Application of Scale Fire Modeling

Issue 75: Application of Scale Fire Modeling

By Lee K. McCarthy, James G. Quintiere, Ph.D., Lenwood S. Reeves, Andrew J. Wolfe

Applications of scale modeling are common among many engineering disciplines such as the design and analysis of aircrafts, ships, vehicles, and bridges. The use of scale modeling for fire applications has been explored by fire researchers for many years, resulting in the successful development of correlations for a wide range of fire phenomena.¹ As with other disciplines, the main advantages to scale fire modeling include the ease, cost, and feasibility of construction.

Recently, interest in scale fire modeling has increased in the fire investigation community.^2,3 A series of full scale experiments were completed in 2008 at the Bureau of Alcohol, Tobacco, Firearms and Explosives (ATF) Fire Research Laboratory in Beltsville, MD (Figure 1). These experiments were designed to examine the fire dynamics of ventilation-limited compartment fires in a scenario often encountered by fire investigators: fire growth in a furnished bedroom. During these experiments, temperature, heat flux, gas species, and video data were collected, which provided a unique opportunity to explore a new scaling technique for a realistic growing fire. Based on the 2008 full scale experiments, quarter (¼) scale experiments were designed and completed in 2011 (Figure 2), pushing the envelope of scaling by exploring fire growth in a furnished room.⁴

Figure 1. 2008 Full Scale Tests Experiments

Figure 2. 2011 Quarter Scale Experiments

Scaling Theory
In order to properly use scale modeling to gain understanding of the fire phenomena in full scale structures of interest, it is necessary to understand the underlying scaling theory to identify and include the important variables. Due to the complex and multivariable nature of fire, it is not possible to get perfect or complete scaling. Therefore, the fire dynamics must be appropriately represented through partial scaling. This can quickly become a difficult endeavor with complex geometries and fuel packages.

Partial scaling is achieved by assessing the governing conservation equations (e.g. mass, momentum, energy, and species) and selecting the appropriate dimensionless groups to keep consistent between the full scale and small scale experiments. These dimensionless groups are determined by deciding which aspects of the fire behavior are priorities for the particular scenario. In other words, the scaling of the heat transfer, fluid flow, and burning rate cannot all be perfectly matched, but one can decide to try to scale the fire power and heat losses in order to maintain the same temperature and species concentrations at similar times for the model and full scale. More detailed description of scaling theory and previous variations, including applications of Froude scaling which were used in these experiments, are provided by Quintiere^1,5 and Carey.²

While the fire growth in a furnished bedroom is a common scenario among fire investigators, it is difficult to scale such a fire. To explore this, a new scaling methodology based on the principles of Froude scaling was used to complete quarter scaled experiments at the ATF Fire Research Laboratory in 2011. Quarter scaling implies that the ratio of a length scale (l) in the model to that of the full scale is one to four (1^m/1^FS = 1/4). Froude scaling requires that the fire power and heat loss follow or 1^5/2 or (1^m/1^FS)^5/2, but this cannot be achieved for a growing fire due to conflicting behavior of radiation and convection. The criterion for scaling for these experiments was decided based on previous work, understanding of fire behavior, as well as the ease of construction and convenience. The requirements for the quarter scale model included:

1. Scaling the dimensions, openings, and objects geometrically [1¹]
2. Maintaining the same materials and same thicknesses of construction and contents [1⁰]

In order to meet both of the above requirements, the full scale material thicknesses were contained within the geometric boundaries of the quarter scale objects as much as possible. Keeping all of the materials the same allows for the heat transfer and burning to be the same over time, given the same heat flux.

The overall layout of the bedroom and location of instrumentation that was included in both the full scale and quarter scale experiments are displayed in Figure 3. For both series of experiments, the fire was ignited in the trash can next to the chair in the rear of the compartment.

Figure 3. General room layout with instrumentation locations. (Note: THF = Total Heat Flux Gauge, GS = Gas species, TC = Thermocouple)

Results
A comparison of the longest duration full scale (FS3) and quarter scale (QS2) experiments demonstrated that this scaling approach provided a practical means of conducting scaled experiments, similar overall fire progression, and a means of predicting specific relationships among the variables measured.

Table 1 lists a comparison of the times that events occurred in the full scale and quarter scale experiments. Figure 4 – Figure 6 show a summary of the data comparison between FS3 and QS2 experiments. These fires were allowed to burn with steady flames out of the door for approximately two minutes prior to extinguishment.

Table 1. Summary of events with approximate times

Figure 4. Temperature at "TC-B" for three heights: TC1 – near the floor, TC4 – near the middle, TC7 – near the ceiling

Figure 5. Heat flux at "THF-B” and "THF-C"

Figure 6. Gas Species at "GS-B (high)”

Analysis
The early fire growth was expected to be faster in the model based on lateral flame spread theory. The flame spread velocity is directly proportional to the induced air flow, and in Froude scaling the air velocity follows l^1/2, therefore:

t_spread,QS - t_{spread, FS} (1/4)^1/2 = ^{tspread, FS}/2

This faster lateral spread was the likely reason for higher temperatures in the quarter scale experiment during early growth of the fire (Figure 4). Gas species followed this behavior as well (Figure 6). Additionally, interior video showed the onset of rapid flame spread over the chair occurred at 103 seconds in the model and 117 seconds for the full scale.

At about 150 to 170 seconds, the model and full scale temperatures and concentrations were nearly the same. A photo of the fire conditions at 165 seconds in Figure 7 indicates that the fire shapes were also nearly the same.

Figure 7. Flames similar shape between FS3 (left) and QS2 (right).

Theory indicates that Froude scaling should work when fire sizes are the same relative size (i.e. flame height and diameter ~ l¹) because Q follows l^5/2; therefore the temperatures and concentrations should be the same. This was supported by the data in these experiments.

Oxygen concentrations measured above the fire near the ceiling were zero at about 150 seconds for the quarter scale and about 170 seconds for the full scale, which is an indication of ventilation-limited conditions. Theory indicates that for the ventilation-limited conditions, the concentrations of the model and full scale should be the same because the burning rate is controlled by the inflow of air, which follows l^5/2. Figure 6 shows that these equalities persisted from about 150 to about 380 seconds, when the fires were terminated.

After the fire sizes were the same relative size (approximately 165 seconds), the full scale temperatures and heat fluxes were greater because of an increase in radiant heating by the thicker smoke layer. This led to more rapid fire growth in the full scale, and flames were observed to move away from the origin earlier in the full scale (225 seconds) than the quarter scale (255 seconds). The measurements of the corner heat flux gauges dropped at about these times (Figure 5), indicative of the flame moving away from the corner.

Later, at about 300 seconds in the model and 254 seconds in the full scale, the flame emerged from the door and moved away from the opposite far wall. Roughly correlating with the flames emerging from the door, the temperatures from floor to ceiling within the compartment merged to a unified value in both the model (300 seconds) and full scale (255 seconds).

Acknowledgements
The scale fire modeling experiments were partially funded by the National Institute of Justice. In addition, the experiments would not have been nearly as valuable without the data from previous tests completed by ATF Special Agent / Certified Fire Investigators Dan Heenan, Mike Marquardt, and Steve Carmen, along with ATF Fire Protection Engineer Jason Ouellette.

Lee K. McCarthy and Lenwood S. Reeves are with U.S. Department of Justice, Bureau of Alcohol, Tobacco, Firearms and Explosives (ATF), James G. Quintiere, Ph.D. is with the University of Maryland, and Andrew J. Wolfe is with Hughes Associates, Inc.

References

1. Quintiere, J.G., "Scaling Applications in Fire Research,” Fire Safety Journal, 15, 1989 p. 3-29.
2. Carey, A.C., "Scale Modeling of Static Fires in a Complex Geometry for Forensic Fire Applications,” MS thesis, University of Maryland, College Park, 2010.
3. Campbell, M.A., "Current Research and Future Expectations of RSE Burning,” Proceeding of the 5th International Symposium on Fire Investigation Science and Technology, 2012.
4. Quintiere, J.G., Reeves, L.S., McCarthy, L.K. "Scale Model Testing of Fire Growth in a Furnished Room,” Presentation at The International Association of Arson Investigators, Inc. (IAAI) 2012 Annual Training Conference, Dove, DE, 2012.
5. Quintiere, J.G., Fundamentals of Fire Phenomena, Wiley, p. 377-403, 2006.

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