# Development of a CFD-Suitable Deep Neural Network Model for Laminar Burning Velocity
## 4 CFD Simulations
Results are unshifted in time to show the delay in the laminar phase simulation obtained with the DNN model compared to the Malet correlation. The DNN model provides a longer duration of quasi-laminar phase (overall slower flame propagation rate until the first obstacle). However, flameFoam with the TFC model does not simulate a quasi-laminar regime correctly [52]. The assumption is made that in turbulent cases, the main transient is controlled by the turbulent regime and the influence of the laminar phase is limited to a larger or smaller shift in time of the onset of the turbulent phase. This is partially illustrated in this case in Figures 9 and 10 since different methods of laminar flame speed estimation led to different evolution and duration of the quasi-laminar regime; however, when flame accelerates due to turbulence, pressure evolutions become very similar, even including the shockwave propagation and reflection. Figure 8: Vertical flame propagation velocity profiles in ENACCEF2 facility. Figure 11 presents flow streamlines and laminar burning velocity values calculated in both cases when the flame is in a similar location. Only values on the flame brush (progress variable source term larger than 1000 1/s) are shown. There is a clear difference in the laminar flame velocity values obtained with both methods. The influence of pressure and temperature are far more pronounced in the Malet correlation case, where the burnt-mixture side of the flame brush exhibits two to three times higher velocity values than the leading side or whole brush in the case of the DNN model. Consequently, a very thin flame brush is obtained with Malet correlation, since combustion is completed at a higher rate. However, at the leading side of the brush, both methods seem to produce similar values of laminar burning velocity, corresponding to the similar overall flame propagation rate in both cases (Figure 8); higher values at the trailing side mostly only impact the flame brush thickness. Figure 10: Pressure evolution at 6.227 m height of ENACCEF2. Figure 9: Pressure evolutions at different heights of ENACCEF2 (time-shifted). To validate the DNN model at a somewhat higher concentration, where the Malet correlation becomes not valid, a simulation of 22.65% hydrogen-air mixture combustion in the vented laboratory-scale chamber of the University of Sydney (US) [54] was performed. The US chamber is a rectangular box of 5 \(\times\) 5 \(\times\) 25 cm dimensions with an open top. Flame acceleration can be achieved with various configurations of obstacles. In the simulated experiment, three rows of baffles and a small upper obstacle were used, the so-called configuration BBBS (Figure 12a). The flame is ignited at the bottom center and propagates upwards. The computational mesh (Figure 12b) of the facility was composed of the structured orthogonal grid of the chamber-free volume and additional volume outside the top opening to simulate surroundings. 2D axisymmetric mesh with 0.25 mm cell sizes was used in the presented simulations. Around the obstacles, the mesh was graded up to 0.03125 mm (Figure 12c). Initial conditions were set according to the experiment--20 \({}^{\circ}\)C temperature and 100,000 Pa pressure. Turbulence was modeled using the k-u-SST RANS model. Negligible values for initial turbulence parameters were selected. The adiabatic boundary condition for temperature was set. Figure 13 shows overpressure evolution at the facility's bottom. Results obtained by flameFoam-ANN simulation are close to the experimental, including the shape of the  
Figure 11: Simulated LBV distribution in ENACCEF2 at selected moments. Figure 12: Vented chamber and computational grid: (**a**) chamber scheme, (**b**) overall mesh view and (**c**) computational mesh details below the upper obstacle. pressure curve. However, overpressure values are slightly over-predicted.