Settings for the Surface-to-Surface Radiation Interface

The is used primarily as a scope prefix for variables defined by the physics interface. Refer to such physics interface variables in expressions using the pattern <name>.<variable_name>. In order to distinguish between variables belonging to different physics interfaces, the name string must be unique. Only letters, numbers, and underscores (_) are permitted in the field. The first character must be a letter.

The default (for the first physics interface in the model) is rad.

Define the .

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Keep the default value, , to define a diffuse gray radiation model. In this case, the surface properties (emissivity, radiosity, reflectivity, transmissivity, critical angle) have the same definition for all wavelengths. The surface properties can still depend on other quantities, in particular on the temperature.

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Select to define a diffuse spectral radiation model with two spectral bands, one for short wavelengths, [0, λsol/amb], (solar radiation) and one for large wavelengths, [λsol/amb, +∞[, (ambient radiation). It is then possible to define the (SI unit: m), λsol/amb, to adjust the wavelength intervals corresponding to the solar and ambient radiation. The surface properties can be defined for each spectral band. In particular it is possible to define the solar absorptivity for short wavelengths and the surface emissivity for large wavelengths.

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Select and set the value of the for each spectral band in the table, to define a diffuse spectral radiation model. The value of the must be entered without unit. Modify the to set the unit of all the endpoints. values should be set in an ascending order. The values of the for the next spectral band are updated automatically. It is possible to provide a definition of the surface properties for each spectral band.

	The first Left endpoint and the last Right endpoint are predefined and equal to 0 and +∞, respectively. Parameters can be used to set the value of the Right endpoint.

	The wavelengths λ set in Solar and ambient and Multiple spectral bands are the wavelengths in vacuum.

Modify the to define the refractive index. Vacuum has a refractive index of 1, which is usually a good approximation for air refractive index.

Select the check box to be able to define Radiation Group (Surface-to-Surface Radiation Interface). Radiation groups can be used to speed up the radiation calculations by gathering boundaries that can see one another.

Select the : , (the default), or :

Table 5-4: Surface-to-surface radiation methods
	Direct area integration	hemicube	Ray shooting
Supported dimensions	3D, 2Daxi, 2D, 1D axi,1D	3D, 2Daxi, 2D, 1D axi,1D	3D, 2D, 2Daxi
Shadowing effects		√	√
Diffuse reflection	√	√	√
Specular reflection			√
Refraction			√
Directional properties			√
Wavelength- dependent properties	√ (Solar and ambient / Multiple spectral bands)	√ (Solar and ambient / Multiple spectral bands)	√ (Solar and ambient / Multiple spectral bands)
External radiation source	√	√	√
Symmetry	√	√	√
View factor update control	√	√	√

Hemicube is the default method for the heat transfer interfaces. The more sophisticated and general hemicube method uses a z-buffered projection on the sides of a hemicube (with generalizations to 2D and 1D) to account for shadowing effects. Think of it as rendering digital images of the geometry in five different directions (in 3D; in 2D only three directions are needed), and counting the pixels in each mesh element to evaluate its view factor.

Its accuracy can be influenced by setting the of the virtual snapshots. The number of z-buffer pixels on each side of the 3D hemicube equals the specified resolution squared. Thus the time required to evaluate the irradiation increases quadratically with resolution. In 2D, the number of z-buffer pixels is proportional to the resolution property, and thus the time is, as well.

For an axisymmetric geometry, Gm and Famb must be evaluated in a corresponding 3D geometry obtained by revolving the 2D boundaries about the axis. COMSOL Multiphysics creates this virtual 3D geometry by revolving the 2D boundary mesh into a 3D mesh. The resolution can be controlled in the azimuthal direction by setting the number of , which is the same as the number of elements to a full revolution. Try to balance this number against the mesh resolution in the rz-plane.

COMSOL Multiphysics evaluates the mutual irradiation between surface directly, without considering which face elements are obstructed by others. This means that shadowing effects (that is, surface elements being obstructed in nonconvex cases) are not taken into account. Elements facing away from each other are, however, excluded from the integrals.

Direct area integration is fast and accurate for simple geometries with no shadowing, or where the shadowing can be handled by manually assigning boundaries to different radiation groups.

	If shadowing is ignored, global energy is not conserved. Control the accuracy by specifying a Radiation integration order. Sharp angles and small gaps between surfaces may require a higher integration order for accuracy but also more time to evaluate the irradiation.

The ray shooting algorithm accounts for directional properties in the view factor evaluation. This includes specular reflection and transmission of radiation and also the angular dependence of surface properties. Select this method to enable the Opaque Surface (Surface-to-Surface Radiation Interface) and Semitransparent Surface (Surface-to-Surface Radiation Interface) boundary conditions.

To compute the radiation incident upon surfaces, the ray shooting algorithm uses a backward ray tracing approach, emitting rays from each element outwards, to determine the total irradiation from surrounding elements. For each element, n+1 rays are launched in 2D and n²+1 rays in 3D where n is the value selected for . To determine the direction of these rays, the hemisphere (angular space) is divided into n tiles in 2D and n² in 3D. The trajectories are computed as the rays are absorbed, reflected or transmitted on the model surfaces until their intensity becomes too small or if the rays go far away from the geometry. The threshold where the ray trajectory is no longer computed is controlled by the . On their trajectory, two adjacent rays can hit boundaries belonging to two different features, or detects differences in the radiosity. In such cases, the number of tiles can be locally refined up to a number of times defined by the . This aims to detect irradiation from boundaries that are smaller than the tile size.

Set the (default value is 1000) to define the maximal number of times that a specific ray is allowed to be reflected by a surface. This avoids infinite loops in case of perfectly reflecting surfaces. Using large values improves the view factor accuracy while small ones can be used to limit the view factor evaluation time.

When using directional dependent surface properties, set to define how the selected directional functions are evaluated.

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Select to sample the directional function on a grid with (k+1) points for Polar functions and (k+1)² grid points for Polar and Azimuthal functions. k is the (default value is 100), a strictly positive integer. The evaluation is done using linear interpolation between the sampled values. This option can speed up the view factor evaluation when directional dependent surface properties are used.

To improve the accuracy of the radiation computation the user may increase the (default value is 8), decrease the (default value is 1e-3) or increase the (default value is 3). Conversely changing these values in the opposite direction should decrease computational time. Also, higher values of the under node may improve the results.

For an axisymmetric geometry, Gm and Famb must be evaluated in a corresponding 3D geometry. The number of bounces of the rays in the azimuthal direction can be controlled by setting the (default value is 100).

This section is available by clicking the button (

) and selecting in the dialog box.

Select the check box to verify that the radiation directions are defined in a consistent manner in the model. A warning is issued in the solver when a boundary sees the back of a boundary emitting in the opposite direction. The boundary hit on its back has no radiative properties defined on the side receiving radiation. The following points should be considered when addressing this issue:

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The radiation directions of the boundaries and the opacity of the adjacent domains should be verified together with the variables rad.Fbacksided and rad.Fbacksideu. These variables can be plotted to show the faces that see the opposite side of other boundaries.

may require additional computational resources when using the hemicube algorithm. Once the consistency of the radiation model has been verified, it’s recommended to clear this check box when using hemicube.

Select the check box to store the view factors (mutual and external irradiation) in the model after the next computation. View factors are reused automatically provided the mesh, the selection of the radiating boundaries, the radiation direction, external radiation sources or symmetry conditions are unchanged. However, adding or removing a feature or modifying a feature selection in the always forces to recompute view factors. The view factors are reused for example if only the value of the surface emissivity is changed. When coupled to a interface through a multiphysics coupling, changes for example on temperature, source or flux conditions can be made in the interface without having to recompute the view factors. The view factors are stored in the model file which may induce a noticeable increase in file size. When this check box is cleared and the model is saved, view factors are removed from the model file. View factors are also removed from the model when clearing the mesh and the solution. This option is not compatible with cluster computing.

Define the to control the frequency of view factors computation in time-dependent simulation. This setting is used in models containing a node under , when the feature uses one or more moving symmetry planes or with time-dependent specular surface properties.

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Select to update the view factors at least every Nth time where N is the (SI unit: s). For example, set to 1e-3[s] to enforce the update every millisecond of simulation time.

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Select to define the view factors update threshold manually. The view factors are updated each time the changes by more than the . By default, the tolerance is set to -1 to force the view factor to be recomputed every nonlinear iteration. For example, set to intop1(1) and to 0.15[m], where intop1() is an integration operator over a deforming boundary, to update view factors when the boundary length changes more than 0.15 m compared with the previous view factors calculation.

Select the check box to use the mesh elements as they are defined by the geometry shape functions to compute view factors. This option is designed to improve the accuracy and is expected to be more computationally expensive. When a mesh element is concave with respect to the radiation direction, the self-irradiation is always accounted for when this option is selected. If not selected, the view factors are computed using linearized mesh elements.

This section is available by clicking the button (

) and selecting in the dialog box.

Set the .

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Keep the default value, , to exclude the irradiation contribution to the Jacobian matrix block corresponding to the radiosity degrees of freedom. This option is expected to reduce dramatically the time and the memory required to solve the model.

Provided a converged solution is obtained with both options, the same solution is obtained, within the solver tolerance.

Select (the default), ,, , or to define the discretization level used for the shape function.

When a Fluence Rate Calculation (Surface-to-Surface Radiation Interface) domain condition is present, the fluence rate is stored in each mesh element of the selected domains, at Gauss points corresponding to the selected order. When the fluence rate is evaluated using E0 variable, an interpolation is performed from the values stored at Gauss points. To improve the accuracy of the E0 variable, the user may increase the Gauss points order by changing the value (default is 0). Conversely, changing this value in the opposite direction decreases computational time.