# DNS Study of Spherically Expanding Premixed Turbulent Ammonia-Hydrogen Flame Kernels, Effect of Equivalence Ratio and Hydrogen Content

^{1}

^{2}

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## Abstract

**:**

_{2}and H species were responsible for differential rates of fuel consumption in the positively curved and negatively curved regions of the flame. The indication of a critical amount of hydrogen in the fuel mixture was observed, after which the trends of reactions involving H radical reactions were flipped with respect to the sign of the curvature. This also has implications on NO formation. Finally, the spatial profiles of heat release and temperature for 50% hydrogen were studied, which showed that the flame brush of the lean case increases in width and that the flame propagation is slow for stoichiometric and rich cases attributed to suppression of flame chemistry due to preferential diffusion effects.

## 1. Introduction

_{3}emissions decreased, while there was no effect on unburnt H

_{2}. They also observed that secondary air injection led to NO generation again in extremely rich conditions. Many 1D flame studies have also been conducted to study reaction pathways and to develop reaction mechanisms [4,11,12,13,14].

## 2. Numerical Set-Up and Conditions

## 3. Results and Discussion

#### 3.1. Flame Structure

#### 3.2. Curvature Effects on Flame Chemistry

_{2}O and notated as c. The progress variable is normalized using the maximum and minimum values of the same from the corresponding one-dimensional unstrained flame solution.

_{2}as reactants will see enhancement of the positive curvature as the local equivalence ratio increases for these curvature values. However, as the global ratio is increased, these reactions are not further enhanced for positive curvatures as the local equivalence ratio gets higher, and the points on the flame front with negative curvature are now closer to the stoichiometric ratio. An H radical reacts with NH

_{x}to produce H

_{2}. This reaction is enhanced again for a positive flame curvature, since the production of an H radical is higher in these areas; however, this does not reduce the H

_{2}consumption since the reaction rates are approximately 3 to 5 times less than the consumption reaction:

_{3}source term is lower, as expected, since the diffusive mobility for NH

_{3}is lesser compared to H

_{2}.

_{2}is also seen here, where for positive curvature values, a higher rate of consumption is observed, whereas the stoichiometric and lean cases have the opposite trend. This is, however, only observed for the case with the most ammonia. We see that as the amount of ammonia is reduced, for the lean case, the trend in which there is higher consumption for positive curvature reverses, contrary to the behaviour of H

_{2}. The major consumption reaction of ammonia is:

_{3}-consuming reactions increase for negative curvatures as the amount of ammonia is reduced. This also hints at a critical amount of hydrogen in the fuel mixture at which the signs of the curvature affect the concentration of H radicals. This has effects on NO reactions as well, which is discussed further. The final OH-producing reaction, Equation (6), involves H

_{2}O, which will have higher concentrations for positive curvatures due to a higher equivalence ratio, hence enhancing the reaction.

_{3}and H

_{2}. Similar to the source term of hydrogen, we see the enhancement of the NO source term for lean cases, while for rich cases, we see decreased NO production compared to corresponding one-dimensional unstrained flames.

_{3}, where the H radical, although it is supposed to enhance reactions for negative curvatures, does not for the highest amount of ammonia due to a possible competition between the reaction and diffusion timescales of the species. Additionally, the increased consumption of NH

_{3}for negative curvatures also causes fuel-borne NO emissions, which contributes to the increased production of NO. Finally, the negative source terms disappear as the percentage of ammonia is decreased, since the reduction of NO is rate-dependent on fundamental reactions involving NH

_{3}[3]. For rich cases, Netzer et. al [15] observed that the main pathway for NO is through Thermal-NO, and since the adiabatic flame temperature for negative curvatures are higher, due to the local equivalence ratio being closer to stoichiometry, the NO production is also higher. The practical implication for this is that if the curvature of the flame can be controlled in the combustors, a balance between positively curved and negatively curved flame surfaces could be achieved where the NO production is reduced.

_{2}O have been plotted just as the source terms of NO. Interestingly, unlike previous source terms, the production of N

_{2}O remains consistently higher in the negatively curved regions across all equivalence ratios and mixture ratios.

_{2}O producing reaction is

#### 3.3. Time Evolution of Temperature and Heat Release

## 4. Conclusions

- Due to variations in local equivalence ratio, the flame surface is distorted for all cases;
- As the equivalence ratio is increased for each amount of hydrogen, the flame surface smoothens out, forming strongly curved leading edges with positive curvature;
- As the amount of hydrogen is increased, the flame structure becomes more wrinkled due to the increase in spread of the local equivalence ratios as the preferential diffusion effects of hydrogen becomes stronger.

_{2}and NH

_{3}and NO

_{x}emissions.

- Due to the increase in equivalence ratio to near stoichiometry for all lean cases, the reactivity of all reactions are increased compared to the unstrained flat flame cases;
- For all rich cases, the opposite is observed again as the equivalence ratio is pushed to high levels, decreasing reactivity;
- The effect of the sign of the curvature influences the flame significantly. The role of the H radical is quite important in this perspective;
- The existence of a critical amount of hydrogen in the fuel mixture is observed, after which the trend of some reactions with respect to the sign of the curvature is flipped speculated to be due to competing reactive and diffusive timescales of hydrogen radicals.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Characteristics of the initial turbulent field. (

**a**) Turbulent energy spectrum of a sample turbulence field. (

**b**) Decay of turbulence intensity. The rms velocity has been non-dimensionalised with initial rms velocity and the time has been non-dimensionalised with $\tau $, the eddy turnover time.

**Figure 2.**Flame structure of all the cases after one eddy turnover time. The iso-surface is taken at the inner layer temperature calculated from a one-dimensional freely propagating flat flame. The surface is coloured with curvature values.

**Figure 3.**Probability density functions of curvature on the flame surface (isotherms at laminar inner layer temperature).

**Figure 4.**Iso-surfaces of the flame kernel taken after one eddy turnover time, coloured with local equivalence ratio. Significant deviation from the global equivalence ratio can be seen from this image.

**Figure 5.**Conditional average of the source term of hydrogen split by positive and negative curvature.

**Figure 6.**Reaction rates of reactions involving H

_{2}doubly conditioned on curvature and progress variables for 75% ammonia case.

**Figure 7.**Conditional average of the source term of ammonia split by positive and negative curvature.

**Figure 8.**Reaction rates of key reactions involving the consumption of NH

_{3}and production of OH radicals at a constant equivalence ratio of 0.8 for 75% and 25% NH

_{3}. The y-axis for the 25% case is on the right.

**Figure 10.**Reaction rates of NO-producing reaction for a constant equivalence ratio of 0.8 for 75% and 25% NH

_{3}. The rates for the 25% NH

_{3}case have been plotted on the right y-axis.

**Figure 11.**Conditional average of the source term of N

_{2}O split by positive and negative curvatures.

**Figure 12.**Conditional averages split by the sign of the curvature for reaction rates of N

_{2}O reactions for 50% ammonia at a stoichiometric equivalence ratio.

Case | % NH3 | $\mathit{\varphi}$ | ${\mathit{T}}_{\mathbf{il}}$ [K] | ${\mathit{s}}_{\mathit{l}}$ [m/s] | ${\mathit{l}}_{\mathit{f}}$ [m] | $\frac{{\mathit{v}}^{\prime}}{{\mathit{s}}_{\mathit{l}}}$ | $\frac{{\mathit{l}}_{\mathit{t}}}{{\mathit{l}}_{\mathit{f}}}$ | Re | ${\mathit{v}}^{\prime}$ [m/s] | $\mathit{\eta}$ [m] | $\mathit{\tau}$ [s] |
---|---|---|---|---|---|---|---|---|---|---|---|

A | 75 | 0.8 | 1763 | 0.09 | 1.51 × 10${}^{-3}$ | 4.64 | 1 | 4.64 | 0.425 | 4.78 × 10${}^{-4}$ | 3.55 × 10${}^{-3}$ |

B | 75 | 1.0 | 1847 | 0.14 | 1.13 × 10${}^{-3}$ | 4.64 | 1 | 4.64 | 0.673 | 3.58 × 10${}^{-4}$ | 1.68 × 10${}^{-3}$ |

C | 75 | 1.2 | 1685 | 0.17 | 1.02 × 10${}^{-3}$ | 4.64 | 1 | 4.64 | 0.777 | 3.22 × 10${}^{-4}$ | 1.31 × 10${}^{-3}$ |

D | 50 | 0.8 | 1644 | 0.27 | 6.08 × 10${}^{-4}$ | 4.64 | 1 | 4.64 | 1.258 | 1.92 × 10${}^{-4}$ | 4.83 × 10${}^{-4}$ |

E | 50 | 1.0 | 1740 | 0.39 | 5.14 × 10${}^{-4}$ | 4.64 | 1 | 4.64 | 1.818 | 1.63 × 10${}^{-4}$ | 2.83 × 10${}^{-4}$ |

F | 50 | 1.2 | 1749 | 0.43 | 4.94 × 10${}^{-4}$ | 4.64 | 1 | 4.64 | 1.978 | 1.56 × 10${}^{-4}$ | 2.50 × 10${}^{-4}$ |

G | 25 | 0.8 | 1442 | 0.68 | 3.69 × 10${}^{-4}$ | 4.64 | 1 | 4.64 | 3.140 | 1.17 × 10${}^{-4}$ | 1.17 × 10${}^{-4}$ |

H | 25 | 1.0 | 1493 | 0.97 | 3.38 × 10${}^{-4}$ | 4.64 | 1 | 4.64 | 4.492 | 1.07 × 10${}^{-4}$ | 7.53 × 10${}^{-5}$ |

I | 25 | 1.2 | 1534 | 1.13 | 3.12 × 10${}^{-4}$ | 4.64 | 1 | 4.64 | 5.249 | 9.85 × 10${}^{-5}$ | 5.93 × 10${}^{-5}$ |

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**MDPI and ACS Style**

Mukundakumar, N.; Bastiaans, R.
DNS Study of Spherically Expanding Premixed Turbulent Ammonia-Hydrogen Flame Kernels, Effect of Equivalence Ratio and Hydrogen Content. *Energies* **2022**, *15*, 4749.
https://doi.org/10.3390/en15134749

**AMA Style**

Mukundakumar N, Bastiaans R.
DNS Study of Spherically Expanding Premixed Turbulent Ammonia-Hydrogen Flame Kernels, Effect of Equivalence Ratio and Hydrogen Content. *Energies*. 2022; 15(13):4749.
https://doi.org/10.3390/en15134749

**Chicago/Turabian Style**

Mukundakumar, Nithin, and Rob Bastiaans.
2022. "DNS Study of Spherically Expanding Premixed Turbulent Ammonia-Hydrogen Flame Kernels, Effect of Equivalence Ratio and Hydrogen Content" *Energies* 15, no. 13: 4749.
https://doi.org/10.3390/en15134749