# Effects of Ozone Addition on Multi-Wave Modes of Hydrogen–Air Rotating Detonations

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^{2}

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## Abstract

**:**

## 1. Introduction

_{3}to an H

_{2}/O

_{2}mixture to investigate the changes in the initiation and propagation of detonation waves by using numerical simulations. Ozone has been utilized as an accelerant in partially accelerated and controlled combustion [30]. The integration of ozone significantly alters the ignition process without altering the mixture properties. Previous studies have investigated various aspects of RDEs, including their flow field variations, design parameters, and propagation mechanisms. To prevent the high temperatures from burnt products, inert diluents are introduced into the fuel–oxidizer mixture, leading to a longer induction length and time. This can significantly affect the rotating detonation structure. Considering the ignition difficulties associated with certain fuels such as propellants, the idea of adding O

_{3}to the propellant aims to improve the detonation within the RDEs. However, limited research has been conducted on the use of ozone in RDEs. Therefore, it is essential to investigate the addition of ozone to RDEs propellants.

## 2. Materials and Methods

_{2}/air mechanisms of Burke [31], which includes 19 species and 32 reactions, together with an O

_{3}submechanism consisting of eight steps [28]. To solve the equations, an implicit Euler time integration method was utilized, along with the KNP (Kurganov, Noelle, and Petrova) scheme [32], known for its stability and efficiency in shock capturing. The van Leer limiter was adopted for correct flux calculations.

- For $p$ ≥ ${p}_{st}$, there is no inflow, the sonic nozzle is chocked, where ${p}_{st}$ is the inlet total pressure;
- For ${p}_{st}$ > $p$ > ${p}_{cr}$, the speed of inflow can be obtained by isentropic expansion:$$T={T}_{st}{(\frac{p}{{p}_{st}})}^{\frac{\gamma -1}{\gamma}}$$$$u=\sqrt{R{T}_{st}\frac{2\gamma}{\gamma -1}[1-{\left(\frac{p}{{p}_{st}}\right)}^{\frac{\gamma -1}{\gamma}}]}$$
- For $p$ ≤ ${p}_{cr}$, the sonic nozzle is chocked, $p={p}_{cr}$, and the temperature and velocity are computed using Equation (4).

## 3. Results

#### 3.1. Effects of Total Temperature on the Modes of Detonation

_{2}/air. The sonic nozzle was evenly distributed at the bottom, with an inlet total pressure of 0.5 MPa.

#### 3.2. Effects of Ozone Addition

_{3}and H

_{2}O

_{2}, can significantly shorten the induction length and time scale, which has a significant impact on the structure of the detonation, consistent with the results we calculated. This suggests that the effect of the induction time of the reactive gas ahead of the detonation wave on the detonation wave mode is not the primary factor. The formation of more hotspots for detonation wave is related to changes in the state of the inflow gas, including static temperature and velocity, as well as the interaction with the wall. The largest number of detonation waves occurred at ${T}_{st}$ = 600 K. Additionally, the temperature of the banded products near the wall area increased as the total temperature increased, making it easier to create new hot spots and leading to an increase in detonation waves. It also seems that ozone acts as an ignition promoter, accelerating the reaction process and producing O radicals that speed up the chain branching, leading to the production of OH, a crucial indicator of the detonation reaction. This is consistent with the findings in Wang’s study [39] in that ozone molecules decompose into O radicals, which accelerates the H-abstraction reactions during the combustion process. Wang [39] found that the addition of ozone promotes the combustion process in hydrocarbon fuels by affecting the active free radicals and heat release rate. As a result, the increase in the ozone concentration has a more significant impact on the reaction rate and can lead to various forms of reactive flow fields. These observations suggest that the primary reason for both re-ignition and mode transition is the reduction in the induction time ahead of the wave. Ozone exhibits a more prominent impact on reducing the induction time of inflow with lower total temperature.

#### 3.3. Discussion of Propagation Behaviors and Propulsion Performances

## 4. Conclusions

_{2}and O, reducing the induction time of unburnt gas in front of the detonation by accelerating the reaction process.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**(

**a**) Temperature fields; (

**b**) along the line y = 0.005 m and y = 0.010 m; based on different grids for ${T}_{st}$ = 300 K and φ = 0.1%.

**Figure 4.**Temperature fields at ${T}_{st}$ = 300 K with different ozone additions: (

**a**) φ = 0.1%; (

**b**) φ = 1.0%; (

**c**) φ = 2.0%.

**Figure 5.**Temperature fields at ${T}_{st}$ = 400 K with different ozone additions: (

**a**) φ = 0.1%; (

**b**) φ = 1.0%; (

**c**) φ = 2.0%.

**Figure 6.**Temperature fields at = 600 K with different ozone additions: (

**a**) φ = 0.1%; (

**b**) φ = 1.0%; (

**c**) φ = 2.0%.

0% | 0.1% | 0.5% | 1.0% | ||
---|---|---|---|---|---|

${V}_{d}/\left(\mathrm{m}\xb7{\mathrm{s}}^{-1}\right)$ | 400 K | 1875.1 | 1869.1 | 1811.2 | 1822.6 |

600 K | 1776.4 | 1707.3 | 1773.0 | 1763.4 | |

$HRR/\left(\mathrm{J}\xb7{\mathrm{s}}^{-1}\right)$ | 400 K | 5.21938 × 10^{6} | 5.26051 × 10^{6} | 5.07845 × 10^{6} | 5.28373 × 10^{6} |

600 K | 4.43678 × 10^{6} | 4.27587 × 10^{6} | 4.48233 × 10^{6} | 4.36204 × 10^{6} |

0% | 0.1% | 0.5% | 1.0% | ||
---|---|---|---|---|---|

${P}_{st}/$MPa | 400 K | 0.538 | 0.533 | 0.528 | 0.527 |

600 K | 0.476 | 0.466 | 0.470 | 0.486 | |

${I}_{sp}$/s | 400 K | 209.5 | 206.4 | 201.3 | 201.7 |

600 K | 220.3 | 212.7 | 219.3 | 226.3 |

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**MDPI and ACS Style**

Wang, Y.; Tian, C.; Yang, P.
Effects of Ozone Addition on Multi-Wave Modes of Hydrogen–Air Rotating Detonations. *Aerospace* **2023**, *10*, 443.
https://doi.org/10.3390/aerospace10050443

**AMA Style**

Wang Y, Tian C, Yang P.
Effects of Ozone Addition on Multi-Wave Modes of Hydrogen–Air Rotating Detonations. *Aerospace*. 2023; 10(5):443.
https://doi.org/10.3390/aerospace10050443

**Chicago/Turabian Style**

Wang, Yang, Cheng Tian, and Pengfei Yang.
2023. "Effects of Ozone Addition on Multi-Wave Modes of Hydrogen–Air Rotating Detonations" *Aerospace* 10, no. 5: 443.
https://doi.org/10.3390/aerospace10050443