MMH impinging combustion chambers

CJA 1380 10 September 2019 Chinese Journal of Aeronautics, (2019), xxx(xx): xxx–xxx

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Chinese Society of Aeronautics and Astronautics & Beihang University

Chinese Journal of Aeronautics [email protected] www.sciencedirect.com

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Experimental of combustion instability in NTO/MMH impinging combustion chambers

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Anlong YANG *, Bin LI, Yu YAN, Shuaijie XUE, Lixin ZHOU

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Science and Technology on Liquid Rocket Engine Laboratory, Xi’an Aerospace Propulsion Institute, Xi’an 710100, China

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Received 26 December 2018; revised 26 March 2019; accepted 5 May 2019

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KEYWORDS

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Atomization; Combustion stability; Impinging jet injector; Klystron effect; Liquid rocket engine

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Abstract This paper presents an experimental study into dynamics of chamber pressure and heat release rate during self-excited spinning and standing azimuthal mode in NTO/MMH (nitrogen tetroxide/monomethylhydrazine) impinging combustion chambers. Nine cases including two combustion chamber configurations were conducted. The operating conditions of all unstable cases were located in the instability region according to Hewitt empirical correlation. The results show that chamber pressure oscillations keep pace with the corresponding OH* chemiluminescence intensity over the whole combustion region in the spinning and standing modes. It is indicated that the Rayleigh index is positive over the whole combustion area in all the unstable cases. A significant supersonic flame front structure of the first-order spinning mode was found in a cylindrical chamber, which means that a detonation wave could exist in the cylindrical chamber without a center body. The pressure and heat release rate oscillations at the pressure node are nonnegligible although their amplitudes are lower than those at the pressure antinode in the first-order standing mode with an annular chamber. Besides, the dominant frequency of pressure and heat release rate oscillations at the pressure node is twice as high as that at the pressure antinode. Ó 2019 Production and hosting by Elsevier Ltd. on behalf of Chinese Society of Aeronautics and Astronautics. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).

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1. Introduction

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Combustion instabilities generated by the coupling of heat release and chamber pressure in the combustor are very complicated and dangerous phenomena in high performance

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* Corresponding author. E-mail address: [email protected] (A. YANG). Peer review under responsibility of Editorial Committee of CJA.

Production and hosting by Elsevier

devices like jet engines, ramjets engines and liquid rocket engines. These powerful combustion instabilities often lead to failure and in extreme cases the destruction of the system, because they interrupt original energy supplies, generate undesired intense pressure fluctuations, and result in excessive heat transfer to combustor walls and injector plates. Although research on acoustic combustion instabilities in rocket engines is quite intense worldwide since the 1940s,1,2 prediction of these processes at the design stage is still a huge challenge, because of the complexity of the problem, the generally inaccessible environment of the rocket engine combustion chamber, and the lack of appropriate diagnostic techniques available to study the problem.

https://doi.org/10.1016/j.cja.2019.08.010 1000-9361 Ó 2019 Production and hosting by Elsevier Ltd. on behalf of Chinese Society of Aeronautics and Astronautics. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Please cite this article in press as: YANG A et al. Experimental of combustion instability in NTO/MMH impinging combustion chambers, Chin J Aeronaut (2019), https://doi.org/10.1016/j.cja.2019.08.010

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Azimuthal modes are typically the most unstable and dangerous in combustion instabilities because it is only weakly damped in thrust chambers. However, investigation of azimuthal instabilities remains a scientific challenge since it requires a full combustion chamber configuration whose diameter is directly related to the time and length scales of azimuthal instabilities. Azimuthal modes can appear as standing or spinning (also referred to as turning) modes and both are observed in combustion chambers. Bifurcations between standing and spinning modes may be due to nonlinear effects: Refs. 3,4 propose a non-linear theoretical approach showing that standing wave modes can be found at low oscillation amplitudes but that only one spinning mode is found for large amplitude limit cycles. Other explanations can be found in linear approaches: spinning modes would appear only in perfectly axisymmetric configurations while any symmetry modification would lead to standing modes 5. The fundamental understanding of the process leading to combustion instabilities is attributed to Rayleigh6 who indicated that heat release rate must be in phase with pressure oscillations to allow acoustic interaction between combustion and the pressure field. It is notable that pressure fluctuations in the unstable combustion chambers feature two significant characteristics: high amplitudes and obvious periodicity, in comparison with that in the stable combustion chambers. Thus, the combustion heat release should also be periodic to catch a stable phase angle with respect to the periodic pressure fluctuations as required by Rayleigh criterion. Periodicity of combustion heat release in the occurrence of combustion instabilities has been certified in previous literatures experimentally7,8 and numerically.9–11 An emerging issue is how the combustion heat release is modulated to be periodic by acoustic fluctuations. Prior to these recent studies, the structure and dynamics of pressure and heat release rate fluctuations during self-excited standing azimuthal modes were presented. Dawson and Worth7,8 found that during standing wave modes the amplitude of heat release rate fluctuations varied spatially around the annulus with peak fluctuations produced at the pressure antinodes and negligible fluctuations produced at the pressure nodes in a gas turbine combustor. Urbano et al.11 investigated combustion dynamics in a complete small-scale rocket engine by making use of a combination of large eddy simulation and acoustic modal identification. Simulation results showed that the contribution of flames at the pressure antinodes to Rayleigh index was significantly higher than that at the pressure nodes. It is concluded that the flames driving unsteady acoustics are those located at the pressure antinodes. Miller et al.12 conducted a gas-centered, fuel-swirled injector element liquid rocket combustion experiment and achieved strong spontaneous longitudinal instabilities with peak-to-peak amplitudes of 0.69 to 1.38 MPa in a model combustor. Due to absence of optical measurements, Rayleigh index could not be obtained in their experiment. Pomeroy et al.13,14 using the same injector element as Miller’s conducted transverse combustion stability experiments in which CH* chemiluminescence maps of flames were captured by a high-speed camera. The dominant frequency of overall CH* chemiluminescence at the pressure node was twice the first transverse frequency. Pomeroy and Anderson15 further tested transverse combustion stability experiments using different injector arrangements and

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A. YANG et al. found that the strongest instability occurred in the case with injector locations nearest to the pressure antinodes. Popov and Sirignano16 presented a computational analysis of the first transverse acoustic instability for Pomeroy’s experimental combustion chamber. It was found that fluctuation amplitudes of the chamber pressure and heat release rate at the pressure node were much lower than those at the pressure antinodes but could not be neglected. Furthermore, heat release rate fluctuations keep pace with pressure fluctuations at the pressure node and their dominant frequencies were both twice the frequency of the first transverse mode, as shown in Fig. 5 and Fig. 7 of Ref. 16. By contrast, there are obvious differences in standing mode instabilities between the gas turbine combustor7,8 and the liquid-propellant combustor13–16 in terms of pressure and heat release rate fluctuations at the pressure nodes. The possible reason of these differences is that the waveform of pressure and heat release rate fluctuations in the gas turbine combustor is sinusoidal but that in the liquid-propellant combustor is steep-fronted. Higher-order effects of the steep-fronted wave lead to nonnegligible pressure and heat release rate fluctuations at the pressure node. Besides, the pressure fluctuation amplitude in the liquid-propellant combustor (MPa)16 is higher by three orders of magnitudes than that in the gas turbine combustor (kPa).7 Several investigators17–22 in 1960s suggested that the high-pressure amplitudes and steep-frontedness in unstable liquid combustors were not reconcilable with the classical acoustical models used to explain tangential instabilities even though the period of the disturbance did approximate the predictions of those models. They also suggested the significance of detonative processes to rocket combustion instability. Although the frequency of acoustic combustion instabilities is mainly determined by the geometrical dimensions of combustion chambers, whether combustion instabilities occur strongly depends on some injector characteristics that can be roughly quantified by Strouhal number (St). In gas turbine combustion instabilities, Strouhal numbers of injectors relate to vortex formation.10,23 Mass flow rates modulated by acoustic pressure oscillations lead to periodically consecutive vortex structures and collective heat releases. Wolf et al.10 suggested that there exists an obvious and stable phase difference between mass flow and heat release rates in occurrence of combustion instabilities. Swirl injectors used in liquid-propellant rocket engines feature frequency cutoff phenomenon.12,24 Khalil et al.24 investigated the response of unconfined swirling jets undergoing vortex breakdown to axial pulsing. It was found that the Strouhal number of shear-layer vortex shedding is fixed at Stn = 0.78 for an unforced swirling jet and the highest receptive shedding frequency is 2Stn . Miller et al.12 conducted an experiment characterizing the combustion dynamics of a single gas-centered, fuel-swirled injector element at five different lengths, from 25.4 to 88.9 cm. The experimental results indicated that the particular injector element is not prone to exciting instabilities at fundamental frequencies below 1050 Hz and above 1810 Hz. For liquid-propellant rocket engines employing impinging-jet injectors, Hewitt stability correlation25 has demonstrated good agreements in matching the stability characteristics of more than 20 fullscale engines used for production or for technology programs. According to Hewitt stability correlation, the highest sustainable frequency of combustion instability is lower than

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Experimental of combustion instability in NTO/MMH

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Uj =10 do , where Uj is the injection velocity and do is the orifice diameter. In other words, Strouhal number of impinging injectors is smaller than 0.1 when combustion instabilities occur. In our study, operating conditions of all unstable cases were located in the instability region according to Hewitt empirical correlation25 to trigger self-excited transverse instabilities. This paper investigates the relationship between unsteady flame and pressure fluctuations during spinning and standing wave modes in an effort to improve our understanding of the physical mechanisms that drive the unsteady heat release rate for azimuthal modes in liquid-propellant combustors. To do this, OH* chemiluminescence images of flames and chamber pressure were recorded synchronously. The remainder of this paper is organized as follows: In Section 2, the apparatus, operating conditions and analysis methodology are described. Section 3 presents experimental results of spinning and standing modes. The conclusions are drawn in Section 4.

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2. Experimental methods

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2.1. Experimental apparatus

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A schematic of a hypergolic propellant combustor without center body or with center body is shown in Fig. 1. Nitrogen tetroxide (NTO) and monomethylhydrazine (MMH) are oxidizer and fuel, respectively. The injector plate of the combustor possesses 24 like-unlike impinging injector elements. The oxidizer orifice diameter do is 0.39 mm and the fuel orifice diameter df is 0.31 mm. The angle between the oxidizer orifice and the injector face is 51° and the angle between fuel orifices and the injector face is 53°. Two piezoresistive sensors were mounted with the oxidizer and fuel manifold walls, respec-

Fig. 1

Schematic of hypergolic propellant combustor.

3 tively. The mass flow coefficients of the oxidizer manifold and fuel manifold were calibrated using real propellants before hot fire tests. In hot fire tests, mass flow rates were calculated on basis of the mass flow coefficients and injection pressure drops. The axial distance from impingement points to the injector face is 2 mm and the radial distance from the impingement points to the central axis is 20 mm. The inter diameter of the outer body D is 60 mm and its length L is 140 mm. A center body could be fixed on the injector plate to form an annular chamber with the outer body together or only the outer body forms a cylindrical chamber without a center body. One end diameter of the center body near injector plate D1 = 26 mm is smaller than the other of the center body near the chamber outlet D2 = 48.6 mm in order to form a throat. The axial distance L1 from the injector face to the throat is 100 mm. Detailed dimensions of the three center bodies are shown in Table 1. A piezoresistive sensor and two piezoelectric sensors were mounted at the side wall of the outer body for monitoring the static and high-frequency pressure, respectively. The piezoelectric sensors were mounted in a small recess of 3 mm to provide protection from hot gases. The axial distance from the sensors to the injector plate was 20 mm. The azimuthal angle difference between two piezoelectric sensors P01 and P02 was 90°, as shown in Fig. 3. The sample rates of the data collector are up to 102.4 kHz. The two piezoelectric sensors have the same order of effectively responsive frequency with pressure measured in the range of 0–5 MPa and measuring error of 0.15%. Three piezoresistive sensors mounted with the side wall of the chamber are capable of effectively responsive frequency up to 200 Hz with pressure measuring error of 0.5%. The piezoresistive sensor mounted with the side wall of the chamber is in the range of 0–2 MPa and the two piezoresistive sensors mounted with the supply manifolds are in the range of 0– 6 MPa. A TTL falling edge signal generated by a DG535 (Delay/Pulse Generator) was used to synchronize the pressure signals with the high-speed image records. As shown in Fig. 2, images of OH* chemiluminescence were acquired using a high-speed camera (Phantom v12.1) and UV intensifier (HiCATT25 with hybrid gen2 imager intensifier). The images were acquired using a 45 mm lens (f/1.8) and band-pass filter (310 ± 20 nm). The spatial resolution of the images was approximately 0.285 mm/pixel. The images were collected with an intensifier gate time of 0.9 ls at a sample frequency of 67066 Hz. Photographic settings were all the same for every case, so that OH* chemiluminescence intensity in different cases could be compared with. Images were recorded for about 1.5 s resulting in 100,000 images for each operating condition. The spatial and temporal resolutions are sufficient to minimize blurring effects (less than 2 mm) associated with imaging of the acoustic azimuthal combustion instabilities. The position relation between OH* chemiluminescence images and piezoelectric sensors is shown in Fig. 3.

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2.2. Operating conditions

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A total of 9 combustion cases were conducted in this study, as shown in Table 1. The duration of a typical experiment is about 1.0 s in every case except building pressure and blowdown time. Three piezoresistive sensors measured the static chamber pressure Pc and injection pressures. Pc listed in Table 1 is gage pressure. The pressure drop between the cham-

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A. YANG et al. Table 1

Test summary conditions and results.

Case

Case1-1

Case1-2

Case1-3

Case1-4

Case1-5

Case2-1

Case2-2

Case2-3

Case2-4

Center body Oxidizer flow rate (g/s) Fuel flow rate (g/s) Mixture ratio Pc (MPa) Mode

None 139.8

None 142.0

None 157.4

None 181.0

None 199.8

Yes 116.7

Yes 135.0

Yes 147.9

Yes 156.8

70.1

80.9

79.3

80.9

80.9

70.6

79.6

89.6

78.4

1.99 0.010 Stable

1.98 0.035 First-order spinning 9850

2.24 0.041 First-order spinning 9800

2.47 0.046 First-order spinning 9600

1.65 0.202 Stable

None

1.76 0.010 First-order spinning 8600

None

1.70 0.250 First-order standing 7600

1.65 0.286 First-order standing 7700

2.00 0.280 First-order standing 8000

None None None

0.26 0.100 0.053

0.41 0.101 0.061

0.45 0.089 0.060

0.51 0.079 0.059

None None None

0.37 0.091 0.047

0.34 0.085 0.042

0.42 0.082 0.050

Unstable frequency, f (Hz) DP0c (MPa) Sto , fdo =Uo Stf , fdf =Uf

Fig. 2

Schematic of OH* chemiluminescence imaging setup.

Fig. 3 Schematic of photograph view illustrating piezoelectric sensor locations.

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chamber pressure oscillations DP0c for spinning modes are mean value of mean-to-peak pressure oscillations from the piezoelectric sensors P01 and P02 . The second is the first-order standing mode including Case2-2, Case2-3 and Case2-4. The chamber pressure oscillations DP0c for standing modes are mean-to-peak pressure oscillations at the pressure antinode (Choosing P01 or P02 depends on the location of pressure antinode).

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2.3. Analysis methodology of OH* chemiluminescence images

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The combustion response could presumably be determined from time- and space-resolved measurements of OH* chemiluminescence emission due to combustion. In order to obtain time-resolved spatial distribution of heat release rate, the grayscale intensity of OH* chemiluminescence images was calculated by using an in-house code of image processing based on Matlab. In this paper, grayscale intensity of images ranges from 0 to 1. First of all, polar coordinates are introduced to define OH* chemiluminescence distribution gðr; h; kDtÞ, where r is the radial distance from the geometric center of the combustor, h is the azimuthal angle, Dt is a time interval of two temporally adjacent images, and k is the sequence number of images. There are two configurations to grid OH* chemiluminescence images. As shown in Fig. 4, a series of annular interrogation windows were set up with Ri from 1 mm to 30 mm and a radial interval DR of 1 mm. The radial OH* chemiluminescence distribution with time is expressed as

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ber and the oxidizer/fuel manifold was used to calculate the oxidizer/fuel mass flow rate. f is the oscillation frequency in the unstable cases. Sto and Stf are Strouhal numbers of the oxidizer and fuel injectors based on experimental data, respectively. According to Hewitt empirical correlation,25 operating conditions of all unstable cases fall into the instability region (f1t d=Uj < 0.1, where d is oxidizer or fuel orifice diameter, Uj is oxidizer or fuel jet velocity, and f1t is the predictable firstorder azimuthal acoustic frequency of the combustor). Highamplitude instabilities were spontaneously excited in 7 of the 9 tests reviewed. There are two kinds of combustion instability modes listed in Table 1. The first is the first-order spinning mode including Case1-2, Case1-3, Case1-4 and Case1-5. The Fig. 4

Schematic of annular interrogation windows.

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Z Gr ðRi ; kDtÞ ¼

Z

Ri r¼Ri DR

Z

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Ri

r¼Ri DR

ð1Þ

h¼0

As shown in Fig. 5, a series of sectorial interrogation windows were set up with hi from 0 to 359 and an angular interval Dh of 1 . The azimuthal OH* chemiluminescence distribution with time is expressed as  Z Rout Z Rout Z hi þDh=2 Gh ðhi ; kDtÞ ¼ gðr; h; kDtÞdrdh 

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h¼0

Z gðr; h; kDtÞdrdh

drdh

Z

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2p

2p

h¼hi Dh=2

r¼Rin

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Fig. 6 Temporally average radial OH* chemiluminescence distribution Gmax ðRi Þ.

Schematic of sectorial interrogation windows.

Fig. 5

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5

hi þDh=2

drdh h¼hi Dh=2

r¼Rin

ð2Þ

Rout , the inter radius of the outer body, is 30 mm. The value of Rin depends on combustor configurations and work conditions. Rin is 17 mm in Case1-1–Case1-5 and Rin is 24 mm in Case2-1–Case2-4. If the two configurations are put together, a discrete OH* chemiluminescence distribution in polar coordinates is expressed as  Z hi þDh=2 Z Rj   G Rj ; hi ; kDt ¼ gðr; h; kDtÞdrdh r¼Rj 1

Z



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h¼hi Dh=2

hi þDh=2

drdh h¼hi Dh=2

ð3Þ

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3. Experimental results

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3.1. OH* chemiluminescence distribution along radius without a center body

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In order to demonstrate the radial OH* chemiluminescence distribution, a temporally-averaged radial OH* chemiluminescence distribution was introduced as Gmax ðRj Þ ¼

N X

  max GðRj ; hi ; kDtÞ; hi =N

ð4Þ

k¼1

where N isthe total number  of images during the hot fire test and max GðRj ; hi ; kDtÞ; hi is the maximum value of GðRj ; hi ; kDtÞ along the azimuthal dimension of hi . Fig. 6 shows Gmax ðRj Þ in those cases without a center body. In the stable Case1-1, the OH* chemiluminescence along radius is relatively uniform. In the other unstable cases, the

radial distribution of OH* chemiluminescence intensity is closer to the combustion chamber wall than the impingement points (the radial distance from the impingement points to the central axis is 20 mm), especially in Case1-3, Case1-4 and Case1-5. There are two possible causes for the fact that heat release in unstable cases is close to the chamber wall. First of all, it is possible that hot gases in the unstable chamber have a strong azimuthal movement that produces centrifugal forces. Hot gases and other unreacted propellants are banded into regions near the chamber wall in the effect of the centrifugal forces. Second, the processes from injection to heat release in these unstable cases could be much quicker than those in Case1-1, which means that unreacted propellants have not enough time to diffuse to the central part of the combustion chamber. A more visualized comparison is shown in Fig. 7. Fig. 7(a) shows a temporally-averaged OH* chemiluminescence image of Case 1-1 during the whole hot fire test. Fig. 7 (b) shows a phase-averaged OH* chemiluminescence image of Case1-5. Phase-averaged images are obtained by averaging approximately 30 instantaneous images that contain a flame front within 0:5 of a particular azimuthal position.

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3.2. Initiation phase of spinning mode combustion instabilities

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Fig. 8 synchronously shows chamber pressure oscillations (solid line) P01 and the corresponding azimuthal OH* chemiluminescence intensity Gh ðh1 ; kDtÞ (dashed line) with time at the beginning of combustion instability in Case1-3, where h1 of 108 is the azimuthal position of P01 . It is found that the chamber pressure oscillations have the same phase angle and growth trend of amplitude as the OH* chemiluminescence intensity, which means that they have a strong coupling with each other and meet Rayleigh criterion apparently. Furthermore, Fig. 9 shows 6 OH* chemiluminescence images corresponding to 6 instants marked with circles in Fig. 8. Figs. 8 and 9 clearly show the relation between the distribution of OH* chemiluminescence intensity and the chamber pressure oscillations. OH* chemiluminescence intensity is consistent with the pressure oscillations in time when the peak-to-peak amplitude of the chamber pressure oscillations is about 0.1 MPa, although differences of OH* chemiluminescence intensity along azimuthal direction are not obvious. When the peak-to-peak amplitude of the chamber pressure oscillations is up to 1 MPa, a rotating flame front obviously appears near the combustion chamber wall. The flame front rotates along the combustion chamber wall with a speed of Uff ¼ pDt f, where Uff is the speed of the flame front, f is the unstable frequency as shown in Table 1,

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Fig. 7

OH* chemiluminescence images in stable and unstable cases.

Fig. 8 Synchronous chamber pressure oscillations P01 and corresponding azimuthal OH* chemiluminescence intensity Gh ðh1 ; tÞ (dashed line) with time at beginning of combustion instability in Case1-3.

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and Dt is the diameter of the flame propagation trace. The maximum of Dt is the inter diameter of the combustion chamber, 60 mm. The minimum of Dt is 40 mm, since the radial width of the flame front is about 10 mm. Hence, Uff is between 1240 m/s and 1850 m/s. This speed is larger than the sound velocity of combustion products that is 1167 m/s according to the mixture ratio. As shown in Table 1 and Fig. 8, the pressure ratio of the steep-fronted pressure is up to 7 at least (Pp =Pf > P0 =Pc ¼ 1=0:1 þ 0:035  7, where Pp is the post wave pressure, Pf is the front wave pressure, P0 is the peakto-peak amplitude and Pc is the absolute average chamber pressure). According to the pressure ratio of the steepfronted pressure and the supersonic propagation speed of the flame front, it is possible that there is a shock wave coupling with the flame front, which means that a detonation wave could exist. If the shock wave does exist, the calculation of

Fig. 9

the unstable frequency based on classical acoustic modes could be unsuitable any more, since the sound propagation is isotropic in classical acoustic modes but shock waves are anisotropic. The radial distribution of OH* chemiluminescence intensity is closer to the combustion chamber wall in unstable cases than in the stable case. Most of heat release is distributed in a small region near the flame front. Chemiluminescence intensity away from the flame front in unstable cases is lower than average intensity in the stable case of which mass flow rate is the smallest. There are two possible causes of the concentrated OH* chemiluminescence emission. First, the detonation wave front depletes combustible mixture where it passes. Fresh combustible mixture cannot be generated immediately, since the rapid and full combustion of liquid propellants requires a preparation process of injection, atomization and evaporation that needs time, even for hypergolic propellants. Second, the pressure just behind the detonation wave front is high enough that the injection and atomization processes are periodically modulated. Most of propellant droplets could be periodically generated at a fixed phase angle of every period, due to klystron effect.26 The injection pressure drop oscillations accompany the flow oscillations that cause the velocities of the liquid particles to vary with time. Then a large proportion of fluid particles are superposed together at certain point where the liquid particles with high velocities overtake those with low velocities. This phenomenon is called the klystron effect, and has been reported in impinging jet injectors1,27,28 and swirl injectors.29–32 It is indicated that there is a strong klystron effect of pressure drop oscillations on atomization if the relative amplitude of pressure drop oscillations is larger than about 0.1.26 The relative amplitudes of pressure drop oscillations are all larger than 0.1 in our rotating detonation cases, except that of oxidizer pressure drop oscillations is about 0.09 in Case1-2.

OH* chemiluminescence images during initial phase in Case1-3.

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3.3. Spinning mode

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Fig. 10 shows phase-averaged OH* chemiluminescence images at six different phase angles in four cases of the first-order spinning mode. The propagation direction of flame fronts is anticlockwise in from Case1-3 to Case1-5, and the propagation direction is clockwise in Case1-2. Details of how to calculate phase-averaged OH* chemiluminescence images are shown in Section 3.1. In order to demonstrate the temporally-averaged azimuthal OH* chemiluminescence distribution about the flame front in cases of the first-order spinning mode, a temporally-averaged azimuthal OH* chemiluminescence distribution fixed on the flame front was introduced as

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Gh ðhi Þ ¼

N X

Gh ð mod ðhi  hmax ðkDtÞ þ 180 ; 360 Þ; kDtÞ=N

Fig. 11 Azimuthal distribution of OH* chemiluminescence in four unstable cases of first-order spinning mode and in a stable case.

k¼1

ð5Þ

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where hmax ðkDtÞ is the azimuthal angle of the maximum of Gh ðhi ; kDtÞ at kDt and mod ðA; BÞ is a function of calculating the modulus of A divided by B. The aim of calculating mod ðhi  hmax ðkDtÞ þ 180 ; 360 Þ is to move the azimuthal position of flame front of all images to 180 , so that the OH* chemiluminescence distributions with different azimuthal positions can be averaged. For the stable Case1-1, a temporally-averaged and azimuthally-averaged OH* chemiluminescence distribution was introduced as Gh ¼

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359 X N X

Gh ðhi ; kDtÞ=N=360

ð6Þ

hi ¼0 k¼1

Fig. 11 shows Gh ðhi Þ in from Case1-2 to Case1-5 and Gh in Case1-1. There are significant characteristics of chemiluminescence images between the first-order spinning mode unstable cases, compared with the stable case. There is a flame front rotating along the combustion chamber wall at a supersonic speed in the first-order spinning mode. Chemiluminescence intensity near the flame front is much stronger than that in other azimuthal locations, which means that most of heat release is distributed in a small region near the flame front. Flame fronts are all steep-fronted like the chamber pressure oscillations. Chemiluminescence intensity away from the flame front in unstable cases is lower than average intensity of the

Fig. 10 OH* chemiluminescence phase-averaged images in firstorder spinning modes.

stable Case1-1, although mass flow rates of these unstable cases are larger than that of Case1-1. These results indicate that chemical reaction and heat release could be conducted in a region near the flame front. Combustion processes in regions away from the flame front seem to be suspended periodically. Each suspended time interval is about 5/6 of one oscillation period. Taking account of hypergolic characteristics of the propellants in this study, the suspension of combustion processes is quite remarkable. It is indicated that immediately after the flame front passes, there is no fresh reactant to burn. There are two possible causes leading to suspending combustion processes. First, the flame front depletes combustible mixture where it passes. Fresh combustible mixture cannot be generated immediately, since some time is needed from injection to atomization. Second, the pressure just behind the flame front is high enough that the injection and atomization processes are modulated periodically. Most of propellant droplets could be periodically generated at a fixed phase angle of every period, due to klystron effect. The fixed phase angle should be exactly right to keep pace with the upcoming flame front. It is found that peak values of OH* chemiluminescence intensity Gh ð180 Þ have a positive correlation with pressure oscillations DP0c , as shown in Fig. 11 and Table 1. Gh ð180 Þ and DP0c of Case 1–2 are minimum among the four unstable cases, but its OH* chemiluminescence intensity Gh ðhi Þ away from the flame front is apparently stronger than the others’ intensity. Fig. 12(a) shows chamber pressure oscillations P0c and azimuthal OH* chemiluminescence intensity Gh ð108 ; kDtÞ with time. As expected, azimuthal OH* chemiluminescence intensity Gh ð108 ; kDtÞ synchronizes with chamber pressure oscillations P0c and they feature the similar waveform. Fig. 12(b) shows FFT (Fast Fourier Transform algorithm) plots of P0c and Gh ð108 ; kDtÞ together. Their fundamental oscillation frequency and two higher harmonic frequencies are completely consistent with each other.

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Fig. 13 shows nine successive instantaneous images of the OH* chemiluminescence from two counter-rotating flame fronts. The flame fronts propagate in opposite azimuthal directions. Intensity of flame fronts is unstable during propagation, which

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Fig. 12 Pressure oscillations P01 and OH* chemiluminescence intensity at hi of 108° in Case 1–5. 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510

could result from some occasional effect of non-ideal mixing between the fuel and oxidizer. Pace of pre-combustion processes is the same for every injector element in the spinning mode cases, since every injector element features the same OH* chemiluminescence emission and pressure oscillations. In contrast, injector elements in different locations have different OH* chemiluminescence emission and pressure oscillations in standing mode cases. Pace of pre-combustion processes depends on locations of injector elements in respect to the pressure node and antinode. In one oscillation period, there is only one collective heat release at pressure anti-nodes, but there are two collective heat releases at pressure nodes. Like most of standing modes, azimuthal locations of antinodes and nodes are not fixed but move slowly in our study. To gain further insight into the standing modal dynamics, pres-

Fig. 13

sure oscillations of two points (P01 and P02 ) and the azimuthal OH* chemiluminescence intensity Gh ðhi ; kDtÞ were divided into small sections of about 10 oscillation periods. Based on the azimuthal OH* chemiluminescence intensity Gh ðhi ; kDtÞ, angular locations of pressure antinodes and pressure nodes were determined. 20 sections were picked out when angular locations of antinodes or nodes were within h1  5 . Fig. 14(a)–(b) shows chamber pressure oscillations P0c and azimuthal OH* chemiluminescence intensity Gh ðhi ; kDtÞ during one section at a pressure antinode and the corresponding pressure node, respectively. Fig. 14(c)–(d) shows averaged FFT plots of P0c and Gh ðhi ; kDtÞ at a pressure antinode and the corresponding pressure node, respectively. These averaged FFT plots were obtained by averaging FFT plots of 20 sections. As shown in Fig. 14(a) and (c), azimuthal OH* chemiluminescence intensity Gh ðhi ; kDtÞ keeps pace with chamber pressure oscillations P0c at the pressure antinode and their fundamental oscillation frequency and two higher harmonic frequencies are completely consistent with each other, which is similar to spinning modes. As shown in Fig. 14(b), Gh ðhi ; kDtÞ also keeps pace with P0c at the pressure node. However, the dominant frequency of Gh ðhi ; kDtÞ and P0c at the pressure node is twice as high as that of Gh ðhi ; kDtÞ and P0c at the pressure antinode as shown in Fig. 14(b) and (d). It is worth noting that the amplitude of P0c at the pressure node is about 60% of that of P0c at the pressure antinode, which means that there are not pure velocity fluctuations in the unstable combustion chamber. Our result is similar to transverse combustion instability in a rectangular rocket13–16 although relative amplitudes of pressure and heat release rate oscillations at the pressure nodes are higher than those of Ref. 16. Combined with other cases of standing azimuthal instabilities,7–11 two kinds of standing modes have been found at present. The first one features sinusoidal pressure and heat release rate at low oscillation amplitudes. The pressure and heat release rate oscillations at the pressure nodes are both negligible. The second one features steep-fronted pressure and heat release rate at high oscillation amplitudes. The pressure and heat release rate oscillations at the pressure nodes are nonnegligible although their amplitudes are lower than those at the pressure antinodes.

Successive instantaneous OH* chemiluminescence images during one oscillation period in Case2-2.

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Fig. 14 Pressure oscillations P0c and OH* chemiluminescence intensity Gh ðhi ; kDtÞ at pressure antinode and corresponding node in Case2-2.

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4. Conclusions The current paper describes an experimental investigation into the modal dynamics of self-excited azimuthal instabilities in an NTO/MMH impinging combustion chamber. 9 cases including two combustion chamber configurations were conducted. The first-order spinning mode combustion instabilities occurred in the cylindrical chamber without a center body. The chamber pressure oscillations keep pace with the corresponding local OH* chemiluminescence intensity in terms of phase angle and oscillation amplitude in the entire initiation phase. However, combustion patterns have a great transformation with huge increase of the chamber pressure oscillation amplitude. A flame front takes shape and rotates along the combustion chamber wall at a supersonic speed until a limitcycle is reached. The radial distribution of OH* chemiluminescence intensity is close to the combustion chamber wall in unstable cases. Most of heat release is distributed in a small region near the flame front. Chemiluminescence intensity away from the flame front in unstable cases is lower than average intensity in the stable case of which mass flow rate is smaller than these unstable cases. The standing mode combustion instabilities are prone to occur in the annular combustion chamber with a center body. Azimuthal OH* chemiluminescence intensity totally keeps pace with chamber pressure oscillations P0c at both the pressure antinode and the pressure node. The dominant frequency of Gh ðhi ; kDtÞ and P0c at the pressure node is twice as high as that of Gh ðhi ; kDtÞ and P0c at the pressure antinode. P0c and Gh ðhi ; kDtÞ at the pressure node cannot be neglected, since their amplitude are both approximately 60% of those at the pressure antinode.

The results show that chamber pressure oscillations P0c keep pace with the corresponding OH* chemiluminescence intensity over the whole combustor no matter in the spinning mode or in the standing mode. It is indicated that the Rayleigh criterion is valid over the whole combustion area in our unstable cases.

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This work was co-supported by the National Natural Science Foundation of China (Nos. 11502186 and 51506157) and the National Key Basic Research Program of China.

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