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Gas Property Models

The radiative properties (absorption and scattering coefficients) of the combustion products and enclosure wall emittance are required for the modelling. In an enclosure fire, the gas radiative properties vary considerably from the comparatively transparent entrained air close to the floor to the highly emissive, luminous flames of fire source, and the optically dense ceiling smoke layer. Various models are available to predict the gas radiative properties.

The participating media models (see, for example, (TienCL:1982)) currently available for characterizing the flaming and smouldering fires and the resulting combustion products differ in their generality, sophistication, accuracy and computational cost. They are assessed in terms of their ability to predict radiative heat transfer from one-dimensional, idealised representations of the internal structure of buoyant and jet fires.

Exact results can be obtained by line-by-line calculations of spectral absorption-emission lines of molecular gases. However, such calculations are useful in the study of radiative transfer in the atmosphere but are not practical for most engineering applications, and are therefore not discussed here. Narrow-band and wide-band models constructed from the spectral lines, and on a simpler level, the gray gas representation of the molecular spectrum can be considered. The simplest treatment for the case of enclosure fire is to consider the gas to be a gray gas of prescribed constant absorption coefficient.

Narrow Band Model

A well known narrow band model is that proposed by Grosshandler and Modak (GrosshandlerWL:1981), which is based on the statistical model by Goody (GoodyRM:1964) for tri-atomic molecules with equal line strengths within each narrow band region, and with homogeneous effects accounted for through the Curtis-Godson approximation which employs suitable averages along a line-of-sight. For hydrogen flame, the five gas bands of the H2O, the main combustion products in the infrared region (1-6 μm) are considered which are 1.14 μm, 1.38 μm, 1.87 μm, 2.7 μm and 6.3 μm. For flames involving mixtures of hydrogen and hydrocarbon (e.g., hydrogen flame diluted by CH4), band overlap is also taken into account for multiple bands and mixture of CO2, H2O, CO and CH4 gases, particularly for 4.3 μm of CO2, 2.3 μm and 3.3 μm of CH4, and 4.7 μm of CO.

Wide Band Model

Edwards and Balakrishnan (EdwardsDK:1973) developed a spectral version of exponential wide band model, which is based on the fact that the absorption and emission of radiation by a molecular gas is concentrated in between one and six vibrational bands. Within these bands, the spectral lines associated with rotational modes of energy storage are reordered in wave number space with exponentially decreasing line intensities moving from the band head. The band shape is then approximated by one of the three simple exponential functions, with radiative properties of each absorption band obtained from specified model parameters.

Grosshandler’s Total Transmittance, Non-Homogeneous (TTNH) Model

The total transmittance, non-homogeneous (TTNH) model for CO2 and H2O mixture is based on total transmittance data for homogeneous systems, with effective pressure-path lengths and temperatures for non-homogeneous systems taken as gas concentrations weighted averages along a line-of-sight (GrosshandlerWL:1980).

Mixed Gray Gas Model

The most popular mixed gray gas model for modeling combustion products (including soot) from fires is that proposed by Truelove (TrueloveJS:1976), which is based on representing the banded spectra of CO2 and H2O as a mixture of clear and gray gases. The total emittance of the combined emissions of the CO2 and H2O vapors was obtained by Truelove by fitting the spectral data of the gases as gray gas mixture of one clear and three gray gases.

Banded Mixed Gray Gas Model

Truelove’s mixed gray gas model, employing one clear and three gray gas representations, can be written in a banded form where, for a given model spectrum, the gray gas weightings are determined as the fractional amount of black body energy in the spectral regions where “gray gas absorption coefficients” exist (ModestMF:1991). Recently, Cumber and Fairweather (CumberPS:1999) have improved the method by incorporating CO and CH4 emissions. Expressing total absorptivity and emissivity of a gas in terms of the weighted-sum of gray gases are useful, especially for the zonal method of analysis of radiative transfer.

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Page last modified on February 18, 2009, at 02:28 PM