A New Simplified PDF Method for Calculating Major Species Concentrations and Burning in Turbulent Fires

A simpl i fied method is presented for calculati ng mean major species concentrations (02' CO2, CO) in turbulent fires for any fuel given the species distribution of the same fuel in a laminar diffusion flame. This method, verified by extensive measurements, uses a probability d Iat r t bution function (Pdf) for the conserved scalar in turbulent fires together wi th a uniform mi xedness parameter throughout the flames, first proposed in this work. For minor species concentrations (e.g., NO x' soot) that also de pend on the local Kolmogorov straining rates of turbulence, the present method might be extended by including the distribution of turbulent straining rates in a fashion strongly suggested by recent evidence of soot-flame radiation and NO x yield in turbUlent diffusion flames. Finally, based on the present method, an integral model is outlined for turbulent buoyant jet flames. CHEMICAL SPECIES IN TURBULENT FIRES It is surprising that data obtained by L. Orloff(1) on mean major species concentrations in turbulent pool fires can be correlated with the mean corresponding mixture fraction independently of 1) location inside the f ire plume, 2) the total heat release rate, or 3) the diameter of the fire. Figure 1(a,b,c) illustrates this result notwithstanding the scatter close to the maximum concentration values. Figure 1 also Incl udea the corresponding data for the opposing laminar flame of Tsuji and Yamaoka(2). Plotting the experimental data in terms of the coordinates of Figure 1 implies 1) equal diffusivities and 2) chemical reactions unaffected by the straining action of the flowfield. The average elemental fraction or mixture fraction used as abscissa in Figure 1 is a conserved quantity in the fire and represents, for example, the ratio of car-bon at om mass at a given place relative to the carbon atom mass at the source l 1 J. If the previous assumptions are accepted, the results of L. Orloff(1) as illustrated in Figure 1 suggest the possibility of predicting the major species concentrations in turbulent fires by using a simple mixing and combustion model. First, we observe that turbulent buoyant flames generate large eddies that move rather lazily inside the fire plume. The visible Kolmogorov micr-oscale is about 1-2 em. The diffusivity is of order of 2 cm2;sec so that 9,2 the Kolmogorov time scale 'K D is of the order of a second. This time FIRE SAFETY SCIENCE-PROCEEDINGS OF THE SECOND INTERNATIONAL SYMPOSIUM, pp. 149-158 149 Copyright © International Association for Fire Safety Science scale is quite insensitive to the heat release rate or the flame s i z For common fuels, the reaction times are much smaller than the Kolmogor time scales characteristic for turbulent buoyant fires. It follows th the r e ac t l on zones are also much smaller than the Kolmogorov microsca and thus, the instantaneous diffusion flame structure is unaffected by t transient nature of the turbulent field.* In addition, experiments ha established that, away from extinction conditions, the chemical structu within laminar diffusion flames is quite insensitive to their loc straining rates or flow times, so that the concentration of major stab species is a unique function of the mixture fraction, I; : Y = Y (I; (cf with Figure 1). Therefore, we may conclude that in t3r~ulen€'hr the instantaneous concentration of a stable species should be equal to i value corre:sJPonding to laminar diffusion flame conditions. Such a simple relationship suggests that one can predict the mean speci concentrations in turbulent fires if the probability distribution, P(I; of the random varying value of the mixture fraction, 1;, is known, i.e. 1 f YS,L(I;) P(I;,~,~) dl; o where we assume that P(U is functionally dependent on the average val of I; and its mean square fluctuations ~. It is difficult to predict or measure the probability distribution fun tion of t(he) conserved scalar, 1;, notwi thstanding the recent advances this area 4. (Two areas not yet satisfactorily modeled are: a) t dissipation and mixing of a conserved scalar, and b) the velocity-co centration correlations u'I;'). Instead, we used a pdf for the conserv scalar having parameters that match measured_J2I' p~":-~~'?.t.-e_~) values of t mean mixture fraction ~ and its fluctuations 1;'2 = (I; ~ ~)2. In genera the pdf of a conserved scalar has the following form: