# Experimental Study on the Propagation Characteristics of Rotating Detonation Wave with Liquid Hydrocarbon/High-Enthalpy Air Mixture

^{1}

^{2}

^{*}

## Abstract

**:**

^{2}s). Both the propagation velocity and peak pressure of the rotating detonation wave decrease as the mass flux and equivalence ratio are reduced while the number of detonation wavefronts increases. Detonation wave instability tends to occur when the inlet mass flux decreases. There is a transition progress from thermo-acoustic combustion to rotating detonation combustion in the experiment under the condition of mass flux 350 kg/(m

^{2}s) and the equivalent ratio 0.8. The static pressure in the chamber is higher during detonation combustion than during thermo-acoustic combustion. These experimental results provide evidence that rotating detonation waves have the potential to significantly improve propulsion performance. The findings can serve as a valuable reference for the practical engineering application of rotating detonation engines.

## 1. Introduction

## 2. Experimental Facilities

^{2}, and the nozzle throat area is 22,698 mm

^{2}. In the experiment, the inlet mass flux of the chamber is adjusted by the different mass flow rates of the vitiator components, but the temperature remains unchanged.

## 3. Results and Discussion

#### 3.1. One-Direction Propagation Mode for the Rotating Detonation Wave

^{2}s). As shown in Figure 3a, when the equivalence ratio is 0.8, the rotating detonation wave propagates in a fully developed single-wave mode. The average value of the detonation wave pressure peak is approximately 2 MPa, with a rotating detonation wave frequency of around 1814.4 Hz. The detonation wave propagation velocity can be calculated as 1710 m/s. As the equivalence ratio decreases, the detonation wave peak pressure decreases while the number of rotating detonation wavefronts increases. As shown in Figure 3b, the pressure sequences collected by PCB1 and PCB3 are similar, and the frequency of the rotating detonation wave is 3325 Hz, so it presents a two-wave, one-direction propagation mode for the rotating detonation wave when the equivalence ratio is 0.7. A three-wave, one-direction propagation mode of the rotating detonation wave appears when the equivalence ratios are 0.6 and 0.5, as depicted in Figure 3c,d, with the frequencies of the rotating detonation wave being 4810 Hz and 4701 Hz, respectively. The propagation velocity of the detonation wave is also provided in the pressure sequence figures. The detonation wave velocity is calculated by dividing the circumference of the outer cylinder of the combustion chamber by the time interval between two adjacent detonation wave peaks collected by PCB1. When the equivalent ratio decreases, the theoretical propagation velocity of the detonation wave decreases, and the decrease in the equivalent ratio is associated with a decrease in nozzle stiffness. This reduction in stiffness is influenced by factors such as decreased fuel injection pressure and diminished nozzle recovery time after the detonation wave passes. Consequently, the filling height of the subsequent cycle becomes insufficient, resulting in a decrease in detonation wave quality, peak pressure, and velocity. In the non-premixed chamber, a dual-wave system can emerge. This occurs when unburned reactants survive the leading detonation wave in the injector near field and are subsequently consumed within a trailing azimuthal reflected-shock combustion zone [39]. Furthermore, the trailing oblique shock wave reflects off the outer wall of the detonation chamber further downstream from the detonation wave. Since the detonation chamber lacks an inner tube structure, the unburned mixture begins to burn and gradually forms a new detonation front. Eventually, the system reaches a natural steady state of operation that balances mixture quality and wavefront quantity. Since the rotating detonation combustion cannot be initiated when the mixture equivalence ratio is lower than 0.5 in the tests, the equivalence ratio range is set between 0.5 and 0.8.

#### 3.2. Transition of Tangential Thermo-Acoustic Combustion to Rotating Detonation Combustion

^{2}s), and the equivalent ratio is 0.8. The dynamic pressure sequence, along with the results of FFT and STFT, are displayed in Figure 4. In the dynamic pressure sequence diagram, the ignition time of the pre-detonation tube is at time zero. It can be observed that the basic frequency of the pressure wave is 1500 Hz during the first 4.2 s and 1750 Hz during the last 0.3 s. The frequency of 1500 Hz corresponds to thermo-acoustic combustion, while the frequency of 1750 Hz corresponds to rotating detonation wave combustion. A partially enlarged detail of tangential thermo-acoustic combustion is shown in Figure 5a. The total temperature of the incoming flow is 1250 K, and the mixture equivalence ratio is 0.8. Consequently, the total temperature of the burned gas can be estimated to be around 2610 K using the program developed by the research group. Since the Mach number of the gas flow is less than 0.3 in the chamber, the static temperature is close to the total temperature. Thus, the sound velocity of the burned gas can be estimated to be 959 m/s using the total temperature. With an outer diameter of 300 mm for the chamber, the tangential oscillation frequency in the combustion chamber is calculated to be 1425 Hz, based on the method introduced in the literature [43]. This presents a deviation of 5% when compared with the measured 1500 Hz in the test. Considering that there are errors in the test and calculation processes, the combustion mode during the first 4.2 s can be confirmed as tangential thermo-acoustic coupling combustion. The pressure sequence and propagation velocity of rotating detonation combustion are shown in Figure 5b. The average value of the detonation wave pressure peak is approximately 2 MPa, and the average velocity of detonation wave propagation is about 1610 m/s based on the frequency of 1750 Hz. Because the total temperature of the incoming air is as high as 1250 K, the kerosene quickly turns into steam in the high-temperature airflow. So, it assumes that the mixture in front of the detonation is gaseous, and the air and gaseous kerosene are mixed well. The C-J values of the pressure and the propagation velocity of the rotating detonation wave are computed by the NASA CEA [44]. The C-J theoretical velocity and pressure of the detonation wave are estimated to be 1694 m/s and 2.1 MPa, respectively. The measured velocity of rotating detonation wave propagation is slightly lower than the C-J theoretical value, as is the peak pressure. Since the deviation range is within 5%, it is confirmed that the rotating detonation wave is in the C-J detonation state during the last 0.3 s. Figure 6 displays the dynamic pressure and static pressure sequences of the combustion chamber when the combustion mode transitions from thermo-acoustic combustion to rotating detonation combustion. It can be observed that the static pressure in the combustion chamber increases from 0.368 MPa to 0.386 MPa. This results in a static pressure increase of about 5% for the rotating detonation combustion mode in the chamber. The pressure in the vitiator is higher than 2 MPa; meanwhile, the average pressure in the rotating detonation chamber is lower than 0.4 MPa, so the mass flow rate of the chamber is constant. According to the one-dimensional flow equation of $\mathrm{m}=0.04\frac{{\mathrm{P}}^{\mathrm{*}}}{\sqrt{{\mathrm{T}}^{\mathrm{*}}}}\mathrm{q}\left(\mathsf{\lambda}\right)$, the total pressure increases by 5%, so the total temperature should increase by about 10%. It can be concluded that the efficiency of rotating detonation combustion in the chamber is higher than that of thermo-acoustic combustion. The specific impulse of RDE is improved by more than 10%, demonstrating the superior performance of detonation combustion.

#### 3.3. Axial Pressure Pulsation Superimposed on Rotating Detonation Combustion

^{2}s), the total temperature of the incoming flow is 1250 K, and the equivalent ratio is 0.8, the peak pressure of the rotating detonation wave is lower than 0.8 MPa, and there is a low-frequency pulsation superimposed on rotating detonation combustion, as shown in Figure 7. The low-frequency pulsation with a period of about 5.7 ms is likely caused by pressure wave oscillation between the heater acoustic throat and the nozzle acoustic throat. As shown in Figure 1, the distance from the heater acoustic throat to the PCB1 sensor is 1510 mm, the distance from the PCB1 sensor to the combustion nozzle throat is 490 mm, and the total temperature of incoming flow is 1250 K. Because the Mach number of the incoming flow in the inlet section is less than 0.3, the static temperature is close to the total temperature, and the sound velocity is estimated to be about 709 m/s based on the total temperature. Therefore, it takes about 4.26 ms for the pressure wave to propagate from PCB1 upstream to the heater throat and back to PCB1. When the total temperature of the burned gas in the combustion chamber is about 2610 K, and the velocity of sound in the chamber is about 959 m/s, then it takes about 1.02 ms for the pressure wave propagating from PCB1 to the nozzle throat and back to PCB1. It shows the pressure sequence measured by the dynamic pressure sensor and the filtered results in Figure 7a, and a period of the filtered pressure sequence is enlarged in Figure 7b. In the figure, the compression wave propagates upstream through the dynamic pressure sensor PCB1 and then reaches the heater acoustic throat at moment 1, and the reflected expansion wave propagates downstream; the expansion wave reaches the dynamic pressure sensor PCB1 at moment 2 and then propagates to the nozzle acoustic throat reflecting a compression wave; the compression wave reaches the dynamic pressure sensor PCB1 again at moment 1′. It takes about 4.4 s from moment 1 to 2, longer than the estimated time of 4.26 ms, probably because the intake ducting absorbs the heat of the incoming flow, the total temperature drops, and the velocity of sound is also reduced. It takes about 1.3 ms from moment 2 to 1′, also longer than the estimated value, probably because that (1) the actual combustion efficiency is less than 1, and the total temperature of burned gas in the combustion chamber is less than the total theoretical temperature of 2610 K, and (2) it takes some time for the heat release of combustion progress, so the gas would reach the maximum temperature at the end of the combustion chamber. Therefore, the average velocity of sound for the burned gas in the combustion chamber is also less than 959 m/s. In general, the period of axial pulsation propagation of the pressure wave is longer than the estimated value.

#### 3.4. Rotating Detonation Combustion Mode of Two-Wave Collision

^{2}s), the rotating detonation wave in the detonation chamber tends to be a two-wave collision mode. When the equivalent ratio is 0.8, it can be seen that the time interval of the pressure peak appears alternately in the time sequence of PCB1, which is a typical two-wave collision propagation mode of the rotating detonation waves. When the equivalent ratios are 0.7 and 0.6, it can be seen from Figure 9b,c. The number of pressure peaks collected by PCB3 is about twice that of PCB1, so the collision point of the rotating detonation waves is near the PCB1 sensor, and the peak pressure measured by PCB1 at the equivalent ratio 0.7 is higher than that of equivalent ratio 0.8. In Figure 9, when the equivalent ratio changes, the propagation frequency of the collision rotating detonation waves changes slightly, and the propagation speed is much lower than the C-J theoretical value due to the process of developing from transmit shock to the rotating detonation wave each period after collision.

## 4. Conclusions

- (1)
- With the use of liquid hydrocarbon fuel, a fully developed rotating detonation wave can be achieved under conditions of high incoming air total temperature of 1250 K.
- (2)
- The stability of the rotating detonation wave is more favorable at higher inlet mass flux. In the tested engine structure, the rotating detonation pressure peak and velocity in single-wave mode are close to those of C-J theoretical values at an equivalent ratio of 0.8 when the mass flux is 400 kg/(m
^{2}s). - (3)
- When the mixture equivalent ratio decreases from 0.8 to 0.5 at the same inlet mass flux, the quantity of rotating detonation waves in the combustion chamber increases while the pressure peak of the detonation wave and its propagation velocity decrease.
- (4)
- A transformation from thermo-acoustic combustion to rotating detonation operation is observed. This effect shows an increase in mean chamber pressure and Isp of the engine—both of which indicate a potential for higher performance of an engine from detonative operation.
- (5)
- At an inlet mass flux of 350 kg/(m
^{2}s), axial pressure pulsation is observed superimposed on rotating detonation combustion in the combustion chamber, indicating a positive correlation between the pressure peak of the detonation wave and the change in static pressure in the combustion chamber. - (6)
- In collision mode, the rotating detonation wave undergoes a transition process from transmitted shock to detonation wave during each period, resulting in the propagation velocity significantly lower than the C-J theoretical velocity.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 3.**Pressure sequence and FFT results of rotating detonation wave in combustion chamber as the inlet mass flux is 400 kg/(m

^{2}s).

**Figure 4.**Analysis results of STFT and FFT for the measured pressure wave at an equivalence ratio of 0.8 as the inlet mass flux is 375 kg/(m

^{2}s).

**Figure 5.**Two combustion modes in the combustion chamber at an equivalence ratio of 0.8 as the inlet mass flux is 375 kg/(m

^{2}s): (

**a**) thermo-acoustic combustion; (

**b**) rotating detonation combustion.

**Figure 6.**Dynamic pressure and static pressure in combustion chamber at an equivalent ratio of 0.8 as the inlet mass flux is 375 kg/(m

^{2}s): (

**a**) dynamic pressure in combustion chamber; (

**b**) static pressure in combustion chamber.

**Figure 7.**Dynamic pressure and the filtered results in combustion chamber at an equivalent ratio of 0.8 as the inlet mass flux is 350 kg/(m

^{2}s): (

**a**) dynamic pressure and the filtered results; (

**b**) enlarged partial view.

**Figure 8.**Dynamic pressure in combustion chamber and the FFT results at an equivalence ratio of 0.8 as the inlet mass flux 350 kg/(m

^{2}s).

Condition No. | Inlet Mass Flux kg/(m^{2}s) | Equivalent Ratio Range |
---|---|---|

1 | 400 | 0.5~0.8 |

2 | 375 | 0.5~0.8 |

3 | 350 | 0.5~0.8 |

4 | 300 | 0.5~0.8 |

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**MDPI and ACS Style**

Jia, B.; Zhang, Y.; Meng, H.; Meng, F.; Pan, H.; Hong, Y.
Experimental Study on the Propagation Characteristics of Rotating Detonation Wave with Liquid Hydrocarbon/High-Enthalpy Air Mixture. *Aerospace* **2023**, *10*, 682.
https://doi.org/10.3390/aerospace10080682

**AMA Style**

Jia B, Zhang Y, Meng H, Meng F, Pan H, Hong Y.
Experimental Study on the Propagation Characteristics of Rotating Detonation Wave with Liquid Hydrocarbon/High-Enthalpy Air Mixture. *Aerospace*. 2023; 10(8):682.
https://doi.org/10.3390/aerospace10080682

**Chicago/Turabian Style**

Jia, Bingyue, Yining Zhang, Hao Meng, Fanxiao Meng, Hu Pan, and Yanji Hong.
2023. "Experimental Study on the Propagation Characteristics of Rotating Detonation Wave with Liquid Hydrocarbon/High-Enthalpy Air Mixture" *Aerospace* 10, no. 8: 682.
https://doi.org/10.3390/aerospace10080682