# Development of a CFD-Suitable Deep Neural Network Model for Laminar Burning Velocity
## 4 CFD Simulations  
This chapter presents a couple of flameFoam-DNN calculation examples showing that the developed DNN model is usable with CFD simulation and provides results in line with the Malet correlation or experimental data. The developed model was implemented in the open-source turbulent premixed combustion solver flameFoam [52] v0.10. flameFoam is an OpenFOAM-based solver using a progress variable approach and turbulent flame speed closure model to simulate combustion. The turbulent flame speed closure model requires turbulent flame speed values, which in turn require LBV values. In the flameFoam-DNN simulations, presented below, these LBV values were estimated on-the-fly in the flameFoam using the DNN model programmed according to Equations (3)-(6) with the weights exported from the DNN training. The solver source code, including the DNN model, is available on GitHub: [[https://github.com/flameFoam/flameFoam](https://github.com/flameFoam/flameFoam)]([https://github.com/flameFoam/flameFoam](https://github.com/flameFoam/flameFoam)) (accessed on 29 June 2022). To compare flameFoam calculation results obtained using the DNN model versus Malet correlation, simulation of ENACCEF2 facility (France, CNRS-ICARE) TEST1 from ETSON-MITHYGENE benchmark [53] was performed. ENACCEF2 is a closed vertical steel tube of 7.65 m height and 0.23 m inner diameter (Figure 6(a)). Flame acceleration is achieved in the simulated experiment by 9.2 mm thin annular obstacles situated in the lower part of the facility (Figure 6(b)). The flame is ignited at the bottom center and propagates upwards. The hydrogen concentration in the homogenous combustible mixture with air was 13%. The experiment was performed at 23 \({}^{\circ}\)C temperature and 100,000 Pa pressure. The computational mesh (Figure 6(c)) of the facility was composed of the structured orthogonal grids of the facility-free volume (fluid region, blue in Figure 7) and facility wall  
Figure 7: ENACCEF2 facility and computational grid: (**a**) overall scheme, (**b**) obstacle region close-up and (**c**) computational mesh around the obstacle. (solid region, yellow in Figure 7). 2D axisymmetric mesh with 1 mm cell sizes was used in the presented simulations. In the fluid region, flameFoam solves Navier-Stokes, turbulence and combustion equations, while in the solid region heat conductivity equation is solved. The regions are coupled through standard OpenFOAM inter-region boundary condition for temperature compressible:turbulentTemperatureCoupledBAffleMixed. Initial conditions were set according to the experiment. Turbulence was modeled using the k-\(\epsilon\) RANS model. Negligible values for initial turbulence parameters were selected. The boundary condition for temperature on the external side of the solid grid was set to 23 \({}^{\circ}\)C.  
Figure 8 presents the flame propagation velocity profile (obtained from flame arrival times) obtained by both simulations. Results are very similar, showing that the DNN model hasn't introduced any regressions compared to the Malet correlation around the experimental conditions [52]. There was no significant difference of computation time between Malet and DNN calculations. Figure 9 presents pressure evolutions at three different heights of the facility, time-shifted to facilitate comparison. Pressure evolutions corresponding to the turbulent combustion phase (accelerated flame) are also very similar in both cases. Differences between evolutions obtained with Malet and DNN seem to be mostly related to a slower (quasi-) laminar combustion phase and, consequentially, a relatively stronger impact of turbulent acceleration, which results in a higher peak pressure wave value. At a 4 m height, the peak value obtained with DNN is slightly lower; however, this seems to be a local result caused by coincidental interference, since further, at 6.2 m (Figure 10), DNN results already show higher pressure values. Figure 10 presents pressure evolutions at a height of 6.227 m. Initial shockwave propagation and reflected shockwave arrival are visible.