# Ultra-Lean Gaseous Flames in Terrestrial Gravity Conditions

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## Abstract

**:**

## 1. Introduction

## 2. Problem Setup

## 3. Numerical Methods

## 4. Results and Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

JANAF | Joint Army, Navy and Air Force |

## References

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**Figure 1.**Schematic of the problem setups. (

**a**) Ultra-lean combustion of hydrogen-air mixture initiated near the bottom wall of the domain via instantaneous local temperature rise. (

**b**) Rise of the light gaseous bubble under terrestrial gravity conditions in the “immiscible gases” approximation.

**Figure 2.**Grid sensitivity analysis for the combustion process in 6% H${}_{2}$-Air mixture. Temperature isolines $T=1000$ K are presented for computational domains with cell size $\Delta x=0.2$ mm (solid black lines) and $\Delta x=0.4$ mm (orange dashed lines).

**Figure 3.**Flame structures in near-limit ultra-lean hydrogen-air mixtures. Top—5.0% H${}_{2}$-Air; middle—5.5% H${}_{2}$-Air; bottom—6.0% H${}_{2}$-Air. Color palette indicates gas temperature.

**Figure 4.**Time histories of the maximal temperature, equivalent radius and $d{R}_{eq}/dt$ in 6.0% hydrogen-air mixture. Solid lines—ignition region with ${R}_{0}=1$ mm, dash-dotted lines—ignition region with ${R}_{0}=2$ mm, dashed lines—ignition region with ${R}_{0}=4$ mm.

**Figure 5.**(

**a**) Flame structure in ultra-lean 4.5% hydrogen-air mixture ignited by the heated region with ${R}_{0}=2$ mm. (

**b**) Time histories of the maximal temperature and equivalent radius in 4.5% hydrogen-air mixture.

**Figure 6.**The diagram in Re-Fr plane. (

**a**) Linear segments obtained via non-reactive bubbles computations. Linear approximations of those segments divide the plane into five sectors. Initial radius of the bubble defines the slope of the linear segment, density ratio defines starting point and length of the linear segment. Arrows indicate the direction of density ratio ${\theta}_{b}$ increase. Linear segments colors: white—${\theta}_{b}=1.5$, yellow—${\theta}_{b}=2$, blue—${\theta}_{b}=3$, red—${\theta}_{b}=4$. (

**b**) Flame trajectories in Re-Fr plane for different mixture compositions: green—6% H${}_{2}$-Air, ${R}_{0}=1$ mm, black—5.5% H${}_{2}$-Air, ${R}_{0}=1$ mm, orange—4.5% H${}_{2}$-Air, ${R}_{0}=2$ mm, blue—5.0% H${}_{2}$-Air, ${R}_{0}=1$ mm. Characteristic bubble structures for ${R}_{0,b}=1\u20134$ mm for each sector are presented outside the Re-Fr plane.

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**MDPI and ACS Style**

Yakovenko, I.; Kiverin, A.; Melnikova, K.
Ultra-Lean Gaseous Flames in Terrestrial Gravity Conditions. *Fluids* **2021**, *6*, 21.
https://doi.org/10.3390/fluids6010021

**AMA Style**

Yakovenko I, Kiverin A, Melnikova K.
Ultra-Lean Gaseous Flames in Terrestrial Gravity Conditions. *Fluids*. 2021; 6(1):21.
https://doi.org/10.3390/fluids6010021

**Chicago/Turabian Style**

Yakovenko, Ivan, Alexey Kiverin, and Ksenia Melnikova.
2021. "Ultra-Lean Gaseous Flames in Terrestrial Gravity Conditions" *Fluids* 6, no. 1: 21.
https://doi.org/10.3390/fluids6010021