Surface emissive power

The emissive power of a surface is the flux density (energy per time-surface area) due to emission from it throughout a hemisphere. If the intensity 7 of emission from a surface is independent of the angle of emission, Eq. (5-iii) may be integrated to showthat the surface emissive power is TC7, though the emission is throughout 2% sr. 

The surface-emissive power of a propane-pool fire calculated in this way equals 98 kW/m (31,(XX) Btu/hr/ft ). The surface-emissive power of a BLEVE is suggested to be twice that calculated for a pool fire. 

The surface-emissive powers of fireballs depend strongly on fuel quantity and pressure just prior to release. Fay and Lewis (1977) found small surface-emissive powers for 0.1 kg (0.22 pound) of fuel (20 to 60 kW/m 6300 to 19,000 Btu/hr/ ft ). Hardee et al. (1978) measured 120 kW/m (38,000 Btu/hr/ft ). Moorhouse and Pritchard (1982) suggest an average surface-emissive power of 150 kW/m (47,500 Btu/hr/ft ), and a maximum value of 300 kW/m (95,000 Btu/hr/ft ), for industrialsized fireballs of pure vapor. Experiments by British Gas with BLEVEs involving fuel masses of 1000 to 2000 kg of butane or propane revealed surface-emissive powers between 320 and 350 kW/m (100,000-110,000 Btu/hr/ft Johnson et al. 1990). Emissive power, incident flux, and flame height data are summarized by Mudan (1984). 

Radiation effects, as well as combustion behavior, were measured. LNG and refrigerated liquid propane cloud fires exhibited similar surface emissive power values of about 173 kW/m. ... 

Table 6.2 presents an overview of surface-emissive powers measured in the British Gas tests, as back-calculated from radiometer readings. Peak values of surface-emissive powers were approximately 100 kW/m higher than these average values, but only for a short duration. Other large-scale tests include those conducted to investigate the performance of fire-protection systems for LPG tanks. 

TABLE 6.2. Average Surface-Emissive Powers Measured in the Tests Performed by British Gas ... 

Test No. Fuel Mass (kg) Release Pressure (bar) Average Surface-Emissive Power (kWIm )... 

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. 

Emissive Power. Pape et al. (1988) used data of Hasegawa and Sato (1977) to determine a relationship between emissive power and vapor pressure at time of release. For fireballs from fuel masses up to 6.2 kg released at vapor pressures to 20 atm, the average surface-emissive power E can be approximated by... 

This equation is limited to vapor pressures at release time at or below 2 MPa, and thus to surface-emissive powers at or below 310 kW/m. ... 

The surface-emissive power E, the radiation per unit time emitted per unit area of fireball surface, can be assumed to be equal to the emissive powers measured in full-scale BLEVE experiments by British Gas (Johnson et al. 1990). These entailed the release of 1000 and 2(XK) kg of butane and propane at 7.5 and IS bar. Test results revealed average surface-emissive powers of 320 to 370 kW/m see Table 6.2. A value of 350 kW/m seems to be a reasonable value to assume for BLEVEs for most hydrocarbons involving a vapor mass of 1000 kg or more. 

Emissive power The total radiative power discharged from the surface of a fire per unit area (also referred to as surface-emissive power). 

The HSE report states that analysis of damage at the Meissner control building at 13.4 m from the manway source indicated that at this building the jet flame was 4.7 m diameter. The jet lasted some 25 seconds and had a surface emissive power of about 1000 kW/m2. The temperature at 6 m from the manway would have been about 2300°C. 

The surface emissive power of a fireball is usually assumed to be in the range 150-300 kW/m. Values for LPG of 270 kW/m for releases below 125 tons and 200 kW/m for larger releases have been used in the UK. Experimental measurements of average surface emissive power of butane fireballs have been reported as 300-350 kW/m (Spouge, 1999). Uncertainty in determining the surface emissive power accounts for much of the inaccuracy in fireball modeling. 

Radiation that is emitted by the surface originates from the thermal energy of matter bounded by the surface. The rate at which energy is released per unit area Wjvr ) is determined by the surface emissive power E. For a blackbody the emissive power (representing a theoretical maximum rate) is prescribed by the Stefan-Boltzmann law ... 

The surface emissive power (SEP) for a cylindrical flame is calculated as follows... 

In Eq. (10.130) is the maximum surface emissive power of a flame without soot production in W/m, fs the fraction of the combustion energy radiated from the flame (fs = 0.4 is considered to be a conservative value), and L the flame length, which is either equal to Li according to Eq. (10.125) or equal to L2 according to Eq. (10.126) (see above) r is the pool radius in m. In addition we need the surface emissive power of soot... 

In Eq. (10.132) is the actual surface emissive power in W/m and empirical fraction of the flame surface covered by soot. For oil products = 0.8 is an appropriate value. 

In order to determine the impact on the surroundings the surface emissive power of the fire has to be known. According to [37] q" , = 173 kW/m is an appropriate value. 

An important parameter for determining the damage caused by a fireball is its specific surface emissive power ( SEP ), at least if the object to be protected is not inside the ball and hence directly exposed. The model used here is the solid flame model. According to [39] the result of the calculation strongly depends on how the SEP is defined and measured. In [2] a low value of 141 kW/m and a maximum value of 450 kW/m are quoted [37] indicates a range from 320 kW/m to 350 kW/m. In view of these values the use of a value of = 350 kW/m for the SEP is recommended. 

The mechanism of vessel failure appears to be a two-step process The formation of an initiating overpressure crack in the high-temperature, vapor-wetted walls of the vessel, followed by the final catastrophic unzipping of the containment and a nearly instantaneous release of its contents. The distribution and hashing of the lading causes a fireball if the contents are flammable. The failure of the vessel and the surface emissive power of the BLEVE fireball do not appear to be directly related to the superheat of the contents at failure and indeed may be most severe for conditions when the vessel fails while undergoing a pressure reduction at low superheat. 

Fireball characteristics—size, duration and surface emissive power (SEP)—should therefore be functions not only of the mass of the liquid involved (Roberts, 1982) but also the time delay from the LBB initiator to the final LOC and whether the LOC occurs with the contents still increasing in pressure and prior to the liquid contents becoming homogeneous. If vessel LOC occurs with a stratified liquid layer and a subcooled core under increasing pressure, the flreball should be less buoyant and have an appreciable flash fraction and/or rainout and thus a lower SEP than in a case with dropping pressure and therefore homogeneous boiling. 

TABLE 21.4 Fireball Surface Emissive Powers (SEP), Duration and Size... 

Burning rate, flame height, flame tilt, surface emissive power, and atmospheric transmissivity are all empirical, but well established, factors. The geometric view factor is soundly based in theory, but simpler equations or summary tables are often employed. The Stefan-Boltzmann equation is frequently used to estimate the flame surface flux and is soundly based in theory. However, it is not easily used, as the flame temperature is rarely known. 

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