CN108319775A - The near field dynamic modeling method of composite material in a kind of heat conduction problem - Google Patents
The near field dynamic modeling method of composite material in a kind of heat conduction problem Download PDFInfo
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- CN108319775A CN108319775A CN201810090276.1A CN201810090276A CN108319775A CN 108319775 A CN108319775 A CN 108319775A CN 201810090276 A CN201810090276 A CN 201810090276A CN 108319775 A CN108319775 A CN 108319775A
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- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
- G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
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- G06F2119/08—Thermal analysis or thermal optimisation
Abstract
The present invention discloses a kind of near field dynamic modeling method of composite material in heat conduction problem, includes the following steps：(1) physical model is established；(2) divide physical model, determine the regional location of the layering of each material in model, and corresponding material properties are assigned to each region；(3) to physical model division unit grid；(4) initial temperature value at physical model each unit is set；(5) the near field dynamics constitutive relation Integrated Models parameter based on mass diffusion, determines in entire physical model temperature change computational methods at each unit, the operational parameter of all units in computational entity model；(6) it submits and calculates.The modeling method precision of the present invention is high, and mesh adaption is good, by being anticipated to all parameters in model, can greatly reduce complexity when operation so that algorithm greatly optimizes；Moreover, the modeling method and calculating process applicability of the present invention are wide, great number of issues can be suitable for.
Description
Technical field
The present invention relates to a kind of near field dynamic modeling methods of composite material in heat conduction problem, belong to conduction-convection problem
Design and manufacturing technology field.
Background technology
With the development of aeronautical and space technology, thermal protection technology is also grown rapidly therewith.In the field, composite material has
The thermodynamic property more excellent than traditional material disclosure satisfy that a variety of needs, while also have good mechanical property and plastic
Property, preparation is also very convenient, thus is applied to more and more widely in various aircraft safeguard structures.Increasingly with application
Increase, in design structure, the demand to its Simulation its security reliability is also more and more.
Conventional modeling method to composite material is FInite Element, and this method is there is only model foundation process is cumbersome, work
The problems such as work amount is big, and it is too big to mesh dependence, in order to obtain higher precision, need the very close of mesh generation, structure
It builds up very difficult, and also has very high requirement to the performance of computer, meanwhile, solving precision is low at singular point, difficult
Needs are solved to meet.How to improve computational accuracy, how to effectively reduce workload, becomes those skilled in the art urgently
The emphasis of the technical issues of solution and research.
Invention content
Goal of the invention：The problem of, heavy workload small for computational accuracy existing for existing finite element modeling method, the present invention
A kind of near field dynamic modeling method of composite material in heat conduction problem is provided, which has very high reliability and height
Precision simultaneously can greatly reduce workload.
Technical solution：The near field dynamic modeling method of composite material in heat conduction problem of the present invention, including such as
Lower step：
(1) physical model is established, outer profile size is the composite gauge that need to be modeled；
(2) divide the physical model according to each component regularity of distribution in practice of composite, determine each in physical model
The delamination area position of material, and corresponding material properties are assigned to each region, while obtaining the boundary of composite material each component
Face；
(3) it to physical model division unit grid, and is successively segmented according to each component size, until each section unit size
Meet computational accuracy requirement；
(4) temperature boundary condition of physical model, i.e. initial temperature value at physical model each unit are set；
(5) the near field dynamics constitutive relation Integrated Models parameter based on heat transfer, determines each list in entire physical model
Temperature change computational methods at member, the operational parameter of all units in computational entity model；
(6) it submits and calculates.
It, can division unit grid as follows in above-mentioned steps (3)：
I) entire model is divided roughly, wherein unit is square in two dimensional model, and unit is in threedimensional model
Square, a length of d of element sides1；
Ii) in Selection Model in existing mesh generation be located at each material interface at unit, based on quaternary tree principle according to
It is secondary that the unit is further segmented, new unit size d2=d1/2；
Iii ii) is repeated) process, until the unit size of subdivision meets to the computational accuracy requirement at interface, Ge Jidan
Elemental size is followed successively by d1,d2,…,dn, wherein di=d1/2i-1(i=1,2 ..., n).
Preferably, in step i), d1=L/150~L/300, L are the length of side of the physical model longest edge.
In above-mentioned steps (4), physical model temperature boundary condition, the temperature side are assigned according to composite material actual conditions
Boundary's condition is as follows：
It is t in the time0When,
Wherein xi(i=1,2 ..., n) is the corresponding centre of form of each unit in physical model, θ (xi,t0) it is t0At the moment point
Temperature value.
In above-mentioned steps (5), the computational methods of temperature change are at each unit in entire physical model：
θ (t+dt)=(I+A) θ (t)；
In formula, I is unit matrix, and θ (t) represents in t moment model corresponding temperature matrix at all units, and A is coefficient square
Battle array；
Wherein,θ(xi, t) and it is point xiCorresponding unit is in the corresponding temperature value of t moment；
Wherein, | | xi- x | | it is point xiAt a distance between point x, point xiIt is respectively its respectively corresponding unit geometric form with point x
The heart；For point xiNear field domain H of the corresponding unit in point xxPart in range, in two dimensional modelCorresponding is area,
In threedimensional modelCorresponding is volume；HxFor the near field range of point x corresponding units；α(xi, x) and it is at point x, with point xiBetween
Thermal diffusivity；With α (xi, x) be each unit in model operational parameter.
Wherein, unitary operation parameterComputational methods be：
Wherein δxFor near field domain HxRadius, δx=3dx~4dx；| | ξ | |=| | xi- x | | it is distance between two points；dxFor point x
The length of side of corresponding unit,For point xiThe length of side of corresponding unit,Value be derived from d1,d2,…,dn；Point xiThe area of corresponding unitOr volume
Further, unitary operation parameter alpha (xi, x) computational methods be：
Wherein α0For the coefficient of heat conduction in classical theory.
In above-mentioned steps (6), remembers I+A=K, the computational methods θ (t+dt)=(I+A) θ (t) is reduced to θ (t+
Dt)=K θ (t), are calculated according to iteration theorem, according to actual demand in fixed value t=tsOr θ (xi, t) and=θsWhen terminate
Iteration；Wherein, tsRefer to the calculating duration of corresponding composite material actual needs, θsIt refer to the permission highest to corresponding composite material
Temperature.
Advantageous effect：Compared with prior art, remarkable advantage of the invention is：(1) the present invention is based near field dynamics
Theoretical modeling method precision is high, and mesh adaption is good, and when generating unit in model, this method both can guarantee quadtree mesh
The quality of newly-generated unit in ciphering process, and Approximation effect of the grid to curved boundary can be optimized；(2) modeling of the invention
Method first anticipates all parameters in entire model before being included in final submission operation, is greatly reduced in operation
The complexity of iteration so that algorithm greatly optimizes；(3) present invention firstly provides near field dynamic method is used for heat transfer
Composite material greatly extends the utilization of near field dynamic method, moreover, the modeling method of the present invention and calculating process are applicable in
Property it is wide, meet various complex models design prepare demand, great number of issues can be suitable for.
Description of the drawings
Fig. 1 be the present invention a kind of heat conduction problem in composite material near field dynamic modeling method flow chart；
Fig. 2 (a) is Blunt-cone Body aircraft physical model synoptic chart in embodiment, and Fig. 2 (b) is that Blunt-cone Body flies in embodiment
Device boundary interface schematic diagram；
Fig. 3 is physical model local unit distribution schematic diagram in embodiment；
Fig. 4 is physical model boundary temperature distribution schematic diagram in embodiment；
Fig. 5 is α (xi, x) value distribution pattern figure；
Fig. 6 is the Temperature Distribution schematic diagram of model in embodiment result of calculation；
Specific implementation mode
Technical scheme of the present invention is described further below in conjunction with the accompanying drawings.
The near field dynamic modeling method of composite material in a kind of heat conduction problem of the present invention, method flow diagram is as schemed
1, which, for studying composite material heat conduction problem, has very high reliability, high-precision by near field dynamic method
And workload can be greatly reduced.
Embodiment
By taking the heat transfer of Blunt-cone Body aircraft front end material as an example, carries out near field dynamics using the method for the present invention and build
Mould.Wherein, in the material of Blunt-cone Body aircraft front end include air, thermal protective coating and internal aluminum alloy materials totally 3 kinds of components.
Modeling method key step is as follows：
1) physical model is established, the outer profile size Blunt-cone Body aircraft front end size of physical model is identical；
2) according to each component regularity of distribution in real material, divide physical model, determine the demixing zone of each material in model
Domain position, and corresponding material properties are assigned to each region, while the interface of composite material each component, such as Fig. 2 are obtained, wherein
Fig. 2 (a) is the general view of entire physical model；Fig. 2 (b) is Blunt-cone Body aircraft boundary, and color is shallow corresponding empty respectively by being deep to
Gas, thermal protective coating and internal material region；
3) it to model partition unit grid, and is successively segmented according to each component size：
I) entire model is divided roughly, unit is square in two dimensional model, and unit is pros in threedimensional model
Body, the present embodiment establish two dimensional model for Blunt-cone Body aircraft, take its length of side d1=100mm/200=0.5mm；
Ii the unit for being located at and being located in existing mesh generation in model at the interface of each material) is chosen, based on four forks
Tree principle successively further segments the unit, and new unit size d2=d1/ 2=0.25mm；In the present embodiment, subdivision
Part focuses primarily upon the interface location of thermal protective coating and other materials.
Iii ii) is repeated) process, until the unit size of subdivision meets to the computational accuracy requirement at interface, Ge Jidan
Elemental size is followed successively by d1,d2,…,dn, wherein di=d1/2i-1(i=1,2 ..., n).
Cell distribution, such as Fig. 3 at finally formed part thermal protective coating.
4) boundary condition of model is set：
It is t in the time0When,Wherein xi(i=1,2 ..., n) it is the corresponding shape of each unit in model
The heart, θ (xi,t0) be the point at temperature value.In the present embodiment, it is 2000 DEG C to choose initial temperature in air, thermal protective coating and interior
Portion is 0 DEG C, such as Fig. 4.
5) unit completed to step 3), following steps traverse all units in model and calculate corresponding parameter：
A) Integrated Models parameter determines computational methods
At x point corresponding units, near field kinetic model in the case of no external field, the near field dynamics of heat transfer
Constitutive relation is as follows：
Wherein | | x '-x | | --- point x ' between point x at a distance from, point x ' and x are respectively its respectively corresponding unit geometric form
The heart；dVx′--- the range of point x ' corresponding units, corresponding two dimensional model is area, and corresponding threedimensional model is volume；Hx——
The near field range of point x corresponding units；θ (x ', t) and θ (x, t) --- point x ' and point x respectively unit in t moment corresponding temperature；α
(x ', x) --- at point x, with x ' thermal diffusivities of point (being different from the thermal diffusion coefficient in traditional theory).
The rate of temperature change at x points can be obtained after discretization is
Wherein xiFor near field domain HxThe centre of form corresponding to unit in range,It is its corresponding unit in the near field of point x
Part within the scope of domain.
Further, within the Minimum-time dt times, following relationship as available from the above equation
I.e.：
It can obtain, following relationship is met to entire model：
θ (t+dt)=θ (t)+A θ (t)=(I+A) θ (t)；
Wherein I is unit matrix, and θ (t) represents in t moment model corresponding temperature matrices at all units, and A is coefficient square
Battle array.
The calculated relationship met by model is it is found that the operational parameter of each unit is in modelWith α (xi,x)。
B) it calculates at each pointValue
Computational methods are：
Wherein δxFor near field domain HxRadius, take δ in the present embodimentx=3dx, dxFor the length of side of point x corresponding units, | | ξ | |
=| | xi- x | | it is distance between two points,For point xiCorresponding unit the length of side (can value be d1,d2,…,dn), point xiCorresponding unit
AreaIt can suitably be corrected if having higher requirements to precision.
C) α (x at each point are calculatedi, x) and value
Computational methods are：
Wherein α0For the coefficient of heat conduction in classical theory, δxFor near field domain HxRadius, | | ξ | | be point-to-point transmission distance,
Such as Fig. 5.
In the present embodiment, the thermal diffusion coefficient between corresponding a variety of materials takes respectively：Air and air α01=2.33 × 10- 4m2/ s, air and thermal protective coating α02=1.17 × 10-4m2/ s, thermal protective coating and thermal protective coating α03=6.0 × 10-7m2/ s, solar heat protection
Coating and internal aluminum alloy materials α04=2.6 × 10-5m2α between/s and internal aluminum alloy materials05=5.15 × 10-5m2/s。
6) it submits and calculates
θ (t+dt)=(I+A) θ (t) remembers I+A=K.
As：θ (t+dt)=K θ (t), is calculated according to iteration theorem.
When t=2s result of calculations are as shown in Figure 6.The depth of color represents the height of corresponding position temperature in figure, and color is got over
Deep temperature is higher.
Claims (8)
1. the near field dynamic modeling method of composite material in a kind of heat conduction problem, which is characterized in that include the following steps：
(1) physical model is established, outer profile size is the composite gauge that need to be modeled；
(2) divide the physical model according to each component regularity of distribution in practice of composite, determine the delamination area of each material
Position, and corresponding material properties are assigned to each region, while obtaining the interface of each component；
(3) it to physical model division unit grid, and is successively segmented according to each component size, until each section unit size meets
Computational accuracy requirement；
(4) temperature boundary condition of physical model is set, that is, the initial temperature value at model each unit is set；
(5) the near field dynamics constitutive relation Integrated Models parameter based on heat transfer, determines in entire physical model at each unit
Temperature change computational methods, the operational parameter of all units in computational entity model；
(6) it submits and calculates.
2. the near field dynamic modeling method of composite material in heat conduction problem according to claim 1, which is characterized in that
In step (3), division unit grid as follows：
I) entire model is divided roughly, wherein unit is square in two dimensional model, and unit is pros in threedimensional model
Body, a length of d of element sides1；
Ii the unit) being located in existing mesh generation in Selection Model at each material interface, it is right successively based on quaternary tree principle
The unit further segments, new unit size d2=d1/2；
Iii ii) is repeated) process, until the unit size of subdivision meets to the computational accuracy requirement at interface, unit rulers at different levels
It is very little to be followed successively by d1,d2,…,dn, wherein di=d1/2i-1(i=1,2 ..., n).
3. the near field dynamic modeling method of composite material in heat conduction problem according to claim 2, which is characterized in that
In step i), d1=L/150~L/300, L are the length of side of the physical model longest edge.
4. the near field dynamic modeling method of composite material in heat conduction problem according to claim 2, which is characterized in that
In step (4), physical model temperature boundary condition is assigned according to composite material actual conditions, the temperature boundary condition is as follows：
It is t in the time0When,
Wherein xi(i=1,2 ..., n) is the corresponding centre of form of each unit in physical model, θ (xi,t0) it is t0Temperature at the moment point
Angle value.
5. the near field dynamic modeling method of composite material in heat conduction problem according to claim 4, which is characterized in that
In step (5), the computational methods of temperature change are at each unit in the entire physical model：
θ (t+dt)=(I+A) θ (t)；
In formula, I is unit matrix, and θ (t) represents in t moment model that corresponding temperature matrix, A are coefficient matrix at all units；
Wherein,θ(xi, t) and it is point xiCorresponding unit is in the corresponding temperature value of t moment；
Wherein, | | xi- x | | it is point xiAt a distance between point x, point xiIt is respectively its respectively corresponding unit geometric centroid with point x；For point xiNear field domain H of the corresponding unit in point xxPart in range, in two dimensional modelCorresponding is area, three-dimensional
In modelCorresponding is volume；HxFor the near field range of point x corresponding units；α(xi, x) and it is at point x, with point xiBetween thermal expansion
The rate of dissipating；With α (xi, x) be each unit in model operational parameter.
6. the near field dynamic modeling method of composite material in heat conduction problem according to claim 5, which is characterized in that
The unitary operation parameterComputational methods be：
Wherein δxFor near field domain HxRadius, δx=3dx~4dx；| | ξ | |=| | xi- x | | it is distance between two points；dxIt is corresponded to for point x
The length of side of unit,For point xiThe length of side of corresponding unit,Value be derived from d1,d2,…,dn；Point xiThe area of corresponding unitOr volume
7. the near field dynamic modeling method of composite material in heat conduction problem according to claim 5, which is characterized in that
Unitary operation parameter alpha (the xi, x) computational methods be：
Wherein α0For the coefficient of heat conduction in classical theory.
8. the near field dynamic modeling method of composite material in heat conduction problem according to claim 5, which is characterized in that
In step (6), remembers I+A=K, the computational methods θ (t+dt)=(I+A) θ (t) is reduced to θ (t+dt)=K θ (t),
It is calculated according to iteration theorem, as fixed value t=tsOr θ (xi, t) and=θsWhen terminate iteration；Wherein, tsRefer to corresponding compound
The calculating duration of material actual needs, θsIt refer to the permission maximum temperature to corresponding composite material.
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| CN115995278A (en) * | 2023-03-22 | 2023-04-21 | 中国空气动力研究与发展中心计算空气动力研究所 | Method, device, equipment and readable storage medium for evaluating thermodynamic characteristics of material |
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