By Charlie Hopkin and Michael Spearpoint
Introduction
The verification and validation process for computational models is a necessary and ongoing process. Over time, new capabilities are incorporated into the models and new experimental data become available. Computational models such as the Fire Dynamics Simulator (FDS) are regularly used to assess the expected sprinkler actuation time in an enclosure. It is therefore important to know whether the tools used can evaluate times at an appropriate level of accuracy.
One method to determine whether a model can encapsulate behaviors observed in real life is to benchmark against experimental data. The FDS Validation Guide1 provides a large collection of benchmarking exercises. In certain cases, simulations have been shown to match within the bounds of experimental uncertainty, while others have more variation in values. This provides an indication of the FDS model accuracy based on the available experiments.
In a recent paper by Hopkin et al.,2 FDS version 6.6.0 has been benchmarked against data from a series of sprinkler actuation time experiments. The work includes sensitivity analyses for grid size, conductivity factor and radiative fraction. This article provides a summary of the Hopkin et al. paper, the results of which have been incorporated into the latest FDS Validation Guide.
Previous Work
Work by Bittern3 and Wade et al.4 involved experiments on sprinkler actuation in a room-sized enclosure and comparing the results against simulations using the FDS 3 and BRANZFIRE (now known as B-RISK) computational models. In a set of 22 fire experiments, a single upholstered chair was burned within an enclosure (Figure 1). The enclosure had internal dimensions of 8 m by 4 m by 2.4 m high, with timber-framed walls and ceiling, and was lined with 10 mm thick gypsum plasterboard. A single 0.8 m wide by 2.1 high door was in one of the short walls; during the experiments, it was either fully open or closed.
Figure 1: Enclosure layout (plan view).4
The upholstered chair consisted of a metal frame with a seat made of two non-fire-retardant flexible polyurethane foam slabs of density 28 kg/m3, covered with a 10 g/m2 acrylic fabric. Each slab measured approximately 0.5 m by 0.4 m by 0.1 m thick, with one forming the horizontal “base” of the seat and the other the vertical “back.” Plasterboard formed a backing for the seat. The chair was on a load cell to record mass loss; the base of the seat was approximately 0.65 m from floor level. The seat was in one of two locations in the enclosure — either the center or the corner opposite the door — and was ignited using a solid petroleum firelighter.
The heat release rate (HRR) was estimated from the recorded values of mass loss rate and heat of combustion of the foam. The average heat of combustion was measured in a cone calorimeter to be 21.0 MJ/kg (Experiment 1 through 10) and 20.4 MJ/kg (Experiment 11 through 22).
The experiments incorporated different residential and standard response sprinkler heads installed as a pair, flush beneath the ceiling. The sprinkler heads were not charged with flowing water, but pipe sections connected to the head contained a small volume of water under pressure. Pressure gauges were installed immediately upstream of each sprinkler head to indicate actuation.
Simulations
The material and thermal properties used in these experiments are in line with those assumed previously.3-4 The simulations apply the FDS burner capability using the experimentally derived HRR with a burner area of 0.4 m by 0.5 m assumed for the base of the seat.
The experiments only recorded the mass loss rate for a brief period after sprinkler activation. In some instances, the simulations are not able to determine the time of sprinkler activation before the end of the available HRR data. Therefore, additional simulations have been run that assumed the fire is capped once it has reached peak HRR and continues to burn at this rate for an indefinite period, referred to as a capped fire (Figure 2).
Figure 2: Example of capped HRR curve (Experiment 4).
The assumed sprinkler characteristics were based on the manufacturer’s specification or otherwise estimated based on literature. One important input is the C-factor, which characterizes the heat loss to the sprinkler housing from conduction. While a C-factor of 0.4 (m/s)½ was selected previously,4 an analysis has been undertaken in FDS for one of the experiments, where the C-factor varied between 0.0 (m/s)½ and 0.8 (m/s)½. The results indicate that a C-factor between 0.2 (m/s)½ and 0.4 (m/s)½ provides the most-consistent match.
A sensitivity analysis aimed to determine an appropriate grid size that best reflects the results from the experiments. A single experiment considered four uniform grid sizes, from 0.2 m to 0.025 m. The differences between a 0.025 m and 0.05 m grid size are small (0% difference in actuation time for sprinkler head 1 and 1% for head 2). For grid sizes of 0.1 m and 0.2 m, FDS was not able to predict sprinkler actuation time for both sprinklers before the end of the simulation. Thus, for this specific set of experiments, a 0.05 m grid size is able to capture sprinkler actuation times appropriately.
The FDS Validation Guide1 provides parameters for numerical resolution to outline the range of applicability of the validation studies. For the selected grid size of 0.05 m, the plume resolution index (D*/𝛿𝑥) is in the range of 5.8–10.0. McGrattan5 undertook a series of sensitivity analyses for FDS where suitable D*/𝛿𝑥 values typically ranged from 4 (coarse) to 16 (refined), and McDermott et al.6 have indicated that “D*/𝛿𝑥 ≈ 10 has historically been considered adequate grid resolution.”
FDS incorporates a radiative fraction based on species, where the default for “all other species” is 0.35. The radiative fraction has an impact on the simulated convective heat flow, which in turn affects sprinkler actuation. A radiative fraction of 0.46 has been adopted based on GM23 foam consistent with the previous work.4 A sensitivity analysis between the two radiative fractions indicates a more-consistent match using 0.46 for a selected experimental case, where the variation of sprinkler actuation times is 6% and 7% for head 1 and head 2 respectively.
Results and Discussion
The FDS Validation Guide1 suggests a relative standard deviation for experimental uncertainty in sprinkler actuation time of approximately 6%. The guide also describes the concept of model uncertainty and model bias, with a model relative standard deviation of 0.19 and a model bias factor of 1.02 determined for FDS 6.6.0.Figure 3(a) provides a comparison of the experimental sprinkler actuation times against the FDS simulations for the “uncapped fire,” with experimental uncertainty shown as a black, small-dashed line and model uncertainty shown as a red, long-dashed line (discussed further in the FDS Validation Guide). The graph has 35 data points in total, with six missing data points from the simulations were not able to determine the sprinkler actuation time before the end of the experimental HRR data. With a few exceptions, the simulation results are within the bounds of model uncertainty.
(a) (b)
Figure 3: FDS simulations against experiment sprinkler actuation time: (a) uncapped fire; (b) capped fire.
For a capped fire, per Figure 3(b), all sprinkler heads are actuated in the simulations. However, in the corner fire cases with the door closed (Experiment 16 to 22), FDS is less-accurate and over-predicts the actuation time by as much as 108 s.
Hopkin et al.2 includes an assessment of the enclosure leakage areas, along with calculations for “Goodness of fit” that indicate that FDS is able to provide an average prediction of sprinkler actuation time within a Euclidean Relative Difference of 0.18. The work also compares previously different modeling approaches and versions of FDS,3 illustrating the importance of the decisions made by the modeler in representing fire scenarios, even when modeling “simple” experiments where data are available for inputs such as heat release rate, geometry and sprinkler characteristics. The full paper provides a more-detailed discussion of these topics.
Charlie Hopkin and Michael Spearpoint are with OFR Consultants, Manchester, UK.
References
1McGrattan K, Hostikka S, McDermott R, Floyd J, Vanella M, Weinschenk C, Overholt K. NIST Special Publication 1018 Sixth Edition, Fire Dynamics Simulator technical reference guide, volumes 1 and 2, 2017.
2Hopkin C, Spearpoint M, Bittern A. Using experimental sprinkler actuation times to assess the performance of Fire Dynamics Simulator, Journal of Fire Sciences, 36(4), 2018.
3Bittern A, Analysis of FDS predicted sprinkler activation times with experiments, master’s of engineering in Fire Engineering Report, University of Canterbury, Christchurch, New Zealand, 2004.
4Wade C A, Spearpoint M, Bittern A, Tsai K. Assessing the sprinkler activation predictive capability of the BRANZFIRE fire model, Fire Technology, 43(3), 175–193, 2007.
5McGrattan, K. NUREG-1824, Verification & validation of selected fire models for nuclear power plant applications, volume 7: Fire Dynamics Simulator, U.S. Nuclear Regulatory Commission, Office of Nuclear Regulatory Research, 2007.
6McDermott R, Forney G, McGrattan K, Mell W. Fire Dynamics Simulator, version 6: complex geometry, embedded meshes and quality assessment, at European Conference on Computational Fluid Dynamics, Lisbon, 2010.