Miniature reactor transient multi-physics field rapid prediction method based on reduced-order model

Abstract

The invention discloses a micro reactor transient multi-physical field rapid prediction method based on a reduced-order model, and the method comprises the steps: taking a reactor core parameter change and a time change in a transient process as all discrete parameter points in a parameter space, and building a response matrix of the reactor core power, the reactor core reactivity, the reactor core temperature and the matrix expansion rate, which serve as target information; reducing the order of the response matrix into a low-dimensional matrix by utilizing intrinsic orthogonal decomposition (POD); in a new parameter point input in real time in an online stage, a radial basis function is used to establish a relationship between the parameter point and a response vector, and rapid prediction is performed through a low-dimensional matrix, so that a result with relatively high calculation precision is obtained at low calculation cost. According to the method, transient multi-physics field coupling simulation is carried out on the reactor starting process of the micro reactor based on an intrinsic orthogonal decomposition radial basis function (POD-RBF) method, so that the calculation efficiency is remarkably improved, and meanwhile, relatively high prediction precision is ensured. A traditional high-fidelity simulation method usually faces high calculation cost when multi-physics coupling calculation is carried out, and the calculation amount is remarkably reduced on the premise that the precision is guaranteed.

Description

Technical Field

[0001] The present invention relates to a technology in the field of reactor control, in particular to a method for rapid prediction of transient multi-physical fields of a micro reactor based on a reduced-order model. Background Art

[0002] Existing simulations of the startup process of micro-reactors usually rely on high-fidelity calculation methods. Although they are highly accurate, they take a long time to calculate and cannot meet the needs of real-time response and efficient simulation in engineering practice. Therefore, how to significantly improve the calculation efficiency while ensuring accuracy has become a technical challenge in micro-reactor transient simulation. Summary of the invention

[0003] In view of the defect that the existing technology cannot solve the transient problem of micro-reactors, the present invention proposes a micro-reactor transient multi-physics field rapid prediction method based on a reduced-order model, and performs transient multi-physics field coupling simulation on the startup process of the micro-reactor based on the intrinsic orthogonal decomposition radial basis function (POD-RBF) method, thereby significantly improving the calculation efficiency and ensuring a high prediction accuracy. Traditional high-fidelity simulation methods usually face high calculation costs when performing multi-physics field coupling calculations. Under the premise of ensuring accuracy, the amount of calculation is significantly reduced.

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

[0005] The present invention relates to a method for rapid prediction of transient multi-physical fields of a micro reactor based on a reduced-order model. The method takes the core parameter changes and time changes in the transient process as discrete parameter points in the parameter space, establishes a response matrix of core power, core reactivity, core temperature and matrix expansion rate as target information, and uses proper orthogonal decomposition (POD) to reduce the response matrix to a low-dimensional matrix. For new parameter points input in real time in the online stage, a radial basis function is used to establish the relationship between the parameter point and the response vector and a rapid prediction is performed through the low-dimensional matrix, thereby obtaining a result with high calculation accuracy at a low calculation cost.

[0006] The intrinsic orthogonal decomposition is: take M discrete points p in the parameter space 1 ,p 2 ,…,p M ∈R t , and the response vector u corresponding to each parameter point 1 ,u 2 ,…,u M ∈R n Stored as the response matrix U = [u 1 …u M ], the response matrix is ​​decomposed by singular value decomposition (SVD) to obtain: Φ = U·V, where: C·V = Λ·V, C = U T U, Φ∈RN×M is the orthogonal basis matrix of the response matrix, which is a unitary matrix; Λ∈R M×M is a diagonal matrix containing singular values. Usually, the diagonal singular values ​​are arranged in descending order; V∈R M×M Also a unitary matrix, C∈R M×M is the characteristic matrix of V.

[0007] When only the first r = k columns of the matrix Φ are retained, the truncated orthogonal basis of the response matrix is ​​obtained. parameter Where: τ is a number less than 1, usually selected as 0.9999; λ i is the diagonal element of Λ, that is, the singular value of the response matrix. This inequality shows that the proportion of the retained orthogonal basis in the total information is the size, and the first r columns of the matrix Φ are recorded as the reduced-order basis matrix The reduced basis matrix Acting on the response matrix, the amplitude matrix of the response matrix will be obtained

[0008] The radial basis function refers to the distance between a parameter point in a continuous parameter space and a discrete parameter point: Where: p 1 ,p 2 ,…,p M ∈R t is M discrete parameter points in the parameter space, which usually contains the micro-stack macro parameters, such as substrate temperature, heat pipe temperature and control drum angle; p∈R t is a continuous parameter point in the parameter space; r is a smoothing factor, which ensures that the interpolation function matrix cond(F)<10 12 In the case of , the smoothing factor is increased as much as possible; the interpolation function matrix of M discrete parameter points can be defined by the radial basis function Among them: The condition number of the interpolation function matrix depends on the smoothing factor r. When ensuring that the interpolation function matrix cond(F)<10 12 In this case, the smoothing factor should be increased as much as possible. At the same time, to ensure the interpolation accuracy, r>0.011 should be satisfied. The coefficient matrix B∈R^ of the parameter points and amplitude matrix is ​​established by inverting the interpolation function matrix F. For the new parameter p, we can get an approximate value of its response vector u(p): in:

[0009] The present invention relates to a system for implementing the above method, comprising: a data generation unit, a POD-RBF modeling unit, a fast prediction unit and a verification unit, wherein: the data generation unit uses OpenMC to calculate the response matrix (power distribution and reactivity) corresponding to the input parameters based on the input core geometry, temperature, material properties and other parameters; the POD-RBF modeling unit uses the POD method to reduce the order of the physical quantities of the core (such as power distribution, reactivity, etc.) based on the generated training data, and extracts the dominant characteristic mode; then, these low-dimensional features are modeled by the radial basis function (RBF) interpolation method, so as to generate a low-dimensional approximate model of the core response; the fast prediction unit predicts the physical quantities such as the core power distribution and reactivity under new input parameters in real time according to the low-dimensional model generated by the POD-RBF modeling unit; it can quickly respond to new transient conditions and provide efficient calculation results while ensuring accuracy; the verification unit verifies the calculation results of the fast prediction unit, and evaluates the accuracy of the prediction by comparing with the simulation results of the high-fidelity model. Technical Effects

[0010] The present invention uses the transient data of the micro-reactor, obtains the relationship between the parameter point and the response vector through the intrinsic orthogonal decomposition and the radial basis function, quickly predicts the transient multi-physical field of the micro-reactor, and obtains the key physical quantities such as the transient neutron flux, power distribution, core temperature and stress distribution of the micro-reactor, which can be applied to the rapid prediction and safety analysis of the micro-reactor state. Compared with the prior art, the present invention reduces the calculation time of a single time step from 800 seconds to 3 seconds, shortens the overall start-up simulation time from 74 days to 7.5 hours, and improves the efficiency by about 99.6%. At the same time, the present invention maintains a high prediction accuracy while ensuring high calculation efficiency. The average error of power distribution prediction is 0.77%, the maximum error does not exceed 3.04%, and the average reactivity prediction error is less than 50pcm, and the maximum does not exceed 100pcm. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Figure 1 It is a flow chart of the present invention;

[0012] Figure 2 is a flow chart of an embodiment;

[0013] Figure 3 Comparison of power distribution predictions of the embodiment and the high-resolution model;

[0014] Figure 4 is the error distribution histogram of the embodiment and the high-resolution model;

[0015] Figure 5 This is the temperature and power variation diagram of the micro reactor at low power startup;

[0016] Figure 6This is a diagram of temperature and power changes during the micro-pile power regulation stage. DETAILED DESCRIPTION

[0017] like Figure 1 As shown, a method for rapid prediction of transient multi-physical fields of a micro-reactor based on a reduced-order model is provided in this embodiment, comprising:

[0018] Step 1, determine the input parameters and divide the training set and test set: select the input parameters and value range, divide 80% of the input parameters into the training set and 20% into the test set, which are used to build and calibrate the low-dimensional approximate model and verify the prediction accuracy and stability of the model;

[0019] The input parameters include temperature, geometric structure dimensions, and control drum angle.

[0020] Step 2: Use OpenMC to calculate the response vector at each input parameter point: Under the parameter combination determined by the training set samples, call OpenMC to perform multi-physics field simulation calculations on the micro-pile to obtain the corresponding response vector.

[0021] The response vectors include: power distribution, reactivity and temperature distribution.

[0022] Step 3: Use the proper orthogonal decomposition radial basis function (POD-RBF) method to construct a low-dimensional approximate model: Use proper orthogonal decomposition (POD) to extract characteristic modes or dominant physical modes from the response vector to obtain a low-dimensional matrix.

[0023] Step 4: Use the radial basis function (RBF) interpolation method to fit or interpolate the data at different parameter points of the low-dimensional matrix to obtain a reduced-order approximate model that can quickly predict the system response.

[0024] Step 5: Use OpenMC to simulate the input parameter points in the test set and obtain the corresponding response vectors (including physical quantities such as power distribution and reactivity). Use these high-fidelity results as benchmark data and compare them point by point with the prediction results of the low-dimensional approximate model to calculate the error.

[0025] like Figure 2 As shown, in specific scenarios, this is achieved through the following methods:

[0026] 1) Setting initial parameters: Select the control drum angle of 150°-50°, step size of 10°, fuel temperature of 300K-1000K, step size of 100K, a total of 88 samples, including 70 training sets and 18 test sets. The rapid prediction of core power distribution and reactivity is achieved through the POD-RBF-based reduced-order model;

[0027] 2) Establish the core thermal model;

[0028] 3) Calculate the core temperature field, count the matrix and fuel temperatures; calculate the heat pipe temperature and update the core thermodynamic model boundary conditions; calculate the core axial and radial geometric changes and update the core grid; use POD-RBF to predict reactivity and power distribution based on neutron, temperature and geometric information; adjust the control drum according to the reactivity to keep the reactivity near 0 and cycle until the temperature change is less than the convergence condition;

[0029] 4) The control drum uses a PID controller to track the target power until it reaches the rated power.

[0030] like Figure 3 As shown in Figure 2, the comparison between the POD-RBF model and the high-resolution model in power distribution prediction is shown in Figure 2. Figure 4 The figure shows the error distribution between the power prediction of the POD-RBF model and the high-resolution model. As can be seen from the figure, the maximum error of the power distribution prediction is 3.04%, and the average error is 0.77%; the average error of the reactivity prediction is less than 50pcm, and the maximum error does not exceed 100pcm. Through the POD-RBF method, the calculation time of each time step of the startup process is shortened from 800 seconds to 3 seconds, and the calculation time of the entire startup process is shortened from 74 days to 7.5 hours, and the efficiency is improved by about 99.6%. In the process of micro-reactor startup, the fast prediction model based on the POD-RBF method is used to quickly predict the reactivity and power distribution of the micro-reactor, and obtain stable and convergent multi-physics coupling results, which effectively improves the calculation efficiency of transient multi-physics coupling problems, meets the needs of real-time simulation and dynamic response, and has high engineering application value.

[0031] like Figure 5 As shown in the figure, the temperature and power variation trends of the micro reactor at the low power startup stage are verified, which verifies the dynamic prediction ability of the POD-RBF method at the low power stage and shows that the method can effectively reflect the variation law of temperature and power under the condition of maintaining a certain accuracy; Figure 6 As shown in the figure, the temperature and power variation trends in the micro-reactor power regulation stage further verify the stability of the POD-RBF method in the startup process, indicating that this method can significantly improve the calculation efficiency while ensuring accuracy.

[0032] In summary, this method reduces the calculation time of each time step from 800 seconds to 3 seconds by introducing a fast prediction model based on POD-RBF, and the calculation time of the overall startup process is shortened from 74 days to 7.5 hours, with an efficiency improvement of about 99.6%. In addition, the POD-RBF model maintains a high accuracy in power distribution and reactivity prediction, with the maximum power prediction error being only 3.04%, and the reactivity prediction error being less than 50pcm on average, and no more than 100pcm at most. Through these technological innovations, the present invention not only significantly reduces the computing cost, but also can provide efficient and real-time prediction results, meeting the real-time simulation requirements during the nuclear reactor startup process, and has significant engineering application value.

[0033] 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 rapid prediction of transient multi-physics fields of micro-reactor based on reduced-order model, characterized in that: The core parameter changes and time changes in the transient process are used as discrete parameter points in the parameter space, and the response matrix of core power, core reactivity, core temperature and matrix expansion rate as the target information is established. The response matrix is ​​reduced to a low-dimensional matrix using proper orthogonal decomposition (POD). For new parameter points input in real time during the online stage, the radial basis function is used to establish the relationship between the parameter point and the response vector, and a low-dimensional matrix is ​​used for rapid prediction, thereby obtaining results with higher calculation accuracy at a low calculation cost.

2. The method for rapid prediction of transient multi-physical fields of a micro-reactor based on a reduced-order model according to claim 1 is characterized in that: The intrinsic orthogonal decomposition is: take M discrete points p1, p2, ..., p in the parameter space M ∈R t , and the response vector u1,u2,…,u corresponding to each parameter point M ∈R n Stored as the response matrix U = [u1…u M ], the response matrix is ​​decomposed by singular value to obtain: Φ = U·V, where: C·V = Λ·V, C = U T U, Φ∈R N×M is the orthogonal basis matrix of the response matrix, which is a unitary matrix; Λ∈R M×M is a diagonal matrix containing singular values; V∈R M×M Also a unitary matrix, C∈R M×M is the characteristic matrix of V.

3. The method for rapid prediction of transient multi-physical fields of a micro-reactor based on a reduced-order model according to claim 2 is characterized in that: When only the first r = k columns of the matrix Φ are retained, the truncated orthogonal basis of the response matrix is ​​obtained. parameter Where: τ is a number less than 1, usually selected as 0.9999; λ i is the diagonal element of Λ, that is, the singular value of the response matrix. The inequality shows that it is the proportion of the retained orthogonal basis in the total information. The first r columns of the matrix Φ are recorded as the reduced-order basis matrix The reduced basis matrix Acting on the response matrix, the amplitude matrix of the response matrix will be obtained 4. The method for rapid prediction of transient multi-physical fields of a micro-reactor based on a reduced-order model according to claim 1 is characterized in that: The radial basis function refers to the distance between a parameter point in a continuous parameter space and a discrete parameter point: Where: p1, p2, …, p M ∈R t is a discrete parameter point in the parameter space, p∈R t is a continuous parameter point in parameter space; r is a smoothing factor. The interpolation function matrix of M discrete parameter points can be defined by the radial basis function. Among them: The condition number of the interpolation function matrix depends on the smoothing factor r.

5. The method for rapid prediction of transient multi-physical fields of a micro reactor based on a reduced-order model according to claim 4 is characterized in that: In order to ensure that the interpolation function matrix cond(F) < 10 12 In this case, the smoothing factor should be increased as much as possible. At the same time, to ensure the interpolation accuracy, r>0.011 should be satisfied.

6. The method for rapid prediction of transient multi-physical fields of a micro-reactor based on a reduced-order model according to claim 4 is characterized in that: The coefficient matrix B∈R of the parameter point and amplitude matrix is ​​established by inverting the interpolation function matrix F ^ , For the new parameter p, we can get an approximate value of its response vector u(p): in:

7. A micro-reactor transient multi-physics field rapid prediction system based on a reduced-order model for implementing any of the methods described in claims 1-6, characterized in that: include: The data generation unit, the POD-RBF modeling unit, the fast prediction unit and the verification unit, wherein: the data generation unit uses OpenMC to calculate the response matrix corresponding to the input parameters based on the input core geometry, temperature and material properties; the POD-RBF modeling unit uses the POD method to reduce the order of the physical quantities of the core based on the generated training data, and after extracting the dominant characteristic modes, the radial basis function (RBF) interpolation method is used to model these low-dimensional features, thereby generating a low-dimensional approximate model of the core response; the fast prediction unit predicts the physical quantities such as the core power distribution and reactivity under new input parameters in real time based on the low-dimensional model generated by the POD-RBF modeling unit; the verification unit verifies the calculation results of the fast prediction unit, and evaluates the accuracy of the prediction by comparing them with the simulation results of the high-fidelity model.

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