Reconstruction of Grenfell Tower fire. Part 3—Numerical simulation of the Grenfell Tower disaster: Contribution to the understanding of the fire propagation and behaviour during the vertical fire spread

The dramatic event of the Grenfell Tower (June 2017), involving a combustible façade system, has raised concerns regarding the fire risk that these systems address. Indeed, as façades are complex systems, it is not straightforward to assess which part of the system is involved in the global fire behaviour. Understanding such façade fires is thus very complex as it depends on a combination of various products and system characteristics, including window frames or air gap or cavity barriers. Fire development inside the initial apartment was investigated using an appropriate CFD model with different scenarios for the fire source and ventilation conditions in a previous study. Fire propagation through the window to the external façade and to higher apartments was modelled and validated against visual observations. This paper describes CFD modelling of the complete Grenfell tower facade, and investigates vertical fire spread behaviour over the full height façade from the initial apartment. Contributions from the combustion of all the apartments' furniture, depending on window failure, and architectural details of the refurbished façade are considered in the numerical model. The modelling results are validated by comparison with photographic and video observations of the real fire.

detailed in expert reports [2][3][4] and is shown in video and photographic records of the real fire. These records have been used to provide an analysis of the post-breakout vertical and horizontal fire propagation on the whole façade of the Grenfell Tower in Guillaume et al. 5 This reference proposes several hypotheses for further investigation.
After the Grenfell event, the UK government commissioned seven large scale BS 8414-1 fire tests. 6,7 The objective was to determine the combinations of insulation and aluminium composite material (ACM) cladding that could be safely used. However, the BS 8414-1 test method requires that a test is stopped if flames are observed higher than the test rig or, here, when criterion 8 of BR135 has failed. Therefore, this BS 8414-1 test campaign does not provide a tool to examine all façade fire scenarios. Numerical simulation is, thus, a useful tool to investigate, understand, and analyse such fires, and, of particular use, specific phenomena can be isolated and evaluated more easily. Several studies have shown the feasibility and usefulness of numerical simulation for highrise buildings fires [9][10][11] and for post incident analysis. [12][13][14][15] Numerical simulations, using the CFD code FDS (fire dynamics simulator), [16][17][18][19] were used after the World Trade Center disaster in 2001 to provide deeper analysis of the fire propagation inside the structure. 12 In Dréan, 20 the influence of scale on the fire behaviour of ACMcladding façade systems was investigated. Numerical simulations were performed to reproduce the fire tests commissioned and detailed in previous reports. 21 -23 The façade systems were simulated using a validated model. 24,25 The results of the simulations closely matched the experimental fire test results and showed that the ACM cladding was the main element driving the overall fire behaviour of façade constructions. In particular, systems that featured ACM cladding made with a polyethylene core (ACM-PE) showed very extensive fire propagation regardless of the insulation used.
At a real scale, the model, using the CFD code FDS, was then used to assess the fire performance of the façade system used on the Grenfell Tower in Guillaume et al. 26 One of the most important factors in properly assessing the fire behaviour of a façade system is to accurately represent fire spread from the compartment of origin to the façade. Flames venting through an opening, such as a window aperture, expose the façade system to heat and leads to ignition of, and fire spread to, the façade. 27 This then poses a significant risk of fire spread to adjacent floors or buildings. Fire exposure, resulting from flames venting through a compartment opening, has been extensively studied experimentally and numerically at different scales. 28,29 The development of the fire, inside the kitchen of the apartment of origin at Grenfell, and its behaviour at the kitchen window were investigated in Guillaume et al. 26 Fire spread over the façade and at the cavity barrier locations were also explored, as was fire propagation from the façade, through the windows, and into higher apartments. A thermomechanical analysis of window failure was performed. 30 The overall heat release rate (HRR) for typical apartment rooms and window failure criteria were evaluated. The results can be used to investigate fire breakout to the external façade and to higher apartments in a larger numerical model of the Grenfell Tower. For the scenario investigated in the previous study, 26 observations from the real event correlate with the results of the numerical modelling. There was no evidence of flashover in the initial apartment kitchen, but fire propagation within the kitchen was clearly visible. The window frame appeared to have failed. However, this study was only dedicated to fire spread over a small part of the façade, two floors high. Fire spread over the whole tower façade, including the impact of burning contents, was not addressed. Thus, the results generated can only be used as individual boundary conditions in a larger scale analysis.
In the current work, the full height of the Grenfell Tower façade is addressed, using a numerical tool, to determine its fire behaviour. A three-dimensional CFD model is used to evaluate fire spread to and vertically over the whole east face of the Tower. This fire breaks out from the apartment of origin (Flat 16), located on the fourth floor of the east face of the Grenfell Tower, through its kitchen window, as investigated in Guillaume et al. 26 The thermal and combustion characteristics used for the façade system are those validated in Dréan et al. 20 The heat release rate for this initial fire and the apartment fire contributions detailed in Guillaume et al 5  Modelling of the vertical fire spread over the east face of the Tower is described herein. It is validated by comparison with video and photographic records of the real fire. 5 The impact of different façade components on vertical fire propagation is investigated by modelling the different façade system build-ups. The influence of cavity barriers on fire propagation is shown as well as the fire performance of windows. This paper presents the hypothesis selected, the methodology applied, and the results for each step of the study performed. This paper considers the full scale fire on the east face of Grenfell Tower, using the numerical model validated for the façade system, the initial apartment fires, and windows failure. Fire spread over the external façade and to higher apartments is addressed.

| Numerical set-up
A three-dimensional CFD model is used to simulate vertical fire spread over the east face of Grenfell Tower. This fire is initiated at the kitchen window of the apartment of origin (Flat 16), as investigated in Guillaume et al. 26 The thermal and combustion characteristics of the materials of which the façade system is comprised are those validated in Dréan et al. 20 The heat release rate of the initial fire, as well as the apartment fire contributions detailed in Guillaume et al, 5 16 The default sub-models of FDS were used for the gas phase radiation exchanges with 100 (default value) solid angles. The combustion model with primitive and lumped gas species definition to solve a transport equation for each species to be tracked was also investigated as well as the use of a single step reaction for the CO production because of uncertainty in the occurrence of this phenomena and regarding well-ventilated conditions for the combustion observed experimentally and numerically.
The fuel burnout in each solid numerical cell is accounted by the specification of the combustible mass of the object through the bulk density parameter. Thus, when the mass contained in each solid cell is consumed, then the solid disappears from the calculation cell by cell.
This feature is used to consider for the destruction of the cladding as

| Façade system and constructive details
In this paper, the description ACM-PE refers to Reynobond PE, 32 36,37 Namely, a density of 2300 kg/m 3 is used in this study. The heat capacity and thermal conductivity are extracted from previous studies. 36,37 The emissivity of concrete is taken at 0.8.
The window glasses are considered as a sandwich constituted with glass/air/glass. Their thermal properties are extracted from Efectis databases for standard glazing and from Mikkola et al. 38 It is has a density of 2490 kg/m 3 . The emissivity is taken at 0.87.
The thermal properties of XPS are taken from previous studies, [38][39][40] namely, a density of 20 kg/m 3 is used in this study; the heat capacity and thermal conductivity are 1.13 J/g/K and 0.03 W/m/K, respectively; and the emissivity is taken at 1. The ignition temperature of XPS protected by a metallic sheet can be estimated around 500°C . 38 XPS has a heat of combustion of 40 MJ/kg. 39,40 The CO yield is of 0.06 g/g 39,40 and the soot yield is 0.2 g/g. 39 The asymptotic mass loss rate is 0.032 kg/m 2 /s. 39 The thermal properties of PVC are taken from previous studies, [39][40][41][42] namely, a density of 1380 kg/m 3 is used in this study. The emissivity is taken at 0.95. The ignition temperature of PVC can be estimated around 200°C. 40 PVC has a heat of combustion of 16.4 MJ/kg. 40,41 The CO yield is of 0.063 g/g, 39,41 the soot yield is 0.176 g/g, 39

and
the HCl yield is 0.27 g/g. 39,43 The asymptotic mass loss rate is 0.016 kg/m 2 /s. 39 The thermal properties for mineral wool are extracted from the Efectis databases and from the product datasheet. 34 It has a density  The total surfaces of these rooms are conserved in the numerical model. For the "X1" flats, the HRR per unit area of the "X6" flats was used. Thus, the HRR of each "X1" room varies according to its surface area. It was assumed that these compartments, fire starts at 3 minutes after window breakage, corresponding to the time taken for flames to enter a compartment and ignite furniture.

| Numerical modelling of the east façade
As can be seen in Figure 3, the modelling described in this paper focuses on the part of the Grenfell Tower that suffered vertical fire spread in the first phase of the event from 1:08 AM to 1:29 AM. A close-up view of the Tower model is shown in Figure 4. The flats from the fourth floor to the 23rd floor are included. The apartment of origin, Flat 16, is highlighted in yellow. Half a floor is considered to represent the crown of the Tower.
The internal layout (identical for each floor) of the parts of the Tower included in the model is provided in Figure 5. In each room, fire is applied as a boundary condition on its whole surface using the HRR evolution

| Partial models
Two partial numerical models were investigated before addressing the full-scale tower, for which local mounting details can be evaluated using a finer grid.
The main characteristics of the addressed numerical models are indicated in Table 1 below.  In the FDS reference guide 16 and literature, 45 a criterion for the quality of the mesh resolution is given for simulations involving buoyant plumes. It is assessed using the non-dimensional D*/Δx ratio, where Δx is the representative length of the grid cells and D* is the characteristic fire diameter calculated with the following relation: ; where Q is the fire HRR, ρ ∞ , C p , T∞, and g are the ambient gas density (approximately 1.2 kg/m 3 ), gas specific heat (approximately 1 kJ/kg/K), gas temperature (20°C), and gravitation acceleration (9.81 m/s 2 ), respectively. Following this expression, the 0.25-m grid size considered is sufficiently fine to capture accurately the combustion and turbulence phenomena of the system for heat release rates up to 1 MW.

| Numerical evaluation of the initial fire propagation from Flat 16 to Flat 26
Video and photographic records and other evidence, extensively detailed in expert reports, [46][47][48] show that the initial fire was located   • at 01:14 AM the PIR insulation begins to contribute to the fire ( Figure 10); the blue and red colours in Figure 10 are used to illustrate the burning rate of the insulation (when cladding is removed).
Blue means no burning while red represents the local burning. • after 01:21 AM, the fire has spread to the cladding of the column, and infill combustion is observed; the fire has reached the ninth floor.
The development of the fire in its early stages is illustrated in

| INVESTIGATION OF THE IMPACT OF MODIFICATION OF THE FAÇADE SYSTEM ON VERTICAL FIRE PROPAGATION
The impact of modifications in the insulation and the ACM cladding on vertical fire propagation over the east face of the Tower is investigated using the numerical model. The influence of apartment furniture and that of cavity barriers is also investigated.

| Investigation into changing the insulation material
The impact of using a non-combustible insulation is investigated using the numerical model: mineral wool (MW) is considered instead of the PIR insulation that was used on the Grenfell Tower. The cladding   This energy is then available for the cladding combustion.

| Investigation into changing the cladding material
The impact of using an inert ACM cladding, ACM-A2 instead of the ACM-PE cladding which was used on the Grenfell Tower, is

| Synthesis
A comparison between the simulated vertical propagation over the east face as a function of time for the different façade configurations investigated is shown in Figure 34.  Even if the numerical model addressed in this paper correlates well with the observations during the Grenfell event, several modelling assumptions were needed.
As discussed in Dréan et al, 24 numerical hypothesis must be considered for the model developed for the accurate fine grid in another study 20 to be applied to a coarser one as used in the present model.
The main objective is to reproduce the thermal gradients achieved with the initial model in the gas phase because exchange between the solid and gas phases will be evaluated in a larger cell. Thus, to reproduce the numerical results that were validated against the test data using a fine grid, the computed ignition temperature for the insu- Talal Fateh https://orcid.org/0000-0002-4204-0540