Experimental study of perforated-wall rotating detonation combustors

Combustion and Flame 213 (2020) 52–62

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Experimental study of perforated-wall rotating detonation combustors Haocheng Wen, Bing Wang∗ School of Aerospace Engineering, Tsinghua University, Beijing 100084, China

a r t i c l e

i n f o

Article history: Received 7 August 2018 Revised 30 January 2019 Accepted 18 November 2019

Keywords: Rotating detonation Perforated wall Instability control Acoustic mode

a b s t r a c t Perforated walls are potentially applied in rotating detonation combustors (RDCs) to stabilize combustion and perform transpiration cooling. This study involves an experimental investigation on the rotating detonation in perforated-wall combustors for the first time. Five types of walls with different hole sizes and perforated area ratios that range from 0 to 3.5% are examined to analyze acoustics and combustion characteristics, and performance of the RDC. The stable and unstable rotating detonation are both observed in the experiments, and the unstable phenomena mainly correspond to the counter two-wave rotating detonation that co-exists with the acoustic modes of the combustor. The acoustic modes are effectively suppressed by the perforated wall with area ratios over 1.75%, and the stability of rotating detonation significantly improves. The perforated walls significantly weaken the measured detonation pressure peaks and mitigate the impact of rotating detonation on the H2 plenum, while they do not evidently reduce the specific impulse. It is proposed that the acoustic modes are excited by local high-pressure spots generated by the collision of two detonation waves, and they induce the fluctuating pressure peaks and wave velocity by affecting the H2 injection. The perforated holes dissipate high-pressure spots, and thereby suppress the acoustic modes. © 2019 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

1. Introduction Rotating detonation is expected to significantly improve the performance of propulsion systems, and thus it exhibits potential applications for aerospace propulsion systems, owing to its high thermodynamic and inherent pressure-gain property [1]. Over the past decade, various attempts were made to apply the rotating detonation in traditional engines, including rocket- [2–5], turbine[6,7] and ramjet- [8,9] type engines. Extant studies indicate that it is necessary to solve two important issues for the practical applications of rotating-detonation-based engines as follows: the stabilization of rotating detonation and the cooling of combustor. Generally, a stable rotating detonation with predictable and steady pressure peaks is always desirable. Intensive pressure fluctuations of unstable rotating detonation can lead to undesired effects on the combustor, propellant supply system, and the engine performance. Unfortunately, the unstable rotating detonation is observed to widely exist in experiments for both gaseous [4,10–12] and liquid [13,14] fuel. Unstable phenomena including mode switching [10] and counter two-wave rotating detonation [11] are observed. In order to improve the stability of rotating detonation, multiple approaches are tested and mainly include employing

∗

Corresponding author. E-mail address: [email protected] (B. Wang).

oxygen-enriched air [15], changing the combustor geometry [16– 18] and injection configuration [11,19,20] and heating the reactant [14]. The heat release of rotating detonation combustor (RDC) concentrates within a short zone of the head where the waves propagate, and thus, the combustor suffers a high local heat load. Bykovskii et al. [21] and Theuerkauf et al. [22] made early attempts to measure the heat flux in the RDC. It was determined that the maximum heat flux is located at the mixing region [21]. Without cooling, the duration of present experiments on rotating detonation is generally limited and especially for fuel/oxygen reactant even if a heat resistant material is adopted [23]. Although cooling is necessary for long-duration operation, there is a paucity of studies on it. The perforated wall (PW) is considered as a potential approach to solve the aforementioned problems and it is extensively used in the traditional combustors to control the combustion instability via damping acoustics [24] and to cool the wall exposed to hightemperature gas via transpiration. However, acoustically absorbing walls including perforated or porous walls are also validated to exhibit a detonation suppression effect [25]. Experiments conducted in the detonation tube [26] indicated that the detonation can attenuate and even quench when entering the section with a porous wall. The aforementioned facts indicated that the perforated wall can also exhibit a suppression effect on rotating detonation. However, this is not expected. Therefore, prior to applying a perfo-

https://doi.org/10.1016/j.combustflame.2019.11.028 0010-2180/© 2019 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

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Fig. 1. Schematic of (a) the rotating detonation combustor, (b) the configuration of instruments and (c) the experimental system.

rated wall to RDC, its effect on the behavior of rotating detonation should be first clarified and this is the focus of the present study. In this study, perforated walls with different geometric parameters are tested to explore their effects on the rotating detonation combustor. The effects on acoustic modes, the behavior of rotating detonation, plenums and specific impulse are analyzed. A physical mechanism is proposed to explain the unstable phenomena and effect of the perforated wall. The conclusions from the study provide guidance for the instability control of rotating detonation and the design for cooling.

Table 1 Geometric parameters of the combustor. Part

Parameter

Dimension

Combustor channel

Length Lch Outer diameter Dch Width Wch

70 mm 70 mm 5 mm

Injection configuration

Width of oxidizer slot Width of fuel holes Number of the fuel holes

0.4 mm 0.8 mm 80

2. Experimental methodology The experiments are conducted in an annular combustor as shown in Fig. 1(a). The geometric parameters of the combustor are listed in Table 1. The reactant employed in the study corresponds to H2 /air mixture, and the equivalence ratio is fixed as 1.0. The air is injected into the combustor from an annular slot while H2 is injected from 80 holes which are arranged in the circumferential direction and locate downstream the air injection slot. The mass flow rate m˙ is controlled by m˙ =kP, where P denotes the pressure of gas tanks and k denotes the flow coefficient of the calibrated needle valve installed at the exit of each gas tank. The mass flow rates are considered as constant during the operation because the decrease in pressure of the gas tanks during an operation is less than 5%. Figure 1(c) shows the schematic of the experimental system which

consists of four subsystems: (A) a propellant delivery system, (B) an adjustable ignition system, (C) the rotating detonation combustor, (D) a synchronous data acquisition and control system. As shown in Fig. 1(b), two high-frequency piezoelectric transducers (type: PCB-113B24) and an igniter are placed circumferentially on the same plane, which is 15 mm downstream from the air injection slot, to record the pressure histories of the combustor. An adjustable igniter is placed in the same plane, and its ignition energy is fixed at 1 J in the study. Two static pressure sensors (type: Omega-PX409) and another two PCBs (not shown in the figure) are mounted into plenums to measure the injection pressures and high-frequency oscillations in H2 /air plenums, respectively. Additionally, the combustor is placed on a slide rail and pushed against a load cell (type: PCB-208C03) to measure thrust.

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Fig. 2. Schematic of (a) the perforated wall and (b) two configurations of holes.

Table 2 Parameters of perforated walls (PWs). Scheme

Configuration

dPW (mm)

bPW (mm)

θ

SW PW1 PW2 PW3 PW4

Solid 1 2 1 2

– 1.0 1.5 1.5 1.5

– 5 10 5 5

– 14° 30° 15° 15°

Perforated Area Ratio 0 0.85% 0.88% 1.75% 3.50%

The time-dependent drift of PCB1/PCB2 is due to the high temperature in the combustor, and it is eliminated in the subsequent figures. The increase in static pressure in the H2 plenum after ignition is caused by the high back-pressure of rotating detonation waves. The thrust signals obtained in experiments are always oscillating. The high-frequency oscillation results from the non-axial component of the periodic exhaust. The low-frequency component is due to vibration of the testbed and decays with time although it cannot disappear completely in limited experiment duration. Therefore, in the study, the thrust for each run is defined as the mean thrust within 100 ms before H2 stops, and it is used to calculate the specific impulse. 3. Effect on the acoustics and combustion characteristic of RDC In this study, the air flow rate ranges from 100 g/s to 210 g/s and the equivalence ratio is fixed at 1.0. A set of experiments are performed at intervals of 5 g/s for air flow rate. 3.1. Occurrence and suppression of acoustic modes

Fig. 3. Raw signals and operation sequence, SW, m˙ air =165 g/s.

The maximum response frequency of PCB pressure sensors corresponds to 500 kHz and 1 kHz for static pressure sensors and 36 kHz for the load cell. The data acquisition device (type: NIUSB6366) records data at a sampling rate of 2 MHz. The outer wall of combustor consists of three layers (Fig. 1(a)). The outer layer is a solid wall. The inner layer can be replaced with the solid wall (SW) or different perforated walls (Fig. 2(a)). A 5mm wide annular gap exists between the inner and outer wall. Four types of perforated walls are tested in the experiments and two configurations of holes are adopted as shown in Fig. 2(b). The length of the perforated walls LPW is 55 mm, and the thickness tPW is 3 mm. The parameters of the perforated walls are listed in Table 2. The perforated area ratio is defined by the ratio of perforated area to the gross area of the wall. A comparison of Perforated Wall Scheme 1 (PW1)/PW2 shows the influence of hole sizes while the comparison of PW1/PW3/PW4 examines the influence of area ratios. Figure 3 shows the raw signals and the operation sequence in an experiment. The section from the ignition to H2 stop is adopted for analysis and its duration is approximately 200 ms for each run.

With respect to a stable rotating detonation, its pressure wave structures including the leading shock and oblique shock propagate in the same frequency. Additionally, the energy release is coupled with the leading shock, and thus other rotating pressure waves with a certain but different frequency should not exist at the head of combustor. While analyzing the FFT result of combustor pressure signals, only the base frequency of rotating detonation and its multiple frequencies are identified with the exception of the Helmholtz frequency of plenums [10]. This has been validated in the previous experimental studies [12,18]. Conversely, additional frequency peaks can be observed when unstable phenomena occur [10,12], and they are considered as the natural acoustic modes of the combustor which are excited by unstable rotating detonation in this study, and the details is discussed in Section 3.3. Figure 4(a) shows the combustor pressure histories obtained with the solid wall for a typical unstable case, in which the counter two-wave rotating detonation is observed. The two waves collide and generate fluctuating pressure peaks. As shown in Fig. 4(b), the FFT result of PCB1 exhibit a complex distribution of frequencies wherein frequencies corresponding to 4844 Hz and 9719 Hz denote the base frequency of rotating detonation (represented as 1D) and its double frequency (represented as 2D). The phase differences of PCB1/PCB2 for 1D and 2D are 89.7° and 174.5°, respectively. The ratio of the remaining three peak frequencies (i.e., 2209 Hz, 7026 Hz and 11,811 Hz) is 1:3.18:5.37, and the phase differences are 3.0°, 84.0°, and 174.9°, respectively. The ratio of the three peak frequencies for the unstable cases in experiments fluctuates slightly, and

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Fig. 4. Case of counter two-wave rotating detonation, SW, m˙ air =170 g/s: (a) pressure histories in the combustor; (b) FFT results of PCB1 and the phase difference of PCB1/PCB2. Table 3 Parameters of peak frequencies. Abbr.

Definition

Approximate Value (Hz)

1D 2D 1L 2 L/1T

Base frequency of rotating detonation Double frequency of 1D 1st longitudinal acoustic mode 2nd longitudinal–1st tangential hybrid acoustic mode 3rd longitudinal–2nd tangential hybrid acoustic mode

~ ~ ~ ~

3 L/2T

its range is 1: (3.1–3.2): (5.2–5.4). The combustor with solid wall adopted in the study can be approximately considered as a rectangular duct with a periodic boundary. The inlet boundary is considered as a rigid wall, and the outlet is open. If the flow field in the combustor is assumed as uniform, then the theoretical solution of the natural acoustic frequency based on acoustic theory [27] is as follows:

fn,m

c0 = 2π



(2n − 1)π 2Lch

2

+

 2mπ 2 π Dch

(1)

where c0 denotes the reference sound speed, and n and m denote the orders of the longitudinal and tangential modes. Based on Eq. (1), the theoretical ratio of the 1st longitudinal mode (1 L), 2nd longitudinal–1st tangential mode (2 L/1T), and 3rd longitudinal– 2nd tangential mode (3 L/2T) is 1:3.26:5.61. The theoretical phase differences of PCB1/PCB2 correspond to 0°, 90°, and 180°, and these are close to the values measured in the experiment (Fig. 4(b)). Assumed that 2197 Hz corresponds to the 1 L acoustic mode, the reference sound speed is solved as c0 = 615 m/s. The ChapmanJouguet (CJ) sound speed after the stoichiometric one-dimensional CJ detonation as calculated by CEA [28] is 1089 m/s with an initial temperature of 300 K and an initial pressure of 1 atm. The reference sound speed c0 is within a reasonable range, given that the actual mean sound speed in RDC should be less than 1089 m/s (which is the maximum sound speed in the combustor) and greater than the sound speed of the unburned region that is 408 m/s (which is the minimum sound speed in the combustor). Therefore, the three peak frequencies observed for an unstable rotating detonation are identified corresponding to the 1 L, 2 L/1T, and 3 L/2T acoustic modes of the combustor. Evidently, the 1 L mode plays a dominant role in the case due to its high amplitude. In addition, the small peak frequency in the vicinity of 1D (wherein

Theoretical Phase Difference of PCB1/PCB2

4900 9200 2300 7200

90° 180° 0° 90°

~ 11,800

180°

the frequency is 4433 Hz and the phase difference is 5.1°) is determined as the double frequency of 1 L. Table 3 list the parameters of all the peak frequencies identified in the experiments. Figure 5 shows the FFT distribution of PCB1 for SW as a function of air flow rate. Expect for the unsuccessful ignition as m˙ air >180 g/s, the acoustic modes of combustor are always observed when the flow rate ranges from 100 to 180 g/s, indicating that the rotating detonation is maintained as unstable. When the flow rate decreases, the amplitudes of the detonation base frequency 1D and 1 L acoustic mode reduce due to the decrease of reactant injection pressure, while the latter reduce more rapidly than the former. The amplitude of 1 L is approximately twice that of 1D at m˙ air = 180 g/s while their amplitudes become approximately equal at m˙ air = 100 g/s. The aforementioned features suggest that the acoustic modes of combustor weaken as the flow rate decrease. Additionally, the frequency of each peak frequency exhibits a slight increase with the decrease in the flow rate. The variation range of 1D is from 4737 to 4981 Hz, and that of 1 L is from 2200 to 2479 Hz. The increase of 1D frequency is possibly due to the increase in the detonation wave velocity caused by improvements in the stability, while increases of the acoustic frequencies are related to the enhanced average sound speed of the flow field in the combustor. When the solid wall is replaced with perforated walls, the frequency distribution of the pressure signals in the combustor changes. Figure 6 shows the FFT distribution for four perforated walls as a function of air flow rate. As shown in Fig. 6(a) and (b), the acoustic modes still exist when PW1 and PW2 are used. With respect to PW1, the amplitude of 1D does not significantly change and maintains approximately 12.5 kPa over the full range of flow rate. While the amplitude of 1D for PW2 exhibits the clear increasing trend when the flow rate increase for m˙ air >115 g/s. This indi-

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successively, and this shows the dampening effect of perforated walls on the rotating detonation. Based on the aforementioned facts, it is concluded that a larger perforated area ratio is more beneficial to suppress acoustic modes in the combustor although it also weakens the rotating detonation. The comparison of PW1 and PW2 illustrates that when the perforation area ratio is similar, the suppression effect is improved by enlarging the holes at high flow rates. However, the above conclusions are only the qualitative evaluation of the influence of geometric parameters on the suppression effect and the quantitative conclusions need further experiments. 3.2. Behavior of rotating detonation

Fig. 5. FFT distribution of PCB1 and the amplitude of peak frequency for SW as a function of air flow rate.

cates the better improving effect of PW2 on the stability of rotating detonation at high flow rates. Additionally, when the flow rate decreases, the frequency of 1D first decreases slightly and then increases for the two perforated walls, although the frequency of 1 L monotonically increases, which is different from the phenomenon obtained with the solid wall. The variation ranges of 1 L for PW1 and PW2 also enlarge when compared with those of the solid wall, and they correspond to 2021–2426 Hz and 2052–2456 Hz, respectively. The acoustic modes are effectively suppressed over the full range of flow rate while adopting PW3 and PW4. In Fig. 6(c) and (d), only the rotating detonation frequencies 1D and 2D are clearly identified. The amplitude of 2D for PW3 increases significantly. As will be shown in Section 3.2 (see Fig. 9(a)), this is because PCB1 happens to be located at the mid-point between the two collision points, and this renders its waveform similar to that of a rotating detonation propagating in two times of the real detonation wave velocity, and thus the 2D frequency component is strengthened. In a manner similar to PW1 and PW2, the 1D and 2D frequency components of PW3 also exhibit an initial trend of decreasing and then increasing as the flow rate decreases. With respect to PW4, 1D occupies a dominant position, due to the formation of one-wave rotating detonation in the combustor (see Section 3.2). The comparison of the FFT results at m˙ air =165 g/s for different walls is shown in Fig. 7 to further illustrate the variations in the strength and bandwidth for each frequency component. The ratios of 1 L/1D amplitudes of three walls (i.e., SW, PW1, and PW2) are 2.37, 1.55, and 1.47, respectively, and the 1 L amplitudes of SW and PW1 are both approximately 26 kPa. This indicates that PW2 suppresses the acoustic modes more effectively than PW1. When compared with SW, the bandwidth of 1D for PW1 is significantly narrower and this suggests the improvement in the stability of rotating detonation, which is a possible reason for the increase in 1D amplitude. Furthermore, the 1D amplitudes of all PW1–4 weaken

The perforated walls change the intensitiy of acoustic modes, and also affect the stability of rotating detonation and the map of combustion regimes. Figure 8 shows the combustion regimes in RDC for different operation conditions. The unstable phenomena observed in the experiments are counter two-wave rotating detonations that are divided into acoustic and regular types based on whether the acoustic modes appear. When SW and PW1–3 are used, the combustion regime always maintains a counter two-wave under the present flow rate conditions, however, the one-wave rotating detonation is obtained when PW4 is adopted and the detailed mechanism is still an open question. Additionally, the perforated walls also change the upper limit of successful rotating detonation. Based on the numerical results, the ignition failure that occurs at high flow rates is caused by the decrease in the H2 penetration depth in the cold flow field before ignition when the air flow rate increases. Thus, the local equivalence ratio in the vicinity of the igniter is not sufficient to generate an intense local hot spot and leads to the unsuccessful transition to detonation. Subsequently, the flame core is blown to the downstream and the reactant was observed to be ignited outside the combustor and burn as deflagration in the experiments. To a certain extent, the perforate walls change the mixing condition of reactant and the H2 penetration depth, and thereby change the upper limit of successful rotating detonation. However, the aforementioned effect is not always conducive to extend the upper limit. When compared with SW, only PW3 significantly extends the upper limit, and the limit is even reduced slightly while using PW1. It should be noted that the ignition possesses a certain degree of randomness, because it is associated with the transient flow field structure. Therefore, each operating condition close to the upper limit is repeated thrice, and it is defined as ‘Failure’ if all the three operations fail and no rotating detonation forms. As shown in Fig. 9(a), the pressure signals of PCB1 for different walls at the same flow rate (m˙ air =165 g/s) are compared to elucidate the variation in the stability of rotating detonation. When SW is used, the repeatability of waveform in different periods is poor and the pressure peaks fluctuate intensively. The fluctuation indicates the continuous alternation of the strength of the two counter-propagating detonation waves after collision, and its frequency corresponds to the 1 L acoustic mode. The aforementioned situation is not evidently improved by adopting PW1 and PW2. However, when PW3 is adopted, the waveform is more regular and the fluctuation in the pressure peaks almost disappears, indicating that the two detonation waves are approximately of equal intensity and propagates stably after the collision. With respect to the onewave rotating detonation obtained with PW4, its waveform and pressure peaks are also maintained as relatively steady. Figure 9(b) shows the distribution of pressure peaks for the period of 40 0–50 0 ms and several statistic parameters of the distribution are listed in Table 4. Based on the theoretical solution of shock wave collision, when two counter-propagating rotating detonation waves with the ZND structure collide, a high-pressure

H. Wen and B. Wang / Combustion and Flame 213 (2020) 52–62

Fig. 6. FFT distribution of PCB1 and the amplitude of peak frequency for perforated walls as a function of air flow rate: (a) PW1; (b) PW2; (c) PW3; (d) PW4.

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H. Wen and B. Wang / Combustion and Flame 213 (2020) 52–62 Table 4 Statistic of pressure peaks.

Fig. 7. Comparison of the FFT results of PCB1 for different walls, m˙ air =165 g/s.

Fig. 8. Combustion regime in the combustor.

Type

90% of Peaks (MPa) PCB1/PCB2

SW PW1 PW2 PW3 PW4

< < < < <

0.62/< 0.62/< 0.59/< 0.32/< 0.31/<

0.62 0.46 0.49 0.44 0.31

Maximum Peak (MPa) PCB1/PCB2 0.91/0.92 0.95/0.72 0.72/0.67 0.57/0.39 0.40/0.38

zone is generated at their induction zones in which the pressure exceeds the initial state (i.e., Von Neumann state). The reflected shock waves re-ignite new detonation waves in the fresh reactant zone, while the pressure of the high-pressure zone decays. When the collision occurs close to the pressure measurement point, a strong pressure peak can be obtained. If the collision is farther from the measurement point, the pressure peak returns to the Von Neumann state. As shown in Fig. 9(b), when SW, PW1 and PW2 are used, the pressure peaks at PCB1 and PCB2 exhibit strong dispersion. With respect to SW, the statistic parameters at PCB1 and PCB2 that are shown in Table 4 are similar and this is a consequence of the averaging effect due to the continuous movement of the collision point. With respect to PW1, although the intensity of pressure peaks at PCB1 is close to that of SW, the distribution of pressure peaks at PCB2 significantly shifts downward and the dispersion is reduced. The difference in the distribution at the two measurement points suggests that the collision occurs more frequently close to PCB1. With respect to PW2, the pressure peaks at PCB1 are slightly weaker than those for PW1, while the pressure values at PCB2 are slightly stronger, thereby indicating that the collision point is farther away from PCB1 but closer to PCB2. When PW3 is adopted, an evident stratification on the distribution of pressure peaks appears, and the dispersion is further weakened. This suggests that the collision point is relatively fixed near PCB2 and no collision occurs near PCB1. With respect to PW4, given the disappearance of counter two waves, the pressure peaks measured at PCB1 and PCB2 maintain a similar level. The aforementioned phenomena indicate that the perforated walls can weaken the pressure peak of rotating detonation and dampen its fluctuation, and the effect is more significant when the perforated area ratio increases.

Fig. 9. Comparison of (a) the pressure profiles (PCB1) and (b) pressure peaks distribution for different walls, m˙ air =165 g/s.

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Fig. 10. Normalized mean wave velocity and fluctuation ratio for different walls as a function of air flow rate: (a) mean wave velocity; (b) fluctuation ratio.

Fig. 11. Schematic showing the collision process of counter two-wave rotating detonation: (a) before the collision; (b) after the collision.

The preforated walls also influence the wave velocity of rotating detonation. Figure 10 shows the normalized mean velocity V¯ /VCJ and its fluctuation ratio for different walls. The theoretical CJ velocity VCJ = 1937 m/s is calculated by CEA. The initial pressure is given as 1 atm, the temperature is 300 K, and the equivalence ratio is 1. The wave velocity is defined as V = π Dch /t, where t corresponds to the time interval of pressure peaks in the adjacent cycle measured at PCB1. The velocity fluctuation ratio is defined as the standard deviation of V/VCJ . As shown in Fig. 10(a), the wave velocity obtained in the experiments varies from 0.51VCJ to 0.58VCJ . The dominant reason for the large velocity deficit is due to the non-uniform injection. The wave velocity for SW only exhibits a slight increasing trend as the flow rate decreases and remains close to 0.550VCJ with a maximum fluctuation of 0.008VCJ in the range of 110–180 g/s. However, with respect to perforated walls, the mean wave velocities change markedly and exhibit a Vshaped trend with the variation in the air flow rate. When the flow rate is high (m˙ air >165 g/s), the wave velocities of four perforated walls approach or even exceed that of SW, although the velocities are reduced rapidly as the flow rate decreases. All the velocities reach the minumum values at approximately m˙ air =140 g/s and then increase again. For example, when adopting PW3, the detonation wave velocity is 0.578VCJ at m˙ air =210 g/s, and the minimum velocity of 0.520 VCJ is obtained at m˙ air =150 g/s. Subsequently, the velocity is restored to 0.546VCJ at m˙ air =100 g/s. The five velocity

curves in Fig. 10(a) exhibit different increasing rate at large flow rates. With respect to PW3 and PW4, the wave velocities exceed those of SW at large flow rates and this can result from the reduction of velocity deficit caused by the instability. Specifically, with respect to PW4, the velocity attenuation due to the collision process is eliminated, and thus the increasing rate of wave velocity is higher than that of PW3. An explanation is given to illustrate the commencement of Vshaped trend when adopting perforated walls. The previous study on detonation tube [26] revealed that the detonation wave propagating in a solid tube attenuates rapidly upon it enters the porous wall section, and the velocity deficit is higher for the reactant of lower sensitivity. The phenomenon observed in RDC is related to the varying mixing condition in the combustor when the air flow rate changes. Within a specific flow rate range, the overall sensitivity of reactant is reduced due to the decrease in mixing efficiency, and this leads to the larger velocity deficit for perforated walls when compared with solid wall. Because the mixing efficiency mainly depends on the flow rate, this perspective can also reasonably explain why the minimum mean velocities for all perforated walls are obtained at approximately the same flow rate. It should also be noted mention that although the velocity deficits augment when the perforated area ratio increases within the range of 135–160 g/s, the V¯ /VCJ curves for different perforated walls exhibit a similar slope when m˙ air <130 g/s. Additionally, the curves

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for perforated walls that have the identical hole size, namely PW2, PW3 and PW4, even overlap. It is still unclear as to whether this phenomenon is merely a coincidence or controlled by a certain inherent mechanism. As shown in Fig. 10(b), when the acoustic modes are suppressed by employing PW3 and PW4, the velocity fluctuation ratios are also significantly reduced to a similar level. Both this feature and the behavior of pressure fluctuation (Fig. 9) indicate the improvement in the stability. The aforementioned change in the mixing efficiency also leads to the variation in the fluctuation ratio. In the flow rate range of 140–180 g/s, the velocity fluctuation ratios for perforate walls with the exception of PW2 show an increasing trend as the flow rate decreases, and subsequently the fluctuation ratio is reduced. 3.3. Discussion on the physical mechanism As a type of acoustic dampers, perforated plates convert sound energy into kinetic energy by vortex shedding and dissipate it [24]. They are adopted to suppress acoustic modes and stabilize combustion in conventional engine combustors. The sound absorption effect of perforated plates is influenced by the hole size, shape, thickness and other factors. Generally, a perforated plate with constant parameters has a narrow bandwidth of sound absorption [29]. However, based on the Fig. 6, all the acoustic modes disappear synchronously in the present experiments, and perforated walls with the same hole size (PW2–4) exhibit completely different effects on suppressing acoustic modes. Hence, the suppression mechanism of perforated walls adopted in the study should be different from that in a conventional perforate plate damper. The acoustic modes of the RDC observed in the study are closely related to the collision of counter two-wave rotating detonation. Figure 11(a) shows a schematic flow field structures of two waves that are about to collide. The real detonation wave has complex three-dimensional structure. In addition to the leading shock wave, multiple transverse shock waves propagate in the induction zone [30]. After the collision occurs (Fig. 11(b)), two reflected shock waves and a high-pressure zone are formed. Furthermore, several local high-pressure spots are generated by the collision of shock waves. With respect to the unstable counter two-wave rotating detonation, the collision point is varied and random in space, and thus the formation of high-pressure spots is also random. The pressure waves are randomly generated and propagate all around and the modes are selected by the combustor. Finally, specific acoustic modes are excited. The acoustic modes can induce the instability of rotating detonation by influencing the injection in a reverse manner. Within zones behind the detonation fronts at which the pressure is over 0.528 times that in reactant plenums, the injection slot and holes do not meet the sonic condition, and the oscillating back-pressure can even transmit into the plenums. Figure 12 shows the FFT result of the pressure in air and H2 plenums when SW is used, in which the peak frequency of 2202 Hz corresponds to the 1 L acoustic mode. The other unmarked peak frequencies (such as 3240 Hz, 3713 Hz and 4974 Hz for the air plenum) are only detected in the plenums and they always exist for all flow rates and perforated walls. This fact indicates that these frequencies are related to the resonances of gas supply systems. However, it is difficult to accurately identify each of them with a theoretical value due to the complexity of the real gas supply systems. The relative amplitude of different peak frequencies indicates the 1 L acoustic mode significantly impacts the H2 plenum. In contrast, the impact on the air plenum is weaker because of its high static pressure. If the H2 injection hole is located at the crest of acoustic mode, then non-injection zone that is blocked by the intensified high pressure after the detonation front becomes longer, and thus the H2

Fig. 12. FFT result of high-frequency pressure in the H2 /air plenums (the DC offset is removed), SW, m˙ air =155 g/s.

injection decreases. Conversely, the H2 injection increases. Therefore, the equivalence ratio of the mixing zone fluctuates with the acoustic mode and the intensity of rotating detonation is affected, thereby leading to fluctuations in pressure peaks (Fig. 9(a)) and wave velocity (Fig. 10(b)). When perforated walls are adopted, the propagating pressure waves are dissipated in the perforated holes. Because the released energy for exciting acoustics decreases, the acoustic modes of RDC are dampened. The perforated areas of PW1 and PW2 are not sufficient to dissipate the pressure waves, and thus the acoustic modes still exist (Fig. 6(a) and (b)). When the perforate area increases, the acoustic modes are almost completely suppressed (Fig. 6(c)). Hence, the fluctuations in pressure peaks and wave velocity weaken significantly although the combustion regime for PW3 is still counter two-wave. With respect to PW4, the source of acoustics excitation disappears due to the establishment of onewave rotating detonation, and acoustic modes are no longer observed. 4. Effect of wall perforation on the performance of RDC Figure 13(a) shows the variation in static pressure in H2 plenum as the air flow rate changes. The solid line corresponds to the fitted line that denotes the initial pressure before ignition. As previously mentioned, the H2 injection holes cannot meet the sonic condition in high-pressure zones behind the wave front where the pressure is over 0.528 times the H2 plenum pressure. However, because the flow rate is fixed and controlled by needle valves, the pressure in H2 plenum increases after ignition (Fig. 3). The difference of static pressures in the plenum before and after the ignition is used to evaluate the intensity of back-pressure and the influence of rotating detonation on the gas supply systems. The smaller the pressure difference is, the weaker the influence is. As shown Fig. 13(a), the pressure in H2 plenum linearly decreases after ignition when the air flow rate decreases. With the exception of failed cases at high flow rates, the pressure differences for each wall remains approximately constant when the flow rate varies. In the flow rate range of 10 0–20 0 g/s, the mean pressure differences for the walls of SW and PW1–4 correspond to 38.37 kPa, 32.95 kPa, 32.76 kPa, 29.78 kPa, and 6.31 kPa, respectively. Obviously, all the four perforated walls contribute to alleviating the influence of rotating detonation although there are differences in the effects due to the different geometric parameters. With respect to PW1 and PW2 whose perforated area ratios are similar, the levels of pressure dif-

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Fig. 13. Variation in static pressure in H2 plenum and specific impulse Isp as a function of air flow rate: (a) static pressure; (b) Isp .

ference are also similar. The pressure difference is reduced when the area ratio increases. The level of back-pressure of the combustor is characterized by the static pressure in the plenum, while the specific impulse Isp is associated with the total pressure of the combustor pc . Given the specific impulse equation

 Isp =



 p  γcγ−1 c

2γc b R T 1− γc − 1 c c pc

(2)

assumed that the mean temperature in combustor Tc and the ambient pressure Pb are fixed, Isp is positively correlated to pc . Isp obtained in the experiments is defined as the ratio of mean thrust (Fig. 3) to the total flow rate of the reactant, and Fig. 13(b) shows its variation as the air flow rate changes. The cases of unsuccessful detonation are not shown in the figure. With the decrease in the flow rate, Isp exhibits a linear declining trend. The specific impulses of all perforated walls are reduced to a certain extent when compared with those of the solid wall. By the least-squares fit method, the linear functions describing the relationship between specific impulse and air flow rate are obtained for SW and PW4, and they are plotted as solid and dash lines in Fig. 13(b). The Pearson correlation coefficients R2 of the two fitted lines are 0.9895 and 0.9941, respectively. Although the specific impulse of PW4 is always lower than that of SW over the full range of flow rate, its growth rate is slightly higher. When m˙ air =100 g/s, the fitted specific impulse of SW and PW4 are 42.5 s and 39.8 s, respectively. The absolute difference is 2.7 s and the relative difference is 6.3%. When the flow rate increases to 200 g/s, the absolute and relative difference are reduced to 1.7 s and 2.4%, and the fitted specific impulse of SW and PW4 are 70.2 s and 68.5 s, respectively. Evidently, the negative effect on the specific impulse caused by PW4 is gradually weakened as the flow rate increases. A similar phenomenon is also observed for PW3 in which the specific impulse is approximately equal to that of SW when m˙ air >150 g/s. The aforementioned facts indicate that the perforated walls indeed negatively affect the Isp at low flow rates, and this is potentially due to the dissipation of total pressure pc in the holes. However, the unstable rotating

detonation can also have negative contribution to the specific impulse and benefiting from the improvement in stability, the loss is compensated and the specific impulse even tends to exceed that of the solid wall at high flow rates for PW3 and PW4. 5. Conclusion In the study, the effects of perforated wall on rotating detonation and combustor performance have been investigated by examining several types of walls with different hole sizes and perforated area ratios. The main conclusions are as follows: A perforated wall with proper geometric parameters can effectively suppress acoustic modes over the full range of flow rate, and this is mainly due to the function of perforated holes to dissipate pressure waves that excite acoustic modes in the RDC. When acoustic modes attenuate or disappear, the rotating detonation becomes more stable, and the fluctuation in pressure peak and wave velocity is significantly reduced. Based on the current results, the dominant factor that determines the suppression effect corresponds to the perforated area ratio, and the effect is weak for a ratio less than 1.75%. With respect to perforated walls with similar area ratio, namely PW1 and PW2, the wall with larger holes exhibits a relatively better suppression effect at high flow rates. The counter two-wave rotating detonation is obtained with SW and PW1–3, while the stable one-wave rotating detonation establishes when PW4 is adopted. Perforated walls cause an additional velocity deficit of rotating detonation. Additionally, because the mixing efficiency and overall sensitivity of the reactant changes with the variation in the flow rate, the curves of wave velocity exhibit a V-shaped trend. In contrast, the velocity does not exhibit a significant change for the solid wall. With the increase in the perforated area ratio, both the overall level and maximum value of the pressure peaks decreases. Additionally, the impact of the detonation on the H2 plenum also weakens. Specifically, with respect to PW4, the aforementioned values are significantly lower than those of the other walls, due to the formation of one-wave rotating detonation. Although the perforated wall alleviates the load on the combustor structure and gas supply system, it does not evidently reduce the specific impulse. The experimental data indicates that the specific impulse of PW4 is only 2.4% when the air flow rate is 200 g/s lower when compared with

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that of the SW, and its growth rate as a function of flow rate is even slightly higher. This study preliminarily verifies the potential feasibility of applying a perforated wall in RDC to control the instability of rotating detonation. Nevertheless, it is necessary to conduct further studies to examine the effect of other factors, such as the width of combustor channel and the thickness of perforated wall. It is also important to perform experiments on transpiration cooling in RDC with perforated walls. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgment This work was supported by the NSFC [grant number 51676111] and NSAF [grant number U1730104]. References ´ , Detonative propulsion, Proc. Combust. Inst. 34 (2013) 125–158. [1] P. Wolanski [2] F.A. Bykovskii, S.A. Zhdan, E.F. Vedernikov, Continuous spin detonation in annular combustors, Combust. Explos. Shock Waves 41 (2005) 449–459. ´ , Z. Gut, Experimental research on the rotating detona[3] J. Kindracki, P. Wolanski tion in gaseous fuels–oxygen mixtures, Shock Waves 21 (2011) 75–84. [4] S.M. Frolov, V.S. Aksenov, V.S. Ivanov, I.O. Shamshin, Large-scale hydrogen–air continuous detonation combustor, Int. J. Hydrogen Energy 40 (2015) 1616–1623. [5] J. Kasahara, Y. Kato, K. Ishihara, K. Goto, K. Matsuoka, A. Matsuo, I. Funaki, H. Moriai, D. Nakata, K. Higashino, N. Tanatsugu, Application of detonation waves to rocket engine chamber, in: J.-M. Li, C.J. Teo, B.C. Khoo, J.-P. Wang, C. Wang (Eds.), Detonation control propuls. pulse detonation rotating detonation engines, Springer International Publishing, Cham, 2018, pp. 61–76. [6] J. Higashi, S. Nakagami, K. Matsuoka, J. Kasahara, A. Matsuo, I. Funaki, H. Moriai, Experimental study of the disk-shaped rotating detonation turbine engine, 55th AIAA Aerospace Sciences Meeting (2017). ´ , P. Kalina, W. Balicki, A. Rowinski ´ , W. Perkowski, B. Kawalec [7] P. Wolanski Michałand Łukasik, Development of gasturbine with detonation chamber, in: J.-M. Li, C.J. Teo, B.C. Khoo, J.-P. Wang, C. Wang (Eds.), Detonation control propuls. pulse detonation rotating detonation engines, Springer International Publishing, Cham, 2018, pp. 23–37. [8] S.M. Frolov, V.I. Zvegintsev, V.S. Ivanov, V.S. Aksenov, I.O. Shamshin, D.A. Vnuchkov, D.G. Nalivaichenko, A.A. Berlin, V.M. Fomin, A.N. Shiplyuk, N.N. Yakovlev, Hydrogen-fueled detonation ramjet model: wind tunnel tests at approach air stream Mach number 5.7 and stagnation temperature 1500K, Int. J. Hydrogen Energy 43 (2018) 7515–7524.

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