# Predicting NOx Distribution in a Micro Rich–Quench–Lean Combustor Using a Variational Autoencoder

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Structure of the Combustor

#### 2.2. Simulation Methods and Validation

#### 2.3. Artificial Neural Networks and Variational Auto-Encoders

#### 2.4. Dataset

#### 2.5. Architectural Details

## 3. Results

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

a_{1} | model constant | μ | laminar viscosity [kg/(m·s)] |

c | standard gas concentration | μ_{e} | effective viscosity [kg/(m·s)] |

c′ | test gas concentration | μ_{t} | turbulent viscosity [kg/(m·s)] |

F_{1}/F_{2} | blending function | ρ | density [kg/m^{3}] |

k | turbulent kinetic energy [J] | σ_{h}/σ_{k}/σ_{Y}/σ_{ω} | model constants |

S_{m}/S_{u}/S_{v}/S_{w}/S_{h}/S_{Y} | source terms | Ω | vorticity [1/s] |

t | time [s] | ω | dissipation rate [1/s] |

u | velocity in x direction [m/s] | Abbreviations | |

v | velocity in y direction [m/s] | AE | auto encoder |

V | standard gas fraction | ANN | artificial neural network |

V’ | test gas fraction | CBM | coal bed methane |

w | velocity in z direction [m/s] | FGM | flamelet-generated manifold |

Greek Symbols | MSE | mean squared error | |

β/β* | model constants | probability density function | |

κ | model constant | VAE | variational auto-encoder |

## References

- Balli, O.; Caliskan, H. Various thermoeconomic assessments of a heat and power system with a micro gas turbine engine used for industry. Energy Convers. Manag.
**2022**, 252, 114984. [Google Scholar] [CrossRef] - Mollo, M.; Kolesnikov, A.; Makgato, S. Simultaneous reduction of NOx emission and SOx emission aided by improved efficiency of a Once-Through Benson Type Coal Boiler. Energy
**2022**, 248, 123551. [Google Scholar] [CrossRef] - Islam, A.; Teo, S.H.; Ng, C.H.; Taufiq-Yap, Y.H.; Choong, S.Y.T.; Awual, M.R. Progress in recent sustainable materials for greenhouse gas (NOx and SOx) emission mitigation. Prog. Mater. Sci.
**2023**, 132, 101033. [Google Scholar] [CrossRef] - Ávila, C.D.; Cardona, S.; Abdullah, M.; Younes, M.; Jamal, A.; Guiberti, T.F.; Roberts, W.L. Experimental assessment of the performance of a commercial micro gas turbine fueled by ammonia-methane blends. Prog. Energy Combust. Sci.
**2023**, 13, 100104. [Google Scholar] [CrossRef] - Liu, Y.Z.; Sun, X.X.; Sethi, V.; Nalianda, D.; Li, Y.G.; Wang, L. Review of modern low emissions combustion technologies for aero gas turbine engines. Prog. Aerosp. Sci.
**2017**, 94, 12–45. [Google Scholar] [CrossRef][Green Version] - Nam, L.; Yoh, J.J. Large eddy simulation of combustion instabilities in multiple combustors densely interacting with each other. Appl. Therm. Eng.
**2023**, 220, 119714. [Google Scholar] [CrossRef] - Assareh, E.; Birgani, K.; Keykhah, S.; Ershadi, A.; Lee, M. An integrated system for producing electricity and fresh water from a new gas-fired power plant and a concentrated solar power plant—Case study—(Australia, Spain, South Korea, Iran). Renew. Energy
**2023**, 44, 19–39. [Google Scholar] [CrossRef] - Zhu, G.Y.; Chow, T.T.; Fong, K.F.; Lee, C.K. Comparative study on humidified gas turbine cycles with different air saturator designs. Appl. Energy
**2019**, 254, 113592. [Google Scholar] [CrossRef] - Speight, J.G. Natural Gas; Gulf Publishing Company: New York, NY, USA, 2008; pp. 131–160. [Google Scholar]
- Fortunato, V.; Mosca, G.; Lupant, D.; Parente, A. Validation of a reduced NO formation mechanism on a flameless furnace fed with H2-enriched low calorific value fuels. Appl. Therm. Eng.
**2018**, 144, 877–889. [Google Scholar] [CrossRef] - Zhang, X.; Hou, X.S.; Wang, Y.; Zhang, J.B. Study on flame characteristics of low heat value gas. Energy Convers. Manag.
**2019**, 196, 344–353. [Google Scholar] [CrossRef] - Zhang, L.; Li, S.; Yao, M.; Ren, Z.Y. Analysis of operating limits and combustion state regulation for low-calorific value gases in industrial burners. Int. J. Hydrogen Energy
**2022**, 47, 1306–1318. [Google Scholar] [CrossRef] - Rudolph, C.; Freund, D.; Kaczmarek, D.; Atakan, B. Low-calorific ammonia containing off-gas mixture: Modelling the conversion in HCCI engines. Combust. Flame
**2022**, 243, 112063. [Google Scholar] [CrossRef] - Du, Y.B.; Xing, M.; Zhang, J.K.; Zhang, J.P.; Deng, L.; Che, D.F. Combustion characteristic of low calorific gas under pilot ignition condition—Exploring the influence of pilot flame products. Fuel
**2023**, 333, 126613. [Google Scholar] [CrossRef] - Mosier, S.A.; Pierce, R.M. Advanced Combustor Systems for Stationary Gas Tubine Engines; US Environmental Protection Agency: Washington, DC, USA, 1980. [Google Scholar]
- Božo, M.G.; Mashruk, S.; Zitouni, S.; Valera-Medina, A. Humidified ammonia/hydrogen RQL combustion in a trigeneration gas turbine cycle. Energy Convers. Manag.
**2021**, 221, 113625. [Google Scholar] [CrossRef] - Christo, F.C.; Levy, Y.; Costa, M.; Balelang, G.A.F. Effect of jet momentum flux and heat density on NO emission in a flameless gas turbine combustor. Aerosp. Sci. Technol.
**2021**, 119, 107137. [Google Scholar] [CrossRef] - Choi, J.; Ahn, M.; Kwak, S.; Lee, J.G.; Yoon, Y. Flame structure and NOx emission characteristics in a single hydrogen combustor. Int. J. Hydrogen Energy
**2022**, 47, 29542–29553. [Google Scholar] [CrossRef] - Okafor, E.C.; Kurata, O.; Yamashita, H.; Inoue, T.; Tsujimura, T.; Iki, N.; Hayakawa, A.; Ito, S.; Uchida, M.; Kobayashi, H. Liquid ammonia spray combustion in two-stage micro gas turbine combustors at 0.25 MPa; Relevance of combustion enhancement to flame stability and NOx control. Appl. Energy Combust. Sci.
**2021**, 7, 100038. [Google Scholar] [CrossRef] - Li, J.Z.; Chen, J.; Jin, W.; Yuan, L.; Hu, G. The design and performance of a RP-3 fueled high temperature rise combustor based on RQL staged combustion. Energy
**2020**, 209, 118480. [Google Scholar] [CrossRef] - Rodrigues, N.S.; Busari, O.; Senior WC, B.; McDonald, C.T.; Chen, Y.T.; North, A.J.; Laster, W.R.; Meyer, S.E.; Lucht, R.P. NOx reduction in an axially staged gas turbine model combustor through increase in the combustor exit Mach number. Combust. Flame
**2020**, 212, 272–294. [Google Scholar] [CrossRef] - Fu, Z.G.; Gao, H.H.; Zeng, Z.X.; Liu, J.; Zhu, Q.Z. Generation characteristics of thermal NOx in a double-swirler annular combustor under various inlet conditions. Energy
**2020**, 200, 117487. [Google Scholar] [CrossRef] - Liu, Z.G.; Xiong, Y.; Zhu, Z.R.; Zhang, Z.D.; Liu, Y. Effects of hydrogen addition on combustion characteristics of a methane fueled MILD model combustor. Int. J. Hydrogen. Energy
**2022**, 47, 16309–16320. [Google Scholar] [CrossRef] - Cho, C.H.; Baek, G.M.; Sohn, C.H.; Cho, J.H.; Kim, H.S. A numerical approach to reduction of NOx emission from swirl premix burner in a gas turbine combustor. Appl. Therm. Eng.
**2013**, 59, 454–463. [Google Scholar] [CrossRef] - Meisl, J.; Koch, R.; Kneer, R.; Wittig, S. Study of NOx emission characteristics in pressurized staged combustor concepts. Symp. Int. Combust.
**1994**, 1, 1043–1049. [Google Scholar] [CrossRef] - Holdeman, J.D.; Vardakas, M.A.; Chang, C.T. Mixing of multiple jets with a confined subsonic crossflow, part iii:the effects of air preheat and number of orifices on flow and emissions in an RQL mixing section. J. Fluids Eng.
**2008**, 129, 1460–1467. [Google Scholar] [CrossRef] - Göke, S.; Füri, M.; Bourque, G.; Bobusch, B.; Göckeler, K.; Krüger, O.; Schimek, S.; Terhaar, S.; Paschereit, C.O. Influence of steam dilution on the combustion of natural gas and hydrogen in premixed and rich-quench-lean combustors. Fuel Process. Technol.
**2013**, 107, 14–22. [Google Scholar] [CrossRef] - Laranci, P.; Zampilli, M.; D’Amico, M.; Bartocci, P.; Bidini, G.; Fantozzi, F. Geometry optimization of a commercial annular RQL combustor of a micro gas turbine for use with natural gas and vegetal oils. Energy Proc.
**2017**, 126, 875–882. [Google Scholar] [CrossRef] - Oechsle, V.; Mongia, H.; Holdeman, J. Comparison of mixing calculations for reacting and non-reacting flows in a cylindrical duct. In Proceedings of the 32nd Aerospace Sciences Meeting and Exhibit, Reno, NV, USA, 10–13 January 1994. [Google Scholar]
- Yan, P.L.; Fan, W.J.; Qi, S.C.; Zhang, R.C.; Liu, J.; Bai, N.J.; Zhao, W.S.; Yang, X.Y. Numerical investigation on the effect of g-load on high-g ultra-compact combustor. Aerosp. Sci. Technol.
**2022**, 121, 107305. [Google Scholar] [CrossRef] - Yan, P.L.; Fan, W.J.; Xu, H.Q.; Zhang, R.C. Numerical Study of NOx Generation in a Trapped Vortex Combustor Fuelled by Kerosene Blended with Ethanol. In Proceedings of the 5th International Conference on Energy and Environmental Science, Malaya, Malaysia, 8–10 January 2021. [Google Scholar]
- Corporan, E.; Williams, V.; Stouffer, S.; Hendershott, T.; Monfort, J. High temperature fuel impacts on combustion characteristics of a swirl-stabilized combustor. Fuel
**2023**, 335, 126993. [Google Scholar] [CrossRef] - An, J.; Wang, H.Y.; Liu, B.; Luo, K.H.; Qin, F.; He, G.Q. A deep learning framework for hydrogen-fueled turbulent combustion simulation. Int. J. Hydrogen Energy
**2020**, 45, 17992–18000. [Google Scholar] [CrossRef] - Zhou, Y.C.; Zhang, C.; Han, X.; Lin, Y.Z. Monitoring combustion instabilities of stratified swirl flames by feature extractions of time-averaged flame images using deep learning method. Aerosp. Sci. Technol.
**2021**, 109, 106443. [Google Scholar] [CrossRef] - Kingma, D.P.; Welling, M. Auto-encoding variational Bayes. In Proceedings of the International Conference on Learning Representations, Banff, AB, Canada, 14–16 April 2014. [Google Scholar]
- Yan, P.L.; Fan, W.J.; Zhang, R.C. Predicting the NOx emissions of low heat value gas rich-quench-lean combustor via three integrated learning algorithms with Bayesian optimization. Energy
**2023**, 273, 127227. [Google Scholar] [CrossRef] - McCulloch, W.S.; Pitts, W. A logical calculus of the ideas immanent in nervous activity. Bull. Math. Biol.
**1943**, 5, 115–133. [Google Scholar] [CrossRef] - Rumelhart, D.E.; Hinton, G.E.; Williams, R.J. Learning representations by back-propagating errors. Nature
**1986**, 6088, 533–536. [Google Scholar] [CrossRef] - Kramer, M.A. Nonlinear principal component analysis using auto-associative neural networks. AIChe J.
**1991**, 37, 233–243. [Google Scholar] [CrossRef] - Kingma, D.P.; Welling, M. An Introduction to Variational Autoencoders. Found. Trends Mach. Learn.
**2019**, 12, 307–392. [Google Scholar] [CrossRef][Green Version]

**Figure 1.**The self-designed micro RQL combustor structure. (

**a**) Combustor model; (

**b**) swirler model; (

**c**) micro RQL combustor.

**Figure 6.**Mean loss of each image data per epoch. The result is the sum of the mean square errors of pixels in all the three channels.

**Figure 7.**Comparison between real and generated NO distribution. (

**a**) generated NO distribution (

**b**) real NO distribution.

Equation Type | φ | Γ_{φ} | S_{φ} |
---|---|---|---|

Continuity equation | 1 | 0 | S_{m} |

Momentum equation in the x-direction | u | μ_{e} | S_{u} |

Momentum equation in the y-direction | v | μ_{e} | S_{v} |

Momentum equation in the z-direction | w | μ_{e} | S_{w} |

Energy equation | h | μ_{e}/σ_{h} | S_{h} |

Component equation | Y | μ_{e}/σ_{Y} | S_{Y} |

Parameter | Values | Unit |
---|---|---|

Inlet air temperature | 400, 500, 600, 700, 800 | K |

Inlet air mass flow rate (corresponding lean burn zone equivalence ratio) | 0.08 (0.883), 0.09 (0.783), 0.1 (0.695), 0.11 (0.623), 0.12 (0.566), 0.13 (0.518) | kg/s (None) |

Swirler installation angle | 40 | deg |

Pressure | 1, 2, 3, 4 | bar |

Hyperparameter | Alternative Values | Chosen Value |
---|---|---|

Learning rate | 5 × 10^{−4}, 5 × 10^{−5}, 5 × 10^{−6} | 5 × 10^{−4} |

Kernel size | 3, 5, 7 | 7 |

Latent vector dimension | 4, 16, 64 | 64 |

Convolutional channel number | 8, 16, 32 | 32 |

Stride | 2, 3, 5 | 3 |

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**MDPI and ACS Style**

Yan, P.; Fan, W.; Zhang, R.
Predicting NOx Distribution in a Micro Rich–Quench–Lean Combustor Using a Variational Autoencoder. *Entropy* **2023**, *25*, 604.
https://doi.org/10.3390/e25040604

**AMA Style**

Yan P, Fan W, Zhang R.
Predicting NOx Distribution in a Micro Rich–Quench–Lean Combustor Using a Variational Autoencoder. *Entropy*. 2023; 25(4):604.
https://doi.org/10.3390/e25040604

**Chicago/Turabian Style**

Yan, Peiliang, Weijun Fan, and Rongchun Zhang.
2023. "Predicting NOx Distribution in a Micro Rich–Quench–Lean Combustor Using a Variational Autoencoder" *Entropy* 25, no. 4: 604.
https://doi.org/10.3390/e25040604