# Experimental Proof of Concept of a Noncircular Rotating Detonation Engine (RDE) for Propulsion Applications

^{*}

## Abstract

**:**

## 1. Introduction

_{2}H

_{4}+ O

_{2}mixture is about r

_{in}⁄λ = 23.0 where H = 20.0 mm. Matsuo et al. [15] numerically investigated the detonation behaviors in a 2D curved channel and showed that the critical radius of curvature is about r⁄λ = 27.2 when the r

_{out}⁄r

_{in}= 1.5 and 2.0. Pan et al. [16,17] experimentally studied the propagation characteristics of the curved detonation wave in helical channels utilizing a similar configuration to the computational domain used in [1,11]. Xia et al. showed that the detonation wave steadily propagated in the combustion channel when r

_{in}+ 0.464 P

_{a}≥ 80.932 or r

_{in}≥ 40 mm [18]. Kawasaki et al. experimentally investigated the effect of an inner radius ranging from 0 to 31 mm and showed that the critical radius is 15 mm [19]. Katta et al. numerically and experimentally demonstrated that, as the channel width increases, the inclined detonation front is formed between walls, and the detonation wave of the outer wall becomes stronger [20]. Zhou et al. showed that, as the channel width increased, the variation in the flow field became apparent, while the detonation height and specific impulse nearly showed variation [21]. Kudo et al. showed that the critical curvature of a rectangular cross-section bent tube is 14~40-times the detonation cell width [12]. Zhao et al. numerically investigated the effect of 5-, 8-, and 12-mm channel widths and showed that the thrust and specific impulse reached their highest at 5 mm [22]. Wang et al. numerically studied the effect of corner angle at the trapezoidal cross-section and showed that the detonation wave can propagate at right, acute, and obtuse angles [23]. From these studies, it is considered that the radius of curvature is an important geometric parameter for the stable propagation of detonation waves. Therefore, it is suggested that the local radius of curvature should be greater than the critical value for designing a noncircular RDE cross-section for stable propagation of detonation wave.

## 2. Experimental Setup

^{2}, respectively. Gaseous ethylene (GC

_{2}H

_{4}) and oxygen (GO

_{2}) are used as fuel and oxidizer, where they are injected from each plenum into the combustion channel through each injection slot, as shown in Figure 3. The dimensionless radius of curvatures of both RDEs expressed as r⁄H, is shown in Table 1.

## 3. Mass Flow Rate Calibration

## 4. Experimental Procedure

## 5. Operational Characteristics

#### 5.1. Operational Characteristics at Reference Mass Flow Rate

#### 5.2. Operational Characteristics at Low Mass Flow Rate

#### 5.3. Operational Characteristics at High Mass Flow Rate

## 6. Wall Pressure Characteristics

_{1/2}/∆y = 7 corresponding to 200 grid cells in channel width, which is enough for fine cell structures [27]. Slip and adiabatic boundary conditions were used for the combustor walls. Homogeneous premixed gas was assumed as natural for the present study.

## 7. Thrust Performance

## 8. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Numerical smoked-foil records of detonation wave propagation through various cross-sectional shapes, adapted from [1].

**Figure 3.**(

**a**) Longitudinal cross-section of the tri-arc/circular RDEs, (

**b**) details of fuel and oxidizer injectors.

**Figure 6.**Pressure history of plenums, combustion channel, and pre-detonator at $\dot{m}=80.3\pm 0.20$ g/s for $\mathsf{\Phi}=1.04\pm 0.001$ ((

**a**) overall operation, (

**b**) combustion phase).

**Figure 8.**Experimental visualization (

**upper**), STFT (

**lower-left**) and FFT (

**lower-right**) results at reference mass flow rate, $\dot{m}=80.3\pm 0.20$ g/s for $\mathsf{\Phi}=1.04\pm 0.001$; tri-arc (

**a**) and circular (

**b**) RDEs.

**Figure 9.**Experimental visualization (

**upper**), STFT (

**lower-left**), and FFT (

**lower-right**) results at low mass flow rate, $\dot{m}=54.3\pm 0.04$ g/s for $\mathsf{\Phi}=0.9688\pm 0.00056$; tri-arc (

**a**) and circular (

**b**) RDEs.

**Figure 10.**Experimental visualization (

**upper**), STFT (

**lower-left**), and FFT (

**lower-right**) results at high mass flow rate, $\dot{m}=130.7\pm 0.71$ g/s for $\mathsf{\Phi}=1.042\pm 0.0013$; tri-arc (

**a**) and circular (

**b**) RDEs.

**Figure 11.**Local maximum pressure traces showing detonation cell structures from numerical analysis of the tri-arc RDE.

**Figure 14.**Dominant amplitudes of detonation pressure at the concave (p1) and convex (p2) corners of the outer wall of the combustion channel acquired from the FFT.

**Figure 17.**Various noncircular RDE cross-section configurations: (

**a**) oval-shaped, (

**b**) rounded- rectangular, (

**c**) triangular, (

**d**) arbitrary-shaped with changing width, and (

**e**) connected channels [1].

Combustor Length (mm) | Slot Width (mm) | Cross-Sectional Area (mm^{2}) | r/H | ||||
---|---|---|---|---|---|---|---|

Fuel Slot | Oxidizer Slot | Fuel Slot | Oxidizer Slot | Combustor | |||

Tri-arc RDE | 75.00 | 0.34 | 0.40 | 46.80 | 63.30 | 771.4 | 3.55–6.50 |

Circular RDE | 75.00 | 0.30 | 0.46 | 47.10 | 72.80 | 758.7 | 6.06 |

Hansmetzger [25] | 90 | 0.3 | 0.5 | 47.12 | 79.33 | 1885.00 | 3.5 |

**Table 2.**Operation characteristics of tri-arc and circular RDEs for the other mass flow rate conditions.

$\dot{\mathit{m}}$ (g/s) | Φ | RDE Type | Stability | Dominant Frequency (kHz) | Velocity Deficit (m/s) |
---|---|---|---|---|---|

64.8 $\pm $0.32 | 1.03 $\pm $0.001 | Tri-arc | Stable | 16.71 | 844.40 |

Circular | Stable, temporarily unstable | 16.88 | 826.96 | ||

80.3 $\pm $0.20 | 1.04 $\pm $0.001 | Tri-arc | Stable | 16.72 | 843.47 |

Circular | Stable | 17.60 | 760.16 | ||

107.7 $\pm $0.71 | 1.04 $\pm $0.008 | Tri-arc | Stable | 17.78 | 745.24 |

Circular | Stable | 17.70 | 750.88 |

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

Specific heat ratio | Unburned gas | 1.602 |

Burned gas | 1.288 | |

Dimensionless heat addition | 24.2 | |

Dimensionless activation energy | 32.46 |

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**MDPI and ACS Style**

Lee, J.-H.; Ryu, J.-H.; Lee, E.-S.; Han, H.-S.; Choi, J.-Y.
Experimental Proof of Concept of a Noncircular Rotating Detonation Engine (RDE) for Propulsion Applications. *Aerospace* **2023**, *10*, 27.
https://doi.org/10.3390/aerospace10010027

**AMA Style**

Lee J-H, Ryu J-H, Lee E-S, Han H-S, Choi J-Y.
Experimental Proof of Concept of a Noncircular Rotating Detonation Engine (RDE) for Propulsion Applications. *Aerospace*. 2023; 10(1):27.
https://doi.org/10.3390/aerospace10010027

**Chicago/Turabian Style**

Lee, Jae-Hyuk, Jae-Hoon Ryu, Eun-Sung Lee, Hyung-Seok Han, and Jeong-Yeol Choi.
2023. "Experimental Proof of Concept of a Noncircular Rotating Detonation Engine (RDE) for Propulsion Applications" *Aerospace* 10, no. 1: 27.
https://doi.org/10.3390/aerospace10010027