|
[Sponsors] |
Understanding the Marshak boundary condition (radiation) |
![]() |
|
LinkBack | Thread Tools | Search this Thread | Display Modes |
![]() |
![]() |
#1 |
Senior Member
Join Date: Oct 2013
Posts: 397
Rep Power: 19 ![]() |
I'm currently working on implementing a non-gray P1 model. This also requires me to modify the Marshak BC.
The problem is that I don't quite understand how it works. I know that the radiative flux incident to the wall is: ![]() With e=emissivity at the surface, sigma= Stefan Boltzmann constant and G the spectral intensity integrated over all angles. And also: ![]() The implementation uses a mixed boundary condition, that means it uses an equation of the form a*G+b*dG/dn = c. Does that mean that here this evaluates to: -e_w/(2*(2-e_w))*G_w + q_rw = -e_w/(2*(2-e_w))*4*sigma*T_w^4 --> -e_w/(2*(2-e_w))*G_w - Gamma * dG/dn = -e_w/(2*(2-e_w))*4*sigma*T_w^4 I don't quite understand the code of the implementation of the Marshak BC in OF. The mixed BC fixes the value to this: ![]() with x_p = refValue(), w=valueFraction(), dx/dn = refGrad() and x_c = value in adjacent cell. In Marshak BC refValue() is 4*sigma*T^4, refGrad() is 0 and valueFraction() is 1.0/(1.0 + Gamma*Delta/(e_w/(2*(2 - e_w))). I don't understand if and how this matches the mixed equation above. Can anyone shed some light? In the non-gray model, G is exchanged with G_i, and sigma*T^4 with pi*B_i, where B_i is the integral over the black body spectrum over the frequency range of the band. Does that mean I can simply replace these values in the code and it will be fine? I suppose this should work, but I would like to understand how OpenFOAM implements this. |
|
![]() |
![]() |
![]() |
![]() |
#2 |
New Member
|
I think it's okay, because:
![]() Assume that ![]() it becomes ![]() you know that ![]() from the Fluent Guide, at the boundaries is ![]() so it becomes ![]() ![]() where ![]() If you explicit ![]() ![]() Here you can find the explanation of the mixed BC and it's easy to recognize that in this case ![]() ![]() ![]() because ![]() the f value (called valueFraction in OpenFOAM) can also be written as ![]() In the source code of MarhaskRadiationBC we can find Code:
refGrad() = 0.0; Code:
refValue() = 4.0*constant::physicoChemical::sigma.value()*pow4(Tp); Code:
valueFraction() = 1.0/(1.0 + gamma*patch().deltaCoeffs()/Ep); ![]() ![]() Code:
const scalarField Ep(temissivity/(2.0*(2.0 - temissivity))); ![]() So I think it's ok! I have some doubts regarding the emissivity I choose in the BC, especially in case of conjugated heat transfer (chtMultiRegion solver) in OpenFOAM 2.3. If I set (in the coupled wall patch, fluid side obviously) Code:
emissivityMethod lookup; Code:
emissivity uniform 0.9; Code:
emissivityMethod solidRadiation; In the AbsorptionEmissionModel dictionary to be precise. Code:
radiation on; radiationModel opaqueSolid; absorptionEmissionModel constantAbsorptionEmission; constantAbsorptionEmissionCoeffs { absorptivity absorptivity [ 0 -1 0 0 0 0 0 ] 0.0; //opaque emissivity emissivity [ 0 -1 0 0 0 0 0 ] 0.1; E E [ 1 -1 -3 0 0 0 0 ] 0; } scatterModel none; sootModel none; ![]() Anyone can shed more light? ![]() Elia
__________________
SnappyWiki |
|
![]() |
![]() |
![]() |
![]() |
#3 |
Senior Member
Join Date: Oct 2013
Posts: 397
Rep Power: 19 ![]() |
Thanks, I think it's clear now how the formula translates to the implementation.
I would also agree with you that the emissivity at the surface should be in [0 .. 1]. Since the opaqueSolid radiation model doesn't do anything, I suspect it's just a different (somewhat unlucky) place to store the value in. |
|
![]() |
![]() |
![]() |
![]() |
#4 | |
Member
Kaufman
Join Date: Jul 2013
Posts: 55
Rep Power: 13 ![]() |
Quote:
|
||
![]() |
![]() |
![]() |
![]() |
#5 |
Senior Member
Join Date: Oct 2013
Posts: 397
Rep Power: 19 ![]() |
But a wavelength-dependent emissivity still is dimensionless, as it's not a density like a spectral intensity for example.
Also, the emissivity in radiationProperties is used in two different contexts in the models, which is somewhat confusing. |
|
![]() |
![]() |
![]() |
![]() |
#6 |
New Member
Germilly Barreto
Join Date: Jul 2016
Location: Portugal
Posts: 25
Rep Power: 10 ![]() |
Hello,
I was searching in the forum and this thread seems to be the right place to post my question. I'm modelling radiation transfer inside a pipe which contain a participating media. My problem is about the boundary condition for the incident radiation G (I'm using the P1 radiationModel). In that pipe, I have 3 boundary patches: 1) "inlet" of the pipe: Which is in direct contact with the environment 1) "outlet" of the pipe: also in direct contact with the environment 3) "wall" (cylindrical surface): Bounded by a solid diffuse surface For the wall, I'm using in the 0/G file the MarshakRadiation boundary condition: Code:
wall { type MarshakRadiation; T Ts; // Ts is the name of my temperature field value uniform 0;; } Code:
wall { type boundaryRadiation; mode lookup; emissivity uniform 0.8; // The emissivity of the wall value uniform 0; } But, for the inlet and outlet, I dont know what should I do. I cannot define an emissivity for the inlet and outlet because there are no solid surface, there are only the participating media. Do you know what should I define for these two boundary conditions (inlet and outlet)? Thank you Best regards, Germilly Barreto Last edited by Germilly; June 21, 2018 at 13:31. |
|
![]() |
![]() |
![]() |
![]() |
#7 |
New Member
Joanne
Join Date: Aug 2017
Location: Ireland
Posts: 6
Rep Power: 9 ![]() |
Hi Germilly,
I am interested in a similar problem as yours, I am unsure which BC to use for flow inlets/outlets when implementing a radiation model. Please let me know if you make any discoveries, and I will do likewise. Kind regards, Joanne Last edited by Joanne; June 27, 2018 at 06:30. Reason: grammar |
|
![]() |
![]() |
![]() |
![]() |
#8 |
New Member
Germilly Barreto
Join Date: Jul 2016
Location: Portugal
Posts: 25
Rep Power: 10 ![]() |
Hello Joanne,
See my last post in the following thread: Radiation boundary conditions for flow through boundaries in openFoam I hope it can be helpful. Regards, Germilly Barreto |
|
![]() |
![]() |
![]() |
![]() |
#9 |
Senior Member
Join Date: Oct 2013
Posts: 397
Rep Power: 19 ![]() |
Hello,
I replied to the other thread, I hope this helps somewhat. |
|
![]() |
![]() |
![]() |
Thread Tools | Search this Thread |
Display Modes | |
|
|
![]() |
||||
Thread | Thread Starter | Forum | Replies | Last Post |
Low Mixing time Problem | Mavier | CFX | 5 | April 29, 2013 00:00 |
Velocity profile boundary condition | Tuca | FLOW-3D | 1 | April 23, 2013 12:02 |
External Radiation Boundary Condition (Two sided wall), Grid Interface | CFD XUE | FLUENT | 0 | July 8, 2010 06:49 |
[Commercial meshers] Trimmed cell and embedded refinement mesh conversion issues | michele | OpenFOAM Meshing & Mesh Conversion | 2 | July 15, 2005 04:15 |
The Boundary Condition about the Flat Plate | boing | Main CFD Forum | 1 | January 6, 2002 16:53 |