Improvement of the P1-model
Posted: Thu May 06, 2010 11:46 am
Hello,
I'm starting a improvement of the P1-model. Currently, the radiative calculation doesn't take account of the scattering, and the P1-model is not efficiency in thin optically media. I will make an improvement of this model :
- addition of the scattering, possibility to have a linear anisotropic scattering.
- improvement of the P1-model in optically thin media thanks to the IDA (Improved Differential Approximation).
I have made the first improvement and compare the result with those of Tan and Hsu (Transient radiative transfer in three-dimensional homogeneous and non-homogeneous participating media, JQSRT 1992). They calculate the radiative heat flux in a box of 1m x 1m x 1m with a face at 86.28K, the other faces and the media are at 0K, the optical thickness is equal to 1 with an albedo of 0.1 (so absorption = 0.9 and scattering = 0.1). The scattering is isotropic.
I have put the results of the P1-model in 3 cases + 1 result in DOM (128 directions) by ploting the radiative heat flux along the center line of the box, which starts in the center of the "hot" face and finish in the center of the opposite face :
- P1 : absorption = 1 (black)
- P1 : absorption = 0.9 (red)
- P1 : absorption = 0.9 + scattering = 0.1 (blue)
-DOM : absorption = 1 (green)
The result in DOM are very close to those of Tan and Hsu. It's a little disturbing because we don't consider the scattering in DOM model.
For the P1 model, we show an improvement of the result when we take account of the scattering.
Now, i will start the add of the IDA. The IDA consist to launch ray from all the wall to measure the optically thickness between the walls and the elements. There is a weighting between the result of the P1-model and the radiosity of the wall through the optically thickness. The IDA will improve the results in optically thin media (when the radiosity from the wall is more accurate than the P1-model) and near the wall (in optically thick media, when you are near the wall, the optical thickness could be thin because of the small distance).
I'm starting a improvement of the P1-model. Currently, the radiative calculation doesn't take account of the scattering, and the P1-model is not efficiency in thin optically media. I will make an improvement of this model :
- addition of the scattering, possibility to have a linear anisotropic scattering.
- improvement of the P1-model in optically thin media thanks to the IDA (Improved Differential Approximation).
I have made the first improvement and compare the result with those of Tan and Hsu (Transient radiative transfer in three-dimensional homogeneous and non-homogeneous participating media, JQSRT 1992). They calculate the radiative heat flux in a box of 1m x 1m x 1m with a face at 86.28K, the other faces and the media are at 0K, the optical thickness is equal to 1 with an albedo of 0.1 (so absorption = 0.9 and scattering = 0.1). The scattering is isotropic.
I have put the results of the P1-model in 3 cases + 1 result in DOM (128 directions) by ploting the radiative heat flux along the center line of the box, which starts in the center of the "hot" face and finish in the center of the opposite face :
- P1 : absorption = 1 (black)
- P1 : absorption = 0.9 (red)
- P1 : absorption = 0.9 + scattering = 0.1 (blue)
-DOM : absorption = 1 (green)
The result in DOM are very close to those of Tan and Hsu. It's a little disturbing because we don't consider the scattering in DOM model.
For the P1 model, we show an improvement of the result when we take account of the scattering.
Now, i will start the add of the IDA. The IDA consist to launch ray from all the wall to measure the optically thickness between the walls and the elements. There is a weighting between the result of the P1-model and the radiosity of the wall through the optically thickness. The IDA will improve the results in optically thin media (when the radiosity from the wall is more accurate than the P1-model) and near the wall (in optically thick media, when you are near the wall, the optical thickness could be thin because of the small distance).