View factors fireball

The thermal radiation received from the fireball on a target is given by equation 9.1-31, where Q is the radiation received by a black body target (kW/m ) r is the atmospheric transmissivity (dimensionless), E = surface emitted flux in kW/m", and f is a dimensionless view factor. 

The heat flux, E, from BLEVEs is in the range 200 to 350 kW/m is much higher than in pool fires because the flame is not smoky. Roberts (1981) and Hymes (1983) estimate the surface heat flux as the radiative fraction of the total heat of combustion according to equation 9.1-32, where E is the surface emitted flux (kW/m ), M is the mass of LPG in the BLEVE (kg) h, is the heat of combustion (kJ/kg), is the maximum fireball diameter (m) f is the radiation fraction, (typically 0.25-0.4). t is the fireball duration (s). The view factor is approximated by equation 9.1-34. where D is the fireball diameter (m), and x is the distance from the sphere center to the target (m). At this point the radiation flux may be calculated (equation 9.1-30). 

A fireball is represented as a solid sphere with a center height H and a diameter D. Let the radius of the sphere be / (/ = DU). (See Figure 3.11.) Distance x is measured from a point on the ground directly beneath the center of the fireball to the receptor at ground level. When this distance is greater than the radius of the fireball, the view factor can be calculated. 

For a vertical surface beneath the fireball (jc < D/2), the view factor is given by... 

The total radiation received by an object also depends on the fireball s position relative to the object (i.e., the view factor) and radiation adsorption by the atmosphere. 

The solid-flame model, presented in Section 3.5.2, is more realistic than the point-source model. It addresses the fireball s dimensions, its surface-emissive power, atmospheric attenuation, and view factor. The latter factor includes the object s orientation relative to the fireball and its distance from the fireball s center. This section provides information on emissive power for use in calculations beyond that presented in Section 3.5.2. Furthermore, view factors applicable to fireballs are discussed in more detail. 

View Factor. The view factor of a point on a plane surface located at a distance L from the center of a sphere (fireball) with radius r depends not only on L and r, but also on the orientation of the surface with respect to the fireball. If 2 is the view angle, and 0 is the angle between the normal vector to the surface and the line connecting the target point and the center of the sphere (see Figure 6.9), the view factor (F) is given by... 

When the distance (X) is greater than the radius of the fireball, the view factor for... 

Radiation effects from a fireball of the size calculated above, and assumed to be in contact with the ground, have been calculated by Pietersen (1985). A fireball duration of 22 s was calculated from the formula suggested by Jaggers et al. (1986). An emissive power of 350 kW/m was used for propane, based on large-scale tests by British Gas (Johnson et al. 1990). The view factor proposed in Section 6.2.5. 

For a point on a plane surface located at a distance L from the center of a sphere (fireball) that can see all of the fireball (see Appendix A), the view factor (F) is given by (see Figure A-1) ... 

Estimate the geometric view factor on the basis of the fireball diameter and the position of the receptor using the relationships presented in Section 9.1.4, Section 3.5.2, or Appendix A. Also, tables presented in Appendix A can be applied. 

Estirrurte the geometric view factor. The center of the fireball has a height of 66.5 m, and thus the view factor (for a vertical object) follows from the relation given in Section 9.1.3 ... 

Figure A-1. View factor of a fireball. (A) Receiver sees" the sphere partially.

Fireballs are modelled as spheres radiating onto a plane receiver. Assuming that the fireball has not yet lifted from the ground the following view factors are... 

It is necessary, therefore, to know the value of the emissive power E ), the view factor (F), the atmospheric transmissivity (t), and the distance between the flame and the target. To know this distance, it is necessary to estimate the height at which the fireball is located. In fact, this height is a function of the specific volume and the latent heat of vaporization of the fuel therefore, strictly speaking, it varies with the substance. This is not usually taken into account. Diverse correlations have been proposed to estimate this height one of the most simple ones is the following ... 

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