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41.1.1 CAVITY RADIATION
Products: Abaqus/Standard Abaqus/CAE
References
• “Defining an analysis,” Section 6.1.2
• “Heat transfer analysis procedures: overview,” Section 6.5.1
• *CAVITY DEFINITION
• *COUPLED THERMAL-ELECTRICAL
• *CYCLIC
• *EMISSIVITY
• *HEAT TRANSFER
• *MOTION
• *PERIODIC
• *PHYSICAL CONSTANTS
• *RADIATION FILE
• *RADIATION PRINT
• *RADIATION OUTPUT
• *RADIATION SYMMETRY
• *RADIATION VIEW FACTOR
• *REFLECTION
• *SURFACE
• *SURFACE PROPERTY
• *VIEW FACTOR OUTPUT
• “Cavity radiation,” Section 2.11.4 of the Abaqus Theory Guide
• “Defining a cavity radiation interaction,” Section 15.13.21 of the Abaqus/CAE User’s Guide, in the HTML version of this guide
• “Defining a cavity radiation interaction property,” Section 15.14.3 of the Abaqus/CAE User’s Guide, in the HTML version of this guide
Overview
Abaqus/Standard provides a cavity radiation capability for modeling heat transfer effects due to radiation in enclosures. This cavity radiation functionality:
• can be included in heat transfer analysis problems without deformation (“Uncoupled heat transfer analysis,” Section 6.5.2, and “Coupled thermal-electrical analysis,” Section 6.7.3);
• is provided for two-dimensional, three-dimensional, and axisymmetric cases;
• accounts for symmetries, surface blocking, and surface motion within cavities; and
• can include closed cavities or open cavities (implying that some radiation takes place to an exterior medium).
Cavity radiation equations are not symmetric; therefore, the nonsymmetric matrix storage and solution scheme is invoked automatically in models that include cavity radiation (see “Cavity radiation,” Section 2.11.4 of the Abaqus Theory Guide, and “Defining an analysis,” Section 6.1.2). Each cavity defines a view factor matrix involving the geometric relations between the surfaces in the enclosure. These matrices may be updated a number of times during the analysis (due to moving surfaces in the cavity). Therefore, large cavity radiation problems may be computationally expensive. Instead, you should consider using:
• gap radiation (see “Thermal contact properties,” Section 37.2.1) for modeling radiation between closely spaced surfaces;
• average-temperature radiation conditions for modeling enclosures that are approximately isothermal, with constant emissivity, and do not require blocking or reflection considerations (see “Thermal loads,” Section 34.4.4); or
• parallel cavity decomposition for parallel calculation of view factors and solution of the radiative heat transfer equations (see “Decomposing large cavities in parallel” below).
Defining a cavity radiation problem
Since cavity radiation effects are calculated only in heat transfer and coupled thermal-electrical procedures, the only kind of thermal-stress analysis that can include these effects is sequentially coupled thermal-stress analysis (see “Sequentially coupled thermal-stress analysis,” Section 16.1.2). Moreover, unless you allow cavity parallel decomposition (see “Decomposing large cavities in parallel” below), there is a software limit of 16,000 nodes and facets in Abaqus/Standard.
Model definition
When you define the model for a cavity radiation problem, you must:
- define all of the surfaces in the cavity (see “Defining surfaces”);
- define the radiation properties of each surface (i.e., the emissivity) and the physical constants (see “Defining surface radiation properties”); and
- construct cavities from the surfaces (see “Constructing a cavity”).
History definition
In the first step of a cavity radiation analysis you must associate with each cavity a radiation view factor definition, which controls the calculation of view factors for the cavity. You then may:
- define cavity symmetries, if any (see “Defining cavity symmetries”);
- prescribe the motion of surfaces (see “Prescribing motion during a cavity radiation analysis”);
- define boundary conditions such as temperature and forced convection (see “Boundary conditions”);
- control the cavity radiation and view factor calculations in each step (the specifications from the previous step are used if they are not redefined in a step; see “Controlling view factor calculation during the analysis”);
- request output of heat transfer variables to the data and results files (see “Requesting surface variable output”); and
- request output of the radiation view factor matrices (see “Writing the view factor matrices to the results file”).
If any of the above are included in your analysis, they must be defined within a heat transfer or coupled thermal-electrical step definition.
Defining surfaces
Cavities are defined in Abaqus/Standard as collections of surfaces, which are composed of facets. In axisymmetric and two-dimensional cases a facet is a side of an element; in three-dimensional cases a facet is a face of a solid element or a surface of a shell element. Rigid surfaces cannot be used in cavity radiation problems.
Surfaces are defined as described in “Element-based surface definition,” Section 2.3.2. You may associate each surface with a surface property definition as part of the surface option, or you may associate surfaces with surface properties as part of the cavity definition option. The surface properties are defined as described below.
| Input File Usage: | Use the following option to define a surface with a surface property for use in a cavity radiation analysis:*SURFACE, TYPE=ELEMENT, NAME=surface_name,PROPERTY=property_nameUse the following option to define a surface for use in a cavity radiation analysis in which surface properties are defined as part of the cavity definition:*SURFACE, TYPE=ELEMENT, NAME=surface_name |
| Abaqus/CAE Usage: | Interaction module: Create Interaction: Cavity radiation:select the initial surface region |
Restrictions
Surfaces that are associated with cavity radiation are subject to the following restrictions in addition to the general surface definition restrictions outlined in “Element-based surface definition,” Section 2.3.2:
• Surfaces cannot overlap because of the ambiguity that would result in the associated property definitions and in the blocking specification.
• A surface can be used only in one cavity definition (the same surface cannot appear in two different cavities).
In addition, the three-dimensional quadrilateral facets should be as close to planar as possible; otherwise, the quality of the view factor calculations will be compromised.
Controlling spurious spatial oscillations
The radiation flux for each facet is calculated based on the average of the nodal temperatures on that facet (see “Cavity radiation,” Section 2.11.4 of the Abaqus Theory Guide). This value of radiation flux is then distributed to each node in proportion to its area. Consequently, the mesh must be sufficiently fine that temperature differences across elements are small. Otherwise, computed fluxes at nodes with temperatures above the facet average will be excessively low, and the fluxes at nodes with below-average temperatures will be too high. This tends to induce a spatially oscillatory solution. This effect can be eliminated by reducing the element size in the vicinity of high temperature gradients.
Defining surface radiation properties
Cavity radiation problems are intrinsically nonlinear, due to the dependence of the radiative flux on the fourth power of the facet temperature. Further, nonlinearity can be introduced by describing the emissivity, , as a function of temperature.
Defining the emissivity
Emissivity is a dimensionless quantity with a value that is greater than or equal to zero and less than or equal to one. A value of corresponds to all radiation being reflected by the surface. A value of corresponds to black body radiation, where all radiation is absorbed by the surface. You can define the emissivity, , of a surface as a function of temperature and other predefined field variables.
You must assign a name to the surface property that defines the emissivity.
| Input File Usage: | Use both of the following options to define the emissivity of a surface:*SURFACE PROPERTY, NAME=property_name*EMISSIVITYThe *EMISSIVITY option must appear directly after the *SURFACE PROPERTY option in the model definition section of the input file.If black body radiation is being defined (ε = 1), the following option can be used in the step definition to improve efficiency:*RADIATION VIEW FACTOR, REFLECTION=NO |
| Abaqus/CAE Usage: | Use the following input to define gray body radiation:Interaction module: Create Interaction Property: Cavity radiation: enter the emissivity (ε)You can define the emissivity as a function of temperature and/or field variables.Use the following input to define black body radiation:Interaction module: Create Interaction: Cavity radiation: Use heat reflection: No |
Controlling the accuracy of temperature-dependent emissivity changes
Abaqus/Standard evaluates the emissivity, , based on the temperature at the start of each increment and uses that emissivity value throughout the increment. When emissivity is a function of temperature or field variables, you can control the time incrementation for the heat transfer or coupled thermal-electrical step by specifying the maximum allowable emissivity change during an increment, \Delta \epsilon _ { m a x } . If this tolerance is exceeded, Abaqus/Standard will cut back the increment size until the maximum change in emissivity is less than the specified value. If you do not specify a value for \Delta \epsilon _ { m a x } , a default value of 0.1 is used.
Input File Usage: Use either of the following options: *HEAT TRANSFER, MXDEM= *COUPLED THERMAL-ELECTRICAL, MXDEM=
Abaqus/CAE Usage: Step module: Create Step: Heat transfer or Coupled thermal-electric: Incrementation: Automatic: Max. allowable emissivity change per increment: \Delta \epsilon _ { m a x }
Defining the Stefan-Boltzmann constant and value of absolute zero
You must define the Stefan-Boltzmann constant, , and the value of absolute zero, \theta ^ { Z } ; there are no default values for these constants.
Input File Usage: *PHYSICAL CONSTANTS, STEFAN BOLTZMANN= , ABSOLUTE ZERO= This option can appear anywhere in the model definition portion of the input file.
Abaqus/CAE Usage: Any module: Model→Edit Attributes→model_name. Enter values for Absolute zero temperature and Stefan-Boltzmann constant
Constructing a cavity
You construct cavities as collections of the surfaces defined as described above. Each surface can be used only in one cavity definition. Each cavity must have a unique name; this name is used to specify view factor calculations. The cavity name can also be used to request output.
Setting surface properties
By default, a cavity is assumed to consist of surfaces for which surface properties have already been defined. Instead, you may define surface properties as part of the cavity definition.
Input File Usage: Use the following option to construct a cavity: *CAVITY DEFINITION, NAME=cavity_name, SET PROPERTY surface name, surface property name By using the SET PROPERTY parameter, you define the surface properties used in the cavity, overriding any property defined as part of the surface option.
Abaqus/CAE Usage: Interaction module: Create Interaction: Cavity radiation: select the surface region. Use the Properties table to add or edit surfaces and cavity radiation interaction properties (emissivity).
Creating a closed cavity
By default, a cavity is assumed to be closed.
Input File Usage: Use the following option to construct a closed cavity:
*CAVITY DEFINITION, NAME=cavity_name
Abaqus/CAE Usage: Interaction module: Create Interaction: Cavity radiation:
Definition: Closed
Creating an open cavity
You can specify an open cavity by defining the reference temperature of the external medium. This ambient temperature value is converted to an absolute temperature scale based on the definition of absolute zero. You can verify the degree of opening in the cavity by specifying a tolerance for the accuracy of the view factor calculations; radiation to the external medium will take place only if the deviation of the sum of the view factors from unity is more than this tolerance. See “Controlling the accuracy of view factor calculations” below for details.
Input File Usage: Use the following option to create an open cavity:
*CAVITY DEFINITION, NAME=cavity_name, AMBIENT TEMP=
Abaqus/CAE Usage: Interaction module: Create Interaction: Cavity radiation: Definition:
Open, Ambient temperature: \theta _ { a m b }
Creating a cavity with multiple openings or complex ambient conditions
The open cavity definition allows for a cavity with a single opening into an ambient environment with a single, constant temperature value. If the cavity has multiple openings or the ambient temperature is not constant, you should model the surroundings differently.
You should close any cavity openings with elements, and prescribe the temperatures of the external media on these elements. Since the cavity is now closed, you should not specify an ambient temperature with the cavity definition. The temperature definition that you use for the closing elements provides the ambient temperature, and it allows you to specify different temperatures, including variable temperatures, at the cavity openings. The elements modeling the external media should not share nodes with the cavity elements (so that conduction will not take place between them). The surfaces defined by the external media elements should have an emissivity of 1.
Decomposing large cavities in parallel
By default, Abaqus/Standard uses a single working thread for the calculation of the view factor matrix and solution of the radiative heat transfer equations (see “Cavity radiation,” Section 2.11.4 of the Abaqus Theory Guide). This method is robust and works well for small cavities composed of hundreds of facets, but it becomes inefficient and computationally expensive for large cavities composed of thousand of
facets. Moreover, the memory requirements for these cavities may be prohibitively large for a single computational node (the view factor matrix is the size of the number of facets squared). In these cases you should consider allowing Abaqus/Standard to decompose the cavity among all CPUs during view factor calculations and solution of the radiative heat transfer equations.
Input File Usage: Use the following option to activate cavity parallel decomposition:
*CAVITY DEFINITION, NAME=cavity_name, PARALLEL
DECOMPOSITION=ON
Abaqus/CAE Usage: Cavity parallel decomposition is not supported in Abaqus/CAE.
Solving radiative heat transfer equations in parallel
Abaqus/Standard uses an iterative solution technique for obtaining the radiative heat fluxes when cavity parallel decomposition is enabled. This technique is based on Krylov methods, employs a preconditioner, and uses only MPI-based parallelization (see “Parallel execution in Abaqus/Standard,” Section 3.5.2 for details). This iterative technique is used only to solve the cavity radiation equations and does not require user intervention. You may still opt to use the either the iterative or direct sparse solvers for the solution of the heat transfer finite element equations.
Convergence of models with decomposed cavities
The exact cavity radiation equations are solved whether parallel decomposition is allowed or not; however, when parallel decomposition is active, Abaqus/Standard may require more iterations to obtain a solution. This slower rate of convergence comes from an approximation to the Jacobian (the linearization of the radiation fluxes) that is based on small changes of the irradiation (any part not due to emission from the surface). Models involving surfaces with low emissivities and steady-state analyses might be especially affected. If you encounter convergence problems with parallel decomposed cavities, you may consider
• changing the analysis from steady-state to transient (“Uncoupled heat transfer analysis,” Section 6.5.2); or
• allowing more solver iterations per time increment (“Convergence criteria for nonlinear problems,” Section 7.2.3).
Kinematic constraints on models with decomposed cavities
Kinematic constraints (for example, coupling constraints, linear constraint equations, multi-point constraints, or surface-based tie constraints) can be applied to any node or surface belonging to a cavity where parallel decomposition is allowed. However, the nodes or surfaces must be the independent (master) nodes or surfaces in the constraint definition.
Defining cavity symmetries
Taking advantage of geometric symmetry can reduce computational model size and simulation time. Instead of modeling all of the parts or components in a symmetric assembly, you can model a smaller repeated component and take symmetry into account in the definition of the cavity radiation interaction.
In Abaqus/Standard cavity definitions with defined symmetries take into account the radiation interactions between each cavity facet and between all of the facets in the cavity and all of its symmetric images. Abaqus/Standard does not check that the model created using cavity symmetries is physically realistic. You must check the input and results carefully to ensure that a valid model is created.
You must assign a name to each radiation symmetry definition for reference by a radiation view factor definition. The radiation view factor definition and corresponding radiation symmetry definition must appear in the same step.
Cyclic, periodic, and/or reflection symmetries can be defined as described below.
Input File Usage: Use all of the following options to define symmetry in a cavity radiation problem:
*RADIATION VIEW FACTOR, SYMMETRY=symmetry_name
*RADIATION SYMMETRY, NAME=symmetry_name
*REFLECTION and/or *PERIODIC and/or *CYCLIC
Abaqus/CAE Usage: Interaction module: Create Interaction: Cavity radiation: Symmetry: Reflection, Periodic, and/or Cyclic
Reflection symmetry
You define reflection symmetry to create a cavity that is composed of the user-defined cavity surface plus its reflected image through a line or plane. You must identify the dimensionality of the cavity when you define reflection symmetry.
Reflection of two-dimensional cavities
You can define the cavity symmetry by reflecting the cavity surface through a line, as shown in Figure 41.1.1–1. This type of reflection can be used only with two-dimensional cavities.
Input File Usage: *REFLECTION, TYPE=LINE
Abaqus/CAE Usage: Interaction module: Create Interaction: Cavity radiation: Symmetry: Reflection: select the symmetry line
Reflection of three-dimensional cavities
You can define the cavity symmetry by reflecting the cavity surface through a plane, as shown in Figure 41.1.1–2. This type of reflection can be used only with three-dimensional cavities.
Input File Usage: *REFLECTION, TYPE=PLANE
Abaqus/CAE Usage: Interaction module: Create Interaction: Cavity radiation: Symmetry: Reflection: select the symmetry plane
Reflection of axisymmetric cavities
You can define the cavity symmetry by reflecting the cavity surface through a line of constant z-coordinate, as shown in Figure 41.1.1–3. This type of reflection can be used only with axisymmetric cavities.
text_image
a Y X b n
Figure 41.1.1–1 Reflection symmetry through a line.
text_image
Z Y X a c b n
Figure 41.1.1–2 Reflection symmetry through a plane.
Input File Usage: *REFLECTION, TYPE=ZCONST
Abaqus/CAE Usage: Interaction module: Create Interaction: Cavity radiation: Symmetry:
Reflection: enter the z-axis symmetry value for the line of symmetry
text_image
z = const symmetry line z r
Figure 41.1.1–3 Reflection symmetry through a line of constant z-coordinate.
Periodic symmetry
You can define cavity symmetry by periodic repetition in a given direction. Physically, periodic symmetry is understood as an infinite number of repetitions of the same image at a periodic interval. Numerically, periodic symmetry has to be represented by a finite number of repetitions of the periodic image. You can define the number of repetitions used in the numerical calculation, n.
The periodic symmetry will result in a cavity composed of the user-defined cavity plus twice n similar images, since the periodic symmetry is assumed to apply in both the positive and negative directions. By default, n=2.
Although symmetries do not increase the size of the view factor matrix, they do make its calculation more expensive. Therefore, the number of repetitions should be minimized, but the value of n should be large enough that the view factor matrix is calculated accurately. Output variable VFTOT can be used to check the amount of closure implied by the symmetry. (See “Controlling the accuracy of view factor calculations” below.) Periodic symmetry for defining the cavity radiation view factor matrix does not impose symmetry conditions automatically in the heat transfer analysis. It may be necessary to impose appropriate constraints on the temperature and loading conditions at the nodes on the periodic symmetry planes to obtain a meaningful solution from the underlying heat transfer analysis.
You must identify the dimensionality of the cavity when you define periodic symmetry.
Periodic symmetry of two-dimensional cavities
You can create a cavity that is composed of a series of similar images generated by repetition along a two-dimensional distance vector, as shown in Figure 41.1.1–4.