Evaluation of a zone model for fire safety engineering in large spaces

14 Thanks to simple and straightforward calculation methods it is rather easy to estimate gas 15 temperatures in smallor medium sized enclosures; however, the problem becomes more complex 16 if fire safety analyses are to be performed in large spaces where the hot gas layer cannot be 17 regarded as uniform. Using a multi-zone modelling concept could be a good alternative for such 18 situations. However, few such models exist and the evaluation of the concept is scarce. This paper 19 is therefore dedicated to study the multi-zone modelling concept and its usefulness in fire safety 20 engineering by comparing results from such a model with results from a more established 21 numerical method as well as experimental data. The results indicate that the multi-zone model 22 gives reasonable estimates of gas temperatures in well-ventilated large spaces. It is also concluded 23 that there is a potential for the multi-zone concept to be a complement to more advanced numerical 24 modelling methods like Computational Fluid Dynamics. 25 26


Introduction 29
Fires in small-and medium-sized enclosures will cause turbulence that mixes the hot gases, which 30 results in a hot gas layer with rather uniform temperature. This has sometimes been referred to as 31 the "compartment fire framework", and it applies to both the stratified pre-flashover fire and the 32 post-flashover fire. The framework also includes the concept of flashover, which occurs when the 33 heat from the stratified hot gas layer is so intense that all combustibles in the enclosure will ignite. 34 The first comprehensive work in this area was done by Kawagoe in the 1950s [1], and a lot of 35 effort has been conducted within the area since then. This has resulted in different types of 36 analytical methods, like the time-temperature curves in Eurocode 1 [2], and numerical models, like 37 2-zone models, that are very valuable for fire safety engineering under certain conditions. 38 2 The situation becomes more complex in large spaces where the hot gas layer cannot be regarded 39 as uniform. Outside the compartment fire framework, the concepts of flashover, and pre-and post-40 flashover fires becomes obsolete, and the non-uniform hot gas layer calls for other modelling 41 methods. There is no clear definition when the compartment fire framework should or should not 42 be applied. However, the International Standards Organization have published some guidance on 43 the use of zone models [3], which gives some hints of the possible enclosure dimension limits of 44 the compartment fire framework. 45 In the compartment fire framework, the fire is normally considered to be fuel-controlled initially 46 and grows in size until flashover occurs. The fire then becomes ventilation-controlled, and the heat 47 release rate is controlled by the supply of oxygen. The terms regime I and regime II [4] are 48 sometimes used to distinguish between ventilation-controlled and the fuel controlled-burning, 49 respectively. It has been argued that fires in large spaces are likely to be within regime II [4], since 50 the availability of air most likely will be high due to the presence of large openings and leakages 51 to the surroundings. 52 Stern-Gottfried and Rein [5] present the so-called traveling fires framework in which the thermal 53 field induced by the fire is divided into two regions: the near field and far-field. The position and 54 size of the regions are relative to the position of the fire, and moves within the enclosure as the fire 55 spreads. The near field is the burning region of the fire, and the far-field is the region where no 56 burning or flames are present and where the hot gas layer will provide a thermal exposure. properties like gas temperature can be calculated at many locations, and consequently the 87 temperature distribution in the hot gas layer can be found. 88 89 Figure 2: Principles of the different types of models. 90 The multi-zone concept is not as established as two-zone models since only a few models have 91 been presented (see e.g. [11] and [13]). The accuracy and possible benefits of models using the 92 multi-zone concept is therefore rather unknown. So, the scope of this paper is to evaluate the multi-93 zone concept and its usefulness in fire safety engineering compared to other more established 94 numerical methods. 95 96

Method 97
The evaluation of the multi-zone concept is performed by comparing data from a MZ-model to 98 previously published experimental data (see Section 3) and data from simulations with FDS. The 99 comparisons between the models and between models and experimental data are preformed 100 qualitatively, with graphs, and quantitatively, with functional analysis. Functional analysis is used 101 to quantify the agreement between two sets of data by treating time series curves as vectors x = 102 (x1, x2, … xn) [14]. This makes it possible to quantify the length, angle and distance between two 103 different sets of data or graphs. Three different metrics are used, the first one is Euclidean Relative 104 Distance (ERD) which gives the average difference between the data sets. The second metric is 105 the Euclidean Projection Coefficient (EPC) and the shift, which the value that if multiplied with 106 the value of the test will give the best possible agreement. The final metric is the Secant Cosine 107 (SC), which gives a value of how well the shape of the graphs correspond to each other. 108 guidance on what zone size to use. However, at least three zones in each direction is needed to run 160 the model. Furthermore, it is reasonable to think that the horizontal dimensions of the fire region 161 should be large enough that the plume, that extends laterally as it moves upwards, can be enfolded 162 by the region. Another aspect to consider is the expected property distribution (e.g. temperature) 163 and the zone resolution needed to capture that distribution to a reasonable extent. In the simulations 164 performed in this paper a zone size of 4´4´0.5 m 3 is used. 165 The

Fire model benchmarking and validation exercise 190
The first set of data originates from the International Fire Model Benchmarking and Validation 191 Exercise #3 (BE#3) [21]. The experimental series was conducted in an enclosure that was designed 192 to represent a room in a nuclear power plant and it measured 21.7´7´3.8 m 3 , see Validation Exercise [21]. 200 In the test used in this paper (Test#3) a pan with heptane, corresponding to a maximum heat release 201 rate of 1050 kW (corrected value: 1140 kW), was used as fire source. The fire was ramped up 202 during 3 minutes and the total duration of the test was 26 minutes. Seven different thermocouple 203 trees were used; however, only data from thermocouple TC Tree#7 (see Figure 4) is used in this 204  The time-temperature curves at z = 2.25 m (green curves in the right part of Figure 7) are analysed 247 with functional analysis. The results in Table 1 confirms that the results from FDS and the MZ 248 model are similar. The average distance (ERD) between FDS and MZ is low (1%), the shift (EPC) 249 is close to 1 and the curves are more or less identical, i.e. SC-value close to 1. Author's pre-print of: Johansson, N., "Evaluation of a zone model for fire safety engineering in large spaces" Fire Safety Journal, 2020. DOI: 10.1016/j.firesaf.2020.103122 9

Murcia fire test 254
Results from the simulations of the Murcia fire test are presented in Figure 8. The results from 255 FDS and the MZ model simulations are similar. The temperature in the lower part of the enclosure 256 (see left part of Figure 8) is however predicted to be higher with FDS than with the MZ model. 257 Both models give lower temperatures at higher elevation (z = 18 m) than the test data. give similar values as for the BE#3 test; however, the shape of the curves (SC) does not correspond 264 as well in this case. 265  A functional analysis is performed on the data at z =15 m (green curves in the right part of Figure  278 9), see Table 3. The average distance (ERD) and the shift (EPC) shows a close agreement between 279 FDS and the MZ model, and the shape of the two curves are considered to correspond rather well 280 (SC=0.83). The experimental data deviates rather much from the model results, especially after 281 150 seconds when the shapes of the curves diverge. 282  Figure 8, between test data and FDS simulations. 296  Author's pre-print of: Johansson, N., "Evaluation of a zone model for fire safety engineering in large spaces" Fire Safety Journal, 2020. DOI: 10.1016/j.firesaf.2020.103122

11
When it comes to the PolyU/USTC case there is a larger difference between experimental and 297 model results than in the two other cases. The main reason for this is probably the limited 298 ventilation. The only opening in the building was a 0.2 m high gap at floor level, which most likely 299 will result in that the flames were in the hot gas layer after a couple of minutes which probably 300 influenced the combustion negatively. The mass loss rate is used in the original paper [24] to 301 estimate the heat release rate, and no effort have been made in the paper to present if or how the 302 heat release rate is affected by the descending hot gas layer. Under-ventilated fires are in general 303 difficult to model and limited ventilation is not accounted for in the MZ model. This probably 304 explains the larger difference between model and experimental results in this case. 305 The MZ model is much simpler than FDS and has a more limited area of use. For example, the 306 rather course zone resolution makes it difficult to include obstructions with fine details. There is 307 no modelling of turbulence and the plume, that drives the flow of gases is based on an empirical 308 plume model. Even so, there are benefits of the model. The main benefit is that simulations of 309 scenarios like the cases used in this paper are performed within 1-2 minutes. This is in the order 310 of 0.1% of the time to perform a similar FDS simulation on a desktop computer. The computation 311 time for CFD simulations will most likely decrease with increased computer capacity, which might 312 reduce the need for a quicker and less accurate tools like the MZ model. However, the multi-zone 313 concept is still so much quicker that it could be of value, especially for fire safety analyses in large 314 spaces. A possible increased demand for multiple simulations as inputs to fire risk analyses, might 315 also make this type of model appealing. 316 There is limited information to do any detailed assessment of the experimental uncertainty of the 317 test data used in this study, which makes it difficult to assess the model uncertainty. Nevertheless, 318 in the case of the BE#3 tests the relative expanded uncertainty of the hot gas layer temperature rise 319 has been estimated to 12% in a previous study [22], and it was shown that FDS can make 320 predictions within this uncertainty. Additional studies are needed in order to further quantify the 321 accuracy of the MZ model, as have been done with other fire models. 322 323

Conclusions 324
Experimental data and simulations with FDS are used in this paper in order to evaluate the MZ 325 model in large spaces. The results show that the MZ model predicts gas temperatures within 5% 326 of FDS results and within 10% of the experimental data in two well-ventilated large spaces. In the 327 third case there is a discrepancy between the modelling and the experimental data, the main reason 328 for this is most likely the limited ventilation in the experimental test. The results are promising and 329 there might be a future for the MZ model; however, further studies are needed in order to quantify 330 the accuracy of the model and its limitations. 331