๐ฅ Radiation in Participating Media (P1 Model)
Evaluate radiative heat flux in absorbing, emitting, and scattering semitransparent gray media using P1 differential spherical harmonics and Rosseland diffusion conductivity.
โก Fortran 90 Engine
Double Precision (IEEE 754)
โ ISO / ASME Validated
Radiation
๐ Solver Telemetry
โ ACTIVE
๐๏ธ Views
27
โก Solves
22
๐พ Downloads
235
๐ฆ Fortran Code
5.4 KB
๐
Released
Jun 2026
โฑ๏ธ Latency
< 1 ms
๐ฅ Participating Semitransparent Medium & Photon Scattering Field
Real-time visual simulation of photon emission, volumetric gas absorption & isotropic scattering attenuation๐ Configuration & Presets
๐ฅ Glass Melting Furnace
๐ญ Coal Boiler Flue Gas
๐ Rocket Soot Plume
๐งฑ Porous Radiant Burner
P1 Spherical Harmonics Formulation:
โข Extinction Coeff: ฮฒ = a + ฯs | Optical Thickness: ฯโ = ฮฒ ยท L
โข P1 Heat Flux: qr = ฯ (Tโโด โ Tโโด) / [ (1/ฮตโ โ ยฝ) + (1/ฮตโ โ ยฝ) + ยพ ฯโ ]
โข Rosseland Diffusion: krad = 16 ฯ Tmeanยณ / (3 ฮฒ) [W/(mยทK)]
โข Scattering Albedo: ฯ = ฯs / ฮฒ
โข Extinction Coeff: ฮฒ = a + ฯs | Optical Thickness: ฯโ = ฮฒ ยท L
โข P1 Heat Flux: qr = ฯ (Tโโด โ Tโโด) / [ (1/ฮตโ โ ยฝ) + (1/ฮตโ โ ยฝ) + ยพ ฯโ ]
โข Rosseland Diffusion: krad = 16 ฯ Tmeanยณ / (3 ฮฒ) [W/(mยทK)]
โข Scattering Albedo: ฯ = ฯs / ฮฒ
๐ Radiative Flux Results
Configure inputs and click Compute to view results.
๐ Calculation Methodology & P1 Spherical Harmonics Standards
P1 Differential Approximation
The P1 method expands the directional radiative intensity into spherical harmonics, converting the complex integro-differential RTE into an elliptic Helmholtz equation:
โยฒG โ 3aฮฒ G = โ12aฮฒ ฯ Tโด
Rosseland Diffusion Analogy
In optically thick media ($\tau_0 \ge 3$), radiation acts like pure non-linear heat conduction with equivalent radiative conductivity $k_{rad} = \frac{16\sigma T^3}{3\beta}$.
Key Engineering Assumptions
- 1D planar participating medium slab.
- Gray gas with wavelength-independent absorption and isotropic scattering.
- Opaque diffuse gray wall boundaries ($\epsilon_1, \epsilon_2$).