The B-numbers were then used in the flame spread model as described in Section 5 to predict the flame heights for both the bench-scale and large-scale cases. The mass-loss rate data were trimmed to contain only the time period where upward flame spread occurred along the sample, removing data prior to ignition of the sample and after the pyrolysis front has reached the top of the sample. By reviewing the video recordings and mass-loss data for a particular test, Figure 7 shows the period after ignition and the omitted period after the flame reached the top of the sample. The trimmed portion of the data was used to determine an average ˙m00f . After the mass-loss rate was trimmed, it was then fit with a 4th-order polynomial to obtain a smooth mass-loss curve; the 4th order fits exhibited at least a 99% R2 value for each of the mass-loss data sets.Figure 9 shows a schematic of the upward flame spread model from Sibulkin and Kim that was used to predict the flame heights as a function of the B-number. The pyrolysis zone is defined as the region of the solid fuel up to the pyrolysis height where combustible fuel vapors are outgassing. Some of the fuel burns directly in front of the combusting fuel surface, while some of the fuel is carried by buoyancy above its height of origin and burns above,grow bench which heats the virgin material in the preheat zone up to its ignition temperature. The fuel carried above the pyrolysis zone has been called excess pyrolyzate and forms the physical flame height in which the resulting heat output drives the flame spread process.
The rate of upward flame spread depends both on the amount of energy released by the combusting fuel and the rate at which the material pyrolyzes due to the flame heat flux, ˙q 00 . This energy feedback from the gas phase to the condensed phase is the driving mechanism for the flame spread process. The analytical model from Sibulkin and Kim was adapted and solved numerically by using heat flux profiles from previous correlations. The heat flux is assumed to be constant along the pyrolysis region up to the pyrolysis height, and the flame spread occurs in one-dimension along the sample. In the preheat region , the heat flux decays exponentially as a function of distance , which follows from the heat flux distribution mea-surements by Sibulkin and Lee. This heat flux condition is detailed in Eqs. 5a & 5b. Once the material in the preheat region reaches its pyrolysis temperature, it begins to outgas combustible vapors and the pyrolysis region grows, resulting in a larger flame height and more energy feedback to the unburned fuel; then the process repeats. Therefore, the process of upward flame spread can be thought of as a moving ignition front, similar to the leapfrogging process first described by de Ris. The results from the flame spread model were compared to the bench scale results by using the observed flame heights from the videos of each of the 9 tests. Figure 10 shows the flame heights for corrugated cardboard as predicted by the model versus the bench-scale flame heights from the experiments.
The flame height predictions for corrugated cardboard are in good agreement with the experimental flame heights. Figure 10 shows the flame heights for polystyrene as predicted by the model versus the bench scale flame heights from the experiments. The flame height predictions for polystyrene are in good agreement with the experimental flame heights at the bench-scale. The bench-scale predictions are in reasonable agreement with the experimental flame heights because the dominant mode of heat transfer in the tests was assumed to be laminar, natural convection on a vertical plate, and the same mode of heat transfer is assumed in the flame spread model as shown in Eq. 6. The thermal behavior of the fuel samples was considered to be a slab of finite thickness, and a more detailed analysis can be found in Overholt. The average B-number for corrugated cardboard was used in the large-scale flame spread predictions because it is non-dimensional and describes the mass flux for both the bench-scale and large-scale scenarios. Previous studies have shown that the B-number is not constant, but varies to some degree in both time and space. Spatial variation cannot be captured using the method discussed in this paper; however, a time-averaged B-number has been shown to be valid to predict flame heights. For the purposes of the large-scale, in-rack flame height predictions, the B-number was assumed to have a constant value of 1.7. The results from the flame spread model were then compared to the large-scale by using in-rack flame heights from the rack-storage warehouse fire tests.
The in-rack flame heights for the large-scale warehouse fires were obtained from video data from three large-scale warehouse commodity fire tests that were performed at Underwriter’s Laboratory in Northbrook, Illinois. The fuel consisted of paper cups that were packed in corrugated cardboard boxes and stacked between 6.1 m to 9.1 m in height in a rack-storage configuration. The boxes were ignited along the bottom edge in the flue space between the racks. Figure 11 shows a snapshot from a warehouse fire test as the flame spreads up through the flue space between the boxes. The flame spread model predictions for the in-rack flame heights were compared to experimental flame heights from the three large-scale UL tests described above, and the results are shown in Figure 12. The points on the graph indicate observations of experimental flame heights from three large-scale UL tests as extracted from the test videos. The spread in the flame height data may be caused by many factors including minor deviations in ignition and ambient conditions, especially the moisture content of the cardboard. The data still, however, present a representative range of realistic tests performed. The three dashed lines indicate the flame height predictions using the experimentally determined B-number for three different flame heat fluxes. To incorporate various modes of heat transfer that are present in the large-scale, three different values of the flame heat flux, ˙q 00 , were used in the flame spread model as described in Section 5. Case used a flame heat flux equal to 5.2 kW/m2 , Case used a heat flux equal to 80 kW/m2 , and Case used a heat flux equal to 27 kW/m2 . The flame heat flux that resulted in the best in-rack flame height predictions, Case , accounts for both convective and radiative heat transfer by using a radiation correlation based on heat transfer between two parallel plates as shown in Eq. 13a. This is the most representative of the fire conditions in the large-scale warehouse fire tests because the fire is ignited in the flue space between the commodity boxes and spreads upwards between the stack of commodity boxes. In this case, radiant energy feedback was occurring between the parallel fuel surfaces as the flames grew larger and increased the flame heat flux and the flame spread rate. The model shows good agreement for the initial stage of fire growth at the large-scale in which the primary fuel is the cardboard packaging of the cartons. Additionally, Figure 12 includes a comparison to several existing correlations to large-scale,plant nursery benches in-rack flame heights and corrugated cardboard flues for comparison. Alvares et al.performed experiments on the impact of separation distance between parallel panels of corrugated cardboard on the in-rack flame height as a function of time and presented a correlation, xf = 0.24e, where d is the separation distance between the panels.
This correlation is shown as a dotted line in Figure 12 where the separation distance was fixed as 0.015 m, as was present in the UL tests. Flame heights between solid sheets of cardboard are significantly lower than rack-storage test data, which may have been caused by different types of cardboard or the greater oxygen entrainment in the rack-storage configuration due to additional side flues that increased the heat flux in the center flue and, therefore, flame heights and flame spread rates. This supports the contention that this correlation is based on geometry, not the fuel, and is still appropriate in this case. To compare this in-rack flame height correlation to the results of this study as a function of time, the heat release rates of full-scale rack storage experiments have been used in the comparison. Exponential fits to rack-storage data agree best with the present flame height data, and a correlation of heat release rates by Ingason to 4-tier, double tri-wall corrugated board, Q = 2.266e 0.102t , which is shown as a dashed line in Figure 12. A range of other experimental correlations are available in Zalosh where polystyrene chips represent the worst-case scenario, and the corresponding flame height is shown as a dash-dot line in Figure 12. The slowest advancing case shown in Zalosh , which is Prototype class II and is only 2 tiers high, does not appear in Figure 12. Although the present curves do fall within the range of the observed in-rack flame heights, heat release data for full-scale tests as tall as the UL tests was not found by the authors in the available literature, which reinforces the need for more universal correlations that do not necessitate new full-scale tests to predict results whenever a parameter is modified. One must remember that these data were derived directly from experimental tests performed at UL, whereas the modification of the Sibulkin and Kim model match the data due to experimental parameters that can be measured at the small scale. In this study, a bench-scale method was used to experimentally determine the average B-number of a given material, and the results from the bench scale tests were then used to model flame heights in the flue space during a warehouse test with commodity stacked up to a height of 9.1 m . The flame spread model that showed the best agreement with the large scale experimental flame heights used the flame heat flux that incorporates both convective heat transfer and a correlation for radiative heat transfer between parallel plates. Therefore, using this bench-scale B-number calculation method, the processes of heat transfer and mass transfer were coupled and expressed independently of one another, which enabled the extrapolation of the mass-loss rates from the bench-scale tests to the early stage of the large-scale warehouse conditions. The B-number was obtained from bench-scale experiments where the flow conditions were mostly laminar and could be controlled to better understand the effects of material properties. Three different flow conditions were used to model heat transfer in the large scale, and the in-rack flame heights were compared to previous experimental correlations by using large-scale commodity fire test data. Additionally, because the soot yield is non-dimensional, intrinsic to a given material, and can be measured at the bench-scale, it can be a useful parameter to model the radiation effects at the large-scale. As Ys increases, the radiant feedback from the gas phase combustion to the fuel increases, which results in an increased rate of flame spread. Future work involves more understanding of the physical interaction between multiple material samples to quantify the effects of a mixed commodity on the overall flame spread process. This method has demonstrated that the B-number can be determined from bench-scale test methods and utilized in flame height predictions that are valid in large-scale fires. In future work, the soot yield can also be determined from bench-scale tests and incorporated into the model. This is important because the flammability of a commodity is coupled with the upward flame spread process, which is the most significant hazard in a warehouse storage fire, and the B-number and soot yield seem to describe the process well for the vertical flue space in the warehouse scenario. A framework has been demonstrated for which the results from bench-scale tests can be used to predict large-scale flame heights of single fuels at the large scale. If the pyrolysis rate of the fuels is effectively described by the B-number in CFD codes, then the flow conditions for more complex geometries may be more easily resolved, which highlights the potential applications of this work in the future.