## 3 Numerical Strategy
### Overall Solution Strategy
The flame was inflicted at the bottom of the specimen for 10 s. Once this time passed, the flame was taken out, and the fire did not stop spreading along the sample, as shows in Figure 4. As a consequence of this behavior during the test, the material was classified as \"no rating\" according to [5]. ### Numerical Setup

The geometry and dimensions of the computational domain are presented in Figure 5a. The domain of the polymer and air are discretized by a non-structured tetrahedra mesh of 100,902 and 286,850 elements, respectively (Figure 5b). Note that only the fourth part of the whole problem was considered when assuming symmetry conditions. This assumption is based on the fact that although the flame was applied with a Bunsen burner at 45 degrees, it was always in full contact with the bottom of the polymer rather than with the vertical sides. No vertical side was ever directly exposed to the flame. Thus, in this example, the symmetry was never lost, and, therefore, the heat provided by the flame was maximum in the lower part of the polymer [6, 7, 34]. In fact, previous studies have explored the same idea independently of the size of the domain for simulation (one fourth or full domain) [8, 34] and with consideration of the fact that the heat of the specimen has a varied height. Regarding the boundary conditions (Figure 5a), for both domains over the symmetric faces, we set the normal velocity component and the normal gradients of all flow variables (including temperature) to zero. The clamping of the polymer and the Bunsen were

Figure 3: Position of the thermocouples. Figure 2: Viscosity of MDH30/PP in the dynamic temperature step mode. modelled by fixing all of the velocity components to zero and applying a face heat flux, respectively. The latter was set to 85 [kW/m2] during the first 10 s following the criteria adopted in [8]. On the other hand, a constant uniform velocity was prescribed in the inlet and a pressure value at the outlet of the air domain. The constant velocity boundary condition is indeed an approximation. Considering variable velocity, the boundary condition is possible; however, such a boundary condition leads to the divergence of the numerical solver due to the appearance of velocities in some parts of the inlet boundary pointing in the opposite direction (downwards). On the other hand, the initial conditions consisted of initializing the gas temperature, oxygen, and fuel mass fractions to 298 K, 0.23, and 1, respectively. Once the surface of the polymer reached the ignition temperature, \(Y_{\rm O}\) was fixed to 0 and \(Y_{F}\) to 1. Figure 4: Images of the UL 94 test at different time steps. Figure 5: Problem definition. (**a**) Computational domains with boundary conditions. (**b**) Meshes of the polymer and the air. The input parameters for both solvers are summarize in Table 1.

The expression of the adjusted curve corresponding to the experimental viscosity values presented in Figure 2 is given in Algorithm 2. Note that the viscosity is reported to be 453.15 to 533.15 K. However, the registered temperatures of the polymer during the flame test are clearly higher (Figure 6). As viscosity is the key parameter for modeling the dripping behavior [6; 7], in this work, it was estimated on the basis of the viscosity curve provided by NIST [12] and the images of the experiment for those ranges where the curve was not available. These two sources allowed us to estimate the viscosity-temperature curve as follows: (i) if temperature \(<\) 453.15 K, viscosity is directly approximated using the NIST curve [12]; (ii) if temperature \(>\) 533.15 K and temperature \(<\) 724 K, viscosity is set to 20,000 [m\({}^{2}\)/s] (last known value of the rheological study) since the polymer does not considerably move according to the experiment ); (iii) if temperatures \(>\) 725 K, three ways to decrease the viscosity are proposed following the pattern showed by the NIST curve. It should be noted that these curves are from hereon referred to as curve 1, curve 2, and curve 3.