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By: Nils Johansson, Lund University, Sweden.

There is a range of different models available for fire safety engineering, and the different models have different areas of application. When performing traditional calculations with the purpose to analyze times to untenable conditions or heat exposure to structural members the available models can roughly be grouped into three categories: hand-calculation methods; zone models; and CFD models.

Examples of hand-calculation methods are the Yamana-Tanaka methods for smoke filling, or the MQH- and Eurocode methods for calculating gas temperatures in pre- and post-flashover compartment fires, respectively. Zone models normally refer to numerical computer programs like CFAST and that is also the distinction used here. However, several hand-calculations methods also utilize, in a sense, the zone model approach by assuming that the hot gas layer holds a uniform temperature. In CFD models the domain is divide into several smaller control volumes, and the Navier-Stokes equations are solved numerically for each one of these. A typical control volume in the well-known CFD model, the Fire Dynamics Simulator (FDS) is in the order of 0.1x0.1x0.1 m³

The step from two-zone models to CFD models is in many ways large, and sometimes maybe a bit too large when it comes to practical engineering situations. Traditional two-zone models, like CFAST, often perform well in validations studies as long as the studied situations are strongly stratified, and the hot gas layer can be assumed to be uniform in regard to temperature and composition. This normally limits the use of two-zone models to fire scenarios in small- and medium-sized spaces, like rooms in residential buildings. Consequently, the usefulness of two-zone models for fire safety engineers is limited, because engineering calculations are most often only conducted in larger commercial or industrial buildings where the prescriptive building regulations cannot be fulfilled.

CFD models, on the other hand, allows for retrieving the distribution of temperature and species concentrations in large spaces, which means that the model does not hold the same limitations in regard to compartment sizes as two-zone models. However, the computational time and complexity of the models are much greater than in zone models. This can result in that the engineer needs limit the number of calculations performed, and special training is normally needed in order to understand the model, correctly setting up the input file, and to interpret the results.

Altogether, one can perceive that there is an obvious gap in modelling capability between two-zone models and CFD models. That is the capability to perform analysis of large spaces, where prescriptive solutions might be problematic, in a short time with a model that is not more advanced than a two-zone model. This gap led to the incentive to develop a multi-zone fire model.

The Multi-Zone Concepts

The multi-zone concept is based on the conservation of mass and energy to calculate hot gas temperatures, and the Bernoulli equation to calculate flows between the different zones. In contrast to two-zone models, where each enclosure consists of two zones, the domain is divided into several regions (horizontal) and layers (vertical) in the multi-zone concept. This makes it possible to get some estimate of the distribution of properties, like temperature, in a large space in just a couple of minutes.

The fire is specified as a heat release rate, the heat and hot gases rise upwards from the fire in a plume that enters the highest located layer in the fire region. Air and hot gases are entrained in the plume from the layers that it passes through. Mass is transported horizontally to layers in adjacent regions due to hydrostatic pressure differences. There is also a flow of mass vertically between layers in each region, which is calculated based on the conservation of mass and energy. Heat is transferred to solid obstructions through convection and radiation. 1-D conduction is used in solids. Heat is transferred between zones through the flow of hot gases and radiation. The underlying principles of the multi-zone concept have been presented in previous publications [1][2] and the reader is referred to them for a deeper explanation of the concept.  

Figure 1: Principles of the different types of models.

The multi-zone concept is not as established as two-zone models since only a few models have been presented (see e.g. [1][3][4]). This means that the accuracy and possible benefits of models using the multi-zone concept is rather unknown. However, in a recent paper [5] the multi-zone concept and its usefulness in fire safety engineering, when prescriptive fire safety requirements can be hard to fulfil, have been evaluated.

The Evaluation Study

The evaluation of the multi-zone concept is performed by comparing data from a multi-zone model, called the Multi-zone (MZ) fire model [6], to previously published experimental data and data from simulations with FDS. The MZ fire model is freely available for download and testing at http://mzfiremodel.com.

One problem when doing this type of evaluation study is to find relevant existing experimental data, where the experimental conditions are described in such detail that it is possible to represent the experimental situation in the model. There are little data from fire experiments in large spaces available in the literature, and when it exists, the description of the experimental conditions is often inadequate to be able to use the data reliably. However, there are some examples of experimental data that were considered useful for the evaluation study. Data from three different experimental setups were used by Johansson [5].

The first set of data originates from Test#3 in the International Fire Model Benchmarking and Validation Exercise #3, BE#3, [7]. The experimental series was conducted in an enclosure that was designed to represent a room in a nuclear power plant and it measured 21.7´7´3.8 m³. The fire was placed in the center of the room and there was a 2.0´2.0 m² door on one of the short ends. A heptane pool fire of just over 1 MW was used as fire source in the test.

The second set of data comes from the Murcia Atrium Fire Tests were conducted in a 19.5´19.5´20 m³ open space [8]. The enclosure boundaries were made of steel plate and the experimental series consisted of different setups in regard to fire size and ventilation conditions. The test data used in this in the evaluation originates from a Test#3 where the exhaust fans were shut off and only used for natural ventilation. The fire source used was a fuel pan with heptane and an estimated maximum heat release rate of 2.34 MW.

The third and final data set originated from the PolyU/USTC Atrium used to study smoke filling [9]. The facility consisted of a single room constructed of concrete that measured 22.4´11.9´27 m³. The average heat release rate, from the diesel pool used, was estimated to be 1.6 MW.

The experimental data were collected by Johansson [5], and the scenarios was modelled with the MZ fire model and FDS version 6.7.1. A visual and quantitative comparison, with functional analysis, of the correspondence between the modelling results, and the modelling and experimental results were conducted. 

Result of Evaluation

Results from the simulations of test 3 in BE#3 is presented in Figure 2. The results from FDS and the MZ fire model corresponds well, whilst the experimental data indicates a more rapid temperature increase during the first 100 s, especially at higher elevation (z = 3.5 m).

Figure 2: Temperature development (left) and vertical temperature profile at two time points (right) in the BE#3 scenario.  

Results from the simulations of the Murcia fire test are presented in Figure 3. The results from FDS and the MZ fire model simulations are rather similar. The temperature in the lower part of the enclosure (see left part of Figure 3) is however predicted to be higher with FDS than with the MZ fire model. Both models give lower temperatures at higher elevation (z = 18 m) than the experimental data.

Figure 3: Temperature development (left) and vertical temperature profile at two time points (right) in the Murcia scenario.

It is clear from Figure 4 that the agreement between simulation results and experimental data is not as good in the PolyU/USTC case as in the two other experiments. Still, the results from the two simulation models corresponds rather well, even though the MZ model results in a slightly slower temperature development than FDS.

Figure 4: Temperature development (left) and vertical temperature profile at two time points (right) in the PolyU/USTC scenario.

Conclusion

If one recognizes that there is a gap between the simple but fast two-zone models and the more precise but time-consuming CFD models, the multi-zone concept might be of interest. The results presented in the evaluation study show that the MZ fire model predicts gas temperatures within 5% of FDS results and within 10% of the experimental data in two well-ventilated large spaces. In the third case there is a discrepancy between the modelling and the experimental data, the main reason for this is most likely the limited ventilation in the experimental test, that is not explained in any detail in the original description of the experiment.

The MZ fire model is simpler than FDS and is not as flexible. For example, the rather course zone resolution makes it difficult to include obstructions with fine details. There is no modelling of turbulence and the plume, that drives the flow of gases, is based on an empirical plume model. Still, there are clear benefits of the model. The main benefit is that simulations of scenarios like the ones used in the evaluation are performed within 1-2 minutes. This is in the order of 0.1% of the time to perform a similar FDS simulation on a desktop computer. The computation time for CFD simulations will most likely decrease with increased computer capacity, which might reduce the need for a quicker and less accurate tools like the MZ fire model. Nevertheless, the multi-zone concept is so much quicker that it still could be of value, especially for fire safety analyses in large spaces or as a part fire risk analyses, where hundreds of simulations might be needed. All in all, the results are promising and there might be a future for the MZ fire model; however, further studies are needed in order to quantify the accuracy of the model and its limitations.

References

• [1]K. Suzuki, K. Harada, T. Tanaka, A Multi-layer Zone Model for Predicting Fire Behavior In A Single Room. Fire Safety Science 7:851-862, 2002, http://dx.doi.org/10.3801/IAFSS.FSS.7-851
• [2]K. Suzuki, K. Harada, T. Tanaka, H. Yoshida, An Application of a Multi-Layer Zone Model to a Tunnel Fire, in: 6th Asia-Oceania Symposium on Fire Science and Technology, 2004.
• [3]Multi-Zone Fire Model – General Documentation and User Guide, available at http://mzfiremodel.com accessed September 17, 2020).
• [4] W.K. Chow, Multi-cell concept for simulating fire in big enclosures using a zone model, Journal of fire sciences 14:186-197 , 1996. https://doi.org/10.1177/073490419601400302
• [5]N. Johansson, Evaluation of a Zone Model for Fire Safety Engineering in Large Spaces, Fire Safety Journal, 2020, https://doi.org/10.1016/j.firesaf.2020.103122
• [6]Multi-Zone Fire Model, http://mzfiremodel.com, 2019 (accessed September 17, 2020).
• [7]A A. Hamins, A. Maranghides, R. Johnsson, M. Donnelly, J. Yang, G. Mulholland, R.L. Anleitner, Report of Experimental Results for the International Fire Model Benchmarking and Validation Exercise #3, NIST Special Publication 1013, National Institute of Standards and Technology, Gaithersburg, MD, USA , 2005.
• [8]C. Gutiérrez-Montes, E. Sanmiguel-Rojas, A. Viedma, G. Rein, Experimental data and numerical modelling of 1.3 and 2.3MW fires in a 20m cubic atrium, Building and Environment, 44(9):1827-1839, 2009. https://doi.org/10.1016/j.buildenv.2008.12.010

W.K. Chow, Y.Z. Li, E. Cui, R. Huo, Natural smoke filling in atrium with liquid pool fires up to 1.6 MW, Building and Environment, 36(1):121-127, 2001. https://doi.org/10.1016/S0360-1323(00)00032-9