# Modelling of fire spread in car parks

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2 occurs in a wide range. The choice of a probabilistic approach in combination with a deterministic model limits the possibilities for the deterministic model. CFD for example can give a detailed and accurate solution for a specific case with specific parameters, however it is too time consuming to be used in combination with a probabilistic approach. Furthermore the reliability of such a solution should not be overestimated, because large uncertainties are introduced by the uncertain parameters. Figure 1. Picture after the fire in the car park near Schiphol airport (picture from [1]) The model focuses on fire spread by radiation, because this accounts approximately for the heat transfer of 30-40% of the heat released by the fire. Therefore, radiative heat transfer is expected to have the largest influence on fire spread. Furthermore radiative heat transfer does not require mass exchange or direct contact between the heat exchanging bodies and is described by wellknown equations which can easily be solved. However, there is still the possibility to add the effects of the pool fires (due to the leakage of fuel from the fuel tanks) in the model, when the results based on radiative heat transfer turn out to be insufficient. This study is to be seen as a first step to approach the trends which to a large degree undermine the current safety concepts: closer parking distances, large cars, more cars, application of more combustible materials, more electrical appliances (increasing the probability of short-circuits and self-ignition) and so fort. The probability and the consequences of large(r) fires seem to increase; this underscores the necessity to initiate the development of more fundamental research into fire spread in car parks. 210

5 and most shapes can be approximated using rectangles. So in this model, it is assumed that all objects are built of rectangular surfaces orientated perpendicular or parallel to each other, which makes the calculations much more efficient. real car model 2,00m 1,80m 1,60m cabin cabin 0,50m 0,50m 0,50m bumper wheel/ tire coachwork bumper wheel/ tire bumper coachwork bumper 1,80m 0,25m 0,50m 0,50m 2,00m 0,50m 0,50m 0,50m Figure 3. Example of a car built of rectangular surfaces orientated perpendicular or parallel to each other The model is chosen such that the main parts that contribute to the fire development can be treated separately and, if desired, in relative great detail. This means the cars in the car park are built of rectangular surfaces orientated perpendicular or parallel to each other. The surfaces have different properties, depending on the material used. In figure 3 is shown how a car can be built of this kind of surfaces. The exact size and location of the parts in a car can be chosen which results in a different type of car. The car can also be refined by building it of more, smaller rectangles resulting in a more detailed model. The cars can now be placed in the car park, but again all surfaces have to be orientated perpendicular or parallel to each other, which results in four possible orientations for a car with respect to another car. The radiation flux on a surface is the result of a number of visible (hot) surfaces close to it. Those surfaces have a constant temperature. Let s now consider the radiative heat transfer between two surfaces. The discussed procedure can easily be extended if there are more hot surfaces (which are not located behind each other) by taking the sum of all fluxes as the total radiation flux on a surface, which is also done in the model. The radiation flux on a surface is calculated in a few points (infinitesimal small surfaces) on the surface in so-called sensor points and depends on the thermal properties of both surfaces and the position and orientation of the surfaces. The position and orientation of the surfaces can be combined in one coefficient: the view factor or configuration factor, which resembles the part of the total solid angle covered by the other surface. This leads to the following equation for the incoming radiative flux in a sensor point Ad1 (on a surface A1) caused by a (hot) surface A2: 4 Q2 d1 = aεσa2t2 Fd1 2 (3) 213

7 450 ignition time (s) ABS polyster poyethylene ploypropylene polystyrene foam (EPS) polyvinyl ester PVC (flexible) radiative heat flux Figure 4. The time to ignition as a function of the radiative heat flux on the surface for different plastics 3 Results The development of this model is in an early stage and the model is not validated yet. Nevertheless the first results show realistic ways of fire spread and realistic temperature predictions. A few qualitative pictures are presented here to show how the results of the model can look like. Note that in the current model each part of a car is built of surfaces, but the surfaces have to be the faces of a block. So a complete bumper is made of three faces on a block. The blocks are used to model fire spread within a car, for example from one side of the bumper to another side of the bumper. Currently the fire spread within a block is not really modelled, because a whole block will be in fire when one of the surfaces starts burning. This will significantly increase the fire spread, but this will be changed in a later version. A fire starts with a burning car in a car park, which can ignite other cars. In figure 5 an example of a car park with 6 cars is showed after some time. The dark surfaces in the figure are on fire and the second car from the left was initially on fire. In the figure, it can be seen that at the current time the compartment of the car in the front is on fire too. In the figure the surfaces are showed. Note that the burning surfaces have a different height than in the initial (non-burning) situation. This represents the flame height, which depends on the mass loss rate, which on its turn depends on the incoming radiation flux. 215

8 Figure 5. The surfaces on fire after a certain time. The dark surfaces are on fire, note that the height of a burning surface represents the flame height and is based on the heat release rate Figure 6. Parts on fire in the car park after a certain time. The dark parts are on fire, the lighter parts are non-burning. This only indicates whether or not a part is burning In figure 6 the same car park with 6 cars is showed, only from a different point of view. In this figure all blocks (resembling car parts) are showed. The dark blocks now represent car parts that are on fire. In this figure it is much easier to see which parts are burning. Now can be seen that even the bumper of the car parked behind the initially burning car is on fire. Normally the showed figures are in colour, where the colour is a measure for the temperature and state (not yet burning, burning, finished burning) of the block or surface. 216

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