Propagation behaviors of rotating detonation in an obround combustor

Abstract

In the study, the propagation behaviors of rotating detonation are investigated in an obround slit-channel combustor which has four curvature transition sections by employing a H 2 single bondO2 single bondN2 mixture with different oxygen volume fractions (α ) and equivalence ratios (ERs). High-frequency pressure sensors are circumferentially mounted into the outer wall to obtain pressure temporal variations. Statistical indexes related to wave velocities are adopted to characterize the behaviors of rotating detonation based on which the experiment data are divided into stable and unstable regions. The stable rotating detonation is obtained within wide-range ERs for α  = 40% and 35% in which the detonation velocity fluctuation ratio is approximately 1%. The pressure histories indicate that the instability of the detonation front is induced by the curvature transition for α  = 30% and 21%. Complicated unstable phenomena associated with the detonation propagation are observed in which the acoustic modes can be identified. With respect to α  = 21%, the unstable propagation of rotating detonation and the intensity of the first longitudinal acoustic mode are heightened when the oxidizer flow rate increases and even lead to detonation quenching. It is proposed that the unstable propagation of rotating detonation results from the coupling of acoustic modes and the curvature transition induced instability of detonation front. The stabilization of rotating detonation is affected by the curvature transition and requires smaller equivalent detonation cell size, i.e. higher activity reactants, in the obround combustor when compared to that in annular combustors.

Introduction

The rotating detonation engine (RDE) is a potential pressure gain combustion engine that was first achieved within a disk-shaped channel by Voitsekhovskii [1]. Recently, RDE attracted extensive attention due to its high thermodynamic efficiency [2], increased specific impulse [3], and compact mechanical structure. Currently, most studies on rotating detonation are conducted in annular combustors where rotating detonation waves propagate circumferentially and periodically in the head region [4].

The stable rotating detonation is always expected in practical applications. However, diverse unstable propagation phenomena in annular combustors were detected in experiments such as longitudinal pulsed detonation (LPD) instability [5], [6], [7], [8], low frequency instability [9], [10], [11] and counter-rotating waves [12], [13], [14], [15], [16]. The LPD instability refers to a type of longitudinal pulsed detonation mode occurred in the rotating detonation combustor, and it is observed only under certain conditions [5]. The low frequency instability exhibits as a hundreds-of-Hertz sinusoidal oscillation of the detonation pressure peak, and this instability is strongly associated with the injection and reactant plenums dynamics [9], [11]. The counter-rotating waves have been observed in the annular combustors not only as a transient mode in a short period after the ignition [14], but also as a sustained mode during the entire run time [13]. Some studies show that the formation of the counter-rotating waves can be affected by the injection configurations [12], [16], but the exact formation mechanism is still not very clear.

Summarizing extant studies, three types of factors can play important roles on the stabilization of rotating detonation wave, namely: reactant properties [15], [17], [18], [19], injection conditions [12], [20], [21], and combustor geometry [22], [23], [24]. Xie et al. [18] investigated the behavior of rotating detonation wave under different mass flow rates and equivalence ratios and indicated that rotating detonation transforms from unstable to stable as flow rates increase. Furthermore, it was reported that the one-wave detonation can bifurcate into two-wave detonation for high flow rates [15]. The oxygen volume fraction can also affect the stability, and the oxygen-enriched air is verified to expand the lean and rich limit of rotating detonation [19], [25]. Rankin et al. [12] examined different injection configurations and revealed that a few configurations can induce counter-rotating waves and change the shape of detonation wave front. Fotia et al. [20] investigated the influence of injection pressure on the ignition process and suggested that proper pressure of plenums is necessary for successful ignitions. Additionally, the influence of lengths of the combustor inner cylinder was tested, and the results indicated that a hollow combustor exhibits a lower lean limit when compared with an annular one as indicated by Zhang et al. [22].

Although the stabilization of rotating detonation depends on various factors, a few criteria are proposed to predict the behavior of rotating detonation and reveal the relationship between the stability and detonation cell sizes, combustor geometry. Bykovskii [26] determined the width of combustor channel W ch and the filling height of mixture h are critical to the stability. He proposed a few requirements for a successful rotating detonation including h ≈ (12±5) λ and W ch > 0.2h, where λ is the detonation cell size of the mixture. In comparison, George et al. [23] suggested that the limitation of successful rotating detonation is W ch > 0.5λ. They also revealed that the number of detonation waves increases for C > 7.4λ where C denotes the perimeter of a detonation wave front and is related to the flow rate.

The extant studies indicate that the combustor channel width is a key parameter for the stable rotating detonation although there are very few investigations on the influence of the channel length and channel shape. Theoretically, the rotating detonation can be designed as non-annular or any closed shape. However, these conclusions and criteria are obtained in the annular combustors that exhibit uniform curvature. A few studies on the detonation propagation in the curved channels and tubes indicated that the curvature transition can lead to instability of detonation [27], [28]. It is suggested that critical curvature radii or detonation cell sizes are required for stabilization when straight propagating detonation enters the curved section [27]. A few recent experiments conducted in the obround combustor have shown that the similar effect on rotating detonation which can induce counter-rotating waves and the parasitic combustion [29], [30]. However, the discussion is far from sufficient. It is still necessary to verify as well as determine how the curvature transition section influences the propagation behavior of rotating detonation. Furthermore, it is also worthy to determine the unstable propagation phenomena and criteria for stable rotating detonation in a channel with curvature transition section.

In order to answer these questions, an experimental study is conducted in an obround combustor that has four curvature transition sections. Statistical indexes and operating maps are adopted to illustrate the behavior of rotating detonation and unstable propagation phenomena for different oxygen volume fractions (α) and equivalence ratios (ERs). An acoustics analysis is employed to analyze unstable behaviors of rotating detonation, and a mechanism for the unstable propagation phenomena is proposed. The conclusions from this study will also be helpful for the design of non-annular rotating detonation combustors.

Section snippets

Experimental set-up

The experiment system consists of three subsystems, namely an oxidizer/fuel delivery system, a synchronous data acquisition system, and an obround combustor testbed. The fuel used in the experiments is H2, and the oxidizer corresponds to an αO2-(1-α)N2 mixture. Four oxygen volume fractions of the oxidizer (α = 21%, 30%, 35% and 40%) are tested, and the equivalence ratio ranges from 0.6 to 1.3. In order to control the mass flow rate, calibrated sonic nozzles are installed into the pipelines. The

Overview of the behaviors of rotating detonation

A series of experiments with different flow rates, equivalence ratios, and oxygen volume fractions were completed in the study. The test time for each run is set as approximately 170 ms to protect pressure sensors from damage by the high temperature. Given the limitation of minimum and maximum pressures of the fuel supply system, the ranges of oxidizer flow rates are different for each ER and α.

Two types of velocity are defined in the study as shown in Fig. 1b. Specifically, Vi (i = 1, 2, 3)

Stable region

Figure 4 shows a typical case in the stable region. As shown in Fig. 4a, the pressure profiles exhibit clear periodicities, and both the pressure peaks and the normalized round velocity V/V CJ do not evidently fluctuate. V approximately corresponds to −0.79V CJ (i.e. −1757 m/s) and its fluctuation ratio is 0.5%. The negative sign denotes that the propagation direction of detonation wave is clockwise. The pressure peaks are observed to vary at four pressure measurement points. Conversely, in the

Discussion on the mechanism of unstable propagation

In this section, factors including acoustics, the curvature transition effect and the operating conditions are considered to analyze the mechanism of the unstable propagation phenomena in the unstable region. Specifically, the role of acoustic modes is emphasized since they are always observed in conjunction with unstable propagation phenomena in experiments.

Figure 8 shows the cases in the unstable region denoting the following three types of unstable propagation phenomena: acoustics-detonation

Conclusion

In the study, rotating detonation in an obround combustor is examined with a H2 single bondO2 single bondN2 mixture under different oxygen volume fractions and equivalence ratios. The results indicate that the curvature transition sections of the combustor channel can affect the behavior and stability of rotating detonation. The physical mechanisms are presented based on the analysis of statistical indexes, pressure histories, and acoustics of the combustor. The main conclusions from the experimental study include the

Acknowledgment

The study was supported by the National Natural Science Foundation of China (No. 51676111) and NASF (No. U1730104).

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