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air continuous rotating detonation wave in a hollow chamber
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Effects of the pintle injector on H2/air continuous rotating detonation wave in a hollow chamber Siyuan Huang, Yangpeng Li, Jin Zhou*, Shijie Liu, Haoyang Peng Science and Technology on Scramjet Laboratory, National University of Defense Technology, Changsha, 410073, China
article info
abstract
Article history:
Series of experiments have been conducted in a hollow chamber with pintle injector to
Received 31 January 2019
investigate the relationship between continuous rotating detonation (CRD) and tangential
Received in revised form
instability. The results show that the insertion length of pintle has great influence on the
28 March 2019
operation range of CRD. When it exceeds 10 mm, the CRD will be unrealizable. The influ-
Accepted 1 April 2019
ence of pintle diameter is finite. The deflagration in head recirculation zone and mixing
Available online 25 April 2019
delay lead to a poor quality of detonation waves. Three different propagation modes are presented. Most of the successful CRD in this work are single-wave mode. The highest
Keywords:
frequency and velocity are 6.55 kHz and 2010.40 m/s, respectively. Two dominant peak
Rotating detonation
one-wave mode (TDPO) has been observed and it is a fairly new one which has not been
Tangential combustion instability
sufficiently studied. Sawtooth-wave mode is a critical mode which always shows around
Hollow chamber
the lean limit. The intrinsic frequency of the combustion chamber has been calculated and
Pintle injector
compared with the experiment results. It shows great agreement with the frequencies of
Intrinsic frequency
TDPO with the error less than 5%. This work shows the effects of the pintle injector on H2/air CRD wave in a hollow chamber. And it will contribute to a better understanding of the relationship between CRD and tangential instability. © 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
Introduction Due to its advantages of high specific impulse, long operation duration and capability of repeated ignitions, liquid rocket engine (LRE) has become the main propulsion system for spaceflight. In the development of LRE programs, combustion instabilities are vital and inevitable. According to the frequency and acoustic characteristic, combustion instabilities in LRE can be classified mainly into three typical modes [1]: low frequency (or chugging instability), intermediate frequency (or buzzing instability) and high frequency (or acoustic instability). Of all these combustion instabilities, high
frequency instabilities do most severe damage to the engines and they have attracted a lot of attention in recent years [2e4]. And due to its fierce destruction and uncertainty, high frequency tangential instability (HFTI) has been regarded as the most challenging issue [2e5]. Based on the current researches [6,7], HFTI has been attributed to a variety of factors. A combustion-acoustic coupling in the form of an acoustic wave, “detonation-like” wave, velocity fluctuations and liquid stream shattering are some of the proposed theories. As for the prevention of HFTI, existing methods include designing acoustic cavity, installing baffle and adapting the size of combustion chamber [5]. However, according to the test records of TRW, LRE with pintle injector has never appeared
* Corresponding author. E-mail address: [email protected] (J. Zhou). https://doi.org/10.1016/j.ijhydene.2019.04.011 0360-3199/© 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 4 ( 2 0 1 9 ) 1 4 0 4 4 e1 4 0 5 4
HFTI [8]. Extensive pintle injector experiments conducted by TRW have proved that it has inherent stability to prevent HFTI [8]. Compared with other proposed inducing mechanisms of HFTI, “detonation-like” wave has been well studied because the HFTI has extensive similarities to the real CRD wave [9]. Several researchers [10e12] studying rocket engines (both liquid propellant engines and solid motors) have observed “detonation-like” waves spinning around the combustion chamber at thousands of Hertz. And these waves are similar to CRD waves in terms of wave velocity and pressure. However, it is to be emphasized that the detailed relationship between CRD wave and HFTI is still unclear. Rotating detonation is a supersonic combustion mode which can be used to design CRD engine. A shock wave coupled with flame and an oblique wave are typical characteristics of detonation wave. There is one or more detonation waves propagating circumferentially at the head of combustion chamber. In the 1950s, Voitsckhovskii [13] observed rotating detonation firstly in a disk-shaped experimental rig. After that, CRD attracted considerable attention due to its higher thermodynamic efficiency and faster heat release rate. Nicholls et al. [14] and Ar'kov [15] conducted their researches respectively and both of them found the similarities between rotating detonation and tangential combustion instability in LRE. However, due to the restrictions of experiment condition, the relative investigations had not been conducted continuously. Until 21st century, along with the explorations of new propulsion system, researches on CRD came back into the spotlight. In recent years, a number of researches [4,9], [16e22] are focused on the CRD in a hollow chamber. And the relationship between CRD and HFTI has attracted much attention once again. William et al. [16,17]experimentally validate the expanded design of hollow CRD engines. They realized detonation in the chamber without inner cylinder. Lin et al. [18] realized CH4/O2 continuous rotating detonation in a hollow chamber. They found that higher flow rates usually gave rise to simultaneous existence of multiple detonation waves. Rankin et al. [19] confirmed the feasibility of CRD in a hollow chamber with converging-diverging nozzle downstream. Peng et al. [20] conducted researches on ethylene-air CRD wave in a hollow chamber with Laval nozzle. Three different propagation modes were observed and the results showed that the lean limit increased while operating domain decreased with the contraction ratio increasing. Tang et al. [21] carried out numerous studies on H2/Air detonation in a hollow chamber. The results showed that the shock wave reflection from detonation wave propagation would reduce obviously without the inner wall. Zhang et al. [9] analyzed the similarities between CRD and HFTI by conducting investigations on H2/Air detonation in a hollow chamber. They got three propagation modes and compared the experimental frequencies with intrinsic frequency of the combustion chamber. Anand V et al. [4,22], realized CRD in a hollow chamber with hydrogen-air mixtures and ethylene-air mixtures, respectively. They found two mechanisms to cause rotating detonations in a hollow combustor. And they also tried to explain the“detonation-like” behavior in HFTI. All these works have shown the possibility of realizing CRD in the hollow chamber, and this makes contributions to explaining the HFTI in LRE. However,
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the injection methods of all these CRD engines are quite different from that of LRE. Actually, there are plenty of differences between the LRE and CRD engine in combustion chamber [23e26], injection method [27e31] and ignition [32,33]. In this work, we focused on the distinction of injection method. For typical injection of CRD engine, propellants are injected via a slit-orifice collision pattern [20]. The oxidizer and fuel are injected through a convergent-divergent slit and multiple orifices, respectively. Then they collide at the entrance of the chamber and get mixed completely near the outer wall. For the LRE, there are several optional injection methods [34]. Among them, pintle injector has the advantages of simple structure, wide range of flux adjustment, high combustion efficiency. The successful applications in Apollo Moon-landing Project [35] and Falcon 9 of Space X have proved that the pintle injector is a kind of mature and widely used technology. And as mentioned above, HFTI has never appeared in LRE with pintle injector [8]. Diameter and the insertion depth are two dominant elements of pintle injector, and they are also the main distinctions between it and typical injection of CRD engine. The effects of these two elements on CRD engine will be discussed respectively in the present paper. Since the CRD and HFTI share a lot of similarities and HFTI has never appeared in LRE with pintle injector. So whether the pintle injector can suppress CRD wave is valuable and interesting to verify. From the former researches, the experiment of CRD engines with a hollow chamber contributes to the understanding of HFTI, and HFTI can be suppressed by pintle injector, but the effects of pintle injector on CRD wave is still unclear. In this paper, series of experiments have been conducted in a hollow chamber with gaseous H2/Air mixture to realize detonation. The propellants are injected into the combustion chamber through different configurations of pintle injectors to investigate their effects on CRD wave. The operation range, propagation mode and dominant frequency of the pressure oscillation are analyzed. The results are expected to make a contribution to a better understanding of detonation theory and the relationship between CRD and HFTI.
Experiment system and measurement methodology The experiment system is composed of a combustion chamber, a gas supply system and a measure and control system. The sketch of combustion chamber and Laval nozzle are shown in Fig. 1. The diameter and length of the combustion chamber are 100 mm and 130 mm, respectively. A Laval nozzle is connected to the chamber, with a contraction ratio of 4. The contraction ratio is defined as ε ¼ Ai =At , where Ai is the area of the inlet of the Laval nozzle and At is the area of nozzle throat. The design of pintle injector has been adopted in this work. There are 4 pintle injectors with the radius (R1) of 45 mm, 40 mm, 35 mm and 25 mm, respectively. The pintle injector can be inserted into the combustion chamber with 5 depths (H), which are 0 mm, 5 mm, 10 mm, 15 mm and 20 mm. In this case, the injection of propellants can be neither near the outer wall nor at the entrance of the chamber any longer. More precisely, the propellants can be injected to several positions through this gas pintle injector, which is quite different from the typical injection method of CRD engine. For the specific
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Fig. 1 e The sketch of the combustion chamber and Laval nozzle.
injection, H2 and air are injected in the form of slit-orifice collision. The air is injected through a convergent-divergent slit with a throat width of 0.7 mm. The gaseous hydrogen is injected through 90 orifices distributed uniformly at the head of the pintle injector. The experiments are conducted at normal pressure, and the average temperatures of all the propellants are normal temperature. A non-premixed supply scheme is adopted in the experiment. The standard sonic nozzles are installed in the feeding lines to guarantee the accuracy of the propellant supply. The experiment uses a turbine flow meter to measure the mass flows of propellant. The average pressures in the injection manifolds and combustion chamber are captured by piezo-resistance sensors. And for high-frequency pressure of detonation wave, piezoelectric sensors (PCB113B24) are applied with a sample frequency of 2 MHz. The distribution of these pressure sensors on the chamber wall is shown in Fig. 2. As shown in the figure, P1eP7 are piezo-resistance sensors installed along axial direction to capture the average pressures of the combustion chamber. PCB1 and PCB5 are installed at the same axial location and their circumferential angle is 90 . Same distribution goes for PCB3 and PCB6. The experimental test time sequence is shown in Fig. 3. The green arrow means valve on and the red one means off. A hot tube tangent to the combustion chamber is used to
realize detonation initiation in the experiment and its sketch is shown in Fig. 4. The hot tube filled with hydrogen/oxygen can provide hot jet once ignited by a spark.
Results and analysis Series of experiments have been conducted by changing the pintle configuration and ER. The pintle configuration changes with different diameters and insertion lengths. The mass flow rate of air is kept at about 300 g/s, then the range of ER can be obtained by different mass flow rate of hydrogen. In consideration of safety, the maximum ER is limited to 1.1. Based on the results, the operation range with different pintle configurations has been summarized and three different CRD propagation modes have been introduced. The intrinsic frequency of combustion chamber is calculated and compared with the propagation frequency of CRD waves. Based on the results, the relationship between CRD and HFTI has been investigated.
Operation range Fig. 5(a) shows the experiment results with different insertion lengths of the pintle injector (90 mm in diameter). It can be seen that there are 4 operation modes named failure, sawtooth-wave mode, single-wave mode and two dominant
Fig. 2 e Installation and distribution of the transducers.
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Fig. 3 e Time sequence of the experiment.
Fig. 4 e The sketch of hot tube.
peak one-wave mode (TDPO). Failure means that the rotating detonation cannot be realized. Sawtooth-wave mode is a critical mode which can be obtained near the lean limit. Most of the successful detonations are single-wave mode, which is a typical propagation mode of CRD wave. And for TDPO, It has some similarities in wave velocity and pressure when compared with single-wave mode. But there are two dominant peaks which make it differ from the single-wave mode [3]. It is clear that the CRD realization gets harder as the insertion length grows. When the insertion length exceeds
10 mm, the CRD will not be realizable with any ER in the experiment. And when the insertion length is 10 mm, the CRD can be realized only with ER no less than 0.78. Sawtooth-wave mode is obtained with ER around 0.6 (0.54, 0.58 and 0.68). When the insertion length is less than 10 mm, CRD can be realized with most ER in the experiment. Based on the results shown in Fig. 5(a) it can be concluded that as the pintle insertion length getting deeper, the realization of CRD getting harder. Especially when it exceeds a certain value (10 mm in the experiment), the CRD will no longer be realizable. According to the numerical study on the pintle injector [36], there are always two recirculation zones in the combustion chamber, and deflagration combustion can always be found in these areas. As shown in Fig. 6, these two recirculation zones can be named as head recirculation zone and central recirculation zone according to their positions. In head recirculation zone, deflagration combustion can maintain for a long time with entrained propellants. Due to the consumption in this area, less propellant can arrive the chamber wall and realize detonation. Increasing the insertion length will give rise to a larger head recirculation zone, which will finally lead to a poor quality of detonation. In addition, a deeper injection position of hydrogen will decrease the mixing time before the fresh mixtures are ignited, leading to a bad mixing equality, which will also suppress the CRD realization.
Fig. 5 e Operation range of different pintle configurations.
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Fig. 6 e Schematic of the recirculation zones.
PCB6 are installed at the same axial location with a circumferential angle of 90 , it can be inferred that the CRD wave propagates clockwise from PCB3-0deg to PCB6-90deg. The PCB pressure signal rise repeats as ‘a1-b1-a2-b2’ with a notable pressure peak value of 0.8 MPa, which is consistent with the characteristics of CRD wave reported by many researchers [9], [37e39]. Although the pressure is low for detonation wave, the pressure fluctuations are always used to characterize detonation wave. With the calculation method adopted by Lin et al. [18], an instantaneous average frequency can be acquired byfi ¼ 1=Dti , and Dti is the time interval between two contiguous peaks of same signal. Counting N periods, the average frequency can be calculated by Eq. (1). With the diameter of combustion chamber D, the propagation velocity of CRD wave can be calculated by Eq. (2). The average frequency and propagation velocity of Test #1 are 6.55 kHz and 2010.40 m/s, respectively.
Fig. 5(b) shows the experiment results with different pintle injector diameters (0 mm in insertion length). There are also 4 operation modes as mentioned above. CRD can be realized with pintle injectors of all diameters in the tests. It can be seen that the operation range decreases slightly with the decrease of pintle diameter. For pintle injector with diameter of 90 mm, the lean limit is 0.4, but for pintle injector with diameter of 50 mm, this value is up to 0.56. So it is a little harder to realize CRD with pintle injector of a smaller diameter. For pintle injector with diameter of 70 mm and 80 mm, sawtooth wavemode is obtained around the lean limit. The decrease of pintle diameter will also lead to a larger head recirculation zone and suppress CRD sequentially. Different from the increase of insertion length, the increase of head recirculation zone is finite in this way, so the CRD still can be realized with pintle injectors of small diameter.
Propagation mode
PN f¼
As mentioned previously, three propagation modes, namely, single-wave mode, TDPO and sawtooth-wave mode, will be detailed in this section. For single-wave mode, it is one of the common and typical modes and its characteristics have been discussed a lot [3,9,18,20]. And in this section, the analyses will be mainly focused on the effects of different pintle configurations on CRD waves by comparing single-wave modes captured under different operation conditions. For the other two modes, their characteristics will be introduced in detail. Some typical experiments are chosen and their operation conditions are listed in Table 1.
i¼1 f i
(1)
N
v ¼ f pD
(2)
Fig. 8 shows the average frequency of all the single-wave modes in the experiments. In Fig. 8(a), the effects of insertion length and ER on frequency have been illustrated. Since the propagation modes with the insertion length of 0 mm are nearly all TDPO (except for ER ¼ 0.40), their frequencies will be discussed in next section. In this figure, it can be seen that with an increase of insertion length from 5 mm to 10 mm, the frequencies for ER 0.8e1.1 drop to a certain degree. The decrease of frequency may explain why the realization of CRD gets harder with a deeper insertion length. A larger recirculation zone contributes to the deflagration and lead to a decrease of CRD wave propagation frequency. Fig. 8(b) shows
Single-wave mode Fig. 7 shows the local view of high frequency pressure and propagation frequency distribution of Test #1. Since PCB3 and
Table 1 e The typical experiment conditions. Test No. #1 #2 #3 #4
Propagation mode
Diameter (mm)
Insertion length (mm)
Mass flow of air (g/s)
ER
Frequency (kHz)
Single wave Single wave TDPO Sawtooth wave
90 90 90 90
5 10 0 10
300.44 300.32 300.32 303.10
0.97 0.97 0.97 0.54
6.55 5.87 6.35 5.06
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Fig. 7 e Pressure of Single-wave mode(Test #1).
the effects of pintle diameter change and ER on propagation frequency. The propagation frequency decline with the decrease of pintle diameter for almost all single-wave modes. Test #2 is another typical single wave mode, and its local view of high-frequency pressures is shown in Fig. 9. With the 70 mm interval in axial direction, the signals of PCB1 and PCB4 show obvious differences. It can be seen that there is no dominant peak pressure for PCB1, while PCB4 has a clear peak pressure (about 0.6 MPa) for each cycle. The waveforms of PCB4 are just the same as normal single-wave modes. But for PCB1, its waveforms are more complicated and they do have some in common with sawtooth-wave mode which will be introduced later in this paper. It can be concluded that CRD wave intensity in head position of the combustion chamber is weaker than that of downstream. Since the insertion length is up to 10 mm under this experiment condition, and the axial distance between the PCB1 and chamber head is 20 mm, its signal may be influenced by the deflagration in the head
recirculation zone. In other words, this phenomenon may be a verification of the previous assumption about head recirculation zone.
Two dominant peak one-wave mode (TDPO) Fig. 10 shows the signals of high frequency pressure of Test #3. Fig. 10(a) is a local view of original voltage signals of PCB1, 3and 6. In this figure, the signal of PCB1 shows a typical characteristic of single-wave mode and its equivalent pressure rise is up to 2.0 MPa. But for PCB3 and PCB6, their signals of waveforms are obviously different from that of PCB1. To discuss them in detail, the magnified pressure results are shown in Fig. 10(b). The pressure signal rises repeat as ‘a11-b11a12-b12-a21-b21-a22-b22’. Combined with the signal of PCB1, it can be concluded that there are two peak pressures (a11 and a12) in one cycle (a11-a21) for PCB3 (or PCB6). This waveforms are quite different from typical single-wave mode and
Fig. 8 e Frequencies comparison of all the single-wave modes.
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configurations. This phenomenon is interesting, but the mechanism behind it is still unclear and further research is needed.
Sawtooth-wave mode
Fig. 9 e Pressure comparison of PCB1 and PCB4 (Test #2).
two-wave mode. Zhang et al. [3] observed this phenomenon in their experiments firstly and named it by ‘two dominant peak one-wave mode (TDPO)’. They concluded that the second wave was generated by the reflection of oblique shock waves on the Laval nozzle. Fig. 11(a) shows the frequency of Test #3. With the method mentioned above, the average propagation frequency and velocity of Test #3 can be calculated by Eq. (1) and Eq. (2). The results are 6.35 kHz and 1992.89 m/s and the referred C-J velocity is 1962.89 m/s (initial state P ¼ 1 atm, T ¼ 300 K, ER ¼ 0.97). The average velocity is a little larger than C-J velocity and analogous phenomenon has been observed and discussed by Zhang et al. [3] as well. It can be concluded that TDPO and single-wave mode share many similarities in propagation frequency and pressure characteristics. Fig. 11(b) shows the frequency comparison of 3 similar pintle configurations. The frequencies of TDPO are always lower than that of single-wave with similar pintle
Fig. 12 shows the local view of high frequency pressure and propagation frequency distribution of Test #4. In Fig. 12(a), it can be seen that this waveform shows significant differences with that of the typical single-wave mode, and this propagation mode has been named as sawtooth-wave mode [20]. It has a shorter duration and more complicated waveforms due to its instability. There is no notable pressure rise but still a fluctuation of pressure signals, so the frequency can be calculated by the same method as mentioned above. The instantaneous propagation frequencies are shown in Fig. 12(b), its average frequency is 5.06 kHz with a more discrete distribution. The average propagation velocity is 1427.79 m/s, which accounts for about 86.43% of corresponding C-J velocity (initial state P ¼ 1 atm, T ¼ 300 K, ER ¼ 0.54). In fact, the sawtooth-wave mode is more likely to be a critical mode between single-wave mode and deflagration. It has been observed that this mode can be transformed into deflagration or single-wave detonation with disadvantageous factors or advantageous factors [20]. According to typical ZND theory, the inducing shock wave should be strong enough to provide plenty of heat and pressure, so the combustion flame can be coupled with it to form a detonation wave. However, with a weak inducing shock wave, the coupling of inducing shock wave and flame may not be guaranteed. As a result, the sawtooth-wave mode appears as a transition form from detonation to deflagration.
Comparing with the intrinsic frequency The intrinsic acoustic frequency of combustion chamber is always related to the combustion instability. In this section, the frequencies of CRD waves are compared with intrinsic frequency to investigate the relationship between CRD and
Fig. 10 e Pressure of TDPO (Test #3).
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Fig. 11 e Frequencies of TDPO (Test #3).
HFTI. Zhang et al. [3] came up with a modified model to calculate the intrinsic frequency of test combustion chamber, which can be described as Eq. (3) and Eq. (4).
fiT;jR;kA
a0 ¼ 2
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 aij k þ Lc Rc
2 Lc ¼ Lch þ Lcv 3
(3)
(4)
In Eq. (3), i, j, k are the orders of the tangential, radial and axial, respectively. a0 is the sound velocity in combustion chamber and aij is the value of Bessel Function.Rc is the radius of combustion chamber andLc is the characteristic length of chamber which can be calculated by Eq. (4).Lch is the real length of chamber andLcv is the length of contraction section of Laval nozzle.
The average pressure of chamber are captured by piezoresistance sensors installed along axial direction. And the average temperature and sound velocity in combustion chamber can be acquired by thermodynamic calculation [3]. It can be seen that in Fig. 13, the temperature and sound velocities are mainly determined by ER while the pintle configuration has little influence on them. In order to simplify the calculation, sound velocities calculated with pintle configuration of 90e0 mm (diameter of 90 mm and insertion length of 0 mm) are adopted to all the frequency calculations. When there is only one wave in the combustion chamber, the corresponding tangential order (i) is usually 1. Fig. 14 shows the comparison between experimental frequencies and intrinsic frequencies with different pintle diameters. It can be seen that frequency of pintle diameter of 90 mm shows a great agreement with the first tangential
Fig. 12 e Pressure of Sawtooth-wave mode(Test #4).
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Fig. 13 e Variety of the temperature and sound velocity with ER.
mode (1T mode), and the error is within 5%. The propagation mode for this configuration is TDPO, which shares a lot of common characteristics with typical single-wave mode. With the decrease of pintle diameter, the frequencies of CRD waves deviate from the intrinsic frequency more or less. In LRE research field, there is one way to suppress the HFTI by changing chamber configuration to make combustion wave frequency differ from the intrinsic frequency. However, the variations of pintle diameter change the CRD wave's frequencies rather than intrinsic frequency. The decrease of pintle diameter changes the CRD wave's frequencies and make them differ from the intrinsic frequency as well. Since the “detonation-like” wave may be an explanation for HFTI when its frequency is close to the intrinsic frequency of combustion chamber. This variation of CRD wave's frequency may be a suppression for HFTI.
Fig. 14 e Comparison between experimental frequencies and intrinsic frequency.
Conclusion By keeping the mass flow rate of air at about 300 g/s, varying the ER, series of CRD experiments are conducted in the designed combustion chamber with different configurations of pintle injectors. The operation range is analyzed and three propagation modes are observed and discussed. The intrinsic frequency of combustion chamber is calculated and compared with the experiment results. The results are concluded as follows: (1) CRD has been realized in the hollow chamber with different configurations of pintle injectors. The realization of CRD gets harder as the insertion length grows deeper. The detonation cannot be realized when the insertion length goes beyond 10 mm. The decrease in pintle diameter also has some inhibiting effects on the realization of CRD, but the influence is fairly finite. The increase of insertion length and decrease of pintle diameter may lead to a larger recirculation zone and finally suppress the CRD. (2) Three propagation modes of CRD have been observed and detailed in this work. For typical single-wave mode, the highest propagation frequency and velocity in the experiment are 6.55 kHz and 2010.40 m/s, respectively. For TDPO, the frequency and velocity of it are found to be always lower than that of single wave with similar pintle configuration. Finally, for the sawtooth-wave mode, it is more likely to be a critical mode between single-wave mode and deflagration. It is unstable and always shows around lean limit. (3) The intrinsic frequency of the designed combustion chamber has been calculated. When compared with the experiment results, it shows great agreement with the frequencies of TDPO with the errors less than 5%. The injection method which lead to this propagation mode is also most similar to the typical injection method of CRD engine. This provides an evidence that CRD wave
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may be one of the inducing mechanisms of HFTI in LRE. The decrease of pintle diameter changes the CRD wave's frequencies and make them differ from the intrinsic frequency. This variation of CRD wave's frequency may be a suppression for HFTI. The realization of CRD in the hollow chamber with pintle injector is a new attempt of detonation engines. The results will enrich the detonation wave theory and give a better understanding of HFTI in LRE. However, the understanding of recirculation zone theory is quite preliminary and it remains to be further studied by means of numerical investigation in the future.
Acknowledgement This work was supported by the National Natural Science Foundation of China (Nos.51776220, and Nos.91541103).
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[14] Nicholls JA, Cullen RE, Ragland KW. Feasibility studies of a rotating detonation wave rocket motor. J Spacecr Rocket 1966;3(6):893e8. [15] Ar'kov OF, Voitsekhovskii BV, Mitrofanov VV. On the spinning-detonation-like properties of high frequency tangential oscillations in combustion chambers of liquid fuel rocket engines. ZhurnaI Prikl Mekhanikii Tekhnicheskoi Fiz 1970;11:155e7. [16] Stoddard William A, Andrew St George, Robert G, Vijay A, Ephraim JG. Experimental validation of expanded centerbodiless design. In: 54th AIAA aerospace sciences meeting. San Diego, California, USA: AIAA; 2016. p. 0128. https://doi.org/10.2514/6.2016-0128. 4-8 January 2016. [17] Stoddard W, Gutmark EJ. Numerical investigation of centerbodiless RDE design variations. In: 53rd AIAA aerospace sciences meeting; 2015. Kissimmee, FL, USA. [18] Lin W, Zhou J, Lin ZY, Liu SJ. An experimental study on CH4/O2 continuously rotating detonation wave in a hollow combustion chamber. Exp Therm Fluid Sci 2015;62:122e30. [19] Rankin BA, Hoke JL, Schauer FR. Periodic exhaust flow through a converging-diverging nozzle downstream of a rotating detonation engine. In: 52nd aerospace sciences meeting. Maryland: National Harbor; 2014. [20] Peng HY, Liu WD, Liu SJ, Zhang HL. Experimental investigations on ethylene-air Continuous Rotating Detonation wave in the hollow chamber with Laval nozzle. Acta Astronaut 2018;151:137e45. [21] Tang XM, Wang JP, Shao YT. Three-dimensional numerical investigations of the rotating detonation engine with a hollow combustor. Combust Flame 2015;162:997e1008. [22] Vijay Anand, Andrew St George, Ephraim Gutmark. Hollow rotating detonation combustor. In: 54th AIAA aerospace sciences meeting; 2016. San Diego, California, USA; 4-8 January, https://doi.org/10.2514/6.2016-0124. [23] Kailasanath K. Review of propulsion applications of detonation waves. AIAA J 2000;38(9):1698e708. [24] Bykovskii FA, Zhdan SA, Vedernikov EF. Continuous spin detonations. J Propuls Power 2006;22:1204e16. [25] Wolanski P. Detonative propulsion. Proc Combust Inst 2013;34:125e58. [26] Liu SJ, Lin ZY, Liu WD, Lin W, Zhuang FC. Experimental realization of H2/air continuous rotating detonation in a cylindrical combustor. Combust Sci Technol 2012;184(9):1302e17. [27] Lin W, Zhou J, Liu SJ, Lin ZY, Zhuang FC. Experimental study on propagation mode of H2/Air continuously rotating detonation wave. Int J Hydrogen Energy 2015;40(4):1980e93. [28] Anand V, St George A, Driscoll R, Gutmark E. Characterization of instabilities in a rotating detonation combustor. Int J Hydrogen Energy 2015;40:16649e59. [29] Robert D, Andrew SG, Ephraim JG. Numerical investigation of injection within an axisymmetric rotating detonation engine. Int J Hydrogen Energy 2016;41:2052e63. [30] Frolov SM, Dubrovskii AV, Ivanov VS. Three-dimensional numerical simulation of the operation of a rotating detonation chamber with separate supply of fuel and oxidizer. Russ J Phys Chem B 2013;7(1):35e43. [31] Wang C, Liu WD, Liu SJ, Jiang LX, Lin ZY. Experimental verification of air-breathing continuous rotating detonation fueled by hydrogen. Int J Hydrogen Energy 2015;40:9530e8. [32] Wang YH, Wang JP. Coexistence of detonation with deflagration in rotating detonation engines. Int J Hydrogen Energy 2016;41:4302e9. [33] Peng L, Wang D, Wu XS, Ma H, Yang CL. Ignition experiment with automotive spark on rotating detonation engine. Int J Hydrogen Energy 2015;40:8465e74.
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[34] Casiano MJ, Hulka JR, Yang V. Liquid-propellant rocket engine throttling: a comprehensive review. J Propuls Power 2010;26(5):897e923. [35] Gilroy R, Sackheim R. The lunar module descent engineea historical perspective. 25th AIAA Joint Propulsion Conference. Monterey; 1989. [36] Son Min, Radhakrishnan Kanmaniraja. Numerical study on the combustion characteristics of a fuel-centered pintle injector for methane rocket engines. Acta Astronaut 2017;135:139e49.
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Effects of the pintle injector on H2/air continuous rotating detonation wave in a hollow chamber Siyuan Huang, Yangpeng Li, Jin Zhou*, Shijie Liu, Haoyang Peng Science and Technology on Scramjet Laboratory, National University of Defense Technology, Changsha, 410073, China
article info
abstract
Article history:
Series of experiments have been conducted in a hollow chamber with pintle injector to
Received 31 January 2019
investigate the relationship between continuous rotating detonation (CRD) and tangential
Received in revised form
instability. The results show that the insertion length of pintle has great influence on the
28 March 2019
operation range of CRD. When it exceeds 10 mm, the CRD will be unrealizable. The influ-
Accepted 1 April 2019
ence of pintle diameter is finite. The deflagration in head recirculation zone and mixing
Available online 25 April 2019
delay lead to a poor quality of detonation waves. Three different propagation modes are presented. Most of the successful CRD in this work are single-wave mode. The highest
Keywords:
frequency and velocity are 6.55 kHz and 2010.40 m/s, respectively. Two dominant peak
Rotating detonation
one-wave mode (TDPO) has been observed and it is a fairly new one which has not been
Tangential combustion instability
sufficiently studied. Sawtooth-wave mode is a critical mode which always shows around
Hollow chamber
the lean limit. The intrinsic frequency of the combustion chamber has been calculated and
Pintle injector
compared with the experiment results. It shows great agreement with the frequencies of
Intrinsic frequency
TDPO with the error less than 5%. This work shows the effects of the pintle injector on H2/air CRD wave in a hollow chamber. And it will contribute to a better understanding of the relationship between CRD and tangential instability. © 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
Introduction Due to its advantages of high specific impulse, long operation duration and capability of repeated ignitions, liquid rocket engine (LRE) has become the main propulsion system for spaceflight. In the development of LRE programs, combustion instabilities are vital and inevitable. According to the frequency and acoustic characteristic, combustion instabilities in LRE can be classified mainly into three typical modes [1]: low frequency (or chugging instability), intermediate frequency (or buzzing instability) and high frequency (or acoustic instability). Of all these combustion instabilities, high
frequency instabilities do most severe damage to the engines and they have attracted a lot of attention in recent years [2e4]. And due to its fierce destruction and uncertainty, high frequency tangential instability (HFTI) has been regarded as the most challenging issue [2e5]. Based on the current researches [6,7], HFTI has been attributed to a variety of factors. A combustion-acoustic coupling in the form of an acoustic wave, “detonation-like” wave, velocity fluctuations and liquid stream shattering are some of the proposed theories. As for the prevention of HFTI, existing methods include designing acoustic cavity, installing baffle and adapting the size of combustion chamber [5]. However, according to the test records of TRW, LRE with pintle injector has never appeared
* Corresponding author. E-mail address: [email protected] (J. Zhou). https://doi.org/10.1016/j.ijhydene.2019.04.011 0360-3199/© 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
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HFTI [8]. Extensive pintle injector experiments conducted by TRW have proved that it has inherent stability to prevent HFTI [8]. Compared with other proposed inducing mechanisms of HFTI, “detonation-like” wave has been well studied because the HFTI has extensive similarities to the real CRD wave [9]. Several researchers [10e12] studying rocket engines (both liquid propellant engines and solid motors) have observed “detonation-like” waves spinning around the combustion chamber at thousands of Hertz. And these waves are similar to CRD waves in terms of wave velocity and pressure. However, it is to be emphasized that the detailed relationship between CRD wave and HFTI is still unclear. Rotating detonation is a supersonic combustion mode which can be used to design CRD engine. A shock wave coupled with flame and an oblique wave are typical characteristics of detonation wave. There is one or more detonation waves propagating circumferentially at the head of combustion chamber. In the 1950s, Voitsckhovskii [13] observed rotating detonation firstly in a disk-shaped experimental rig. After that, CRD attracted considerable attention due to its higher thermodynamic efficiency and faster heat release rate. Nicholls et al. [14] and Ar'kov [15] conducted their researches respectively and both of them found the similarities between rotating detonation and tangential combustion instability in LRE. However, due to the restrictions of experiment condition, the relative investigations had not been conducted continuously. Until 21st century, along with the explorations of new propulsion system, researches on CRD came back into the spotlight. In recent years, a number of researches [4,9], [16e22] are focused on the CRD in a hollow chamber. And the relationship between CRD and HFTI has attracted much attention once again. William et al. [16,17]experimentally validate the expanded design of hollow CRD engines. They realized detonation in the chamber without inner cylinder. Lin et al. [18] realized CH4/O2 continuous rotating detonation in a hollow chamber. They found that higher flow rates usually gave rise to simultaneous existence of multiple detonation waves. Rankin et al. [19] confirmed the feasibility of CRD in a hollow chamber with converging-diverging nozzle downstream. Peng et al. [20] conducted researches on ethylene-air CRD wave in a hollow chamber with Laval nozzle. Three different propagation modes were observed and the results showed that the lean limit increased while operating domain decreased with the contraction ratio increasing. Tang et al. [21] carried out numerous studies on H2/Air detonation in a hollow chamber. The results showed that the shock wave reflection from detonation wave propagation would reduce obviously without the inner wall. Zhang et al. [9] analyzed the similarities between CRD and HFTI by conducting investigations on H2/Air detonation in a hollow chamber. They got three propagation modes and compared the experimental frequencies with intrinsic frequency of the combustion chamber. Anand V et al. [4,22], realized CRD in a hollow chamber with hydrogen-air mixtures and ethylene-air mixtures, respectively. They found two mechanisms to cause rotating detonations in a hollow combustor. And they also tried to explain the“detonation-like” behavior in HFTI. All these works have shown the possibility of realizing CRD in the hollow chamber, and this makes contributions to explaining the HFTI in LRE. However,
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the injection methods of all these CRD engines are quite different from that of LRE. Actually, there are plenty of differences between the LRE and CRD engine in combustion chamber [23e26], injection method [27e31] and ignition [32,33]. In this work, we focused on the distinction of injection method. For typical injection of CRD engine, propellants are injected via a slit-orifice collision pattern [20]. The oxidizer and fuel are injected through a convergent-divergent slit and multiple orifices, respectively. Then they collide at the entrance of the chamber and get mixed completely near the outer wall. For the LRE, there are several optional injection methods [34]. Among them, pintle injector has the advantages of simple structure, wide range of flux adjustment, high combustion efficiency. The successful applications in Apollo Moon-landing Project [35] and Falcon 9 of Space X have proved that the pintle injector is a kind of mature and widely used technology. And as mentioned above, HFTI has never appeared in LRE with pintle injector [8]. Diameter and the insertion depth are two dominant elements of pintle injector, and they are also the main distinctions between it and typical injection of CRD engine. The effects of these two elements on CRD engine will be discussed respectively in the present paper. Since the CRD and HFTI share a lot of similarities and HFTI has never appeared in LRE with pintle injector. So whether the pintle injector can suppress CRD wave is valuable and interesting to verify. From the former researches, the experiment of CRD engines with a hollow chamber contributes to the understanding of HFTI, and HFTI can be suppressed by pintle injector, but the effects of pintle injector on CRD wave is still unclear. In this paper, series of experiments have been conducted in a hollow chamber with gaseous H2/Air mixture to realize detonation. The propellants are injected into the combustion chamber through different configurations of pintle injectors to investigate their effects on CRD wave. The operation range, propagation mode and dominant frequency of the pressure oscillation are analyzed. The results are expected to make a contribution to a better understanding of detonation theory and the relationship between CRD and HFTI.
Experiment system and measurement methodology The experiment system is composed of a combustion chamber, a gas supply system and a measure and control system. The sketch of combustion chamber and Laval nozzle are shown in Fig. 1. The diameter and length of the combustion chamber are 100 mm and 130 mm, respectively. A Laval nozzle is connected to the chamber, with a contraction ratio of 4. The contraction ratio is defined as ε ¼ Ai =At , where Ai is the area of the inlet of the Laval nozzle and At is the area of nozzle throat. The design of pintle injector has been adopted in this work. There are 4 pintle injectors with the radius (R1) of 45 mm, 40 mm, 35 mm and 25 mm, respectively. The pintle injector can be inserted into the combustion chamber with 5 depths (H), which are 0 mm, 5 mm, 10 mm, 15 mm and 20 mm. In this case, the injection of propellants can be neither near the outer wall nor at the entrance of the chamber any longer. More precisely, the propellants can be injected to several positions through this gas pintle injector, which is quite different from the typical injection method of CRD engine. For the specific
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Fig. 1 e The sketch of the combustion chamber and Laval nozzle.
injection, H2 and air are injected in the form of slit-orifice collision. The air is injected through a convergent-divergent slit with a throat width of 0.7 mm. The gaseous hydrogen is injected through 90 orifices distributed uniformly at the head of the pintle injector. The experiments are conducted at normal pressure, and the average temperatures of all the propellants are normal temperature. A non-premixed supply scheme is adopted in the experiment. The standard sonic nozzles are installed in the feeding lines to guarantee the accuracy of the propellant supply. The experiment uses a turbine flow meter to measure the mass flows of propellant. The average pressures in the injection manifolds and combustion chamber are captured by piezo-resistance sensors. And for high-frequency pressure of detonation wave, piezoelectric sensors (PCB113B24) are applied with a sample frequency of 2 MHz. The distribution of these pressure sensors on the chamber wall is shown in Fig. 2. As shown in the figure, P1eP7 are piezo-resistance sensors installed along axial direction to capture the average pressures of the combustion chamber. PCB1 and PCB5 are installed at the same axial location and their circumferential angle is 90 . Same distribution goes for PCB3 and PCB6. The experimental test time sequence is shown in Fig. 3. The green arrow means valve on and the red one means off. A hot tube tangent to the combustion chamber is used to
realize detonation initiation in the experiment and its sketch is shown in Fig. 4. The hot tube filled with hydrogen/oxygen can provide hot jet once ignited by a spark.
Results and analysis Series of experiments have been conducted by changing the pintle configuration and ER. The pintle configuration changes with different diameters and insertion lengths. The mass flow rate of air is kept at about 300 g/s, then the range of ER can be obtained by different mass flow rate of hydrogen. In consideration of safety, the maximum ER is limited to 1.1. Based on the results, the operation range with different pintle configurations has been summarized and three different CRD propagation modes have been introduced. The intrinsic frequency of combustion chamber is calculated and compared with the propagation frequency of CRD waves. Based on the results, the relationship between CRD and HFTI has been investigated.
Operation range Fig. 5(a) shows the experiment results with different insertion lengths of the pintle injector (90 mm in diameter). It can be seen that there are 4 operation modes named failure, sawtooth-wave mode, single-wave mode and two dominant
Fig. 2 e Installation and distribution of the transducers.
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Fig. 3 e Time sequence of the experiment.
Fig. 4 e The sketch of hot tube.
peak one-wave mode (TDPO). Failure means that the rotating detonation cannot be realized. Sawtooth-wave mode is a critical mode which can be obtained near the lean limit. Most of the successful detonations are single-wave mode, which is a typical propagation mode of CRD wave. And for TDPO, It has some similarities in wave velocity and pressure when compared with single-wave mode. But there are two dominant peaks which make it differ from the single-wave mode [3]. It is clear that the CRD realization gets harder as the insertion length grows. When the insertion length exceeds
10 mm, the CRD will not be realizable with any ER in the experiment. And when the insertion length is 10 mm, the CRD can be realized only with ER no less than 0.78. Sawtooth-wave mode is obtained with ER around 0.6 (0.54, 0.58 and 0.68). When the insertion length is less than 10 mm, CRD can be realized with most ER in the experiment. Based on the results shown in Fig. 5(a) it can be concluded that as the pintle insertion length getting deeper, the realization of CRD getting harder. Especially when it exceeds a certain value (10 mm in the experiment), the CRD will no longer be realizable. According to the numerical study on the pintle injector [36], there are always two recirculation zones in the combustion chamber, and deflagration combustion can always be found in these areas. As shown in Fig. 6, these two recirculation zones can be named as head recirculation zone and central recirculation zone according to their positions. In head recirculation zone, deflagration combustion can maintain for a long time with entrained propellants. Due to the consumption in this area, less propellant can arrive the chamber wall and realize detonation. Increasing the insertion length will give rise to a larger head recirculation zone, which will finally lead to a poor quality of detonation. In addition, a deeper injection position of hydrogen will decrease the mixing time before the fresh mixtures are ignited, leading to a bad mixing equality, which will also suppress the CRD realization.
Fig. 5 e Operation range of different pintle configurations.
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Fig. 6 e Schematic of the recirculation zones.
PCB6 are installed at the same axial location with a circumferential angle of 90 , it can be inferred that the CRD wave propagates clockwise from PCB3-0deg to PCB6-90deg. The PCB pressure signal rise repeats as ‘a1-b1-a2-b2’ with a notable pressure peak value of 0.8 MPa, which is consistent with the characteristics of CRD wave reported by many researchers [9], [37e39]. Although the pressure is low for detonation wave, the pressure fluctuations are always used to characterize detonation wave. With the calculation method adopted by Lin et al. [18], an instantaneous average frequency can be acquired byfi ¼ 1=Dti , and Dti is the time interval between two contiguous peaks of same signal. Counting N periods, the average frequency can be calculated by Eq. (1). With the diameter of combustion chamber D, the propagation velocity of CRD wave can be calculated by Eq. (2). The average frequency and propagation velocity of Test #1 are 6.55 kHz and 2010.40 m/s, respectively.
Fig. 5(b) shows the experiment results with different pintle injector diameters (0 mm in insertion length). There are also 4 operation modes as mentioned above. CRD can be realized with pintle injectors of all diameters in the tests. It can be seen that the operation range decreases slightly with the decrease of pintle diameter. For pintle injector with diameter of 90 mm, the lean limit is 0.4, but for pintle injector with diameter of 50 mm, this value is up to 0.56. So it is a little harder to realize CRD with pintle injector of a smaller diameter. For pintle injector with diameter of 70 mm and 80 mm, sawtooth wavemode is obtained around the lean limit. The decrease of pintle diameter will also lead to a larger head recirculation zone and suppress CRD sequentially. Different from the increase of insertion length, the increase of head recirculation zone is finite in this way, so the CRD still can be realized with pintle injectors of small diameter.
Propagation mode
PN f¼
As mentioned previously, three propagation modes, namely, single-wave mode, TDPO and sawtooth-wave mode, will be detailed in this section. For single-wave mode, it is one of the common and typical modes and its characteristics have been discussed a lot [3,9,18,20]. And in this section, the analyses will be mainly focused on the effects of different pintle configurations on CRD waves by comparing single-wave modes captured under different operation conditions. For the other two modes, their characteristics will be introduced in detail. Some typical experiments are chosen and their operation conditions are listed in Table 1.
i¼1 f i
(1)
N
v ¼ f pD
(2)
Fig. 8 shows the average frequency of all the single-wave modes in the experiments. In Fig. 8(a), the effects of insertion length and ER on frequency have been illustrated. Since the propagation modes with the insertion length of 0 mm are nearly all TDPO (except for ER ¼ 0.40), their frequencies will be discussed in next section. In this figure, it can be seen that with an increase of insertion length from 5 mm to 10 mm, the frequencies for ER 0.8e1.1 drop to a certain degree. The decrease of frequency may explain why the realization of CRD gets harder with a deeper insertion length. A larger recirculation zone contributes to the deflagration and lead to a decrease of CRD wave propagation frequency. Fig. 8(b) shows
Single-wave mode Fig. 7 shows the local view of high frequency pressure and propagation frequency distribution of Test #1. Since PCB3 and
Table 1 e The typical experiment conditions. Test No. #1 #2 #3 #4
Propagation mode
Diameter (mm)
Insertion length (mm)
Mass flow of air (g/s)
ER
Frequency (kHz)
Single wave Single wave TDPO Sawtooth wave
90 90 90 90
5 10 0 10
300.44 300.32 300.32 303.10
0.97 0.97 0.97 0.54
6.55 5.87 6.35 5.06
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Fig. 7 e Pressure of Single-wave mode(Test #1).
the effects of pintle diameter change and ER on propagation frequency. The propagation frequency decline with the decrease of pintle diameter for almost all single-wave modes. Test #2 is another typical single wave mode, and its local view of high-frequency pressures is shown in Fig. 9. With the 70 mm interval in axial direction, the signals of PCB1 and PCB4 show obvious differences. It can be seen that there is no dominant peak pressure for PCB1, while PCB4 has a clear peak pressure (about 0.6 MPa) for each cycle. The waveforms of PCB4 are just the same as normal single-wave modes. But for PCB1, its waveforms are more complicated and they do have some in common with sawtooth-wave mode which will be introduced later in this paper. It can be concluded that CRD wave intensity in head position of the combustion chamber is weaker than that of downstream. Since the insertion length is up to 10 mm under this experiment condition, and the axial distance between the PCB1 and chamber head is 20 mm, its signal may be influenced by the deflagration in the head
recirculation zone. In other words, this phenomenon may be a verification of the previous assumption about head recirculation zone.
Two dominant peak one-wave mode (TDPO) Fig. 10 shows the signals of high frequency pressure of Test #3. Fig. 10(a) is a local view of original voltage signals of PCB1, 3and 6. In this figure, the signal of PCB1 shows a typical characteristic of single-wave mode and its equivalent pressure rise is up to 2.0 MPa. But for PCB3 and PCB6, their signals of waveforms are obviously different from that of PCB1. To discuss them in detail, the magnified pressure results are shown in Fig. 10(b). The pressure signal rises repeat as ‘a11-b11a12-b12-a21-b21-a22-b22’. Combined with the signal of PCB1, it can be concluded that there are two peak pressures (a11 and a12) in one cycle (a11-a21) for PCB3 (or PCB6). This waveforms are quite different from typical single-wave mode and
Fig. 8 e Frequencies comparison of all the single-wave modes.
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configurations. This phenomenon is interesting, but the mechanism behind it is still unclear and further research is needed.
Sawtooth-wave mode
Fig. 9 e Pressure comparison of PCB1 and PCB4 (Test #2).
two-wave mode. Zhang et al. [3] observed this phenomenon in their experiments firstly and named it by ‘two dominant peak one-wave mode (TDPO)’. They concluded that the second wave was generated by the reflection of oblique shock waves on the Laval nozzle. Fig. 11(a) shows the frequency of Test #3. With the method mentioned above, the average propagation frequency and velocity of Test #3 can be calculated by Eq. (1) and Eq. (2). The results are 6.35 kHz and 1992.89 m/s and the referred C-J velocity is 1962.89 m/s (initial state P ¼ 1 atm, T ¼ 300 K, ER ¼ 0.97). The average velocity is a little larger than C-J velocity and analogous phenomenon has been observed and discussed by Zhang et al. [3] as well. It can be concluded that TDPO and single-wave mode share many similarities in propagation frequency and pressure characteristics. Fig. 11(b) shows the frequency comparison of 3 similar pintle configurations. The frequencies of TDPO are always lower than that of single-wave with similar pintle
Fig. 12 shows the local view of high frequency pressure and propagation frequency distribution of Test #4. In Fig. 12(a), it can be seen that this waveform shows significant differences with that of the typical single-wave mode, and this propagation mode has been named as sawtooth-wave mode [20]. It has a shorter duration and more complicated waveforms due to its instability. There is no notable pressure rise but still a fluctuation of pressure signals, so the frequency can be calculated by the same method as mentioned above. The instantaneous propagation frequencies are shown in Fig. 12(b), its average frequency is 5.06 kHz with a more discrete distribution. The average propagation velocity is 1427.79 m/s, which accounts for about 86.43% of corresponding C-J velocity (initial state P ¼ 1 atm, T ¼ 300 K, ER ¼ 0.54). In fact, the sawtooth-wave mode is more likely to be a critical mode between single-wave mode and deflagration. It has been observed that this mode can be transformed into deflagration or single-wave detonation with disadvantageous factors or advantageous factors [20]. According to typical ZND theory, the inducing shock wave should be strong enough to provide plenty of heat and pressure, so the combustion flame can be coupled with it to form a detonation wave. However, with a weak inducing shock wave, the coupling of inducing shock wave and flame may not be guaranteed. As a result, the sawtooth-wave mode appears as a transition form from detonation to deflagration.
Comparing with the intrinsic frequency The intrinsic acoustic frequency of combustion chamber is always related to the combustion instability. In this section, the frequencies of CRD waves are compared with intrinsic frequency to investigate the relationship between CRD and
Fig. 10 e Pressure of TDPO (Test #3).
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Fig. 11 e Frequencies of TDPO (Test #3).
HFTI. Zhang et al. [3] came up with a modified model to calculate the intrinsic frequency of test combustion chamber, which can be described as Eq. (3) and Eq. (4).
fiT;jR;kA
a0 ¼ 2
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 aij k þ Lc Rc
2 Lc ¼ Lch þ Lcv 3
(3)
(4)
In Eq. (3), i, j, k are the orders of the tangential, radial and axial, respectively. a0 is the sound velocity in combustion chamber and aij is the value of Bessel Function.Rc is the radius of combustion chamber andLc is the characteristic length of chamber which can be calculated by Eq. (4).Lch is the real length of chamber andLcv is the length of contraction section of Laval nozzle.
The average pressure of chamber are captured by piezoresistance sensors installed along axial direction. And the average temperature and sound velocity in combustion chamber can be acquired by thermodynamic calculation [3]. It can be seen that in Fig. 13, the temperature and sound velocities are mainly determined by ER while the pintle configuration has little influence on them. In order to simplify the calculation, sound velocities calculated with pintle configuration of 90e0 mm (diameter of 90 mm and insertion length of 0 mm) are adopted to all the frequency calculations. When there is only one wave in the combustion chamber, the corresponding tangential order (i) is usually 1. Fig. 14 shows the comparison between experimental frequencies and intrinsic frequencies with different pintle diameters. It can be seen that frequency of pintle diameter of 90 mm shows a great agreement with the first tangential
Fig. 12 e Pressure of Sawtooth-wave mode(Test #4).
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Fig. 13 e Variety of the temperature and sound velocity with ER.
mode (1T mode), and the error is within 5%. The propagation mode for this configuration is TDPO, which shares a lot of common characteristics with typical single-wave mode. With the decrease of pintle diameter, the frequencies of CRD waves deviate from the intrinsic frequency more or less. In LRE research field, there is one way to suppress the HFTI by changing chamber configuration to make combustion wave frequency differ from the intrinsic frequency. However, the variations of pintle diameter change the CRD wave's frequencies rather than intrinsic frequency. The decrease of pintle diameter changes the CRD wave's frequencies and make them differ from the intrinsic frequency as well. Since the “detonation-like” wave may be an explanation for HFTI when its frequency is close to the intrinsic frequency of combustion chamber. This variation of CRD wave's frequency may be a suppression for HFTI.
Fig. 14 e Comparison between experimental frequencies and intrinsic frequency.
Conclusion By keeping the mass flow rate of air at about 300 g/s, varying the ER, series of CRD experiments are conducted in the designed combustion chamber with different configurations of pintle injectors. The operation range is analyzed and three propagation modes are observed and discussed. The intrinsic frequency of combustion chamber is calculated and compared with the experiment results. The results are concluded as follows: (1) CRD has been realized in the hollow chamber with different configurations of pintle injectors. The realization of CRD gets harder as the insertion length grows deeper. The detonation cannot be realized when the insertion length goes beyond 10 mm. The decrease in pintle diameter also has some inhibiting effects on the realization of CRD, but the influence is fairly finite. The increase of insertion length and decrease of pintle diameter may lead to a larger recirculation zone and finally suppress the CRD. (2) Three propagation modes of CRD have been observed and detailed in this work. For typical single-wave mode, the highest propagation frequency and velocity in the experiment are 6.55 kHz and 2010.40 m/s, respectively. For TDPO, the frequency and velocity of it are found to be always lower than that of single wave with similar pintle configuration. Finally, for the sawtooth-wave mode, it is more likely to be a critical mode between single-wave mode and deflagration. It is unstable and always shows around lean limit. (3) The intrinsic frequency of the designed combustion chamber has been calculated. When compared with the experiment results, it shows great agreement with the frequencies of TDPO with the errors less than 5%. The injection method which lead to this propagation mode is also most similar to the typical injection method of CRD engine. This provides an evidence that CRD wave
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 4 4 ( 2 0 1 9 ) 1 4 0 4 4 e1 4 0 5 4
may be one of the inducing mechanisms of HFTI in LRE. The decrease of pintle diameter changes the CRD wave's frequencies and make them differ from the intrinsic frequency. This variation of CRD wave's frequency may be a suppression for HFTI. The realization of CRD in the hollow chamber with pintle injector is a new attempt of detonation engines. The results will enrich the detonation wave theory and give a better understanding of HFTI in LRE. However, the understanding of recirculation zone theory is quite preliminary and it remains to be further studied by means of numerical investigation in the future.
Acknowledgement This work was supported by the National Natural Science Foundation of China (Nos.51776220, and Nos.91541103).
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