CN115688525A - Coating structure optimization design method - Google Patents
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Abstract
The invention discloses a coating structure optimization design method, which takes key characteristic parameters of a coating system as an objective function, takes the structure size and material property of the system as design variables, and takes the requirement of the system in practical application as a constraint condition to establish a novel structure optimization method.
Description
Technical Field
The invention relates to a coating structure optimization design method.
Background
The united states national aerospace agency has introduced the concept of Thermal Barrier Coatings (TBCs) in the fifties of the twentieth century, which is a complex multi-layer coating for providing thermal insulation in the aerospace industry and reducing the surface temperature of hot end components of engines. As shown in FIG. 1, a conventional thermal barrier coating system generally includes four parts: a high temperature resistant alloy Substrate (SUB), a metal Bond Coat (BC) with excellent oxidation and corrosion resistance, a Thermally Grown Oxide (TGO) to prevent oxygen diffusion, a ceramic top coat (TopCoat, TC) to provide good thermal insulation for hot end components.
The TBC system can be subjected to thermal cycle action for a long time in the service process to cause TC delamination and spalling, thereby further causing the failure of the thermal barrier coating system. The material property and the 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 accordingly, however, no technology is available to simulate and predict the changed conditions, which brings great challenges to TBC system design.
The Chinese patent with the prior art publication number of CN114561613A discloses a coating double-tube structure for a 700 ℃ ultra-supercritical power station, as shown in figure 2, which comprises a main steam pipeline (1) made of ferrite heat-resistant steel, wherein the inner surface of the main steam pipeline (1) adopts plasma sprayed 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 that of the 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 established 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, the finite element model is established, and the influence of the thickness of the TC layer on the temperature and stress distribution of the coating pipeline system is analyzed, the finite element model with the corresponding thickness needs to be established again each time, so that huge workload is brought to the research of the thermal barrier coating.
Disclosure of Invention
The invention aims to provide a coating structure optimization design method, which solves the problem that in the prior art, when the influence of TC layer thickness change on the temperature and stress distribution of a coating pipeline system is researched, a finite element model with corresponding thickness needs to be repeatedly established, and the workload is huge.
The technical scheme adopted by the invention is as follows: a method for optimizing a coating structure, comprising the steps of:
s1, establishing an initial finite element model of a TBC coating structure in ABAQUS, and making an inp file; the established TBC coating structure initial finite element 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, and has 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), the unit type used in the stress analysis is an eight-node bidirectional secondary axisymmetric quadrilateral unit, and the reduction integral (CAX 8R).
S2, creating an objective function m file in an MATLAB; the method comprises the following steps:
s2.1, 5 optimization variables of TC layer thickness, TC layer heat conductivity coefficient, TC layer thermal expansion coefficient, cooling steam temperature and cooling steam pressure are defined.
S2.2, calculating the vertical distance r0 from the outer surface of the TC layer to the central axis according to the formula 1,
r0= initial TC layer boundary from center axis distance- (post-change TC layer thickness-TC layer initial thickness) (equation 1).
S2.3, calculating the number of units on one line in the x direction of the TC layer according to the formula 2;
the number of cells in one row in the x direction = TC layer thickness/length of one cell in the x direction (equation 2), and the calculation result is an integer.
S2.4, calculating the number of units in a row in the Y direction of the TC layer according to the formula 3;
the number of cells in one column in the y direction = TC layer initial length/length in one cell y direction (equation 3), and the calculation result is an integer.
S2.5, calculating the number of TC layer summary points; because the model established in step S1 is divided into mesh types by using eight-node types, the node calculation method under this type is as follows: and calculating the number of TC layer summary points according to the number of the units in the x and y directions as follows:
total node number = (number of units in x direction + 1) × (number of units in y direction × 2+ 1)
The number of cells in the + x direction x (the number of cells in the y direction + 1) (formula 4).
Step S2.6, defining numbers for all nodes by the following process:
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).
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).
S2.6.3, calculating the ordinate of the node on the a1 line: firstly, defining the number of units in the n1= y direction multiplied by 2+1; defining the number of the units in the n2= y direction to be +1; the abscissa value of the node on the line a1 is unchanged, and the ordinate value of the node on the line a1 is increased from 0 to n1 times by gradually increasing the distance dy between two nodes in the y direction from the y value from bottom to top.
S2.6.4, calculating the abscissa of the left side line of each row of units; specifically, the left side line of the unit of the adjacent row at the right side of the a1 line is set as a2 line, then a3 line, \8230;, am line, and the number of the units in the m = x direction is +1; the abscissa of the line a1 is r0, and the abscissa of the line a2 is r0+2 × dx; the abscissa of the line a3 is r0+4 × dx; 8230the line am has the abscissa of r0+ x the number of cells x 2 x dx.
S2.6.5, calculating the ordinate of the node on the b1 line: the ordinate value of the intersection of the line b1 and the x-axis is 0, and the y value is increased by 2dy from 0 to n2 times from bottom to top.
S2.6.6, calculating the horizontal coordinates of the central lines of the rest column units; specifically, the central lines from left to right are defined as a b1 line, a b2 line, \8230;, a bz line, and the number of units in the z = x direction; the abscissa of the line b1 is r0+ dx, and the abscissa of the line b2 of the cell in the adjacent column on the right side is r0+ dx +2dx, \8230 \ 8230;, and the abscissa of bz is r0+ dx +2 × (the number of cells in the x direction is-1) × dx.
S2.6.7, resetting the node numbers in the units, and specifically operating as follows:
each unit in the model selects 8 numbers to define the node number, and the methods for numbering the units and the nodes in the model are reset as follows:
the cell number method is set as: the leftmost column of the model is a first column unit, and the number of columns is increased by 1 from left to right; the lowest unit of the first column unit is 1 unit, the number of the unit of the column where the 1 unit is located is increased by 1 from bottom to top, the number of the lowest unit of the second column unit on the right side of the 0 th column unit is the number of the highest unit of the first column unit plus 1, then the number of the second column unit is increased by 1 from bottom to top, and all the column units of the model are numbered by analogy in sequence.
The node numbering method comprises the following steps:
(1) The numbering method of the nodes on the left side of the unit is as follows: setting the node number of the lower left corner of each unit as b, the node numbers of the two nodes above the unit are b +1 and b +2 in turn, namely the node numbers of the three nodes on the left side of the unit from bottom to top are b, b +1, b +2 in turn; wherein, the value of b starts from 1, namely the node at the lower left corner of the 1 unit is numbered as 1, and the value of b in the following unit is increased by 2 compared with the value of b in the previous unit.
The above is the numbering rule of the first row of unit nodes, and the numbering rule of the lowest unit node of the second row of units is as follows: the node numbers of the left lower corner of the second row of units and the lowest unit are as follows: the node number of the upper left corner of the uppermost unit in the first column is increased by 1; the number of the unit nodes in the second column is the same as the rule in the first column, and the rest is done in sequence;
(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 b + n1, b + n1+2, wherein n1 is the total number of the nodes on the left side of the unit in the column, and the value of b is the node number of the lower left corner of the unit.
(3) The numbers of the lower nodes and the upper nodes of the model 1 unit are respectively as follows: m +1, m +2, wherein m is the sum of the numbers of nodes on the left sides of all the column units of the TC layer, and the numbers of the lower nodes and the upper nodes of the following units are increased by 1 and increased progressively.
Step S2.7, setting in MATLAB:
(1) When the thickness of a TC layer in the model is increased, cell columns are added from the left side edge of the initial TC layer to the left, and the number of the added cell columns is as follows: the TC layer increases in thickness/dx; when the column is added, the number of the initial unit of the TC layer and the number of the node are not changed; adding new unit numbers and node numbers, wherein the added new unit initial numbers are greater than the initial model maximum node numbers; 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 is reduced in thickness/dx; the number information of the deletion unit is abandoned, and the reserved unit number and the node number are not changed.
An objective function m file is formed through the above operations.
S3, placing the inp file manufactured in the step S1 under the same path as the m file of the target function; reading an inp file in MATLAB; after reading, the inp file is stored in a matlab in a cellular array form; in an inp file read in MATLAB, the thickness of a TC layer is defined by node coordinates; when the thickness of the TC layer is increased, namely the number of unit columns is increased, firstly calculating the node coordinates of the increased units in the MATLAB; then, adding the node coordinates of the added units into the inp file, and adding the added units according to the numbers of the added nodes; obtaining a model with the thickness of the TC layer increased through the operation; when the thickness of the TC layer is reduced, namely the number of the unit columns is reduced, the coordinates of the corresponding column number in the inp file are deleted, specifically, the deletion is started from the left column of the model, and the model with the reduced thickness of the TC layer can be obtained.
Further, in step S1, the parameters are set in ABAQUS as follows: the thickness dc of the TC layer is 0.8mm, the thickness dt of TGO is 0.001mm, the thickness db of the BC layer is 0.199mm, the thickness dp of a metal matrix (SUB), namely a main steam pipeline, is 30mm, and the inner radius R0=120mm; the TC and TGO interface and the TGO and BC interface adopt an ideal cosine morphology interface to reflect the geometrical morphology characteristic, and the used functions are as follows:
the bottom edge of the built model coincides with the x-axis and the central axis c coincides with the y-axis in ABAQUS.
Next, the boundary conditions are set in the software as follows: the pressure inside and outside the main steam pipeline is respectively P i =35MPa and P O =5MPa; the lower boundary applies symmetric constraint in the axial direction to limit displacement in the axial direction; applying multi-point constraint to the upper boundary to ensure that all nodes of the upper boundary have the same axial displacement; it is assumed that the multicomponent material is isotropic and homogeneous and other material parameter values over a wide temperature range are estimated based on linear interpolation of existing data.
Further, step S4, writing the modified data into an inp file; calling abaqus to perform simulation calculation, firstly performing temperature calculation, and then performing stress calculation to obtain an odb file; then the simulation result, odb file is called and read through MATLAB
And
；
and
hoop stresses of the TC outer surface and the BC inner surface, respectively; the objective function value is calculated from the above values in Matlab
。
Further, a master optimizer is included, which is created in MATLAB.
(1) Defining three parameters of a result, an objective function value and an iteration number; 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;
further, the upper boundary of the thickness of the TC layer was set to 3mm, the lower boundary was 0, and the upper boundary of the thermal conductivity of the TC layer was set to 1.5W/m
The lower boundary is set to 1W/m
(ii) a The lower boundary of the thermal expansion coefficient of the TC layer is set as
The upper boundary is set to
(ii) a The upper limit of the cooling steam temperature is set to 500
The lower boundary is set to 100
(ii) a The lower boundary of the cooling vapor pressure was set to 5MPa, and the upper boundary was set to 10MPa.
(2) Inputting an initial value; the initial value of the thickness of the TC layer 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 the options structure, specifically:
function termination margin is set to 1 × 10 -9 ；
The termination margin at X is set to 1X 10 -9 ；
The maximum number of iterations 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 clock plot of the target function.
(4) Performing unconstrained nonlinear optimization on the objective function by applying an fminsearch function; and outputting the optimal target root value, the function value corresponding to the optimal target root value and the fmincon additional condition value.
(5) The fminsearch function in the main optimization program randomly selects a TC layer thickness, which is an arbitrary number between 0.0000-3.0000 mm.
The use method and functions of the main optimization program are as follows:
calling the objective function value by the main optimization program 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 lower than 580 ℃;
and if the objective function value is the minimum value and the temperature of the interface on the left side of the SUB layer is less than 580 ℃, outputting the result.
The invention has the beneficial effects that: in the optimized design method of the coating structure, the thickness of a TC layer is defined through a node coordinate; when the thickness of the TC layer is increased, namely the number of unit columns is increased, firstly calculating the node coordinates of the increased units in MATLAB; then, adding the node coordinates of the added units into the inp file, and adding the added units according to the numbers of the added nodes; obtaining a model with the thickness of the TC layer increased 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 number of columns in the inp file are deleted, and the deletion is started from the left side column of the model, so that the model with the reduced thickness of the TC layer can be obtained; the optimization efficiency is improved.
Drawings
FIG. 1 is a block diagram of an initial finite element model of a coating structure constructed in an embodiment of the present invention.
Fig. 2 is a schematic perspective view of a coated double tube structure in an embodiment of the present invention.
Fig. 3 is a table of material parameter settings data in an embodiment of the present invention.
Fig. 4 is a diagram illustrating part of information in an INP file generated according to an embodiment of the present invention.
FIG. 5 is a partially schematic illustration of a finite element model of the initial coating architecture found in ABAQUS, where the numbers shown are the element and node numbers.
FIG. 6 is a diagram showing the content of the read inp file in MATLAB according to an embodiment of the present invention.
Detailed Description
Exemplary embodiments of the present disclosure are described below with reference to the accompanying drawings, in which various details of the embodiments of the disclosure are included to assist understanding, and which are to be considered as merely exemplary. Accordingly, those 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 disclosure. Also, descriptions of well-known functions and constructions are omitted in the following description for clarity and conciseness.
Examples
A coating structure optimization design method comprises the following steps:
s1, establishing an initial finite element model of a TBC coating structure in ABAQUS, and making an inp file.
The initial finite element model of the coating structure established in the embodiment is shown in fig. 1, the model is a section of a coating double-pipe structure for a 700 ℃ ultra-supercritical power station disclosed in the Chinese patent with the publication number of CN114561613A, and a section of the single-coating double-pipe structure in the embodiment 1 in the patent with the axial length of 0.6mm (L in the figure) is specifically intercepted to establish the finite element model. The parameters of the established finite element model are shown in figure 1, and the finite element 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 have a four-layer structure; in this embodiment, the parameters of each layer are set in software as follows: wherein, the thickness dc of the TC layer is 0.8mm, the thickness dt of the TGO is 0.001mm, the thickness db of the BC layer is 0.199mm, the thickness dp of a metal matrix (SUB), namely the main steam pipeline, is 30mm, and the inner radius R0=120mm. Due to the spraying process, the TC and TGO interface and the TGO and BC interface are rough and uneven, an ideal cosine morphology interface is adopted to reflect the geometrical morphology characteristic, and the used function is as follows:
the bottom edge of the model is coincident with the x-axis and the central axis c is coincident with the y-axis in ABAQUS.
Next, boundary conditions and material parameters were set in the software as follows: the pressure inside and outside the main steam pipeline is respectively P i =35MPa and P O =5MPa. The lower boundary applies symmetric constraint in the axial direction to limit displacement in the axial direction; the upper boundary applies a multi-point constraint so that all nodes of the upper boundary have the same axial displacement. Assuming anisotropic multicomponent materialsIs both homogenous and linear interpolation based on existing data to estimate other material parameter values over a wide temperature range. The material parameters are shown in FIG. 3.
Then, respectively establishing a heat transfer analysis model and a stress analysis model; specifically, 249061 nodes and 80883 units are shared in the model; the heat transfer analysis adopts an eight-node secondary axisymmetric heat transfer quadrilateral unit (DCAX 8), the unit type used in the stress analysis is an eight-node bidirectional secondary axisymmetric quadrilateral unit, and the reduction integral (CAX 8R).
The inp file is formed by the above operation.
Step S2, creating an objective function m file in MATLAB, comprising the following steps:
and 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.
S2.2, calculating the vertical distance r0 from the outer surface of the TC layer to the central axis according to the formula 1,
r0= initial TC layer boundary distance from central axis- (post-change TC layer thickness-TC layer initial thickness) (equation 1);
for example, r0=119- (Wc-0.8) in this embodiment.
S2.3, calculating the number of units on one line of the TC layer in the x direction according to the formula 2;
the number of cells in a row in the x direction = TC layer thickness/length of one cell in the x direction (formula 2), and the calculation result is an integer; in this embodiment, the length of one cell in the x direction is 0.02, the number of cells in one row in the x direction of the initial TC layer is 0.8-0.022/0.02=39, and since the interface between TC and TGO is rough and uneven, when the geometric feature is reflected by using an ideal cosine morphology interface, an incomplete cell column is formed at the interface, and the width of the incomplete cell column is 0.022, so that the number of cells 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 cells in a row in the y direction = TC layer initial length/length in the y direction of one cell (equation 3), and the calculation result is an integer; in this embodiment, the number of cells in a row in the y direction of the TC layer is 0.6/0.01, and the integer of the calculation result is 60.
And S2.5, calculating the number of TC layer summary points. Specifically, the eight-node type is adopted for establishing the model division mesh type in step S1 of the present application, and therefore, the node calculation method under this type is as follows: as shown in fig. 4, when there is only one cell, the node includes points at the four corners of the cell and the midpoint of the four sides. Therefore, in the invention, the number of the TC layer summary points calculated according to the number of the cells in the x and y directions is:
total node number = (number of units in x direction + 1) × (number of units in y direction × 2+ 1)
The number of cells in the + x direction x (the number of cells in the y direction + 1) (formula 4).
The number of the TC layer summary points in this embodiment is: (39 + 1) × (60 × 2+ 1) +39 × (60 + 1) =7219.
Step S2.6, define the numbers for all nodes by the following process, and the node numbers in this embodiment are 1-7219.
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 was 0.01.
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 embodiment dy is 0.005.
Step S2.6.3, calculating the ordinate of the node on the line a1 (namely the left side line of the TC layer in the model of figure 1): first, in the present invention, the number of units in the n1= y direction is defined as × 2+1 (n 1=121 in the present embodiment); defining the number of units in n2= y direction +1 (n 2=61 in the embodiment); as shown in FIG. 1, the coordinates of the intersection of the line a1 and the x-axis are (119, 0), and the coordinates of the nodes on the line a1 are the x-value, and the y-value from bottom to top is from 0, and the distance dy between two nodes in the y-direction is gradually increased until n1 times.
In this example, n1 is 121, dx is 0.01, and the intersection of the line a1 and the x-axis is (119, 0), and the bottom-up node is (119, 0.005), (119, 0.01), (119, 0.015) \\ 8230; (119, 0.6).
S2.6.4, calculating the abscissa of the left sideline of each row of units; specifically, the left side line of the cell of the adjacent column on the right side of the a1 line is set as a2 line, and then is set as a3 line, \ 8230 \ 8230;, am line (m = the number of cells in the x direction + 1); because the abscissa of the line a1 is r0, the abscissa of the line a2 is r0+2 × dx; the abscissa of the line a3 is r0+4 × dx; 8230the line am has the abscissa of r0+ x the number of cells x 2 x dx.
In this embodiment, the abscissa of the a1 line is 119, the abscissa of the a2 line is 119.02, the abscissa of the a3 line is 119.04, \ 8230 \ 8230;, and the abscissa of the last a40 line is 119.78.
Step S2.6.5, calculating the ordinate of the node on the line b1 (namely the vertical central line of the leftmost column unit of the TC layer): the vertical coordinate value of the intersection of the b1 line and the x-axis is 0, and the y value from bottom to top is increased by 2dy from 0 to n2 times.
In the embodiment, the vertical coordinates of the nodes on the b1 line from bottom to top are 0,0.01,0.02, \ 8230 \ 8230; \ 8230and 0.6 in sequence.
S2.6.6, calculating the horizontal coordinates of the central lines of the rest column units; specifically, the central lines from left to right are defined as a b1 line, a b2 line, \8230;, a bz line, and the number of units in the z = x direction; the abscissa of the line b1 is r0+ dx, the abscissa of the line b2 of the line of the cells in the adjacent column on the right side is r0+ dx +2dx, \8230 \ 8230;, and the abscissa of bz is r0+ dx +2 x (the number of cells in the x direction is-1) × dx.
In the present embodiment, the abscissa of the line b1 is 119.01, the abscissa of the line b2 is 119.03, and the abscissa of the line b3 is 119.05 \8230; 8230; 119.77.
S2.6.7, resetting the node numbers in the units, and specifically operating as follows:
first, it should be noted that: when the coating structure initial finite element model is established in ABAQUS, the software defaults to set numbers for all the units and the nodes, and forms an INP file, wherein all information in the model establishing process, including material properties, the numbers of the units, the numbers and coordinates of the nodes and boundary conditions, is recorded in the file. Fig. 4 is a diagram illustrating part of information in the INP file generated in the present embodiment, where the left frame part is a unit number and the right frame part is a node number. Fig. 5 shows the cell number information (cell central number) and node number (cell four corners and side numbers) displayed by the initial finite element model of the coating structure established in ABAQUS.
In the invention, each unit selects 8 numbers to define the node numbers on the unit, and all nodes of the initial model define 1-7401 numbers in the embodiment; as shown in fig. 5, the 1 unit 8 nodes are numbered as: 1,2,3 (three nodes on the left side); 122 123,124 (three nodes on the right side); 4841 4842 (lower and upper nodes);
the serial numbers of the 8 nodes in the 2 units are as follows: 3,4,5 (three nodes on the left side); 124 125, 126 (three nodes on the right side); 4842 4843 (lower and upper nodes).
The invention resets the method for numbering the units and the nodes in the model as follows:
the cell number method is set as: the leftmost column of the model is a first column unit, and the number of columns is increased by 1 from left to right; the lowest unit of the first column unit is 1 unit, the number of the unit in the column of the 1 unit is increased by 1 from bottom to top, the number of the lowest unit of the second column unit on the right side of the first column unit is the number of the uppermost unit of the first column unit and is increased by 1, then the number of the second column unit is increased by 1 from bottom to top, and all the column units of the model are numbered by analogy in sequence.
The node numbering method comprises the following steps:
(1) The numbering method of the nodes on the left side of the unit is as follows: setting the node number of the lower left corner of each unit as b, the node numbers of the two nodes above the unit are b +1 and b +2 in sequence, namely the node numbers of the three nodes on the left side of the unit from bottom to top are b, b +1, b +2 in sequence; wherein, the value of b starts from 1, namely the node number of the lower left corner of the 1 unit is 1, and the b value in the following unit is increased by 2 compared with the b value of the previous unit; in the embodiment, the node number of the lower left corner of the unit 2 is 3, and the node number of the lower left corner of the unit 3 is 5;
the above is the numbering rule of the first row of unit nodes, and the numbering rule of the lowest unit node of the second row of units is as follows: the nodes at the left lower corner of the second row of units and the lowest unit are numbered as follows: the node number of the upper left corner of the uppermost unit in the first column is increased by 1; for example, in this 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 second column unit and the lowermost unit is 122; the numbering of the unit nodes in the second column is the same as the rule in the first column, and so on.
(2) The numbering method of 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 b + n1, b + n1+2 in sequence, wherein n1 is the total number of the nodes on the left side of the row unit, and the value of b is the node number on the lower left corner of the row unit; for example, in this embodiment, the total number of the left side nodes of the row of the 1 unit is 121, the number of the left bottom node of the 1 unit is 1, and the numbers of the bottom-to-top nodes of the three right side nodes of the 1 unit are 122,123 and 124.
(3) The numbers of the lower nodes and the upper nodes of the model 1 unit are respectively as follows: m +1, m +2, where m is the sum of the left nodes of all column units in the TC layer, and m is 4840 in this embodiment; the lower and upper nodes of unit 1 are numbered 4841 and 4842, respectively; the numbers of the lower nodes and the upper nodes of the following units are increased by 1.
Step S2.7, setting in MATLAB:
(1) When the thickness of the TC layer in the model is increased, the cell columns are increased leftwards from the left side of the initial TC layer, and the number of the increased cell columns is as follows: the TC layer increases in thickness/dx; when the columns are added, the initial unit number and the node number of the TC layer are unchanged; adding new unit numbers and node numbers, wherein the added new unit initial numbers are greater than the initial model maximum node numbers; for example, in this embodiment, the maximum node number of the initial model is 249061, and the start number of the newly added unit number may be customized to 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 is reduced in thickness/dx; the number information of the deletion unit is abandoned, and the reserved unit number and the node number are not changed.
An objective function m file is formed through the above operations.
S3, placing the inp file manufactured in the step S1 under the same path as the m file of the target function; reading an inp file in MATLAB; after reading, the inp file is stored in the matlab in a cellular array form.
The content of the inp file read in MATLAB is shown in FIG. 6 below, and the TC layer thickness is defined by node coordinates; when the thickness of the TC layer is increased, namely the number of unit columns is increased, firstly calculating the node coordinates of the increased units in the MATLAB; then, adding the node coordinates of the added units into the inp file, and adding the added units according to the numbers of the added nodes; obtaining a model with the thickness of the TC layer increased through the operation; when the thickness of the TC layer is reduced, namely the number of the unit columns is reduced, the coordinates of the corresponding number of the columns in the inp file are deleted, and the model with the reduced thickness of the TC layer can be obtained by deleting the coordinates from the left side column of the model.
In addition, 5 optimized variables defined in the step S2.1, namely TC layer thickness, TC layer heat conductivity coefficient, TC layer thermal expansion coefficient, cooling steam temperature and cooling steam pressure; the heat transfer model can modify the heat conductivity coefficient of the TC layer and the temperature of cooling steam; and modifying the thermal expansion coefficient of the TC layer and the cooling steam pressure of the stress model.
Writing the modified data into an inp file; and calling abaqus to perform simulation calculation, firstly performing temperature calculation, and then performing stress calculation to obtain an odb file. And then the simulation result is called and read through MATLAB, namely the data in the odb file
And
。
and
the hoop stress of the TC outer surface and BC inner surface, respectively. In Matlab by the above valuesCalculating objective function values
。
Further, the present invention also provides a master optimizer that creates the master optimizer in MATLAB.
(1) Defining three parameters of a result, an objective function value and an iteration number; 5 optimized variables of TC layer thickness, TC layer heat conductivity coefficient, TC layer thermal expansion coefficient, cooling steam temperature and cooling steam pressure are defined.
Further, the upper boundary of the TC layer thickness was set to 3mm and the lower boundary was set to 0, and the upper boundary of the TC layer thermal conductivity was set to 1.5W/m
The lower boundary is set to 1W/m
(ii) a The lower boundary of the thermal expansion coefficient of the TC layer is set as
The upper boundary is set to
(ii) a The upper limit of the cooling steam temperature is set to 500
Lower boundary set to 100
(ii) a The lower boundary of the cooling vapor pressure was set to 5MPa, and the upper boundary was set to 10MPa.
(2) Inputting an initial value; the embodiment specifically includes: the initial value of the thickness of the TC layer is 0.8mm, the initial value of the thermal conductivity 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 the options structure, specifically:
the function termination margin is set to 1 × 10 -9 ；
The termination margin at X is set to 1X 10 -9 ；
The maximum number of iterations 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 clock plot of the target function.
(4) Performing unconstrained nonlinear optimization on the objective function by applying an fminsearch function; and outputting the optimal target root value, the function value corresponding to the optimal target root value and the fmincon additional condition value.
(5) Randomly selecting the thickness of a TC layer by an fmisearch function in a main optimization program, wherein the thickness of the selected TC layer is an arbitrary number between 0.0000 and 3.0000 mm; for example 0.7.
The use method and functions of the main optimization program are as follows:
calling an objective function value by the main optimization program to judge whether the objective function value is the minimum value;
judging whether constraint conditions are met: whether the temperature of the interface on the left side of the SUB layer is lower than 580 ℃;
and if the objective function value is the minimum value and the temperature of the interface on the left side of the SUB layer is less than 580 ℃, outputting the result. After optimization, an optimization 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 variations, 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 (4)
1. A method for optimally designing a coating structure is characterized by comprising the following steps:
s1, establishing an initial finite element model of a TBC coating structure in ABAQUS, and making an inp file; the established TBC coating structure initial finite element 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, and has a four-layer structure; then, respectively establishing a heat transfer analysis model and a stress analysis model; an eight-node secondary axisymmetric heat transfer quadrilateral unit (DCAX 8) is adopted for heat transfer analysis, the unit type used for stress analysis is an eight-node bidirectional secondary axisymmetric quadrilateral unit, and the reduction integral (CAX 8R);
s2, creating an objective function m file in an 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;
s2.2, calculating the vertical distance r0 from the outer surface of the TC layer to the central axis according to the formula 1,
r0= initial TC layer boundary distance from central axis- (post-change TC layer thickness-TC layer initial thickness) (equation 1);
s2.3, calculating the number of units on one line of the TC layer in the x direction according to the formula 2;
the number of cells in a row in the x direction = TC layer thickness/length of one cell in the x direction (formula 2), and the calculation result is an integer;
s2.4, calculating the number of units in a row in the Y direction of the TC layer according to the formula 3;
the number of cells in a row in the y direction = TC layer initial length/length in the y direction of one cell (equation 3), and the calculation result is an integer;
s2.5, calculating the number of TC layer summary points; because the model established in step S1 is divided into mesh types by using eight-node types, the node calculation method under this type is as follows: calculating the number of TC layer summary points according to the number of the units in the x and y directions as follows:
the total node number = (number of units in x direction + 1) × (number of units in y direction × 2+ 1) + number of units in x direction x (number of units in y direction + 1) (formula 4);
step S2.6, the following procedures are used for defining the numbers of all nodes:
step S2.6.1, calculating the distance dx of 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);
s2.6.3, calculating the ordinate of the node on the a1 line: firstly, defining the number of units in the n1= y direction multiplied by 2+1; defining the number of the units in the n2= y direction to be +1; the abscissa value of the node on the line a1 is unchanged, the ordinate value of the node on the line a1, from bottom to top, is y from 0, and the distance dy between two nodes in the y direction is gradually increased until n1 times;
s2.6.4, calculating the abscissa of the left sideline of each row of units; specifically, the left side line of the unit of the adjacent row at the right side of the a1 line is set as a2 line, then a3 line, \8230;, am line, and the number of the units in the m = x direction is +1; the abscissa of the line a1 is r0, and the abscissa of the line a2 is r0+2 × dx; the abscissa of the line a3 is r0+4 × dx; \8230 \ 8230;, the am line abscissa is the number of cells in the r0+ x direction × 2 × dx;
s2.6.5, calculating the vertical coordinate of the node on the b1 line: the longitudinal coordinate value of the intersection point of the b1 line and the x axis is 0, and the y value from bottom to top is increased by 2dy from 0 to n2 times;
s2.6.6, calculating the horizontal coordinates of the central lines of the rest column units; specifically, the central lines from left to right are defined as a b1 line, a b2 line, \8230;, a bz line, and the number of units in the z = x direction; the abscissa of the line b1 is r0+ dx, the abscissa of the line b2 of the cell in the adjacent column on the right side is r0+ dx +2dx, \8230: \ 8230:, the abscissa of bz is r0+ dx +2 × (the number of cells in the x direction is-1) × dx;
s2.6.7, resetting the node numbers in the units, and specifically operating as follows:
each unit in the model selects 8 numbers to define the node number, and the method for numbering the units and the nodes in the model is reset as follows:
the cell number method is set as: the leftmost column of the model is the first column unit, and the number of columns increases by 1 from left to right; the lowermost unit of the first column unit is 1 unit, the number of the unit in the column of 1 unit is increased by 1 from bottom to top, the number of the lowermost unit of the second column unit on the right side of the first column unit is the number of the uppermost unit of the first column unit plus 1, then the number of the second column unit is increased by 1 from bottom to top, and all the column units of the model are numbered by analogy in sequence;
the node numbering method comprises the following steps:
(1) The numbering method of the nodes on the left side of the unit is as follows: setting the node number of the lower left corner of each unit as b, the node numbers of the two nodes above the unit are b +1 and b +2 in turn, namely the node numbers of the three nodes on the left side of the unit from bottom to top are b, b +1, b +2 in turn; wherein, the value of b starts from 1, namely the node number of the lower left corner of the 1 unit is 1, and the b value in the following unit is increased by 2 compared with the b value of the previous unit;
the above is the numbering rule of the first row of unit nodes, and the numbering rule of the lowest unit node of the second row of units is as follows: the node numbers of the left lower corner of the second row of units and the lowest unit are as follows: the node number of the upper left corner of the uppermost unit in the first column is increased by 1; the number of the unit node in the second column is the same as the rule in the first column, and the like are performed in sequence;
(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 b + n1, b + n1+2 in sequence, wherein n1 is the total number of the nodes on the left side of the row unit, and the value of b is the node number on the lower left corner of the row unit;
(3) The numbers of the lower node and the upper node of the model 1 unit are respectively as follows: m +1, m +2, wherein m is the sum of the numbers of nodes on the left sides of all the column units of the TC layer, and the numbers of the lower nodes and the upper nodes of the following units are increased by 1 and increased progressively;
step S2.7, setting in MATLAB:
(1) When the thickness of the TC layer in the model is increased, the cell columns are increased leftwards from the left side of the initial TC layer, and the number of the increased cell columns is as follows: the TC layer increases in thickness/dx; when the column is added, the number of the initial unit of the TC layer and the number of the node are not changed; adding new unit numbers and node numbers, wherein the added new unit initial numbers are greater than the initial model maximum node numbers; 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 is reduced in thickness/dx; the number information of the deletion unit is abandoned, and the reserved unit number and the 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 m file of the target function; reading an inp file in MATLAB; after reading, the inp file is stored in a cellular array form in matlab;
in an inp file read in MATLAB, the thickness of a TC layer is defined by node coordinates; when the thickness of the TC layer is increased, namely the number of unit columns is increased, firstly calculating the node coordinates of the increased units in MATLAB; then, adding the node coordinates of the added units into the inp file, and adding the added units according to the numbers of the added nodes; obtaining a model with the thickness of the TC layer increased through the operation; when the thickness of the TC layer is reduced, namely the number of the unit columns is reduced, the coordinates of the corresponding number of the columns are deleted in the inp file, specifically, the deletion is started from the left side column of the model, and the model with the reduced thickness of the TC layer can be obtained.
2. The method for optimized design of coating structure as claimed in claim 1, wherein in step S1, parameters are set in ABAQUS as follows: the thickness dc of the TC layer is 0.8mm, the thickness dt of TGO is 0.001mm, the thickness db of the BC layer is 0.199mm, the thickness dp of a metal matrix (SUB), namely a main steam pipeline, is 30mm, and the inner radius R0=120mm; the TC and TGO interface and the TGO and BC interface adopt an ideal cosine morphology interface to reflect the geometrical morphology characteristic, and the used functions are as follows:
the bottom edge of the built model is coincident with the x axis in the ABAQUS, and the central axis c is coincident with the y axis;
next, the boundary conditions are set in the software as follows: main steamThe pressure inside and outside the pipeline is respectively P i =35MPa and P O =5MPa; the lower boundary applies symmetric constraint in the axial direction to limit displacement in the axial direction; applying multi-point constraint to the upper boundary to ensure that all nodes of the upper boundary 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 existing data.
3. The method for optimally designing the coating structure according to claim 1, further comprising the steps of S4, writing modification data into an inp file; calling abaqus to perform simulation calculation, firstly performing temperature calculation, and then performing stress calculation to obtain an odb file; and then the simulation result is called and read through MATLAB, namely the data in the odb file
And
；
and
hoop stresses of the TC outer surface and BC inner surface, respectively; calculating the objective function value from the above values in Matlab
。
4. The coating architecture optimization design method of claim 3, further comprising a master optimizer that is created in MATLAB.
(1) Defining three parameters of a result, an objective function value and an iteration number; defining 5 optimization variables of TC layer thickness, TC layer heat conductivity coefficient, TC layer thermal expansion coefficient, cooling steam temperature and cooling steam pressure;
further, the upper boundary of the thickness of the TC layer was set to 3mm, the lower boundary was 0, and the upper boundary of the thermal conductivity of the TC layer was set to 1.5W/m
The lower boundary is set to 1W/m
(ii) a The lower boundary of the thermal expansion coefficient of the TC layer is set as
The upper boundary is set to
(ii) a The upper limit of the cooling steam temperature is set to 500
The lower boundary is set to 100
(ii) a 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 thickness of the TC layer 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 the options structure, specifically:
the function termination margin is set to 1 × 10 -9 ；
The termination margin at X is set to 1X 10 -9 ；
The maximum number of iterations 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 clock plot of an objective function;
(4) Performing unconstrained nonlinear optimization on the objective function by applying an fminsearch 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 the thickness of a TC layer by an fmisearch function in a main optimization program, wherein the thickness of the selected TC layer is an arbitrary number between 0.0000 and 3.0000 mm;
the use method and functions of the main optimization program are as follows:
calling the objective function value by the main optimization program to judge whether the objective function value is the minimum value;
judging whether constraint conditions are met: whether the temperature of the interface on the left side of the SUB layer is lower than 580 ℃;
and if the objective function value is the minimum value and the temperature of the interface on the left side of the SUB layer is less than 580 ℃, outputting the result.
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