CN115730471A - Gas turbine uncertainty quantitative data mining method based on cubic convolution - Google Patents
Gas turbine uncertainty quantitative data mining method based on cubic convolution Download PDFInfo
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Abstract
The invention discloses a gas turbine uncertainty quantitative data mining method based on cubic convolution, which comprises the steps of generating original dense grid vertex data by using geometric parameters of a gas turbine and gas-heat parameters to be researched, constructing an initial Delaunay triangular grid on grid vertices, constructing a sparse Delaunay triangular grid after data sparseness, then generating a sparse regular rectangular grid, calculating gas-heat parameters and uncertainty indexes of each grid vertex of the sparse regular rectangular grid, then generating a dense regular rectangular grid, and obtaining the uncertainty indexes of the gas-heat parameters of each grid vertex of the dense regular rectangular grid by using a double BiCubic function cubic convolution method; and finally, inputting the space coordinates of each grid vertex of the dense regular rectangular grid and the uncertainty index of the gas-heat parameter into an open source computing library matplotlib to generate a distribution cloud chart of the uncertainty index of the gas-heat parameter.
Description
Technical Field
The invention belongs to the technical field of turbine design, and particularly relates to a gas turbine uncertainty quantitative data mining method based on cubic convolution.
Background
There are many inherent uncertainties in gas turbine manufacturing. Such as machining assembly errors and thermal ablation induced geometric profile degradation of the turbine blade tip clearance. Conventional gas turbine studies reduce these uncertainty parameters to deterministic values for the study. Thus, the performance predictions of conventional research and the actual operation of the gas turbine often fail to match resulting in premature failure of the turbine blades. Uncertainty quantification algorithms were introduced into the field of turbine design in the last decade. But at present, mainstream domestic and foreign uncertainty quantitative research focuses on providing algorithm efficiency and neglects mining of data obtained by the algorithm. The rich data obtained by the uncertain vectorization calculation still uses the processing method under the deterministic framework, thereby losing a large amount of effective information. Since the uncertainty quantization field of the gas turbine is the forefront field of the current domestic and foreign research, there is only a research on an excavation algorithm of uncertainty quantization data in the current open literature. Compared with a processing method under a deterministic framework, the mining of the uncertainty quantization data has the following problems:
(1) The data involved in the quantification of the uncertainty of a gas turbine comprise millions of grid vertices, which requires a large expenditure of time and costs even with parallel algorithms, not to mention the huge amount of computing and memory resources involved, given such huge amount of data.
(2) Uncertainty quantification studies require the computation of samples of different geometries. And the space coordinates of the grid vertexes at the same position in the characterization space of different geometric samples cannot be superposed, so that subsequent uncertainty quantitative calculation aiming at the same space position cannot be carried out. Currently, researchers have proposed using clustering methods to solve this problem. However, the clustering method can only be applied to data mining of mesh vertices near the wall surface of the structured mesh. For the grid vertex at the far wall surface or the non-structural grid, the clustering method fails due to the strong distortion of the grid space coordinate.
(3) At present, the visualization of the gas turbine calculation data mainly used in China is commercial software relying on a deterministic framework, such as Fluent or ANSYS CFX. The use of these commercial software not only requires a high cost to pay, but also the graphical computing process is completely closed. Researchers cannot custom set the computed data processing images that meet the uncertainty quantification requirements.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention aims to provide a gas turbine uncertainty quantitative data mining method based on cubic convolution, which is based on cubic convolution and a Delaunay triangulation interpolation technology, can simultaneously support the processing of uncertainty quantitative calculation data of a structured grid and an unstructured grid, and is completely independent of any commercial software in an image calculation process. The cloud images of the uncertainty distribution of the three-dimensional model obtained by the method are not shown in the current published documents, and have great engineering value for disclosing uncertainty phenomena in the processing operation of the gas turbine and guiding the robustness optimization design of the turbine blade.
In order to achieve the purpose, the invention adopts the technical scheme that:
a gas turbine uncertainty quantification data mining method based on cubic convolution comprises the following steps:
generating original dense grid vertex data by using geometric parameters of a gas turbine and gas thermal parameters to be researched, and constructing an initial Delaunay triangular grid on a grid vertex;
secondly, performing data sparseness on the initial Delaunay triangular grid by using a method such as a Visvalingam-Whyatt sparse algorithm and the like to greatly reduce the number of grid vertexes required to be calculated in the subsequent steps;
constructing a sparse Delaunay triangular grid on the grid vertex after the data are sparse;
generating a sparse regular rectangular grid at equal intervals according to preset precision parameters, and obtaining the space coordinate of each grid vertex of the sparse regular rectangular grid;
calculating the gas-heat parameters of each grid vertex of the sparse regular rectangular grid by adopting methods such as Delaunay triangle interpolation and the like according to the space coordinates of each grid vertex of the sparse Delaunay triangular grid and the sparse regular rectangular grid;
step six, performing the operations from step one to step five on all working conditions which need to be calculated for carrying out uncertainty quantitative calculation to obtain the space coordinates and the air-heat parameters of each grid vertex of each sparse regular rectangular grid of each working condition; calculating uncertainty indexes, namely mean values and standard deviations, of the gas-heat parameters of the vertexes of each grid of each sparse regular rectangular grid by using a polynomial chaos method;
step seven, generating dense regular rectangular grids according to the preset precision parameters at equal intervals, and obtaining the space coordinates of each grid vertex of the dense regular rectangular grids;
step eight, encrypting by using a double BiCubic function cubic convolution method according to the spatial coordinates and the uncertainty indexes of the gas-heat parameters of each grid vertex of the sparse regular rectangular grid and the spatial coordinates of each grid vertex of the dense regular rectangular grid to obtain the uncertainty indexes of the gas-heat parameters of each grid vertex of the dense regular rectangular grid;
and step nine, inputting the spatial coordinates of each grid vertex of the dense regular rectangular grid and the uncertainty indexes of the gas-heat parameters into an open source computing library matplotlib to generate a distribution cloud chart of the uncertainty indexes of the gas-heat parameters.
Compared with the prior art, the invention has the beneficial effects that:
(1) Through the introduction of the Visvalingam-Whyatt sparse algorithm, the number of grid vertices required to be processed by subsequent time-consuming uncertainty quantification calculation is greatly reduced. The number of grid vertices that need to be processed for uncertainty quantization computation is reduced to 33.2% of the original in one embodiment.
(2) The grid vertex data of all samples are mined by a Delaunay triangulation interpolation algorithm and mapped to the same sparse regular rectangular grid, so that the problem that the space coordinates of grid vertexes at the same position in different geometric sample representation spaces cannot be overlapped is fundamentally solved. Compared with a clustering method, the method provided by the invention can be simultaneously suitable for data mining of structured or unstructured grids, and the vertexes of the grids on the near wall surface or the far wall surface.
(3) The invention combines a double BiCubic function cubic convolution method to carry out high-fidelity encryption on the sparse regular rectangular grid, and greatly improves the image calculation precision of the distribution cloud chart of the uncertainty index of the gas thermal parameter with extremely low cost.
(4) The invention greatly reduces the calculated amount of the uncertainty quantitative data mining process, and even can realize the calculation of the distribution cloud chart of the uncertainty index of the gas-heat parameters of the three-dimensional gas turbine model. The distribution cloud pictures are not reported to be researched in the published literature at present. The abundant information which can be expressed has important significance for a turbine designer to know the flow mechanism of uncertain behaviors in the actual operation process of the gas turbine.
(5) The method can calculate the distribution cloud picture of the gas-heat parameters under the deterministic framework only by skipping the step six. Therefore, the method can be suitable for the uncertainty quantitative research of the leading edge and can also be applied to the traditional certainty quantitative research.
(6) The invention is completely based on a self-development algorithm and a small part of open libraries, and does not depend on any domestic and foreign commercial software.
Drawings
FIG. 1 is a schematic diagram of the system of the present invention.
Fig. 2 is a schematic diagram of the implementation of the dual BiCubic function cubic convolution method.
Fig. 3 is a cloud of standard deviation distributions of heat exchange amounts generated by the present invention, in which Q represents the standard deviation of the heat exchange amounts.
Detailed Description
The embodiments of the present invention will be described in detail below with reference to the drawings and examples.
In the embodiment of the present invention, the heat exchange amount is used as the gas thermal parameter to be studied, and the specific geometric parameters are shown in table 1.
TABLE 1GE (leaf form of E3)
| Name of geometric parameter | Numerical value (mm) |
| Axial chord length | 86.1 |
| Depth of groove | 5.08 |
| Tip clearance | 1.97 |
| Pitch of | 122 |
| Thickness of shoulder wall | 2.29 |
On the basis, referring to fig. 1, the specific flow of the uncertainty quantization data mining algorithm based on the cubic convolution method of the present invention is as follows:
step one, generating an initial Delaunay triangular grid.
And receiving the vertex data of the original dense mesh, and quickly constructing an initial Delaunay triangular mesh on the vertex of the dense mesh by using a Lawson algorithm.
In one embodiment, the raw dense grid vertex data is obtained by inputting the geometric parameters of the gas turbine and the gas thermal parameters to be studied into the open computational fluid dynamics library OPENFOAM. The original dense grid vertex data output by OPENFORM is a matrix M of L rows and 4 columns Densen . The number of L is the number of the original dense grid vertex data, each row represents the space coordinate and the gas-heat parameter of one grid vertex, wherein the first three columns represent the x coordinate, the y coordinate and the z coordinate of the grid vertex, and the fourth column represents the gas-heat parameter of the grid vertex. The initial Delaunay triangulated mesh is generated to establish the topological relationship of all the original dense mesh vertices. In this embodiment, L is 3497810, and the gas-heat parameter is the heat exchange amount.
The invention uses Lawson algorithm to construct initial Delaunay triangular mesh on the vertex of the original dense mesh, the method is as follows:
1) Memory matrix M Densen The first row of (2) represents a mesh vertex-based point P Base Traversing the matrix M Densen All mesh vertices and find the base point P Base The mesh vertex with the largest Euclidean distance is marked as P Tail Is connected to P Base And P Tail To obtain a line segment P Base P Tail Marked as a basic line; matrix M Densen Any one of the mesh vertices P Any To the base point P Base Euclidean distance of d Any The calculation formula of (a) is as follows:
in the formula (x) Any ,y Any, z Any ) Is P Any (x) is a space coordinate of (c) base ,y base, z base ) Is a base point P Base The spatial coordinates of (a).
2) Traverse matrix M Densen All grid vertices of (2) compute all x-coordinates greater thanBase point P Base From the mesh vertex to the line segment P Base P Tail The Euclidean distance of (c) to find the line segment P Base P Tail Point P having the smallest euclidean distance Min . Matrix M Densen Any one of the mesh vertices P Any To the base line P Base P Tail Euclidean distance d Anyline The calculation formula of (a) is as follows:
in the formula (x) Any ,y Any ,z Any ) Is P Any (x) is a space coordinate of (c) Stroke ,y Stroke ,z Stroke ) Is a point P Any To line segment P Base P Tail The spatial coordinates of the vertical point can be obtained by solving the following simultaneous equations:
x Stroke ＝(x a -x b )·t+x a (4)
y Stroke ＝(y a -y b )·t+y a (5)
z Stroke ＝(z a -z b )·t+z a (6)
in the formula, t is an auxiliary variable required for solving the equation. (x) a ,y a ,z a ) And (x) b ,y b ,z b ) Is a line segment P Base P Tail The spatial coordinates of any two points, P in this step Base And P Tail 。
3) Connection point P Min And P Base Obtain a line segment P Min P Base Point of attachment P Min And P Tail Obtain a line segment P Min P Tail . Line segment P Base P Tail Line segment P Min P Base And a line segment P Min P Tail Form aTriangle P Base P Tail P Min The triangle is a Delaunay triangle. Then, by line segment P Min P Base And a line segment P Min P Tail As a new base line, point P Min As a line segment P Min P Base Base point of (1), point P Tail As a line segment P Min P Tail The base point of (2).
4) Repeating 2) and 3) until the matrix M Densen All the mesh vertices of (a) are in a certain Delaunay triangle, and all the Delaunay triangles constitute the initial Delaunay triangle mesh. The topological relation of all the mesh vertices at this time can be represented by the initial Delaunay triangular mesh.
And step two, data sparseness is achieved.
And receiving an initial Delaunay triangular grid, and performing data sparseness on the initial Delaunay triangular grid by using a Visvalingam-Whyatt sparse algorithm so as to greatly reduce the number of grid vertices required to be calculated in a subsequent step. The implementation steps of the Visvalingam-Whyatt sparse algorithm are as follows:
1) The initial Delaunay triangulated mesh is received and the vertex of the Delaunay triangle with the smallest area that is not on the longest side is deleted. Area S of any one Delaunay triangle Delaunay The calculation method of (2) is as follows:
s 1 ＝(x 2 -x 1 ) 2 +(y 2 -y 1 ) 2 +(z 2 -z 1 ) 2 (8)
s 2 ＝(x 3 -x 1 ) 2 +(y 3 -y 1 ) 2 +(z 3 -z 1 ) 2 (9)
in the formula, s 1 And s 2 Auxiliary variables needed to solve the equations. (x) 1 ,y 1 ,z 1 )、(x 2 ,y 2 ,z 2 ) And (x) 3 ,y 3 ,z 3 ) Delaunay III for area to be solvedSpatial coordinates of the three vertices of the angle.
2) And regenerating the Delaunay triangular mesh on the remaining mesh vertexes by using the method of the step one.
3) Carrying out 1) operation on the regenerated Delaunay triangular mesh, and deleting one mesh vertex again until the number of the residual mesh vertices and the original matrix M Densen The ratio of the number of the grid vertexes reaches a preset value N res 。N res The larger the drawing accuracy, but the slower the calculation speed, N in the present embodiment res The setting was 30%.
4) Putting the space coordinates of the sparse grid vertex and the corresponding heat exchange quantity into a new matrix M Sparse The matrix stores the sparse grid vertex data.
And step three, generating a sparse Delaunay triangular grid.
Receiving sparse grid vertex data matrix M Sparse And quickly constructing a sparse Delaunay triangular mesh on the sparse mesh vertex, wherein the construction method is completely consistent with the first step.
And step four, generating a sparse regular rectangular grid.
Receiving sparse grid vertex data matrix M Sparse Traverse matrix M Sparse Let x be the x coordinate of the mesh vertex with the largest x coordinate max Let x be the x coordinate of the mesh vertex with the smallest x coordinate min ，x max And x min The difference is d x . Let y be the y coordinate of the mesh vertex with the largest y coordinate max Recording the y coordinate of the grid vertex with the minimum y coordinate as y min ，y max And y min The difference is d y . Let the z coordinate of the vertex of the mesh with the largest z coordinate be z max Let z be the z coordinate of the vertex of the mesh with the smallest z coordinate min ，z max And z min The difference is d z . Will d x Equally spaced apart by N x Each portion has a length d x /N x . Will d y Equally spaced apart by N y Each portion has a length d y /N y . D is to be z Equally spaced apart by N z Each portion has a length d z /N z . Wherein N is x 、N y And N z All are preset precision parameters, namely, the precision parameters defined by the invention comprise N x 、N y And N z ；N x 、N y And N z The larger the image, the higher the image calculation accuracy, but the longer the calculation time. In this embodiment, N x Is set to 400,N y Is set to 400,N z Set to 400. Then a sparse regular rectangular grid containing a total of 64000000 grid vertices is generated for 400 rows and 400 columns of 400 pages, i.e., the number of grid vertices of the generated sparse regular rectangular grid is N x ×N y ×N z . The calculation method of the space coordinates of the grid vertex of the ith row, j columns and k pages is as follows:
wherein i is a value from 1 to N x J is an integer of from 1 to N y K is an integer of from 1 to N z The sparse regular rectangular grid is a two-dimensional grid because the three-dimensional model is surrounded by two-dimensional planes. This represents d x 、d y And d z Must have one of 0. In this embodiment, d is given z Subsequent operation in the case of 0, and for d x Or d y In the case of 0, d may be replaced by setting the x-axis or the y-axis as the z-axis z A case of 0 (i.e., interchanging the z-coordinate of all mesh vertices with the x-coordinate or interchanging the z-coordinate of all mesh vertices with the y-coordinate). The subsequent operation of this embodiment can therefore be adapted to d x 、d y And d z Chinese character of anyOne is 0. Due to d z 0, the sparse regular rectangular grid is a 400 row 400 column sparse regular rectangular grid containing a total of 160000 grid vertices.
And step five, interpolating the Delaunay triangulation.
And receiving the space coordinates of each grid vertex of the sparse Delaunay triangular grid and the sparse regular rectangular grid, and calculating the heat exchange quantity of each grid vertex of the sparse regular rectangular grid. For each grid vertex of any sparse regular rectangular grid, the method for calculating the heat exchange amount of the sparse regular rectangular grid according to the sparse Delaunay triangular grid firstly needs to traverse the sparse Delaunay triangular grid, and judges which Delaunay triangle each grid vertex of the sparse regular rectangular grid to be calculated falls in. Judging whether the grid vertex is in a certain Delaunay triangle or not, wherein a ray along the positive direction of the x axis needs to be led out from the grid vertex, and if the intersection point of the ray and the three sides of the Delaunay triangle is an even number, the grid vertex is outside the Delaunay triangle. If the intersection of the three edges of the Delaunay triangle is odd, the mesh vertex is inside the Delaunay triangle. The Delaunay triangulation interpolation calculation method of the heat exchange quantity of the ith row and j column grid vertex of the sparse regular rectangular grid is as follows:
wherein (x) O ,y O )，(x P ,y P )，(x Q ,y Q ) The spatial coordinates, Q, of the three vertices of the Delaunay triangle in which the mesh vertices of the ith row and j columns are located O ，Q P ，Q Q Respectively corresponding to the gas-heat parameters of three vertexes of the Delaunay triangle in which the drawing nodes of the ith row and the j columns are positioned, calculating the gas-heat parameters of the grid vertexes of all sparse regular rectangular grids, and putting the space coordinates of the corresponding grid vertexes into a new matrix M Qsparse . In this example M Qsparse 160000 rows and 3 columns. Each row represents a mesh vertex of a sparse regular rectangular mesh. The first two columns are respectively the x coordinate and the y coordinate of the grid vertex, and the third column is the gas heat parameter, namely the heat exchange quantity, of the corresponding grid vertex.
And sixthly, carrying out uncertainty quantitative calculation.
And (4) performing operations from the first step to the fifth step on all samples, namely the working conditions required to be calculated by performing uncertainty quantitative calculation, and obtaining the space coordinate and the air-heat parameter of each grid vertex of each sparse regular rectangular grid of each sample. The uncertainty indexes (mean and standard deviation) of the gas-heat parameters of each grid vertex of each sparse regular rectangular grid can be calculated by inputting the uncertainty indexes into a public uncertainty quantitative calculation library aPC _ Matlab, and the standard deviation of the heat exchange quantity is researched in the embodiment. Calculating the standard deviation of the heat exchange quantity of the grid vertexes of all the sparse regular rectangular grids, and putting the space coordinates of the corresponding grid vertexes into a new matrix M Usparse 。M Usparse 160000 rows and 3 columns. Each row represents a mesh vertex of a sparse regular rectangular mesh. The first two columns are respectively the x coordinate and the y coordinate of the grid vertex, and the third column is the standard deviation of the heat exchange quantity of the corresponding grid vertex.
And step seven, generating a dense regular rectangular grid.
Receiving matrix M Usparse Traverse matrix M Usparse Let x be the x coordinate of the mesh vertex with the largest x coordinate Umax Let x be the x coordinate of the mesh vertex with the smallest x coordinate Umin ，x Umax And x Umin The difference is d Ux . Mesh vertex with maximum y coordinateHas a y coordinate of Umax Let y be the y coordinate of the mesh vertex with the smallest y coordinate Umin ，y Umax And y Umin The difference is d Uy . Will d Ux Equally spaced apart by N Ux Each portion has a length d Ux /N Ux . Will d Uy Equally spaced apart by N Uy Each portion has a length d Uy /N Uy . Wherein N is Ux 、N Uy And N Uz All are preset precision parameters, namely the precision parameter two of the invention comprises N Ux 、N Uy And N Uz 。N Ux And N Uy The larger the image, the higher the image calculation accuracy, but the longer the calculation time. In this embodiment, N Ux Is set to 2000,N Uy Set to 2000. A sparse regular rectangular grid of 4000000 grid vertices is generated for 2000 rows and 2000 columns, i.e. the number of grid vertices of the generated dense regular rectangular grid is N Ux ×N Uy And (4) respectively. Wherein the ith U Line j U The calculation method of the spatial coordinates of the grid vertices of the columns is as follows:
in the formula i U To take values from 1 to N Ux Integer of (j) U To take values from 1 to N Uy Is an integer of (1).
And step eight, carrying out double BiCubic function cubic convolution encryption.
Receiving matrix M Usparse And the space coordinates of each grid vertex of the dense regular rectangular grid are encrypted by using a double BiCubic function cubic convolution method to obtain the standard deviation of the heat exchange quantity of each grid vertex of the dense regular rectangular grid. For the ith dense regular rectangular grid U Line j U Grid vertex P of a column U Uncertainty index for solving gas thermal parameters by using BiCubic function cubic convolution methodThe steps of calibration (i.e., standard deviation of heat exchange amount in the present embodiment) are as follows:
1) Traverse matrix M Usparse Four mesh vertices are found that meet the following requirements: x coordinate and P U Is negative, and the absolute value of the difference is the smallest and penultimate of all grid vertices and the y-coordinate is associated with P U The difference of the y coordinates of (a) is a negative number, and the absolute value of the difference is the minimum of all the mesh vertices and the mesh vertex with the second lowest; x coordinate and P U Is positive, and the absolute value of the difference is the smallest and penultimate of all mesh vertices and the y coordinate is associated with P U The difference of the y coordinates of (a) is a negative number, and the absolute value of the difference is the minimum of all the mesh vertices and the mesh vertex with the second lowest; x coordinate and P U Is negative, and the absolute value of the difference is the smallest and penultimate of all grid vertices and the y-coordinate is associated with P U The difference of the y coordinates of (a) is a positive number, and the absolute value of the difference is the minimum and the second to last smallest of all the mesh vertices; x coordinate and P U Is positive, and the absolute value of the difference is the smallest and penultimate of all mesh vertices and the y coordinate is associated with P U The difference of the y-coordinate of (a) is a positive number and the absolute value of the difference is the smallest and penultimate mesh vertices of all mesh vertices. Sixteen points are finally found as shown in fig. 2: a is a 11 、a 12 、a 13 、a 14 、a 21 、a 22 、a 23 、a 24 、a 31 、a 32 、a 33 、a 34 、a 41 、a 42 、a 43 、a 44 。
2) The BiCubic function was constructed as follows:
wherein a is 0.5.x is the number of Bi Are the parameters of the auxiliary calculation.
3) Then P is U The uncertainty index of the gas thermal parameter can be calculated as follows：
In the formula i PU Is an integer having a value ranging from 1 to 4, j PU Are integers ranging from 1 to 4.
As mesh vertices
The deviation of the heat exchange quantity is the uncertainty index of the gas-heat parameters calculated here.
in the formula, floor () mathematically means rounding down.
When the density is regular rectangular grid ith U Line j U Grid vertex P of a column U When the grid is positioned at the boundary of the dense regular rectangular grid, the number of grid top points around the grid is less than 16, and the matrix M needs to be traversed at the moment Usparse . Using the nearest principle to connect the Euclidean distance with P U Minimum mesh apex heat exchange deviation assignment P U The calculation method of the euclidean distance is as follows:
in the formula (x) close ,y close ) To be solved for and P U Space coordinates of mesh vertices of Euclidean distance, (x) PU ,y PU ) Is P U The spatial coordinates of (a).
After uncertainty indexes of gas-heat parameters of each grid vertex of the dense regular rectangular grid are calculated, a new matrix M is put into the space coordinates of each grid vertex of the dense regular rectangular grid Udense 。M Udense A 4000000 matrix of rows and 3 columns, each row of which represents a grid vertex of a dense regular rectangular grid. The first two columns are respectively the x coordinate and the y coordinate of the grid vertex, and the third column is the uncertainty of the gas-heat parameter of the corresponding grid vertexThe index, i.e., the standard deviation of the heat exchange amount in the present embodiment.
And step nine, generating a distribution cloud picture of uncertainty indexes of gas-heat parameters.
The space coordinates of each grid vertex of the dense regular rectangular grid and the standard deviation of the heat exchange quantity are received and input into the open source computer library matplotlib, and the distribution cloud chart of the standard deviation of the heat exchange quantity shown in the figure 3 can be generated.
Fig. 3 is a cloud view of the standard deviation distribution of the heat exchange amount obtained in the example of the present invention, in which Q represents the standard deviation of the heat exchange amount. From the figure, it can be seen that two high heat exchange deviation areas (area I and area II) exist on the groove-shaped blade top. Wherein zone i is located near the impact point of the leading edge and zone ii is located near the fins. Therefore, in the design and manufacture of the gas turbine blade, the film cooling structure should be designed in the areas I and II to enhance cooling so as to protect the wall surface. In the spray coating of the thermal barrier coating, the coating thickness in zone i and zone ii needs to be significantly greater than in the other zones. In fact, the spray scheme of the thermal barrier coating can be directly determined according to the standard deviation distribution cloud chart of the heat exchange quantity given in the figure 3. The darker the colored areas in the figure require a thicker thermal barrier coating. The standard difference cloud pattern of the heat exchange quantity shown in fig. 3 cannot be obtained by using the traditional uncertainty data mining method, so that the thermal barrier coating is sprayed by adopting an interference strategy according to experience. Actual thermal barrier coatings tend to be too thick, not only affecting aerodynamic performance, but also wasting expensive thermal barrier coating materials. The standard difference distribution cloud picture of the heat exchange quantity calculated according to the invention can design the thermal barrier coating according to the requirement of accurate wall protection. Therefore, the method has important significance for understanding the uncertainty phenomenon in the gas turbine top operation process and guiding the turbine design with a turbine designer.
Claims (9)
1. A gas turbine uncertainty quantification data mining method based on cubic convolution is characterized by comprising the following steps:
generating original dense grid vertex data by using geometric parameters of a gas turbine and gas thermal parameters to be researched, and constructing an initial Delaunay triangular grid on a grid vertex;
secondly, performing data sparseness on the initial Delaunay triangular grid;
constructing a sparse Delaunay triangular grid on the grid vertex after the data are sparse;
generating a sparse regular rectangular grid at equal intervals according to preset precision parameters;
calculating the gas-heat parameters of each grid vertex of the sparse regular rectangular grid according to the sparse Delaunay triangular grid and the space coordinates of each grid vertex of the sparse regular rectangular grid;
step six, performing the operations from step one to step five on all working conditions which need to be calculated for carrying out uncertainty quantitative calculation to obtain the space coordinates and the air-heat parameters of each grid vertex of each sparse regular rectangular grid of each working condition; calculating uncertainty indexes, namely mean values and standard deviations, of the gas-heat parameters of each grid vertex of each sparse regular rectangular grid by using a polynomial chaos method;
step seven, generating dense regular rectangular grids according to the preset precision parameters at equal intervals;
step eight, encrypting by using a double BiCubic function cubic convolution method according to the spatial coordinates and the uncertainty indexes of the gas-heat parameters of each grid vertex of the sparse regular rectangular grid and the spatial coordinates of each grid vertex of the dense regular rectangular grid to obtain the uncertainty indexes of the gas-heat parameters of each grid vertex of the dense regular rectangular grid;
and step nine, inputting the space coordinates of each grid vertex of the dense regular rectangular grid and the uncertainty indexes of the gas-heat parameters into an open source computing library matplotlib to generate a distribution cloud chart of the uncertainty indexes of the gas-heat parameters.
2. The cubic convolution based gas turbine uncertainty quantitative data mining method of claim 1, wherein the geometric parameters of the gas turbine are axial chord length, flute depth, tip clearance, pitch, and shoulder wall thickness of a squealer tip of a gas turbine blade; the gas thermal parameter to be studied is the heat exchange quantity.
3. The gas turbine uncertainty quantitative data mining method based on cubic convolution according to claim 1 or 2, characterized in that, in the first step, geometric parameters of a gas turbine and gas thermal parameters to be researched are input into an open computational fluid dynamics library OPENFOAM to obtain original dense grid vertex data; the original dense grid vertex data is a matrix M with L rows and 4 columns Densen The number of L is the number of the original dense grid vertex data, each row represents the space coordinate and the gas-heat parameter of one grid vertex, wherein the first three columns represent the x coordinate, the y coordinate and the z coordinate of the grid vertex, and the fourth column represents the gas-heat parameter of the grid vertex.
4. The cubic convolution-based gas turbine uncertainty quantitative data mining method according to claim 3, wherein the first step is to construct an initial Delaunay triangular mesh on the original dense mesh vertices by using Lawson's algorithm as follows:
1) Memory matrix M Densen The first row of (2) represents a mesh vertex-based point P Base Traverse matrix M Densen All mesh vertices and find the base point P Base The mesh vertex with the largest Euclidean distance is marked as P Tail Is connected to P Base And P Tail Obtain a line segment P Base P Tail Marking as a basic line; matrix M Densen Any one mesh vertex P Any And a base point P Base Euclidean distance of d Any The calculation formula of (a) is as follows:
in the formula (x) Any ,y Any ,z Any ) Is P Any (x) is a space coordinate of (c) base ,y base ,z base ) Is a base point P Base The spatial coordinates of (a);
2) Traverse matrix M Densen Calculating all x coordinates greater than the base point P Base From the mesh vertex to the line segment P Base P Tail The Euclidean distance of (1) to find the line segment P Base P Tail Point P having the smallest euclidean distance Min (ii) a Matrix M Densen Any one of the mesh vertices P Any To line segment P Base P Tail Euclidean distance of d Anyline The calculation formula of (a) is as follows:
wherein (x) Stroke ,y Stroke ,z Stroke ) Is P Any To line segment P Base P Tail The following simultaneous equations are solved to obtain the spatial coordinates of the vertical points:
x Stroke ＝(x a -x b )·t+x a (4)
y Stroke ＝(y a -y b )·t+y a (5)
z Stroke ＝(z a -z b )·t+z a (6)
where t is an auxiliary variable required to solve the equation, (x) a ,y a ,z a ) And (x) b ,y b ,z b ) Is a line segment P Base P Tail The spatial coordinates of any two points, P in this step Base And P Tail ；
3) Connection point P Min And P Base Obtain a line segment P Min P Base Point of attachment P Min And P Tail Get the line segment P Min P Tail (ii) a Line segment P Base P Tail Line segment P Min P Base And a line segment P Min P Tail Form a triangle P Base P Tail P Min The triangle is a Delaunay triangle; then, by line segment P Min P Base And a line segment P Min P Tail As a new base line, point P Min As a line segment P Min P Base Base point of (1), point P Tail As a line segment P Min P Tail A base point of (a);
4) Repeating 2) and 3) until the matrix M Densen All the grid vertexes are in a certain Delaunay triangle, and all the Delaunay triangles form an initial Delaunay triangle grid; the topological relation of all the mesh vertices at this time is represented by the initial Delaunay triangular mesh.
5. The cubic convolution-based gas turbine uncertainty quantitative data mining method according to claim 4, wherein in the second step, the initial Delaunay triangular mesh is subjected to data sparsification by using a Visvalingam-Whyatt sparse algorithm, and the steps are as follows:
1) Receiving an initial Delaunay triangular mesh, deleting the vertex of the Delaunay triangle with the smallest area, which is not at the longest edge, and the area S of any Delaunay triangle Delaunay The calculation method of (2) is as follows:
s 1 ＝(x 2 -x 1 ) 2 +(y 2 -y 1 ) 2 +(z 2 -z 1 ) 2 (8)
s 2 ＝(x 3 -x 1 ) 2 +(y 3 -y 1 ) 2 +(z 3 -z 1 ) 2 (9)
in the formula, s 1 And s 2 Auxiliary variables required to solve the equation, (x) 1 ,y 1 ,z 1 )、(x 2 ,y 2 ,z 2 ) And (x) 3 ,y 3 ,z 3 ) The space coordinates of three vertexes of the Delaunay triangle with the area to be calculated are obtained;
2) Regenerating Delaunay triangular grids on the vertexes of the rest grids by using the method in the step one;
3) Carrying out 1) operation on the regenerated Delaunay triangular mesh, and deleting one mesh vertex again until the number of the residual mesh vertices and the original matrix M Densen The ratio of the number of the grid vertexes reaches a preset value N res ；
3) Putting the space coordinates of the grid vertex after sparse and the corresponding gas thermal parameters to be researched into a new matrix M Sparse The matrix stores the sparse grid vertex data.
6. The cubic convolution-based gas turbine uncertainty quantitative data mining method according to claim 5, wherein step four, traversing matrix M Sparse Let x be the x coordinate of the mesh vertex with the largest x coordinate max Let x be the x coordinate of the mesh vertex with the smallest x coordinate min ，x max And x min The difference is d x (ii) a Let y be the y coordinate of the mesh vertex with the largest y coordinate max Recording the y coordinate of the grid vertex with the minimum y coordinate as y min ，y max And y min The difference is d y (ii) a Let the z coordinate of the grid vertex with the largest z coordinate be z max Let z be the z coordinate of the vertex of the mesh with the smallest z coordinate min ，z max And z min The difference is d z (ii) a Will d x Equally spaced into N x Each portion has a length d x /N x (ii) a Will d y Equally spaced apart by N y Each portion has a length d y /N y (ii) a D is to be z Equally spaced into N z Each portion has a length d z /N z (ii) a The first precision parameter comprises N x 、N y And N z The number of grid vertexes of the generated sparse regular rectangular grid is N x ×N y ×N z (ii) a The calculation method of the space coordinates of the grid vertex of the ith row, j columns and k pages is as follows:
wherein i is a value from 1 to N x J is an integer of from 1 to N y K is an integer of from 1 to N z Is an integer of (1).
7. The cubic convolution-based gas turbine uncertainty quantitative data mining method according to claim 6, wherein in the fifth step, the Delaunay triangulation interpolation calculation method of the gas thermal parameters of the ith row and j column grid vertices of the sparse regular rectangular grid is as follows:
in the formula (x) O ，y O )，(x P ，y P )，(x Q ，y Q ) The spatial coordinates, Q, of three vertexes of the Delaunay triangle in which the mesh vertexes of the ith row and the j column are positioned O ，Q P ，Q Q Respectively corresponding to the gas-heat parameters of three vertexes of the Delaunay triangle in which drawing nodes of the ith row and the j column are positioned, calculating the gas-heat parameters to be researched of the grid vertexes of all sparse regular rectangular grids, and putting the space coordinates of the corresponding grid vertexes into a new matrix M Qsparse (ii) a Matrix M Qsparse Each row of the grid data represents a grid vertex of a sparse regular rectangular grid, the first two columns are respectively an x coordinate and a y coordinate of the grid vertex, and the third column is a gas-heat parameter of the corresponding grid vertex.
8. The gas turbine uncertainty quantitative data mining method based on cubic convolution of claim 7, characterized in that, in the sixth step, after uncertainty indexes of gas-heat parameters of grid vertices of all sparse regular rectangular grids are calculated, space coordinates of corresponding grid vertices are put together into a new matrix M Usparse (ii) a Step seven, traversing the matrix M Usparse Let x be the x coordinate of the mesh vertex with the largest x coordinate Umax Let x be the x coordinate of the mesh vertex with the smallest x coordinate Umin ，x Umax And x Umin The difference is d Ux (ii) a Let y be the y coordinate of the mesh vertex with the largest y coordinate Umax Recording the y coordinate of the grid vertex with the minimum y coordinate as y Umin ，y Umax And y Umin The difference is d Uy (ii) a Will d Ux Equally spaced apart by N Ux Each portion has a length d Ux /N Ux (ii) a D is to be Uy Equally spaced apart by N Uy Each portion has a length d Uy /N Uy (ii) a The second precision parameter comprises N Ux 、N Uy And N Uz The number of the grid vertexes of the generated dense regular rectangular grid is N Ux ×N Uy I th U Line j U The calculation method of the spatial coordinates of the grid vertices of the columns is as follows:
in the formula i U To take values from 1 to N Ux Integer of (j) U To take values from 1 to N Uy Is an integer of (1).
9. The cubic convolution-based gas turbine uncertainty quantitative data mining method of claim 8, wherein step eight is performed on ith regular square grid U Line j U Grid vertex P of a column U The method for solving the uncertainty index of the gas thermal parameter by using the BiCubic function cubic convolution method comprises the following steps:
1) Traverse matrix M Usparse Four mesh vertices are found that meet the following requirements: x coordinate and P U Is negative, and the absolute value of the difference is the smallest and penultimate of all grid vertices and the y-coordinate is associated with P U The difference of the y coordinates of (a) is a negative number, and the absolute value of the difference is the minimum of all the mesh vertices and the mesh vertex with the second lowest; x coordinate and P U Is positive, and the absolute value of the difference is the smallest and penultimate of all mesh vertices and the y coordinate is associated with P U The difference of the y coordinates of (a) is a negative number, and the absolute value of the difference is the minimum of all the grid vertexes and the grid vertex with the second smallest reciprocal; x coordinate and P U Is negative, and the absolute value of the difference is the smallest and penultimate of all grid vertices and the y-coordinate is associated with P U The difference of the y coordinates of (a) is a positive number, and the absolute value of the difference is the minimum and the second to last smallest of all the mesh vertices; x coordinate and P U Is a positive number, andthe absolute value of the difference is the minimum and penultimate of all mesh vertices and the y-coordinate is associated with P U The difference of the y coordinates of (a) is a positive number, and the absolute value of the difference is the minimum of all the grid vertexes and the grid vertex with the second smallest reciprocal;
2) The BiCubic function was constructed as follows:
wherein a is 0.5, x Bi Is a parameter for auxiliary calculation;
3)P U the uncertainty index of the gas thermal parameter of (a) is calculated as follows:
in the formula i PU Is an integer having a value ranging from 1 to 4, j PU Are integers having values ranging from 1 to 4,
as mesh vertices
Is determined by the uncertainty indicator of the gas-thermal parameter,
and
are the parameters of the aided calculation. To pair
To pair
To pair
To pair
To pair
To pair
To pair
To pair
Wherein u is PU And v PU For the auxiliary calculation of the variable, the calculation method is as follows:
in the formula, floor () mathematically represents rounding down;
when the density is regular rectangular grid ith U Line j U Grid vertex P of a column U When the grid is positioned at the boundary of the dense regular rectangular grid, the number of the grid top points around the grid is less than 16, and the matrix M is traversed at the moment Usparse (ii) a Using the nearest principle to connect the Euclidean distance with P U Assignment of uncertainty index P to the gas thermal parameter of the smallest mesh vertex U The calculation method of the euclidean distance is as follows:
in the formula (x) close ,y close ) To be solved for and P U Space coordinates of mesh vertices of Euclidean distance, (x) PU ,y PU ) Is P U The spatial coordinates of (a);
after uncertainty indexes of gas-heat parameters of each grid vertex of the dense regular rectangular grid are calculated, a new matrix M is put into the space coordinates of each grid vertex of the dense regular rectangular grid Udense Each row of the grid-based gas-heat parameter estimation method represents a grid vertex of a dense regular rectangular grid, the first two columns are respectively an x coordinate and a y coordinate of the grid vertex, and the third column is an uncertainty index of the gas-heat parameter of the corresponding grid vertex.
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