Introduction
Fire in an enclosure is an example where the overall combustion rate is controlled by ventilation conditions. Flow of fresh air and combustion products in an enclosure has significant bearing on development and state of fire. It controls heat transfer and therefore the temperature distribution. It also importantly influences gas composition, which determines flammability limits and combustion rate of the available fuel.
As fire scenarios are often encountered in residential buildings and other enclosed spaces, they have been a subject of recurrent fire safety studies. The initial systematic studies were conducted by Steckler et al. [1] to quantify the temperature distribution in the enclosure and the amount of entrained air.
Mathematical modelling of such fire scenarios has to include convective and radiative heat transfer, turbulence, transport of chemical species (reactants and combustion products) and a suitable approximation of the combustion reaction rate. Interaction of these modelling principles makes their simulation particularly challenging.

Objectives
The fire validation cases examine capabilities of the CFD model to correctly capture an interaction between the combustion process, induced flow of fresh air, turbulence, convective and radiative heat transfer.
They are based on experimental tests 18, 19 and 20 that were conducted by Steckler et al. [1] using different fuel mass flow rates. All parameters of experimental tests that are required for CFD modelling are not specified in [1]. For that reason, use of additional resources [e.g. 2 & 3] is necessary.
The conditions in the enclosure are determined by the size of the fire. In the studied fire environment, the flow conditions are transient. Strong buoyant flow causes thermal stratification that is clearly distinguishable from the vertical temperature profile. Another important parameter is the entrainment rate of fresh air, which can be quantified through the velocity profile of the induced flow.
It is important to warn against the use of a coarse numerical grid to approximate the combustion process. A grid sensitivity study of CFD results is highly advised.

Geometry

• Length, width and height of the enclosure (L_c, W_c & H_c ) are 2.8, 2.8 & 2.128 m.
• Dimensions of the additional, ambient space (L, L_a, W_a & H_a) are 2.698, 3.6, 4.4 & 3.0 m
• Wall thickness (T_w) is 0.102 m.

Fuel source is located on a square pedestal in the middle of the enclosure.

• Length and width (L_s) of the pedestal are 0.42 m.
• Pedestal elevation (H_s) is 0.02 m.
• Fuel source diameter (D_s) is 0.3 m.

Note that small variations in the fuel source location and elevation may cause signification changes in fire behaviour especially where the fire interacts with a boundary layer.

Loading
Fluid motion is induced by combustion of methane gas, which is introduced to the simulation domain via a prescribed mass flow rate of a predetermined caloric value. Three test cases [1] are analysed:

• test 18:   `Q_(source) = 62.9` `"kW"`
• test 19:   `Q_(source) = 31.6` `"kW"`
• test 20:   `Q_(source) = 105.3` `"kW"`

Material properties
Material properties of ideal, thermally perfect gases are used for the analysis:
CH₄:   `M = 16.04` `"kg"//"kmol"`,   `mu = 11.1*10^(-6)` `"Pa·s"`,   `lambda = 0.0343` `"W"//"mK"`
O₂:   `M = 31.99` `"kg"//"kmol"`,   `mu = 19.2*10^(-6)` `"Pa·s"`,   `lambda = 0.0266` `"W"//"mK"`
N₂:   `M = 28.01` `"kg"//"kmol"`,   `mu = 17.7*10^(-6)` `"Pa·s"`,   `lambda = 0.0259` `"W"//"mK"`
CO₂:   `M = 44.01` `"kg"//"kmol"`,   `mu = 14.9*10^(-6)` `"Pa·s"`,   `lambda = 0.0145` `"W"//"mK"`
H₂O:   `M = 18.02` `"kg"//"kmol"`,   `mu = 9.4*10^(-6)` `"Pa·s"`,   `lambda = 0.0193` `"W"//"mK"`
For the specific heat capacity, NASA SP-273 format [4] is utilised.
Thermal radiation emissivity and absorptivity of gaseous mixture is calculated using a multigrey radiation model [5].

Meshing
A numerical grid with tetrahedral elements is used in all simulation cases with the element size set to 8 cm. In the enclosure, the grid spacing is reduced to 4 cm. The grid is further refined at the surface of the fuel source, where the grid spacing decreases to 2 cm.
Five layers of prismatic elements are used with the first layer height of 4 mm.

The utilised numerical grid contains 0.638 mil nodes and 2.98 mil elements.

Initial conditions
Due to buoyancy induced instabilities, the system exhibits large scale transient flow structures. For that reason, a transient CFD simulation is required.

• Initially, the enclosure as well as the ambient space is occupied by air, which is assumed to contain 21% O₂ and 79% N₂ by volume.
• An ambient temperature (`T_(amb)`) is prescribed to the whole domain. It is 31°C for test 18, 29°C for test 19, and 35°C for test 20.
• A reference pressure of 1 atm is set at the floor level of the enclosure. The vertical variation of pressure follows the hydrostatic relationship of an incompressible fluid.

Boundary conditions

• For the fuel source (marked red), the prescribed caloric value [1] has been converted to the methane mass flow rate:
  
  `dot(m)_(CH_4) = Q_(source)/(Delta H_(CH_4, comb)) M_(CH_4)`
  
  For three analysed tests the following parameters are used:
  
  test 18:   `Q_(source) = 62.9` `"kW"`,  `dot(m)_(CH_4) = 1.25755` `"g"//"s"`, `T_(source)=31^"o""C"`
  test 19:   `Q_(source) = 31.6` `"kW"`,  `dot(m)_(CH_4) = 0.63176` `"g"//"s"`, `T_(source)=29^"o""C"`
  test 20:   `Q_(source) = 105.3` `"kW"`,  `dot(m)_(CH_4) = 2.10536` `"g"//"s"`, `T_(source)=35^"o""C"`
  
  Note that the inflow temperature (`T_(source)`) is assumed to be equal to the temperature of the ambient (`T_(amb)`).
  
  In all case, the turbulence intensity of the inflow is set to 5% and its eddy viscosity to `10mu`. Nevertheless, a limited sensitivity analysis has shown a negligible impact of the inflow turbulence level on the overall results.
• A substantial heat loss is assumed across the walls of the enclosure as indicated in [2 & 3]. For that reason, the overall heat transfer coefficient of 7 W/m²K is prescribed to the internal, top and side surfaces of the enclosure (marked blue).
  
  The ambient temperature (`T_(amb)`) is used as a far-field temperature; 31°C for test 18, 29°C for test 19, and 35°C for test 20.
• The bottom as well as all external surfaces can be treated as adiabatic (marked black).
• Opening conditions that permit inflow and outflow over the same surface are set at the external boundaries of the ambient volume (marked green). The hydrostatic variation of pressure is used as a pressure boundary with the reference pressure of 1 atm at z = 0 m.
  
  The inflow temperature of the entrained air is assumed to be equal to the temperature of the ambient (`T_(amb)`):  31°C for test 18, 29°C for test 19, and 35°C for test 20.

Results
Transient simulations were conducted using a double precision CFD solver. For turbulence modelling, k-ε model was selected. The turbulence production term due to buoyancy:
`P_(kb) = -mu_t/(rho Sc_t) g_i del_i rho`
was included in the turbulence kinetic energy (`k`) and its dissipation rate (`epsilon`) transport equations. The dissipation coefficient `C_3` in the epsilon transport equation was set 0.2:
`P_(epsilon b) = C_3 max(0, P_(kb))`
Figure below shows fire behaviour in the enclosure. The fire is marked by a red isosurface of 300°C. The separation between the hot-upper and the cold-lower layer is illustrated by a grey isosurface, which represents a combined volume fraction of combustion products of 2.4 %.

Vertical distributions of temperature and of flow speed are measured in the corner of the enclosure, 0.305 m from the wall in both horizontal directions. In addition, measurements are also taken in the middle of the door to estimate the entrainment of the ambient air [1].

A comparison of the experimental data and the CFD simulation results is presented below for tests 18, 19 and 20. The cumulative error of thermocouple measurements was estimated to be at least +2/-4°C [1].

Quadratic mean (or RMS) of deviation between the experimental data [1] and the current CFD simulation results is calculated for all three tests:

test 18	RMS of deviation
•   temperature in the corner	8.11°C
•   temperature across the door	8.90°C
•   flow speed across the door	0.111 m/s

test 19	RMS of deviation
•   temperature in the corner	8.00°C
•   temperature across the door	6.52°C
•   flow speed across the door	0.0788 m/s

test 20	RMS of deviation
•   temperature in the corner	9.08°C
•   temperature across the door	11.8°C
•   flow speed across the door	0.125 m/s

Files

• Experimental data [1] for test 18 (2019/03/11)
• Experimental data [1] for test 19 (2019/03/11)
• Experimental data [1] for test 20 (2019/03/11)
• CFD simulation results for test 18 (2019/03/11)
• CFD simulation results for test 19 (2019/03/11)
• CFD simulation results for test 20 (2019/03/11)