CN115688525B - Coating structure optimization design method - Google Patents
Coating structure optimization design method Download PDFInfo
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Abstract
The application discloses a coating structure optimization design method, which takes key characteristic parameters of a coating system as an objective function, takes the structural size and material property of the system as design variables and takes the requirement of the system in practical application as a constraint condition, and establishes a novel structure optimization method which can be used for designing the optimal size and material property of an ultra-temperature thermal barrier coating structure and improving the optimization efficiency.
Description
Technical Field
The application relates to a coating structure optimization design method.
Background
The united states national aviation agency has proposed the concept of Thermal Barrier Coatings (TBCs) in the fifties of the twentieth century, a complex multi-layer coating for providing thermal insulation and lowering the surface temperature of hot end components of engines in the aerospace industry. As shown in FIG. 1, conventional thermal barrier coating systems generally comprise four portions: a high temperature resistant alloy Substrate (SUB), a metal Bond Coat (BC) with excellent oxidation and corrosion resistance, a thermally grown oxide (ThermalGrownOxide, TGO) to prevent oxygen diffusion, a ceramic facing (TopCoat, TC) to provide good thermal insulation for the hot end components.
The TBC system is subjected to the thermal cycle action for a long time in the service process, so that TC layering and spalling are caused, and the thermal barrier coating system is further caused to fail. The material property and thickness of the TC layer are important indexes of the TC layer; the material properties and thickness of the TC layer change, and the stress and heat transfer temperature change correspondingly, however, no technology can simulate and predict the changed situation at present, and great challenges are brought to TBC system design.
The Chinese patent with the prior art publication number of CN114561613A discloses a coated double-tube structure for a 700 ℃ ultra-supercritical power station, which is shown in figure 2, and comprises a main steam pipeline (1) made of ferrite heat-resistant steel, wherein the inner surface of the main steam pipeline (1) adopts plasma spraying heat-insulating material powder to form a thermal barrier coating; a cooling steam pipe (2) is sleeved outside the main steam pipeline (1), and an annular steam channel (3) is formed between the cooling steam pipe (2) and the main steam pipeline (1); cooling steam flows through the annular steam channel (3), and the flowing direction of the cooling steam is opposite to the flowing direction of ultrahigh-temperature steam in the main steam pipeline (1). In the technology, in order to analyze the characteristics of a coating double-tube structure, a finite element model is built through ABAQUS, and then simulation test is carried out; when parameters in the reference model are kept unchanged, only the thickness of the TC layer is changed, a finite element model is built, and the influence of the thickness of the TC layer on the temperature and stress distribution of a coating pipeline system is analyzed, the finite element model with corresponding thickness needs to be built again each time, and huge workload is brought to the research of the thermal barrier coating.
Disclosure of Invention
The application aims to provide a coating structure optimization design method, which solves the problems that when the influence of TC layer thickness change on the temperature and stress distribution of a coating pipeline system is researched in the prior art, a finite element model with corresponding thickness needs to be repeatedly built, and the workload is huge.
The technical scheme adopted by the application is as follows: the coating structure optimization method is characterized by comprising the following steps of:
s1, establishing an initial finite element model of a TBC coating structure in ABAQUS, and manufacturing an inp file; the initial finite element model of the built TBC coating structure comprises a metal matrix-SUB layer, a metal bonding layer-BC layer, a thermally grown oxide-TGO layer and a ceramic surface layer-TC layer, which are of a four-layer structure; then, respectively establishing a heat transfer analysis model and a stress analysis model; the heat transfer analysis adopts an eight-node secondary axisymmetric heat transfer quadrilateral unit (DCAX 8), and the unit type used in the stress analysis is a two-way secondary axisymmetric quadrilateral unit with eight nodes, and the integral is reduced (CAX 8R).
S2, creating an objective function m file in MATLAB; the method comprises the following steps:
and step S2.1, defining 5 optimized variables of the thickness of the TC layer, the heat conductivity coefficient of the TC layer, the thermal expansion coefficient of the TC layer, the temperature of cooling steam and the pressure of the cooling steam.
Step S2.2, calculating the vertical distance r0 of the outer surface of the TC layer from the central axis according to the formula (1),
r0=initial TC layer boundary center axis distance- (post-change TC layer thickness-TC layer initial thickness) (1).
S2.3, calculating the number of units on one row in the x direction of the TC layer according to the formula (2);
the number of units in one line in the x direction=tc layer thickness/length in one unit in the x direction (expression 2), and the calculation result is an integer.
S2.4, calculating the number of units on one column in the y direction of the TC layer according to the formula (3);
the number of units on one column in the y direction=tc layer initial length/length in one unit y direction (expression 3), and the calculation result is an integer.
S2.5, calculating the total number of points of the TC layer; because the model division grid type is established in the step S1 and eight node types are adopted, the node calculation mode under the type is as follows: the number of the total points of the TC layer is calculated according to the number of the units in the x and y directions and is as follows:
total number of points= (number of units in x direction+1) × (number of units in y direction×2+1)
The number of units in the +x direction× (the number of units in the y direction +1) (expression 4).
Step S2.6, defining numbers for all nodes by using the following flow:
step S2.6.1, calculating the distance dx between two nodes in the x direction: dx=tc layer thickness/(number of cells in 2 x direction).
Step S2.6.2, calculating the distance dy between two nodes in the y direction: dy=tc layer width/(number of cells in 2×y direction).
Step S2.6.3, calculating the ordinate of the node on the a1 line: first, the number of units in the n1=y direction is defined×2+1; defining the number of units in the n2=y direction +1; the node horizontal coordinate value on the a1 line is unchanged, the node vertical coordinate value on the a1 line starts from 0 from bottom to top, and the distances dy between two nodes in the y direction are gradually increased until n1 times.
S2.6.4, calculating the abscissa of the left side edge line of each row of units; specifically, the left side edge line of the adjacent column unit on the right side of the a1 line is set to be a2 line, and then a3 line, … …, am line and the number of units in the m=x direction are set to be +1; the abscissa of the a1 line is r0, and the abscissa of the a2 line is r0+2×dx; a3 is r0+4×dx; … … the am line has an abscissa of the number of units in the r0+x direction×2×dx.
Step S2.6.5, calculating the ordinate of the node on the b1 line: the ordinate value of the intersection of the b1 line and the x-axis is 0, and the y value is increased from 0 to 2dy from bottom to top until n2 times.
Step S2.6.6, calculating the abscissa of the central lines of the other columns of units; specifically, the numbers of units in the z=x direction are defined as b1 line, b2 line, … …, bz line from the left to the right; the abscissa of line b1 is r0+dx, the abscissa of line b2 in the right adjacent column of cells is r0+dx+2dx, … …, and the abscissa of bz is r0+dx+2× (number of cells in x direction-1) ×dx.
Step S2.6.7, resetting the node numbers in the units, and specifically performing the following operations:
each unit in the model selects 8 numbers to define node numbers, and the unit numbers and the node number method in the model are reset as follows:
the unit numbering method is set as follows: the leftmost column of the model is a first column of units, and the number of columns increases by 1 from left to right; the lowest unit of the first column unit is 1 unit, the unit number of the column in which the 1 unit is arranged is increased by 1 from bottom to top, the lowest unit number of the second column unit on the right side of the first column unit is increased by 1 from top to top, then the second column unit number is increased by 1 from bottom to top, and all column units of the model are numbered by analogy.
The node numbering method is as follows:
(1) The cell left side node numbering method is as follows: setting the node number of the lower left corner of each unit as b, wherein the node numbers of the two nodes above the unit are sequentially b+1 and b+2, namely the node numbers of the three nodes on the left side of the unit from bottom to top are sequentially b+1 and b+2; wherein the value of b starts from 1, i.e. 1 cell has a lower left corner node number of 1, and the value of b in the following cell is increased by 2 from the value of b in the preceding cell.
The above is the rule of the first row of unit node numbers, and the lowest unit node numbers of the second row of units are numbered according to the following rule: the second column of cells, the lowermost cell, has the lower left corner node number: the node number of the upper left corner of the uppermost unit of the first column is increased by 1; the node numbers of the units in the second column are the same as the rules in the first column, and then the like;
(2) The method for numbering the nodes on the right side of the unit is as follows: the node numbers of the three nodes on the right side of the unit from bottom to top are sequentially b+n1, b+n1+1 and b+n1+2, wherein n1 is the total number of the nodes on the left side of the unit in the row, and the value b is the node number on the lower left corner of the unit.
(3) The numbers of the lower edge nodes and the upper edge nodes of the model 1 unit are respectively as follows: m+1, m+2, where m is the sum of the numbers of nodes on the left side of all columns of cells in the TC layer, and the numbers of the nodes on the lower side and the nodes on the upper side of the subsequent cells are increased by 1.
Step S2.7, setting at MATLAB:
(1) When the thickness of the TC layer in the model is increased, the unit columns are increased leftwards from the left side edge of the initial TC layer, and the number of the increased unit columns is as follows: the TC layer increases the thickness/dx; when adding columns, the initial unit number and the node number of the TC layer are unchanged; adding a new unit number and a node number, wherein the added new unit initial number is larger than the maximum node number of the initial model; then the newly added units and nodes are marked by using new numbers; specifically, the newly added units are numbered from left to right and from bottom to top; the node numbering rule of the newly added unit is the same as the node numbering method.
(2) When the thickness of the TC layer is reduced, deleting the corresponding unit columns from the left side edge of the initial TC layer, wherein the number of the deleted unit columns is as follows: the TC layer reduces the thickness/dx; the number information of the deleted unit is discarded, and the reserved unit number and node number are unchanged.
And forming an objective function m file through the operation.
S3, placing the inp file manufactured in the step S1 under the same path as the objective function m file; reading an inp file in MATLAB; after reading, storing the inp file in a matlab as a cell array form; in the inp file read in MATLAB, the TC layer thickness is defined through node coordinates; when the thickness of the TC layer is increased, namely the number of the unit columns is increased, firstly calculating the node coordinates of the added units in MATLAB; adding node coordinates of the added units in an inp file, and adding new added units according to the new node numbers; the model with increased TC layer thickness can be obtained through the operation; when the thickness of the TC layer is reduced, namely the number of unit columns is reduced, the corresponding column number coordinates are deleted in the inp file, and the model with reduced TC layer thickness can be obtained by deleting the corresponding column number coordinates from the left column of the model.
Further, in step S1, parameters are set in ABAQUS as follows: the TC layer thickness dc is 0.8mm, the TGO thickness dt is 0.001mm, the BC layer thickness db is 0.199mm, the thickness dp of the metal Substrate (SUB), namely the main steam pipe, is 30mm, and the inner radius R0=120mm; the TC and TGO interfaces and the TGO and BC interfaces reflect the geometric feature by adopting an ideal cosine morphology interface, and the functions are as follows:
5)
the bottom edge of the built model coincides with the x-axis in ABAQUS and the central axis c coincides with the y-axis.
Next, the boundary conditions set in the software are as follows: the internal pressure and the external pressure of the main steam pipeline are respectively P i =35 MPa and P O =5 MPa; the lower boundary imposing a symmetrical constraint in the axial directionMaking displacement in the axial direction; applying multi-point constraint on the upper boundary to enable all nodes of the upper boundary to have the same axial displacement; the multicomponent material is assumed to be isotropic and homogeneous and other material parameter values over a wide temperature range are estimated based on linear interpolation of the existing data.
Further, step S4 is included, the modified data is written into the inp file; invoking abaqus to perform simulation calculation, performing temperature calculation first, and then performing stress calculation to obtain an odb file; then the simulation result is called and read by MATLABAnd；andhoop stresses of the TC outer surface and the BC inner surface, respectively; calculating an objective function value in Matlab from the above values。
Further, a main optimizer is also included, which is created in MATLAB:
(1) Defining three parameters of a result, an objective function value and iteration times; defining 5 optimized variables of TC layer thickness, TC layer heat conductivity coefficient, TC layer thermal expansion coefficient, cooling steam temperature and cooling steam pressure;
in addition, the upper boundary of the TC layer thickness was set to 3mm, the lower boundary was set to 0, and the upper boundary of the TC layer thermal conductivity was set to 1.5W/mThe lower boundary is set to 1W/mThe method comprises the steps of carrying out a first treatment on the surface of the The lower boundary of the thermal expansion coefficient of the TC layer is set asThe upper boundary is set asThe method comprises the steps of carrying out a first treatment on the surface of the The upper boundary of the cooling steam temperature is set to 500The lower boundary is set to 100The method comprises the steps of carrying out a first treatment on the surface of the The lower boundary of the cooling steam pressure was set to 5MPa and the upper boundary was set to 10MPa.
(2) Inputting an initial value; the initial value of the TC layer thickness is 0.8mm, the initial value of the thermal conductivity coefficient of the TC layer is 1.2W/m ℃, and the initial value of the thermal expansion coefficient of the TC layer is 9.88 multiplied by 10 -6 The initial value of the steam temperature is 450 ℃, and the initial value of the cooling steam pressure is 5MPa.
(3) Modifying and optimizing options structures, specifically:
the function termination tolerance is set to 1×10 -9 ；
The termination tolerance at X is set to 1X 10 -9 ；
The maximum iteration number is set to 10000;
the maximum number of evaluations was set to 50000;
the last step is set to 5×10 -5 ；
Drawing an optimal plotfval diagram of an objective function.
(4) Applying an fminearch function to perform unconstrained nonlinear optimization on the objective function; outputting an optimal target root value, a function value corresponding to the optimal target root value and an fmincon additional condition value.
(5) The fminearch function in the main optimization program randomly selects a TC layer thickness that is anywhere between 0.0000 mm and 3.0000 mm.
The method and the function of the main optimization program are as follows:
the main optimization program calls the objective function value to judge whether the objective function value is the minimum value;
judging whether constraint conditions are met: whether the temperature of the left interface of the SUB layer is less than 580 ℃;
and outputting a result if the objective function value is the minimum value and the temperature of the interface at the left side of the SUB layer is less than 580 ℃.
The application has the beneficial effects that: in the coating structure optimization design method, the thickness of the TC layer is defined through node coordinates; when the thickness of the TC layer is increased, namely the number of the unit columns is increased, firstly calculating the node coordinates of the added units in MATLAB; adding node coordinates of the added units into the inp file, and adding new added units according to the new node numbers; the model with the increased TC layer thickness can be obtained through the operation; when the thickness of the TC layer is reduced, namely the number of unit columns is reduced, deleting the corresponding column number coordinates in an inp file, and deleting from the left column of the model to obtain the model with reduced TC layer thickness; and the optimization efficiency is improved.
Drawings
FIG. 1 is a block diagram of an initial finite element model of a coating structure built in an embodiment of the present application.
Fig. 2 is a schematic perspective view of a coated double tube structure according to an embodiment of the present application.
FIG. 3 is a table of material parameter settings according to an embodiment of the present application.
Fig. 4 is a partial information presentation view of an INP file generated by an embodiment of the present application.
FIG. 5 is a partial representation of an embodiment of the present application in ABAQUS to build an initial finite element model of a coating structure, with the numbers shown as element numbers and node numbers.
Fig. 6 is a content presentation diagram after reading an inp file in MATLAB according to an embodiment of the present application.
Detailed Description
Exemplary embodiments of the present disclosure are described below in conjunction with the accompanying drawings, which include various details of the embodiments of the present disclosure to facilitate understanding, and should be considered as merely exemplary. Accordingly, one of ordinary skill in the art will recognize that various changes and modifications of the embodiments described herein can be made without departing from the scope and spirit of the present disclosure. Also, descriptions of well-known functions and constructions are omitted in the following description for clarity and conciseness.
Examples
The coating structure optimization design method comprises the following steps:
and S1, establishing an initial finite element model of the TBC coating structure in ABAQUS, and manufacturing an inp file.
The initial finite element model of the coating structure established in this embodiment is shown in fig. 1, and is a section of a coating double-tube structure for a 700 ℃ ultra-supercritical power station disclosed in chinese patent publication No. CN114561613a, and specifically, a section of the single-coating double-tube structure of embodiment 1 in this patent with an axial length of 0.6mm (L in the figure) is cut off to establish the finite element model. The parameters of the built finite element model are shown in figure 1, and the model comprises a metal matrix-SUB layer, a metal bonding layer-BC layer, a thermally grown oxide-TGO layer and a ceramic surface layer-TC layer, which are of a four-layer structure; the setting parameters of each layer in the software in this embodiment are as follows: wherein, TC layer thickness dc is 0.8mm, TGO thickness dt is 0.001mm, BC layer thickness db is 0.199mm, thickness dp of metal Substrate (SUB), i.e. main steam pipe, is 30mm, inner radius R0=120 mm. Because of the spraying process, the interface between TC and TGO and the interface between TGO and BC are rough, the ideal cosine morphology interface is adopted to reflect the geometric morphology feature, and the functions are as follows:
5)
the bottom edge of the model is coincident with the x-axis in ABAQUS, and the central axis c is coincident with the y-axis.
Next, boundary conditions and material parameters are set in the software as follows: the internal pressure and the external pressure of the main steam pipeline are respectively P i =35 MPa and P O =5 MPa. The lower boundary applies symmetrical constraint in the axial direction to limit the displacement in the axial direction; the upper boundary imposes a multi-point constraint such that all nodes of the upper boundary have the same axial displacement. The multicomponent material is assumed to be isotropic and homogeneous and based onLinear interpolation of existing data estimates other material parameter values over a wide temperature range. The material parameters are shown in figure 3.
Then, respectively establishing a heat transfer analysis model and a stress analysis model; specifically, 249061 nodes and 80883 units in the model are added; the heat transfer analysis adopts an eight-node secondary axisymmetric heat transfer quadrilateral unit (DCAX 8), and the unit type used in the stress analysis is a two-way secondary axisymmetric quadrilateral unit with eight nodes, and the integral is reduced (CAX 8R).
Through the above operation, an inp file is formed.
Step S2, creating an objective function m file in MATLAB, wherein the step comprises the following steps:
and step S2.1, defining 5 optimized variables of the thickness of the TC layer, the heat conductivity coefficient of the TC layer, the thermal expansion coefficient of the TC layer, the temperature of cooling steam and the pressure of the cooling steam.
Step S2.2, calculating the vertical distance r0 of the outer surface of the TC layer from the central axis according to the formula (1),
r0=initial TC layer boundary central axis distance- (post-change TC layer thickness-TC layer initial thickness) (1);
for example, r0=119- (Wc-0.8) in this example.
S2.3, calculating the number of units on one row in the x direction of the TC layer according to the formula (2);
the number of units on one row in the x direction=the thickness of the TC layer/the length of one unit in the x direction (formula 2), and the calculated result is an integer; in this embodiment, the length of one unit in the x direction is 0.02, the number of units in one row in the x direction of the initial TC layer is 0.8-0.022/0.02=39, and when the geometric feature is reflected by adopting an ideal cosine morphology interface due to rough interface between TC and TGO, an incomplete unit column is formed at the interface, and the width of the incomplete unit column is 0.022, so that the number of units in one row in the x direction of the TC layer is calculated to be 0.8-0.022.
S2.4, calculating the number of units on one column in the y direction of the TC layer according to the formula (3);
the number of units on one column in the y direction=the initial length of the TC layer/the length of one unit in the y direction (formula 3), and the calculated result is an integer; in this embodiment, the number of units on one column in the y direction of the TC layer is 0.6/0.01, and the calculated result is an integer of 60.
And S2.5, calculating the total number of points of the TC layer. Specifically, because the model grid type is established in the step S1 of the present application with eight node types, the node calculation mode under the type is as follows: when there is only one cell, the nodes include points at the four corners of the cell and points at the midpoints of the four sides, as shown in fig. 4. Therefore, the number of the total points of the TC layer is calculated according to the number of the units in the x and y directions, and the total points are as follows:
total number of points= (number of units in x direction+1) × (number of units in y direction×2+1)
The number of units in the +x direction× (the number of units in the y direction +1) (expression 4).
The number of total points of the TC layer in the embodiment is as follows: (39+1) × (60×2+1) +39× (60+1) =7219.
Step S2.6, defining numbers for all nodes by using the following flow, wherein the node numbers are 1-7219 in the embodiment.
Step S2.6.1, calculating the distance dx between two nodes in the x direction:
dx=tc layer thickness/(number of cells in 2 x direction);
in this example dx is 0.01.
Step S2.6.2, calculating the distance dy between two nodes in the y direction:
dy=tc layer width/(number of cells in 2×y direction);
in this example, dy is 0.005.
Step S2.6.3, calculating the ordinate of the node on line a1 (i.e. the left line of the TC layer in the model of fig. 1): first, in the present application, the number of units in n1=y direction×2+1 (n1=121 in the present embodiment) is defined; defining the number of units +1 in the n2=y direction (n2=61 in the present embodiment); as shown in fig. 1, the intersection point coordinate of the a1 line and the x axis is (119,0), and the node coordinate on the a1 line is unchanged by x value, and the y value from bottom to top is gradually increased from 0 to n1 times by two node distances dy in the y direction.
In this example, n1 is 121, dx is 0.01, the intersection point coordinate of a1 line and the x axis is (119,0), and the node coordinates from bottom to top are (119,0.005), (119,0.01), (119,0.015) … … (119,0.6).
S2.6.4, calculating the abscissa of the left side edge line of each row of units; specifically, the left side line of the adjacent column unit on the right side of the a1 line is set as the a2 line, and then the a3 line, … … and am line (m=the number of units in the x direction+1); because the abscissa of the a1 line is r0, the abscissa of the a2 line is r0+2×dx; a3 is r0+4×dx; … … the am line has an abscissa of the number of units in the r0+x direction×2×dx.
In this embodiment, the abscissa of line a1 is 119, the abscissa of line a2 is 119.02, the abscissas of line a3 is 119.04, … …, and the abscissas of line a40 are 119.78.
Step S2.6.5, calculating the ordinate of the node on the b1 line (namely the vertical central line of the leftmost column unit of the TC layer): the ordinate value of the intersection of the b1 line and the x-axis is 0, and the y value is increased from 0 to 2dy from bottom to top until n2 times.
In this embodiment, the ordinate of the node from bottom to top on the b1 line is 0,0.01,0.02, … … and 0.6 in sequence.
Step S2.6.6, calculating the abscissa of the central lines of the other columns of units; specifically, the numbers of units in the z=x direction are defined as b1 line, b2 line, … …, bz line from the left to the right; the abscissa of line b1 is r0+dx, the abscissa of line b2 in the right adjacent column of cells is r0+dx+2dx, … …, and the abscissa of bz is r0+dx+2× (number of cells in x direction-1) ×dx.
In this example, the abscissa of line b1 is 119.01, the abscissa of line b2 is 119.03, and the abscissa of line b3 is 119.05 … … 119.77.
Step S2.6.7, resetting the node numbers in the units, and specifically performing the following operations:
firstly, it is to be noted that: when the initial finite element model of the coating structure is built in ABAQUS, the software defaults to set numbers for all units and nodes, and forms an INP file, wherein all information in the model building process, including material properties, the numbers of the units, the numbers and coordinates of the nodes and boundary conditions, are recorded in the INP file. Fig. 4 is a diagram showing part of information in the INP file generated in this embodiment, wherein the left frame is a unit number and the right frame is a node number. The cell number information (cell center number) and node number (cell four corner numbers and edge numbers) displayed in ABAQUS in the initial finite element model of the build coating structure are shown in fig. 5.
In the application, 8 numbers are selected for each unit to define the node numbers on the unit, and in the embodiment, all nodes of the initial model define 1-7401 numbers; as shown in fig. 5, 1 unit 8 nodes are numbered: 1,2,3 (three nodes on the left); 122 123,124 (three nodes on the right); 4841 4842 (lower and upper nodes);
the number of 8 nodes of the 2 units is: 3,4,5 (three nodes on the left); 124 125, 126 (three nodes on the right); 4842 4843 (lower and upper nodes).
The application resets the unit number and node number method in the model as follows:
the unit numbering method is set as follows: the leftmost column of the model is a first column of units, and the number of columns increases by 1 from left to right; the lowest unit of the first column unit is 1 unit, the unit number of the column in which the 1 unit is arranged is increased by 1 from bottom to top, the lowest unit number of the second column unit number on the right side of the first column unit is increased by 1 from top to top of the first column unit, then the second column unit number is increased by 1 from bottom to top, and all column units of the model are numbered by analogy.
The node numbering method is as follows:
(1) The cell left side node numbering method is as follows: setting the node number of the lower left corner of each unit as b, wherein the node numbers of the two nodes above the unit are sequentially b+1 and b+2, namely the node numbers of the three nodes on the left side of the unit from bottom to top are sequentially b+1 and b+2; wherein the value of b starts from 1, i.e. 1 cell has a lower left corner node number of 1, and the value of b in the following cell is increased by 2 from the value of b in the previous cell; in the embodiment, the node number of the lower left corner of the 2 units is 3, and the node number of the lower left corner of the 3 units is 5;
the above is the rule of the first row of unit node numbers, and the lowest unit node numbers of the second row of units are numbered according to the following rule: the second column of cells, the lowermost cell, has the lower left corner node number: the node number of the upper left corner of the uppermost unit of the first column is increased by 1; for example, in the present embodiment, the node number of the upper left corner of the uppermost unit in the first column is 121, and the node number of the lower left corner of the lowermost unit and the second column is 122; the cell node numbers in the second column are the same as the rules in the first column, and so on.
(2) The method for numbering the nodes on the right side of the unit is as follows: the node numbers of the three nodes on the right side of the unit from bottom to top are sequentially b+n1, b+n1+1 and b+n1+2, wherein n1 is the total number of the nodes on the left side of the unit in the row, and the value b is the node number on the lower left corner of the unit; for example, in this embodiment, the total number of nodes on the left side of the column where the 1 unit is located is 121, the node number on the lower left corner of the 1 unit is 1, and then the node numbers of the three nodes on the right side of the 1 unit from bottom to top are 122,123,124.
(3) The numbers of the lower edge nodes and the upper edge nodes of the model 1 unit are respectively as follows: m+1, m+2, where m is the sum of the numbers of nodes on the left side of all column units of the TC layer, and m is 4840 in this embodiment; then 1 unit lower edge node and upper edge node numbers 4841 and 4842, respectively; the lower and upper node numbers of the following cells are incremented by 1.
Step S2.7, setting at MATLAB:
(1) When the thickness of the TC layer in the model is increased, the unit columns are increased leftwards from the left side edge of the initial TC layer, and the number of the increased unit columns is as follows: the TC layer increases the thickness/dx; when adding columns, the initial unit number and the node number of the TC layer are unchanged; adding a new unit number and a node number, wherein the added new unit initial number is larger than the maximum node number of the initial model; for example, in this embodiment, the maximum node number of the initial model is 249061, and the initial number of the newly added unit number may be 700000; then the newly added units and nodes are marked by using new numbers; specifically, the newly added units are numbered from left to right and from bottom to top; the node numbering rule of the newly added unit is the same as the node numbering method.
(2) When the thickness of the TC layer is reduced, deleting the corresponding unit columns from the left side edge of the initial TC layer, wherein the number of the deleted unit columns is as follows: the TC layer reduces the thickness/dx; the number information of the deleted unit is discarded, and the reserved unit number and node number are unchanged.
And forming an objective function m file through the operation.
S3, placing the inp file manufactured in the step S1 under the same path as the objective function m file; reading an inp file in MATLAB; after reading, the inp file is stored in matlab in the form of a cell array.
The content of the inp file after reading is shown in FIG. 6 below, which defines the TC layer thickness by node coordinates; when the thickness of the TC layer is increased, namely the number of the unit columns is increased, firstly calculating the node coordinates of the added units in MATLAB; adding node coordinates of the added units into the inp file, and adding new added units according to the new node numbers; the model with the increased TC layer thickness can be obtained through the operation; when the thickness of the TC layer is reduced, namely the number of unit columns is reduced, the coordinates of the corresponding columns are deleted in the inp file, and the model with reduced TC layer thickness can be obtained by starting deleting from the left column of the model.
In addition, the 5 optimized variables of TC layer thickness, TC layer thermal conductivity, TC layer thermal expansion coefficient, cooling steam temperature and cooling steam pressure defined in the step S2.1; the heat conductivity coefficient of the TC layer and the temperature of cooling steam can be modified for the heat transfer model; the TC layer coefficient of thermal expansion, the cooling vapor pressure, is modified for the stress model.
Writing the modified data into an inp file; and calling abaqus to perform simulation calculation, performing temperature calculation first, and then performing stress calculation to obtain an odb file. Then the simulation result is called and read by MATLABAnd。andrespectively TC outer surface and BC inner surfaceHoop stress. Calculating an objective function value in Matlab from the above values。
Furthermore, the application also provides a main optimization program which is created in MATLAB, and the m file process is as follows:
(1) Defining three parameters of a result, an objective function value and iteration times; defining 5 optimized variables of TC layer thickness, TC layer heat conductivity coefficient, TC layer thermal expansion coefficient, cooling steam temperature and cooling steam pressure.
In addition, the upper boundary of the TC layer thickness was set to 3mm, the lower boundary was set to 0, and the upper boundary of the TC layer thermal conductivity was set to 1.5W/mThe lower boundary is set to 1W/mThe method comprises the steps of carrying out a first treatment on the surface of the The lower boundary of the thermal expansion coefficient of the TC layer is set asThe upper boundary is set asThe method comprises the steps of carrying out a first treatment on the surface of the The upper boundary of the cooling steam temperature is set to 500The lower boundary is set to 100The method comprises the steps of carrying out a first treatment on the surface of the The lower boundary of the cooling steam pressure was set to 5MPa and the upper boundary was set to 10MPa.
(2) Inputting an initial value; the embodiment specifically comprises the following steps: the initial value of the TC layer thickness is 0.8mm, the initial value of the thermal conductivity coefficient of the TC layer is 1.2W/m ℃, and the initial value of the thermal expansion coefficient of the TC layer is 9.88 multiplied by 10 -6 The initial value of the steam temperature is 450 ℃, and the initial value of the cooling steam pressure is 5MPa.
(3) Modifying and optimizing options structures, specifically:
the function termination tolerance is set to 1×10 -9 ；
The termination tolerance at X is set to 1X 10 -9 ；
The maximum iteration number is set to 10000;
the maximum number of evaluations was set to 50000;
the last step is set to 5×10 -5 ；
Drawing an optimal plotfval diagram of an objective function.
(4) Applying an fminearch function to perform unconstrained nonlinear optimization on the objective function; outputting an optimal target root value, a function value corresponding to the optimal target root value and an fmincon additional condition value.
(5) Randomly selecting a TC layer thickness by using an fminearch function in a main optimization program, wherein the selected TC layer thickness is any number between 0.0000 and 3.0000 mm; for example 0.7.
The method and the function of the main optimization program are as follows:
the main optimization program calls the objective function value to judge whether the objective function value is the minimum value;
judging whether constraint conditions are met: whether the temperature of the left interface of the SUB layer is less than 580 ℃;
and outputting a result if the objective function value is the minimum value and the temperature of the interface at the left side of the SUB layer is less than 580 ℃. After optimization, an optimized model with improved heat insulation effect and better stability can be obtained.
Other embodiments of the disclosure will be apparent to those skilled in the art from consideration of the specification and practice of the disclosure disclosed herein. This application is intended to cover any adaptations, uses, or adaptations of the disclosure following, in general, the principles of the disclosure and including such departures from the present disclosure as come within known or customary practice within the art to which the disclosure pertains. It is intended that the specification and examples be considered as exemplary only, with a true scope and spirit of the disclosure being indicated by the following claims.
Claims (2)
1. The coating structure optimization method is characterized by comprising the following steps of:
s1, establishing an initial finite element model of a TBC coating structure in ABAQUS, and manufacturing an inp file; the initial finite element model of the built TBC coating structure comprises a metal matrix-SUB layer, a metal bonding layer-BC layer, a thermally grown oxide-TGO layer and a ceramic surface layer-TC layer, which are of a four-layer structure; then, respectively establishing a heat transfer analysis model and a stress analysis model; the heat transfer analysis adopts eight-node secondary axisymmetric heat transfer quadrilateral units, and the type of the units used for stress analysis is equal to that of eight-node bidirectional secondary axisymmetric quadrilateral units, so that the integral is reduced;
s2, creating an objective function m file in MATLAB; the method comprises the following steps:
s2.1, defining 5 optimized variables of TC layer thickness, TC layer heat conductivity coefficient, TC layer thermal expansion coefficient, cooling steam temperature and cooling steam pressure;
step 2.2, calculating the vertical distance r0 of the outer surface of the TC layer from the central axis according to the formula 1, wherein r0 = initial TC layer boundary central axis distance- (TC layer thickness after change-TC layer initial thickness) (formula 1);
s2.3, calculating the number of units on one row in the x direction of the TC layer according to the formula (2);
the number of units on one row in the x direction=the thickness of the TC layer/the length of one unit in the x direction (formula 2), and the calculated result is an integer;
s2.4, calculating the number of units on one column in the y direction of the TC layer according to the formula (3);
the number of units on one column in the y direction=the initial length of the TC layer/the length of one unit in the y direction (formula 3), and the calculated result is an integer;
s2.5, calculating the total number of points of the TC layer; because the model division grid type is established in the step S1 and eight node types are adopted, the node calculation mode under the type is as follows: the number of the total points of the TC layer is calculated according to the number of the units in the x and y directions and is as follows:
total number of points= (number of units in x direction+1) × (number of units in y direction×2+1)
The number of units in the +x direction (the number of units in the y direction +1) (expression 4);
step S2.6, defining numbers for all nodes by using the following flow:
step S2.6.1, calculating the distance dx between two nodes in the x direction: dx=tc layer thickness/(number of cells in 2 x direction);
step S2.6.2, calculating the distance dy between two nodes in the y direction: dy=tc layer width/(number of cells in 2×y direction);
step S2.6.3, calculating the ordinate of the node on the a1 line: first, the number of units in the n1=y direction is defined×2+1; defining the number of units in the n2=y direction +1; the node horizontal coordinate value on the a1 line is unchanged, the node vertical coordinate value on the a1 line starts from 0 from bottom to top, and the distances dy between two nodes in the y direction are gradually increased until n1 times;
s2.6.4, calculating the abscissa of the left side edge line of each row of units; specifically, the left side edge line of the adjacent column unit on the right side of the a1 line is set to be a2 line, and then a3 line, … …, am line and the number of units in the m=x direction are set to be +1; the abscissa of the a1 line is r0, and the abscissa of the a2 line is r0+2×dx; a3 is r0+4×dx; … … the am line has an abscissa of r0+x-direction number of units×2×dx;
step S2.6.5, calculating the ordinate of the node on the b1 line: the vertical coordinate value of the intersection point of the b1 line and the x axis is 0, and the y value is gradually increased by 2dy from 0 from bottom to top until n2 times;
step S2.6.6, calculating the abscissa of the central lines of the other columns of units; specifically, the numbers of units in the z=x direction are defined as b1 line, b2 line, … …, bz line from the left to the right; the abscissa of the b1 line is r0+dx, the abscissa of the b2 line of the line in the right adjacent column is r0+dx+2dx, … …, and the abscissa of bz is r0+dx+2× (the number of units in the x direction-1) ×dx;
step S2.6.7, resetting the node numbers in the units, and specifically performing the following operations:
each unit in the model selects 8 numbers to define node numbers, and the unit numbers and the node number method in the model are reset as follows:
the unit numbering method is set as follows: the leftmost column of the model is a first column of units, and the number of columns increases by 1 from left to right; the lowest unit of the first column unit is 1 unit, the unit number of the column in which the 1 unit is arranged is increased by 1 from bottom to top, the lowest unit number of the second column unit on the right side of the first column unit is increased by 1 from top to top, then the second column unit number is increased by 1 from bottom to top, and all column units of the model are numbered by analogy;
the node numbering method is as follows:
(1) The cell left side node numbering method is as follows: setting the node number of the lower left corner of each unit as b, wherein the node numbers of the two nodes above the unit are sequentially b+1 and b+2, namely the node numbers of the three nodes on the left side of the unit from bottom to top are sequentially b+1 and b+2; wherein the value of b starts from 1, i.e. 1 cell has a lower left corner node number of 1, and the value of b in the following cell is increased by 2 from the value of b in the previous cell;
the above is the rule of the first row of unit node numbers, and the lowest unit node numbers of the second row of units are numbered according to the following rule: the second column of cells, the lowermost cell, has the lower left corner node number: the node number of the upper left corner of the uppermost unit of the first column is increased by 1; the node numbers of the units in the second column are the same as the rules in the first column, and then the like;
(2) The method for numbering the nodes on the right side of the unit is as follows: the node numbers of the three nodes on the right side of the unit from bottom to top are sequentially b+n1, b+n1+1 and b+n1+2, wherein n1 is the total number of the nodes on the left side of the unit in the row, and the value b is the node number on the lower left corner of the unit;
(3) The numbers of the lower edge nodes and the upper edge nodes of the model 1 unit are respectively as follows: m+1, m+2, wherein m is the sum of the numbers of nodes at the left side of all columns of units of the TC layer, and the numbers of the nodes at the lower side and the nodes at the upper side of the later units are increased by 1;
step S2.7, setting at MATLAB:
(1) When the thickness of the TC layer in the model is increased, the unit columns are increased leftwards from the left side edge of the initial TC layer, and the number of the increased unit columns is as follows: the TC layer increases the thickness/dx; when adding columns, the initial unit number and the node number of the TC layer are unchanged; adding a new unit number and a node number, wherein the added new unit initial number is larger than the maximum node number of the initial model; then the newly added units and nodes are marked by using new numbers; specifically, the newly added units are numbered from left to right and from bottom to top; the node numbering rule of the newly added unit is the same as the node numbering method;
(2) When the thickness of the TC layer is reduced, deleting the corresponding unit columns from the left side edge of the initial TC layer, wherein the number of the deleted unit columns is as follows: the TC layer reduces the thickness/dx; discarding the number information of the deleted unit, wherein the reserved unit number and node number are unchanged;
forming an objective function m file through the operation;
s3, placing the inp file manufactured in the step S1 under the same path as the objective function m file; reading an inp file in MATLAB; after reading, storing the inp file in a matlab as a cell array form;
in the inp file read in MATLAB, the TC layer thickness is defined through node coordinates; when the thickness of the TC layer is increased, namely the number of the unit columns is increased, firstly calculating the node coordinates of the added units in MATLAB; adding node coordinates of the added units in an inp file, and adding new added units according to the new node numbers; the model with increased TC layer thickness can be obtained through the operation; when the thickness of the TC layer is reduced, namely the number of unit columns is reduced, deleting the corresponding column number coordinates in an inp file, and particularly deleting the coordinates from the left column of the model, so that the model with reduced TC layer thickness can be obtained;
s4, writing the modified data into an inp file; invoking abaqus to perform simulation calculation, performing temperature calculation first, and then performing stress calculation to obtain an odb file; then the simulation result is called and read by MATLABAnd and->TC outer surface and BC inner surface respectivelyHoop stress of the face; calculating the objective function value +.in Matlab by the above-mentioned value>
The m file process is as follows:
(1) Defining three parameters of a result, an objective function value and iteration times; defining 5 optimized variables of TC layer thickness, TC layer heat conductivity coefficient, TC layer thermal expansion coefficient, cooling steam temperature and cooling steam pressure;
in addition, the upper boundary of the TC layer thickness is set to 3mm, the lower boundary is set to 0, the upper boundary of the TC layer heat conductivity coefficient is set to 1.5W/m ℃ and the lower boundary is set to 1W/m ℃; the lower boundary of the thermal expansion coefficient of the TC layer is set to 6 multiplied by 10 -6 The upper boundary was set to be 14X 10 at/. Degree.C -6 a/DEG C; the upper boundary of the cooling steam temperature is set to 500 ℃, and the lower boundary is set to 100 ℃; the lower boundary of the cooling steam pressure is set to 5MPa, and the upper boundary is set to 10MPa;
(2) Inputting an initial value; the initial value of the TC layer thickness is 0.8mm, the initial value of the thermal conductivity coefficient of the TC layer is 1.2W/m ℃, and the initial value of the thermal expansion coefficient of the TC layer is 9.88 multiplied by 10 -6 Setting the initial value of steam temperature at 450 ℃ and the initial value of cooling steam pressure at 5MPa;
(3) Modifying and optimizing options structures, specifically:
the function termination tolerance is set to 1×10 -9 ；
The termination tolerance at X is set to 1X 10 -9 ；
The maximum iteration number is set to 10000;
the maximum number of evaluations was set to 50000;
the last step is set to 5×10 -5 ；
Drawing an optimal plotfval diagram of an objective function;
(4) Applying an fminearch function to perform unconstrained nonlinear optimization on the objective function; outputting an optimal target root value, a function value corresponding to the optimal target root value and an fmincon additional condition value;
(5) Randomly selecting a TC layer thickness by using an fminearch function in a main optimization program, wherein the selected TC layer thickness is any number between 0.0000 and 3.0000 mm;
the method and the function of the main optimization program are as follows:
the main optimization program calls the objective function value to judge whether the objective function value is the minimum value;
judging whether constraint conditions are met: whether the temperature of the left interface of the SUB layer is less than 580 ℃;
and outputting a result if the objective function value is the minimum value and the temperature of the interface at the left side of the SUB layer is less than 580 ℃.
2. The method for optimizing a coating structure according to claim 1, wherein in step S1, parameters are set as follows in ABAQUS: the TC layer thickness dc is 0.8mm, the TGO thickness dt is 0.001mm, the BC layer thickness db is 0.199mm, the thickness dp of the metal substrate SUB, namely the main steam pipeline, is 30mm, and the inner radius R0=120mm; the TC and TGO interfaces and the TGO and BC interfaces reflect geometric morphology features by adopting ideal cosine morphology interfaces, and the functions used are as follows:
y＝-0.008cos(πx/0.05)
the bottom edge of the built model is overlapped with the x axis in ABAQUS, and the central axis c is overlapped with the y axis;
next, the boundary conditions set in the software are as follows: the internal pressure and the external pressure of the main steam pipeline are respectively P i =35 MPa and P O =5 MPa; the lower boundary applies symmetrical constraint in the axial direction to limit the displacement in the axial direction; applying multi-point constraint on the upper boundary to enable all nodes of the upper boundary to have the same axial displacement; the multicomponent material is assumed to be isotropic and homogeneous and other material parameter values over a wide temperature range are estimated based on linear interpolation of the existing data.
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