|
| 1 | +--- |
| 2 | +layout: datapage |
| 3 | +excerpt: (5 cases) |
| 4 | +title: Premixed Flame H2-Air |
| 5 | +description: Premixed Flame H2-Air DNS in Slot Burner |
| 6 | +header: |
| 7 | + teaser: /assets/img/ico_quentin2024.png |
| 8 | +# image: /assets/img/quentin2024.png |
| 9 | +--- |
| 10 | +<div style="text-align: center;"> |
| 11 | + <img src="./assets/img/quentin2024.png" alt="Image 1" style="max-width: 100%;"> |
| 12 | +</div> |
| 13 | + |
| 14 | +## Description |
| 15 | +The configuration is a slot burner at constant pressure $$P = 1$$ atm and fresh gas temperature $$T_u = 300$$ K used to generate a training database for the modeling of subfilter-scale features in lean premixed H$$_2$$-air reacting flows using a CNN [1]. The physical domain consists of a central inlet where a premixed H2-air mixture flows at a bulk velocity $$U_b = 24$$ m/s with velocity fluctuation $$u′= 2.4$$ m/s, surrounded by two laminar coflows where burnt gas flows at a bulk velocity $$U_c = 3.6$$ m/s. The injection of turbulence at the central inlet corresponds to homogeneous and isotropic turbulence using a Passot-Pouquet turbulence spectrum [2] with an integral length scale $$l_t = 2$$ mm. The domain is rectangular with periodic boundary conditions in the z-direction. Adiabatic walls are specified in the y-direction. Both inlets and outlet are specified in the x-direction. This configuration is computed for five different global equivalence ratios $$\phi_g = $$ 0.35, 0.4, 0.5, 0.6 and 0.7. All other parameters are kept constant. The Reynolds number of the central inlet is about 10,000 for all cases. |
| 16 | +DNS of the slot burner cases are performed using the AVBP [3] massively parallel code solving the |
| 17 | +compressible multi-species Navier-Stokes equations. A third order accurate Taylor–Galerkin scheme is adopted |
| 18 | +for discretization of the convective terms [4]. NSCBC [5] are imposed at the inlets (relaxation factor of 1000 |
| 19 | +s−1) and at the outlet (relaxation factor of 200 s−1). Dynamic viscosity µ follows a power law function of |
| 20 | +temperature $$T$$ |
| 21 | + |
| 22 | + |
| 23 | +$$\mu = \mu_0 \left(\frac{T}{T_0}\right)^\gamma$$ |
| 24 | + |
| 25 | +with $$\mu_0 = 8.062 × 10−5$$ kg/m.s, $$T_0 = 2.645 \times 10^3$$ K and $$γ = 6.481 \times 10^{−1}$$. Thermal diffusivity is computed |
| 26 | +from the viscosity using a constant Prandtl number: $$Pr = 0.66$$. Species diffusivities are computed using |
| 27 | +a constant Schmidt number specific for each species. This approach takes into account non-unity |
| 28 | +Lewis numbers and preferential diffusion between the different species. It was verified that the errors made by |
| 29 | +the simplified transport description are negligible by comparing the results with simulations using a mixture- |
| 30 | +averaged transport model [1]. Soret and Dufour transport processes are ignored in the simulations of the present |
| 31 | +work. Hydrogen chemical kinetics relies on the San Diego mechanism [6], already successfully used for H2-air |
| 32 | +premixed combustion in Coulon et al. [7]. This mechanism comprises 9 species and 21 reactions. |
| 33 | + |
| 34 | +The mesh is a homogeneous Cartesian grid with constant element size $\Delta_x = 80 \mu m$ for $$\phi_g = 0.35, 0.4$$ and |
| 35 | +$$0.6$$, and $$\Delta_x = 50 \mu m$$ for $$\phi_g = 0.6\ \mathrm{and}\ 0.7$$. The length of the domain in the x-direction $$L_x$$ is adapted to the length of turbulent the flame brush. It varies from 76 mm for $$\phi_g = 0.35$$ to $$36$$ mm for $$\phi_g= 0.7$$. |
| 36 | + |
| 37 | +## Application |
| 38 | +This database was generated to train a CNN to infer H$$_2$$-air burning rates. The data-driven, supervised learning |
| 39 | +methodology is described in Malé et al. [1]. It involves using the database, filtered to emulate LES solutions, to train a |
| 40 | +CNN to approximate burning rates based on relevant input variables. The emulated LES database comprises the |
| 41 | +five different global equivalence ratios of the present DNS database and three different filter sizes. Random crops, |
| 42 | +rotations and flips are performed to ensure that the CNN is invariant to translation [8] and has no preferential |
| 43 | +orientation. Once trained, the CNN-based model is shown to infer burning rates on full LES solutions never |
| 44 | +seen during training with high accuracy. In addition to this, the model is found to infer burning rates on filter |
| 45 | +sizes and equivalence ratios other than those used for training. More details can be found in Malé et al. [1]. Code for |
| 46 | +training and inference is available via GitLab at https://gitlab.com/male.quentin/cnn_h2flame. |
| 47 | + |
| 48 | +<div style="text-align: center;"> |
| 49 | + <img src="/assets/img/arch_quentin2024.png" alt="Image 1" style="max-width: 80%;"> |
| 50 | +</div> |
| 51 | + |
| 52 | +## Quick Info |
| 53 | +* Contributors: Quentin Malé |
| 54 | +* N<sub>ɸ</sub> = 6 + 9 |
| 55 | + |
| 56 | +* <a href="https://doi.org/10.1017/dce.2025.1">DOI</a> |
| 57 | +* <a href="./assets/bib/quentin2024.bib">.bib</a> |
| 58 | + |
| 59 | +## Links to different cases |
| 60 | + |
| 61 | +<script src="./assets/js/table.js"></script> |
| 62 | + |
| 63 | +<table align="center"> |
| 64 | + <tr class="header"> |
| 65 | + <th style="width:2%;">ID</th> |
| 66 | + <th style="width:8%;">$$\phi_g$$</th> |
| 67 | + <!-- <th style="width:60%;">TPY</th> --> |
| 68 | + <th style="width:8%;">Grid</th> |
| 69 | + <th style="width:8%;">Size (GB)</th> |
| 70 | + <!-- <th style="width:60%;">Article</th> --> |
| 71 | + <th style="width:12%;">Links</th> |
| 72 | + </tr> |
| 73 | + <tr> |
| 74 | + <td align="center"> 0 </td> |
| 75 | + <td align="center">0.35</td> |
| 76 | + <td align="center">951×401×201</td> |
| 77 | + <td align="center">16</td> |
| 78 | + <td align="center"> |
| 79 | + <a href="https://www.kaggle.com/datasets/blastnet/premixed-flame-slot-burner-dns-h2air-phi035">Kaggle</a>, <a href="./assets/json/quentin2024/premixed-flame-slot-burner-dns-h2air-phi035-info.json">info.json</a><BR> |
| 80 | + </td> |
| 81 | + </tr> |
| 82 | + <tr> |
| 83 | + <td align="center"> 1 </td> |
| 84 | + <td align="center">0.4</td> |
| 85 | + <td align="center">901×401×201</td> |
| 86 | + <td align="center">15</td> |
| 87 | + <td align="center"> |
| 88 | + <a href="https://www.kaggle.com/datasets/blastnet/premixed-flame-slot-burner-dns-h2air-phi04">Kaggle</a>, <a href="./assets/json/quentin2024/premixed-flame-slot-burner-dns-h2air-phi04-info.json">info.json</a><BR> |
| 89 | + </td> |
| 90 | + </tr> |
| 91 | + <tr> |
| 92 | + <td align="center"> 2 </td> |
| 93 | + <td align="center">0.5</td> |
| 94 | + <td align="center">651×401×201</td> |
| 95 | + <td align="center">11</td> |
| 96 | + <td align="center"> |
| 97 | + <a href="https://www.kaggle.com/datasets/blastnet/premixed-flame-slot-burner-dns-h2air-phi05">Kaggle</a>, <a href="./assets/json/quentin2024/premixed-flame-slot-burner-dns-h2air-phi05-info.json">info.json</a><BR> |
| 98 | + </td> |
| 99 | + </tr> |
| 100 | + <tr> |
| 101 | + <td align="center"> 3 </td> |
| 102 | + <td align="center">0.6</td> |
| 103 | + <td align="center">1041×641×321</td> |
| 104 | + <td align="center">31</td> |
| 105 | + <td align="center"> |
| 106 | + <a href="https://www.kaggle.com/datasets/blastnet/premixed-flame-slot-burner-dns-h2air-phi06">Kaggle</a>, <a href="./assets/json/quentin2024/premixed-flame-slot-burner-dns-h2air-phi06-info.json">info.json</a><BR> |
| 107 | + </td> |
| 108 | + </tr> |
| 109 | + <tr> |
| 110 | + <td align="center"> 4 </td> |
| 111 | + <td align="center">0.7</td> |
| 112 | + <td align="center">721×641×321</td> |
| 113 | + <td align="center">45</td> |
| 114 | + <td align="center"> |
| 115 | + <a href="https://www.kaggle.com/datasets/blastnet/premixed-flame-slot-burner-dns-h2air-phi07">Kaggle</a>, <a href="./assets/json/quentin2024/premixed-flame-slot-burner-dns-h2air-phi07-info.json">info.json</a><BR> |
| 116 | + </td> |
| 117 | + </tr> |
| 118 | +</table> |
| 119 | + |
| 120 | +## References |
| 121 | +[1] Malé, Q., Lapeyre, C. J., and Noiray, N. (2024). Hydrogen reaction rate modeling based on convolutional |
| 122 | +neural network for large eddy simulation. Accepted for publication in Data-Centric Engineering, to appear. |
| 123 | +arXiv:2408.16709 [cs.CE]. |
| 124 | +[2] Passot, T. and Pouquet, A. (1987). Numerical simulation of compressible homogeneous flows in the turbulent |
| 125 | +regime. Journal of Fluid Mechanics, 181:441–466. |
| 126 | +[3] Gicquel, L. Y., Gourdain, N., Boussuge, J.-F., Deniau, H., Staffelbach, G., Wolf, P., and Poinsot, T. (2011). |
| 127 | +High performance parallel computing of flows in complex geometries. Comptes Rendus M´ecanique, 339(2- |
| 128 | +3):104–124. |
| 129 | +[4] Colin, O. and Rudgyard, M. (2000). Development of High-Order Taylor–Galerkin Schemes for LES. Journal |
| 130 | +of Computational Physics, 162(2):338–371. |
| 131 | +[5] Poinsot, T. and Lelef, S. (1992). Boundary conditions for direct simulations of compressible viscous flows. |
| 132 | +Journal of Computational Physics, 101(1):104–129. |
| 133 | +[6] Saxena, P. and Williams, F. A. (2006). Testing a small detailed chemical-kinetic mechanism for the |
| 134 | +combustion of hydrogen and carbon monoxide. Combustion and Flame, 145(1-2):316–323. |
| 135 | +[7] Coulon, V., Gaucherand, J., Xing, V., Laera, D., Lapeyre, C., and Poinsot, T. (2023). Direct numerical |
| 136 | +simulations of methane, ammonia-hydrogen and hydrogen turbulent premixed flames. Combustion and Flame, |
| 137 | +256:112933. |
| 138 | +[8] Biscione, V. and Bowers, J. S. (2021). Convolutional neural networks are not invariant to translation, but |
| 139 | +they can learn to be. Journal of Machine Learning Research, 22(229):1–28. |
| 140 | + |
| 141 | + |
| 142 | + |
| 143 | + |
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