1、Lesson content:Thermal ContactIntroduction: Heat Transfer Across Interfaces Thermal Interaction Usage Gap Conduction Gap RadiationWorkshop 4: Reactor: Thermal Contact and Analysis (IA)Workshop 4: Reactor: Thermal Contact and Analysis (KW)Lesson 5: Thermal Interfaces120 minutesBoth interactive (IA) a

2、nd keywords (KW) versions of the workshop are provided. Complete only one.Thermal ContactAbaqus has strong capabilities for solving mechanical contact problems.These same capabilities can be used to solve thermal “contact” problems.Used to model thin regions (insulating liners, for example) in a lar

3、ger modelUsed to match stress analysis model involving contact with similar heat transfer mesh for thermal stress analysisUsed for purposes of mesh refinementHeat transfer across “thin” interfaces is often an important aspect of thermal analysis. Such interfaces typically have relatively low thermal

4、 conductivity. Therefore, they allow relatively large temperature differences across them. However, thin interfaces have negligible “thermal mass.” You can neglect the internal thermal energy, U(q), stored in the interface; that is, you can assume that it has zero specific heat.Introduction: Heat Tr

5、ansfer Across Interfaces (1/6)Thermal interface examplesExamples of thermal interfaces are shown:fluidfluid boundary layerfluid velocity profileSOLIDBoundary layer between a fluid and a solid surfaceIntroduction: Heat Transfer Across Interfaces (2/6)contact layerelectronic device (“chip”)substrateCo

6、ntact layer (gap exaggerated) between two solid componentsIntroduction: Heat Transfer Across Interfaces (3/6)head or coverthermal resistance at interfacesblockBolted head or cover (gap exaggerated)Introduction: Heat Transfer Across Interfaces (4/6)In Abaqus such effects are modeled using the surface

7、-based interaction definitions. These are surfaces (three-dimensional) or lines (two-dimensional) that typically are physically close (or in contact) but have distinct temperatures on their two sides.surface ASURF, qAsurface BSURF, qBIn general, qA qB.Thermal interfacesIntroduction: Heat Transfer Ac

8、ross Interfaces (5/6)These surfaces may be on different bodies, or they may be distinct surfaces of the same body.surface Asurface BThermal interface for a single bodyIntroduction: Heat Transfer Across Interfaces (6/6)Heat can flow across an interface via conduction or radiation. Generally, both mod

9、es of heat transfer are present to some degree. Their relative importance depends on the surface temperatures and the medium between the surfaces.Conduction heat transfer across an interface requires that some form of matter exist between the surfaces.Radiative heat transfer across an interface does

10、 not require that any form of matter exist between the surfaces. In fact, the presence of a media will inhibit the exchange of radiative energy between the surfaces.Thermal Interaction Usage (1/8)Example: Reactor pressure vesselThere are four thermal interfaces.nut-to-bolt interfacenut-to-head inter

11、facehead-to-vessel interfacenut-to-vessel interfaceThermal Interaction Usage (2/8)Specifying thermal contactDefine surfaces.The underlying meshes need not match along the interface.E.g., surfaces boltShank and nutInner will be used to define the bolt-to-nut interface.Surfaces that will interact with

12、 one another are paired.Keywords interfaceThis is identical to what is done to define mechanical contact!boltShanknutInner*SURFACE, NAME=nutInner.*SURFACE, NAME=boltShank.*SURFACE INTERACTION, NAME=gap*GAP CONDUCTANCE4.167e-4, 0. 0., 10.*CONTACT PAIR, INT=gapnutInner, boltShank12Thermal Interaction

13、Usage (3/8)Abaqus/CAE interfacenext slide3boltShanknutInnerThermal Interaction Usage (4/8)Specify thermal properties.*SURFACE, NAME=nutInner.*SURFACE, NAME=boltShank.*SURFACE INTERACTION, NAME=gap*GAP CONDUCTANCE4.167e-4, 0. 0., 10.*CONTACT PAIR, INT=gapnutInner, boltShank3boltShanknutInnerThermal I

14、nteraction Usage (5/8)Available thermal properties include: Gap conductionDetails will be discussed later in section “Gap conduction.”Gap radiationDetails will be discussed later in section “Gap radiation.”User-defined thermal interactions via UINTER or VUINTER user subroutines.Heat transfer (regard

15、less of the mode) between the surfaces is assumed to occur only in the direction of the average surface normal, n. slavemasteraverage surfaceThermal Interaction Usage (6/8)Bonded interfacesBonding surfaces is a simple means of constraining temperatures at corresponding points of an interface to have

16、 the same value.Example: Reactor pressure vesselThe omega seal is welded to the under surface of the closure head and top surface of the vessel.Keywords interface*SURFACE, NAME=sealBot.*SURFACE, NAME=vessel-head-to-seal.*TIE, TYPE=SURFACE TO SURFACEsealBot, vessel-head-to-sealheadvesselsealweldedThe

17、rmal Interaction Usage (7/8)Abaqus/CAE interfaceheadvesselsealweldedThermal Interaction Usage (8/8)Slave nodes (within the distance defined by the POSITION TOLERANCE parameter) can be moved onto the master surface using the optional ADJUST parameter.Sample usage:*TIE, NAME=name, POSITION TOLERANCE=a

18、, ADJUST=NOAdjustments can be displayed in Abaqus/Viewer from a datacheck analysis.Bonding surfaces is a powerful technique to handle patibly meshed regions.Gap Conduction (1/13)Heat transfer by conduction depends on the conductivity of the material within an interface as well as the temperatures of

19、 the respective surfaces: This mode of heat transfer can occur between closely adjacent bodies immersed in a fluid or gas or between surfaces in contact that have some oxide or other surface layer between them.Many structures have thin “l(fā)iners” of insulating material between other solid regionsSince

20、 liners are thin, internal energy storage (specific heat) may be neglectedModel these with thermal contact and set:surface ASURF, qAsurface BSURF, qBkbGap Conduction (2/13)A simple example: Consider two blocks separated by a small distance and three values of gap conductance:ZeroNon-zeroVery large (

21、tending towards infinity)The intent of this example is to illustrate that the temperature will be discontinuous across the interface if conduction across the interface is small.A perfectly bonded surface would not have a temperature jump across the interface. Many interface conditions do not corresp

22、ond to perfect bonding.q =100q =200gapGap Conduction (3/13)Gap conductance = 0Each block is perfectly insulated at its endThere is no heat transfer between the blocks Uniform temperature in each blockGap Conduction (4/13)Gap conductance = 1Heat is exchanged between the blocks Linear temperature vari

23、ation along the length of each blockTemperature jump at interfaceq =147.6q =152.4Gap Conduction (5/13)Gap conductance = 1e6Large value approximates infinite conductance Blocks behave as if they were a single body (as if perfectly bonded) Common temperature at interfaceq =150Gap Conduction (6/13)Gap

24、conductanceWith gap conductance, the heat conducts across the gap in the direction, n, governed by the equationABaverage surfaceGap conductanceGap Conduction (7/13)The definition kb may depend on a number of different quantitiesTemperature-dependent gap conductivity.The gap conductivity can be speci

25、fied as dependent on the average temperature across the gap: If kb is strongly temperature-dependent, the unsymmetric solver can improve the convergence rate in Abaqus/Standard.*GAP CONDUCTANCE, (PRESSURE), DEPENDENCIES=kb, clearance (or pressure), temperature, mass flow rate, field variables1Gap Co

26、nduction (8/13) Field-variable-dependent gap conductivity.Predefined field variables, are any variables that vary with position and time but are known prior to the current calculation. An example might be a magnetic field or a radiation field in a nuclear facility.The conductivity across the gap can

27、 be specified as dependent on the average value of the field variable across the gap:*GAP CONDUCTANCE, (PRESSURE), DEPENDENCIES=kb, clearance (or pressure), temperature, mass flow rate, field variables2Gap Conduction (9/13) Mass flow rate dependent gap conductivity (Abaqus/Standard only).At a fluid/

28、solid interface can simulate convective heat transfer to the boundary layer between a solid and a moving fluid. The nodes on the surface connected to the convective fluid element have mass flow rates prescribed on them via the *MASS FLOW RATE option.The conductivity across the interface can be speci

29、fied as dependent on the average magnitude of the mass flow rate per unit area on either side of the interface:If one of the interacting surfaces is connected to fluid elements with mass flow rates prescribed and the other is connected to solid diffusion elements, will be half the mass flow rate per

30、 unit area in the fluid.At a solid/fluid interface the clearance between the surfaces is typically zero. 3*GAP CONDUCTANCE, (PRESSURE), DEPENDENCIES=kb, clearance (or pressure), temperature, mass flow rate, field variablesGap Conduction (10/13) Clearance and pressure-dependent gap conductivity.Gap c

31、onductivities may depend on the gap clearance |and/or the pressure transmitted across the gap. Dependency is applicable only tofully coupled thermal stress analysis.In uncoupled heat transfer analysis the clearance is constant and the pressure is zero. The gap conductivity kb may vary with time in a

32、 fully coupled temperature-displacement analysis. This coupling of heat transfer across interfaces to the interface clearance and pressure is often a major reason for needing a fully coupled analysis.At least two pairs of gap conductivity-clearance points must be used to define kb as a function of c

33、learance.4*GAP CONDUCTANCE, (PRESSURE), DEPENDENCIES=kb, clearance (or pressure), temperature, mass flow rate, field variablesGap Conduction (11/13)If conductance is a function of clearance and pressure, account for the case of zero pressure by *SURFACE INTERACTION*GAP CONDUCTANCE k, d, data.*GAP CO

34、NDUCTANCE, PRESSURE k, p, data.where k is the gap conductance, d is the gap clearance, p is the contact pressure, is the average temperature of the two surfaces, and data are any mass flow rate and/or field variable dependencies.When k (d, p), a discontinuity is allowed at the state (d = 0, p = 0);

35、the value of k corresponding to the zero pressure data point is used.With Gap ConductanceNo Gap ConductanceEffects of gap conductance clearly evidentInitial StateGap Conduction (12/13)Example: Frictionless self-contact of a rubber ringRubber ring is compressed by a rigid indenter.Heat transfer due t

36、o clearance-dependent gap conductance.When ring contacts itself, heat is conducted across the interface.Gap Conduction (13/13)Subroutine GAPCON (Abaqus/Standard only)Subroutine GAPCON provides the flexibility needed for detailed specification of thermal interface properties. The interface to GAPCON

37、allows very general dependence of kb:Here kb can be direct function of the individual magnitudes of the temperatures, field variables, and mass flow rates of both surfaces rather than average values across the gap.*GAP CONDUCTANCE, USERGap Radiation (1/6)“Gap radiation” in Abaqus models only radiati

38、ve heat transfer directly between two surfaces that are within close proximity of each other. Thermal radiation occurs across a narrow gap (see figure) where temperature gradients along the surfaces are not large.thickness 0.0side B, qBside A, qAThermal interface with gap radiationGap Radiation (2/6

39、)Heat radiates across the gap in the direction n according to whereq= heat flow by radiation per unit of surface area between surfaces A and B,Ta= absolute temperature of surface a : Ta = qa - q0 ,q0= value of absolute zero on the temperature scale being used, C= radiation constant defined asands =

40、Stefan-Boltzmann constant,eA, eB= surface emissivities, andF = effective viewfactor.These are the inputs to Abaqus!Gap Radiation (3/6)Usage*GAP RADIATION0.8, 0.61.0, 0.00.5, 0.10.0, 0.2viewfactor vs. clearancesurface emissivitiesGap Radiation (4/6)The value of the Stefan-Boltzmann constant and also

41、the value of absolute zero, q0, for the temperature scale in use must be specified. For example, if the Celsius temperature scale is being used:*PHYSICAL CONSTANTS, ABSOLUTE ZERO = -273.16, STEFAN BOLTZMANN = 5.6697E-08Gap Radiation (5/6)This gap radiation model is simplified because we assume that

42、the surfaces are so close together that the only significant radiation flux is directly across the interface.However, in many situations several surfaces are exchanging heat via radiation. This general “cavity radiation” exchange between surfaces depends strongly on the surface geometries and their orientations, in addition to their radiative properties and