# GoZone: A Numerical Model for Travelling Fires Based on Cellular Automata Concept
## 5 Fuel Control Situations  
The rate of heat release (RHR) of each burning cell is pre-defined according to the recommendations of Eurocode 1 part 1-2 [47] for a fuel controlled fire, with three main stages: (1) an initial growing phase, depending on the assigned fire growth rate; (2) a stationary regime during which the RHR is equal to the product between the area of the cell and the value of given rate of heat release density; and (3) a linear descending phase starting when 70% of the fire load of the cell is consumed. When the fire propagates, the sum of RHR(t) produced by all cells makes the total fire power in the compartment used by the zone model. The advantage in defining the fire power evolution according to the recommendations of EN1991-1-2 is in having input parameters that are relatively easy to understand, familiar to practitioners (RHR density, fuel load, and fire growth rate). A 20 \(\times\) 20 m\({}^{2}\) well ventilated compartment with the ceiling at 2.7 m was taken to check the growing phase evolution in terms of the rate of heat released evaluated by GoZone through a comparison with the analytical solution of EN1991-1-2. Table 5 shows the three different  
Figure 11: Central axis temperature comparison between Eurocode 1 and the non-local variable method for a fire radius of 2 m.  
Figure 10: Flame length evaluated at the centre of the flame for several fire areas and discretised cells. compartment typologies that were tested with regard to the fuel load density, rate of heat release density, and fire growth rate described in Tables E.4 and E.5 of EN1991-1-2. The fire origin was set in the centre of the compartment and the comparison was made up to the moment when the smoke layer was predominantly influencing the fire dynamics or when the fire completely engulfed the compartment. This is because the equation of Eurocode 1 does not stand when any of these two criteria is met. Figures 12 and 13 show the evolution of the power released during the growing phase of a fast and a medium fire. Outcomes provided by GoZone seem to be reasonably in line with the analytical solution. Figure 14 shows the fire propagation predicted by GoZone, which is representative of a medium fire from the time of first ignition to a moment just before the flashover. Since fast and medium fire development were similar in terms of the shape of the fire evolution, only one case is shown and is considered to be representative of the two. Figure 15 shows the evolution of the power for a slow fire scenario. Although the general trend of the numerical model is still the one of the analytical solution, a different behaviour could be observed compared to Figures 13 and 14, where the power released did not increase monotonously, especially for cruder meshes. Figure 13: Evolution of the power released in an office building: (**a**) Structured quadrilateral mesh; (**b**) Unstructured quadrilateral mesh. Figure 14: Fire evolution from ignition to a moment before flashover representative of medium and fast fire growth scenarios. (**a–c**) Evolution with a structured mesh; (**d–f**) Evolution with unstructured mesh. Figure 15: _Cont._  
This is due to the fact that, in this case, a slow fire produces some kind of radial travelling fire, as can be seen in Figure 16. In this figure, red cells are in the increasing or steady state period of combustion; pink cells are in the descending phase; and black cells are completely burnt. Due to the discretised nature of the floor in cells of finite sizes and to the regular geometry, it may occur that a significant amount of cells enter in the descending branch or are completely consumed, whereas for a certain amount of time, no new cell is ignited. This phenomenon is amplified by the larger size of the meshes and by the double symmetry of the problem, which makes groups of several cells, thus changing their behaviour at the same time.