CFX Mod Radiation
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Page 263ANSYS CFX-Solver, Release 10.0: Modelling
Radiation Modelling
The topics in this section include:
• Introduction (p. 263 in "ANSYS CFX-Solver, Release 10.0: Modelling")
• Rosseland Model (p. 266 in "ANSYS CFX-Solver, Release 10.0: Modelling")
• The P1 Model (p. 267 in "ANSYS CFX-Solver, Release 10.0: Modelling")
• The Discrete Transfer Model (p. 268 in "ANSYS CFX-Solver, Release 10.0: Modelling")
• The Monte Carlo Model (p. 269 in "ANSYS CFX-Solver, Release 10.0: Modelling")
• General Radiation Considerations (p. 270 in "ANSYS CFX-Solver, Release 10.0: Modelling")
Introduction
ANSYS CFX includes several radiation modelling options: The Rosseland model (or Diffusion
Approximation model), the P-1 model (also known as the Gibb’s model or Spherical
Harmonics model), the Discrete Transfer model and the Monte Carlo model.
Many fluid flows of practical interest occur in situations where the fluid and/or the enclosing
boundaries are hot. In such situations, the effect of radiant heat transfer may become
important. A typical environment where radiation plays a significant role is a furnace or
other such combustion chamber.
Two limits can be identified in the way that radiation interacts with a fluid or solid medium.
One extreme is the situation where the medium is transparent to radiation at wavelengths
in which the majority of the heat transfer occurs. In this case, the radiation only affects the
medium by heating or cooling the surfaces of the domain, with no radiant energy transfer
directly to the medium. Only the Monte Carlo model should be used for this limiting case.
The Discrete Transfer model has also been used in this limit, but with limited success.
The opposite extreme is the situation in which the medium is optically dense, and radiation
interacts with the medium throughout the interior of the domain, as well as at surfaces. If
the medium is optically dense, radiant energy is either scattered, or absorbed and
re-emitted in all directions with a small length scale compared to the size of the domain. This
situation is known as the “diffusion limit”, since radiant intensity is independent of direction
(Note that there is no assumption that the radiation is “diffuse”, in the sense of “rarefied”.) In
this limit, the Rosseland and P1 models are an attractive alternative to the Discrete Transfer
and Monte Carlo models because of their simplicity.
Radiation Modelling: Introduction
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For general cases, ranging from optically thin (transparent) to optically thick (diffusion)
regions, like combustion, the Discrete Transfer and the Monte Carlo models more accurately
represent the solution of the radiative transfer equation.
The Thermal Radiation Model can be selected from the Fluids/Solids Models form in the
Domains panel whenever a heat transfer model has been set to Thermal Energy or Total
Energy. The default for the Thermal Radiation Model is None.
Once a thermal radiation model has been selected, two additional submodels must also be
chosen: the spectral model and the scattering model.
• For details, see Spectral Model (p. 273 in "ANSYS CFX-Solver, Release 10.0: Modelling").
• For details, see Scattering Model (p. 275 in "ANSYS CFX-Solver, Release 10.0: Modelling").
The radiation modelling options in ANSYS CFX allow you to:
• Setup a gray/non-gray media enclosed by opaque diffuse surfaces, except at openings (inlets, outlets and openings), which are considered fully transparent. Symmetry planes and periodic boundaries are treated as specular surfaces when using the Discrete Transfer or Monte Carlo models.
• Select any of the thermal radiation models in any fluid domain1. For solid domains, only the Monte Carlo option is available.
• Set up spectral dependent radiation quantities (material properties, radiation sources, directions, surface properties) via CEL expressions by using any of the available spectral variables: frequency, wavelength in vacuum, or wavenumber in vacuum.
• Setting of boundary conditions at walls, domain interfaces, and open boundaries: inlets, outlets and openings
Comparison of the Radiation Models
In problems where thermal radiation is significant, the proper choice of the thermal
radiation will affect not only the quality of the solution, but also the computational time it
requires. Detailed thermal radiation calculations are time consuming, so proper selection
must be made from physical considerations.
For problems in the diffusion or thick limit (t > 5), all the modelling options will produce
nearly the same results. Then, the best alternative is a balance between Rosseland and P1
models. As the optical thickness decreases and approaches 1, the P1 model becomes the
least expensive alternative. Finally, in the thin limit and for purely transparent cases only the
Monte Carlo and Discrete Transfer model should be used. For details, see Optical Thickness
(p. 230 in "ANSYS CFX-Solver, Release 10.0: Theory").
For gray models, where the radiation field is expected to be reasonably homogeneous
everywhere (at least on a local basis), and high spatial resolution is required, the discrete
transfer method is much more efficient and provides very accurate results if sufficient
angular resolution is used.
A major advantage of the discrete transfer method is its fixed sampling in situations where
the same mesh is to be used again and again, as in the case of a combined flow-radiation
calculation for modelling a combustion chamber. In this case the ray paths can be calculated
1. As long as radiation does not travel through the solid separating two fluid domains, it is ok to have different radiation models on each side of the solid.
Radiation Modelling: Introduction
ANSYS CFX-Solver, Release 10.0: Modelling Page 265
once and stored giving a large improvement in efficiency. This is impossible with Monte
Carlo since the photon trajectories depend on the absorption coefficient and wall
emissivities.
A major problem with discrete transfer is the lack of error information. It is possible to
perform angular sub-sampling for surface fluxes for example, but this does not help with ray
effects, since if a source contribution has been missed by the complete ray sample it will also
be missed by the sub-sample. This can be dealt with by running a crude Monte Carlo
simulation to detect any large errors.
The actual computational time needed by the discrete transfer method can also be very
difficult to assess if iterations are needed to converge to the solution, as will be the case if
scattering is present. The efficiency advantage of discrete transfer over Monte Carlo also
rapidly disappears when non-gray models with a large number of spectral bands are to be
computed. Discrete transfer treats each band independently and so the computational time
increases in proportion to the number of bands used. Effectively N separate models are
computed for an N band model. The ray tracking is only done once, however. Since it is the
radiative heat transfer which is computed, and the actual spectrum is of no interest, a Monte
Carlo simulation is hardly affected by the number of bands, since the spectrum is just
another independent parameter to be sampled.
Unlike Monte Carlo all the physical quantities of interest are found at fixed points (due to the
fixed sampling and ray discretisation), not as surface or volume averages.
Terminology
Absorptivity Refers to the fraction of incoming energy that is absorbed at the surface.
Diffuse Refers to quantities that do not depend on incoming or outgoing direction; however, they
might be functions of temperature as well as location.
Gray Refers to quantities that do not have spectral dependency, i.e., they are not function of
frequency, wavelength or wavenumber.
Opaque Refers to a surface through which radiation cannot travel, i.e., radiation is reflected and/or
absorbed at the surface.
Reflectivity Refers to the fraction of incoming energy that is reflected at a surface, and is a function of
direction and frequency.
Spectral Refers to a quantity that is a function of any of the spectrum variables: frequency,
wavelength and wavenumber. The preferred variable is frequency, but to avoid
inconsistencies when dealing with non-unitary refractive index materials the wavelength or
wavenumber in vacuum are also supported.
Transmissivity Transmissivity, τ, refers to the fraction of incoming energy that travels through the surface,
i.e., the surface is semi-transparent when 0 < τ < 1, transparent when τ = 1 and opaque
when τ = 0.
Radiation Modelling: Rosseland Model
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Material Properties for Radiation
There are three material properties that must be defined in the Material Editor for radiation
simulations: absorption coefficient, scattering coefficient and refractive index. For details,
see Materials Editor: Pure Substance (p. 100 in "ANSYS CFX-Pre, Release 10.0"). For
multicomponent flows, we recommend setting the properties in the Mixture Properties
section of the Material Editor, since this can save substantial CPU time.
• For details, see Mixture Properties (p. 105 in "ANSYS CFX-Pre, Release 10.0").
• For details, see Radiation Properties (p. 47 in "ANSYS CFX-Solver, Release 10.0: Modelling").
Absorption coefficient, scattering coefficient and refractive index may be a function of
intensive thermodynamic variables such temperature and pressure, as well as composition.
In some applications, the radiative properties are not uniform in the whole spectrum (i.e.,
non-gray media). In this situation, you may specify these properties as a function of the CEL
spectral variables: frequency, wavelength in vacuum, or wavenumber in vacuum. The
spectral variable is evaluated at the mid-point of the spectral band in frequency space.
Rosseland Model
The Rosseland approximation assumes that the media is optically thick and that radiant
energy emitted from other locations in the domain are quickly absorbed and have no
influence in the local transport. This implies that the approximation is not valid near walls.
In ANSYS CFX, special treatment is applied to wall boundaries to over come this limitation.
Other boundaries are not given any special treatment.
The Rosseland approximation is extremely convenient to use since it does not solve for an
additional transport equation. It is usually valid for an optical thickness/depth greater than
5. It should not be used whenever the optical thickness is below 1 since it will affect
robustness of the flow solver.
For details, see General Radiation Considerations (p. 270 in "ANSYS CFX-Solver, Release 10.0:
Modelling").
Fluid Models
Information on radiation modelling in multiple domains is available. For details, see Domain
Considerations (p. 271 in "ANSYS CFX-Solver, Release 10.0: Modelling").
Include Boundary Temperature Slip
Optional parameter. For simulations where thermal radiation is by far the most dominant
mode of heat transfer, a temperature slip must be allowed at physical boundaries (Siegel
and Howell). By default, the temperature is slip is not included.
Information on the mathematical implementation of this is available. For details, see
Rosseland Model (p. 266 in "ANSYS CFX-Solver, Release 10.0: Modelling").
Spectral Model For details, see Spectral Model (p. 273 in "ANSYS CFX-Solver, Release 10.0: Modelling").
Scattering Model
For details, see Scattering Model (p. 275 in "ANSYS CFX-Solver, Release 10.0: Modelling").
Radiation Modelling: The P1 Model
ANSYS CFX-Solver, Release 10.0: Modelling Page 267
Initial Conditions
Since the Rosseland model does not solve for any additional transport quantity, no initial
guess or condition is required.
Solver Control
No specific advice is required for this model.
The P1 Model
The Differential Approximation or P1 adds an additional transport equation to the
simulation, consequently it is more costly. The P1 model is valid for an optical thickness
greater than 1. For example, the model has proved adequate for the study of pulverised fuel
(PF) flames, in regions away from the immediate vicinity of the flame. However, it has been
used for lower values with varying success.
The P1 model implementation in ANSYS CFX only allows for opaque diffuse walls. That is, the
diffuse fraction setting would then be ignored.
Open boundaries: inlets, outlets and openings are treated as fully transparent boundaries.
That is, they absorb all outgoing energy, and the incoming energy is computed as a
blackbody at either the local temperature or at a user specified external temperature.
For details, see General Radiation Considerations (p. 270 in "ANSYS CFX-Solver, Release 10.0:
Modelling").
Fluid Models
Information on radiation modelling in multiple domains is available. For details, see Domain
Considerations (p. 271 in "ANSYS CFX-Solver, Release 10.0: Modelling").
Spectral Model For details, see Spectral Model (p. 273 in "ANSYS CFX-Solver, Release 10.0: Modelling").
Scattering Model
For details, see Scattering Model (p. 275 in "ANSYS CFX-Solver, Release 10.0: Modelling").
Initial Conditions
The radiation model is an additional energy transport mechanism; it does not create any
additional sources of energy (except where the model provides for increased heat flow at
boundaries). However, it does not follow that switching on the radiation model results in
conservation of total energy within the system. The difference between the incident
radiation and emitted radiation represents a heating or cooling effect. There is, therefore, a
quantifiable energy “storage” (either positive or negative).
Suppose, for example, a combusting flow is solved with the radiation model initially set to
None, and then radiation is turned on. Where the fluid is already hot (e.g., owing to
combustion), the default initial guess introduces a large amount of radiant energy into the
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domain. Note that incident radiation scales with the fourth power of the local temperature.
This extra energy can take a long time to diffuse out of the domain. The default initial guess
can therefore be poor for combusting flows.
By its nature, the incident radiation is more uniform throughout the domain than the
medium temperature, Tf. Thus a uniform value of incident radiation everywhere might be a
better initial guess. It is recommended that the chosen value for the incident radiation result
in as small a change as possible in the energy storage within the flow domain. A suitable
level can be obtained by integrating the radiant energy equation (Eqn. 901) over the entire
flow domain (Ω):
(Eqn. 102)
where is that part of the boundary where an “emissivity-specified” boundary condition
is applied. Hence an average constant value of may be evaluated from:
(Eqn. 103)
where:
(Eqn. 104)
and V is the total volume.
Solver Control
No specific advice is required for this model.
The Discrete Transfer Model
This model is based on tracing the domain by multiple rays leaving from the bounding
surfaces. The technique was developed by Shah (1979) and depends upon the discretisation
of the equation of transfer along rays. The path along a ray is discretised by using the
sections formed from breaking the path at element boundaries. The physical quantities in
each element are assumed to be uniform.
4σ Ka Tf4 Tr
4–( ) VdΩ∫
2σεw
2 εw–( )------------------ Tw
4 Tr4–[ ] Ad
∂Ω∫=
∂Ω
Tr4
Tr4 Ka Vd
Ω∫
εw
2 2 εw–( )--------------------- Ad
∂Ω∫+
⎩ ⎭⎨ ⎬⎧ ⎫
KaTf4[ ] Vd
Ω∫
εw
2 2 εw–( )---------------------Tw
4Ad
∂Ω∫+=
Tr4 1
V--- Tf
4 VdΩ∫=
Radiation Modelling: The Monte Carlo Model
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These rays have to be traced through the domain in the same way that the photons would
be tracked in the Monte Carlo model. Therefore, the model description for both Monte Carlo
and Discrete Transfer is identical.
For the results to be accurate the elements must be chosen so that the radiation field is
reasonably homogeneous inside them. This means, for example, that they must be small
enough that the scattering optical depth is less than unity across each element.
Non-gray models are dealt with by treating each band as a separate calculation (possible
since scattering and reflection are assumed to be coherent). Tracking is only done once, and
the results for the bands are combined to give the total radiative heat transfer.
For details, see General Radiation Considerations (p. 270 in "ANSYS CFX-Solver, Release 10.0:
Modelling").
Fluid Models
Information on radiation modelling in multiple domains is available. For details, see Domain
Considerations (p. 271 in "ANSYS CFX-Solver, Release 10.0: Modelling").
Number of Rays Optional parameter. To determine the direction of the rays, the unitary hemisphere over the
face of a parametric element is discretised using spherical coordinates. The span is divided
into angles by the number of rays, and rays directions are computed to pass through the
center of the angles. In total, the number of rays square are traced from an element surface.
The default is set to 8.
Spectral Model For details, see Spectral Model (p. 273 in "ANSYS CFX-Solver, Release 10.0: Modelling").
Scattering Model
For details, see Scattering Model (p. 275 in "ANSYS CFX-Solver, Release 10.0: Modelling").
Initial Conditions
Since this model is not solving a transport equation, no initial guess or condition is required.
However, if a value is needed to properly evaluate the initial radiation term in the energy
equation, the advice given for the P1 model should be considered.
Solver Control
For details, see Thermal Radiation Control (p. 272 in "ANSYS CFX-Solver, Release 10.0:
Modelling").
The Monte Carlo Model
The Monte Carlo method simulates the underlying processes which govern the system of
interest, i.e., the physical interactions between photons and their environment. A photon is
selected from a photon source and tracked through the system until its weight falls below
some minimum at which point it ‘dies.’ Each time the photon experiences an ‘event,’ a
surface intersection, scattering or absorption for example, the physical quantities of interest
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are updated. This process generates a complete ‘history’ of that photon in the system. Many
photon histories need to be generated to get good estimates of the physical quantities of
interest in a system. Photon sources are selected, i.e., ‘sampled’ on the basis of emitted
radiation, each band being treated independently for non-gray models.
In ANSYS CFX, the main computational overhead in generating a history is in tracking the
photons across the domain. It is therefore essential to produce a balanced description of the
domain to efficiently track the photons. This is done by using a coarser mesh for the
radiation field than for the flow field under the assumption that the radiation field has less
sharp changes than any other transport variables. For details, see Thermal Radiation Control
(p. 272 in "ANSYS CFX-Solver, Release 10.0: Modelling").
Fluid Models
Information on radiation modelling in solid/multiple domains is available. For details, see
Domain Considerations (p. 271 in "ANSYS CFX-Solver, Release 10.0: Modelling").
Number of Histories
Optional parameter to indicate the total number of histories to be tracked for the
simulation. The default value is 10000.
Spectral Model For details, see Spectral Model (p. 273 in "ANSYS CFX-Solver, Release 10.0: Modelling").
Scattering Model
For details, see Scattering Model (p. 275 in "ANSYS CFX-Solver, Release 10.0: Modelling").
Initial Conditions
Similar to the Discrete Transfer model. For details, see Initial Conditions (p. 269 in "ANSYS
CFX-Solver, Release 10.0: Modelling").
Solver Control
For details, see Thermal Radiation Control (p. 272 in "ANSYS CFX-Solver, Release 10.0:
Modelling").
General Radiation Considerations
This section contains modelling advice on forms which appear on one or more of the
radiation modelling forms available in ANSYS CFX-Pre.
Radiation Modelling: General Radiation Considerations
ANSYS CFX-Solver, Release 10.0: Modelling Page 271
Domain Considerations
The following set of rules apply when modelling radiation in solid domains and in
simulations with more than one domain.
• For solid domains where thermal radiation is important, the Monte Carlo model is the only available option.
• For domain interfaces using the Conservative Interface Flux option the radiation model must be the same on both sides of the interface. That is, for Fluid-Solid, Solid-Solid, or Porous-Solid domain interfaces, the Monte Carlo model is the only available option.
• For simulation with multiple solid domains, the radiation model can be set independently for each solid domain.
Boundary Details
The boundary condition options which appear will depend on the type of model you are
using. Choices will come from the following:
External Blackbody Temperature
It represent the temperature of any bodies beyond that boundary. This temperature is not
necessarily the same as the local temperature.
Local Temperature
Indicates that the local fluid temperature must be used to account for the incoming
radiation energy. It is extremely useful for outlets or openings when the external blackbody
temperature is either unknown or much lower than the expected outlet temperature.
Radiation Intensity
Specify the mean radiation intensity only, and it is only supported by the P1 model.
Radiative Heat Flux
You can specify the radiative heat flux directly, and it is only supported by the P1 model.
Emissivity At opaque boundaries, the emissivity must be supplied. It can be set as a function of spectral
variables using CEL expressions when using the Multiband spectral modelling option.
Diffuse Fraction It represents the ratio between the diffuse reflected energy and the specularly reflected
energy at an opaque boundary. If the boundary is black, i.e unitary emissivity, this value has
no meaning since no energy is reflected.
Sources
Non-thermal radiation sources can be set when using either the Discrete Transfer or Monte
Carlo radiation models.
These non-thermal radiation sources (fluxes at boundaries) are divided into 2 groups:
isotropic and directional. The Directional Radiation Source and Directional Radiation Flux is
only supported when using the Monte Carlo model.
The strength of the source or flux can be a function of the spectral variables: frequency,
wavelength in vacuum, or wavenumber in vacuum when using the Multiband spectral
modelling option.
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Directional Radiation Source
It allows the specification of the source strength and its direction. The direction can be
specified by either Cartesian Components or Cylindrical Components using a local axis.
Isotropic Radiation Source
This allows the setting of a single source strength when the source strength is uniform in all
directions.
Directional Radiation Flux
Allows the specification of collimated non-thermal radiation flux at boundaries (SEE
BOUNDARY PANEL). The direction can be set by using Cartesian Components, Cylindrical
Components using a local axis, or Normal to Boundary
Isotropic Radiation Flux
Allows the specification of a directionally uniform non-thermal radiation flux.
Thermal Radiation Control
The radiation modelling options based on ray tracing: Discrete Transfer and Monte Carlo
require additional controls. These controls are found on the Advanced Options tab of the
Solver Control form.
Because these radiation model require considerable time, there are several ways to strike a
balance between accuracy and computer time. This can be done by coarsening the fine
mesh used for the flow field, or calculating the radiation field at a different frequency than
the other transport equations.
Iteration Interval
It sets the frequency of the radiation calculation respect to the flow solver. If left unset,
radiation will be calculated at each flow solver iteration (i.e., 1).
Diagnostic Output Level
When performing the ray tracing calculation, either Discrete Transfer or Monte Carlo several
diagnostic can be written to the output file. The output is controlled as follows:
0 - Quiet. No output is reported to the output file even if minor problems has occurred. If the
solver encounters a fatal error it will stop automatically.
1 - Minimal. A diagnostic results file is written and warnings are reported. The diagnostic
results file include radiation quantities for each radiation element.
2 - Verbose. A diagnostic results file is written every radiation iteration and the solver will
stop even for some warnings. This level is for debugging purposes only.
Coarsening Control
Target Coarsening RateThis represents the target ratio between elements in the fine mesh and radiation elements
in the coarser mesh. The default value is 64, ie. the number of radiation elements is 64 times
smaller than the number of elements in the fine mesh. The actual coarsening could be
smaller than the target specified. A summary is presented in the output file under under the
Radiation Coarsening section.
Small Coarse Grid SizeIt is the minimum number of radiation elements in the coarser mesh. The coarsening
algorithm will stop when either this value or the target coarsening rate is achieved.
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ANSYS CFX-Solver, Release 10.0: Modelling Page 273
Diagnostic Output LevelControl the diagnostic information of the coarsening algorithm that is written to the output
file.
Ray Tracing Control
This section only applies for the Discrete Transfer model.
Iteration IntervalIt sets the frequency for the calculation of the ray tracks. Since the ray tracing is time
consuming and disk intensive it is rarely used. The default value is zero, i.e., the tracks are
computed only once and stored permanently.
Maximum Buffer SizeTo minimise total memory usage and maximise disk throughput information for the tracks
is stored in a memory buffer before is written to disk. This set the maximum allowed buffer
storage in words. Default value is 6000 words.
Maximum Number of TracksA single ray is made of tracks, the fraction of ray within a radiation element. In certain cases,
highly specular surfaces with a small spacing, the rays may have infinite number of
reflections before being totally absorbed. Whenever the number of tracks reaches this
maximum, the tracing for this ray is halted, and the next ray is started. Default value is 4500.
Maximum Number of IterationsLimits the inner loop when there are reflecting boundaries; otherwise, the first iteration
usually satisfies the convergence tolerance (1%).
Ray Reflection ThresholdWhen modelling specular boundaries a ray may get reflected multiple times, when the
energy content of the original ray has dropped below this threshold the tracing is halted.
File PathSpecifies the location to store the track files. This is only required when the local disk space
is not large enough to store the track files, or a slave in a parallel run does not have access to
the run directory.
Spectral Model
In ANSYS CFX, three different spectral models are supported: Gray, Multiband, and Multigray
or Weighted Sum of Gray Gases. Each of radiation modelling option can use the following
spectral models:
Gray It assumes that all radiation quantities are uniform throughout the spectrum. It simplifies
the radiation calculation considerable since less equations should be solved. For
combustion calculations, where certain gases are absorbing in finite regions of the
spectrum and transparent for rest, it will introduce errors in the total radiative heat flux.
Radiation Modelling: General Radiation Considerations
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Multiband It discretises the spectrum into bands of finite width and assumes that radiation quantities
are nearly uniform within the band. The total radiative heat flux is computed by adding the
results within each band. Each spectral band can be defined by different means: Frequency,
Wavelength in Vacuum or Wavenumber in Vacuum.
At least two different spectral bands must be set. The solver will check that the union of all
spectral bands fully cover the thermal radiation part of spectrum and that they do not
overlap. A warning message will be written to the output file otherwise.
When using CEL expressions to describe the spectral variation of any radiation quantity, the
solver will use the frequency for the spectral band.
Multigray/Weighted Sum of Gray Gases
It assumes that gas absorption can be represented by a weighted sum of gray media. The
weights and absorption coefficients have been correlated in the literature for a variety of
gases (Modest). The current implementation does not provide a specific set of weights or
coefficients, though there is a CFX-Pre template available. Therefore, the user must specify
the weights/amplitudes and the absorption coefficients for each gray gas.
Caution should be taken when specifying the set of coefficients:
1 - There must be one clear gas.
2 - Weights must add up to 1. at all times.
A Multigray CCL Template is available in the Library mode of ANSYS CFX-Pre. For details, see
Multigrey Radiation (p. 253 in "ANSYS CFX-Pre, Release 10.0")..
When is a Non-Gray Spectral Model Appropriate?
Although it is convenient to average radiation properties over the whole spectrum (Gray
model), real gases only absorb and emit in discrete bands. Upon diffuse reflection at walls,
radiation emitted by the gases within discrete bands is re-emitted at all wavelengths as
thermal radiation with the characteristic blackbody spectrum. Although much of this
reflected radiation will be re-absorbed by the gases, some will now lie outside the
absorption bands of any of the gases present and will therefore pass through the gas
volume without absorption.
This effect can be significant when it is important to distinguish between emission from
gases and wall reflection, for example, in a reheat furnace where a thermal load is being
heated directly by a gaseous flame (R1) and indirectly by a refractory wall (R2). If the
emissivity of the refractory wall is increased (e.g., by a special coating), the proportion of
radiation with wavelengths outside the gaseous absorption bands increases and the
intensity of radiation reaching the load becomes higher. If the radiative heat transfer in the
reheat furnace is modelled using a Gray spectral model, then this effect would not be
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ANSYS CFX-Solver, Release 10.0: Modelling Page 275
correctly predicted. The Multiband, and Multigray/Weighted Sum of Gray Gases models
include a clear band and correctly predict an increase of radiative heat transfer to the load
as wall emissivity increases in the reheat furnace example.
Figure 33 Example of a Reheat Furnace
A more obvious limitation of the Gray model in combustion calculations is that a single
absorption coefficient is set, independent of the local gas composition. This implies that the
combustion air has the same radiative properties as the combustion products although the
latter contains a high percentage of CO2 and H2O, which are highly efficient emitters of
thermal radiation. The actual error caused by this approximation is not usually large because
combustion air is usually at much lower temperatures than the products but, nevertheless,
it leads to an overestimate of the absorption due to the air.
Scattering Model
The radiative transfer equation includes two terms due scattering: attenuation by scattering
or out-scattering and augmentation by scattering or in-scattering.
In ANSYS CFX, the scattering term can be controlled independently in several ways:
When using the Monte Carlo radiation model, you can optionally specify a scattering model.
If you are using an option other than None, you must specify a Scattering Coefficient on the
Material Properties form. If you specify a Scattering Coefficient, this does not automatically
imply that a scattering model will be used, you must also select either the Gray or Linear
Anisotropy models. For details, see Materials Editor: Pure Substance (p. 100 in "ANSYS
CFX-Pre, Release 10.0").
Option = None The scattering coefficient is ignored, even is a non-zero coefficient has been set for the
medium. For most clean participating gases, not-suspended particles, the absorption is
much larger than scattering.
Option = Isotropic
It assumes that in-scattering is uniform in all directions.
Option = Linear Anisotropy
ANSYS CFX includes support for the linear anisotropic phase function
phi = 1 + c (s’.s)
LOAD
REFRACTORY
FLAME
R2
R1Radiation can reach the load directly from the flame or indirectly via the refractory wall
BURNER
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The anisotropy coefficient c must be supplied. If the coefficient has spectral dependency, it
can be evaluated using CEL expressions using any of the spectral variables: frequency,
wavelength or wavenumber.