RADIATION_SURFACE

Specifies radiative boundary conditions for the enclosure, p1_model and discrete_ordinate radiation models.

For the enclosure model, a radiation heat flux condition is applied to the surface. For the p1_model the condition specifies the emissivity of the surface used by the Marshak boundary condition. For the discrete_ordinate model, the condition specifies surface properties, such as emissivity and diffuse fraction. The emissivity is used to account for radiation emission from the surface. For example, $ε σ T_{w}^{4} / π$ , where $ε$ is the emissivity, $σ$ is Stefan-Boltzmann constant, and $T_{w}$ is the wall temperature.

Type

AcuSolve Command

Syntax

RADIATION_SURFACE("name") {parameters...}

Qualifier

User-given name.

Parameters

shape (enumerated) [no default]

Shape of the surfaces in this set.

three_node_triangle or tri3: Three-node triangle.
four_node_quad or quad4: Four-node quadrilateral
six_node_triangle or tri6: Six-node triangle.

element_set or elem_set (string) [no default]

User-given name of the parent element set.

surfaces (array) [no default]

List of element surfaces.

surface_sets (list) [={}]

List of surface set names (strings) to use in this command. When using this option, the connectivity, shape, and parent element of the surfaces are provided by the surface set container and it is unnecessary to specify the shape, element_set and surfaces parameters directly to the RADIATION_SURFACE command. This option is used in place of directly specifying these parameters. In the event that both of the surface_sets and surfaces parameters are provided, the full collection of surface elements is read and a warning message is issued. The surface_sets option is the preferred method to specify the surface elements. This option provides support for mixed element topologies and simplifies pre-processing and post-processing.

type (enumerated) [=wall]

Type of the boundary surface. For the enclosure and p1_model radiation models, the type can be either wall or opening. For the discrete_ordinate radiation model the type can be wall, opening or radiation_interface.

auto: Automatic radiation surface treatment to determine whether a surface is treated as type = wall or type = opening. Used with all radiation models.
wall: Wall. Requires an emissivity_model for all radiation models and agglomeration for enclosure.
opening: Opening. Requires emissivity_model and opening_temperature.
radiation_interface: Radiation_interface. Enables the transmission and reflection of radiative intensity at an interface between two participating media. Available when radiation = discrete_ordinates.

radiation_interface_type (enumerated) [=internal]

The type of radiation_interface is specified through radiation_interface_type. The parameter has two values: internal and external. If radiation_interface_type = internal, there must be a participating media on each side of an interface, that is, the material for each adjacent ELEMENT_SET has a radiation_model. For this condition, the transfer of radiative intensity is both transmitted and reflected at the interface. If radiation_interface_type = external, there is a participating media on one side of an interface. The radiative intensity in the medium surrounding the model is calculated using the mathematical model. The external radiation interface is used with external_emissivity_model and external_temperature. The radiation_interface_type requires radiation_interface.

external_emissivity_model (string) [=none]

User-given name of the external emissivity model of an exterior facing surface if radiation_interface_type = external.

external_temperature (real)>=0 [= 273.15]

Defines the temperature of the fluid surrounding the domain if radiation_interface_type = external.

external_temperature_multiplier_function (string) [=none]

User-given name of the multiplier function for scaling the external temperature. If none, no scaling is performed.

specular_ordinate_averaging (enumerated) [=one_ordinate]

The specular ordinate averaging parameter is used to determine the direction of the specular ordinate. Two averging methods are available: one_ordinate and three_ordinates. If specular_ordinate_averaging = one_ordinate, this method is to search for the closest specular ordinate direction, if specular_ordinate_averaging = three_ordinates, the specular ordinate direction is calculated by averaging the three closest ordinate directions. This parameter is used for specular interfaces when the diffusion fraction is less than 1.0. Requires radiation_interface. Available when radiation = discrete_ordinates.

emissivity_model (string) [no default]

User-given name of the emissivity model. Used with wall and opening types.

opening_temperature or temp (real) >=0 [=273.15]

Opening temperature. Used with opening type.

opening_temperature_multiplier_function (string) [=none]

User-given name of the multiplier function for scaling the opening temperature. If none, no scaling is performed. Used with opening type.

agglomeration (boolean) [=on]

Flag specifying whether to agglomerate the surface elements. Used with wall type. A value of on requires max_agglomeration_surfaces, max_agglomeration_angle and max_agglomeration_radius.

max_agglomeration_surfaces (integer) >=0 [=25]

Maximum number of surfaces in one agglomeration. Used with on agglomeration. If zero, this option is ignored.

max_agglomeration_angle or angle (real) >=0 <=180 [=10]

Maximum angle between surfaces allowed in any agglomeration. Used with on agglomeration.

max_agglomeration_radius or radius (real) >=0 [=0.25]

Maximum radius of agglomeration. Used with on agglomeration. If zero, this option is ignored.

integrated_output_frequency or intg_freq (integer) >=0 [=1]

Time step frequency at which to output the integrated radiation heat flux. If zero, this option is ignored.

integrated_output_time_interval or intg_intv (real) >=0 [=0]

Time frequency at which to output the integrated radiation heat flux. If zero, this option is ignored.

nodal_output_frequency or nodal_freq (integer) >=0 [=0]

Time step frequency at which to output radiation heat flux at the nodes of the surface. If zero, this option is ignored.

nodal_output_time_interval or nodal_intv (real) >=0 [=0]

Time frequency at which to output radiation heat flux at the nodes of the surface. If zero, this option is ignored.

diffused_fraction (real) [=1.0]

Diffused fraction defines the proportion of reflected radiation intensity at a surface that is diffused.

Description

This command specifies a radiation heat flux condition on a set of surfaces (element faces). This condition is coupled to all other radiation surfaces. The RADIATION command provides a detailed description of this coupling.

The surfaces of a radiation surface are defined with respect to the elements of an element set. For example,

ELEMENT_SET( "interior" ) {
    shape                        = four_node_tet
    elements                     = { 1, 8, 3, 4, 9 ;
                                     3, 3, 4, 9, 5 ;
                                     ... }
    ...
}
RADIATION_SURFACE( "wall" ) {
    type                         = wall
    shape                        = three_node_triangle
    element_set                  = "interior"
    surfaces                     = { 1, 12, 9, 3, 4 ;
                                     3, 52, 5, 3, 4 ; }
    emissivity_model             = "emissivity"
    integrated_output_frequency  = 2
}

specifies a radiation heat flux condition to be applied to two surfaces of the element set "interior" using the emissivity model "emissivity", and the integral of the radiation heat flux is to be output every two steps.

There are two main forms of this command. The legacy version (or single topology version) of the command relies on the use of the surfaces parameter to define the surfaces. When using this form of the command, all surfaces within a given set must have the same shape, and it is necessary to include both the element_set and shape parameters in the command. shape specifies the shape of the surface. This shape must be compatible with the shape of the "parent" element set whose user-given name is provided by element_set. The element set shape is specified by the shape parameter of the ELEMENT_SET command. The compatible shapes are:

Element Shape: Surface Shape
four_node_tet: three_node_triangle
five_node_pyramid: three_node_triangle
five_node_pyramid: four_node_quad
six_node_wedge: three_node_triangle
six_node_wedge: four_node_quad
eight_node_brick: four_node_quad
ten_node_tet: six_node_triangle

The surfaces parameter contains the faces of the element set. This parameter is a multi-column array. The number of columns depends on the shape of the surface. For three_node_triangle, this parameter has five columns, corresponding to the element number, of the parent element set, a unique, within this set surface number, and the three nodes of the element face. For four_node_quad, surfaces has six columns, corresponding to the element number, a surface number, and the four nodes of the element face. For six_node_triangle, surfaces has eight columns, corresponding to the element number, a surface number, and the six nodes of the element face. One row per surface must be given. The three, four, or six nodes of the surface may be in any arbitrary order, since they are reordered internally based on the parent element definition.

The surfaces may be read from a file. For the above example, the surfaces may be placed in a file, such as wall.srf:

1 12 9 3 4
3 52 5 3 4

and read by:

RADIATION_SURFACE ( "no-slip wall" ) {
    shape        = three_node_triangle
    element_set  = "interior"
    surfaces     = Read( "wall.srf" )
    ...
}

The mixed topology form of the RADIATION_SURFACE command provides a more powerful and flexible mechanism for defining the surfaces. Using this form of the command, it is possible to define a collection of surfaces that contains different element shapes. This is accomplished through the use of the surface_sets parameter. The element faces are first created in the input file using the SURFACE_SET command, and are then referred to by the RADIATION_SURFACE command. For example, a collection of triangular and quadrilateral element faces can be defined using the following SURFACE_SET commands.

SURFACE_SET( "tri faces" ) {
   surfaces       = { 1, 1, 1, 2, 4 ;
                      2, 2, 3, 4, 6 ;
                      3, 3, 5, 6, 8 ; }
   shape          = three_node_triangle
   volume_set     = "tetrahedra"
}
SURFACE_SET( "quad faces" ) {
   surfaces       = { 1, 1, 1, 2, 4, 9 ;
                      2, 2, 3, 4, 6, 12 ;
                      3, 3, 5, 6, 8, 15 ; }
   shape          = four_node_quad
   volume_set     = "prisms"

Then, a single RADIATION_SURFACE command is defined that contains the tri and quad faces as follows:

RADIATION_SURFACE ( "no-slip wall" ) {
    surface_sets       = {"tri_faces", "quad_faces"}
    ...
}

The list of surface sets can also be placed in a file, such as surface_sets.srfst:

tri faces
quad faces

and read using:

RADIATION_SURFACE ( "no-slip wall" ) { 
   surface_sets       = Read("surface_sets.srfst")
   ...
}

The mixed topology version of the RADIATION_SURFACE command is preferred. This version provides support for multiple element topologies within a single instance of the command and simplifies pre-processing and post-processing. In the event that both the surface_sets and surfaces parameters are provided in the same instance of the command, the full collection of surface elements is read and a warning message is issued. Although the single and mixed topology formats of the commands can be combined, it is strongly recommended that they are not.

For the enclosure model, all data from all RADIATION_SURFACE commands are pre-processed to form view factors. Since it is usually too expensive to store and process radiation heat transfer between a pair of each element faces, the surface data are "agglomerated" to reduce the number of view factors. Several parameters are provided to help control the agglomeration. For example,

RADIATION_SURFACE( "wall" ) {
    ...
    type                        = wall
    emissivity_model            = "emissivity"
    agglomeration               = on
    max_agglomeration_surfaces  = 100
    max_agglomeration_angle     = 20
    max_agglomeration_radius    = 0.5
    diffused_fraction           = 0.9
}

specifies that each agglomeration contains no more than 100 surfaces, the angles between the outward normals of these surfaces are no more than 20 degrees, and the radius of the agglomerated surface no greater than 50 percent of the radius of the entire surface set. In addition to these constraints, each agglomeration must contain only one emissivity model. Several parameters must be the same across all radiation surfaces; these are given in the RADIATION command. When accuracy is more important than the cost of computing the view factors, for example, a small, hot surface, agglomeration should be set to off. In this case the radiation heat flux will be computed for each element face in the set.

The opening type provides a method of fully enclosing a fluid domain that is not be completely surrounded by walls. This type is appropriate for inlets, outlets, and surfaces that approximate infinity in external flows. The primary assumption is that the surface is at a single given temperature of opening_temperature. This assumption allows the entire set to be combined into one agglomerated facet, so agglomeration and associated parameters are ignored. An opening is typically modeled as a black body, with an emissivity of one. However, other emissivity models may be used with an opening.

The opening_temperature_multiplier_function parameter may be used to scale the opening temperature. For example,

RADIATION_SURFACE( "inlet" ) {
    ...
    type                                    = opening
    emissivity_model                        = "black body"
    opening_temperature                     = 1
    opening_temperature_multiplier_function = "inlet temperature"
}
MULTIPLIER_FUNCTION( "inlet temperature" ) {
    type                                    = cubic_spline
    curve_fit_values                        = { 0, 295 ;
                                               12, 312 ;
                                               24, 320 ; }
    curve_fit_variable                      = time
}
EMISSIVITY_MODEL( "black body" ) {
    type                                    = constant
    emissivity                              = 1
}

If either integrated_output_frequency or integrated_output_time_interval is non-zero, the surface integral of the radiation heat flux will be output at the end of the run. If both are zero, no integrated radiation heat flux data is written to disk.

Similarly, if either nodal_output_frequency or nodal_output_time_interval is non-zero, the nodal values of the radiation heat flux will be output at the end of the run. If both are zero, no nodal radiation heat flux data is written to disk.

Run times may not coincide with integrated_output_time_interval or nodal_output_time_interval. In these cases, the corresponding data are output for every time step which passes through a multiple of output_time_interval or nodal_output_time_interval.

Once the surface quantities have been written to disk, they can be translated to other formats using the AcuTrans program and other post-processing modules; see the AcuSolve Programs Reference Manual for details.

For the discete_ordinate radiation model, exchange of radiative intensity occurs at the interface between participating media. For this case the RADIATION_SURFACE type is set to radiation_interface and the radiation_interface_type can be either internal or external. For the internal radiation_interface_type, the condition is applied between two participating media (two media both with a MATERIAL_RADIATION_MODEL). For the external radiation_interface_type, the RADIATION_SURFACE is applied to the boundary of a semi-transparent media (has a MATERIAL_RADIATION_MODEL) and models radiative exchange with the surrounding environment. The exchange of radiative intensity depends on the diffused_fraction of the interface and the refractive indices of the media. The different scenarios are described below.