Ensemble kalman filter turbulence model assimilation method based on full-field similarity criterion

Abstract

A set Kalman filtering turbulence model assimilation method based on full field similarity criterion is disclosed, which comprises the following steps: sensitivity analysis is performed on the coefficients of the candidate turbulence model to obtain sensitive coefficients and their sampling range for Latin hypercube sampling, i.e., sampling interval; model constant sample combinations are extracted from the sampling interval by using a directional Latin hypercube sampling method, and target flow field results are calculated; a data assimilation algorithm based on the set Kalman filtering algorithm is used for the target flow field results and the model constant sample combinations, and after obtaining the optimized model constant combination, the model constant combination is updated and verified in cycles to obtain the optimal model parameter combination; finally, the improved turbulence model is used to simulate the internal flow field of the fuel assembly in the core of the pressurized water reactor with high similarity. The present application can provide an objective evaluation standard for the full physical field similarity of the data assimilation method, significantly improve the convergence speed of the algorithm, strengthen the robustness of the algorithm, and reduce the calculation cost of the algorithm.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of nuclear reactor simulation, in particular to a set Kalman filter turbulence model assimilation method based on full-field similarity criterion for inverse calculation of turbulence model constants of secondary flow in a rod bundle channel. BACKGROUND

[0002] The existing numerical simulation of internal flow phenomena of a complex nuclear reactor system mostly uses a standard turbulence model, but the prediction result of the model has an engineering-unacceptable error compared with the experimental result, which leads to a design obstacle of the nuclear reactor system. 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, has a large calculation overhead, has constant overshoot, low algorithm robustness, and an unreasonable evaluation basis for the data assimilation effect. SUMMARY

[0003] The present application proposes a set Kalman filter turbulence model assimilation method based on full-field similarity criterion to solve the problems that the existing turbulence model has a large difference between the prediction result of the internal flow field of the reactor and the experimental result, the accuracy of the existing data assimilation result is low, and the calculation overhead in the data assimilation process is high. The similarity between the field data of the experimental observation physical quantity and the field data of the numerical simulation prediction value is used as the non-linear k- The criterion for the data assimilation effect of the turbulence model provides an objective evaluation standard for the full-physical-field similarity of the data assimilation method, significantly improves the convergence speed of the algorithm, strengthens the robustness of the algorithm, and reduces the calculation overhead of the algorithm.

[0004] The present application is implemented by the following technical solutions:

[0005] The present application relates to a set Kalman filter turbulence model assimilation method based on full-field similarity criterion. The sensitivity of the coefficients of the candidate turbulence model is analyzed to obtain the sensitive coefficients and the value range of the Latin hypercube sampling, i.e. the sampling interval. The model constant sample combination is extracted in the sampling interval by the directional Latin hypercube sampling method, 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 to obtain the optimized model constant combination. The model constant combination is updated and verified in a loop to obtain the optimal model parameter combination. Finally, the improved turbulence model is used to simulate the internal flow field of the fuel assembly in the core of a pressurized water reactor with high similarity.

[0006] The sensitivity analysis refers to calculating the sensitivity coefficient of each model constant , and obtaining the value range of the Latin hypercube sampling according to the sensitivity coefficient . The absolute value of the difference between the model constant and the model constant of the previous cycle is used to determine the model constant The sensitivity is determined by the difference between the model constant and the model constant of the previous cycle. The step size .

[0007] The Latin hypercube sampling method adopts, but is 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 a flow field numerical simulation under the same working condition according to each set of model constant in the model constant sample combination, i.e., the same region flow field after reaching a steady state.

[0009] The cycle updating refers to: when the residual error of the model constant sample combination of two adjacent cycles The data assimilation algorithm based on the ensemble Kalman filter algorithm is re-executed.

[0010] The convergence verification refers to: the model constant sample combination is substituted into the same working condition example for verification, and the application flow field similarity determination result is compared with the experimental result to determine whether they are similar. When the similarity meets the requirements, it is indicated that the algorithm recommended constant combination is applicable under the working condition.

[0011] The similarity uses a correlation constant to evaluate the similarity between the flow field predicted by the recommended model constant combination based on data assimilation and the experimental result, specifically: the correlation index , wherein the function is the average value of the sum of the cosine values of the included angles between the predicted velocity field and the PIV flow field at each measurement point.

[0012] The improved turbulent flow model refers to: the optimal model parameter combination is substituted into the cubic nonlinear turbulent flow model.

[0013] The high-similarity simulation refers to: the correlation index ​The correlation between the improved turbulent model and the experimental flow field is obviously higher than that between the original turbulent model and the experimental flow field.

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

[0015] a) combining the model constant sample set and the corresponding calculated target flow field, i.e., the system state space variable, according to the directional sampling method , wherein: , , , represents the velocity component in the direction of the cross section , is the sensitive parameter combination.

[0016] b) calculating the simulation covariance matrix, calculating the experimental error matrix, calculating the Kalman gain, updating the ensemble members, convergence judgment and iterative updating, wherein: the simulation covariance matrix is the self-covariance matrix of the model constant sample set and the corresponding calculated target flow field; the experimental error matrix is the uncertainty of each velocity measurement point given by the PIV experiment , and the error matrix is composed of the errors randomly selected for each velocity measurement point according to the normal distribution with a mean of 0 and a variance of . The experimental error matrix is the self-covariance matrix of the matrix ; the Kalman gain , wherein: , is the covariance matrix of the prior ensemble .

[0017] The simulation covariance matrix is preferably further corrected by a local correction method based on the spatial correlation length measured by the PIV experiment, and specifically: , wherein: is the Hadamard product, , , , represents that the weight of the element in the covariance matrix decreases with the increase of the geometric distance, is a function of the geometric distance between two points, is the correlation length of the flow field.

[0018] c) taking the perturbation , calculating the posterior ensemble Because of the non-linear characteristics of the turbulence phenomenon and the model, a prediction step and multiple update steps need to be performed in the same assimilation round.

[0019] d) performing convergence judgment: wherein: is the experimental measurement value, is the velocity field generated in the assimilation process, and when the result does not converge, the calculation of the step c update stage is re-performed.

[0020] The present application relates to a system for implementing 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 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 forms 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 experimental observation flow field and the simulated flow field to obtain a calibrated sensitive model constant vector; and the field similarity verification unit performs field similarity analysis on the calibrated simulated flow field and the experimental observation flow field based on the flow field numerical simulation expanded based on the calibrated sensitive model constant vector to obtain the similarity degree of the calibrated simulated flow field and the experimental observation flow field.

[0021] Technical effects

[0022] The present application applies the sensitivity analysis and directional sampling method of the turbulence model constant to improve the existing data assimilation process; applies the local correction method to improve the existing ensemble Kalman filter algorithm; and applies the cosine similarity between the simulated physical vector field (such as the velocity field) of the target region and the experimental physical vector field as the similarity between the two fields. Compared with the prior art, the present application reduces the numerical simulation calculation required for one round of data assimilation from 100 times to 20 times through the sensitivity analysis and directional sampling method of the turbulence model constant. In the assimilation strategy, the multiple iteration method is applied to avoid the constant overshooting phenomenon of the optimized turbulence parameters, and in the ensemble Kalman filter algorithm, the local correction method is applied to improve the calculation stability. The cosine similarity between the simulated physical vector field (such as the velocity field) of the target region and the experimental physical vector field is applied as the convergence criterion and optimization standard to improve the reliability of the optimization standard. BRIEF DESCRIPTION OF DRAWINGS

[0023] Figure 1 is the flowchart of the present application;

[0024] Figure 2 Flow chart of the ensemble Kalman filter algorithm;

[0025] Figure 3 Flow chart of the modified algorithm and the iteration residual of the original algorithm;

[0026] Figure 4 Schematic diagram of the test section and the positioning grid;

[0027] In the figure: (a) is a PIV experimental device diagram, (b) is Rod bundle structure schematic diagram, (c) is a fuel assembly cross section, (d) is a mixing grid top view with a shunt type mixing wing, (e) is a mixing wing structure schematic diagram;

[0028] Figure 5 Schematic diagram of the rod bundle geometry model;

[0029] In the figure: (a) left view, (b) top view, (c) sub-channel top view;

[0030] Figure 6 Schematic diagram of the turbulence model constant sensitivity analysis;

[0031] In the figure: Z = 16D h , Y = 0.5P, (a) , (b) , (c) , (d) ;

[0032] Figure 7 Schematic diagram of the directional sampling method and effect;

[0033] In the figure: (a) the change of velocity distribution with sampling method, (b) three-dimensional effect diagram of directional sampling, (c) two-dimensional effect diagram of directional sampling, (d) the change of model constant residual with assimilation round;

[0034] Figure 8 Schematic diagram of the correlation index;

[0035] Figure 9 Schematic diagram of the sub-channel secondary flow;

[0036] In the figure: (a) is the experimental flow field, (b) is the original model predicted flow field, (c) is the optimized model predicted flow field. DETAILED DESCRIPTION

[0037] As Figure 1 shown, a full-field similarity criterion based ensemble Kalman filter turbulence model assimilation method related to the embodiment includes:

[0038] Step 1) Conduct an applicability study on the turbulence model to determine the appropriate turbulence model;

[0039] Step 2) Select the important model constants contained in the chosen turbulence model, combined with experimental observations. A set of sensitive constants. ;

[0040] Step 3) Sensitivity Analysis: Perform sensitivity analysis on the constants involved in the selected turbulence model, and calculate the correlation coefficient and sensitivity coefficient to the model constants. Select The largest front A vector of sensitive constants is composed of several constants. Based on the sensitivity coefficient Determine the directional sampling direction and interval for each sensitive constant, and then perform directional sampling. The group of sensitivity constants constitutes the sample set;

[0041] Step 4) Numerical simulation: Based on the sample set, set the sensitivity constants of the turbulence model and perform N CFD numerical simulations to obtain the predicted value vectors. Step 5) From the model predictions Experimental observations and sensitive constant sample set Starting from this point, the ensemble Kalman filter algorithm is executed to obtain the calibrated turbulence model constants. ;

[0042] Step 6) Determine the constants of the optimized turbulence model Convergence, that is, satisfying: If the condition is met, proceed to step 7); otherwise, repeat step 3), where: The model constant is the iterative residual, and max is the maximum value operator;

[0043] Step 7) Let Substitute back into the turbulence model from step 4 for CFD calculations to obtain the optimized target physical quantities. ;

[0044] Step 8) Compare the experimental measurement results With the target physical quantity When the optimization result is deemed acceptable, i.e., the function... For model predictions Compared with experimental observations correlation coefficient When the value is greater than 0.8, output the constant of the optimized model. Otherwise, return to step 1) and repeat the data assimilation process, where: For the time-averaged velocity field in numerical simulation, This represents the average velocity field observed in the experiment.

[0045] Based on the experimental data of the secondary flow downstream of the 5 × 5 rod bundle with the mixing grid of the split-type mixing wing, the data assimilation research was carried out through specific experiments. The experiment was carried out in the MEdium Scale Hydraulic (MESH) test loop of Shanghai Jiaotong University. As shown in Figure 4 , the length of the 5 × 5 rod bundle was 1100 mm, the rod diameter was 9.5 mm, the rod spacing was 12.6 mm, and the sub-channel hydraulic diameter was 11.78 mm. The internal size of the test section channel was 66.1 × 66.1 mm. The plan view of the split-type mixing grid is shown in Figure 4 (d), the mixing wing height was 9.5 mm, the inclination angle was 30°, and the detailed size of the mixing wing is shown in Figure 4 (c). Taking the upper plane of the grid as the Z = 0 plane and the center of the rod circle as the coordinate origin, the laboratory coordinate system shown in Figure 4 (b), (c) was established. The main flow velocity of the test condition was 1 m / s. The PIV was used to measure the secondary flow at the cross sections of Z = 1Dh, 4Dh, 8Dh and 16Dh downstream of the grid. The uncertainty of the time-averaged velocity relative to the main flow velocity was within 0.4%.

[0046] The commercial CFD software STAR-CCM+ was used for modeling and numerical simulation. The geometric model included the rod bundle and the mixing grid. As shown in Figure 5 (a) (b), the simulation coordinate system was consistent with the experimental coordinate system, the origin of the calculation domain was the center of the center rod circle, the Z = 0 plane was the upper plane of the grid, and the calculation domain range was from Z = -10Dh to Z = 20Dh. The polyhedral grid was selected for the grid, the stretch grid was used for the inlet and outlet parts, the wall surface was set to 5 layers of prism layers, and the total number of grids was 32.91 million. The inlet boundary condition was the fully developed flow in the rod bundle, and the outlet boundary was set to the pressure outlet. The number of subchannels selected in the green box in Figure 5 (b) and Y = 0.5P were the application and evaluation areas of the data assimilation method.

[0047] The existing research compared the calculation results of the nonlinear eddy viscosity model and the Reynolds stress model. The research showed that the nonlinear eddy viscosity model could not predict the evolution characteristics of the transverse vortex structure. However, the model had wide application value in engineering, so the model was selected as the candidate model for data assimilation in the present research. The standard model equation is as follows, and the model constants are shown in Table 1.

[0048] The equation of the nonlinear eddy viscosity model is as follows: wherein: , , , .

[0049] Table 1 Original coefficients of nonlinear eddy viscosity model

[0050]

[0051] Table .

[0052] Selected Figure 5 (b) The No. 7 sub-channel selected by the green frame in (b) as the geometry domain of data assimilation, the above data assimilation strategy and algorithm are applied and evaluated, including parameter sensitivity analysis, application of directional sampling method and covariance matrix correction method, and evaluation of recommended model constant combination.

[0053] Sensitivity analysis is made on the nonlinear eddy viscosity model constants, and the analysis range is shown in Table 2:

[0054] Table 2 Sensitivity analysis range of nonlinear eddy viscosity model constants

[0055]

[0056] The model constants The sensitivity coefficient is calculated , wherein: step . The analysis shows that the sensitivity coefficients of constants , , are much larger than those of other constants, which are , and the velocity distribution at changes with the model constants as shown in Figure 6 . Except for constants , , , the influence of other constants on the velocity distribution is not significant. Therefore, the above three constants are selected as the sensitive constant set The above key model constants are calibrated by using the data assimilation method.

[0057] , , The recommended value range of the above key model constants is shown in Table 3.

[0058] Table 3 Recommended data assimilation value range of , ,

[0059]

[0060] The Latin hypercube sampling is applied to the model constants , , ​The combination sampling is performed to obtain The model constants are combined. The model constants combination is introduced into STAR-CCM+ software to perform numerical simulation to obtain the predicted flow field. The predicted flow field is combined with the experimental data to perform data assimilation to obtain the recommended values of the model constants.

[0061] As shown in Figure 7 (a), compared with the existing random sampling method, the numerical simulation result of the model constants combination obtained by the directional sampling method envelopes the experimental result, which can significantly improve the efficiency and accuracy of data assimilation. As shown in Figure 7 (b), the recommended values of the model constants combination quickly approach the convergence values, wherein, in the first round of data assimilation, the numerical change of the model constants combination is the most significant, indicating that the directional sampling method effectively improves the convergence speed of data assimilation. As shown in Figure 7 (c), the most critical model constants , show the same change trend with the increase of the assimilation rounds. Figure 7 (d) shows that the relative change percentage of the recommended values and the convergence values of the model constants quickly approaches the convergence values with the increase of the assimilation rounds.

[0062] The improved model constants , are substituted into the cubic nonlinear turbulence model to simulate the internal flow field of the fuel assembly in the core of the pressurized water reactor. The following verifies whether the simulated flow field has high similarity with the experimentally observed flow field, and the correlation index is used as the verification standard.

[0063] The single sub-channel in the internal flow field of the 5 5-rod bundle fuel assembly is selected, and the correlation constant is used to evaluate the similarity between the flow field predicted based on the data assimilation recommended model constant combination and the experimental result, and the cross-sectional flow field data assimilation optimal model constant combination is obtained. The correlation index , wherein: the function is the average value of the sum of the cosine values of the angle between the velocity vector direction of each measuring point in the predicted velocity field and the PIV flow field .

[0064] As shown in Figure 8 , the correlation index is only 0.6342 before assimilation, and the standard deviation is 0.5596, which rises to 0.92345 after assimilation, and the standard deviation drops to 0.1847, indicating that the consistency degree of the vector direction of the velocity field in the sub-channel after assimilation and the experimentally observed one significantly rises.

[0065] ​The sub-channel secondary flow prediction results of the original model constant vector and the data assimilation recommended constant vector are compared based on the normalized vorticity, as shown in Figure 9 The optimized turbulence model can effectively predict the secondary flow structure of the sub-channel in the cross section, while the original model cannot predict the secondary flow structure.

[0066] Therefore, the data assimilation method can effectively support the optimization of the turbulence model constant of the rod bundle channel secondary flow. The turbulence model with the optimized model constant can give a simulated flow field with high similarity to the experimentally observed flow field.

[0067] Table 4 Model constant vector recommended by data assimilation

[0068]

[0069] The above specific embodiments can be partially adjusted by those skilled in the art in different ways without departing from the principles and purposes of the present application. The protection scope of the present application is subject to the claims and is not limited by the above specific embodiments. Each implementation within the scope is subject to the constraints of the present application.​

Claims

1. A set Kalman filter turbulence model assimilation method based on full-field similarity criteria, characterized in that, The application comprises the following steps: Step 1) carrying out applicability research on a turbulence model, and determining the selected turbulence model; Step 2) Selecting a set of sensitive constants by combining the selected important model constants contained in the selected turbulence model with experimental observations ;​ Step 3) Sensitivity Analysis: Perform sensitivity analysis on the constants involved in the selected turbulence model, and calculate the correlation coefficient and sensitivity coefficient to the model constants. Select The largest front A vector of sensitive constants is composed of several constants. Based on the sensitivity coefficient Determine the directional sampling direction and interval for each sensitive constant, and then perform directional sampling. The group of sensitivity constants constitutes the sample set; Step 4) Numerical simulation: set the turbulence model sensitive constant according to the sample set to perform N times of CFD numerical simulation, respectively obtain the predicted value vector ; Step 5) From the model predicted values , experimental observations and a sample set of sensitivity constants , perform a set Kalman filter algorithm to obtain calibrated turbulence model constants ; Step 6) judge optimized turbulence model constants converge, i.e. satisfy: Step 7) is entered, otherwise repeat Step 3), where: is the model constant iteration residual, max is the maximum value operator; Step 7) Let , back to the turbulence model of step 4 to perform CFD calculation to obtain the optimized target physical quantity ; Step 8) Compare the experimental measurement results With the target physical quantity When the optimization result is deemed acceptable, i.e., the model's predicted value is... Compared with experimental observations correlation coefficient When the value is greater than 0.8, output the constant of the optimized model. Otherwise, return to step 1) and repeat the data assimilation process, where: For the time-averaged velocity field in numerical simulation, This represents the average velocity field observed in the experiment.

2. The ensemble Kalman filter turbulence model assimilation method based on full-field similarity criteria according to claim 1, characterized in that, The similarity is evaluated by using a correlation constant to combine the prediction model constant based on data assimilation recommendation, specifically: the correlation index Wherein: the function is the predicted velocity field and the PIV flow field is the average value of the cosine value of the included angle between the velocity vector direction of each measuring point .

3. The ensemble Kalman filter turbulence model assimilation method based on full-field similarity criteria of claim 1, wherein, The data assimilation algorithm based on the ensemble Kalman filtering algorithm comprises a calculation and prediction stage of the turbulence model, an updating stage of model parameters and a final output of optimized model constants.

4. A set Kalman filter turbulence model assimilation system based on full-field similarity criteria to implement the method of any one of claims 1-3, characterized in that, The application comprises the following steps: The turbulence model screening unit, the model constant sensitivity analysis unit, the directional sampling unit, the numerical simulation unit, the data assimilation unit and the field similarity verification unit are combined, 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 form a sensitive model constant vector and its sampling direction and sampling interval; the directional sampling unit carries out 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 carries out flow field numerical simulation according to the sensitive model constant set to obtain a simulated flow field; the data assimilation unit carries out data assimilation according to the experimental observation flow field and the simulated flow field to obtain a calibrated sensitive model constant vector; and the field similarity verification unit carries out field similarity analysis on the calibrated simulated flow field and the experimental observation flow field obtained according to the flow field numerical simulation based on the calibrated sensitive model constant vector to obtain the similarity degree of the calibrated simulated flow field and the experimental observation flow field.

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