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In the second step the object is translated −3 length units in the y-direction only. This motion places the object at position D with no additional rotation. Finally, in the third step the object is simultaneously translated 5 length units at an angle of 53.13° to the y-direction and rotated clockwise, again at constant angular velocity, through 180° about the z-axis. This motion returns the object to its original position.
Assuming that each step time is 1.0, the input required for the above motion sequence is as follows:
First step:
*MOTION
node set, 1, 1, 4.
*MOTION, ROTATION, TYPE=VELOCITY
node set, 3.14159265, 0., 3., 0., 0., 3., -1.
Second step:
*MOTION
node set, 2, 2, -3.
Third step:
*MOTION
node set, 1, 2, 0.
*MOTION, ROTATION, TYPE=VELOCITY
node set, 3.14159265, 4., 0., 0., 4., 0., -1.
Controlling the time variation of the motion
For any prescribed motion you can refer to an amplitude curve that gives the time variation of the motion throughout a step (see “Amplitude curves,” Section 34.1.2).
Input File Usage: Use both of the following options:
*AMPLITUDE, NAME=amplitude
*MOTION, AMPLITUDE=amplitude
Abaqus/CAE Usage: Surface motion is not supported with cavity radiation in Abaqus/CAE.
Controlling the frequency of view factor recalculation due to motion
You can control how view factors are recalculated during a step as a result of prescribed motion by specifying a value for the maximum allowable motion, max, for a particular node set. View factor recalculation is triggered if a displacement component at any node in the specified node set exceeds the specified value for max.
You must respecify the value of max and the node set in every step where recalculation is required; the values do not remain in effect for subsequent steps.
View factor recalculation can be expensive; use discretion when choosing a value for max.
Input File Usage: *RADIATION VIEW FACTOR, MDISP=max, NSET=nset
The max and nset values must always be specified together.
Abaqus/CAE Usage: View factor recalculation due to motion is not supported with cavity radiation in Abaqus/CAE.
Controlling view factor calculation during the analysis
The cavity radiation capability can be used in applications such as the simulation of manufacturing sequences where radiation view factors change during the simulation. Therefore, radiation view factor definitions provide significant flexibility for the control of view factor calculations during a step.
Multiple radiation view factor definitions can be specified within a step definition if different types of radiation and view factor calculations are required for different cavities. Different types of view factor calculations can be specified for the same cavity in different steps of the analysis.
By default, view factors are calculated at the beginning of the first step that includes a radiation view factor definition. View factors are recalculated at the beginning of a subsequent step only if the view factor definition changes in that step; for example, if different surface blocking checks are specified for the same cavity. In a restart analysis Abaqus/Standard reads the radiation view factors from the userspecified restart step and increment and recalculates the view factors only if the view factor definitions have changed.
You can specify the name of the cavity for which radiation view factor control is being specified. If you do not specify a cavity name, the radiation view factor definition applies to all cavities in the model.
Input File Usage: *RADIATION VIEW FACTOR, CAVITY=cavity_name
Abaqus/CAE Usage: Radiation view factors are defined separately for each cavity radiation interaction and apply to all steps in which that interaction is active.
Activating and deactivating cavity radiation
There are practical situations in which it may be useful to switch cavity radiation effects on and off during the analysis. For example, radiation may be taking place in a cavity that is then filled with a fluid so that radiation is no longer significant; later in the analysis, radiation may resume when the fluid is drained from the cavity. In such cases you can use a radiation view factor definition to switch the radiation on and off in any particular cavity during one or more steps of the analysis.
When cavity radiation is switched back on after having been switched off, Abaqus/Standard will use the last view factors calculated in the last step in which cavity radiation was active. However, if motion is prescribed during the time that the cavity radiation is switched off and one of the displacement components of a node in the specified node set exceeds the value for the maximum allowable motion, max, specified in the step during which cavity radiation is switched off, the view factors will be recalculated at the beginning of the step in which the cavity radiation is switched back on.
Input File Usage: Use the following option to turn view factor calculation off for a step:
*RADIATION VIEW FACTOR, OFF
Use one of the following options to turn view factor calculation back on in a subsequent step:
*RADIATION VIEW FACTOR
*RADIATION VIEW FACTOR, MDISP=max, NSET=nset
Abaqus/CAE Usage: Radiation view factors cannot be turned off or on for a selected step. You can use the following options to turn a cavity radiation interaction off or on:
Interaction module: Interaction Manager: select a step and a cavity radiation interaction, Activate or Deactivate
Controlling the accuracy of view factor calculations
Abaqus/Standard uses a progressive integration scheme for view factor calculation. When facets are sufficiently far from each other, a lumped area approximation is used. If the facets are close to each other but one of the facets is much larger than the other, an infinitesimal-to-finite approximation is used. For all other cases a contour integral is numerically calculated to compute the view factor. See “View factor calculation,” Section 2.11.5 of the Abaqus Theory Guide, for details.
Two nondimensional parameters are calculated for each facet pair to determine which integration scheme is used:
r _ {1} = \frac {d ^ {2}}{A _ {\mathrm{max}}} \qquad \mathrm{and} \qquad r _ {2} = \frac {A _ {\mathrm{max}}}{A _ {\mathrm{min}}},
where A _ { \mathrm { m i n } } is the area of the smaller facet, A _ { \mathrm { m a x } } is the area of the larger facet, and \pmb { d } is the distance between their centroids. The lumped area approximation is used whenever the nondimensional distance square parameter r _ { 1 } > P _ { 1 } , where P _ { 1 } has a default value of 5.0. \mathrm { I f } r _ { 1 } \le P _ { 1 } , an infinitesimal-to-finite area approximation is used if the facet area ratio r _ { 2 } > P _ { 2 } , where P _ { 2 } has a default value of 64.0. Otherwise, a more precise calculation is performed, involving the numerical integration of a contour integral.
You can customize the accuracy and speed of the view factor calculation by specifying the parameters P _ { 1 } and P _ { 2 } and the number of integration points per edge. For example, Abaqus/Standard will used lumped area approximations throughout the whole model if P _ { 1 } is set to zero. Likewise, the more precise, albeit more expensive, numerical integration method will always be used if P _ { 1 } and P _ { 2 } are set to very large numbers.
Input File Usage: \mathrm { * R A D I A T I O N ~ V I E W ~ F A C T O R } , \mathrm { L U M P E D ~ A R E A } { = } P I , \mathrm { I N F I N I T E S I M A L } = P 2 , \mathrm { I N T E G R A T I O N } = i n t e g r a t i o n p o i n t s p e r e d g e
Abaqus/CAE Usage: Interaction module: Create Interaction: Cavity radiation: View factors: enter new values or accept the defaults for Infinitesimal facet area ratio, Gauss integration points per edge, and Lumped area distance-square value
View factor calculation checks for closed cavities
You can provide a tolerance on the accuracy of the view factor calculation. In a closed cavity the sum of the view factors for each cavity facet should be one. Abaqus/Standard compares the value of the specified tolerance to the largest view factor matrix row sum deviation from unity; that is, _ j ( | \sum _ { i } F _ { i j } - 1 | ) . If the tolerance is violated for a closed cavity, the analysis is terminated. The default view factor tolerance is 0.05. Failure to meet this criterion may indicate a need for mesh refinement.
Input File Usage: * \mathrm { R A D I A T I O N ~ V I E W ~ F A C T O R } , \mathrm { V T O L } { = } t o l e r a n c e
Abaqus/CAE Usage: Interaction module: Create interaction: Cavity radiation: View factors: Accuracy tolerance: tolerance
View factor calculations in cavities with symmetries
The view factor calculations account for the closure of a cavity implied by any cavity symmetries. For cavities without periodic or cyclic symmetries the view factors are calculated exactly for two-dimensional geometries, but approximations are made for axisymmetric and three-dimensional geometries. These approximations become less accurate as the distance between surfaces decreases. Define heat radiation to model closely spaced surfaces (see “Thermal contact properties,” Section 37.2.1).
View factor calculations in open cavities
If the sum of the view factors for facets in an open cavity (defined by specifying a value for the ambient temperature) deviates from unity by more than the specified view factor tolerance, radiation to the ambience will take place. In nearly closed cavities this deviation may be small. If the tolerance is not violated, radiation to the external medium is not included even though the cavity is defined to be open; a warning message is issued to this effect. You can reduce the view factor tolerance to include such radiation.
Controlling checks for surface blocking
Heat is transferred between surfaces that have unobstructed direct views of each other (see Figure 41.1.1–14); “blocking” may occur in geometrically complex cavities.
Surface blocking checks may be computationally expensive in cavities with many surfaces; therefore, significant computational time may be saved by specifying which surfaces are potential blocking surfaces, as described below.
View factor calculations with blocking surfaces are especially sensitive to mesh refinement. If a mesh is too coarse, the view factors may not add up to one (in a closed cavity). To obtain accurate results, the mesh should be refined until the view factors can be summed accurately.
Full blocking checks
By default, Abaqus/Standard will check for blocking of every surface with itself and all other surfaces.
Input File Usage: *RADIATION VIEW FACTOR, BLOCKING=ALL
Abaqus/CAE Usage: Interaction module: Create interaction: Cavity radiation:
Properties: Blocking surface checks: All
Partial blocking checks
You can specify a list of the potential blocking surfaces in the cavity.
Input File Usage: *RADIATION VIEW FACTOR, BLOCKING=PARTIAL
Abaqus/CAE Usage: Interaction module: Create interaction: Cavity radiation: Properties: Blocking surface checks: Partial
natural_image
Simple geometric diagram showing an oval inside a rectangle (no text or symbols)
Cavity with no blocking
natural_image
Simple abstract shape with a white outline on a gray background (no text or symbols)
Example of partial blocking
natural_image
Simple geometric diagram with three vertical bars inside an oval, no text or symbols present
Another example of partial blocking
Figure 41.1.1–14 Illustrations of blocking.
No blocking checks
You can indicate that there are no blocking surfaces in the cavity; in this case Abaqus omits all checks for blocking.
Input File Usage: *RADIATION VIEW FACTOR, BLOCKING=NO
Abaqus/CAE Usage: Interaction module: Create interaction: Cavity radiation: Properties: Blocking surface checks: None
Reducing computations for surfaces that are far apart
In cases where there are many surfaces in the cavity, surfaces separated by more than a certain distance may not be able to “see” each other for the purposes of radiation because of blocking by other surfaces. You can specify the distance beyond which view factors need not be calculated, which reduces the computational effort required for the view factor calculations.
Input File Usage: *RADIATION VIEW FACTOR, RANGE=distance
Abaqus/CAE Usage: Interaction module: Create interaction: Cavity radiation: View factors: toggle on Specify blocking range: distance
Memory usage in cavity radiation analyses
The cavity radiation heat transfer between facets of a surface in Abaqus is modeled using a full, unsymmetric matrix defining interactions between each node and all others in the cavity. For surfaces
with large numbers of nodes this matrix may be large, resulting in memory requirements that are significantly larger than those for the finite element portion of the analysis without the cavity radiation interaction.
To minimize memory requirements and computational cost for cavity radiation heat transfer analysis, the cavity can be defined using a coarser mesh of heat transfer shell elements having a single degree of freedom per node. The overlaid element should have minimal heat capacity and conduction, and it should be used for the definition of the cavity in place of the physical, multiple-degree-of-freedom shell. The overlaid element should be used to define the master surface in a tied coupling constraint (“Mesh tie constraints,” Section 35.3.1); the multiple-degree-of-freedom, physical, heat transfer shell element forms the slave surface.
Initial conditions
By default, the initial temperature of all nodes is zero. You can specify nonzero initial temperatures in a cavity radiation analysis; see “Defining initial temperatures” in “Initial conditions in Abaqus/Standard and Abaqus/Explicit,” Section 34.2.1.
In a heat transfer analysis involving forced convection through the mesh, you can define nonzero initial mass flow rates at the nodes of the forced convection/diffusion heat transfer elements in the model (see “Uncoupled heat transfer analysis,” Section 6.5.2).
Boundary conditions
You can specify boundary conditions to prescribe temperatures (degree of freedom 11) at the nodes (see “Boundary conditions in Abaqus/Standard and Abaqus/Explicit,” Section 34.3.1). Shell elements have additional temperature degrees of freedom 12, 13, etc. through the thickness (see “Conventions,” Section 1.2.2). Boundary conditions can be specified as functions of time by referring to amplitude curves (“Amplitude curves,” Section 34.1.2).
For purely diffusive elements, a boundary without any prescribed boundary conditions (natural boundary condition) corresponds to an insulated surface. For forced convection/diffusion elements, only the flux associated with conduction is zero; energy is free to convect across an unloaded surface. This natural boundary condition correctly models areas where fluid is crossing a surface (as, for example, at the upstream and downstream boundaries of the mesh) and prevents spurious reflections of energy back into the mesh.
Loads
The following types of loading can be prescribed in addition to the cavity radiation, as described in “Thermal loads,” Section 34.4.4:
• Concentrated heat fluxes
• Body fluxes and distributed surface fluxes
• Convective film conditions and radiation conditions
Predefined fields
You cannot specify temperatures as field variables in heat transfer or coupled thermal-electrical analyses. Boundary conditions should be used instead, as described above.
You can specify values of other user-defined field variables during the analysis. These values will affect field-variable-dependent material properties, if any. See “Predefined fields,” Section 34.6.1.
Material options
You must define the radiation properties of the surfaces as described above in “Defining surface radiation properties.” Other thermal properties such as conductivity, density, specific heat, and latent heat are defined as in uncoupled heat transfer analysis—see “Uncoupled heat transfer analysis,” Section 6.5.2, and “Thermal properties: overview,” Section 26.2.1.
You can specify internal heat generation—see “Internal heat generation” in “Uncoupled heat transfer analysis,” Section 6.5.2.
Thermal expansion coefficients are not meaningful in cavity radiation heat transfer analysis since deformation of the structure is not considered.
Elements
Any of the heat transfer or coupled thermal-electrical elements in Abaqus/Standard can be used in a cavity radiation analysis, including forced convection/diffusion heat transfer elements (see “Choosing the appropriate element for an analysis type,” Section 27.1.3; “Uncoupled heat transfer analysis,” Section 6.5.2; and “Coupled thermal-electrical analysis,” Section 6.7.3). Coupled temperature-displacement and coupled thermal-electrical-structural elements cannot be used in a cavity radiation analysis.
In addition to the elements that you define, Abaqus/Standard uses internal elements that are generated automatically from your definition of radiation cavities.
Output
The following output variables are available for cavity radiation:
Surface variables
| RADFL | Radiation flux per unit area. This variable does include heat flux to ambient in an open cavity. |
| RADFLA | Radiation flux over a facet. |
| RADTL | Time integrated radiation per unit area. |
| RADTLA | Time integrated radiation over a facet. |
| VFTOT | Total view factor for a facet (sum of the view factor values in the row of the view factor matrix corresponding to the facet). |
| FTEMP | Facet temperature. |
All of the output variables are listed in “Abaqus/Standard output variable identifiers,” Section 4.2.1. Abaqus/CAE supports motion display and can display surface- and element-based results.
Writing the view factor matrices to the results file
You can write the view factor matrices for cavity radiation interactions in heat transfer or coupled thermalelectrical analyses to the results (.fil) file if parallel decomposition for the cavity is not enabled.. The entire radiation view factor matrix is written for each cavity radiation element in the specified cavity.
You can control the frequency of view factor matrix output by specifying the required output frequency in increments. The default output frequency is 1. Specify an output frequency of 0 to suppress output. The output will always be written at the last increment of each step unless you specify an output frequency of 0.
The record formats for the results file are described in “Results file output format,” Section 5.1.2. The file can be written in binary or ASCII format (see “Controlling the format of the results file in Abaqus/Standard” in “Output,” Section 4.1.1).
Input File Usage: *VIEW FACTOR OUTPUT, CAVITY=cavity_name, FREQUENCY=n
Abaqus/CAE Usage: View factor output is not supported in Abaqus/CAE.
Requesting surface variable output
For the cavity radiation interaction, you can request cavity-, element-, or surface-based radiation output such as radiation fluxes, view factor totals for a facet, and facet temperatures to the data, results, and/or output database files. The output requests can be repeated as often as necessary to request output for different variables, different cavities, different surfaces, different element sets, etc. The surface variables that can be requested are listed above.
You can specify the particular cavity, element set, or surface for which output is being requested. If you do not specify a cavity, element set, or surface, output will be provided for all cavities in the model. The same cavity, element set, or surface can appear in several radiation output requests.
By default, no cavity radiation data output will be provided. If you define a radiation output request without specifying the desired output variables, all six cavity radiation surface variables will be output.
You can control the frequency of radiation output by specifying the required output frequency in increments. The default output frequency is 1. Specify an output frequency of 0 to suppress output. The output will always be written at the last increment of each step unless you specify an output frequency of 0.
Input File Usage: Use one of the following options to obtain output in the data file:
*RADIATION PRINT, CAVITY=cavity_name, FREQUENCY=n
*RADIATION PRINT, ELSET=element_set, FREQUENCY=n
*RADIATION PRINT, SURFACE=surface_name, FREQUENCY=n
Use one of the following options to obtain output in the results file:
*RADIATION FILE, CAVITY=cavity_name, FREQUENCY=n
*RADIATION FILE, ELSET=element_set, FREQUENCY=n
*RADIATION FILE, SURFACE=surface_name, FREQUENCY=n
Use the first option and one of the subsequent options to obtain output in the output database:
*OUTPUT, FREQUENCY=n *RADIATION OUTPUT, CAVITY=cavity_name *RADIATION OUTPUT, ELSET=element_set *RADIATION OUTPUT, SURFACE=surface_name
Abaqus/CAE Usage: Cavity radiation output to the data file and the results file are not supported in Abaqus/CAE.
Use the following options to obtain output in the output database:
Step module: history output request editor: Thermal: select the output variables
Printed output
The output tables generated by a radiation output request to the data file are organized on a surface-bysurface basis. The rows that will appear in a particular table are defined by choosing a cavity, surface, or element set: each row of a table corresponds to an individual element face that is part of the cavity, surface, or element set chosen. If all of the variables in a row of a table are zero, the row is not printed.
The first column of each table is the element number, and the second column is the element face identifier. You choose the variables to appear in the remaining columns. There is no limit to the number of tables that can be defined.
As an example, consider a heat transfer model containing a cavity named CAV1, which, in turn, is composed of surfaces SURF1 and SURF2. If you request output of radiation flux (RADFL) and facet temperature (FTEMP) to the data file for this model, two tables will appear in the data file. One table will contain RADFL and FTEMP output for all element faces composing surface SURF1, and the other table will contain the same output variables for all element faces making up surface SURF2.
By default, Abaqus/Standard writes a summary of the maximum and minimum values in each column of the table. You can choose to suppress this summary. In addition, you can choose to print the total of each column in the table, which is useful, for example, to sum radiation fluxes over all facets composing a radiation surface. By default, these totals are not printed.
Input File Usage: Use the following option to control output of the summary information to the data file:
*RADIATION PRINT, SUMMARY=YES or NO Use the following option to control output of the totals to the data file: *RADIATION PRINT, TOTALS=YES or NO
Abaqus/CAE Usage: Cavity radiation output to the data file is not supported in Abaqus/CAE.
Input file template
The following template shows the options required for a transient, cavity radiation analysis of a closed two-dimensional symmetric cavity. All surfaces within the cavity topcav have the same emissivity. The surface surf2 moves (translation only) during the analysis. In the second step surface surf2 stops
moving, cavity radiation is turned off, all thermal loads except the surface convection are removed, and a steady-state heat transfer analysis is conducted to determine the final temperature of the system.
*HEADING
...
*PHYSICAL CONSTANTS, ABSOLUTE ZERO= \theta^{Z} , STEFAN BOLTZMANN= \sigma *SURFACE, NAME=surf1, PROPERTY=surfp
elset1, S1
elset2, S2
*SURFACE, NAME=surf2, PROPERTY=surfp
elset3,
*SURFACE PROPERTY, NAME=surfp
*EMISSIVITY
Data lines to define the emissivity of the surfaces in the model
*CAVITY DEFINITION, NAME=topcav
surf1, surf2
*INITIAL CONDITIONS, TYPE=TEMPERATURE
Data lines to prescribe initial temperatures at the nodes
*AMPLITUDE, NAME=motion
Data lines to define amplitude curve to be used for motion of surface surf2
*AMPLITUDE, NAME=film
Data lines to define amplitude curve to be used for the convection film coefficient, h
** Step 1
*STEP
*HEAT TRANSFER, MXDEM= \Delta\epsilon_{max} , DELTMX= \Delta\theta_{max} Data line to define incrementation
*RADIATION VIEW FACTOR, CAVITY=topcav, VTOL=tol, SYMMETRY=outer,
NSET=nset, MDISP=max
*RADIATION SYMMETRY, NAME=outer
*REFLECTION, TYPE=LINE
Data line to define line of symmetry
*MOTION, TRANSLATION, TYPE=DISPLACEMENT, AMPLITUDE=motion
Data line to define motion of nodes on surface surf2
*CFLUX and/or *DFLUX
Data lines to define concentrated and/or distributed fluxes
*BOUNDARY
Data lines to prescribe temperatures at selected nodes
*FILM, FILM AMPLITUDE=film
Data lines to define surface convection
**
*RADIATION PRINT, CAVITY=topcav, SUMMARY=YES, TOTALS=YES