Latin hypercube sampling according to the sensitive model constant vector and its sampling direction and sampling interval to obtain the sensitive model constant set; the numerical simulation unit performs numerical simulation of the flow field according to the sensitive model constant set to obtain the simulated flow field; the data assimilation unit performs data assimilation according to the experimentally observed flow field and the simulated flow field to obtain the calibrated sensitive model constant vector; the field similarity verification unit performs field similarity analysis on the calibrated simulated flow field and the experimentally observed flow field obtained by the numerical simulation of the flow field based on the calibrated sensitive model constant vector to obtain the similarity between the calibrated simulated flow field and the experimentally observed flow field.

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