Emissive power

We consider an element of the surface of a radiating body, that has a size of dA The energy flow (heat flow) d E , emitted into the hemisphere above the surface element, is called radiative power or radiative flow, Fig. 5.2. Its Si-unit is the Watt. The radiative power divided by the size of the surface element 

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E = hemispherical emissive power of a blackbody. f = fraction of blackbody radiation lying below X. 

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 first and second Planck-law constants c and C9 are respectively (3.740)(10- ) (Jm )/s and (1.4388)(10- ) m K. The term clearly a function only of the product XT, is given in Fig. 5-11 which may be visualized as the monochromatic emissive power versus wavelength measured in vacuo of a black surface at 1 K discharging in vacuo. 

An additional surface arrangement of importance is a single-zone surface enclosing gas. With the gas assumed gray, the simplest derivation of GSi is to note that the emission from surface Ai per unit of its blackbody emissive power is Ai i, of which the fractions g and (1 - G)ei are absorbed Dy the gas and the surface, respectively, and the surface-reflected residue always repeats this distribution. Therefore,... 

An external combustion engine that has been widely supported as a low-emission power source is the Rankine cycle steam engine. Many different types of expanders can be used to convert the energy in the working fluid... 

The factory-produced, dedicated NGV is the ultimate goal of the NGV industry because it will reduce the incremental cost of the vehicle, the fuel system will be belter integrated into the vehicle, and the vehicle performance can be optimized for natural gas. A dedicated NGV s emissions, power, and driveability can be superior to a comparable gasoline vehicle. There is however, a reluctance by some automobile manufacturers to produce dedicated NGVs until the refueling infrastructure is more fully developed. 

Wooden sticks affected by radiation from the fireball permitted an estimate of the radiation levels emitted. It was thus established that the emissive power of the LPG cloud was approximately 180 kW/m (16 BTU/s/ft ). 

Emissive power is the total radiative power leaving the surface of the fire per unit area and per unit time. Emissive power can be calculated by use of Stefan s law, which gives the radiation of a black body in relation to its temperature. Because the fire is not a perfect black body, the emissive power is a fraction (e) of the black body radiation ... 

Duiser (1989) calculates emissive power from rate of combustion and released heat. As a conservative estimate, he uses a radiation fraction (/) of 0.35. He proposed the following equation for calculating the emissive power of a pool fire ... 

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). 

E = emissive power of emitting surface 2 = incident radiation receiving surface... 

In order to compute the thermal radiation effects produced by a burning vapor cloud, it is necessary to know the flame s temperature, size, and dynamics during its propagation through the cloud. Thermal radiation intercepted by an object in the vicinity is determined by the emissive power of the flame (determined by the flame temperature), the flame s emissivity, the view factor, and an atmospheric-attenuation factor. The fundamentals of heat-radiation modeling are described in Section 3.5. 

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. ... 

The fundamentals of thermal radiation modeling are treated in Chapter 3. The value for emissive power can be computed from flame temperature and emissivity. Emissivity is primarily determined by the presence of nonluminous soot within the flame. The only value for flash-fire emissive power ever published in the open literature is that observed in the Maplin Sands experiments reported by Blackmore... 

Four parameters often used to determine a fireball s thermal-radiation hazard are the mass of fuel involved and the fireball s diameter, duration, and thermal-emissive power. Radiation hazards can then be calculated from empirical relations. For detailed calculations, additional information is required, including a knowledge of the change in the fireball s diameter with time, its vertical rise, and variations in the fireball s emissive power over its lifetime. Experiments have been performed, mostly on a small scale, to investigate these parameters. The relationships obtained for each of these parameters through experimental investigation are presented in later sections of this chapter. 

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 )... 

Experiments show that emissive power depends on fireball size. Moorhouse and Pritchard (1982) present a graph of the relationship of fireball size and emissive power from results obtained by several investigators, among them, Hasegawa and Sato data from both 1977 and 1987. Figure 6.8 presents the Moorhouse and Pritchard (1982) graph to which the data from Johnson et al. (1990) have been added. 

The emissive power of a fireball, however, will depend on the actual distribution of flame temperatures, partial pressure of combustion products, geometry of the combustion zone, and absorption of radiation in the fireball itself. The emissive power ( ) is therefore lower than the maximum emissive power (E ) of the black body radiation ... 

The curve, however, seems to indicate the tendency of a fireball s emissive power to rise as its diameter grows. The results of the experiments described above reveal that the fireball properties of greatest influence on radiation effects are ... 

Figure 6.8. Influence of fireball diameter on emissive power. (--) predictive curve for meth-...

Reference Containment Fuels Fuel Mass m, (kg) Fireball Duration tc(s) Fireball Diameter Oc(m) Emiss. Power kW/m2... 

When the four previous equations are combined with the relation for the initial diameter of the sphere (Dq) [Eq. (6.2.6)], the fireball s temperature and maximum diameter can be calculated. From this model, it follows that the temperature of the fireball, and thus its emissive power, is independent of initial fuel mass. 

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. ... 

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. 

Additional experiments should be performed on a large scale to establish the emissive power of fireballs generated by BLEVEs. The effects of flammable substances involved, fireball diameter, and initial pressure should be investigated. 

The heat radiation received by an object depends on the flame s emissive power, the flame s orientation with respect to the object, and atmospheric attenuation, that is... 

Experimental data on the emissive power of flash fires are extremely scarce. The only value available is 173 kW/m for LNG and propane flash fires. Geometric... 

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