Radiation Modeling
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Hi,
I’m new in working with ANSYS CFX. I searched this forum for clarifying my issue but I did not find a real solution. So I will explain what I want to do. I want to do a thermal analysis of a rough board in space. For the first approach I just want to irradiate this board from the sun in the distance of 1AU (sunearth distance). The board should absorb this radiation in the solar spectrum and emit it in the infrared spectrum. I want to check this easy case of radiation modeling with the calculations I did by my own before I start with the harder simulation. The reason why I use CFX is because of directional radiation. I want to analyze the rough board later for hot spots due to reflections. That is not possible with the thermal steadystate analysis of ANSYS according to the support. At first I want to create the surrounding area close to reality. Therefore I created a box for the vacuum (see attached picture). This domain is defined as a fluid with Air at 25 C (I switched to “false” for solving fluids). In this domain is my board, defined as a solid domain which is connected by a fluidsolid interface with the “vacuum”. My radiation flux at 1AU is about 1367 W/m^2. Therefore I defined a Radiation Source with a Directional Radiation Flux of the mentioned value at the boundary of the fluid domain. Additionally I fixed the temperature (3 K) of the walls of the fluid domain for the heat transfer and set the initial temperature of the board to 273 K. I am using Monte Carlo on both sides of the interface for thermal radiation. Solid and Fluid domain are participating medias. Do you think my definitions for the simulations are correct by now? Here comes my real problem with CFX. As I said, I want to absorb and emit in different spectra. I have totally no idea how I can define this correctly in CFX!? I read something like the emissivity is derived by the absorption coefficient. So I tried to get this connection but I just found information about the “Einstein coefficients” which are not that easy to understand. Is there another possibility to define values like emissivity, absorptivity, transmittance and reflectivity or how should the absorption coefficient defined? I also read that for example the absorptivity is defined in CFX by “absorptivity= diffuse fraction* internal emissivity”. But the internal emissivity is not the same like you can define for the “Opaque” option. Maybe I have to work more on understanding thermal radiation or can you help me?! So all in all my two questions are:
If you need more information please let me know. Best regards, Chris Edit: I forgot to post a part of the data from the outputfile, sorry. LIBRARY: MATERIAL: Air at 25 C Material Description = Air at 25 C and 1 atm (dry) Material Group = Air Data, Constant Property Gases Option = Pure Substance Thermodynamic State = Gas PROPERTIES: Option = General Material EQUATION OF STATE: Density = 1.185 [kg m^3] Molar Mass = 28.96 [kg kmol^1] Option = Value END SPECIFIC HEAT CAPACITY: Option = Value Specific Heat Capacity = 1.0044E+03 [J kg^1 K^1] Specific Heat Type = Constant Pressure END REFERENCE STATE: Option = Specified Point Reference Pressure = 1 [atm] Reference Specific Enthalpy = 0. [J/kg] Reference Specific Entropy = 0. [J/kg/K] Reference Temperature = 25 [C] END DYNAMIC VISCOSITY: Dynamic Viscosity = 1.831E05 [kg m^1 s^1] Option = Value END THERMAL CONDUCTIVITY: Option = Value Thermal Conductivity = 2.61E02 [W m^1 K^1] END ABSORPTION COEFFICIENT: Absorption Coefficient = 0.01 [m^1] Option = Value END SCATTERING COEFFICIENT: Option = Value Scattering Coefficient = 0.0 [m^1] END REFRACTIVE INDEX: Option = Value Refractive Index = 1.0 [m m^1] END THERMAL EXPANSIVITY: Option = Value Thermal Expansivity = 0.003356 [K^1] END END END MATERIAL: Aluminium Material Group = CHT Solids,Particle Solids Option = Pure Substance Thermodynamic State = Solid PROPERTIES: Option = General Material EQUATION OF STATE: Density = 2702 [kg m^3] Molar Mass = 26.98 [kg kmol^1] Option = Value END SPECIFIC HEAT CAPACITY: Option = Value Specific Heat Capacity = 9.03E+02 [J kg^1 K^1] END REFERENCE STATE: Option = Specified Point Reference Specific Enthalpy = 0 [J/kg] Reference Specific Entropy = 0 [J/kg/K] Reference Temperature = 25 [C] END THERMAL CONDUCTIVITY: Option = Value Thermal Conductivity = 237 [W m^1 K^1] END ABSORPTION COEFFICIENT: Absorption Coefficient = 0.0001 [mm^1] Option = Value END END END END FLOW: Flow Analysis 1 SOLUTION UNITS: Angle Units = [rad] Length Units = [m] Mass Units = [kg] Solid Angle Units = [sr] Temperature Units = [K] Time Units = [s] END ANALYSIS TYPE: Option = Steady State EXTERNAL SOLVER COUPLING: Option = None END END DOMAIN: Platte Coord Frame = Coord 0 Domain Type = Solid Location = B18 BOUNDARY: Default Fluid Solid Interface Side 1 1 Boundary Type = INTERFACE Location = F19.18,F20.18,F21.18,F22.18,F23.18,F24.18 BOUNDARY CONDITIONS: HEAT TRANSFER: Option = Conservative Interface Flux END THERMAL RADIATION: Diffuse Fraction = 1. Emissivity = 1. Option = Opaque END END END DOMAIN MODELS: DOMAIN MOTION: Option = Stationary END MESH DEFORMATION: Option = None END END INITIALISATION: Option = Automatic INITIAL CONDITIONS: RADIATION INTENSITY: Option = Automatic END TEMPERATURE: Option = Automatic with Value Temperature = 273 [K] END END END SOLID DEFINITION: Solid 1 Material = Aluminium Option = Material Library MORPHOLOGY: Option = Continuous Solid END END SOLID MODELS: HEAT TRANSFER MODEL: Option = Thermal Energy END THERMAL RADIATION MODEL: Number of Histories = 100000 Option = Monte Carlo Radiation Transfer Mode = Participating Media SCATTERING MODEL: Option = None END SPECTRAL MODEL: Option = Gray END END END END DOMAIN: Umgebung Coord Frame = Coord 0 Domain Type = Fluid Location = B57 BOUNDARY: Default Fluid Solid Interface Side 1 Boundary Type = INTERFACE Location = F64.57,F65.57,F66.57,F67.57,F68.57,F69.57 BOUNDARY CONDITIONS: HEAT TRANSFER: Option = Conservative Interface Flux END MASS AND MOMENTUM: Option = No Slip Wall END THERMAL RADIATION: Diffuse Fraction = 0 Emissivity = 1. Option = Opaque END END END BOUNDARY: Grenze Boundary Type = WALL Location = F58.57,F59.57,F60.57,F61.57,F62.57 BOUNDARY CONDITIONS: HEAT TRANSFER: Fixed Temperature = 3 [K] Option = Fixed Temperature END MASS AND MOMENTUM: Option = No Slip Wall END THERMAL RADIATION: Diffuse Fraction = 0 Emissivity = 1. Option = Opaque END END END BOUNDARY: Quelle Boundary Type = WALL Location = F63.57 BOUNDARY CONDITIONS: HEAT TRANSFER: Fixed Temperature = 3 [K] Option = Fixed Temperature END MASS AND MOMENTUM: Option = No Slip Wall END THERMAL RADIATION: Diffuse Fraction = 0 Emissivity = 1. Option = Opaque END END BOUNDARY SOURCE: SOURCES: RADIATION SOURCE: Radiation Source 1 Option = Directional Radiation Flux Radiation Flux = 1367 [W m^2] DIRECTION: Option = Cartesian Components Unit Vector X Component = 0 Unit Vector Y Component = 0 Unit Vector Z Component = 1 END END END END END 
And the rest:
DOMAIN MODELS: BUOYANCY MODEL: Option = Non Buoyant END DOMAIN MOTION: Option = Stationary END MESH DEFORMATION: Option = None END REFERENCE PRESSURE: Reference Pressure = 1 [atm] END END FLUID DEFINITION: Fluid 1 Material = Air at 25 C Option = Material Library MORPHOLOGY: Option = Continuous Fluid END END FLUID MODELS: COMBUSTION MODEL: Option = None END HEAT TRANSFER MODEL: Option = Thermal Energy END THERMAL RADIATION MODEL: Number of Histories = 100000 Option = Monte Carlo Radiation Transfer Mode = Participating Media SCATTERING MODEL: Option = None END SPECTRAL MODEL: Option = Gray END END TURBULENCE MODEL: Option = Laminar END END INITIALISATION: Option = Automatic INITIAL CONDITIONS: Velocity Type = Cartesian CARTESIAN VELOCITY COMPONENTS: Option = Automatic END RADIATION INTENSITY: Option = Automatic END STATIC PRESSURE: Option = Automatic with Value Relative Pressure = 0 [Pa] END TEMPERATURE: Option = Automatic END END END END DOMAIN INTERFACE: Default Fluid Solid Interface Boundary List1 = Default Fluid Solid Interface Side 1 1 Boundary List2 = Default Fluid Solid Interface Side 1 Interface Type = Fluid Solid INTERFACE MODELS: Option = General Connection FRAME CHANGE: Option = None END HEAT TRANSFER: Option = Conservative Interface Flux HEAT TRANSFER INTERFACE MODEL: Option = None END END PITCH CHANGE: Option = None END THERMAL RADIATION: Option = Side Dependent END END MESH CONNECTION: Option = Automatic END END OUTPUT CONTROL: RESULTS: File Compression Level = Default Option = Standard END END SOLVER CONTROL: ADVECTION SCHEME: Option = High Resolution END CONVERGENCE CONTROL: Length Scale Option = Conservative Maximum Number of Iterations = 200 Minimum Number of Iterations = 10 Solid Timescale Control = Auto Timescale Timescale Control = Auto Timescale Timescale Factor = 1.0 END CONVERGENCE CRITERIA: Conservation Target = 0.01 Residual Target = 1.E4 Residual Type = RMS END DYNAMIC MODEL CONTROL: Global Dynamic Model Control = On END THERMAL RADIATION CONTROL: Iteration Interval = 5 COARSENING CONTROL: Target Coarsening Rate = 4 END END END EXPERT PARAMETERS: solve fluids = f solve radiation = t END END COMMAND FILE: Version = 14.5 Results Version = 14.5.7 END SIMULATION CONTROL: EXECUTION CONTROL: EXECUTABLE SELECTION: Double Precision = On END INTERPOLATOR STEP CONTROL: Runtime Priority = Standard MEMORY CONTROL: Memory Allocation Factor = 1.0 END END PARALLEL HOST LIBRARY: HOST DEFINITION: ry000391 Remote Host Name = RY000391 Host Architecture String = winntamd64 Installation Root = C:\Program Files\ANSYS1457\v%v\CFX END END PARTITIONER STEP CONTROL: Multidomain Option = Independent Partitioning Runtime Priority = Standard EXECUTABLE SELECTION: Use Large Problem Partitioner = Off END MEMORY CONTROL: Memory Allocation Factor = 1.0 END PARTITIONING TYPE: MeTiS Type = kway Option = MeTiS Partition Size Rule = Automatic Partition Weight Factors = 0.50000, 0.50000 END END RUN DEFINITION: Run Mode = Full Solver Input File = Fluiddynamik CFX.def END SOLVER STEP CONTROL: Runtime Priority = Standard MEMORY CONTROL: Memory Allocation Factor = 1.0 END PARALLEL ENVIRONMENT: Number of Processes = 2 Start Method = Platform MPI Local Parallel Parallel Host List = ry000391*2 END END END END 
Update:
I changed the boundary conditions of the vacuum to "openings" and set the opening pressure to 0 Pa and the opening temperature to 3 K. If I choose opaque for the domain interface with an emissivity of 1 I get the correct value for the temperature after adjusting the absorption coefficient. My problem regarding the absorptivity and emissivity is still present. For the first approach I know my ratio from the absorptivity to the emissivity. Therefore if I can set the emissivity to 1 I can multiply my incoming radiation flux with the ratio. That's ok for testing but because of the defined option opaque, the aluminum plate would not be considered. So I have to define also the reflectivity and transmissivity because I want to analyze a specimen with wrinkles. I already read the theory behind radiation modeling from ANSYS CFX but I have still no clue how CFX derives my desired values with the help of the absorption coefficient, scattering coefficient, the refractive index and the radiative transfer equation. Some radiation experts or nonradiation experts :) out there who can help me? Best regards, Chris P.S. Ordered "Thermal Radiation Heat Transfer" from Siegel and Howell. If I get the solution, I let you know. But if someone has an idea for the solution please post it :). 
Below is sample CFX command language code on how to implement a spectral property for a thermal radiation model
You can use 1D interpolation functions, or write your own expression with step functions (or logical CEL if you like as well). The main points are  Gather your spectral data  Decide how many spectral intervals you need  Create either expressions, or 1Dinterp functions  Activate the multiband spectral model  Create as many spectral intervals you decided for this simulation  Use the expressions or function on the appropriate sections: emissivity at boundaries, absorption coefficients for materials, or even radiation fluxes at boundary sources (check with ANSYS support here for care on setting up spectral sources) Code:

Hi Opaque,
Thank you very much for the response. I will implement the code and adjust it to my purposes. I think this definition will work for the different spectra in absorption and emission. But unfortunately I am still confused regarding the relation between the absorption coefficient with the absorptivity, reflectivity and transmissivity :confused:. But I will work on this problem until I got it or one of you can explain this correlation :). Regards, Chris 
Another good book to read is Radiative Heat Transfer by Michael Modest. I think the 3rd edition is the most recent.
The vocabulary used in the radiation literature varies greatly between areas of application, and groups. Many times you must understand the meaning from the context. Overall, you can assume all media absorb, emit and scatter radiative energy. Some media absorbs so much in a very short length that there is no point to model the volumetric effects, and they can be reduced to surface effects. One you are modeling them as surfaces, the interaction at surfaces are split into 2 types: self, and external. Self is emission, external is what happens to the incoming energy: reflected, absorbed, or transmitted. The last 3 must add up to the total incoming amount; therefore, their relative contribution can be represented as fractions: absortptivity(tance or alpha), reflectivity(ance or rho), and transmitivity(ance or tau). They are not independent, and usually you only need to 1 of them:  Opaque : tau = 0, rho = 1  alpha  Semitransparent: alpha = 0, rho = 1  tau  Mirror: tau = 1, rho = alpha = 0  Black : alpha = 1, rho = 0, tau = 0 For practical applications, the surface "properties" (no such a thing since they depend on surface quality as well as material) can be found on handbook, technical literature, or material providers. The relation between the 3 above, and emissivity is only simple for the monochromatic (or spectral) case, where by Kirchoff law emissivity = absorptivity. Once the spectral approximations (such a gray) are used, their relationship is not straightforward, but for rough estimates you can just assume Kirchoff law always applies, and refine your approximation if needed. When talking about nongray (or spectral) modeling, there has been the tendency to use the word emittance for volumetric effects (which definitely depends on the absorption coefficient and other thermodynamic variables), but it is not the same as emissivity at a surface. Hope the above helps, 
Thank you again for your detailed reply :).
Ok, so in my case I think the definition of an opaque boundary should fit because the transmissivity is negligible. But because this simulaion is for a space application with an absorptivity in the solar spectrum and an emissivity in the infrared spectrum it is unfortunately not possible for me to assume Kirchhoff's law of thermal radiation is valid. I assume for the transfer mode "surface to surface" CFX calculates the solution with absorptivity=emissivity without any other specifications in the settings!? Therefore I think I have to work on the spectral approximation. Thank you for the recommendation of the book. If the ordered book, which hopefully will be delivered next week, does not solve the problem I will order Radiative Heat Transfer :). Best regards 
Now I solved the problem with the help of your advices Opaque. Special thanks to you!!
Here the important informations of the output file for those who want to do the same. Code:
LIBRARY: I have just one more question :). I would like to visualize the rays which will be reflected. Is that possible in CFDPost? Particle tracking is possible and maybe also ray tracking? I have to use Monte Carlo, so ray tracing with the DTM would not be possible. Are radiometers possible to visualize adequate the rays? Best regards, Chris 
Glad to hear you made it work..
Unfortunately, the rays used for the radiation modeling cannot be visualized at all. You can visualize rays for a radiometer though by setting the Diagnostic Output level to a value larger than 0. A .csv file will be written for every radiometer with diagnostic output level greater than 0. Such file contain the rays leaving a radiometer including their reflections (so you can track the original source of the ray). To visualize the rays, you create a polyline in CFDPost, select the option From File, and apply. If I recall correctly, a diagnostic output of 1 gives a single .csv file. For value of 2, you can get a .csv per time step. For nondeforming meshes or nonconditional domain interfaces, those .csv files will be the same. so you can just 1. Hope the above helps, 
Could you please tell me how I can model pure radiation without convection or conduction in the domain? I want to model radiation in vacuum.

Use the expert parameters to turn the flow solver and any other solvers you do not want off.

Thanks for your response.
In my problem, I have different solids and fluid domains and I have to solve energy and fluid equation in them except one of them which I want to solve only radiation heat transfer. Therefore, if I turn off the flow and energy equations from expert parameters, the energy and flow will not solve in other domains. 
Then I would make your vacuum a solid domain, and use a solid with a very low (but not zero) conductivity.

Thank you very much ghorrocks.

Hello again :),
I have a further question regarding the radiation modeling. I want to analyze a surface with a wrinkle in vacuum. Nearly the same conditions and properties as for the last simulation (surface to surface, Monte Carlo method, different spectra for absorption and emission, interface between the surface and the vacuum). Since the incoming directional radiation flux reflects, hot spots should occur. The problem is the definition of the vacuum and therefore the convergence. If the fluid solver will be turned off, the surface of the vacuum for the interface has still the properties of the fluid and therefore the conductivity, which leads to wrong results. For these settings, the solver converges. If I create another “material” for the vacuum with low conductivity, low density and high viscosity as ghorrocks recommended in another thread regarding the vacuum definition, the results after 300 iterations (about 3 hours) seem to be correct but the solver does not converges. Is there a possibility to adjust the convergence criteria for the low conductivity or is there another possibility for the definition of a vacuum in CFX? Is CFX generally suitable for such radiation problems with a vacuum? Best regards, Chris 
No, my recommendation for your vacuum material is to make it a solid domain. Then you do not need to worry about any fluid properties. Also low conductivity is required, but high density might be more numerically stable.

Thank you for your reply!
I tried this option for the vacuum definition, too. The problem is the definition of the surfaces of the vacuum domain. I have to set an emissivity and either the surfaces absorb and emit the irradiation from the wrinkle surface for a value of "1" or they reflect the incoming energy, which comes from the wrinkle surface. This leads unfortunately also to wrong results for the temperature distribution due to the radiation from the surrounding "surfaces" of the vacuum. 
I have no idea what you are talking about. I am not an expert on radiation modelling but my understanding is that the same options are available for a solid domain as for a fluid domain. So whatever radiation boundary conditions you defined for the fluid domain can be set for the solid domain.
So whatever settings you have put on the fluid domain you can put them on the solid domain as well. 
If I define the vacuum as a solid domain, I can either choose wall or symmetry for the boundaries. For a wall, I have to set an emissivity which leads to the mentioned problems. If I define the vacuum as a fluid domain, I can define the boundaries as openings and therefore no radiation will be absorbed, reflected or emitted, only transmitted. That is what I want but it is not possible for a solid domain. Or is there any possibility to define a transmissivity of 100% for a surface of a solid domain?

Can you use a solid domain with wall boundaries where the temperature of the wall is set to almost absolute zero (like 1 [K])? Then the wall will absorb radiation but not radiate or reflect.

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