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Effects of pintle injector on ethylene-air rocket-based continuous rotating detonation
Acta Astronautica 164 (2019) 311–320
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Research paper
Effects of pintle injector on ethylene-air rocket-based continuous rotating detonation
T
Si-yuan Huang, Jin Zhou, Shi-jie Liu∗, Hao-yang Peng College of Aerospace Science and Engineering, National University of Defense Technology, Changsha, Hunan Province, 410073, People's Republic of China
A R T I C LE I N FO
A B S T R A C T
Keywords: Ethylene-air Continuous rotating detonation Pintle injector High-frequency tangential instability Intrinsic frequency
Continuous Rotating Detonation (CRD) shares many similarities with the High-Frequency Tangential Instability (HFTI) in liquid rocket engine, and it may be one cause of the HFTI. To investigate the self-sustaining mechanism of CRD/HFTI, a pintle-like injection scheme is adopted in this paper, and series of ethylene-air tests have been conducted. The pintle injector effects on the CRD operation range have been analyzed firstly. By decreasing the diameter of pintle injector, the lean equivalence ratio boundary increases, and the primary combustion mode transfers from CRD to sawtooth-wave mode. By increasing the insertion length, the enlarging of the head recirculation zone is helpful for the realization of multi-CRD waves. Based on the high-frequency pressure results, the propagation characteristics of single-wave, two-waves and sawtooth-wave modes are detailed. Theoretical intrinsic frequencies of the hollow chamber have been calculated and compared with the test results. The singlewave and two-waves modes show good agreements with the first tangential and second tangential theoretical results, respectively, with the relative deviations within just 6%. But the frequency of sawtooth-wave mode is much less than the first tangential theoretical value, and the deviation reaches about 20%. Because the diameter of traditional rocket pintle injector is much smaller than that of combustor, CRD cannot be achieved due to the propellant deficiency around the outer combustor, leading to the depress of HFTI. This paper could improve the understanding of the self-sustaining mechanisms of CRD and HFTI.
1. Introduction Due to the advantages of compact combustion chamber and high thermodynamic efficiency, CRD engine has been considered as a novel and potential aerospace thruster [1]. Combustor for a CRD engine is usually annular, and there is one or multiple detonation waves propagating circumferentially to consume the fresh propellants. The combustion products are discharged through a nozzle with high axial velocity to produce thrust [2]. The possible types of CRD engines may include rocket-based engine [2], ramjet-based engine [3] and turbinebased engine [1]. Among these CRD engines, rocketed-based CRD engine is widely adopted in CRD mechanism investigations for its simple structure and easy realization. In addition to the engine application, CRD also provides guidance for the researches of combustion instability in rocket engines [4]. In the last decade, significant progress has been made in the numerical [5–8] and experimental [9–11] studies of CRD engines fueled by hydrogen. Sun et al. [5] numerically realized CRD with different injection nozzle exit width. Xia et al. [6] carried out numerical study on the CRD engines and they analyzed two-wave collision phenomena as
∗
well as wave structure evolution. Smirnov et al. [7,8] conducted numerical researches on the CRD engines with different size of combustion chambers. They found that CRD waves got unstable as the chamber got wider and a stable CRD process was easier to be acquired with rich mixture. Frolov et al. [9] conducted hydrogen-air CRD experiments on a large-scale combustor to discuss its operation process and propulsion performance. Liu et al. [10] and Rankin et al. [11] conducted plenty of CRD experiments and discussed the characteristics of CRD waves. Based on these researches, the ignition, propagation characteristics of CRD waves and propulsion performance of hydrogen-air CRD engines have been revealed. After the realization of hydrogen-air CRD, researchers have naturally turned to the CRD fueled by hydrocarbon fuels. Lots of ethyleneair CRD researches have been carried out in the traditional annular combustor. Dyer et al. [12] conducted extensive ethylene-air experiments on the typical hydrogen-air CRD engine. However, they obtained stable CRD waves only in a few tests when the oxygen content in the air was added to 24.8%. Wilhite et al. [13] realized ethylene-air CRD in an annular chamber with the outer diameter of 100 mm, but the operation range was quite limited and the main propagation mode was sawtooth-
Corresponding author. E-mail address: [email protected] (S.-j. Liu).
https://doi.org/10.1016/j.actaastro.2019.08.019 Received 27 June 2019; Received in revised form 21 August 2019; Accepted 21 August 2019 Available online 26 August 2019 0094-5765/ © 2019 IAA. Published by Elsevier Ltd. All rights reserved.
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Fig. 1. Schematic of the combustion chamber and Laval nozzle.
Injection method affects the distributions and mixing quality of propellants and finally determines the combustion mode in the chamber. For ordinary injection method of CRD engine, fuel and oxidizer are injected into the chamber via a slit-orifice collision pattern near the chamber wall [25–27]. For LRE, various injection methods have been widely investigated [28–30]. As one of the excellent injectors of LRE, pintle injector has the advantages of simple structure, deep throttling and intrinsic combustion stability [30]. It is worth noting that LRE with pintle injector has never appeared HFTI according to the extensive test records of TRW [31]. In other words, HFTI in LRE can be suppressed when the propellants are injected through a pintle injector. Based on the former studies, pintle injector has the intrinsic combustion stability to suppress the HFTI in LRE, and CRD in a hollow chamber is closely connected with HFTI. So whether the pintle injector can suppress CRD in a hollow chamber is valuable and interesting to verify. In the former research [24], we have performed hydrogen-air CRD experiments with similar configuration of pintle injector. The results showed that the CRD was suppressed when the injector configuration was close to the typical pintle injector. In this paper, gaseous ethyleneair CRD is realized in an obviously narrower operation range. Different configurations of pintle injectors are tested to investigate their effects on the operation range and propagation modes of CRD waves. The intrinsic frequencies of the combustion chamber are calculated and compared with the experimental results. This study will enrich the hydrocarbon detonation theory and make contributions to a better understanding of the relationships between CRD and HFTI.
wave mode with the velocity of 900 m/s. Cho et al. [14] realized ethylene-air CRD in an optical observation combustor. Two-waves in hetero-rotating mode were obtained in their experiments and the propagation velocity of CRD waves was about 994 m/s. Peng et al. [15] realized ethylene-air CRD in the annular combustor with cavity. They concluded that the cavity contributed to the propagation mode transformation from two-waves in hetero-rotating mode to two-waves in homo-rotating mode. The propagation velocity was 1228.68 m/s on stoichiometric equivalence ratio. Above all, realization of ethylene-air CRD in annular chamber are confronted with many challenges. The hollow chamber is another feasible design for CRD engine which is analogous to rocket engine. The detonation cell size of hydrocarbon fuels is always much larger than that of hydrogen, and it is one of the difficulties for the hydrocarbon CRD realization in the traditional annular combustor [16]. Inspired by this, the hollow CRD chamber has been adopted in recent studies. Lin et al. [17] realized methane-oxygen CRD in a hollow chamber. Zhang et al. [18,19] found the operating domain gradually enlarged with the inner body length decreasing. They also proved that the CRD wave was easier to be detonated and self-sustain in the hollow chamber. Tang et al. [20] conducted hydrogen-air CRD numerical investigations in a hollow chamber and they found that deflagration existed in the center of chamber. Without the inner wall, the reflections of CRD waves reduced obviously and clearer structures of CRD waves were presented. Peng et al. [21] realized ethylene-air CRD waves in a hollow chamber with Laval nozzle. Three different propagation modes were obtained with little velocity deficit and notable pressure rise. All these researches make a great foundation to investigate on the possibility of CRD fueled by ethylene in the hollow chamber. In addition to being applied in a potential aerospace thruster, CRD in the hollow chamber is always connected with the combustion instability in rocket engines. With large number of similar characteristics [4,18], studies of CRD in the hollow chamber have been proved to be illuminating to the analysis of combustion instability in rocket engines [4]. In the development of liquid rocket engines (LRE), high-frequency tangential instability (HFTI) has been regarded as one of the most challenging issues and it is also a source of constant adversity [22]. In recent years, researchers have made great progress in the research of CRD in the hollow chamber and the relationships between CRD and HFTI have attracted increased attention. Zhang et al. [18,19] compared the intrinsic frequencies of the hollow chamber with frequencies of CRD waves to investigate their similarities. Anand et al. [23] realized CRD in a hollow chamber with ethylene-air mixture and they summed up two mechanisms to cause CRD in a hollow chamber. They also tried to explain the “detonation-like” behavior in HFTI. Huang et al. [24] realized hydrogen-air CRD in a hollow chamber with pintle injector and they discussed the similarities between CRD and HFTI in terms of frequency. However, it is to be emphasized that the detailed relationships between CRD and HFTI are still unclear.
2. Experiment system and measurement methodology The experiment system mainly consists of combustion chamber, supply system and control system. The schematic of combustion chamber and Laval nozzle is shown in Fig. 1. Diameter and length of the hollow chamber are designed to be 100 mm and 130 mm, respectively. The combustion products are discharged into the atmosphere through a Laval nozzle. The length of contraction section is 100 mm and the contraction ratio is 4. The contraction ratio is defined as ε = Ai / At , where Ai is the area of inlet of the Laval nozzle and At is the area of nozzle throat. The detailed geometrical dimensions are shown in Table 1 for a better understanding. As shown in Fig. 1, the pintle injector is mainly composed of pintle sleeve and inner column. A convergent-divergent slit is designed between pintle sleeve and inner column, and the air is axially injected through this slit with a throat width of 0.5 mm. The gaseous ethylene is injected through 90 orifices distributed uniformly at the head of inner column. In this research, pintle diameter (D) is actually the diameter of inner column and insertion length (H) is defined as the axial distance between the end faces of pintle sleeve and inner column. In the design of pintle injector, diameter (D) and insertion length (H) are two dominant parameters, so we focused on their influences on CRD waves 312
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Table 1 The detailed geometrical dimensions. Geometrical dimensions
Values
Length of combustion chamber Diameter of combustion chamber Length of contraction section of Laval nozzle Diameter of nozzle throat Throat width of air slit Diameter of orifice Number of orifices Pintle diameter (D) Pintle insertion length (H)
130 mm 100 mm 100 mm 50 mm 0.5 mm 0.5 mm 90 90 mm, 80 mm, 70 mm or 50 mm 0 mm, 5 mm, 10 mm, 15 mm or 20 mm
Fig. 3. Time sequence of the experiment.
system. The sensitivity of PCB sensor is 0.725 mV/kPa, and its measurement resolution is 0.035 kPa. The measurement range is 6895 kPa. As shown in Fig. 4, PCB1 and PCB2 are installed at same axial location with a circumferential angle of 90°.
in the experiments, respectively. The pintle configuration can be labeled as “Dxx-Hyy”, while xx and yy are the values of pintle diameter and insertion length, respectively. For example, D90-H5 means the pintle diameter is 90 mm and the insertion length is 5 mm. Eight pintle injectors are adopted in this experiment with the configuration of D90H0, D80-H0, D70-H0, D50-H0, D90-H5, D90-H10, D90-H15 and D90H20. The experiments are conducted at normal pressure, and the total temperatures of propellants are room temperature. As shown in Fig. 2, a hot tube connected tangentially to the chamber is used to initiate the CRD through deflagration to detonation transition (DDT). And this initiation method has been widely used in our previous researches [15,21]. A continuous and non-premixed supply scheme is adopted in this study. Bottled hydrogen and oxygen are supplied to the hot tube to generate detonation wave. Bottled ethylene and compressed air are supplied to be propellants in the hollow chamber. The gases are supplied through pneumatic valves which are controlled by electromagnetic valves. Standard sonic nozzles are installed in the feeding lines to guarantee the accuracy of the propellants supply. Turbine flow meters are used to measure the mass flow of propellants, and the measurement error is within 1%. The experimental test time sequence is shown in Fig. 3. The green arrow means valve on and red one means off. Before the ignition, the air valve and ethylene valve are opened in sequence. The hot tube hydrogen and oxygen are shut once the hot tube has been filled with hydrogen/oxygen mixture. Then the spark ignites the hot tube, namely, pre-detonator. After the DDT process, the CRD in the hollow chamber is initiated subsequently. The CRD maintains about 300 ms in the experiment. In the blow down duration, the nitrogen valve is turned on and ethylene valve is turned off later. Nitrogen and ethylene are injected into the fuel plenum for a while. The flame extinguishes as nitrogen blows off the propellants and combustion products. Measurement methodologies in this experiment are mainly timeaveraged and time-dependent pressure measurements. The time-averaged pressures in pipelines, injection manifolds and chamber are acquired with piezo-resistance sensors (Maxwell, Model MPM480). The measure frequency is 500 Hz, and its error is within 0.5% full scale (FS). As shown in Fig. 4, the Maxwell sensors are placed in the same radial cross section with the equal interval of 15 mm. In order to detect the propagation characteristics of CRD waves, time-dependent piezoelectric sensors (PCB113B24) are applied with NI high-frequency measure
3. Results and analysis Keeping the air mass flow rate in the range of 490–510 g/s, series of tests have been conducted by changing the equivalence ratio (ER) under every pintle injector. In this research, the ER varies between 0.7 and 1.2. When the ER is about 0.7, CRD cannot be realized for all the tests. In consideration of safety, the maximum ER is limited to 1.2. Based on the test results, the pintle configuration effects on the CRD operation range and propagation characteristics of CRD waves are analyzed. The propagation frequencies are also compared with the theoretical LRE intrinsic frequencies to investigate the relationships between CRD and HFTI. 3.1. Effects of pintle injector geometric parameters 3.1.1. Pintle diameter In the present paper, the influences of different pintle diameter and insertion length are discussed independently. The operation range map with pintle injectors of different diameters (H = 0 mm) is shown in Fig. 5(a), Three experiment results named single-wave mode, sawtoothwave mode and failure are shown in this figure. Single-wave mode means there is only one wave propagating in the combustion chamber and it is also the most common propagation mode of CRD waves. Failure means that the CRD cannot be realized. When the fuel is insufficient near the chamber wall, the intensity of CRD wave is extremely weak, and consequently, sawtooth-wave mode can be acquired as a transition mode from failure to detonation. It can be summarized from Fig. 5(a) that pintle injector diameter has a certain impact on the operation range and propagation mode. When diameter shrinks from 90 mm to 70 mm, lean limit ER increases slightly but the main propagation mode is still single-wave mode. When the diameter is reduced to 50 mm, the primary propagation mode transforms from single-wave mode to sawtooth-wave mode. In consideration of the injection method, the air flow is injected axially around the inner column, while the ethylene is injected through orifices with an angle of 45° to the air flow. In this case, a smaller pintle diameter makes it harder for ethylene to penetrate air flow and finally arrive the chamber wall to realize detonation. According to numerical investigations conducted by Tang et al. [20], detonation waves propagate near the chamber wall and deflagration always exists in the center of chamber. With pintle diameter of 50 mm, the dominant combustion form is deflagration fueled by the entrained ethylene in the center of chamber. Ethylene reaching the chamber wall will be insufficient and this will dramatically suppress the realization of CRD. In this situation, only sawtooth-wave mode can be acquired. The propagation frequencies of CRD waves with different pintle diameters are shown in Fig. 5(b). The frequencies are acquired by conducting statistical analysis on PCB signals. For each test, more than 1000 rotating cycles are processed to calculate their average propagation frequency. In Fig. 5(b), it can be seen that propagation frequencies increase as ER increases. Of all the tests, the maximum frequency of
Fig. 2. The sketch of hot tube. 313
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Fig. 4. The distribution of pressure sensors.
of pintle injector. Based on the former researches on pintle injector [32], there are always two recirculation zones in the chamber, which are located at the head and the center of combustion chamber separately. Deflagration is always found in these areas. As shown in Fig. 7, with the increase of insertion length, the head recirculation zone enlarges and more ethylene will be consumed by the deflagration in this area. In the study of annular combustor with cavity, recirculation zone in the cavity has been verified to contribute to the stabilization of CRD waves [15]. In this study, the head recirculation zone plays the similar role. When the deflagration is stabilized at the head of the chamber, exchange of matter and energy with the fresh mixture behind the CRD wave front will occur in this area. In other words, it works like a pilot flame to promote the ignition process and the stabilization of CRD waves. The high-temperature and high-activity combustion products in recirculation zone generate hotspots which finally evolve into new detonation waves. The propagation frequencies of CRD waves with different pintle insertion lengths are shown in Fig. 6(b). It can be seen that frequencies of three propagation modes are markedly different. When the insertion length is no more than 10 mm, most detonation waves are single-wave mode and their frequencies are in the range of 5–6 kHz. When the insertion length exceeds 10 mm, primary modes are two-waves mode and their frequencies are beyond 8 kHz. With pintle insertion length of 20 mm, an obvious rise in frequency can be seen when the ER is 0.91. This rise is consistent with the transition of propagation mode.
CRD waves is 5.62 kHz. It is obtained with the pintle configuration of D80-H0 and the ER is 1.13. When pintle diameter is reduced from 80 mm to 70 mm, the frequencies decrease slightly. Frequencies of sawtooth-wave mode are apparently lower than those of single-wave mode. The frequencies of single-wave mode acquired in this experiment are between 5.06 kHz and 5.62 kHz, and for sawtooth-wave mode, the frequencies are between 3.98 kHz and 4.28 kHz. Just like the negative effects on operation range, the propagation frequencies of CRD waves decrease as the pintle diameter gets smaller. 3.1.2. Pintle insertion length The effects of pintle insertion length are shown as Fig. 6, and there is a new propagation mode named two-waves mode compared with the results of Fig. 5. When the insertion length is within 10 mm, the primary mode is single-wave mode and the lean limit increases as the insertion length gets larger. However, when the pintle insertion length exceeds 10 mm, two-waves mode can be observed in most of the tests. And the lean limit rises as the insertion length increases from 15 mm to 20 mm. In this paper, all the two-waves modes are homo-rotating modes, which means that there are two waves propagating along the same direction. And the frequencies of two-waves mode acquired in this paper are between 8.01 kHz and 8.58 kHz. When the insertion length increases from 10 mm to 15 mm, the primary propagation mode transforms from single-wave mode to twowaves mode and the operation range enlarges unusually. This is a new phenomenon that few publication has mentioned. The mechanism behind mode transition is supposed to be related with flow characteristics
Fig. 5. Effects of pintle diameter (H = 0 mm) on operation range and propagation frequency. 314
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Fig. 6. Effects of pintle insertion length (D = 90 mm) on operation range and propagation frequency.
Fig. 7. Schematic of the recirculation zones.
labeled in Fig. 8(b). The average frequency can be calculated by Eq. (1), and N is the number of calculation periods. With the diameter of combustion chamber (Dc ), the propagation velocity of CRD waves can be acquired by Eq. (2). The average frequency and propagation velocity of Test #1 are 5.53 kHz and 1737.30 m/s, respectively. Propagation frequency-time distribution and Fast Fourier Transformation (FFT) frequency distribution of Test#1 are shown in Fig. 9. A quite concentrated frequency distribution can be seen in Fig. 9(a) and the RSD of frequency is 5.98%. It means that the CRD waves of single-wave mode are quite stable. The results of FFT frequency distribution is shown as Fig. 9(b). It can be summarized that the dominant frequency of Test#1 shows good agreements with its average frequency. With constant pressure of 1 atm and temperature of 300 K, corresponding C-J velocity (ER = 1.05) is computed as 1836.50 m/s. So it can be verified that the number of CRD waves is 1 and its average propagation velocity is about 94.6% of the C-J value.
3.2. Propagation mode As mentioned above, three propagation modes are acquired in this research. In order to study their characteristics further, detailed analysis will be conducted in this section. The operation conditions of three typical tests are listed in Table 2. In order to describe the propagation stability, relative standard deviations (RSD) of frequency are calculated. For single-wave mode and two-waves mode, RSD of frequency is within 10%. And for sawtooth-wave mode, the value is within 25%.
3.2.1. Single-wave mode The original and local view of high-frequency pressure results of single-wave mode are shown in Fig. 8. In Fig. 8(b), Δt2 is about three times of Δt1, and PCB 1, 2 are installed at same axial location with a circumferential angle of 90°. So it can be inferred that there is a single detonation wave propagates as ‘a1-b1-a2-b2’ with a notable pressure rise of 1.5 MPa. The instantaneous frequency can be acquired by fi = 1/ ΔTi , where ΔTi is time interval of two contiguous peaks of same signal, as
f =
ΣiN= 1 fi (1)
N
Table 2 The typical experiment conditions. Test No.
Propagation mode
Pintle diameter(mm)
Insertion length (mm)
Mass flow of air (g/s)
ER
Frequency (kHz)
RSD of frequency (%)
#1 #2 #3
Single wave Two waves Sawtooth wave
90 90 50
0 15 0
497.71 ± 5 503.32 ± 5 502.29 ± 5
1.05 ± 0.02 1.02 ± 0.02 1.05 ± 0.02
5.53 8.58 4.21
5.98 8.01 21.92
315
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Fig. 8. High-frequency pressure results of single-wave mode (Test#1).
v = f πDc
Eqs. (3)–(5) are introduced to confirm the number of CRD waves.
(2)
3.2.2. Two-waves mode The original and local view of high-frequency pressure results of two-waves mode are shown in Fig. 10. In Fig. 10(b), the peak pressure is below 0.6 MPa, which is apparently lower than that of single-wave mode (about 1.5 MPa). This implies that CRD wave intensity of twowaves mode is weaker. Besides, It can be seen that time interval of two contiguous peaks of same signal ( ΔTi ) is much smaller than that of single-wave mode. With same method, the average frequency and propagation velocity can be calculated with Eqs. (1) and (2). The results are 8.58 kHz and 2695.49 m/s, respectively. Propagation frequencytime distribution and FFT frequency distribution of Test#2 are shown in Fig. 11. It can be seen in Fig. 11(a) that the distribution of instantaneous frequency of two-waves mode is a little more scattered and the RSD of average frequency is 8.01%. In Fig. 11(b), results of FFT dominant frequency is 8.56 kHz and it shows good agreements with average frequency as well. So it can be concluded that although the intensities are weaker, CRD waves of two-waves mode are still regular and stable. The corresponding C-J velocity (initial state P = 1 atm, T = 300 K, ER = 1.02) is calculated as 1829.05 m/s. The experimental velocity is much bigger than theoretical C-J value. So it can be inferred that there is more than one wave propagating in the chamber. For further study,
ta11a12 =
πDc 1 ⋅ v n
(3)
ta11b11 =
πDc θ ⋅ v 2π
(4)
n=
2π ta11b11 ⋅ θ ta11a12
(5)
where n is the number of CRD waves, θ is circumferential angle between PCB 1 and PCB 2 (π/2 in this research). The value of t a11b11/t a11a12 is about 1/2, so the number of CRD waves is calculated to be 2. As a result, the propagation velocity should be cut in half to 1347.74 m/s, which accounts for 73.69% of theoretical C-J velocity. 3.2.3. Sawtooth-wave mode In Fig. 12(a), it can be seen that the waveforms are very complicated since sawtooth-wave mode is itself an unstable mode. The average frequency calculated is 4.21 kHz, which is obviously lower than that of single-wave mode. Besides, there are no notable pressure peaks in this mode, while only some pressure fluctuations can be captured. The distribution of instantaneous frequency is shown in Fig. 12(b), and the RSD of average frequency is 21.92%. The propagation velocity of Test#3 is 1322.61 m/s. With constant pressure of 1 atm and temperature of 300 K, corresponding C-J velocity (ER = 1.05) is computed as
Fig. 9. Propagation frequency of single-wave mode (Test#1). 316
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Fig. 10. High-frequency pressure results of two-waves mode (Test#2).
In this model, i, j, k mean the orders of tangential (T), radial (R) and axial (A), respectively. a 0 is local sound velocity in the chamber and αij is the value of Bessel Function. R c and Lc are radius and characteristic length of the combustion chamber, respectively. Lch is the length of cylinder section of the chamber and Lcv is the length of contraction section of Laval nozzle. As shown in Fig. 4, there are 7 piezo-resistance sensors installed along axial direction to capture time-averaged pressures of combustion chamber and their measurement errors are 0.01 MPa. The pressure distributions along the chamber of some typical tests with the ER in the range of 0.98–1.02 are shown in Fig. 13. It can be seen that for different propagation modes, the pressures show clear distinctions. The pressures of single-wave mode are the highest, followed by the two-waves mode, and the pressures of sawtooth-wave mode are the lowest. For all the tests, the combustor pressure decreases firstly and then increases along the axial direction. It can be seen that P4 is always the minimum pressure in the chamber for different propagation modes (or pintle configurations). In this research, the minimum chamber pressure varies in the range of 0.20 MPa–0.40 MPa. Based on the LRE thermodynamic theory, the corresponding constant-pressure combustion temperature can be calculated with combustor pressure and ER. The calculated temperature distribution under different ER and combustor pressure conditions are shown in Fig. 14. It can be seen that ER has a significant impact on the combustor temperature while chamber pressure has little impact on it. For ER = 1.0 with the combustor pressure ranging from 0.20 MPa to 0.40 MPa, the
1836.50 m/s. The average velocity accounts for 72.02% of C-J velocity. According to typical ZND theory, a detonation wave is composed of an inducing shock wave and following combustion flame. To ensure the coupling of them, the inducing shock wave should be strong enough. The inducing shock wave of sawtooth-wave mode is weak, so the coupling may be unstable, which finally leads to an unstable detonation wave. As mentioned above, sawtooth-wave mode is a critical mode between failure and detonation. And it has been observed that this critical mode can transform into detonation or deflagration with advantageous or disadvantageous factors [21]. 3.3. Comparing with intrinsic frequencies of the chamber In the study of LRE, intrinsic frequencies of the chamber have been verified to be closely related to combustion instability. To investigate the similarities between CRD and HFTI, the frequencies of CRD waves can be compared with the intrinsic acoustic frequency of the hollow chamber. Based on the former research [19], a modified model has been adopted to calculate intrinsic frequencies of the test combustion chamber. The model can be described as Eqs. (6) and (7).
fiT , jR, kA =
2 2 a 0 ⎛ αij ⎞ k +⎛ ⎞ 2 ⎝ Rc ⎠ ⎝ Lc ⎠
Lc = Lch +
⎜
2 Lcv 3
⎟
⎜
⎟
(6) (7)
Fig. 11. Propagation frequency of two-waves mode (Test#2). 317
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Fig. 12. Pressure and average frequency distribution of sawtooth-wave mode (Test#3).
temperature ranges from 2283.48 K to 2299.49 K. It means that in this research, the pressure measured has a minor effect on the temperature. With corresponding minimum pressures and ER, average temperature and sound velocity in the chamber can be acquired by conducting thermodynamic calculation [19]. The variation of average temperature and sound velocity in the chamber with different pintle configurations are given in Fig. 15 and Fig. 16. In Fig. 15(a), it can be seen that temperature is mainly determined by ER while pintle diameter has little impact on it. Similarly, in Fig. 15(b), pintle insertion length also has little impact on temperature. In Fig. 16, similar conclusion can be drawn when discussing their influence on sound velocity. Based on Figs. 15 and 16, it can be concluded that pintle configuration has little impact on temperature and sound velocity. This is consistent with thermodynamic rules. To simplify the calculation process, sound velocities in the chamber with pintle configuration of D90-H0 are adopted as a 0 to calculate the intrinsic frequencies. And the tangential order (i) is always believed to be consistent with the number of waves in the chamber [19]. So tangential order for the single-wave mode and sawtooth-wave mode is 1, and for two-waves mode the value is 2. With above methods, the intrinsic frequencies for the test chamber are calculated and compared with the experimental frequencies of CRD waves. As shown in Fig. 17(a), frequencies of single-wave mode (D90H0 and D80-H0) are consistent with intrinsic frequency of first tangential (1T) mode. And for two-waves mode (D90-H15 and D90-H20), their frequencies are also close to the intrinsic frequency of second tangential (2T) mode. As illustrated in Fig. 17(b), relative deviations of single-wave mode and two-waves mode are within 6%. But for sawtooth-wave mode, their frequencies differ greatly from intrinsic frequency, and the relative deviations are about 20%, as shown in Fig. 17(b).
Fig. 13. Pressure distribution along the chamber.
4. Conclusion Series of ethylene-air continuous rotating detonation experiments have been conducted in the hollow chamber with different pintle injectors. The mass flow rate of air is kept in the range of 490–510 g/s, with equivalent ratio of 0.70–1.20. The effects of pintle diameter and insertion length are discussed and three propagation modes are detailed in the present paper. To investigate the relationships between continuous rotating detonation and high-frequency tangential instability, intrinsic frequencies of combustion chamber are calculated and compared with experimental results. Main conclusions can be summarized as follows:
Fig. 14. Theoretical temperature distribution.
(1) Ethylene-air continuous rotating detonation has been realized in 318
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Fig. 15. Variation of temperature with ER.
Fig. 16. Variation of sound velocity with ER.
Fig. 17. Comparison of CRD waves propagation frequency and intrinsic frequency.
due to the propellant deficiency around the outer chamber. (2) The realization of continuous rotating detonation gets harder in the increase of the pintle insertion length. However, when the insertion length increases from 10 mm to 15 mm, the operation range enlarges unusually. The primary propagation mode transforms from
this paper with designed pintle injectors. The operation range shrinks as the pintle diameter decreases. When diameter is reduced to a certain level, more propellants are entrained to the center of hollow chamber and less propellants arrive the outer chamber. In this situation, continuous rotating detonation cannot be achieved 319
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single-wave mode to two-waves mode during this process. In consideration of flow characteristics of pintle injector, the deflagration in head recirculation zone is believed to promote this mode transition. (3) Three propagation modes have been discussed in this work. Detonation waves of single-wave mode have been realized with notable pressure rise and little velocity deficit. With pintle configuration of D80-H0, the highest frequency and propagation velocity are 5.62 kHz and 1765.58 m/s, respectively. Two-waves mode is acquired with weaker intensity and larger velocity deficit. Sawtooth-wave mode is a critical mode between failure and detonation. (4) Based on the measured combustor pressure and liquid rocket engine thermodynamic theory, intrinsic frequencies of the hollow chamber have been calculated and compared with experimental frequencies of rotating detonation waves. The frequencies of single-wave mode and two-waves mode show good agreements with the first tangential mode and second tangential mode results, respectively. The relative deviations are within 6%. It can be inferred that continuous rotating detonation may be one cause of the high-frequency tangential instability in rocket engines. (5) Significant error can be found between the frequencies of sawtoothwave mode and theoretical intrinsic frequencies of hollow chamber. When pintle diameter gets smaller, primary combustion mode transforms from single-wave mode to sawtooth-wave mode, and the combustion instability can be suppressed.
[8]
[9] [10]
[11]
[12]
[13]
[14]
[15]
[16] [17]
[18] [19]
[20]
More detailed observation of continuous rotating detonation wave structure and propagation mode transition is still insufficient and it remains to be further studied by means of optical observation and numerical investigation in the future.
[21]
[22]
Acknowledgement [23]
This work was supported by the National Natural Science Foundation of China (Nos.51776220, and Nos.91541103).
[24]
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Contents lists available at ScienceDirect
Acta Astronautica journal homepage: www.elsevier.com/locate/actaastro
Research paper
Effects of pintle injector on ethylene-air rocket-based continuous rotating detonation
T
Si-yuan Huang, Jin Zhou, Shi-jie Liu∗, Hao-yang Peng College of Aerospace Science and Engineering, National University of Defense Technology, Changsha, Hunan Province, 410073, People's Republic of China
A R T I C LE I N FO
A B S T R A C T
Keywords: Ethylene-air Continuous rotating detonation Pintle injector High-frequency tangential instability Intrinsic frequency
Continuous Rotating Detonation (CRD) shares many similarities with the High-Frequency Tangential Instability (HFTI) in liquid rocket engine, and it may be one cause of the HFTI. To investigate the self-sustaining mechanism of CRD/HFTI, a pintle-like injection scheme is adopted in this paper, and series of ethylene-air tests have been conducted. The pintle injector effects on the CRD operation range have been analyzed firstly. By decreasing the diameter of pintle injector, the lean equivalence ratio boundary increases, and the primary combustion mode transfers from CRD to sawtooth-wave mode. By increasing the insertion length, the enlarging of the head recirculation zone is helpful for the realization of multi-CRD waves. Based on the high-frequency pressure results, the propagation characteristics of single-wave, two-waves and sawtooth-wave modes are detailed. Theoretical intrinsic frequencies of the hollow chamber have been calculated and compared with the test results. The singlewave and two-waves modes show good agreements with the first tangential and second tangential theoretical results, respectively, with the relative deviations within just 6%. But the frequency of sawtooth-wave mode is much less than the first tangential theoretical value, and the deviation reaches about 20%. Because the diameter of traditional rocket pintle injector is much smaller than that of combustor, CRD cannot be achieved due to the propellant deficiency around the outer combustor, leading to the depress of HFTI. This paper could improve the understanding of the self-sustaining mechanisms of CRD and HFTI.
1. Introduction Due to the advantages of compact combustion chamber and high thermodynamic efficiency, CRD engine has been considered as a novel and potential aerospace thruster [1]. Combustor for a CRD engine is usually annular, and there is one or multiple detonation waves propagating circumferentially to consume the fresh propellants. The combustion products are discharged through a nozzle with high axial velocity to produce thrust [2]. The possible types of CRD engines may include rocket-based engine [2], ramjet-based engine [3] and turbinebased engine [1]. Among these CRD engines, rocketed-based CRD engine is widely adopted in CRD mechanism investigations for its simple structure and easy realization. In addition to the engine application, CRD also provides guidance for the researches of combustion instability in rocket engines [4]. In the last decade, significant progress has been made in the numerical [5–8] and experimental [9–11] studies of CRD engines fueled by hydrogen. Sun et al. [5] numerically realized CRD with different injection nozzle exit width. Xia et al. [6] carried out numerical study on the CRD engines and they analyzed two-wave collision phenomena as
∗
well as wave structure evolution. Smirnov et al. [7,8] conducted numerical researches on the CRD engines with different size of combustion chambers. They found that CRD waves got unstable as the chamber got wider and a stable CRD process was easier to be acquired with rich mixture. Frolov et al. [9] conducted hydrogen-air CRD experiments on a large-scale combustor to discuss its operation process and propulsion performance. Liu et al. [10] and Rankin et al. [11] conducted plenty of CRD experiments and discussed the characteristics of CRD waves. Based on these researches, the ignition, propagation characteristics of CRD waves and propulsion performance of hydrogen-air CRD engines have been revealed. After the realization of hydrogen-air CRD, researchers have naturally turned to the CRD fueled by hydrocarbon fuels. Lots of ethyleneair CRD researches have been carried out in the traditional annular combustor. Dyer et al. [12] conducted extensive ethylene-air experiments on the typical hydrogen-air CRD engine. However, they obtained stable CRD waves only in a few tests when the oxygen content in the air was added to 24.8%. Wilhite et al. [13] realized ethylene-air CRD in an annular chamber with the outer diameter of 100 mm, but the operation range was quite limited and the main propagation mode was sawtooth-
Corresponding author. E-mail address: [email protected] (S.-j. Liu).
https://doi.org/10.1016/j.actaastro.2019.08.019 Received 27 June 2019; Received in revised form 21 August 2019; Accepted 21 August 2019 Available online 26 August 2019 0094-5765/ © 2019 IAA. Published by Elsevier Ltd. All rights reserved.
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Fig. 1. Schematic of the combustion chamber and Laval nozzle.
Injection method affects the distributions and mixing quality of propellants and finally determines the combustion mode in the chamber. For ordinary injection method of CRD engine, fuel and oxidizer are injected into the chamber via a slit-orifice collision pattern near the chamber wall [25–27]. For LRE, various injection methods have been widely investigated [28–30]. As one of the excellent injectors of LRE, pintle injector has the advantages of simple structure, deep throttling and intrinsic combustion stability [30]. It is worth noting that LRE with pintle injector has never appeared HFTI according to the extensive test records of TRW [31]. In other words, HFTI in LRE can be suppressed when the propellants are injected through a pintle injector. Based on the former studies, pintle injector has the intrinsic combustion stability to suppress the HFTI in LRE, and CRD in a hollow chamber is closely connected with HFTI. So whether the pintle injector can suppress CRD in a hollow chamber is valuable and interesting to verify. In the former research [24], we have performed hydrogen-air CRD experiments with similar configuration of pintle injector. The results showed that the CRD was suppressed when the injector configuration was close to the typical pintle injector. In this paper, gaseous ethyleneair CRD is realized in an obviously narrower operation range. Different configurations of pintle injectors are tested to investigate their effects on the operation range and propagation modes of CRD waves. The intrinsic frequencies of the combustion chamber are calculated and compared with the experimental results. This study will enrich the hydrocarbon detonation theory and make contributions to a better understanding of the relationships between CRD and HFTI.
wave mode with the velocity of 900 m/s. Cho et al. [14] realized ethylene-air CRD in an optical observation combustor. Two-waves in hetero-rotating mode were obtained in their experiments and the propagation velocity of CRD waves was about 994 m/s. Peng et al. [15] realized ethylene-air CRD in the annular combustor with cavity. They concluded that the cavity contributed to the propagation mode transformation from two-waves in hetero-rotating mode to two-waves in homo-rotating mode. The propagation velocity was 1228.68 m/s on stoichiometric equivalence ratio. Above all, realization of ethylene-air CRD in annular chamber are confronted with many challenges. The hollow chamber is another feasible design for CRD engine which is analogous to rocket engine. The detonation cell size of hydrocarbon fuels is always much larger than that of hydrogen, and it is one of the difficulties for the hydrocarbon CRD realization in the traditional annular combustor [16]. Inspired by this, the hollow CRD chamber has been adopted in recent studies. Lin et al. [17] realized methane-oxygen CRD in a hollow chamber. Zhang et al. [18,19] found the operating domain gradually enlarged with the inner body length decreasing. They also proved that the CRD wave was easier to be detonated and self-sustain in the hollow chamber. Tang et al. [20] conducted hydrogen-air CRD numerical investigations in a hollow chamber and they found that deflagration existed in the center of chamber. Without the inner wall, the reflections of CRD waves reduced obviously and clearer structures of CRD waves were presented. Peng et al. [21] realized ethylene-air CRD waves in a hollow chamber with Laval nozzle. Three different propagation modes were obtained with little velocity deficit and notable pressure rise. All these researches make a great foundation to investigate on the possibility of CRD fueled by ethylene in the hollow chamber. In addition to being applied in a potential aerospace thruster, CRD in the hollow chamber is always connected with the combustion instability in rocket engines. With large number of similar characteristics [4,18], studies of CRD in the hollow chamber have been proved to be illuminating to the analysis of combustion instability in rocket engines [4]. In the development of liquid rocket engines (LRE), high-frequency tangential instability (HFTI) has been regarded as one of the most challenging issues and it is also a source of constant adversity [22]. In recent years, researchers have made great progress in the research of CRD in the hollow chamber and the relationships between CRD and HFTI have attracted increased attention. Zhang et al. [18,19] compared the intrinsic frequencies of the hollow chamber with frequencies of CRD waves to investigate their similarities. Anand et al. [23] realized CRD in a hollow chamber with ethylene-air mixture and they summed up two mechanisms to cause CRD in a hollow chamber. They also tried to explain the “detonation-like” behavior in HFTI. Huang et al. [24] realized hydrogen-air CRD in a hollow chamber with pintle injector and they discussed the similarities between CRD and HFTI in terms of frequency. However, it is to be emphasized that the detailed relationships between CRD and HFTI are still unclear.
2. Experiment system and measurement methodology The experiment system mainly consists of combustion chamber, supply system and control system. The schematic of combustion chamber and Laval nozzle is shown in Fig. 1. Diameter and length of the hollow chamber are designed to be 100 mm and 130 mm, respectively. The combustion products are discharged into the atmosphere through a Laval nozzle. The length of contraction section is 100 mm and the contraction ratio is 4. The contraction ratio is defined as ε = Ai / At , where Ai is the area of inlet of the Laval nozzle and At is the area of nozzle throat. The detailed geometrical dimensions are shown in Table 1 for a better understanding. As shown in Fig. 1, the pintle injector is mainly composed of pintle sleeve and inner column. A convergent-divergent slit is designed between pintle sleeve and inner column, and the air is axially injected through this slit with a throat width of 0.5 mm. The gaseous ethylene is injected through 90 orifices distributed uniformly at the head of inner column. In this research, pintle diameter (D) is actually the diameter of inner column and insertion length (H) is defined as the axial distance between the end faces of pintle sleeve and inner column. In the design of pintle injector, diameter (D) and insertion length (H) are two dominant parameters, so we focused on their influences on CRD waves 312
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Table 1 The detailed geometrical dimensions. Geometrical dimensions
Values
Length of combustion chamber Diameter of combustion chamber Length of contraction section of Laval nozzle Diameter of nozzle throat Throat width of air slit Diameter of orifice Number of orifices Pintle diameter (D) Pintle insertion length (H)
130 mm 100 mm 100 mm 50 mm 0.5 mm 0.5 mm 90 90 mm, 80 mm, 70 mm or 50 mm 0 mm, 5 mm, 10 mm, 15 mm or 20 mm
Fig. 3. Time sequence of the experiment.
system. The sensitivity of PCB sensor is 0.725 mV/kPa, and its measurement resolution is 0.035 kPa. The measurement range is 6895 kPa. As shown in Fig. 4, PCB1 and PCB2 are installed at same axial location with a circumferential angle of 90°.
in the experiments, respectively. The pintle configuration can be labeled as “Dxx-Hyy”, while xx and yy are the values of pintle diameter and insertion length, respectively. For example, D90-H5 means the pintle diameter is 90 mm and the insertion length is 5 mm. Eight pintle injectors are adopted in this experiment with the configuration of D90H0, D80-H0, D70-H0, D50-H0, D90-H5, D90-H10, D90-H15 and D90H20. The experiments are conducted at normal pressure, and the total temperatures of propellants are room temperature. As shown in Fig. 2, a hot tube connected tangentially to the chamber is used to initiate the CRD through deflagration to detonation transition (DDT). And this initiation method has been widely used in our previous researches [15,21]. A continuous and non-premixed supply scheme is adopted in this study. Bottled hydrogen and oxygen are supplied to the hot tube to generate detonation wave. Bottled ethylene and compressed air are supplied to be propellants in the hollow chamber. The gases are supplied through pneumatic valves which are controlled by electromagnetic valves. Standard sonic nozzles are installed in the feeding lines to guarantee the accuracy of the propellants supply. Turbine flow meters are used to measure the mass flow of propellants, and the measurement error is within 1%. The experimental test time sequence is shown in Fig. 3. The green arrow means valve on and red one means off. Before the ignition, the air valve and ethylene valve are opened in sequence. The hot tube hydrogen and oxygen are shut once the hot tube has been filled with hydrogen/oxygen mixture. Then the spark ignites the hot tube, namely, pre-detonator. After the DDT process, the CRD in the hollow chamber is initiated subsequently. The CRD maintains about 300 ms in the experiment. In the blow down duration, the nitrogen valve is turned on and ethylene valve is turned off later. Nitrogen and ethylene are injected into the fuel plenum for a while. The flame extinguishes as nitrogen blows off the propellants and combustion products. Measurement methodologies in this experiment are mainly timeaveraged and time-dependent pressure measurements. The time-averaged pressures in pipelines, injection manifolds and chamber are acquired with piezo-resistance sensors (Maxwell, Model MPM480). The measure frequency is 500 Hz, and its error is within 0.5% full scale (FS). As shown in Fig. 4, the Maxwell sensors are placed in the same radial cross section with the equal interval of 15 mm. In order to detect the propagation characteristics of CRD waves, time-dependent piezoelectric sensors (PCB113B24) are applied with NI high-frequency measure
3. Results and analysis Keeping the air mass flow rate in the range of 490–510 g/s, series of tests have been conducted by changing the equivalence ratio (ER) under every pintle injector. In this research, the ER varies between 0.7 and 1.2. When the ER is about 0.7, CRD cannot be realized for all the tests. In consideration of safety, the maximum ER is limited to 1.2. Based on the test results, the pintle configuration effects on the CRD operation range and propagation characteristics of CRD waves are analyzed. The propagation frequencies are also compared with the theoretical LRE intrinsic frequencies to investigate the relationships between CRD and HFTI. 3.1. Effects of pintle injector geometric parameters 3.1.1. Pintle diameter In the present paper, the influences of different pintle diameter and insertion length are discussed independently. The operation range map with pintle injectors of different diameters (H = 0 mm) is shown in Fig. 5(a), Three experiment results named single-wave mode, sawtoothwave mode and failure are shown in this figure. Single-wave mode means there is only one wave propagating in the combustion chamber and it is also the most common propagation mode of CRD waves. Failure means that the CRD cannot be realized. When the fuel is insufficient near the chamber wall, the intensity of CRD wave is extremely weak, and consequently, sawtooth-wave mode can be acquired as a transition mode from failure to detonation. It can be summarized from Fig. 5(a) that pintle injector diameter has a certain impact on the operation range and propagation mode. When diameter shrinks from 90 mm to 70 mm, lean limit ER increases slightly but the main propagation mode is still single-wave mode. When the diameter is reduced to 50 mm, the primary propagation mode transforms from single-wave mode to sawtooth-wave mode. In consideration of the injection method, the air flow is injected axially around the inner column, while the ethylene is injected through orifices with an angle of 45° to the air flow. In this case, a smaller pintle diameter makes it harder for ethylene to penetrate air flow and finally arrive the chamber wall to realize detonation. According to numerical investigations conducted by Tang et al. [20], detonation waves propagate near the chamber wall and deflagration always exists in the center of chamber. With pintle diameter of 50 mm, the dominant combustion form is deflagration fueled by the entrained ethylene in the center of chamber. Ethylene reaching the chamber wall will be insufficient and this will dramatically suppress the realization of CRD. In this situation, only sawtooth-wave mode can be acquired. The propagation frequencies of CRD waves with different pintle diameters are shown in Fig. 5(b). The frequencies are acquired by conducting statistical analysis on PCB signals. For each test, more than 1000 rotating cycles are processed to calculate their average propagation frequency. In Fig. 5(b), it can be seen that propagation frequencies increase as ER increases. Of all the tests, the maximum frequency of
Fig. 2. The sketch of hot tube. 313
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Fig. 4. The distribution of pressure sensors.
of pintle injector. Based on the former researches on pintle injector [32], there are always two recirculation zones in the chamber, which are located at the head and the center of combustion chamber separately. Deflagration is always found in these areas. As shown in Fig. 7, with the increase of insertion length, the head recirculation zone enlarges and more ethylene will be consumed by the deflagration in this area. In the study of annular combustor with cavity, recirculation zone in the cavity has been verified to contribute to the stabilization of CRD waves [15]. In this study, the head recirculation zone plays the similar role. When the deflagration is stabilized at the head of the chamber, exchange of matter and energy with the fresh mixture behind the CRD wave front will occur in this area. In other words, it works like a pilot flame to promote the ignition process and the stabilization of CRD waves. The high-temperature and high-activity combustion products in recirculation zone generate hotspots which finally evolve into new detonation waves. The propagation frequencies of CRD waves with different pintle insertion lengths are shown in Fig. 6(b). It can be seen that frequencies of three propagation modes are markedly different. When the insertion length is no more than 10 mm, most detonation waves are single-wave mode and their frequencies are in the range of 5–6 kHz. When the insertion length exceeds 10 mm, primary modes are two-waves mode and their frequencies are beyond 8 kHz. With pintle insertion length of 20 mm, an obvious rise in frequency can be seen when the ER is 0.91. This rise is consistent with the transition of propagation mode.
CRD waves is 5.62 kHz. It is obtained with the pintle configuration of D80-H0 and the ER is 1.13. When pintle diameter is reduced from 80 mm to 70 mm, the frequencies decrease slightly. Frequencies of sawtooth-wave mode are apparently lower than those of single-wave mode. The frequencies of single-wave mode acquired in this experiment are between 5.06 kHz and 5.62 kHz, and for sawtooth-wave mode, the frequencies are between 3.98 kHz and 4.28 kHz. Just like the negative effects on operation range, the propagation frequencies of CRD waves decrease as the pintle diameter gets smaller. 3.1.2. Pintle insertion length The effects of pintle insertion length are shown as Fig. 6, and there is a new propagation mode named two-waves mode compared with the results of Fig. 5. When the insertion length is within 10 mm, the primary mode is single-wave mode and the lean limit increases as the insertion length gets larger. However, when the pintle insertion length exceeds 10 mm, two-waves mode can be observed in most of the tests. And the lean limit rises as the insertion length increases from 15 mm to 20 mm. In this paper, all the two-waves modes are homo-rotating modes, which means that there are two waves propagating along the same direction. And the frequencies of two-waves mode acquired in this paper are between 8.01 kHz and 8.58 kHz. When the insertion length increases from 10 mm to 15 mm, the primary propagation mode transforms from single-wave mode to twowaves mode and the operation range enlarges unusually. This is a new phenomenon that few publication has mentioned. The mechanism behind mode transition is supposed to be related with flow characteristics
Fig. 5. Effects of pintle diameter (H = 0 mm) on operation range and propagation frequency. 314
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Fig. 6. Effects of pintle insertion length (D = 90 mm) on operation range and propagation frequency.
Fig. 7. Schematic of the recirculation zones.
labeled in Fig. 8(b). The average frequency can be calculated by Eq. (1), and N is the number of calculation periods. With the diameter of combustion chamber (Dc ), the propagation velocity of CRD waves can be acquired by Eq. (2). The average frequency and propagation velocity of Test #1 are 5.53 kHz and 1737.30 m/s, respectively. Propagation frequency-time distribution and Fast Fourier Transformation (FFT) frequency distribution of Test#1 are shown in Fig. 9. A quite concentrated frequency distribution can be seen in Fig. 9(a) and the RSD of frequency is 5.98%. It means that the CRD waves of single-wave mode are quite stable. The results of FFT frequency distribution is shown as Fig. 9(b). It can be summarized that the dominant frequency of Test#1 shows good agreements with its average frequency. With constant pressure of 1 atm and temperature of 300 K, corresponding C-J velocity (ER = 1.05) is computed as 1836.50 m/s. So it can be verified that the number of CRD waves is 1 and its average propagation velocity is about 94.6% of the C-J value.
3.2. Propagation mode As mentioned above, three propagation modes are acquired in this research. In order to study their characteristics further, detailed analysis will be conducted in this section. The operation conditions of three typical tests are listed in Table 2. In order to describe the propagation stability, relative standard deviations (RSD) of frequency are calculated. For single-wave mode and two-waves mode, RSD of frequency is within 10%. And for sawtooth-wave mode, the value is within 25%.
3.2.1. Single-wave mode The original and local view of high-frequency pressure results of single-wave mode are shown in Fig. 8. In Fig. 8(b), Δt2 is about three times of Δt1, and PCB 1, 2 are installed at same axial location with a circumferential angle of 90°. So it can be inferred that there is a single detonation wave propagates as ‘a1-b1-a2-b2’ with a notable pressure rise of 1.5 MPa. The instantaneous frequency can be acquired by fi = 1/ ΔTi , where ΔTi is time interval of two contiguous peaks of same signal, as
f =
ΣiN= 1 fi (1)
N
Table 2 The typical experiment conditions. Test No.
Propagation mode
Pintle diameter(mm)
Insertion length (mm)
Mass flow of air (g/s)
ER
Frequency (kHz)
RSD of frequency (%)
#1 #2 #3
Single wave Two waves Sawtooth wave
90 90 50
0 15 0
497.71 ± 5 503.32 ± 5 502.29 ± 5
1.05 ± 0.02 1.02 ± 0.02 1.05 ± 0.02
5.53 8.58 4.21
5.98 8.01 21.92
315
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Fig. 8. High-frequency pressure results of single-wave mode (Test#1).
v = f πDc
Eqs. (3)–(5) are introduced to confirm the number of CRD waves.
(2)
3.2.2. Two-waves mode The original and local view of high-frequency pressure results of two-waves mode are shown in Fig. 10. In Fig. 10(b), the peak pressure is below 0.6 MPa, which is apparently lower than that of single-wave mode (about 1.5 MPa). This implies that CRD wave intensity of twowaves mode is weaker. Besides, It can be seen that time interval of two contiguous peaks of same signal ( ΔTi ) is much smaller than that of single-wave mode. With same method, the average frequency and propagation velocity can be calculated with Eqs. (1) and (2). The results are 8.58 kHz and 2695.49 m/s, respectively. Propagation frequencytime distribution and FFT frequency distribution of Test#2 are shown in Fig. 11. It can be seen in Fig. 11(a) that the distribution of instantaneous frequency of two-waves mode is a little more scattered and the RSD of average frequency is 8.01%. In Fig. 11(b), results of FFT dominant frequency is 8.56 kHz and it shows good agreements with average frequency as well. So it can be concluded that although the intensities are weaker, CRD waves of two-waves mode are still regular and stable. The corresponding C-J velocity (initial state P = 1 atm, T = 300 K, ER = 1.02) is calculated as 1829.05 m/s. The experimental velocity is much bigger than theoretical C-J value. So it can be inferred that there is more than one wave propagating in the chamber. For further study,
ta11a12 =
πDc 1 ⋅ v n
(3)
ta11b11 =
πDc θ ⋅ v 2π
(4)
n=
2π ta11b11 ⋅ θ ta11a12
(5)
where n is the number of CRD waves, θ is circumferential angle between PCB 1 and PCB 2 (π/2 in this research). The value of t a11b11/t a11a12 is about 1/2, so the number of CRD waves is calculated to be 2. As a result, the propagation velocity should be cut in half to 1347.74 m/s, which accounts for 73.69% of theoretical C-J velocity. 3.2.3. Sawtooth-wave mode In Fig. 12(a), it can be seen that the waveforms are very complicated since sawtooth-wave mode is itself an unstable mode. The average frequency calculated is 4.21 kHz, which is obviously lower than that of single-wave mode. Besides, there are no notable pressure peaks in this mode, while only some pressure fluctuations can be captured. The distribution of instantaneous frequency is shown in Fig. 12(b), and the RSD of average frequency is 21.92%. The propagation velocity of Test#3 is 1322.61 m/s. With constant pressure of 1 atm and temperature of 300 K, corresponding C-J velocity (ER = 1.05) is computed as
Fig. 9. Propagation frequency of single-wave mode (Test#1). 316
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Fig. 10. High-frequency pressure results of two-waves mode (Test#2).
In this model, i, j, k mean the orders of tangential (T), radial (R) and axial (A), respectively. a 0 is local sound velocity in the chamber and αij is the value of Bessel Function. R c and Lc are radius and characteristic length of the combustion chamber, respectively. Lch is the length of cylinder section of the chamber and Lcv is the length of contraction section of Laval nozzle. As shown in Fig. 4, there are 7 piezo-resistance sensors installed along axial direction to capture time-averaged pressures of combustion chamber and their measurement errors are 0.01 MPa. The pressure distributions along the chamber of some typical tests with the ER in the range of 0.98–1.02 are shown in Fig. 13. It can be seen that for different propagation modes, the pressures show clear distinctions. The pressures of single-wave mode are the highest, followed by the two-waves mode, and the pressures of sawtooth-wave mode are the lowest. For all the tests, the combustor pressure decreases firstly and then increases along the axial direction. It can be seen that P4 is always the minimum pressure in the chamber for different propagation modes (or pintle configurations). In this research, the minimum chamber pressure varies in the range of 0.20 MPa–0.40 MPa. Based on the LRE thermodynamic theory, the corresponding constant-pressure combustion temperature can be calculated with combustor pressure and ER. The calculated temperature distribution under different ER and combustor pressure conditions are shown in Fig. 14. It can be seen that ER has a significant impact on the combustor temperature while chamber pressure has little impact on it. For ER = 1.0 with the combustor pressure ranging from 0.20 MPa to 0.40 MPa, the
1836.50 m/s. The average velocity accounts for 72.02% of C-J velocity. According to typical ZND theory, a detonation wave is composed of an inducing shock wave and following combustion flame. To ensure the coupling of them, the inducing shock wave should be strong enough. The inducing shock wave of sawtooth-wave mode is weak, so the coupling may be unstable, which finally leads to an unstable detonation wave. As mentioned above, sawtooth-wave mode is a critical mode between failure and detonation. And it has been observed that this critical mode can transform into detonation or deflagration with advantageous or disadvantageous factors [21]. 3.3. Comparing with intrinsic frequencies of the chamber In the study of LRE, intrinsic frequencies of the chamber have been verified to be closely related to combustion instability. To investigate the similarities between CRD and HFTI, the frequencies of CRD waves can be compared with the intrinsic acoustic frequency of the hollow chamber. Based on the former research [19], a modified model has been adopted to calculate intrinsic frequencies of the test combustion chamber. The model can be described as Eqs. (6) and (7).
fiT , jR, kA =
2 2 a 0 ⎛ αij ⎞ k +⎛ ⎞ 2 ⎝ Rc ⎠ ⎝ Lc ⎠
Lc = Lch +
⎜
2 Lcv 3
⎟
⎜
⎟
(6) (7)
Fig. 11. Propagation frequency of two-waves mode (Test#2). 317
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Fig. 12. Pressure and average frequency distribution of sawtooth-wave mode (Test#3).
temperature ranges from 2283.48 K to 2299.49 K. It means that in this research, the pressure measured has a minor effect on the temperature. With corresponding minimum pressures and ER, average temperature and sound velocity in the chamber can be acquired by conducting thermodynamic calculation [19]. The variation of average temperature and sound velocity in the chamber with different pintle configurations are given in Fig. 15 and Fig. 16. In Fig. 15(a), it can be seen that temperature is mainly determined by ER while pintle diameter has little impact on it. Similarly, in Fig. 15(b), pintle insertion length also has little impact on temperature. In Fig. 16, similar conclusion can be drawn when discussing their influence on sound velocity. Based on Figs. 15 and 16, it can be concluded that pintle configuration has little impact on temperature and sound velocity. This is consistent with thermodynamic rules. To simplify the calculation process, sound velocities in the chamber with pintle configuration of D90-H0 are adopted as a 0 to calculate the intrinsic frequencies. And the tangential order (i) is always believed to be consistent with the number of waves in the chamber [19]. So tangential order for the single-wave mode and sawtooth-wave mode is 1, and for two-waves mode the value is 2. With above methods, the intrinsic frequencies for the test chamber are calculated and compared with the experimental frequencies of CRD waves. As shown in Fig. 17(a), frequencies of single-wave mode (D90H0 and D80-H0) are consistent with intrinsic frequency of first tangential (1T) mode. And for two-waves mode (D90-H15 and D90-H20), their frequencies are also close to the intrinsic frequency of second tangential (2T) mode. As illustrated in Fig. 17(b), relative deviations of single-wave mode and two-waves mode are within 6%. But for sawtooth-wave mode, their frequencies differ greatly from intrinsic frequency, and the relative deviations are about 20%, as shown in Fig. 17(b).
Fig. 13. Pressure distribution along the chamber.
4. Conclusion Series of ethylene-air continuous rotating detonation experiments have been conducted in the hollow chamber with different pintle injectors. The mass flow rate of air is kept in the range of 490–510 g/s, with equivalent ratio of 0.70–1.20. The effects of pintle diameter and insertion length are discussed and three propagation modes are detailed in the present paper. To investigate the relationships between continuous rotating detonation and high-frequency tangential instability, intrinsic frequencies of combustion chamber are calculated and compared with experimental results. Main conclusions can be summarized as follows:
Fig. 14. Theoretical temperature distribution.
(1) Ethylene-air continuous rotating detonation has been realized in 318
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Fig. 15. Variation of temperature with ER.
Fig. 16. Variation of sound velocity with ER.
Fig. 17. Comparison of CRD waves propagation frequency and intrinsic frequency.
due to the propellant deficiency around the outer chamber. (2) The realization of continuous rotating detonation gets harder in the increase of the pintle insertion length. However, when the insertion length increases from 10 mm to 15 mm, the operation range enlarges unusually. The primary propagation mode transforms from
this paper with designed pintle injectors. The operation range shrinks as the pintle diameter decreases. When diameter is reduced to a certain level, more propellants are entrained to the center of hollow chamber and less propellants arrive the outer chamber. In this situation, continuous rotating detonation cannot be achieved 319
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single-wave mode to two-waves mode during this process. In consideration of flow characteristics of pintle injector, the deflagration in head recirculation zone is believed to promote this mode transition. (3) Three propagation modes have been discussed in this work. Detonation waves of single-wave mode have been realized with notable pressure rise and little velocity deficit. With pintle configuration of D80-H0, the highest frequency and propagation velocity are 5.62 kHz and 1765.58 m/s, respectively. Two-waves mode is acquired with weaker intensity and larger velocity deficit. Sawtooth-wave mode is a critical mode between failure and detonation. (4) Based on the measured combustor pressure and liquid rocket engine thermodynamic theory, intrinsic frequencies of the hollow chamber have been calculated and compared with experimental frequencies of rotating detonation waves. The frequencies of single-wave mode and two-waves mode show good agreements with the first tangential mode and second tangential mode results, respectively. The relative deviations are within 6%. It can be inferred that continuous rotating detonation may be one cause of the high-frequency tangential instability in rocket engines. (5) Significant error can be found between the frequencies of sawtoothwave mode and theoretical intrinsic frequencies of hollow chamber. When pintle diameter gets smaller, primary combustion mode transforms from single-wave mode to sawtooth-wave mode, and the combustion instability can be suppressed.
[8]
[9] [10]
[11]
[12]
[13]
[14]
[15]
[16] [17]
[18] [19]
[20]
More detailed observation of continuous rotating detonation wave structure and propagation mode transition is still insufficient and it remains to be further studied by means of optical observation and numerical investigation in the future.
[21]
[22]
Acknowledgement [23]
This work was supported by the National Natural Science Foundation of China (Nos.51776220, and Nos.91541103).
[24]
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