Radiation model

The emission model is based on the following assumptions (1) the lamp has an extension given by its used length (Z ) and its radius (Rl), in this extension, emitters are uniformly distributed. (2) Each elementary volume of the lamp is an emitter. The specific intensity associated with each bundle of radiation coming from each emitter, at each wavelength, is spherical. 

According to Cassano et al. (1995), knowing the value of the specific intensity at each point, the value of the Incident Radiation 

In the double integral Q accounts for the lamp length and (f for fhe lamp diamefer. The infegrafion limifs are given by Equations (24)-(26). 

Finally, af any poinf inside fhe annular reaction space, the LVRPA is 

Equation (48) has to be inserted into Equations (38) and (39) to provide the reaction rates for Equation (41). 

---

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. 

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... 

This section covers radiation due to BLEVEs with accompanying fireballs. First, a brief description is given of experimental investigations of BLEVEs and their fireballs. Next, some fireball models, primarily for predicting fireball diameter and combustion duration, are presented. Most of these models evolved from experimental results. Finally, some radiation models, based on experiments and theory, are given. 

TABLE 9.1. Radiation on a (Vertical) Receptor from a 6000-gallon Propane Tank Truck BLEVE Calculated with Solid Flame and Point Source Radiation Models... 

The black body radiation model for the continuum radiation from stars works well but it is not quite right. Careful consideration of the radiation profile shows deviations from the curves shown in Figure 2.1 due to the structure of the star itself. These deviations form the basis of a more detailed analysis including the effects of circulation within the star and will be left to others to explain we shall use black body radiation as our model for stars. 

The rest of the paper is organized as follows. In the next three sections, details of the LES models, the soot and radiation models, and the computational details are presented. The key results of the study follow. The conclusions of the study are then summarized. 

Raman spectra were obtained on a Coberg PHO Raman spectrometer equipped with a Coherent Radiation Model 52B Ar laser using 800-1200 mW of power from the 488.8-nm line a small twoprism monochromator was used to remove Imck-ground plasma lines. 

S. A. Ramsden P. Savic, "A Radiation Model for the Development of Laser-Induced Spark in Air , Nature 203, 1217-19(1964) (Reprint of National Research Council of Canada, Ottawa, Ontario) (In the course of recent work on the spark produced in air... 

Note that the employed definition of a system contains an important asymmetry between the system and the external world. The system s description includes the influence of the external forces on the system, but not the reverse, the influence of the system on the outside world. From a mathematical viewpoint the equations that describe the system s behavior contain the external forces, but the latter have to be taken from information outside the model. As will been shown, the specific hierarchy between system and outside world can often (but not always) be justified based on the respective strength of the interactions. Take the system of the earth. Solar radiation is a very strong driving force for the earth, but the back-radiation from the earth to the sun is so tiny that nobody would want to include it as a feedback mechanism in a radiation model of the sun. 

Such radiation models have been in permanent development over the last 30 years, and the published results may be classified in two main categories incidence models which may be characterized by mathematical models assuming the existence of a given radiant energy distribution in the vicinity of the reactor, and emission models in which lamp characteristics, reaction, and flow processes are taken into account. 

Zerefos C.S., Factors influencing the transmission of solar ultraviolet irradiance through the Earth s atmosphere, in Solar Ultraviolet Radiation, Modelling, Measurements and Effects, edited by C.S. Zerefos and A.F. Bais, pp. 133-142, NATO-ASI Series, vol.52, Springer Verlag, 1997. 

Bais A. F. (1997) Spectrometers Operational errors and uncertainties, in C. S. Zerefos and A. F. Bais (eds,), Solar Ultraviolet Radiation Modelling, Measurements and Effects, NATO AS1 Series, Series 1 Global Environmental Change, Springer-Verlag, VoL 52, pp. 163-173. 

L (70,000 gal). For tanks greater than 266,000 L (70,000 gal), the minimum distance to property lines or buildings shall be 0.7 times the container diameter, but not less than 30 m (100 ft). NFPA 59A also requires that the impoundment area be located to prevent the heat flux from a fire from exceeding certain levels at the property line. The model used to calculate heat flux is described in the Gas Research Institute report GRI0176, LNGFIRE A Thermal Radiation Model for LNG Fires [5.18]. NFPA 59A also recommends that provisions be made to minimize the chance that flammable vapor clouds produced from an LNG spill will reach the property line. The flammable vapor cloud... 

LNGFIRE A Thermal Radiation Model forLNG Fires, Repot GRI0176, Gas Research Institute, Chicago, 111. 

In the case of stacks, radiation plays an even more role important than in the case of a single cell. In fact, in addition to differences in the axial temperature gradients there are differences between the operating temperatures of adjacent cells. A detailed explanation of a radiation model is proposed in the last section. 

Perez R., Stewart R., Arbogast C., Seals R., Scott J., An anisotropic hourly diffuse radiation model for sloping surfaces description, performance validation, site dependency evaluation. Solar Energy 1986 36 481M97. 

CFD fire models can be classified based on many different criteria, with RANS vs. LES being probably the most widely used. Other possibilities would be the type of radiation model, availability, price, user interface, and hardware requirement. All these aspects have been discussed in the review paper of Olenick and Carpenter [6],... 

In enclosure fires, radiation may be the dominant mode of heat transfer. For flames burning in an open atmosphere, the radiative fraction of overall heat transfer ranges from less than 0.1 to 0.4, depending both on the fuel type and the fire diameter [45], Owing to the important role that radiation plays in fires, all fire CFD models have a radiation model that solves the radiation transport equation (RTE) [46,48] ... 

Two physical aspects of thermal radiation make radiation modeling particularly challenging ... 

This type of model works well at high applied heat flux levels, where the pyrolysis front is thin. Simplicity is its advantage it is not necessary to specify any parameters related to the decomposition kinetics. A large body of flame spread modeling work has applied this type of model, but there is a tendency to focus with great detail on gas-phase phenomena (i.e., full Navier-Stokes, detailed radiation models, multistep combustion reactions) and treat the condensed-phase fuel generation process in an approximate manner. 

Zhang, J., Dembele, S., Karwatzki, J., and Wen, J.X. Effect of radiation models on CFD simulations of upward flame spread. In Gottuk, D.T. and Lattimer, B.Y. (eds.) Proceedings of Eighth International Symposium on Fire Safety Science, September 18-23. Beijing, China International Association for Fire Safety Science, 2005, pp. 421 132. 

---