CN110287554A - The finite element method of non-linear Gas-solid Coupling heat transfer problem - Google Patents
The finite element method of non-linear Gas-solid Coupling heat transfer problem Download PDFInfo
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Abstract
The invention discloses a kind of finite element methods of non-linear Gas-solid Coupling heat transfer problem, it is related to thermal conduction study, finite element method, Aeroengine Design technical field, comprising steps of reading the axial symmetry components 3-D geometric model file that CAD system is established, minutia processing is carried out；Axial symmetry meridional plane is selected and intercepted, two-dimensional geometry model is obtained；Meridional plane is divided into triangle element mesh；Establish the finite element model of inside triangle unit and boundary element；The global finite element model in superposition synthesis axial symmetry region, obtains the linear algebraic equation systems about whole node temperatures；The linear algebraic equation systems are solved, the numerical value of node temperature is obtained and carry out computer graphical visualization display.The present invention overcomes the defect of classical analysis of Heat Transfer method, fully considers the coupling effect of gas-solid heat exchange, relative to linear gas-solid thermal coupling hop algorithm, can more precisely compute the thermo parameters method of aerial motor spare part structure, and improve design level.
Description
Technical field
The present invention relates to thermal conduction study, finite element method, Aeroengine Design technical field, more particularly to one kind are non-linear
The finite element method of Gas-solid Coupling heat transfer problem.
Background technique
Aero-engine development is of great significance to national economic development and national defense construction, embodies a national skill
Art level and commercial capacity.China's aero-engine Development Level still has larger gap compared with advanced international standard, dashes forward
Broken foreign technology monopolization and innovatively challenge of the development high-performance aeroengine as scientific and technological circle and industry.
Currently, China is developing high-performance military aero-engine, need to increase substantially turbine to improve thrust
Preceding fuel gas temperature, while construction weight must be reduced in order to improve thrust ratio.It, must in order to reduce effect of the high temperature load to structure
The cooling air scale of construction must be increased, but the thermal efficiency of aero-engine can be reduced again in this way.Therefore, it is precisely calculated thermo parameters method
It is the key core technologies of high-performance aeroengine development, is the basic guarantor for improving the aero-engine thermal efficiency and safety
Card.Turbo blade wall surface Temperature Prediction value is every according to statistics reduces by 28 DEG C, then life prediction value increase accordingly one times.So heat transfer
The accuracy of analysis determines the Performance And Reliability of aero-engine, has to aero-engine whole design technical level is improved
It is significant.
Aero-engine operates under high-speed and high-temperature environment, and local temperature alreadys exceed the limit that material is able to bear, must
It must be cooled down, so needing accurate calculating temperature field and assessment cooling efficiency.Currently, being used in the development of China's aero-engine
Cooling gas temperature is approximately constant by classical Heat Transfer Calculation, is had ignored solid in cooling procedure and is passed to the thermal energy of gas
Pass effect.This classical analysis method, which cannot accurately describe cooling gas, leads to itself temperature due to absorbing heat in solid cooling procedure
Degree increases, to reduce the temperature difference of gas and solid, in turn results in the problem that heat exchange efficiency and cooling effect drastically reduce.Cause
This, the bi-directional machine of energy (heat) between accurate description gas necessary in high-performance aeroengine development and solid
Reason, provides basis for thermal deformation and thermoelastic analysis, could optimize properties of product and improve security reliability.
For wheel disc type components various in aero-engine, can carry out calculating using axial symmetry analysis of Heat Transfer model and
Simulation.Classical axial symmetry analysis of Heat Transfer method describes the internal diabatic process of solid (components) using heat exchange pattern,
Governing equation (governing equation) is as follows:
Also, the boundary condition of solid heat transfer, mathematical model are described using classical Convective Heat Transfer are as follows:
Symbol meaning is as follows in equation (1)-(2):
ρ: the mass density of fluid；
cp: specific heat at constant pressure；
Tw: solid temperature；
Tf: the temperature of cooling gas；
λx,λr, λ: be respectively solid in axial direction, radial direction and boundary method to thermal conductivity；
X, r: axially and radially coordinate；
T: time；
N: heat exchange surface normal vector；
H: the heat exchange surface coefficient of heat transfer；
qv: the inner heat source of solid.
Conventional convection heat transfer problem analytical technology only considers cooling (or heating) effect of fluid (gas) to solid,
And ignore heating (or cooling) effect of solid convective body (gas).So existing business finite element analysing system (such as
ANSYS and NASTRAN etc.) all by the fluid temperature (F.T.) in heat convection problem as constant, i.e. T in hypothesis (2) formulafFor constant.
This traditional analysis of Heat Transfer method does not account for gas-solid boundary coupled and heat-exchange effect, can generate larger calculating in the case of a high temperature
Error can not accurately calculate the components such as turbine temperature field, constrain the design level of China's aero-engine.
Therefore, those skilled in the art is dedicated to developing a kind of FEM calculation of non-linear Gas-solid Coupling heat transfer problem
Method for cooling gas in Aeroengine Design since heat absorption generates temperature rise in flow process, and then leads to gas pair
The technical problem that the cooling efficiency of solid (such as turbine disk) drastically reduces, the present invention overcome lacking for classical analysis of Heat Transfer method
It falls into, fully considers the coupling effect of gas-solid heat exchange, establish non-linear six using the principle of energy balance in heat transfer process
Node triangular element finite element model, and propose effective numerical computation method.It is worthwhile relative to linear gas-solid thermal coupling
Method, nonlinear algorithm proposed by the present invention can more precisely compute the thermo parameters method of aerial motor spare part structure, and
Improve design level.
Summary of the invention
In view of the above drawbacks of the prior art, the technical problem to be solved by the present invention is to how overcome classical heat transfer point
The defect of analysis method fully considers the coupling effect of gas-solid heat exchange, is established using the principle of energy balance in heat transfer process
Finite element model proposes more effective numerical computation method, more precisely computes the temperature field of aerial motor spare part structure
Distribution, and improve design level.
To achieve the above object, the present invention provides a kind of FEM calculation sides of non-linear Gas-solid Coupling heat transfer problem
Method the described method comprises the following steps:
Step 1, the 3-D geometric model file for reading the axial symmetry components established in CAD system, and carry out details
Characteristic processing；
Step 2 selects and intercepts axial symmetry meridional plane, obtains the two-dimensional geometry model of the components；
The meridional plane is divided into triangle element mesh by step 3；
Step 4, the finite element model for establishing the components inside triangle unit；
Step 5, the finite element model for establishing the components boundary element；
Step 6 couples two equation of heat balances for each components boundary element；
Step 7, superposition synthesis axial symmetry region global finite element model, obtain about whole components node temperatures and
The linear algebraic equation systems of components boundary node temperature；
Step 8, selection direct method solve the linear algebraic equation systems, and it is gentle to obtain whole components node temperatures
The numerical value of body boundary node temperature；
Step 9, to whole components node temperatures obtained and gas boundary node temperature value, calculated
Machine graph visualization is shown.
Further, the implementation method of the step 1 are as follows:
The 3-D geometric model file progress data reading for the axial symmetry components established in CAD system, model are shown,
Sketch extraction, feature identification, Parameter Switch, attribute additional operations.
Further, the implementation method of the step 3 are as follows:
According to control parameter, the component structural is divided into the triangle element mesh.
Further, the control parameter includes cell type, overall cell size, quantity, grid precision.
Further, the method that the component structural is divided into the triangle element mesh in the step 3
For one of reflection method, grid+Delaunay method, FREE method.
The implementation method of the step 3 further include:
The quality that the triangle element mesh is automaticly inspected according to the criterion of setting, to the triangle element mesh into
Row local optimum and encryption.
Further, the carry out computer graphical visualization display in the step 9 include: using isopleth, contour surface,
One of cloud atlas, point icon mode are a variety of, show the components temperature field and temperature gradient field data.
Further, the step 5 the following steps are included:
Step 5.1 carries out discretization to the component structural region using the non-linear triangular element of six nodes: by institute
The non-linear triangular element of six nodes that axial symmetry components section is divided into limited quantity is stated, it is every in the component structural
A triangular element includes three vertex i, j, k and three side ij, the intermediate point l, m, n of jk, ki；
Step 5.2, six node is according to the triangular element, j, k, l, m, n, using quadratic nonlinearity multinomial
Establish each triangular element temperature field function:
T=a1+a2x+a3r+a4x2+a5xr+a6r2
Temperature field function representation is Isoparametric function form in the triangular element:
T=NiTi+NjTj+NkTk+NlTl+NmTm+NnTn
For the temperature on the triangular element boundary j-m-k, tectonic boundary unit interpolation equation is as follows:
T=Tj+(4Tm-3Tj-Tk)g+(2Tj+2Tk-4Tm)g2(0≤g≤1)；
Step 5.3, to establish mesh discretization algebraic equation using the golden Weighted Residual method of gal the Liao Dynasty as follows:
Step 5.4, the boundary condition that components heat transfer is described using third boundary condition model, mathematical model
Are as follows:
In formula: TwIndicate components temperature funtion, TfIndicate that gas temperature function, λ are components boundary method to thermal conductivity, n
For heat exchange surface normal vector, h is the heat exchange surface coefficient of heat transfer；
Step 5.5 selects a quadrilateral area as control volume on the components boundary, it is assumed that gas is flowing
Density is constant during dynamic, and the modeling of energy conservation established in the control volume is as follows:
In formula: ρ indicates gas density, and v indicates that gas velocity vectors, n are the border units normal vector for controlling volume, h table
Show that the enthalpy of gas, V indicate the mould of gas velocity vectors,Indicate the heat flow for being externally entering control volume,Indicate control
Volume is within the unit time to external work；
Step 5.6, the gas are flowed along the components boundary, have quality on the control volume front-back
Stream, and there is no quality to flow into or out the control volume two sides, components boundary couples energy balance model such as
Under:
In formula:Indicate the mass flow of gas, cpFor specific heat at constant pressure, hcFor convection transfer rate；
Step 5.7, the gas temperature on the components border segment j-m-k on three nodes of increase, are expressed as Tfj,
Tfm,Tfk, by gas temperature function representation on the components border segment j-m-k are as follows:
Tf=Tfj+(4Tfm-3Tfj-Tfk)g+(2Tfj+2Tfk-4Tfm)g2(0≤g≤1)
The components boundary element temperature stiffness matrix model are as follows:
In formula:
Further, two equation of heat balances described in the step 6 are as follows:
With
Further, the implementation method of the step 7 are as follows:
Laminated structure synthesizes each cell temperature stiffness matrix and load column vector, obtains total body temperature of Gas-solid Coupling heat exchange
Degree stiffness matrix and General load column vector synthesize the transient state temperature of each unit using same method for Transient Heat Transfer problem
Field coefficient matrix is spent, the transient state temperature field coefficient matrix [N] of total is obtained, is enabled(l=1,2 ..., n), are obtained
Obtain the linear algebraic equation systems comprising node solid temperature variable and boundary node gas temperature variable.
The present invention overcomes the defect of classical analysis of Heat Transfer method, the coupling effect of gas-solid heat exchange is fully considered, using heat
Principle of energy balance in transmittance process establishes non-linear six-node triangle element finite element model, and proposes effectively
Numerical computation method.Relative to linear gas-solid thermal coupling hop algorithm, nonlinear algorithm proposed by the present invention can be counted more accurately
The thermo parameters method of aerial motor spare part structure is calculated, and improves design level.
It is described further below with reference to technical effect of the attached drawing to design of the invention, specific structure and generation, with
It is fully understood from the purpose of the present invention, feature and effect.
Detailed description of the invention
Fig. 1 is the borderline fluid control volume-based model of the turbine disk of a preferred embodiment of the invention；
Fig. 2 is models for temperature field in the six-node triangle element of a preferred embodiment of the invention；
Fig. 3 is the solid boundaries unit of a preferred embodiment of the invention and the coupled and heat-exchange process of gas；
Fig. 4 is the aero-engine Gas-solid Coupling heat transfer system frame of a preferred embodiment of the invention；
Fig. 5 is the turbine disk temperature field that the method for a preferred embodiment of the invention is calculated；
Fig. 6 is the turbine disk temperature gradient field that the method for a preferred embodiment of the invention is calculated；
Fig. 7 is the turbine disk key structure point temperature curve that the method for a preferred embodiment of the invention is calculated；
Fig. 8 is the method meter counted aero-engine complete machine temperature field of a preferred embodiment of the invention；
Fig. 9 is the method flow diagram of a preferred embodiment of the invention.
Specific embodiment
The preferred embodiment of the present invention is introduced below with reference to Figure of description, keeps its technology contents more clear and convenient for reason
Solution.The present invention can be emerged from by many various forms of embodiments, and protection scope of the present invention is not limited only to text
In the embodiment mentioned.
The present invention includes the gas of axial symmetry components Gas-solid Coupling heat convection model, six node triangle boundary elements
Temperature Rise Model, overall finite element model, aero-engine Gas-solid Coupling HEAT EXCHANGE ANALYSIS implementer's case etc..
(1) energy balance model in heat convection
In order to accurately calculate gas (fluid) to the cooling of solid (or heating) effect, the present invention is by gas border temperature
TfIt is calculated as physical descriptor.The present invention abandons the single Traditional calculating methods for calculating solid heat transfer process, and uses three
The sub- diabatic process model of a coupling describes solid (such as turbine disk) diabatic process.In particular, the present invention is by solid (whirlpool
Wheel disc) diabatic process decomposition are as follows: solid interior heat transfer process, gas-solid interface (boundary) Convective Heat Transfer and internal fluid
Diabatic process.Wherein, solid interior diabatic process and its boundary condition still use equation (1) and (2) formula, still in (2) formula
Fluid temperature (F.T.) is the function of geometric parameter.
Core of the invention content is to establish internal fluid heat transfer model and fluid boundary mould based on conservation of energy principle
Type.In order to establish internal fluid heat transfer model, present invention employs control volume (control volume) methods and integral shape
The modeling of energy conservation of formula.As shown in Figure 1, we are on solid (turbine disk) side for the physical property of Study of Fluid (gas)
Select a quadrilateral area as control volume in boundary.We assume that fluid density in flow process is constant, i.e., can not press
Contracting.Then according to the first law of thermodynamics, the modeling of energy conservation that we can establish in control volume is as follows:
Wherein
ρ: gas density；
V: gas velocity vectors；
N: surface (or boundary) unit normal vector of volume is controlled；
H: the enthalpy of gas；
V: the mould of gas velocity vectors；
It is externally entering the heat flow of control volume；
Volume is controlled within the unit time to external work.
It will be noted from fig. 1 that gas is flowed along turbine disk boundary；Therefore there is quality on control volume front-back
Stream, and there is no quality to flow into or out control volume two sides.It is available to model (3) left side integral in this way:
Wherein,It is the mass flow of gas,It is the heat flow density into control volume.
The right first item is gas-solid boundary convection heat exchange item in above formula, is unfolded available
Wherein, hcIt is convection transfer rate, TfIt is fluid temperature (F.T.) function, TwIt is solid temperature function.
Unknown quantity in formula (3b) is moved on to the equation left side by us, and known quantity is moved on to the right of equation, then obtains gas
Analysis of Coupled Heat Transfer model:
(2) non-linear triangular element models for temperature field
Material structure region Ω is carried out as shown in Fig. 2, the method for the present invention uses six nodes non-linear triangular element
Axisymmetric parts section, is divided into the unit e of limited quantity by discretization (discretization)i, i.e.,Such as
Shown in Fig. 3, each triangular element in solid structure includes the intermediate point on three vertex and three sides；According to triangular element
Six nodes, the present invention establishes each cell temperature field function using quadratic nonlinearity multinomial:
T=a1+a2x+a3r+a4x2+a5xr+a6r2 (5)
Temperature field function can also be expressed as Isoparametric function form in six-node triangle element:
T=NiTi+NjTj+NkTk+NlTl+NmTm+NnTn (6)
For the temperature on elementary boundary j-m-k, it is as follows that more simple interpolating function can be constructed:
T=Tj+(4Tm-3Tj-Tk)g+(2Tj+2Tk-4Tm)g2(0≤g≤1) (7)
Gas-solid Coupling heat transfer effect occurs in the edge triangles unit of gas-solid interface, the internal element and tradition of solid
Method is completely the same.For six-node triangle element as shown in Figure 3, list can establish using the golden Weighted Residual method of gal the Liao Dynasty
The discrete algebraic equation of member is as follows:
The difference of the present invention and conventional finite element method is mainly reflected in the heat convection processing mode of solid boundaries unit
On, the finite element model method for building up of boundary element is stressed herein.For boundary element Δ ijk as shown in Figure 2, first root
The finite element model of general cell is established according to (8)；Then increase third boundary condition model (2).The present invention and classical convection current
Heat transfer boundary processing mode is not both by fluid (gas) temperature TfAs variable rather than constant, boundary integralThe relevant integral term of middle fluid temperature (F.T.) cannot function as the processing of load constant.
Therefore, it is necessary to increase the gas temperature on three nodes on border segment j-m-k, it is expressed as Tfj,Tfm,Tfk.And
And the present invention is by gas temperature function representation on border segment j-m-k are as follows:
Tf=Tfj+(4Tfm-3Tfj-Tfk)g+(2Tfj+2Tfk-4Tfm)g2(0≤g≤1) (9)
It is available that (7) and (9) formula are substituted into converctive heat transfer boundary integral (4):
(10) in formula
(3) energy balance model of gas-solid boundary element coupled and heat-exchange
Six node triangular temperature field finite element models (10) describe gas and solid (components) more accurately
Heat exchange mechanism, but each model of element can only provide six linear algebraic equations after totally synthesis, but there is nine temperature
It spends variable (gas temperature of i.e. six solid node temperatures and three boundary nodes).Not due to equation number and variables number
Match and calculating solution can not be carried out, therefore, the present invention integrates equation (4), can increase by two algebra for each unit
Equation is as follows:
Integral obtains:
Similarly:
It is obtained after integral:
In this way, the extension finite element model of each unit includes nine temperature variables and eight linear equations, still need
Supplement an equation or solving condition.By examining the coupled interface of gas and component structural, it can be found that n
Six node triangle boundary elements include 2n+1 boundary node.This shows for entire infrastructure boundary element, in gas-solid interface
Locate to share 2n+1 gas temperature, after we measure gas access or (outlet temperature), the then gas of only 2n node
Temperature variable.Each unit can supplement two equation of heat balance (11)-(12), then can increase 2n heat at gas-solid interface
Equilibrium equation.For this explanation for all boundary unit in overall structure region, we increase the gas temperature of 2n boundary node
Spend variable Tf, while 2n equation of heat balance is supplemented, it is equal with the number of equation is increased to increase variable, therefore in overall structure
After region synthesizes whole units, obtained bulk temperature field finite element model can be solved.
(4) numerical computation method of finite element model
The basic thought of finite element method is that structural region discretization is first constituted a certain number of six nodes triangle lists
Then continuity partial differential equation are converted to Weighted Residual integrated form in each unit by member；Finally again by whole units
Weighted Residual integration type be superimposed (synthesis), obtain the linear algebraic equation systems of node temperature variable, carry out calculating solution.
In the present invention, the temperature stiffness matrix of solid interior unit is consistent with classical way, but converctive heat transfer boundary list
Member temperature stiffness matrix from 6 × 6 matrix-expands be 8 × 9 matrixes.Laminated structure synthesizes each cell temperature stiffness matrix and load
Lotus column vector obtains the bulk temperature stiffness matrix and General load column vector of Gas-solid Coupling heat exchange.For Transient Heat Transfer problem,
The transient state temperature field coefficient matrix that each unit is synthesized using same method obtains the transient state temperature field coefficient matrix of total
[N]。
Finally, enabling
The linear algebraic equation systems comprising node solid temperature variable and boundary node gas temperature variable can be obtained, are joined
Close the linear algebraic equation systems obtained by equation of heat balance, so that it may acquire the thermo parameters method of each time step.
As shown in figure 9, application stream of the Gas-solid Coupling HEAT EXCHANGE ANALYSIS technology proposed by the present invention in Aeroengine Design
Journey includes the following steps:
(1) the 3-D geometric model file for the components established in CAD system (such as UG system) is read, and is carried out thin
Save characteristic processing.
(2) axial symmetry meridional plane is selected and intercepted, two-dimensional geometry model is obtained.
(3) meridional plane is divided into triangular mesh.
(4) finite element model of inside triangle unit is established according to classical way.
(5) finite element model of boundary element is established according to the present invention (two) method.
It (6) is that each boundary element couples two equation of heat balances according to (three) method of the invention.
(7) it according to the global finite element model in (four) method superposition synthesis axial symmetry region of the invention, obtains about whole
The linear algebraic equation systems of solid node temperature and gas boundary node temperature.
(8) direct method solving linear algebric equation group is selected, all solids node temperature and gas boundary node temperature are obtained
The numerical value of degree.
(9) to all solids node temperature obtained and gas boundary node temperature value, carrying out computer graphical can
It is shown depending on changing.
Implementer's case of the invention includes geometric modeling subsystem, grid dividing subsystem, Gas-solid Coupling heat exchange point
Analyse subsystem, Data Post subsystem etc..
Geometric modeling subsystem passes through the secondary development of Parasolid graphic kernel platform, realizes independent geometric modeling
Function and with CAD/CAE interface.Parasolid graphic kernel platform provides mature technology and perfect function, supports master
The file format of CAD software is flowed, data reading directly can be carried out to geometrical models such as UG, AutoCAD, model is shown, sketch
The operations such as extraction, feature identification, Parameter Switch, attribute be additional.It, can be with shorter using Parasolid graphic kernel platform
Time, lower cost develop all higher geometric modeling module of practicability, scalability, and support most of CAD/CAE texts
The identification and conversion of part format.This project develops Geometric Modeling system under .Net environment, is driven by API (application programming interfaces)
Dynamic Parasolid graphic assembly (such as curve, entity, curved surface etc.) executes interaction geometric modeling operation, access and editor's geometry
Object.
Grid dividing subsystem according to control parameter (including cell type, overall cell size, quantity, grid precision),
Aircraft engine parts structure is divided using three kinds of reflection method, grid+Delaunay method, FREE method (i.e. AFT method) methods
For triangular element.Grid dividing subsystem can automaticly inspect the quality of grid according to the criterion of setting, carry out part to grid
Optimization and encryption.
Gas-solid Coupling HEAT EXCHANGE ANALYSIS subsystem establishes the unit and totality of components according to (one)~(four) content of the invention
Finite element model, and solving linear algebric equation group.
Data Post subsystem is using isopleth, contour surface, cloud atlas and puts modes, displays temperature field and the temperature such as icon
Gradient field data.
Based on the above-mentioned technical proposal, we have developed aero-engine Gas-solid Coupling analysis of Heat Transfer system, Fig. 4 is system master
Want interface.We have carried out analysis of Heat Transfer to the turbine disk, and in the first kind thermal boundary of turbine disk top load 1800K, two sides add
Carry Convection Heat Transfer Boundary Conditions.Assuming that cooling gas initial temperature is 600K, convection transfer rate 400W/m2K.If disregarded
The temperature-rise effect of gas flow is calculated, available turbine disk thermo parameters method is as shown in figure 5, wherein solid minimum temperature is
673.9K.If calculating the temperature-rise effect of gas flow, and assume that gas mass flow is 0.3kg/s, then calculates
It is as shown in Figure 6 to temperature gradient field.When calculating gas temperature-rise effect, turbine disk minimum temperature is 675.9K, maximum temperature ladder
Degree is 1814K/m.Comparing calculation statistics indicate that, the thermo parameters method in the case of two kinds is in the generally existing 2~3K temperature difference of each node.
This illustrate cooling gas in flow process due to temperature-rise effect, cooling capacity gradually decreases, with classical heat convection model
Calculated result has relatively large deviation.The turbine disk key structure point temperature curve being calculated based on the technology of the present invention method and aviation
Engine complete machine temperature field is as shown in Figure 7 and Figure 8.
Technical method of the invention can more precisely compute thermo parameters method, assess cooling effect, improve product design
Performance And Reliability.The accuracy and efficiency of Aeroengine Design analysis can be improved in the present invention, and being formed has independent intellectual
The software of property right reaches the advanced level of external similar software, gets rid of the dependence to external analysis of Heat Transfer system.
The preferred embodiment of the present invention has been described in detail above.It should be appreciated that the ordinary skill of this field is without wound
The property made labour, which according to the present invention can conceive, makes many modifications and variations.Therefore, all technician in the art
Pass through the available technology of logical analysis, reasoning, or a limited experiment on the basis of existing technology under this invention's idea
Scheme, all should be within the scope of protection determined by the claims.
Claims (10)
1. a kind of finite element method of non-linear Gas-solid Coupling heat transfer problem, which is characterized in that the method includes following
Step:
Step 1, the 3-D geometric model file for reading the axial symmetry components established in CAD system, and carry out minutia
Processing；
Step 2 selects and intercepts axial symmetry meridional plane, obtains the two-dimensional geometry model of the components；
The meridional plane is divided into triangle element mesh by step 3；
Step 4, the finite element model for establishing the components inside triangle unit；
Step 5, the finite element model for establishing the components boundary element；
Step 6 couples two equation of heat balances for each components boundary element；
Step 7, superposition synthesize the global finite element model in axial symmetry region, obtain about whole components node temperatures and gas
The linear algebraic equation systems of boundary node temperature；
Step 8, selection direct method solve the linear algebraic equation systems, obtain whole components node temperatures and gas side
The numerical value of boundary's node temperature；
Step 9, to whole components node temperatures obtained and components boundary node temperature value, carry out computer
Graph visualization is shown.
2. the finite element method of non-linear Gas-solid Coupling heat transfer problem as described in claim 1, which is characterized in that described
The implementation method of step 1 are as follows:
To the 3-D geometric model file for the axial symmetry components established in CAD system carries out data reading, model is shown, sketch
Extraction, feature identification, Parameter Switch, attribute additional operations.
3. the finite element method of non-linear Gas-solid Coupling heat transfer problem as described in claim 1, which is characterized in that described
The implementation method of step 3 are as follows:
According to control parameter, the component structural is divided into the triangle element mesh.
4. the finite element method of non-linear Gas-solid Coupling heat transfer problem as claimed in claim 3, which is characterized in that described
Control parameter includes cell type, overall cell size, quantity, grid precision.
5. the finite element method of non-linear Gas-solid Coupling heat transfer problem as claimed in claim 3, which is characterized in that described
The method that the component structural is divided into the triangle element mesh in step 3 is reflection method, grid+Delaunay
One of method, FREE method.
6. the finite element method of non-linear Gas-solid Coupling heat transfer problem as claimed in claim 3, which is characterized in that described
The implementation method of step 3 further include:
The quality that the triangle element mesh is automaticly inspected according to the criterion of setting, to triangle element mesh carry out office
Portion's optimization and encryption.
7. the finite element method of non-linear Gas-solid Coupling heat transfer problem as described in claim 1, which is characterized in that described
Progress computer graphical visualization display in step 9 includes: using one in isopleth, contour surface, cloud atlas, point icon mode
Kind is a variety of, shows the components temperature field and/or temperature gradient field data.
8. the finite element method of non-linear Gas-solid Coupling heat transfer problem as described in claim 1, which is characterized in that described
Step 5 the following steps are included:
Step 5.1 carries out discretization to the component structural region using the non-linear triangular element of six nodes: by the axis
Symmetric Zero section is divided into the non-linear triangular element of six nodes of limited quantity, each institute in the component structural
Stating triangular element includes three vertex i, j, k and three side ij, the intermediate point l, m, n of jk, ki；
Step 5.2, six node is according to the triangular element, j, k, l, m, n are established using quadratic nonlinearity multinomial
Each triangular element temperature field function:
T=a1+a2x+a3r+a4x2+a5xr+a6r2
Temperature field function representation is Isoparametric function form in the triangular element:
T=NiTi+NjTj+NkTk+NlTl+NmTm+NnTn
For the temperature on the triangular element boundary j-m-k, tectonic boundary unit interpolation equation is as follows:
T=Tj+(4Tm-3Tj-Tk)g+(2Tj+2Tk-4Tm)g2(0≤g≤1)；
Step 5.3, to establish mesh discretization algebraic equation using the golden Weighted Residual method of gal the Liao Dynasty as follows:
Step 5.4, the boundary condition that components heat transfer is described using third boundary condition model, mathematical model are as follows:
In formula: TwIndicate components temperature funtion, TfIndicate that gas temperature function, λ are components boundary method to thermal conductivity, n is to change
Hot surface normal vector, h are the heat exchange surface coefficient of heat transfer；
Step 5.5 selects a quadrilateral area as control volume on the components boundary, it is assumed that gas is flowing over
Density is constant in journey, and the modeling of energy conservation established in the control volume is as follows:
In formula: ρ indicates gas density, and v indicates that gas velocity vectors, n are the border units normal vector for controlling volume, and h indicates gas
The enthalpy of body, V indicate the mould of gas velocity vectors,Indicate the heat flow for being externally entering control volume,Indicate control volume
To external work within the unit time；
Step 5.6, the gas are flowed along the components boundary, have quality stream on the control volume front-back, and
There is no quality to flow into or out the control volume two sides, it is as follows that components boundary couples energy balance model:
In formula:Indicate the mass flow of gas, cpFor specific heat at constant pressure, hcFor convection transfer rate；
Step 5.7, the gas temperature on the components border segment j-m-k on three nodes of increase, are expressed as Tfj,Tfm,
Tfk, by gas temperature function representation on the components border segment j-m-k are as follows:
Tf=Tfj+(4Tfm-3Tfj-Tfk)g+(2Tfj+2Tfk-4Tfm)g2(0≤g≤1)
The components boundary element temperature stiffness matrix model are as follows:
In formula:
9. the finite element method of non-linear Gas-solid Coupling heat transfer problem as described in claim 1, which is characterized in that described
Two equation of heat balances described in step 6 are as follows:
With
10. the finite element method of non-linear Gas-solid Coupling heat transfer problem as described in claim 1, which is characterized in that institute
State the implementation method of step 7 are as follows:
Laminated structure synthesizes each cell temperature stiffness matrix and load column vector, and the bulk temperature for obtaining Gas-solid Coupling heat exchange is rigid
Degree matrix and General load column vector synthesize the transient state temperature field of each unit using same method for Transient Heat Transfer problem
Coefficient matrix obtains the transient state temperature field coefficient matrix [N] of total, enablesIt obtains
Linear algebraic equation systems comprising node solid temperature variable and boundary node gas temperature variable.
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