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ABSTRACT
Investigation of the effect of grey/nongrey particle property models on radiative heat fluxes and source terms is performed in the dilute zone of the lignite-fired 150 kW Middle East Technical University circulating fluidized bed combustor test rig. Predictive accuracy and computational economy of several grey particle models, geometric optics approximation (GOA) with average particle reflectivity (GOA2), GOA with Fresnel solution for particle reflectivity (GOA3), and Planck mean particle properties from spectral Mie solution are tested by benchmarking their predictions against spectrally banded solution of radiative transfer equation (RTE). Comparisons reveal that all grey models lead to accurate and CPU efficient radiative heat flux predictions. On the other hand, only GOA3 and Planck mean properties are in favorable agreement with the benchmark solution for both incident fluxes and source terms. These findings indicate that grey particle approximation with GOA3 is a more practical choice in solution of RTE as it eliminates the need for spectral calculations.
Nomenclature
| c | = | speed of light (m/s) |
| dp | = | particle diameter (m) |
| g | = | asymmetry factor (dimensionless) |
| I | = | radiative intensity (W/m2/sr) |
| Ib | = | blackbody intensity (W/m2/sr) |
| k | = | imaginary part of complex refractive index (dimensionless) |
| kt | = | time constant with dimension (s/m) |
| m | = | complex refractive index (dimensionless) |
| N(dp) | = | particle size distribution function |
| n | = | real part of complex refractive index (dimensionless) |
| N(dp) | = | particle size distribution function |
| Qabs | = | absorption efficiency |
| Qext | = | extinction efficiency |
| Qscat | = | scattering efficiency |
| r | = | position vector (dimensionless) |
| r | = | coordinate axis in cylindrical geometry(dimensionless) |
| T | = | temperature (K) |
| = | average temperature (K) | |
| t | = | time |
| w | = | quadrature weight (dimensionless) |
| x | = | size parameter (dimensionless) |
| z | = | coordinate axis in cylindrical geometry(dimensionless) |
| Greek symbols | = | |
| α | = | absorptivity |
| γ | = | angular differencing coefficient (dimensionless) |
| ε | = | emissivity |
| η | = | direction cosine (dimensionless) |
| Θ | = | scattering angle (rad) |
| κ | = | absorption coefficient (m) |
| λ | = | wavelength (µm) |
| μ | = | direction cosine (dimensionless) |
| ξ | = | direction cosine (dimensionless) |
| ρ⊥ | = | normal reflectivity (dimensionless) |
| = | average reflectivity (dimensionless) | |
| ρ | = | total hemispherical reflectivity (dimensionless) |
| ρp | = | particle density (kg/m3) |
| σ | = | scattering coefficient (m) |
| ϕ | = | azimuthal angle (rad) |
| Φ | = | scattering phase function (sr) |
| Ω | = | direction of radiation intensity (dimensionless) |
| Subscripts | = | |
| g | = | gas |
| i | = | quadrature point |
| j | = | spectral band number |
| ℓ | = | index for a discrete direction |
| ℓ′ | = | incoming discrete direction |
| m | = | ordinate index |
| m′ | = | incoming ordinate |
| p | = | particle |
| λ | = | wavelength (µm) |
| ν | = | wavenumber (1/cm) |
| Superscripts | = | |
| m | = | ordinate index |
| m′ | = | incoming ordinate |
| ℓ | = | index for a discrete direction |
| ℓ′ | = | incoming discrete direction |
Nomenclature
| c | = | speed of light (m/s) |
| dp | = | particle diameter (m) |
| g | = | asymmetry factor (dimensionless) |
| I | = | radiative intensity (W/m2/sr) |
| Ib | = | blackbody intensity (W/m2/sr) |
| k | = | imaginary part of complex refractive index (dimensionless) |
| kt | = | time constant with dimension (s/m) |
| m | = | complex refractive index (dimensionless) |
| N(dp) | = | particle size distribution function |
| n | = | real part of complex refractive index (dimensionless) |
| N(dp) | = | particle size distribution function |
| Qabs | = | absorption efficiency |
| Qext | = | extinction efficiency |
| Qscat | = | scattering efficiency |
| r | = | position vector (dimensionless) |
| r | = | coordinate axis in cylindrical geometry(dimensionless) |
| T | = | temperature (K) |
| = | average temperature (K) | |
| t | = | time |
| w | = | quadrature weight (dimensionless) |
| x | = | size parameter (dimensionless) |
| z | = | coordinate axis in cylindrical geometry(dimensionless) |
| Greek symbols | = | |
| α | = | absorptivity |
| γ | = | angular differencing coefficient (dimensionless) |
| ε | = | emissivity |
| η | = | direction cosine (dimensionless) |
| Θ | = | scattering angle (rad) |
| κ | = | absorption coefficient (m) |
| λ | = | wavelength (µm) |
| μ | = | direction cosine (dimensionless) |
| ξ | = | direction cosine (dimensionless) |
| ρ⊥ | = | normal reflectivity (dimensionless) |
| = | average reflectivity (dimensionless) | |
| ρ | = | total hemispherical reflectivity (dimensionless) |
| ρp | = | particle density (kg/m3) |
| σ | = | scattering coefficient (m) |
| ϕ | = | azimuthal angle (rad) |
| Φ | = | scattering phase function (sr) |
| Ω | = | direction of radiation intensity (dimensionless) |
| Subscripts | = | |
| g | = | gas |
| i | = | quadrature point |
| j | = | spectral band number |
| ℓ | = | index for a discrete direction |
| ℓ′ | = | incoming discrete direction |
| m | = | ordinate index |
| m′ | = | incoming ordinate |
| p | = | particle |
| λ | = | wavelength (µm) |
| ν | = | wavenumber (1/cm) |
| Superscripts | = | |
| m | = | ordinate index |
| m′ | = | incoming ordinate |
| ℓ | = | index for a discrete direction |
| ℓ′ | = | incoming discrete direction |