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Oblique Detonation Wave Control with O_{3} and H_{2}O_{2} Sensitization in Hypersonic Flow

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## Abstract

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## 1. Introduction

## 2. Numerical Method

#### 2.1. Computational Domain

#### 2.2. Boundary and Initial Conditions

#### 2.3. Grid Independence

## 3. Results and Discussions

#### 3.1. ODW Formation with No Additives

#### 3.2. Effect of ${H}_{2}{O}_{2}$ and ${O}_{3}$ Addition at Mach 7

#### 3.3. Effect of ${H}_{2}{O}_{2}$ and ${O}_{3}$ Addition at Mach 8

#### 3.4. Effect of ${H}_{2}{O}_{2}$ and ${O}_{3}$ Addition at Mach 9

#### 3.5. Effect on ODW Initiation Length

## 4. Conclusions

- The mixing of ${\mathrm{H}}_{2}{\mathrm{O}}_{2}$ and ${\mathrm{O}}_{3}$ from a small amount, 1000 PPM, to a moderate amount, 10,000 PPM, can effectively reduce the initiation lengths of an oblique shock to oblique detonation wave transition at all Mach numbers studied.
- At Mach 7, the reduction in initiation length is up to 80% with ${\mathrm{H}}_{2}{\mathrm{O}}_{2}$ and ${\mathrm{O}}_{3}$ addition during the abrupt transition. The ${\mathrm{O}}_{3}$ addition has been found to be more effective in comparison to the ${\mathrm{H}}_{2}{\mathrm{O}}_{2}$ addition for low Mach number abrupt transition conditions, and it can be utilized to increase lower operating flight speeds for ODWE.
- At Mach 8, the moderate abrupt OSW to ODW transition can be modified to a smoother transition by adding a small amount of ${\mathrm{H}}_{2}{\mathrm{O}}_{2}$ and ${\mathrm{O}}_{3}$. Furthermore, ${\mathrm{H}}_{2}{\mathrm{O}}_{2}$ addition has been found to be more effective in reducing the initiation length in comparison to the same amount of ${\mathrm{O}}_{3}$ addition for Mach 8 and 9 during smooth ODW transitions.
- The Mach number dependence of the compressed region in the initiation zone behind the oblique was responsible for the different performances of ${\mathrm{H}}_{2}{\mathrm{O}}_{2}$ and ${\mathrm{O}}_{3}$ addition for initiation length reduction. ${\mathrm{O}}_{3}$ decomposition was dominated regarding the initiation length reduction at a relatively lower Mach number, while $\mathrm{OH}$ formation from ${\mathrm{H}}_{2}{\mathrm{O}}_{2}$ was dominant at higher Mach numbers.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Lee, J.H.S. The Detonation Phenomenon, 1st ed.; Cambridge University Press: Cambridge, UK, 2008. [Google Scholar] [CrossRef]
- Kailasanath, K. Review of Propulsion Applications of Detonation Waves. AIAA J.
**2000**, 38, 1698–1708. [Google Scholar] [CrossRef] - Wolanski, P. Detonative propulsion. Proc. Combust. Inst.
**2013**, 34, 125–158. [Google Scholar] [CrossRef] - Viguier, C.; da Silva, L.F.F.; Desbordes, D.; Deshaies, B. Onset of oblique detonation waves: Comparison between experimental and numerical results for hydrogen-air mixtures. Symp. (Int.) Combust.
**1996**, 26, 3023–3031. [Google Scholar] [CrossRef] - Pratt, D.T.; Humphrey, J.W.; Glenn, D.E. Morphology of standing oblique detonation waves. J. Propuls. Power
**1991**, 7, 837–845. [Google Scholar] [CrossRef] - Powers, J.M.; Stewart, D.S. Approximate solutions for oblique detonations in the hypersonic limit. AIAA J.
**1992**, 30, 726–736. [Google Scholar] [CrossRef] - Wang, A.F.; Zhao, W.; Jiang, Z.L. The criterion of the existence or inexistence of transverse shock wave at wedge supported oblique detonation wave. Acta Mech. Sin.
**2011**, 27, 611–619. [Google Scholar] [CrossRef][Green Version] - Verreault, J.; Higgins, A.J. Initiation of detonation by conical projectiles. Proc. Combust. Inst.
**2011**, 33, 2311–2318. [Google Scholar] [CrossRef] - Rosato, D.A.; Thornton, M.; Sosa, J.; Bachman, C.; Goodwin, G.B.; Ahmed, K.A. Stabilized detonation for hypersonic propulsion. Proc. Natl. Acad. Sci. USA
**2021**, 118, e2102244118. [Google Scholar] [CrossRef] [PubMed] - Silva, F.D.; Deshaies, B. Stabilization of an oblique detonation wave by a wedge: A parametric numerical study. Combust. Flame
**2000**, 121, 152–166. [Google Scholar] [CrossRef] - Teng, H.; Zhang, Y.; Jiang, Z. Numerical investigation on the induction zone structure of the oblique detonation waves. Comput. Fluids
**2014**, 95, 127–131. [Google Scholar] [CrossRef][Green Version] - Zhang, Y.; Yang, P.; Teng, H.; Ng, H.D.; Wen, C. Transition Between Different Initiation Structures of Wedge-Induced Oblique Detonations. AIAA J.
**2018**, 56, 4016–4023. [Google Scholar] [CrossRef] - Teng, H.; Ng, H.D.; Jiang, Z. Initiation characteristics of wedge induced oblique detonation waves in a stoichiometric hydrogen air mixture. Proc. Combust. Inst.
**2017**, 36, 2735–2742. [Google Scholar] [CrossRef][Green Version] - Gao, Y.; Li, H.; Xiang, G.; Peng, S. Initiation characteristics of oblique detonation waves from a finite wedge under argon dilution. Chin. J. Aeronaut.
**2021**, 34, 81–90. [Google Scholar] [CrossRef] - Miao, S.; Zhou, J.; Lin, Z.; Cai, X.; Liu, S. Numerical Study on Thermodynamic Efficiency and Stability of Oblique Detonation Waves. AIAA J.
**2018**, 56, 3112–3122. [Google Scholar] [CrossRef] - Magzumov, A.E.; Kirillov, I.A.; Rusanov, V.D. Effect of small additives of ozone and hydrogen peroxide on the induction-zone length of hydrogen-air mixtures in a one-dimensional model of a detonation wave. Combust. Explos. Shock Waves
**1998**, 34, 338–341. [Google Scholar] [CrossRef] - Crane, J.; Shi, X.; Singh, A.V.; Tao, Y.; Wang, H. Isolating the effect of induction length on detonation structure: Hydrogen–oxygen detonation promoted by ozone. Combust. Flame
**2019**, 200, 44–52. [Google Scholar] [CrossRef] - Kumar, D.S.; Ivin, K.; Singh, A.V. Sensitizing gaseous detonations for hydrogen/ethylene-air mixtures using ozone and H
_{2}O_{2}as dopants for application in rotating detonation engines. Proc. Combust. Inst.**2021**, 38, 3825–3834. [Google Scholar] [CrossRef] - Qin, Q.; Zhang, X. Nitrogen dilution effects on the local detachment of the oblique detonation wave in the 2H
_{2}-O_{2}mixture. Int. J. Hydrogen Energy**2021**, 46, 6873–6884. [Google Scholar] [CrossRef] - Zhang, Y.; Fang, Y.; Ng, H.D.; Teng, H. Numerical investigation on the initiation of oblique detonation waves in stoichiometric acetylene–oxygen mixtures with high argon dilution. Combust. Flame
**2019**, 204, 391–396. [Google Scholar] [CrossRef] - Maeda, S.; Inada, R.; Kasahara, J.; Matsuo, A. Visualization of the non-steady state oblique detonation wave phenomena around hypersonic spherical projectile. Proc. Combust. Inst.
**2011**, 33, 2343–2349. [Google Scholar] [CrossRef][Green Version] - Viguier, C.; Gourara, A.; Desbordes, D. Three-dimensional structure of stabilization of oblique detonation wave in hypersonic flow. Symp. (Int.) Combust.
**1998**, 27, 2207–2214. [Google Scholar] [CrossRef] - Sosa, J.; Rosato, D.A.; Goodwin, G.B.; Bachman, C.L.; Oran, E.S.; Ahmed, K.A. Controlled detonation initiation in hypersonic flow. Proc. Combust. Inst.
**2021**, 38, 3513–3520. [Google Scholar] [CrossRef] - Li, C.; Kailasanath, K.; Oran, E.S. Detonation structures behind oblique shocks. Phys. Fluids
**1994**, 6, 1600–1611. [Google Scholar] [CrossRef] - Li, C.; Kailasanath, K.; Oran, E. Effects of boundary layers on oblique-detonation structures. In Proceedings of the 31st Aerospace Sciences Meeting, Reno, NV, USA, 11–14 January 1993; AIAA: Reston, VI, USA, 1993. Chapter AIAA-93-0450. p. 13. [Google Scholar] [CrossRef]
- Oran, E.S.; Weber, J.W.; Stefaniw, E.I.; Lefebvre, M.H.; Anderson, J.D. A Numerical Study of a Two-Dimensional H2-O2-Ar Detonation Using a Detailed Chemical Reaction Model. Combust. Flame
**1998**, 113, 147–163. [Google Scholar] [CrossRef] - Deiterding, R. Parallel Adaptive Simulation of Multi-Dimensional Detonation Structures. Ph.D. Thesis, Brandenburgische Technische Universitat Cottbus, Cottbus, Germany, 2003. [Google Scholar]
- Deiterding, R. High-Resolution Numerical Simulation and Analysis of Mach Reflection Structures in Detonation Waves in Low-Pressure H
_{2}–O_{2}–Ar Mixtures: A Summary of Results Obtained with the Adaptive Mesh Refinement Framework AMROC. J. Combust.**2011**, 2011, 738969. [Google Scholar] [CrossRef][Green Version] - Deiterding, R. A parallel adaptive method for simulating shock-induced combustion with detailed chemical kinetics in complex domains. Comput. Struct.
**2009**, 87, 769–783. [Google Scholar] [CrossRef][Green Version] - Harmon, P.; Vashishtha, A.; Callaghan, D.; Nolan, C.; Deiterding, R. Study of Direct Gas Injection into stagnation zone of Blunt Nose at Hypersonic Flow. In Proceedings of the AIAA Propulsion and Energy 2021 Forum, Virtual, 9–11 August 2021; AIAA: Reston, VI, USA, 2021. Chapter Session. p. 3529. [Google Scholar] [CrossRef]
- Vashishtha, A.; Callaghan, D.; Nolan, C.; Deiterding, R. Numerical Investigation of Detonation Propagation Through Small Orifice Holes. Trans. Aerosp. Res.
**2021**, 2021, 17–33. [Google Scholar] [CrossRef] - Liu, Y.; Wang, L.; Xiao, B.; Yan, Z.; Wang, C. Hysteresis phenomenon of the oblique detonation wave. Combust. Flame
**2018**, 192, 170–179. [Google Scholar] [CrossRef] - Liu, Y.; Xiao, B.; Wang, L.; Wang, C. Numerical Study of Disturbance Resistance of Oblique Detonation Waves. Int. J. Aerosp. Eng.
**2020**, 2020. [Google Scholar] [CrossRef] - Huang, Y.; Luan, Z.; Li, Z.; Ji, H.; You, Y. Study on the flow characteristics in the non-detonation reaction zones of wedge-induced oblique detonation transitions. Aerosp. Sci. Technol.
**2022**, 120, 107282. [Google Scholar] [CrossRef] - Westbrook, C.K. Chemical kinetics of hydrocarbon oxidation in gaseous detonations. Combust. Flame
**1982**, 46, 191–210. [Google Scholar] [CrossRef] - Zhao, H.; Yang, X.; Ju, Y. Kinetic studies of ozone assisted low temperature oxidation of dimethyl ether in a flow reactor using molecular-beam mass spectrometry. Combust. Flame
**2016**, 173, 187–194. [Google Scholar] [CrossRef] - Atkins, C.W.C.; Deiterding, R. Modelling Hypersonic Flows in Thermochemical Nonequilibrium Using Adaptive Mesh Refinement. In Proceedings of the 7th European Conference on Computational Fluid Dynamics, Glasgow, UK, 11–15 June 2018; pp. 672–683. Available online: https://eprints.soton.ac.uk/420989/ (accessed on 2 April 2022).
- Scoggins, J.B.; Leroy, V.; Bellas-Chatzigeorgis, G.; Dias, B.; Magin, T.E. Mutation++: MUlticomponent Thermodynamic And Transport properties for IONized gases in C++. SoftwareX
**2020**, 12, 100575. [Google Scholar] [CrossRef] - Shi, L.; Shen, H.; Zhang, P.; Zhang, D.; Wen, C. Assessment of Vibrational Non-Equilibrium Effect on Detonation Cell Size. Combust. Sci. Technol.
**2017**, 189, 841–853. [Google Scholar] [CrossRef][Green Version] - Choi, J.Y.; Kim, D.W.; Jeung, I.S.; Ma, F.; Yang, V. Cell-like structure of unstable oblique detonation wave from high-resolution numerical simulation. Proc. Combust. Inst.
**2007**, 31, 2473–2480. [Google Scholar] [CrossRef] - Verreault, J.; Higgins, A.J.; Stowe, R.A. Formation of transverse waves in oblique detonations. Proc. Combust. Inst.
**2013**, 34, 1913–1920. [Google Scholar] [CrossRef] - Browne, S.; Ziegler, J.; Bitter, N.; Schmidt, B.; Lawson, J.; Shepherd, J.E. SDToolbox: Numerical Tools for Shock and Detonation Wave Modeling. In Technical Report GALCIT Technical Report FM2018.001; Revised January 2021; Explosion Dynamics Laboratory: Livermore, CA, USA, 2018. [Google Scholar]
- Goodwin, D.G.; Speth, R.L.; Moffat, H.K.; Weber, B.W. Cantera: An Object-Oriented Software Toolkit for Chemical Kinetics, Thermodynamics, and Transport Processes. Version 2.5.1. 2021. Available online: https://www.cantera.org (accessed on 2 April 2022). [CrossRef]
- Zhang, Z.; Wen, C.; Yuan, C.; Liu, Y.; Han, G.; Wang, C.; Jiang, Z. An experimental study of formation of stabilized oblique detonation waves in a combustor. Combust. Flame
**2022**, 237, 111868. [Google Scholar] [CrossRef]

**Figure 2.**Mach 7 with 10,000 PPM ${\mathrm{H}}_{2}{\mathrm{O}}_{2}$ addition: (

**a**) Pressure, (

**b**) temperature and (

**c**) $\mathrm{OH}$ mass fraction variation at lines parallel to the wedge for all three grids; (

**d**) Temperature and (

**e**) adaptive grid levels for the medium grid.

**Figure 3.**Mach 9 with 10,000 PPM ${\mathrm{O}}_{3}$ addition: (

**a**) Pressure, (

**b**) temperature and (

**c**) $\mathrm{OH}$ mass fraction variation at lines parallel to the wedge for all three grids; (

**d**) Temperature and (

**e**) adaptive grid levels for a medium grid.

**Figure 4.**Induction Length (${\Delta}_{i}$) and Induction Time (${\tau}_{i}$) variation with (

**a**) Additives, based on CJ-ZND calculation (

**b**) Mach number, based on overdriven ZND calculation.

**Figure 5.**(

**a**) Pressure, (

**b**) $\mathrm{OH}$ Mass Fraction and (

**c**) $\mathrm{O}$ Mass Fraction variation along the wedge surface and temperature contours for (

**d**) Machs 7, (

**e**) 8 and (

**f**) 9 freestream flows without additives.

**Figure 6.**(

**a**) Pressure, (

**b**) $\mathrm{OH}$ Radical Mass fraction, (

**c**) $\mathrm{O}$ variation along the wedge surface, (

**d**) temperature, and (

**e**) pressure contour for 1000 PPM ${\mathrm{H}}_{2}{\mathrm{O}}_{2}$ Addition at Mach 7.

**Figure 7.**(

**a**) Pressure, (

**b**) $\mathrm{OH}$ Radical Mass fraction, (

**c**) $\mathrm{O}$ variation along the wedge surface, (

**d**) temperature and (

**e**) pressure contour for 5000 PPM ${\mathrm{O}}_{3}$ addition at Mach 8.

**Figure 8.**(

**a**) Pressure, (

**b**) $\mathrm{OH}$ Radical Mass fraction, (

**c**) $\mathrm{O}$ variation along the wedge surface, (

**d**) temperature and (

**e**) pressure contour for 1000 PPM ${\mathrm{O}}_{3}$ addition at Mach 9.

**Figure 9.**Initiation length (

**a**) variation and, (

**b**) percentage reduction with additives at ${\mathrm{H}}_{2}$–Air ($\varphi =1$) premixed mixture.

Description | Value |
---|---|

Freestream Mach Number (${M}_{\infty}$) | 7, 8, 9 |

Freestream Speed (${V}_{\infty}$) | 2.8–3.6 km/s |

Freestream Pressure (${P}_{\infty}$) | 20 kPa |

Freestream Temperature (${T}_{\infty}$) | 300 K |

${\mathrm{H}}_{2}$-Air Equivalence Ratio ($\varphi $) | 1.0 |

Deflection Angle ($\theta $) | 26.0° |

${M}_{CJ}$ (No Additive) | 4.75 |

CJ Speed | 1940.09 m/s (No Additive) |

1921.37 m/s (10,000 PPM ${\mathrm{H}}_{2}{\mathrm{O}}_{2}$) | |

1943.28 mm (10,000 PPM ${\mathrm{O}}_{3}$) | |

CJ-ZND Induction Length | 1.04 mm (No Additive) |

0.32 mm (10,000 PPM ${\mathrm{H}}_{2}{\mathrm{O}}_{2}$) | |

0.29 mm (10,000 PPM ${\mathrm{O}}_{3}$) |

Mach Number | Theoretical ODW Angle | Numerical ODW Angle |
---|---|---|

Mach = 7 | 47.7° | 47.1° |

Mach = 8 | 42.5° | 44.9° |

Mach = 9 | 39.2° | 38.9° |

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**MDPI and ACS Style**

Vashishtha, A.; Panigrahy, S.; Campi, D.; Callaghan, D.; Nolan, C.; Deiterding, R.
Oblique Detonation Wave Control with O_{3} and H_{2}O_{2} Sensitization in Hypersonic Flow. *Energies* **2022**, *15*, 4140.
https://doi.org/10.3390/en15114140

**AMA Style**

Vashishtha A, Panigrahy S, Campi D, Callaghan D, Nolan C, Deiterding R.
Oblique Detonation Wave Control with O_{3} and H_{2}O_{2} Sensitization in Hypersonic Flow. *Energies*. 2022; 15(11):4140.
https://doi.org/10.3390/en15114140

**Chicago/Turabian Style**

Vashishtha, Ashish, Snehasish Panigrahy, Dino Campi, Dean Callaghan, Cathal Nolan, and Ralf Deiterding.
2022. "Oblique Detonation Wave Control with O_{3} and H_{2}O_{2} Sensitization in Hypersonic Flow" *Energies* 15, no. 11: 4140.
https://doi.org/10.3390/en15114140