CN110287554B - Finite element calculation method for nonlinear gas-solid coupling heat exchange problem - Google Patents
Finite element calculation method for nonlinear gas-solid coupling heat exchange problem Download PDFInfo
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Abstract
The invention discloses a finite element calculation method for solving the problem of nonlinear gas-solid coupling heat exchange, which relates to the technical field of heat transfer, finite element methods and aero-engine design and comprises the following steps: reading an axisymmetric part three-dimensional geometric model file established by a CAD system, and carrying out detail feature processing; selecting and intercepting an axisymmetric meridian plane to obtain a two-dimensional geometric model; dividing meridian planes into triangular unit meshes; establishing a finite element model of an internal triangular unit and a boundary unit; superposing and synthesizing an integral finite element model of the axisymmetric region to obtain a linear algebraic equation set about all the node temperatures; and solving the linear algebraic equation set to obtain the numerical value of the node temperature and performing computer graphic visual display. The method overcomes the defects of the classical heat transfer analysis method, fully considers the coupling effect of gas-solid heat exchange, can more accurately calculate the temperature field distribution of the aeroengine part structure compared with the linear gas-solid heat coupling algorithm, and improves the design level.
Description
Technical Field
The invention relates to the technical field of heat transfer science, finite element methods and aero-engine design, in particular to a finite element calculation method for solving the problem of nonlinear gas-solid coupling heat exchange.
Background
The development of the aero-engine has important significance for national economic construction and national defense construction, and reflects the technical level and industrial capability of a country. The development level of the aeroengine in China still has a larger gap with the advanced level of the world, and breaking through the monopoly of foreign technologies and innovatively developing the high-performance aeroengine becomes a difficult task in the scientific and technological field and the industrial field.
At present, china is developing high-performance military aircraft engines, the temperature of gas in front of a turbine needs to be greatly increased in order to increase thrust, and meanwhile, the structural weight needs to be reduced in order to increase thrust-weight ratio. In order to reduce the effect of high temperature loads on the structure, the amount of cooling gas must be increased, which, however, reduces the thermal efficiency of the aircraft engine. Therefore, accurately calculating the temperature field distribution is a key core technology for developing high-performance aircraft engines, and is a fundamental guarantee for improving the thermal efficiency and safety of the aircraft engines. According to statistics, when the estimated value of the temperature of the wall surface of the turbine blade is reduced by 28 ℃, the estimated value of the service life is correspondingly doubled. Therefore, the accuracy of heat transfer analysis determines the performance and reliability of the aircraft engine, and has important significance for improving the overall design technical level of the aircraft engine.
The aircraft engine runs in a high-speed high-temperature environment, the local temperature exceeds the limit which can be borne by the material, cooling is necessary, and therefore accurate calculation of a temperature field and evaluation of cooling efficiency are needed. At present, the classical heat transfer calculation method is adopted in the development of the aeroengine in China, the temperature of the cooling gas is approximately constant, and the heat energy transfer effect from solid to gas in the cooling process is neglected. The classical analysis method cannot accurately describe the problem that the temperature of the cooling gas rises due to heat absorption in the solid cooling process, so that the temperature difference between the gas and the solid is reduced, and further the heat exchange efficiency and the cooling effect are rapidly reduced. Therefore, in the development of a high-performance aircraft engine, the bidirectional transfer mechanism of energy (heat) between gas and solid must be accurately described, and a basis is provided for thermal deformation and thermoelasticity analysis, so that the product performance can be optimized and the safety and reliability can be improved.
For various wheel disc type parts in the aircraft engine, an axisymmetric heat transfer analysis model can be adopted for calculation and simulation. The classical axisymmetric heat transfer analysis method describes the heat transfer process inside a solid (component) by adopting a heat conduction mode, and the control equation (cavitation) is as follows:
and, the boundary condition of solid heat transfer is described by adopting a classical convective heat transfer process, and the mathematical model is as follows:
the symbols in equations (1) to (2) have the following meanings:
ρ: the mass density of the fluid;
c p : constant pressure specific heat capacity;
T w : the temperature of the solid;
T f : the temperature of the cooling gas;
λ x ,λ r λ: the thermal conductivity of the solid in the axial direction, the radial direction and the normal direction of a boundary respectively;
x, r: axial and radial coordinates;
t: time;
n: a heat exchange surface normal vector;
h: heat exchange coefficient of the heat exchange surface;
q v : solid internal heat source.
The traditional convective heat transfer problem analysis technology only considers the cooling (or heating) effect of fluid (gas) on solid, and neglects the heating (or cooling) effect of the solid on the fluid (gas). Therefore, existing commercial finite element analysis systems (e.g., ANSYS and NASTRAN, etc.) all consider the fluid temperature in the convective heat transfer problem as a constant, assuming T in equation (2) f Is a constant. The traditional heat transfer analysis method does not consider the gas-solid boundary coupling heat exchange effect, generates larger calculation error under the high-temperature condition, cannot accurately calculate the temperature field of parts such as a turbine and the like, and restricts the design level of the aeroengine in China.
Therefore, the technical problem that the cooling efficiency of gas to solid (such as a turbine disc) is rapidly reduced due to temperature rise generated by heat absorption of cooling gas in the flowing process in the design of an aircraft engine is solved, the defects of a classical heat transfer analysis method are overcome, the coupling effect of gas-solid heat exchange is fully considered, a nonlinear six-node triangular unit finite element model is established by adopting an energy balance principle in the heat transfer process, and an effective numerical calculation method is provided. Compared with a linear gas-solid thermal coupling algorithm, the nonlinear algorithm provided by the invention can be used for more accurately calculating the temperature field distribution of the part structure of the aircraft engine and improving the design level.
Disclosure of Invention
In view of the above defects in the prior art, the technical problem to be solved by the invention is how to overcome the defects of the classical heat transfer analysis method, fully consider the coupling effect of gas-solid heat exchange, establish a finite element model by adopting the energy balance principle in the heat transfer process, provide a more effective numerical calculation method, calculate the temperature field distribution of the aeroengine part structure more accurately, and improve the design level.
In order to achieve the purpose, the invention provides a finite element calculation method for the problem of nonlinear gas-solid coupling heat exchange, which comprises the following steps:
step 2, selecting and intercepting an axisymmetric meridian plane to obtain a two-dimensional geometric model of the part;
step 3, dividing the meridian plane into triangular unit meshes;
step 5, establishing a finite element model of the part boundary unit;
step 6, coupling two heat balance equations for each part boundary unit;
step 7, superposing and synthesizing the integral finite element model of the axial symmetric region to obtain a linear algebraic equation set related to the node temperatures of all parts and the boundary node temperatures of the parts;
step 8, solving the linear algebraic equation set by selecting a direct method to obtain the numerical values of the node temperatures of all parts and the gas boundary node temperatures;
and 9, performing computer graphic visual display on the obtained node temperatures of all the parts and the gas boundary node temperature values.
Further, the implementation method of the step 1 is as follows:
and performing data reading, model display, sketch extraction, feature identification, parameter conversion and attribute addition operation on a three-dimensional geometric model file of the axisymmetric part established in the CAD system.
Further, the implementation method of step 3 is as follows:
and dividing the part structure into the triangular unit grids according to the control parameters.
Further, the control parameters include cell type, overall cell size, number, grid accuracy.
Further, the method for dividing the component structure into the triangular unit meshes in step 3 is one of a mapping method, a grid + Delaunay method, and a FREE method.
The implementation method of the step 3 further comprises the following steps:
and automatically checking the quality of the triangular unit mesh according to a set criterion, and carrying out local optimization and encryption on the triangular unit mesh.
Further, the performing of computer graphic visualization in step 9 includes: and displaying the temperature field and temperature gradient field data of the part by adopting one or more of contour line, contour surface, cloud picture and point map marking modes.
Further, the step 5 comprises the following steps:
step 5.1, discretizing the part structure area by adopting a six-node nonlinear triangular unit: dividing the cross section of the axisymmetric part into a limited number of six-node nonlinear triangular units, wherein each triangular unit in the part structure comprises three vertexes i, j, k and middle points l, m, n of three edges ij, jk, ki;
step 5.2, establishing a temperature field function of each triangular unit by adopting a quadratic nonlinear polynomial according to six nodes i, j, k, l, m and n of the triangular unit:
T＝a 1 +a 2 x+a 3 r+a 4 x 2 +a 5 xr+a 6 r 2
the temperature field function in the triangular unit is expressed as an isoparametric function form:
T＝N i T i +N j T j +N k T k +N l T l +N m T m +N n T n
for temperatures on the triangular cell boundary j-m-k, a boundary cell interpolation equation is constructed as follows:
T＝T j +(4T m -3T j -T k )g+(2T j +2T k -4T m )g 2 (0≤g≤1)；
step 5.3, establishing a unit discrete algebraic equation by adopting a Galerkin weighted margin method as follows:
and 5.4, describing the boundary condition of the heat transfer of the parts by adopting a third type of boundary condition model, wherein the mathematical model is as follows:
in the formula: t is w Representing the temperature function, T, of the component f The gas temperature function is represented, lambda is the normal thermal conductivity of the boundary of the part, n is the normal vector of the heat exchange surface, and h is the heat exchange coefficient of the heat exchange surface;
step 5.5, selecting a quadrilateral area as a control volume on the boundary of the part, assuming that the density of the gas is unchanged in the flowing process, establishing an energy conservation model in the control volume as follows:
in the formula: ρ represents the gas density, V represents the gas velocity vector, n is the boundary unit normal vector of the control volume, h represents the enthalpy of the gas, V represents the modulus of the gas velocity vector,
representing the heat flow into the control volume from the outside,
means that the control volume does work to the outside per unit time;
step 5.6, the gas flows along the part boundary with mass flow on the front and back of the control volume and no mass flow into or out of the control volume on both sides, the part boundary coupling energy balance model is as follows:
in the formula:
representing the mass flow of the gas, c p Specific heat capacity at constant pressure, h c Is the convective heat transfer coefficient;
step 5.7, increasing the gas temperature on three nodes on the part boundary segment j-m-k, which is expressed as T fj ,T fm ,T fk And expressing the gas temperature function on the part boundary segment j-m-k as follows:
T f ＝T fj +(4T fm -3T fj -T fk )g+(2T fj +2T fk -4T fm )g 2 (0≤g≤1)
the temperature rigidity matrix model of the boundary unit of the part is as follows:
in the formula:
further, the two heat balance equations in step 6 are:
and
further, the implementation method of step 7 is as follows:
sequentially superposing and synthesizing the temperature rigidity matrix and the load column vector of each unit to obtain the total temperature rigidity matrix and the total load column vector of gas-solid coupling heat exchange, and synthesizing the transient temperature field coefficient matrix of each unit by the same method to obtain the transient temperature field coefficient matrix [ N ] of the whole structure for solving the problem of transient heat transfer]Let us order
(l =1,2,.. Times, n), a system of linear algebraic equations is obtained that contains the node solid temperature variables and the boundary node gas temperature variables.
The invention overcomes the defects of the classical heat transfer analysis method, fully considers the coupling effect of gas-solid heat exchange, establishes a nonlinear six-node triangular unit finite element model by adopting the energy balance principle in the heat transfer process, and provides an effective numerical calculation method. Compared with a linear gas-solid thermal coupling algorithm, the nonlinear algorithm provided by the invention can be used for more accurately calculating the temperature field distribution of the part structure of the aircraft engine and improving the design level.
The conception, the specific structure and the technical effects of the present invention will be further described with reference to the accompanying drawings to fully understand the objects, the features and the effects of the present invention.
Drawings
FIG. 1 is a fluid control volumetric model at the boundary of a turbine disk in accordance with a preferred embodiment of the present invention;
FIG. 2 is a six-node delta cell internal temperature field model in accordance with a preferred embodiment of the present invention;
FIG. 3 is a process of heat exchange coupling a solid boundary element with a gas in accordance with a preferred embodiment of the present invention;
FIG. 4 is a gas-solid coupled heat transfer system framework for an aircraft engine in accordance with a preferred embodiment of the present invention;
FIG. 5 is a calculated turbine disk temperature field of a method according to a preferred embodiment of the present invention;
FIG. 6 is a calculated turbine disk temperature gradient field of a method in accordance with a preferred embodiment of the present invention;
FIG. 7 is a temperature curve of a critical structural point of a turbine disk calculated by the method of a preferred embodiment of the present invention;
FIG. 8 is a graph of an aircraft engine over-all temperature field calculated by a method in accordance with a preferred embodiment of the present invention;
FIG. 9 is a flow chart of a method in accordance with a preferred embodiment of the present invention.
Detailed Description
The preferred embodiments of the present invention will be described below with reference to the accompanying drawings for clarity and understanding of technical contents. The present invention may be embodied in many different forms of embodiments and the scope of the invention is not limited to the embodiments set forth herein.
The invention comprises an axisymmetric part gas-solid coupling convection heat exchange model, a six-node triangular boundary unit gas temperature rise model, an overall finite element model, an aeroengine gas-solid coupling heat exchange analysis technical implementation scheme and the like.
Energy balance model in convective heat transfer
In order to accurately calculate the cooling (or heating) effect of gas (fluid) on solid, the invention uses the gas boundary temperature T f Calculated as physical variables. The present invention abandons the traditional computational method of single calculation of solid heat transfer process and adopts three coupled sub-heat transfer process models to describe the solid (e.g. turbine disk) heat transfer process. Specifically, the present invention breaks down the solid (turbine disk) heat transfer process into: solid internal heat conduction process, gas-solid interface (boundary) convection heat transfer process, and fluid internal heat transfer process. Wherein, the solid internal heat transfer process and the boundary condition thereof still adopt equations (1) and (2), but the fluid temperature in the equation (2) is a function of the geometric parameters.
The core content of the invention is to establish a fluid internal heat transfer model and a fluid boundary model based on the energy conservation principle. In order to establish a fluid internal heat transfer model, the invention adopts a control volume method and an energy conservation model in the form of integration. As shown in fig. 1, to study the physical properties of a fluid (gas), we selected a quadrilateral area as the control volume on the solid (turbine disk) boundary. We assume that the fluid is of constant density, i.e. incompressible, during flow. Then according to the first law of thermodynamics we can model the conservation of energy in the control volume as follows:
wherein
ρ: the density of the gas;
v: a gas velocity vector;
n: surface (or boundary) unit normal vector of the control volume;
h: the enthalpy of the gas;
v: a mode of a gas velocity vector;
As can be seen in fig. 1, the gas flows along the turbine disk boundary; there is thus a mass flow on the front and back of the control volume, while there is no mass flow into or out of the control volume on both sides. Thus integrating the left term of model (3) yields:
wherein the content of the first and second substances,
is the mass flow rate of the gas and,
is the heat flux density into the control volume.
The first term on the right side in the above formula is a gas-solid boundary convection heat transfer term which can be obtained by expansion
Wherein h is c Is the convective heat transfer coefficient, T f Is a function of the temperature of the fluid, T w Is a function of the temperature of the solid.
We move the unknowns in equation (3 b) to the left of the equation and the known quantities to the right of the equation, then we get the coupled heat transfer analysis model of the gas:
(II) nonlinear triangular unit temperature field model
As shown in FIG. 2, the method of the present inventionDiscretizing a material structure region omega by adopting six-node nonlinear triangular units, and dividing the cross section of an axisymmetric part into a limited number of units e i I.e. by
As shown in fig. 3, each triangular unit cell in the solid structure includes three vertices and three-sided midpoints; according to six nodes of the triangular unit, the invention adopts a quadratic nonlinear polynomial to establish a temperature field function of each unit:
T＝a 1 +a 2 x+a 3 r+a 4 x 2 +a 5 xr+a 6 r 2 (5)
the temperature field function in the six-node triangular unit can also be expressed as an isoparametric function form:
T＝N i T i +N j T j +N k T k +N l T l +N m T m +N n T n (6)
for temperatures on cell boundaries j-m-k, a simpler interpolation function can be constructed as follows:
T＝T j +(4T m -3T j -T k )g+(2T j +2T k -4T m )g 2 (0≤g≤1) (7)
the gas-solid coupling heat exchange effect is generated in the boundary triangular unit of the gas-solid interface, and the internal unit of the solid is completely consistent with that of the traditional method. For a six-node triangular unit as shown in fig. 3, a unit discrete algebraic equation can be established by using a galois weighted margin method as follows:
the difference between the method and the traditional finite element method is mainly embodied in the convection heat exchange treatment mode of the solid boundary unit, and the method for establishing the finite element model of the boundary unit is mainly explained here. For the boundary cell Δ ijk as shown in FIG. 2, first, it is constructed according to (8)Establishing a finite element model of a general unit; then add the third kind of boundary condition model (2). The difference between the invention and the classical heat convection boundary treatment mode is that the temperature T of the fluid (gas) f Boundary integral as a variable rather than a constant
The mid-fluid temperature dependent integral term cannot be treated as a load constant.
Therefore, it is desirable to increase the gas temperature at three nodes, denoted T, over the boundary segment j-m-k fj ,T fm ,T fk . Moreover, the invention expresses the gas temperature function on the boundary segment j-m-k as:
T f ＝T fj +(4T fm -3T fj -T fk )g+(2T fj +2T fk -4T fm )g 2 (0≤g≤1) (9)
substituting equations (7) and (9) into the convective heat transfer boundary integral (4) can obtain:
(10) In the formula
Energy balance model for gas-solid boundary unit coupling heat exchange
The six-node triangular temperature field finite element model (10) describes the heat exchange mechanism of gas and solid (parts) more accurately, but each unit model can only provide six linear algebraic equations after overall synthesis, and has nine temperature variables (namely six solid node temperatures and three boundary node gas temperatures). Because the number of equations is not matched with the number of variables, and calculation and solution cannot be carried out, the invention integrates the equation (4), and two algebraic equations can be added for each unit as follows:
integration yields:
the same principle is that:
after integration, we get:
thus, the extended finite element model for each element includes nine temperature variables and eight linear equations, and it is still necessary to supplement one equation or solve one condition. By carefully observing the coupling interface of the gas and the component structure, it can be found that the n six-node triangular boundary units include 2n +1 boundary nodes. This indicates that for all structural boundary units, there are a total of 2n +1 gas temperatures at the gas-solid interface, when we determine the gas inlet or (outlet temperature),there are only 2n node gas temperature variables. Each unit can be supplemented with two heat balance equations (11) - (12), then 2n heat balance equations can be added at the gas-solid interface. This shows that we have increased the gas temperature variation T of 2n boundary nodes for all boundary cells of the overall structural region f And 2n heat balance equations are supplemented, and the number of the addition variables is equal to that of the addition equations, so that after the whole structural area is synthesized for all units, the obtained finite element model of the overall temperature field is solvable.
Numerical calculation method of (IV) finite element model
The basic idea of the finite element method is that a structural region is discretized to form a certain number of six-node triangular units, and then a continuity partial differential equation is converted into a weighting allowance integral form in each unit; and finally, overlapping (synthesizing) the weighted margin integral equations of all the units to obtain a linear algebraic equation system of the node temperature variable, and calculating and solving.
In the invention, the temperature rigidity matrix of the solid internal unit is consistent with that of the classical method, but the temperature rigidity matrix of the convection heat exchange boundary unit is expanded from a 6 x 6 matrix to an 8 x 9 matrix. And sequentially superposing and synthesizing the temperature rigidity matrix and the load column vector of each unit to obtain the total temperature rigidity matrix and the total load column vector of the gas-solid coupling heat exchange. And for the transient heat transfer problem, synthesizing the transient temperature field coefficient matrix of each unit by adopting the same method to obtain a transient temperature field coefficient matrix [ N ] of the whole structure.
Finally, let
A linear algebraic equation system containing the node solid temperature variable and the boundary node gas temperature variable can be obtained, and the temperature field distribution of each time step can be obtained by combining the linear algebraic equation system obtained by the thermal equilibrium equation.
As shown in fig. 9, the application process of the gas-solid coupling heat exchange analysis technology provided by the present invention in the design of an aircraft engine includes the following steps:
(1) Reading a three-dimensional geometric model file of the part built in a CAD system (such as UG system) and carrying out detail feature processing.
(2) And selecting and intercepting an axisymmetric meridian plane to obtain a two-dimensional geometric model.
(3) The meridian plane is divided into triangular meshes.
(4) A finite element model of the interior triangular elements is built according to the classical method.
(5) According to the method (II) of the invention, a finite element model of the boundary element is established.
(6) Two thermal equilibrium equations are coupled for each boundary cell in accordance with the method (iii) of the present invention.
(7) And (3) superposing and synthesizing an integral finite element model of the axially symmetric region according to the method (IV) of the invention to obtain a linear algebraic equation system about all solid node temperatures and gas boundary node temperatures.
(8) And (4) solving a linear algebraic equation system by selecting a direct method to obtain the numerical values of all solid node temperatures and gas boundary node temperatures.
(9) And performing computer graphic visual display on all the obtained numerical values of the solid node temperature and the gas boundary node temperature.
The technical scheme of the invention comprises a geometric modeling subsystem, a grid division subsystem, a gas-solid coupling heat exchange analysis subsystem, a data post-processing subsystem and the like.
The geometric modeling subsystem realizes an independent geometric modeling function and a CAD/CAE interface through secondary development of a Parasolidd graph kernel platform. The Parasolidd graph kernel platform provides mature technology and perfect functions, supports the file format of mainstream CAD software, and can directly perform operations such as data reading, model display, sketch extraction, feature identification, parameter conversion, attribute addition and the like on geometric models such as UG and AutoCAD. By adopting the Parasolidd graph kernel platform, a geometric modeling module with higher practicability and expansibility can be developed in shorter time and lower cost, and the identification and conversion of most CAD/CAE file formats are supported. The project develops a geometric modeling system in a Net environment, drives Parasolidd graphic components (such as curves, entities, curved surfaces and the like) through an API (application program interface), executes interactive geometric modeling operation, and accesses and edits geometric objects.
The grid division subsystem divides the aeroengine part structure into triangular units by adopting three methods, namely a mapping method, a grid + Delaunay method and a FREE method (namely an AFT method) according to control parameters (including unit types, overall unit sizes, quantity and grid precision). The grid division subsystem can automatically check the quality of the grid according to a set criterion, and carry out local optimization and encryption on the grid.
The gas-solid coupling heat exchange analysis subsystem establishes unit and overall finite element models of parts according to the contents of the first to fourth aspects of the invention, and solves a linear algebraic equation system.
The data post-processing subsystem displays data of the temperature field and the temperature gradient field in a contour line mode, an isosurface mode, a cloud picture mode, a point icon mode and the like.
Based on the technical scheme, an aeroengine gas-solid coupling heat transfer analysis system is developed, and a main interface of the system is shown in FIG. 4. We have conducted heat transfer analysis on turbine disks, loading 1800K first class thermal boundary on the top of the turbine disk, and loading convective heat transfer boundary conditions on both sides. Assuming that the initial temperature of the cooling gas is 600K, the convective heat transfer coefficient is 400W/m 2 K. Without calculating the temperature rise effect of the gas flow process, a turbine disk temperature field profile can be obtained as shown in FIG. 5, where the minimum temperature of the solids is 673.9K. If the effect of temperature rise on the gas flow process is calculated and assuming a gas mass flow of 0.3kg/s, the temperature gradient field is calculated as shown in FIG. 6. When calculating the effect of the gas temperature rise, the lowest temperature of the turbine disk is 675.9K, and the maximum temperature gradient is 1814K/m. The comparison and calculation data show that the temperature difference of 2-3K generally exists in the temperature field distribution of each node under the two conditions. This shows that the cooling capacity of the cooling gas is gradually reduced due to the temperature rise effect in the flowing process, and the calculation result has larger deviation with the calculation result of the classical convection heat transfer model. The temperature curve of the key structure point of the turbine disk and the temperature field of the whole aircraft engine calculated based on the technical method are shown in fig. 7 and 8.
The technical method can more accurately calculate the temperature field distribution, evaluate the cooling effect and improve the design performance and reliability of the product. The invention can improve the accuracy and efficiency of the design analysis of the aircraft engine, form software with independent intellectual property rights, achieve the advanced level of foreign similar software and get rid of the dependence on foreign heat transfer analysis systems.
The foregoing detailed description of the preferred embodiments of the invention has been presented. It should be understood that numerous modifications and variations could be devised by those skilled in the art in light of the present teachings without departing from the inventive concepts. Therefore, the technical solutions available to those skilled in the art through logic analysis, reasoning and limited experiments based on the prior art according to the concept of the present invention should be within the scope of protection defined by the claims.
Claims (8)
1. A finite element calculation method for a nonlinear gas-solid coupling heat exchange problem is characterized by comprising the following steps:
step 1, reading a three-dimensional geometric model file of an axisymmetric part established in a CAD system, and carrying out detail feature processing;
step 2, selecting and intercepting an axisymmetric meridian plane to obtain a two-dimensional geometric model of the part;
step 3, dividing the meridian plane into triangular unit meshes;
step 4, establishing a finite element model of the triangular unit in the part;
step 5, establishing a finite element model of the part boundary unit;
the step 5 comprises the following steps:
step 5.1, discretizing the part structure area by adopting a six-node nonlinear triangular unit: dividing the cross section of the axisymmetric part into a limited number of six-node nonlinear triangular units, wherein each triangular unit in the part structure comprises three vertexes i, j, k and middle points l, m, n of three edges ij, jk, ki;
step 5.2, according to the six nodes i, j, k, l, m, n of the triangular units, establishing a temperature field function of each triangular unit by adopting a quadratic nonlinear polynomial:
T＝a 1 +a 2 x+a 3 r+a 4 x 2 +a 5 xr+a 6 r 2
the temperature field function in the triangular unit is expressed as an isoparametric function form:
T＝N i T i +N j T j +N k T k +N l T l +N m T m +N n T n
for temperatures on the triangular cell boundary j-m-k, a boundary cell interpolation equation is constructed as follows:
T＝T j +(4T m -3T j -T k )g+(2T j +2T k -4T m )g 2 (0≤g≤1)；
step 5.3, establishing a unit discrete algebraic equation by adopting a Galerkin weighted margin method as follows:
and 5.4, describing the boundary condition of the heat transfer of the parts by adopting a third type of boundary condition model, wherein the mathematical model is as follows:
in the formula: t is w Representing the temperature function, T, of the component f The gas temperature function is represented, lambda is the normal thermal conductivity of the boundary of the part, n is the normal vector of the heat exchange surface, and h is the heat exchange coefficient of the heat exchange surface;
step 5.5, selecting a quadrilateral area as a control volume on the boundary of the part, assuming that the density of the gas is unchanged in the flowing process, establishing an energy conservation model in the control volume as follows:
in the formula: ρ represents the gas density, V represents the gas velocity vector, n is the boundary unit normal vector of the control volume, h represents the enthalpy of the gas, V represents the modulus of the gas velocity vector,
representing the heat flow into the control volume from the outside,
means that the control volume does work to the outside per unit time;
step 5.6, the gas flows along the part boundary with mass flow on the front and back of the control volume and no mass flow into or out of the control volume on both sides, the part boundary coupling energy balance model is as follows:
in the formula:
denotes the mass flow of the gas, c p Is specific heat capacity at constant pressure, h c Is the convective heat transfer coefficient;
step 5.7, increasing the gas temperature on three nodes on the part boundary segment j-m-k, which is expressed as T fj ,T fm ,T fk And expressing the gas temperature function on the part boundary segment j-m-k as follows:
T f ＝T fj +(4T fm -3T fj -T fk )g+(2T fj +2T fk -4T fm )g 2 (0≤g≤1)
the temperature rigidity matrix model of the boundary unit of the part is as follows:
in the formula:
step 6, coupling two heat balance equations for each part boundary unit;
the two heat balance equations in step 6 are:
and
step 7, superposing and synthesizing the integral finite element model of the axial symmetric region to obtain a linear algebraic equation set related to the node temperatures of all parts and the gas boundary node temperature;
step 8, solving the linear algebraic equation set by selecting a direct method to obtain numerical values of the node temperatures of all parts and the gas boundary node temperatures;
and 9, performing computer graphic visual display on the obtained all part node temperatures and part boundary node temperature values.
2. A finite element calculation method for nonlinear gas-solid coupling heat exchange problem as defined in claim 1, wherein the implementation method of step 1 is:
and performing data reading, model display, sketch extraction, feature identification, parameter conversion and attribute addition operation on a three-dimensional geometric model file of the axisymmetric part established in the CAD system.
3. A finite element calculation method for nonlinear gas-solid coupling heat exchange problem as defined in claim 1, wherein the implementation method of step 3 is:
and dividing the part structure into the triangular unit grids according to the control parameters.
4. A finite element method in accordance with claim 3, wherein the control parameters include cell type, overall cell size, number, mesh accuracy.
5. A finite element method in accordance with claim 3, wherein the method for dividing the component structure into the triangular unit meshes in step 3 is one of mapping method, grid + Delaunay method, and FREE method.
6. A finite element method in accordance with claim 3, wherein the method for realizing step 3 further comprises:
and automatically checking the quality of the triangular unit mesh according to a set criterion, and carrying out local optimization and encryption on the triangular unit mesh.
7. A finite element method of solving the nonlinear gas-solid coupling heat exchange problem as set forth in claim 1, wherein the performing computer graphic visualization in step 9 comprises: and displaying the temperature field and/or temperature gradient field data of the part by adopting one or more of contour line, contour surface, cloud picture and point map marking modes.
8. A finite element calculation method for solving the problem of nonlinear gas-solid coupling heat exchange as defined in claim 1, wherein the implementation method of the step 7 is:
sequentially superposing and synthesizing the temperature rigidity matrix and the load column vector of each unit to obtain the total temperature rigidity matrix and the total load column vector of gas-solid coupling heat exchange, and synthesizing the transient temperature field coefficient matrix of each unit by the same method to obtain the transient temperature field coefficient matrix [ N ] of the whole structure for solving the problem of transient heat transfer]Let us order
And obtaining a linear algebraic equation system containing the node solid temperature variable and the boundary node gas temperature variable.
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