Engineering guide
The K4 module calculates the thermal radiation of gas-solid mixtures according to the VDI Heat Atlas (VDI-Wärmeatlas), 12th edition 2019 — the standard German reference for heat transfer engineering. As soon as a hot gas carries particles — coal ash and fly dust in flue gas, limestone or cement dust, fluidized-bed material or soot particles — its radiative behavior changes fundamentally: unlike gases, particles radiate over a continuous spectrum and can raise the emissivity and absorptivity of the suspension considerably compared with the pure gas.
In practice, this calculation is required wherever dust-laden hot gases transfer heat to walls or heating surfaces: in pulverized-coal-fired steam generators, cyclones and fluidized-bed furnaces, calciners in the cement and lime industry, or in waste-heat boilers downstream of metallurgical processes. Anyone who bases the radiative share of heat transfer on the gas emissivity alone systematically underestimates the heat flow.
The method combines the band radiation of the gas components (H2O, CO2) with the particle radiation, which depends on particle concentration, particle size and the optical properties of the solid (e.g. coal ash, limestone). The results are the emissivity and absorptivity of the suspension as well as the radiative heat flow to the bounding wall at its wall temperature.
Scope
- Thermal radiation from gas-solids mixtures
Typical workflow
Record the gas state and particle loading
The inputs are gas temperature, wall temperature, the partial pressures of the radiatively active gas components, and the characteristics of the particle phase: concentration (loading), mean particle diameter and particle material, such as coal ash or limestone.
Determine the mean beam length of the radiating volume
As with pure gas radiation, the mean beam length is formed from the geometry of the gas space; it enters the optical thickness of the gas and particle phases as the radiation path length.
Calculate the emissivity of the gas phase
For water vapor and carbon dioxide, the emissivity is evaluated from the correlations of the VDI Heat Atlas as a function of temperature and the product of partial pressure and beam length, including the band overlap correction.
Determine the contribution of particle radiation
From particle concentration, particle size and the material-specific optical properties, the extinction contribution of the solid phase is determined. Small particles at high concentration act optically dense and drive the emissivity of the suspension toward the limiting value of a gray radiator.
Form the total emissivity and heat flow
Gas and particle contributions are combined into the emissivity and absorptivity of the suspension, taking into account that gas and particle radiation attenuate each other and do not simply add. With the wall emissivity and the temperatures of suspension and wall, the net radiative heat flow follows.
Frequently asked questions
Why is it not enough to consider only gas radiation when the gas contains dust?
Particles radiate continuously across the entire spectrum, whereas gases are active only in narrow bands. Even moderate dust loadings can raise the emissivity of the suspension well above that of the pure gas — in pulverized-coal-fired furnaces, particle radiation is frequently the dominant share. A pure gas-radiation calculation substantially underestimates the heat flow there.
What influence does particle size have?
At a given mass concentration, many small particles present a far larger projected area than a few large ones and therefore increase the optical thickness of the suspension more strongly. Fine fly dust is consequently much more intense radiatively than coarse ash at the same loading. In addition, the ratio of particle size to wavelength influences the scattering behavior.
Can the emissivity and absorptivity of the suspension exceed that of the pure gas yet still remain below 1?
Yes. With growing optical thickness (high loading, fine particles, long radiation paths), the emissivity approaches asymptotically a limiting value below 1 that is determined by the optical properties of the particles. Scattering at the particles ensures that even an optically dense dust cloud is not an ideal blackbody radiator.
Does the method also apply to fluidized beds?
The correlations are formulated for dilute gas-solid suspensions as found in furnaces, cyclones and freeboard zones. In dense fluidized beds, particle contact and particle convection dominate the near-wall heat transfer; dedicated fluidized-bed approaches must be used there, in which suspension radiation is only one partial contribution.
Technical content source: LV-Solved-Problems-Content 628d313247e7