A particular con- figuration considered in this study is upward flame spread in the flue space between corrugated cardboard, which is typical of warehouse storage arrangements. The model was extended to account for both convective and radiative heat transfer by incorporating convective and radiative heat transfer correlations. This segregated approach effectively uses a non-dimensional parameter to represent the mass transfer processes, the gas phase heat transfer by including an appropriate convective heat transfer correlation, and radiative heat transfer effects that are based on previous studies.Previous studies have attempted to model some of the large-scale effects of warehouse fires by measuring the relevant parameters using bench-scale test methods. One such effort by Hamins and McGrattan constructed single cell replicates of a Group A plastic commodity. The purpose of the Group A plastic tests was to provide input parameters into a computational fluid dynamics model using a measured heat release rate as the thermal loading input for a large-scale warehouse fire. The model predictions were unable to describe the detailed fire growth in storage applications. Several studies have addressed the issue of upward flame spread on corrugated cardboard surfaces. Grant and Drysdale modeled the flame spread along corrugated cardboard during the early growth stages of a warehouse fire by adapting the linearized Satio, Quintiere, and Williams flame spread model with Karlsson’s burnout length and solving numerically. Dimensional parameters that were obtained experimentally were used as inputs to numerically model the flame height, velocity of the flame front, and pyrolysis front progression as a two-dimensional problem. Good agreement between the experimental results and the numerical results were obtained,industrial drying racks although the model was found to be sensitive to averaged input parameters, such as the forward heat flux from the flame.
Alvares et al. studied the effects of panel separation on vertical flame spread and mass-loss rates in small-scale corrugated cardboard tests to determine the rate of fire growth along vertical flues in warehouses. Continued efforts by Ingason and de Ris and Ingason have identified the importance of the commodity configuration, the mode of heat transfer, and the flue spacing of commodity boxes in warehouse fires. Ingason’s work identified some of the dominant factors in the large-scale warehouse fire growth process, and emphasized the importance of separating the material properties of the fuel from the heat transfer and flow conditions that can result due to the various configurations of the fuel packages. Experimental correlations of rack-storage fires are available in previous literature, including heat release rates, boxed in-rack flame heights, in-rack plume temperatures, and heat fluxes. In separating the warehouse fire problem into two distinct phenomena, it then becomes a problem of defining the material properties , flow conditions , and heat transfer . Work performed by de Ris and Orloff [15], de Ris et al. [16], Foley [17], and Foley and Drysdale [18]served to characterize the mode of heat transfer from an upward propagating flame in a warehouse configuration and to quantify the convective and radiative heat transfer that drives the upward flame spread process in the gas phase. Variations in the heat transfer from the small-scale to the largescale was shown by de Ris et al. [16] to be related by similarity effects that are present in buoyant, turbulent boundary layer flows. This result can be used to extend the analytical results that were developed for heat and mass transfer in laminar boundary layers to turbulent boundary layers. In the early stages of a warehouse fire, before the fire sprinklers are activated, the mass transfer is intrinsically coupled to the material properties of the stored commodity, packing material, and outer corrugated cardboard covering. Due to the different burning behavior of each material, which is also a function of the packing and orientation, the problem of classifying a commodity based on its fire hazard is a complex one.
A general approach for describing the heat, mass, and momentum transfer by way of differential equations for simple geometries such as a droplet, flat horizontal, and vertical plate are discussed extensively in previous fire literature.As explained in a recent publication, a number of improved laminar boundary layer types of theories result in formulas that are more complicated than Eq. 3, but the results are qualitatively the same. In larger tests that were previously performed, the fluctuating flames and the incipient turbulence raise questions about the degree of applicability of such theorems. For these reasons, this simple description of the mass transfer, Eq. 3, was chosen in this study over other relevant expressions. In this study, the B-number is primarily a function of the material properties of a given fuel and it is obtained in a controlled experimental environment by assuming that the primary mode of heat transfer at the bench-scale is convection. This assumption is reasonable for the small, laminar flames observed in this study. In examining Eq. 2, the B-number can be considered to be a ratio of the available energy to the energy required to gasify a given fuel . Thus, the B-number is intrinsic to the properties of a material and is therefore independent of a particular scale. This allows for the results from the bench-scale tests to be used as a material input for the prediction of large-scale warehouse fire behavior. Figure 3 shows a schematic of the experimental setup. A total of 9 tests were conducted using two different samples: single-wall corrugated cardboard and polystyrene . The samples measured 5 cm wide by 20 cm in height. This aspect ratio was selected because laminar flames were the primary focus of the bench-scale tests due to the more controllable environment for isolating material properties and separating gas-phase phenomena, and upwardly-spreading flames typically become turbulent above 20 cm, which is accounted for in a later section when large-scale warehouse fires are considered.
For the bench-scale tests, a transition to a turbulent regime was not considered for simplicity, which agreed with visual observations. For this study, the sample width was fixed at 5 cm to minimize the amount of variance between the tests and because a smaller sample size may affect the amount of combustible gases generated by the fuel due to significant diffusion of the fuel to the sides of the sample. The typical mass of the samples was 4 g for corrugated cardboard and 36 g for polystyrene. Corrugated cardboard and polystyrene were chosen to be tested because they are the components of a Group A plastic commodity that is used to represent a worst-case fire scenario in large-scale warehouse tests. Additionally, corrugated cardboard is typically the first item to ignite and sustain flame spread in a warehouse fire. The measured quantities for each test included the mass-loss rate, flame height, and pyrolysis height. The corrugated cardboard used in these tests was identical to the con- figuration and thickness that is used to package standard Group A plastics, and of the same type used in the small-scale tests that were performed by the authors in Part I. The corrugated cardboard samples were of a type ‘C’ flute with a nominal thickness of 4 mm and 135 flutes per meter width [37] as shown in Figure 4. All of the tests were performed with the flutes aligned vertically along the 20 cm dimension,commercial greenhouse benches which is similar to the orientation of the flutes in an upright commodity box. The polystyrene samples were 3 mm thick as shown in Figure 4. The mode of ignition for the tests was a small aluminum tray measuring 5 x 0.5 x 0.5 cm that was placed at the base of the sample and contained a thin strip of glass fiber insulation soaked with n-heptane. This ensured a uniform mode of flaming ignition along the base of the fuel sample. The corrugated cardboard tests used 0.25 mL of n-heptane for ignition, whereas the polystyrene tests used 0.75 mL of n-heptane because it took a longer time for the polystyrene samples to ignite. After initial ignition of the n-heptane, the n-heptane typically burned out within 5-10 seconds and only served to ignite the fuel sample uniformly along the bottom edge. All of the fuel samples were insulated on the back and sides with 0.64 mm thick fiberboard insulation to isolate the burning to the front face of the samples only. The samples were secured in place by the insulating fiberboard sheets that were supported by four metal screws attached to the 1.9 cm thick fiberboard base .
All of the corrugated cardboard tests burned to completion and self-extinguished once the fuel was depleted. The polystyrene samples were manually extinguished after the flame reached a pyrolysis height of about 10 cm due to excessive smoke production and dripping on the bench-scale apparatus. However, the dripping and deformation of the polystyrene was not considered to be significant during the time frame considered in the results because the sample size in the experiment was small, and a significant accumulation of melted polystyrene was not observed during this time period. The mass lost by the specimen was measured continuously using a load cell with an accuracy of ± 0.5 g as specified by the manufacturer. This is approximately 12% of the nominal initial mass of the corrugated cardboard samples and 2% of the nominal initial mass of the polystyrene samples. To measure the flame heights and record the burning history of the tests, video and still images were captured using a Sony Handycam HRR-SR5 model camera and a Canon EOS-5D digital single-lens reflex camera. Figure 5 depicts a visual time history of the vertical flame spread along a corrugated cardboard sample. The images were then loaded onto a computer, and a MATLAB image processing script was used to visually determine the flame heights as a function of time from each test. The flame height was defined as the tip of an attached yellow flame and was selected visually from each picture by using the script. The processed images and resulting flame heights were consistent with visual comparisons from the test videos. Similar to the flame heights, observations of the visual charring on the corrugated cardboard was used to determine the location of the pyrolysis front. For the polystyrene samples, visual bubbling and charring from the video were used to determine the location of the pyrolysis front. The corrugated cardboard and polystyrene tests were fairly repeatable, and the heights of the pyrolysis front in the laminar regime were fairly similar; thus, a best-fit functional approximation of the pyrolysis heights was made. This approximation was later used to determine an average mass-loss rate per unit area , and finally, a B-number was calculated for each test. After the maximum pyrolysis height was reached, a constant height of 20 cm or 10 cm was assumed, which represents the entire surface of the front face of the sample. The results described in this section are based on a total of 9 bench scale tests that were performed using the two samples that were discussed in Section 3. After ignition along the base of the samples, the flame spread in the upward direction along the fuel samples. Due to edge effects along the fuel sample, a small amount of two-dimensional flame spread occurred in the experiment. As the excess pyrolyzate burned above the pyrolysis zone, the unburned fuel above the pyrolysis zone was heated to its ignition temperature and the flame spread in the upward direction at an increasing rate. As described in Section 3, the mass-loss rates were trimmed to the time period during upward flame spread along the samples. During the period of upward flame spread, the average value of ˙m00f for corrugated cardboard was within a range of 7.3 − 7.9 · 10−4 g/cm2 –s, and for polystyrene was within a range of 6.7−6.8·10−4 g/cm2 –s. Figures 6 & 6 show the flame heights that were measured in the bench-scale experiments for corrugated cardboard and polystyrene and the least-squares fit to the pyrolysis height that was used to determine the area burning, and later the average B-numbers for the corrugated cardboard and polystyrene samples. Using an average value from all of the tests that were performed on a given material sample, the B-number for corrugated cardboard was calculated to be 1.7 and for polystyrene was calculated as 1.4 .