A fast prediction method for the internal flow field of RBCC engine based on singular value decomposition
Through the singular value decomposition and response surface analysis methods, the intrafluid field data of RBCC engines are dimensionally reduced and fast prediction, which solves the problem of long traditional CFD simulation time, and achieves fast and accurate intrafluid field prediction, reducing calculation costs and improving Simulation efficiency.
Patent Information
- Application Number
- CN202310574944.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2023-05-19
- Publication Date
- 2024-12-17
- Estimated Expiration
- 2043-05-19
AI Technical Summary
The traditional CFD numerical simulation method has a long simulation time for the flow field in RBCC engines and cannot meet the requirements of fast response.
Using singular value decomposition and response surface analysis methods, the flow field data in RBCC engine is reduced in dimension and reconstruction, and the inflow volume of intra-flow field is reduced through singular value decomposition, and the inflow under new incoming flow conditions is quickly predicted through response surface analysis. Field data.
It significantly improves the intraflow field prediction speed, enhances the interpolation capability of data, reduces the calculation amount and complexity, and can quickly and accurately predict the intraflow field data of the RBCC engine.
Smart Images
Figure CN116595909B_ABST
Abstract
Description
[Technical field]
[0001] The invention belongs to the technical field of rocket-based combined cycle engine internal flow field prediction, and in particular relates to a method for fast prediction of the internal flow field of a RBCC engine based on singular value decomposition. [Background technology]
[0002] Rocket Based Combined Cycle (RBCC) is an ideal power form for future reusable aerospace vehicles. In order to realize the reuse of RBCC engines, it is necessary to quickly obtain the temperature, pressure and other parameters of the flow field in the RBCC engine through the incoming flow conditions. However, due to the complex flow process and combustion reaction inside the RBCC engine, the traditional CFD numerical simulation method takes a long time to simulate the flow field in the RBCC engine and cannot meet the requirements of rapid response. Therefore, a fast RBCC flow field prediction method is needed. [Summary of the invention]
[0003] The purpose of the present invention is to provide a method for rapid prediction of the internal flow field of an RBCC engine based on singular value decomposition, so as to solve the problem that the existing traditional CFD numerical simulation method has a long simulation time for the internal flow field of an RBCC engine and cannot meet the rapid response requirements.
[0004] The present invention adopts the following technical solutions: 1. A method for rapid prediction of the internal flow field of an RBCC engine based on singular value decomposition, comprising the following steps:
[0005] Step 1: Perform singular value decomposition on the characteristic matrix of the physical quantity of the flow field in the RBCC engine:
[0006] Firstly, the internal flow field model of RBCC engine is established;
[0007] The internal flow field model is meshed, and appropriate incoming flow conditions are selected to obtain the internal flow field data under the incoming flow conditions through CFD numerical simulation;
[0008] According to the internal flow field data, the physical quantity matrix M of the internal flow field is constructed, and the physical quantity matrix M of the internal flow field is subjected to singular value decomposition to obtain U i ; U i is the i-th column vector of the left singular matrix U;
[0009] Step 2: Perform response surface analysis on the internal flow field data of the same grid unit under different inflow conditions to obtain the interpolation coefficient α under the kth inflow condition: ik ; Determine the optimal order r through error analysis;
[0010] Step 3: According to the interpolation coefficient α ik, the optimal order r and the singular value decomposition results, and the predicted internal flow field T under the kth incoming flow condition is obtained rom,k ,Right now
[0011] Step 4: The internal flow field T obtained in step 3 rom,k and the kth column vector T of the internal flow field physical quantity matrix M obtained in step 1 k Compare and get the relative error
[0012] Adjust the value of r until the relative error is minimized, at which point the value of r is its optimal value. After determining the optimal value of r, the predicted internal flow field with the minimum error under the kth incoming flow condition can be obtained.
[0013] Furthermore, the specific method for constructing the physical quantity matrix M of the internal flow field in step 1 is: the internal flow field data under each incoming flow condition constitutes a column vector, the internal flow field column vectors under different incoming flow conditions constitute an internal flow field matrix, the number of matrix column vectors is the number of incoming flow conditions, and the number of row vectors is the number of grids.
[0014] Furthermore, the specific method for performing singular value decomposition on the physical quantity matrix of the internal flow field in step 1 is:
[0015] Calculate the singular values of the physical quantity matrix M of the internal flow field. First, calculate the matrix M T M and the matrix MM T , and then find the matrix M T M and the matrix MM T The eigenvalues and eigenvectors of , and finally the eigenvalues are squared to get all singular values σ, assuming there are t singular values;
[0016] Matrix M T The eigenvectors of M are the row vectors of the left singular matrix U, and the matrix MM T The eigenvectors of are right singular value matrices The row vector of , which can complete the singular value decomposition of the matrix M,
[0017] Furthermore, the specific method of error analysis in step 2 is:
[0018]
[0019] Among them, M r is the physical quantity matrix of the internal flow field of the first r orders; σ i is the i-th order singular value, that is, the i-th order element of the singular matrix S; when r is large enough and the error is not greater than ε, r is the optimal order.
[0020] Furthermore, according to α k =(XT X) -1 X T T k Get the interpolation coefficient α ik The vector α composed of the arrangement k , we can get the interpolation coefficient α ik ; Among them, among them, T k is the kth column vector of the matrix M, X is the first column of which is all 1, and the next n-1 columns are the matrix M minus the column vector T k The remaining n-1 columns of the matrix, X T is the transpose of X.
[0021] Furthermore, after step 4, the internal flow field matrix is updated according to the ground direct experimental data and flight data, and the interpolation coefficients and the optimal order are continuously optimized.
[0022] The beneficial effects of the present invention are as follows: the present invention predicts the internal flow field data under new incoming flow conditions by reducing the dimension of the internal flow field data of the RBCC engine through singular value decomposition and response surface analysis. By introducing the singular value decomposition method, the internal flow field matrix is reduced in dimension, thereby reducing the amount of internal flow field data. By introducing the response surface analysis method, the internal flow field data under new incoming flow conditions can be quickly predicted, and the interpolation capability of the data is improved through data interpolation reconstruction. By replacing the solution of complex partial differential equations in fluid mechanics with matrix operations, the internal flow field prediction speed is greatly improved.
Brief Description of the Drawings
[0023] Figure 1 A flowchart of a method for rapid prediction of the internal flow field of an RBCC engine based on singular value decomposition according to the present invention;
[0024] Figure 2.1(a) to Figure 2.1(c) They are respectively simulation result diagrams of static temperature distribution of flow field in the engine obtained when the mass flow rate is 1kg / s, 1.5kg / s and 2.5kg / s;
[0025] Figure 2.2(a) to Figure 2.2(c) They are respectively the predicted result diagrams of the static temperature distribution of the flow field in the engine obtained when the mass flow rates are 1kg / s, 1.5kg / s and 2.5kg / s. [Specific implementation method]
[0026] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.
[0027] The present invention provides a method for rapid prediction of the flow field in an RBCC engine based on singular value decomposition. Figure 1 As shown, the following steps are included:
[0028] Step 1: Perform singular value decomposition on the characteristic matrix of the physical quantity of the flow field in the RBCC engine:
[0029] Firstly, the internal flow field model of RBCC engine is established;
[0030] Meshing the internal flow field model, selecting appropriate incoming flow conditions, and obtaining the internal flow field data under the incoming flow conditions through CFD numerical simulation;
[0031] According to the internal flow field data, the physical quantity matrix M of the internal flow field is constructed, and the physical quantity matrix M of the internal flow field is subjected to singular value decomposition to obtain U i ; U i is the i-th column vector of the left singular matrix U;
[0032] Step 2: Perform response surface analysis on the internal flow field data of the same grid unit under different inflow conditions to obtain the interpolation coefficient α under the kth inflow condition: ik ; Determine the optimal order r through error analysis;
[0033] Step 3: According to the interpolation coefficient α ik , the optimal order r and the singular value decomposition results, and the predicted internal flow field T under the kth incoming flow condition is obtained rom,k ,Right now
[0034] Step 4: The internal flow field T obtained in step 3 is rom,k and the kth column vector T of the internal flow field physical quantity matrix M obtained in step 1 k Compare and get the relative error
[0035] According to the size of the relative error, adjust the value of r until the relative error reaches the minimum. At this time, the value of r is its optimal value. After determining the optimal value r, the internal flow field can be obtained.
[0036] in,
[0037] The resulting column vector T rom,k This is the physical quantity data on m grids under the kth incoming flow condition, that is, to achieve the prediction of the internal flow field.
[0038] In some embodiments, the specific method of constructing the physical quantity matrix M of the internal flow field in step 1 is: the internal flow field data under each incoming flow condition constitutes a column vector, the internal flow field column vectors under different incoming flow conditions constitute an internal flow field matrix, the number of matrix column vectors is the number of incoming flow conditions, and the number of row vectors is the number of grids. The internal flow field matrix M and its row vectors and column vectors, the number of incoming flow conditions is unlimited, and the number of grids is unlimited. Assuming there are n incoming flow conditions and m grid units, the above M matrix can be expressed as:
[0039]
[0040] Among them, the element T in the matrix M ij The subscript i represents different grid nodes, and the subscript j represents different incoming flow conditions.
[0041] In some embodiments, the specific method of performing singular value decomposition on the physical quantity matrix of the internal flow field in step 1 is: calculating the singular values of the physical quantity matrix M of the internal flow field, first calculating the matrix M T M and the matrix MM T , and then find the matrix M T M and the matrix MM T The eigenvalues and eigenvectors of , and finally the eigenvalues are squared to get all singular values σ, assuming there are t singular values; the matrix M T The eigenvectors of M are the row vectors of the left singular matrix U, and the matrix MM T The eigenvectors of are right singular value matrices The row vector of , which can complete the singular value decomposition of the matrix M, that is
[0042]
[0043] Among them, U ij is the element of the left singular matrix U, σ i are the elements of the singular value matrix Σ, V ij is a right singular matrix V T elements.
[0044] In the above singular value decomposition of the M matrix, the matrix Σ is a diagonal matrix with only t non-zero numbers on the diagonal. Each element on the diagonal is called a singular value of the matrix M, and σ1>σ2>…>σ t , the singular value σ is the square root of the matrix eigenvalue. The larger the singular value σ is, the more information the dimension contains in the M matrix, and the greater the contribution of the dimension to the internal flow field value in the M matrix. It can be considered that within a certain error range, the M matrix can be obtained by the first r columns U i It is represented by a combination of (i=1…r) vectors.
[0045] In some embodiments, in step 2, r singular values are selected, and discarding the remaining tr singular values will bring a certain error. The relative error is defined as follows:
[0046]
[0047] Among them, M r is the physical quantity matrix of the internal flow field of the first r orders; σ i is the i-th order singular value, that is, the i-th order element of the singular matrix S; when r is large enough and the error is not greater than a certain accuracy, r is the optimal order.
[0048] In some embodiments, a certain flow condition among n flow conditions is selected as the test object, and the static temperature value of a certain grid node under the flow condition is considered. According to Taylor expansion and retaining quadratic terms, y is the static temperature value of a certain grid under unknown flow conditions, α is the interpolation coefficient, x is the static temperature value of the grid under the remaining n-1 flow conditions, and ε is the observation error.
[0049]
[0050] The above formula can obtain the mathematical relationship between the static temperature value of a grid node under certain flow conditions and the temperature value of the grid node under other flow conditions.
[0051] After multiple experiments, the above formula can be written in matrix form:
[0052]
[0053] The above formula can obtain the mathematical relationship between the static temperature value of each grid node under the kth flow condition and the temperature value of each grid node under other flow conditions.
[0054] The minimum variance is:
[0055]
[0056] in
[0057] When the variance is the smallest, the fitting surface with other n-1 flow conditions as independent variables is closest to the actual value. When the partial derivative of L with respect to α is 0, the minimum variance takes the minimum value. By:
[0058]
[0059] We can get:
[0060] α k =(X T X) -1 X T T k ;
[0061] According to α k =(X T X) -1 X T T k Get the interpolation coefficient α ik The vector α composed of the arrangement k , we can get the optimal interpolation coefficient α ik ; Among them, T k is the kth column vector of the matrix M, X is the first column of which is all 1, and the next n-1 columns are the matrix M minus the column vector T kThe remaining n-1 column vectors are composed of n columns of matrices, X T is the transpose of X.
[0062] In some embodiments, after step 4, the internal flow field matrix is updated based on the ground direct connection experiment data and the flight data, and the interpolation coefficient and the value of the optimal order are continuously optimized. By adding the data of the ground direct connection experiment and the flight experiment to the internal flow field matrix, the number of singular values r retained by the iterative update can be continuously optimized, and the prediction accuracy of the internal flow field can be continuously improved.
[0063] The present invention proposes a method for rapid prediction of the internal flow field of an RBCC engine based on singular value decomposition, including singular value decomposition of a matrix, response surface analysis of data, and interpolation and reconstruction of data. Singular value decomposition is often used for image compression. It can reduce the dimension of the matrix by selecting some singular values of the matrix, and at the same time obtain the main information of the matrix and discard the secondary information. It can greatly reduce the amount of data and data complexity, and is an important method for processing big data. Response surface analysis of the data can obtain the best interpolation coefficient of the data, and has the ability to interpolate the data with high precision. The combination of the above two methods can not only process massive data under existing conditions, but also interpolate and reconstruct the data after dimensionality reduction, deeply mine the implicit information of the existing data, and obtain data under new conditions, and has strong data processing and use capabilities. The present invention first performs singular value decomposition on the internal flow field matrix, selects an appropriate number of singular values r, and the internal flow field under any incoming flow condition can be linearly reconstructed by a corresponding number of r left singular vectors; response surface analysis is performed on the internal flow field data of the same grid unit under different incoming flow conditions to obtain the optimal interpolation coefficient α under different incoming flow conditions. i , the optimal interpolation coefficient can be used as the coefficient for linear reconstruction, that is, This method can obtain the interpolation coefficients of the internal flow field data under each incoming flow condition, so that the existing data set has a strong interpolation ability, and the internal flow field data under other incoming flow conditions can be obtained without solving partial differential equations such as the NS equation. Therefore, it has fast calculation speed and high accuracy, and is one of the ideal methods for predicting the internal flow field of RBCC engines.
[0064] Example
[0065] Use CAD software (such as UG, SolidWorks, SpaceClaim, etc.) to model the internal flow field of the RBCC engine, and then use CFD software (such as ANSYS Fluent, etc.) to simulate and calculate the temperature of the internal flow field of an RBCC engine under different conditions to obtain the temperature field matrix A:
[0066]
[0067] Pair Matrix Perform singular value decomposition:
[0068] Depend on We can get:
[0069] AA T The eigenvalues of are λ1=3 and λ2=1,
[0070] The eigenvector belonging to λ1=3 is:
[0071] The eigenvector belonging to λ2=1 is:
[0072] Similarly, AA T The eigenvalues of are λ1=3, λ2=1 and λ3=0,
[0073] The eigenvector belonging to λ1=3 is:
[0074] The eigenvector belonging to λ2=1 is:
[0075] The eigenvector belonging to λ3=0 is:
[0076] Depend on The singular values σ2=1,
[0077] but
[0078] Response surface analysis can be performed using Ansys DesignXplorer software.
[0079] The flow condition in the figure above is the mass flow rate (Massin), and the static temperature distribution (Static Temperature) is the internal flow field to be predicted by the present invention. Figure 2.1 is the static temperature distribution of the internal flow field of the RBCC engine under five flow conditions obtained by traditional CFD simulation, and Figure 2.2 is the static temperature distribution of the internal flow field of the RBCC engine predicted by the method described in the present invention.
[0080] like Figure 2.2(a) to Figure 2.2(c) As shown, they are respectively the static temperature distribution diagrams of the flow field in the RBCC engine under three incoming flow conditions predicted according to the above embodiment method, as shown in Figure 2.1(a) to Figure 2.1(c) As shown, they are respectively the static temperature distribution diagrams of the flow field in the RBCC engine under three incoming flow conditions obtained by traditional CFD simulation, and the three incoming flow conditions are respectively the mass flow rates of 1kg / s, 1.5kg / s and 2.5kg / s. By analyzing the prediction results obtained by the method described in the present invention, it can be obtained that the method has the following characteristics:
[0081] (1) High calculation accuracy:
[0082] Comparing the static temperature distribution of the simulation results and the predicted results one by one, we can see that:
[0083] Figure 2.1a and Figure 2.2a , Figure 2.1b and Figure 2.2b The static temperature distribution is consistent. Figure 2.1c and Figure 2.2c The static temperature distribution has a small error only in the isolation section, which shows that the prediction results of this method are still accurate when the mass flow rate is high (that is, the internal flow field is more complex).
[0084] (2) Comply with physical laws:
[0085] An overall analysis of the simulation results and the static temperature distribution in Figure 2.2 shows that:
[0086] The static temperature distribution predicted by the method of the present invention is consistent with the basic physical laws of gas dynamics.
[0087] In the expansion channel, the static temperature of supersonic airflow decreases due to the increase of Mach number; in the contraction channel, the static temperature increases due to the decrease of Mach number. In the cavity, due to the sudden expansion of the flow area, the viscous shear force increases, and the airflow forms a backflow in the cavity, resulting in a decrease in velocity and an increase in static temperature.
[0088] The static temperature distribution predicted by the method of the present invention is consistent with the basic physical laws of combustion.
[0089] Kerosene is sprayed into the front end of the cavity and mixed with the incoming air for combustion. When the incoming mass flow rate is small, the combustion area is located in the center of the flow channel; as the mass flow rate increases, the combustion position gradually approaches the wall and extends backward along the flow channel wall. The cavity has a significant flame stabilization effect. When the mass flow rate increases, most of the combustion is located in the cavity and its rear. And there is a static temperature mutation area caused by expansion waves and shock waves in the cavity at the rear of the combustion chamber.
[0090] (3) Small amount of calculation and fast speed:
[0091] The method described in the present invention only needs to perform CFD simulation on the static temperature distribution of the internal flow field of the RBCC engine under a small amount of incoming flow conditions, and can quickly derive the static temperature distribution of the internal flow field under a large number of incoming flow conditions through matrix operations. There is no need to perform CFD simulation on the static temperature distribution of the internal flow field under a large number of incoming flow conditions one by one, so the calculation cost is lower and the speed is faster.
[0092] In summary, the static temperature distribution predicted by the method of the present invention has a small error with the traditional CFD simulation results, can reflect the basic physical laws, and also has the advantages of small calculation amount and fast speed. Therefore, the method of the present invention can ensure that the simulation cost is greatly reduced and the simulation efficiency is improved within the allowable error range.
Claims
1. A fast prediction method for the internal flow field of RBCC engine based on singular value decomposition, It is characterized in that The following steps are involved: Step 1: Perform singular value decomposition on the characteristic matrix of the physical quantity of the flow field in the RBCC engine: Firstly, the internal flow field model of RBCC engine is established; Meshing the internal flow field model, selecting appropriate incoming flow conditions, and obtaining the internal flow field data under the incoming flow conditions through CFD numerical simulation; According to the internal flow field data, the physical quantity matrix M of the internal flow field is constructed, and the physical quantity matrix M of the internal flow field is subjected to singular value decomposition to obtain U i ; U i is the i-th column vector of the left singular matrix U; Step 2: Perform response surface analysis on the internal flow field data of the same grid unit under different inflow conditions to obtain the interpolation coefficient α under the kth inflow condition: ik ; Determine the optimal order r through error analysis; The specific method of error analysis in step 2 is: Among them, M r is the physical quantity matrix of the internal flow field of the first r orders; σ i is the i-th order singular value, that is, the i-th order element of the singular matrix S; when r is large enough and the error is not greater than ε, r is the optimal order; Step 3: According to the interpolation coefficient α ik , the optimal order r and the singular value decomposition results, and the predicted internal flow field T under the kth incoming flow condition is obtained rom,k ,Right now Step 4: The internal flow field T obtained in step 3 is rom,k and the kth column vector T of the internal flow field physical quantity matrix M obtained in step 1 k Compare and get the relative error Adjust the value of r until the relative error is minimized, at which point the value of r is its optimal value. After determining the optimal value of r, the predicted internal flow field with the minimum error under the kth incoming flow condition can be obtained.
2. A method for rapid prediction of the internal flow field of an RBCC engine based on singular value decomposition as claimed in claim 1, It is characterized in that The specific method for constructing the physical quantity matrix M of the internal flow field in step 1 is: the internal flow field data under each incoming flow condition constitutes a column vector, and the internal flow field column vectors under different incoming flow conditions constitute an internal flow field matrix. The number of matrix column vectors is the number of incoming flow conditions, and the number of row vectors is the number of grids.
3. A method for rapid prediction of the internal flow field of an RBCC engine based on singular value decomposition as claimed in claim 2, It is characterized in that The specific method of performing singular value decomposition on the physical quantity matrix of the internal flow field in step 1 is: Calculate the singular values of the physical quantity matrix M of the internal flow field. First, calculate the matrix M T M and the matrix MM T , and then find the matrix M T M and the matrix MM T The eigenvalues and eigenvectors of , and finally the eigenvalues are squared to get all singular values σ, assuming there are t singular values; Matrix M T The eigenvectors of M are the row vectors of the left singular matrix U, and the matrix MM T The eigenvectors of are right singular value matrices The row vector of , which can complete the singular value decomposition of the matrix M, 4. A method for rapid prediction of the internal flow field of an RBCC engine based on singular value decomposition as claimed in claim 1 or 2, It is characterized in that According to α k =(X T X) -1 X T T k Get the interpolation coefficient α ik The vector α composed of the arrangement k , we can get the interpolation coefficient α ik ; Among them, T k is the kth column vector of the matrix M, X is the first column of which is all 1, and the next n-1 columns are the matrix M minus the column vector T k The remaining n-1 columns of the matrix, X T is the transpose of X.
5. A method for rapid prediction of the internal flow field of an RBCC engine based on singular value decomposition as claimed in claim 1 or 2, It is characterized in that After step 4, the internal flow field matrix is updated according to the ground direct connection experimental data and flight data, and the interpolation coefficients and the optimal order are continuously optimized.