CN116894406A - A fast prediction method for the temperature field of space thermionic reactor based on model order reduction - Google Patents

Abstract

A method for quickly predicting the temperature field of space thermionic reactors based on model order reduction. 1. Specify the operating power range of the space thermionic reactors and randomly generate a power sample space; 2. Calculate the temperature field of each power in the power sample space. Solve to obtain the data snapshot matrix of the entire power sample space; 3. Perform intrinsic orthogonal decomposition of the data snapshot matrix to obtain the orthogonal basis matrix and modal coefficient matrix, and decompose the temperature field of the entire space thermionic reactor into the sample temperature field The form of adding the average value and the product of several orthogonal basis vectors and modal coefficients; 4. Based on the generalized energy percentage, select a certain number of orthogonal basis vectors as the main modes to establish a reduced-order model; 5. Based on back propagation Algorithm, use each power value and corresponding modal coefficient in the sample space to train the neural network to obtain the surrogate model; 6. Enter the power value into the trained surrogate model to obtain the modal coefficient, and then combine it with the reduced-order model to obtain Temperature values of all grid nodes. The method of the present invention is fast in calculation and has accurate results.

Description

A fast prediction method for the temperature field of space thermionic reactor based on model order reduction

Technical field

The invention relates to the technical field of space thermal ion reactor operation analysis, and specifically relates to a method for rapid prediction of the temperature field of the space thermal ion reactor based on model order reduction.

Background technique

The space thermionic reactor uses in-reactor thermionic power generation technology. Thermionic power generation efficiency is closely related to temperature. Accurate and rapid prediction of the temperature field distribution of the space thermionic reactor is of great significance to the on-orbit operation control of the space thermionic reactor. Currently, computational fluid dynamics (CFD) methods are used to calculate the temperature field of a full-scale three-dimensional spatial thermal ion reactor, which often requires a large amount of computing resources and takes a long time to calculate. If calculations are carried out under multiple working conditions, the calculation time will also double, which is not conducive to rapid prediction of the temperature field. The essence of model reduction is to use low-dimensional data information to express high-dimensional data information. The advantage is that while retaining the spatial dimensions and physical properties of the problem, it not only reduces the computational cost, but also ensures sufficient accuracy requirements.

Contents of the invention

In order to overcome the problems existing in the above-mentioned prior art, the purpose of the present invention is to provide a method for rapid prediction of the temperature field of the space thermionic reactor based on model reduction, and to solve the calculation time required in the process of solving the temperature field of the space thermionic reactor using the CFD simulation method. , the calculation amount is large, and it is a problem that requires repeated calculations under similar working conditions.

In order to achieve the above objects, the present invention adopts the following technical solutions:

A fast prediction method for the temperature field of space thermionic reactors based on model order reduction. The method includes the following steps:

Step 1: Specify the operating power interval of the space thermionic reactor, and randomly generate a power sample space within the operating power interval.

Step 2: Use CFD software to solve the temperature field of each power in the power sample space, thereby obtaining the data snapshot matrix of the entire power sample space.

The specific form of the data snapshot matrix is as follows:

In the formula, M——the number of grid nodes;

N——the number of numerical simulation data samples;

A——data snapshot matrix;

X _i ——The i-th column vector of the data snapshot matrix, i=1,2,3...N;

x——grid node temperature, K.

Step 3: Perform intrinsic orthogonal decomposition on the data snapshot matrix to obtain the orthogonal basis matrix and modal coefficient matrix, and decompose the temperature field of the entire space thermal ion reactor into the average value of the sample temperature field and several eigenmodes and modes. The form of adding the products of coefficients.

First, convert the data snapshot matrix into a square matrix:

[B] _N×N ＝[A ^T ] _N×M [A] _M×N (2)

In the formula, B——the square matrix of data snapshot matrix;

[A ^T ]——The transpose of the data snapshot matrix.

Eigenvalue decomposition of square matrix B:

In the formula, φ - eigenvector matrix;

C——Eigenvalue matrix;

ψ _i ——i-th eigenvector, i=1,2,3…N;

λ _i ——i-th eigenvalue, i=1,2,3…N.

The eigenvalues in the eigenvalue matrix C are arranged in descending order according to their size, and the form of the orthogonal basis matrix obtained is:

In the formula, β——is an orthogonal basis matrix;

θ _i ——is the i-th order orthogonal basis vector, i=1,2,3…N.

The characteristic coefficient matrix D can be obtained from the orthogonal basis matrix β and the transpose A ^T of the data snapshot matrix. Its specific form is:

[D] _N×N ＝[A ^T ] _N×M [β] _M×N ＝[a ₁ a ₂ … a _N ] (5)

In the formula, D——is the characteristic coefficient matrix;

a _i ——is the modal coefficient of the i-th order orthogonal basis vector, i=1,2,3…N.

According to the orthogonal basis vectors and characteristic coefficients, each column vector in the data snapshot matrix can be expressed in the following form:

After completing the above process, the temperature on all grid nodes in the calculation area of the space thermionic pile is decomposed into the form of the average value of the sample temperature field and the sum of the products of several orthogonal basis vectors and modal coefficients:

In the formula, ——is the temperature prediction value, K;

X ₀ ——is the average value of the sample temperature field, K;

r——The number of selected eigenmodes.

Step 4: Based on the generalized energy percentage, select a certain number of orthogonal basis vectors as the main modes to establish a reduced-order model.

The form of generalized energy percentage is:

In the formula, E _r - generalized energy percentage;

λ _j ——The jth eigenvalue;

ε——Energy ratio.

Step 5: Based on the back propagation algorithm, use each power value and corresponding modal coefficient in the sample space to train the neural network to obtain the surrogate model.

Step 6: Input the power value into the trained proxy model to obtain the modal coefficient, and then combine it with the reduced-order model to obtain the temperature values of all grid nodes.

Compared with the prior art, the present invention has the following outstanding features:

The present invention provides a method based on model reduction to quickly predict the temperature field of the space thermionic reactor under different power operating conditions. It establishes a reduction model through a certain number of CFD software calculation result data, and obtains a high-precision proxy model through neural network training, thereby Quickly obtain the temperature field of the space thermionic reactor under different powers. This method can greatly shorten the solution time and reduce repeated costs while ensuring sufficient accuracy, and provides an effective method for rapid numerical simulation of the operation of the space thermionic reactor. Methods.

Description of the drawings

Figure 1 is a flow chart of the method of the present invention.

Detailed ways

The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments:

The present invention is a method for rapid prediction of the temperature field of space thermal ion reactors based on model order reduction, as shown in Figure 1. The specific process of the method includes the following aspects:

Step 1: Specify the operating power interval of the space thermionic reactor, and randomly generate a power sample space within the operating power interval. This embodiment specifies a power operating range of 50% to 100%.

Step 2: Use CFD software to solve the temperature field of each power in the power sample space, thereby obtaining the data snapshot matrix of the entire power sample space. This embodiment uses ANSYS Fluent to solve the temperature field of 100% power of the space thermionic reactor.

The specific form of the data snapshot matrix is as follows:

In the formula, M——the number of grid nodes;

N——the number of numerical simulation data samples;

A——data snapshot matrix;

X _N ——The Nth column vector of the data snapshot matrix;

x——grid node temperature, K.

Step 3: Perform intrinsic orthogonal decomposition on the data snapshot matrix to obtain the orthogonal basis matrix and modal coefficient matrix, and decompose the temperature field of the entire space thermal ion reactor into the average value of the sample temperature field and several eigenmodes and modes. The form of adding the products of coefficients.

First, convert the data snapshot matrix into a square matrix:

[B] _N×N ＝[A ^T ] _N×M [A] _M×N (2)

In the formula, B——the square matrix of data snapshot matrix;

[A ^T ]——The transpose of the data snapshot matrix.

Eigenvalue decomposition of square matrix B:

In the formula, φ - eigenvector matrix;

C——Eigenvalue matrix;

ψ _N ——The Nth eigenvector;

λ _N ——The Nth eigenvalue.

The eigenvalues in the eigenvalue matrix C are arranged in descending order according to their size, and the form of the orthogonal basis matrix obtained is:

In the formula, β——is an orthogonal basis matrix;

θ _i ——is the i-th order orthogonal basis vector, i=1,2,3…N.

The characteristic coefficient matrix D can be obtained from the orthogonal basis matrix β and the transpose A ^T of the data snapshot matrix. Its specific form is:

[D] _N×N ＝[A ^T ] _N×M [β] _M×N ＝[a ₁ a ₂ … a _N ] (5)

In the formula, D——is the characteristic coefficient matrix;

a _i ——is the modal coefficient of the i-th order orthogonal basis vector, i=1,2,3…N.

According to the orthogonal basis vectors and characteristic coefficients, each column vector in the data snapshot matrix can be expressed in the following form:

After completing the above process, the temperature on all grid nodes in the calculation area of the space thermionic pile is decomposed into the form of the average value of the sample temperature field and the sum of the products of several eigenmodes and modal coefficients:

In the formula, ——is the temperature prediction value, K;

X ₀ ——is the average value of the sample temperature field, K;

r——The number of selected eigenmodes.

Step 4: Based on the generalized energy percentage, select a certain number of eigenmodes as main modes to establish a reduced-order model. In this embodiment, when the energy ratio is set to 0.99, r=3 (this is just an example, it can also be other numbers, determined by actual problems).

The form of generalized energy percentage is:

In the formula, E _r - generalized energy percentage;

λ _j ——The jth eigenvalue;

ε——Energy ratio.

Step 5: Based on the back propagation algorithm, use each power value and corresponding modal coefficient in the sample space to train the neural network to obtain the surrogate model.

Step 6: Input the power value into the trained proxy model to obtain the modal coefficient, and then combine it with the reduced-order model to obtain the temperature information of all grid nodes.

Claims (1)

1. A method for rapidly predicting a temperature field of a space thermal ion stack based on model reduction is characterized by comprising the following steps: the method comprises the following steps:

step 1: designating an operation power interval of the space thermionic stack, and randomly generating a power sample space in the operation power interval;

step 2: solving a temperature field of each power in the power sample space by using CFD software, so as to obtain a data snapshot matrix of the whole power sample space;

the specific form of the data snapshot matrix is as follows:

wherein M is the number of grid nodes;

n—number of numerical analog data samples;

a-data snapshot matrix;

X _i -the ith column vector of the data snapshot matrix, i=1, 2,3 … N;

x-grid node temperature, K;

step 3: carrying out intrinsic orthogonal decomposition on the data snapshot matrix to obtain an orthogonal base matrix and a modal coefficient matrix, decomposing the temperature field of the whole space thermal ion stack into a mode of adding the average value of the sample temperature field and the products of a plurality of characteristic modes and modal coefficients;

firstly, converting a data snapshot matrix into a square matrix:

[B] _N×N ＝[A ^T ] _N×M [A] _M×N (2)

b is a square matrix of a data snapshot matrix;

[A ^T ]-transpose of the data snapshot matrix;

and decomposing the eigenvalue of the square matrix B:

wherein phi is a characteristic vector matrix;

c, a characteristic value matrix;

ψ _i -ith eigenvector, i=1, 2,3 … N;

λ _i -ith eigenvalue, i=1, 2,3 … N;

the eigenvalues in the eigenvalue matrix C are arranged according to the size thereof in a descending order, and the orthogonal base matrix is obtained in the form of:

wherein, beta-is an orthogonal base matrix;

θ _i -i-th order orthogonal basis vector, i=1, 2,3 … N;

transpose a of the data snapshot matrix from the orthogonal base matrix β ^T The mode coefficient matrix D is obtained, and the specific form is as follows:

[D] _N×N ＝[A ^T ] _N×M [β] _M×N ＝[a ₁ a ₂ …a _N ] (5)

wherein D is a modal coefficient matrix;

a _i -the modal coefficient of the i-th order orthogonal basis vector, i=1, 2,3 … N;

each column vector in the data snapshot matrix is represented in terms of an orthogonal basis vector and a modal coefficient as follows:

after the above process is completed, the temperatures at all grid nodes in the calculation region of the space thermionic stack are decomposed into the form of the average value of the sample temperature field and the product of several orthogonal basis vectors and modal coefficients added:

in the method, in the process of the invention,-temperature predicted value, K;

X ₀ -is the average value of the sample temperature field, K;

r-the number of selected characteristic modes;

step 4: based on the generalized energy percentage, a certain number of orthogonal basis vectors are selected as a main mode to establish a reduced order model;

the generalized energy percentage is in the form of:

wherein E is _r -generalized energy percentage;

λ _j -a j-th eigenvalue;

epsilon-energy ratio;

step 5: training a neural network by utilizing each power value and a corresponding modal coefficient in a sample space based on a back propagation algorithm, thereby obtaining a proxy model;

step 6: and inputting power values into the trained agent model to obtain modal coefficients, and combining the modal coefficients with the reduced order model to obtain the temperature values of all grid nodes.