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Transition of combustion instability in hybrid rocket by swirl injection
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Transition of combustion instability in hybrid rocket by swirl injection Jungeun Kim, Changjin Lee∗ Department of Aerospace Engineering, Konkuk University, Seoul, 05029, South Korea
A R T I C LE I N FO
A B S T R A C T
Keywords: Low frequency instability Hybrid rocket Combustion visualization POD Positive coupling
A series of experimental tests was conducted to investigate the effect of swirl injection on the combustion instability in hybrid rocket using combustion visualization technique. As a result, swirl injection seems to modify two main physical processes responsible for the initiation of LFI. First one is the transition of coupling status between two fluctuations of combustion pressure (p') and heat release (q') of 500 Hz band. The transition of p' and q' to negative coupling seems to be a crucial modification for stabilizing the combustion. Another noticeable effect of swirl injection is the gradual increase in the peak frequency of pressure oscillation from its initial value of around 20 Hz–50 Hz band, which is caused by the thermal lag, as the swirl intensity increases. Also, POD (Proper Orthogonal Decomposition) analysis was done to understand flow response to the swirl injection near the fuel surface. The analysis of temporal behavior of mode 1 and 2 suggested that the swirl injection with proper intensity not only suppress the generation of p' of 500 Hz band but induces a shift of low frequency peaks of 20 Hz band by adjusting the turbulent structures in boundary layer. And the shift of low frequency peaks seems to be another contributing factor for combustion stabilization.
1. Introduction Hybrid rocket combustion displays nonlinear characteristics that produce low frequency instability (LFI), under which combustion pressure of less than 100 Hz is amplified at a certain condition. LFI is a manifestation of physical resonance between the thermal lag closely related to the heat transfer characteristics of the solid fuel and the pressure oscillation that occurs to response to external disturbances in the combustion boundary layer [1]. Recent studies reported that LFI accompanies a strong low frequency pressure oscillation of 20 Hz band and pressure oscillation of 500 Hz band with small amplitude [2]. Also, Kim et al. [3] suggested that the origin of pressure oscillation of 500 Hz band is the result of introducing small-sized vortex flow into the post chamber, which was formed by the mutual interference between the fuel evaporative flow and the axial oxidizer flow. Another study [4,5] using combustion visualization found very interesting results that the combustion reaction fluctuates at a frequency of about 500 Hz. They also found an interesting relation between combustion pressure oscillation (p') and heat release oscillation (q') of 500 Hz band. These two oscillations were confirmed to have a positive coupling of about 14–17 times per second, when the LFI occurred. The establishment of a positive coupling between p' and q' of 500 Hz band, in turn, seems the initiation mechanism of LFI through the resonance between the boundary layer adjustment and thermal delay of solid fuel.
∗
On the other hand, swirl injection is usually used to increase the regression rate of solid fuel in hybrid rocket combustion. Yuasa et al. [6] visualized the flame distribution and behavior when axial and swirl oxidizer injection was applied respectively to hybrid rocket combustion. Their results show that swirl injection induces helical velocity component near surface region whereas rotating component appears around the centerline. This helical velocity component enhanced convective heat transfer to solid fuel and increased regression rate. In recent studies, swirl oxidizer injection was found not only to increase the regression rate but also to stabilize combustion in a hybrid rocket. Bellomo et al. [7] reported that swirl injection could significantly reduce the amplitude of the combustion pressure oscillations compared to those with axial injection. Also, Pucci et al. [8] conducted an experimental study on the improvement of combustion stability by swirl injection. Their results show that the pressure fluctuations of 20 Hz and 600 Hz bands were amplified when the swirl intensity was less than a certain value or none. Messineo et al. [9] also performed similar study on the combustion instability using swirl injection. Their results showed that small-sized vortex generation and their shedding are reduced, when swirl injection is applied. And the reduction in vortex generation decreased the amplitude of the pressure fluctuations of 500 Hz band and to enhance combustion stabilization. Although many studies reported that swirl injection enhances combustion stabilization, detailed physics has not been investigated.
Corresponding author. E-mail addresses: [email protected] (J. Kim), [email protected] (C. Lee).
https://doi.org/10.1016/j.actaastro.2018.07.036 Received 25 January 2018; Received in revised form 12 June 2018; Accepted 21 July 2018 0094-5765/ © 2018 IAA. Published by Elsevier Ltd. All rights reserved.
Please cite this article as: Kim, J., Acta Astronautica (2018), https://doi.org/10.1016/j.actaastro.2018.07.036
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Meanwhile, Lee et al. [4] recently confirmed that the establishment of a positive coupling of p' and q' in 500 Hz band is the necessary condition for the LFI occurrence. Interestingly, it has been found that the establishment of a positive coupling occurs at specific O/F (oxidizer/fuel) ratios. However, no study has yet been reported on the coupling behavior of p' and q' in 500 Hz band with swirl injection. Generally, swirl motion in a pipe flow enhances the heat transfer to the wall [10]. However, convective heat transfer in hybrid rocket combustion seems to have more complicated behavior because the fuel evaporation flow inside the boundary layer makes more complex turbulence characteristics. Combustion flow visualization is an effective way to directly investigate changes of both flow and heat release dynamics in hybrid rocket combustion. By combustion visualization, Obata et al. [11] have observed that the diffusion flame in the hybrid rocket combustion moves further to the fuel surface as the swirl intensity increases. And the shift of flame location will increase the convective heat transfer to the surface. Therefore, swirl injection not only modifies the flow structure of the main combustion chamber, but the convective heat transfer and turbulent flow structures in post combustion chamber. However, the effect of swirl injection on flame position, near surface flow and convective heat transfer is not well known. In this regard, POD (Proper Orthogonal Decomposition) through flow visualization seems a very suitable tool for analyzing the flow structure. Choi et al. [12] have successfully done POD analysis by visualizing combustion flow in the post chamber. As a result, they reported that the occurrence of LFI was closely related to the appearance of rotational flow motion. Thus, the main objective of this study is to understand the change in flow structure by swirl injection using POD technics. In the analysis, flow structures were decomposed into several dominating low-dimensional modes. And each mode would provide temporal and spatial behavior of fluctuating flow component when swirl injection was applied. Also, CH* chemiluminescence was used to visualize the combustion flow. Analyzing flow structure by combustion visualization may not be accurate enough to resolve very sensitive changes in flow fluctuation. However, previous results in Ref. [12] already proved that CH* chemiluminescence technics would provide sufficient accuracy in analyzing flow structures with low frequency characteristics in hybrid rocket. The change of photon emission was additionally monitored by PMT (Photo-Multiplier Tube) to measure the heat release oscillation.
Table 1 Summary of test configurations of each case. Test
Test 1
Injector
Axial injector
Swirl angle (degree) Main chamber length (mm) Post chamber length (mm) Mass flow rate (g/s) Remarks
0 400 105 20 Stable
Test 2
Test 3
Test 4
Swirl injector 0 400 75 20 LFI
7 400 75 20 Weak LFI
10 400 75 20 Stable
50%. In the test, Casio Ex-1 camera and photomultiplier tube (PMT) H10722 by Hamamatsu were used. Camera and PMT have the same shooting area. The operation of both devices was synchronized by event-based synchronization technique. Using LED as trigger, it can start to synchronize pressure measurement and image capturing process. Visualization was made in complete darkroom in order to minimize the noise in the PMT measurement. In addition, a band pass filter for 430 nm wavelengths was placed at the camera lens and PMT to clearly capture the heat release oscillations. Since this filter only passes through the wavelength of CH*, combustion heat release can be estimated. The shooting speed of the camera is 1200 fps sufficiently enough to measure any events with frequency characteristics up to 600 Hz. Details of visualization technics and post processing method including extraction of the light intensity from the captured images are well documented in reference [12]. Kitagawa [13] claimed that the regression rate increases with increasing number of LOx (liquid oxygen) injection holes and the crosssectional area. They also reported that the combustion can be stabilized when the swirl intensity is above a certain value. Thus, number of injection holes and injection speed can be possibly two factors controlling the swirl intensity. In another experimental study, Potchara [14] also observed that as the swirl intensity increases, the fuel regression rate increases. Takashi et al. [15] were conducted a series of experimental tests using PMMA and GOx as fuel and oxidizer. They found that as the swirl intensity increases by increasing the number of holes, the fuel regression rate increases. However, the increase in the regression rate did not produce a uniform increase in the axial direction but a biased increase limited to the front part of the fuel. In this study, the tests were carried out only with varying the swirl intensity while keeping all other conditions unchanged. The swirl intensity was increased using the injection angle from 0°, 7° to 10°. Fig. 2 shows schematics of an axial (Test 1) and swirl injector of 10° (Test 4). Rayleigh criterion is generally a mathematical tool for determining the coupling correlation between p' and q', which states that if p' and q' are in positive coupling, the combustion pressure is amplified by the coupling process [12]. The phase difference of the two fluctuations is a critical factor determining the physical correlation defined by equation (1). Mathematical formulation of the criterion can be expressed as
2. Combustion tests with swirl injection 2.1. Experimental setup A series of combustion test was conducted with a lab scale hybrid rocket motor of GOx (Gaseous Oxygen) and PMMA (Poly Methyl Meth Acrylate) combination. Solenoid and check valves were used to control oxidizer feeding. Oxidizer mass flow rate was controlled up to 40 g/sec by the mass flow controller. Nitrogen gas was used to purge after the combustion by PLC (Programmable Logic Controller) control. Piezotype sensors were installed to measure the combustion pressure. Pressure sensor is located in pre chamber. DAQ board and LabVIEW program were also implemented for data acquisition process. Table 1 summarizes details of test configurations and remarks of each case. In the tests, both axial injectors (Test 1, 2) and swirl injectors (Test 3, 4) were adopted. Test 1 is a stable combustion case and Test 2 represents the case of LFI. In tests 3 and 4, swirl injectors were used under the same test condition of Test 2 in which combustion instability was observed. Swirl angle in Test 4 was increased from 7° to 10° to control the swirl intensity. Fig. 1 shows the test setup for visualizing the combustion flow. One side of the main chamber was modified with quartz window for visualizing the combustion flow. The light from the combustion chamber was divided into two directions using special glass with a reflectance of
R=
1 T
T
∫ p′ (x, t )⋅q′ (x, t ) dt 0
(1)
Rayleigh criterion can determine two kinds of correlation; positive and negative coupling. In a positive coupling, the amplitude of combustion pressure gradually increases over time leading to combustion instability. On the other hand, the negative coupling is the case where the amplitude gradually decreases. Coupling status can be determined by evaluating the sign of Rayleigh index (RI). A transfer function F(f) is an effective way of estimating the phase angle ∅pq between p' and q'. Equation (2) defines the transfer function in the frequency domain, which is obtained by using FFT (Fast Fourier Transform) results for combustion pressure and luminosity time signals.
2
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Fig. 1. Experimental setup for (a) hybrid rocket combustion and (b) visualization.
F(f) =
(p′ / p ) = G (f )exp(j∅ (f ) ⎞⎟ (L′/ L ) ⎠
of p' and q' in 500 Hz band. This is the detailed description of frequency characteristics of p' and q' in 20 Hz band and in 500 Hz band in stable combustion. Fig. 5 shows the comparison of combustion pressure and heat release oscillations in Test 2, 3 and 4 as swirl intensity increases. As mentioned, Test 2 is the reference case, where an axial injection was used and LFI occurred. In this case, the maximum amplitude of LFI was measured at about 23% of the average pressure. As the swirl intensity increases, the maximum amplitude gradually decreased to 14.4% in Test 3 and eventually became a stable combustion only with 2.3% of the average pressure in Test 4. Note that a sudden amplification of combustion pressure and heat release fluctuation was completely suppressed in Test 4 and a stable combustion was achieved. Test results confirmed that combustion became stable by increasing the swirl intensity. Even though detailed mechanism is not completely understood, previous studies suggested that the generation of p' and q' in 500 Hz band could be linked with turbulent flow structures entering the post chamber, and the additional combustion of unburned fuel along the shear layer [2,3]. Fig. 6 compares FFT results of the frequency waterfall for p' and q' in 500 Hz band measured in Test 2, 3 and 4, as the swirl intensity increases. In all cases, the location of peak frequencies of p' and q' remained nearly at the same range of 420–480 Hz, even if swirl intensity increased. Fig. 7 shows the overlay and the phase difference between p' and q' in 500 Hz band in Test 2, 3 and 4 with increasing the swirl intensity. Also, the behavior of Rayleigh index for two fluctuations was compared. This comparison may enlarge the basic understanding how the swirl injection affects to stabilize unstable combustion. In Test 2 with an axial injection, two fluctuations of p' and q' in 500 Hz band shows little phase difference of less than π/2, so that two fluctuations are in a very strong positive coupling. With slight increase in swirl intensity in Test 3, even if the swirl is applied, the phase difference of two fluctuations is still less than π/2 and maintains a strong positive coupling. As can be seen at the bottom of Fig. 7, the evaluation of Rayleigh index for Tests 2 and 3 produces about 14–16 peaks per second. The appearance of RI peaks means that the pressure and the heat release
(2)
Here, p′ / p is the Fourier transform of pressure and L′/ L is that of luminosity. G(f) is the modulus or the transfer function gain, while ∅pq is its phase angle. And the positive coupling is defined as the case where the phase angle ∅pq is less than π/2. And a negative coupling is the case where ∅pq is larger than π/2. 2.2. Coupling behavior of p', q' by swirl injection In a recent study, two types of frequency characteristics were observed in the stable combustion of a hybrid rocket. These include a frequency band of 14–18 Hz associated with thermal lag of the fuel and the frequency characteristic in 450–500 Hz band with very small amplitudes. Fig. 3 shows a trajectory of combustion pressure and FFT results for the stable combustion with an axial injector (Test 1). In FFT results, a frequency peak in 20 Hz band is observed, and frequency peaks in 500 Hz band with very weak amplitudes are also observed discontinuously. In hybrid rocket, the occurrence of LFI is the result of physical resonance between the thermal lag closely related to the heat transfer characteristics of the solid fuel and the pressure oscillation of less than 100 Hz. Moon et al. [5] investigated the phase difference of p' and q' in 500 Hz band by using the combustion images in post combustion chamber. In their results, the two fluctuations were in a negative coupling at stable combustion and a positive coupling was found in an unstable combustion. Therefore, the coupling status and the occurrence of LFI seem to be physically related to each other. Lee et al. [4] also observed that Rayleigh index (RI) for p' and q' in 500 Hz band displayed about 14–18 peaks per second, when the LFI occurs. Therefore, they suggested that this may act as external disturbances perturbing the boundary layer resulting in LFI occurrence by mutual resonance. Fig. 4 shows the overlay of p' and q' in 20 Hz band and 500 Hz band respectively in stable combustion. As can be seen, since the phase difference is almost π/2, there is no clear correlation between p' and q' in 20 Hz band. This feature can be found in the overlay of the fluctuations
Fig. 2. Schematics of top and cross-section view of (a) axial and (b) swirl injector. 3
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Fig. 3. Trajectory of (a) combustion pressure oscillation and (b) FFT results in stable combustion (Test 1).
flow, flow characteristics in hybrid rocket are expected different from those in pipe flow. Nonetheless, when swirl injection is applied, a helical flow structure near the fuel surface is observed, which results in an increase in heat transfer to the solid. Fig. 8 shows the transition of peak frequency of p' and q' of 20 Hz band with increasing swirl intensity. In Test 2, the frequency peak of p' and q' locates at approximately 20 Hz, which is consistent with thermal lag frequency of the solid fuel. However, as the swirl intensity increased (Test 3), the frequency peak was shifted from 20 Hz to 30 Hz. In Test 4, where the swirl intensity was the highest, it can be seen that the frequency peak further increases and shifted to about 50 Hz band. It is believed that the swirl injection increases the convective heat transfer, which affects the thermal lag characteristics of the solid fuel and increases thermal lag frequency. In summary, the swirl injection of proper intensity changes the phase difference between p' and q' of 500 Hz band and leads to the transition of coupling status from positive to negative coupling. Thus, the transition to negative coupling appears to be a critical modification contributed by swirl injection to stabilize combustion. Another noticeable change is the gradual shift of peak frequency of p' and q' up to 50 Hz band from the initial 20 Hz band representing thermal lag frequency, as the swirl intensity increases. The direct comparison of visualization images with and without the swirl injection shows the differences in the flow pattern in post chamber. Fig. 9 compares time-averaged flame images of combustion visualization with and without the swirl injection. For baseline case (Test 1), the flame image displays a steady structure stretched in the axial direction, exhibiting a chamber-axis symmetric distribution, and gradually expands in the radial direction shortly after the inlet. However, in Test 4, the flame image shows a rounded shape of gradually expanding in the radial direction due to the influence of centrifugal force. Thus, the change in momentum distribution due to swirl injection in the main chamber significantly affects flame shape and turbulence structure in post chamber. Therefore, it is necessary to understand the
oscillations in 500 Hz band coincide with each other about 14–16 times per second, leading to the amplification of pressure fluctuations. However, as the swirl intensity increases further in Test 4, the phase difference between p' and q' becomes larger than π/2, and the coupling status of two fluctuations changes to a negative coupling. And the evaluation of Rayleigh index does not produce any resonance peaks at all. Fig. 7 (c) shows details of the change in phase difference and coupling status in Test 4. However, interesting physical changes are found in the comparison of the results of Test 3 with Test 4. In Test 3, the swirl intensity was not sufficiently strong enough to change the phase difference larger than π/ 2 leading to a negative coupling. Details of physical processes that change the phase difference have not been revealed yet. On the other hand, if the swirl intensity becomes strong enough as in Test 4, the coupling status between p' and q' transitions from positive to negative coupling as the phase difference increases by more than π/2. Also, no peaks are observed in the evaluation of Rayleigh index. Therefore, applying swirl injection of sufficient intensity, rather than applying simple swirl injection, can be a crucial factor in combustion stabilization, with which the coupling status of p' and q' of 500 Hz band shifts from positive to negative coupling. However, the criterion for determining how much is sufficient swirl intensity to stabilize unstable combustion has not been proposed yet. From this point of view, studying the change of flow structure using POD technique is expected to be able to provide a practical criterion for determining the sufficient swirl intensity for combustion stabilization. As mentioned, the occurrence of p' of 20 Hz band is the result of the amplification of thermal time lag of solid fuel to external perturbations, even though the type of external perturbations is not specified. Note that thermal lag is the physical time scale determined by the heat transfer and the thermal inertia of solid fuel. Thus, an increase in heat transfer may result in a change in thermal lag characteristics. It is well known that increasing the swirl intensity in the pipe flow increases the convective heat transfer [10]. However, because of the fuel evaporative
Fig. 4. Overlay of p' and q' in (a) 20 Hz band and (b) 500 Hz band in stable combustion (Test 1). 4
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Fig. 5. Comparison of combustion pressure and heat release oscillations in Test (a) 2, (b) 3 and (c) 4.
change in the flow structure in the main chamber by the swirl injection with increasing swirl intensity. In this regard, POD technique is a suitable tool to analyze the change of flow structure by the swirl injection.
2.3. Flow characteristics in the main chamber 2.3.1. POD analysis It is well known that POD is one of the most efficient tools to investigate complex turbulent flows with varying sizes of flow structures. In particular, POD is widely applied to the system with multi-scale structures such as turbulent flows and the chemical reactions in order to
Fig. 6. Frequency characteristics of p' and q' in 500 Hz band in Test (a) 2, (b) 3 and (c) 4. 5
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Fig. 7. Overlay, phase difference and Rayleigh index of p', q' in 500 Hz band in Test (a) 2, (b) 3 and (c) 4.
Fig. 8. Transition of frequency peaks of p' and q' in 20 Hz band in Test (a) 2, (b) 3 and (c) 4 with swirl injection.
understand the flow dynamics and the combustion characteristics. This technic generates an orthogonal basis function that can effectively describe given data set, for example visualized images in the present study. The derived orthogonal basis function, called as modes, can be
used to decompose the data set both spatially and temporally. POD is attractable as it can capture the dominant features of the data set with first few basis functions. Orthogonal basis can be found by firstly describing the given physical quantity q (x,t) as described in Eq. (3). 6
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Fig. 9. Comparison of flame raw images in stable combustion in Test (a) 1 and (b) 4. M
q(x, t) ≅ q0 +
∑ ai (t ) ϕi (x ) i=1
(3)
Here q(x, t), q 0, ai (t) , and ϕi (x) represent snapshots, time-averaged field, time coefficients, and spatial distribution of the i-th mode of the data set, respectively. Fluctuation is consisted of the sum of temporal coefficient and spatial distribution of total number of the modes, M. The number of mode M corresponds to either the number of data points per each snapshot, or the number of snapshots. Physically, mode 1 represents the average flow. Two or more modes represent the flow characteristics including perturbations. A detailed description of the method of POD analysis using flame visualization data is well documented in Ref. [11].
Fig. 10. Distribution of energy contents of each mode in Test 2.
2.3.2. POD analysis for flow field in the main chamber with axial injection The flow field in the main chamber was analyzed by POD technique to the image data set of the combustion visualization. The combustion visualization does not accurately represent the actual flow field, but it is assumed that the streak lines in the combustion images can be sufficiently approximate the flow changes and fluctuations. And this method was already proved as a very simple and efficient one for analyzing the characteristics of the flow field if the flow velocity was not so fast as in the hybrid rocket combustion [12]. The swirl injection in the main chamber alters the flow structure in terms of the axial flow velocity, helical velocity component near the wall, and small-sized vortices generation by interfering with the fuel vaporization flow. All of these are related to the increase in convective heat transfer and are physically important parameters that determine the flow and combustion characteristics in post chamber as well. In particular, the swirl injection is expected to significantly affect the formation of small-sized vortices and their shedding into the post chamber. Therefore, although the flow is reconstructed only in mode 1–5, the mode used for reconstruction involves most physically significant changes in the flow structure, and the analysis using the reconstructed flow is expected to provide sufficient information about the flow characteristics induced by swirl injection. Reference 11 shows an example of reconstructing the complex flow with modes 1 to 5 and analyzing the flow characteristics by applying the POD technique. Fig. 10 shows the distribution of energy levels of each mode up to mode 25 of the flow structure in Test 2 (with LFI). The energy level of mode 1 is about 33%, and the sum of energy of modes 1 to 5 is larger than 50% of the total. To understand the basic features of the internal combustion flow in Test 1 (stable combustion with axial injection), first 5 spatial modes are displayed in Fig. 11. The most dominant mode shall be the axial flow represented by mode 1. Considering the basic behavior of turbulent flows and the orderly arrangement of POD modes, mode 2 or higher
Fig. 11. POD images of mode 1 to 5 in Test 1 (Mode (a) 1, (b) 2, (c) 3, (d) 4, (e) 5).
represent smaller flow characteristics such as small vortices generated near the surface region or small flow structures dissipated from large scale structures. Fig. 11 shows the chamber-axis symmetric structures are observed in all modes because it is the flow of Test 1 with axial injection. Mode 2, in particular, represents a flow mode that is closely related to convective heat transfer. In this regard, Obata et al. [11] claimed that mode 2 flow is related to the formation of small-sized turbulent structures near the fuel surface and is a crucial mode for determining turbulent heat transfer characteristics. And it is analyzed that the flow structure of mode 3 or more is a flow mode in which the large turbulent structure is dissipated. On the other hand, since the time coefficient represents the temporal characteristic of each spatial mode, FFT analysis on the time coefficient can provide the frequency characteristic of the spatial mode. 7
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Fig. 12. FFT of time coefficients of mode 1, 2 in Test 1 ((a) 0–100 Hz, (b) 400–600 Hz).
observed in Test 1 is still found weakly in the frequency domain of Mode 2 of Test 2 where unstable combustion occurs. At this moment, the generation mechanism of fluctuations of the frequency is not clearly understood. Presumably, the physical process triggering the frequency peaks of 60 Hz band is related to the frequency band shift that has been occurred with the swirl injection.
In particular, we expect that FFT analysis on the time coefficient of mode 2 provide better understanding how the flow mode near the fuel surface changes by swirl injection. First of all, to understand the frequency characteristics of each flow mode in stable combustion, FFT analysis was done for the time coefficients of mode 1–5 in Test 1. For simple analysis, the frequency was divided into two regions; 0–100 Hz and 400–600 Hz region. Fig. 12 summarizes the temporal characteristics of each mode of 1, 2 in the two frequency regions. In mode 1, two consecutive frequency peaks are firstly observed near at 17 Hz and 25 Hz in the frequency region less 100 Hz and distinctive frequency peaks are also observed at around 430 Hz. Compared with Fig. 3, which displays the FFT analysis of the combustion pressure in Test 1, Fig. 12 shows very similar results. In Fig. 3, dominant frequency peaks are shown near at 14–18 Hz and very weak frequency peaks are also found near at 450–500 Hz. Interestingly, in frequency analysis of mode 2, the frequency peak is observed very weakly at around 60 Hz as well as around 20 Hz. However, in mode 3 and above, no frequency peaks are observed in both frequency regions. Note that frequency peaks of 16–18 Hz represents a frequency exhibited by the thermal lag of the fuel. And the turbulent flow containing the small vortices generated in the boundary layer of the main chamber shows the frequency characteristics of 500 Hz band [3]. However, when the LFI occurs, new frequency characteristics appear because the flow structure changes. Fig. 13 shows the FFT results of the time coefficients of modes 1, 2 in Test 2, where the LFI occurred. First of all, the frequency peak in mode 1 is approximately 15–30 Hz, very similar to the frequency peak measured in test 1, but amplified over a much wider range. This is the typical example of the resonating amplification of the heat transfer fluctuation due to the boundary layer adjustment to external disturbances and the thermal lag of the fuel. Interestingly, when unstable combustion occurs, a very strong frequency peak of 470–530 Hz is observed in mode 2, which is not observed in stable combustion. Considering that Mode 2 represents the boundary layer flow, the appearance of strong frequency peak at 470–530 Hz in Mode 2 implies that external disturbances with this frequency characteristic is interfering with the boundary layer flow. No other frequency peaks are observed in modes other than mode 1 and mode 2. However, the frequency of the very weak 60 Hz band
2.3.3. High frequency characteristics of flow mode by swirl injection Swirl injection has been reported to improve not only the fuel regression rate but also stabilizing the combustion by simply changing the flow from axial to rotational structure. Nevertheless, much research has not been done on why the swirl flow stabilizes the combustion. In this regard, it is particularly valuable to see how swirl injections have changed the boundary layer flow near the fuel surface. Fig. 14 compares the high frequency characteristics of FFT results for the time coefficients of modes 1 and 2, as the swirl intensity increases. Here the swirl intensity was controlled by the variation of injection angle from 7(Test 3) to 10° (Test 4). In FFT results of test 3, where the swirl intensity is weak, the frequency peaks in 450–485 Hz band are clearly seen in both modes 1 and 2. As mentioned, test 3 is a case where the combustion is not stabilized due to insufficient swirl strength even though swirl injection is applied. However, the swirl injection of sufficient intensity changes the phase difference of the pressure and combustion fluctuation of high frequency band and leads to combustion stabilization. Test 4 is the case where the swirl angle was increased to 10° and swirl intensity shows the max among the cases. From FFT results, Fig. 14 shows that the high-frequency characteristics almost disappeared both in modes 1 and 2. Therefore, it is believed that the swirl injection could significantly eliminate flow fluctuations having a frequency around 450 Hz band by changing the flow structure, and the high frequency peak disappeared eventually in modes 1 and 2 as the swirl intensity increased. Nevertheless, there is still a lack of understanding how swirl injection affects to change the combustion chamber flow including mode 1 and 2. Fig. 15 shows the comparison of the images of the instantaneous combustion flow in the main chamber as swirl intensity increases. Note that the combustion visualization does not exactly represent the actual flow field, but it is assumed that the streak lines in the combustion flow 8
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Fig. 13. FFT of time coefficients of mode 1, 2 in Test 2 ((a) 0–100 Hz, (b) 400–600 Hz).
can be sufficiently approximate the flow change by swirl injection. Reviewing the trajectory of the streak lines of Test 2, the axial flows is obviously dominant. In the trajectory image of Test 3, the flow upstream of the main chamber shows spiral trajectories due to swirl injection. However, since the swirl intensity gradually decreases toward the downstream, the flow trajectories recover to the axial ones and then enter the post chamber. In the previous discussion of Fig. 7, it was suggested that the combustion stability was not achieved in Test 3 due to insufficient swirl injection intensity. Nevertheless, the physical explanation of what sufficient swirl intensity is has not been addressed. In Fig. 15, we could suggest the definition of sufficient swirl intensity simply by comparing streak line images of Test 3 and 4. In Test 3, the occurrence of the LFI seems to be closely related to the flow conditions entering the post chamber. Reference [3] claimed that the primary
Fig. 15. Instant images of flow streak lines in Test (a) 2, (b) 3 and (c) 4.
source of pressure fluctuations of 500 Hz band is the introduction of turbulent flow containing small vortices into the post chamber. Therefore, despite the swirl injection, it can be assumed that when the
Fig. 14. FFT of time coefficients of mode 1–2 in Test (a) 3 and (b) 4 (400–600 Hz). 9
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recovered axial flow enters into the post chamber, p' and q' of 500 Hz band maintain positive coupling, leading to the occurrence of the LFI. The basis for this assumption can be seen in Fig. 15 (c), which shows the streak lines of Test 4. In other words, the streak line of Test 4 enters the post chamber while maintaining the helical trajectories to the end of the main chamber. As discussed in Fig. 7, the swirl injection brought about combustion stabilization only when the swirl component survived until the end of the chamber and entered the post chamber. Therefore, if these flow conditions are satisfied, it is known that the phase difference between p 'and q' of 500 Hz band is changed by the turbulent flow structure modified by the swirl injection, and the combustion stabilization is achieved.
turbulence characteristics of mode 2, which represents the boundary layer flow near the fuel surface but also by generating rotational velocity component in mode 1 representing the axial flow. As discussed in Fig. 7, Rayleigh index (RI) shows resonance peaks 14 to 18 per a second in unstable combustion by establishing positive couplings between p' and q' of 500 Hz band. And the appearance of RI resonance peaks may act as external perturbations by disturbing the boundary layer flow near the solid fuel. In this regard, the application of swirl injection induces to shift phase difference and changes to negative coupling between p' and q' of 500 Hz band suppressing the occurrence of LFI. Therefore, the swirl injection seems to bring about two very important changes related to combustion stabilization. The first is the increase of the thermal lag frequency due to the enhancement of the convective heat transfer, and the second is to suppress the occurrence of the resonance peak of RI by changing the phase difference between high frequencies p 'and q'. However, it is very difficult to conclude which of the two effects contributes more to combustion stabilization. Rather, it is believed that two effects such as an increase in the thermal lag frequency and the shift in the phase difference of the high frequency fluctuations contribute to the combustion stabilization at the same time.
2.3.4. Low frequency characteristics of flow mode by swirl injection As mentioned, the swirl injection increases the convective heat transfer near the fuel surface in hybrid rocket combustion. Obata et al. [11] visualized the main combustion chamber and investigated flow and flame behavior using POD method in hybrid rocket. In the results, they claimed that as the swirl intensity increases, the thickness of the diffusion flame increases in the boundary layer and thereby enhances the convective heat transfer. They also performed a frequency analysis on the time coefficient of flow mode 2 and found that the frequency peaks gradually increase as the swirl intensity increased. Note that mode 2 represents a turbulent flow in the boundary layer containing small size vortices. Therefore, the amplification of the frequency peaks with increasing swirl intensity leads to the increase in the convective heat transfer. As shown in Fig. 8, frequency peaks of 14–17 Hz in pressure fluctuations were always measured in all cases with axial injection regardless of the occurrence of LFI. Note that low-frequency peaks of 14–18 Hz band represents the frequency bands of thermal lag characteristic of the solid fuel. However, when the swirl injection is used, the peaks of the low frequency band are shifted due to the enhancement of the heat transfer. Fig. 16 shows the shift of low frequency peaks of mode 1 and 2 in Test 3 and 4 respectively. In mode 1 of Test 3, two distinctive frequency peaks of 12 Hz and 38 Hz are observed. And, the frequency peak in Test 4 shifted to around 50 Hz as the swirl intensity increased. Thus, we can suggest that the application of the swirl injection increases the thermal lag frequency not only by changing the
3. Conclusion The occurrence of LFI in hybrid rocket combustion is the result of physical resonance between the thermal lag closely related to the heat transfer characteristics of the solid fuel and the pressure perturbations in response to external disturbances in the boundary layer. Recent studies have shown that swirl oxidizer injection not only increases the regression rate but also significantly stabilizes combustion. In this study, a series of experimental tests has been done to investigate the effect of swirl injection on flow changes near the fuel surface and combustion stabilization by using combustion visualization technique and POD method. To this end, tests were designed only with varying the swirl intensity while keeping all other experimental conditions unchanged. As a result, the application of the swirl injection seems to significantly modify the two major physical processes responsible for the initiation of LFI. First modification is the change of the coupling status between two fluctuations of p' and q' of 500 Hz band to a negative coupling from a
Fig. 16. FFT of time coefficients of mode 1–2 in Test (a) 3 and (b) 4 (0–100 Hz). 10
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References
positive coupling by shifting the phase difference. In the results, the swirl injection with proper intensity contributes to shift the phase difference between p' and q' of 500 Hz band, and transits to a negative coupling. Therefore, the transition of p' and q' to a negative coupling by swirl injection seems to be a critical modification for stabilizing combustion. Another noticeable effect of swirl injection is the steady increase in the pressure oscillation frequency from its initial value of 20 Hz up to 50 Hz band, which is caused by the thermal lag, as the swirl intensity increases. To understand the effect of the flow change on the combustion stabilization with increasing swirl intensity, POD technique was also used on the visualization image data. FFT analysis on the time coefficients of flow modes in each image data set provides temporal information in terms of peak frequency location. Results of POD analysis show a qualitatively good agreement with both low- and high-frequency behavior of pressure fluctuations. The analysis of temporal behavior of mode 1 and 2 confirmed that the swirl injection with proper intensity possibly suppress the generation of p' of 500 Hz band. Also, the swirl injection induces a frequency shift from around 20 Hz–50 Hz band both in mode 1 and mode 2. This frequency shift is the result of heat transfer increase due to swirl injection. And this seems to be another contributing factor for combustion stabilization.
[1] M. Arif Karabeyoglu, D. Altman, Dynamics modeling of hybrid rocket combustion, J. Propul. Power 15 (1999) 562–571. [2] K. Park, C. Lee, Low frequency instability in laboratory-scale hybrid rocket motors, Aero. Sci. Technol. 42 (2015) 148–157. [3] D. Kim, C. Lee, De-stabilization of the shear layer in the post-chamber of a hybrid rocket, J. Mech. Sci. Technol. 30 (2016) 1671–1679. [4] D. Lee, Y.J. Moon, C. Lee, Equivalence ratio variation and pressure oscillations in the hybrid rocket combustion, 53rd AIAA Joint Propulsion Conference, 2017. [5] Y.J. Moon, C. Lee, Pressure oscillation and combustion in shear layer of hybrid rocket post chamber, 52nd AIAA Joint Propulsion Conference, 2016. [6] S. Yuasa, T. Ide, M. Masugi, T. Sakurai, N. Shiraishi, T. Shimada, Visualization of flames in combustion chamber of swirling-oxidizer-flow-type hybrid rocket engines, J. Therm. Sci. Technol. 6 (2011) 268–277. [7] N. Bellomo, F. Barato, M. Faenza, M. Lazzarin, A. Bettella, D. Pavarin, Numerical and experimental investigation of unidirectional vortex injection in hybrid rocket engines, J. Propul. Power 29 (2013) 1097–1113. [8] J.M. Pucci, The effects of swirl injector design on hybrid flame-holding combustion instability, 38th AIAA Joint Propulsion Conference & Exhibit, 2002. [9] J. Messineo, J. Lestrade, J. Hijlkema, J. Anthoine, 3D miles simulation of a hybrid rocket with swirl injection, Space Propulsion 2016 (2016). [10] M. Yilmaz, O. Comakli, S. Yapici, Enhancement of heat transfer by turbulent decaying swirl flow, J. Energ. Convers. Manag. 40 (1999) 1365–1376. [11] K. Obata, T. Shimada, K. Kitagawa, Imaging analysis of boundary layer combustion with tangential and radial oxidizer injection in a cylinder, 7th European Conference for Aeronautics and Space Sciences, Milan, 2017. [12] G.E. Choi, C. Lee, The change in flow dynamics inside the post chamber of hybrid rocket, J. Mech. Sci. Technol. 29 (2015) 4711–4718. [13] K. Kitagawa, T. Mitsutani, T. Ro, S. Yuasa, Effects of swirling liquid oxygen flow on combustion of a hybrid rocket engine, 40th AIAA Joint Propulsion Conference and Exhibit, 2004. [14] W. Potchara, D.R. Greatrix, Regression rate estimation for swirling-flow hybrid rocket engines, J. Propul. Power 32 (2016) 18–22. [15] T. Takashi, S. Yuasa, K. Yamamoto, Effects of swirling oxidizer flow on fuel regression rate of hybrid rocket, 35th Joint Propulsion Conference and Exhibit, 1999.
Acknowledgements This work was possible with financial supports by the National Research Foundation [NRF-2015R1D1A1A01058070] of the Republic of Korea.
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Contents lists available at ScienceDirect
Acta Astronautica journal homepage: www.elsevier.com/locate/actaastro
Transition of combustion instability in hybrid rocket by swirl injection Jungeun Kim, Changjin Lee∗ Department of Aerospace Engineering, Konkuk University, Seoul, 05029, South Korea
A R T I C LE I N FO
A B S T R A C T
Keywords: Low frequency instability Hybrid rocket Combustion visualization POD Positive coupling
A series of experimental tests was conducted to investigate the effect of swirl injection on the combustion instability in hybrid rocket using combustion visualization technique. As a result, swirl injection seems to modify two main physical processes responsible for the initiation of LFI. First one is the transition of coupling status between two fluctuations of combustion pressure (p') and heat release (q') of 500 Hz band. The transition of p' and q' to negative coupling seems to be a crucial modification for stabilizing the combustion. Another noticeable effect of swirl injection is the gradual increase in the peak frequency of pressure oscillation from its initial value of around 20 Hz–50 Hz band, which is caused by the thermal lag, as the swirl intensity increases. Also, POD (Proper Orthogonal Decomposition) analysis was done to understand flow response to the swirl injection near the fuel surface. The analysis of temporal behavior of mode 1 and 2 suggested that the swirl injection with proper intensity not only suppress the generation of p' of 500 Hz band but induces a shift of low frequency peaks of 20 Hz band by adjusting the turbulent structures in boundary layer. And the shift of low frequency peaks seems to be another contributing factor for combustion stabilization.
1. Introduction Hybrid rocket combustion displays nonlinear characteristics that produce low frequency instability (LFI), under which combustion pressure of less than 100 Hz is amplified at a certain condition. LFI is a manifestation of physical resonance between the thermal lag closely related to the heat transfer characteristics of the solid fuel and the pressure oscillation that occurs to response to external disturbances in the combustion boundary layer [1]. Recent studies reported that LFI accompanies a strong low frequency pressure oscillation of 20 Hz band and pressure oscillation of 500 Hz band with small amplitude [2]. Also, Kim et al. [3] suggested that the origin of pressure oscillation of 500 Hz band is the result of introducing small-sized vortex flow into the post chamber, which was formed by the mutual interference between the fuel evaporative flow and the axial oxidizer flow. Another study [4,5] using combustion visualization found very interesting results that the combustion reaction fluctuates at a frequency of about 500 Hz. They also found an interesting relation between combustion pressure oscillation (p') and heat release oscillation (q') of 500 Hz band. These two oscillations were confirmed to have a positive coupling of about 14–17 times per second, when the LFI occurred. The establishment of a positive coupling between p' and q' of 500 Hz band, in turn, seems the initiation mechanism of LFI through the resonance between the boundary layer adjustment and thermal delay of solid fuel.
∗
On the other hand, swirl injection is usually used to increase the regression rate of solid fuel in hybrid rocket combustion. Yuasa et al. [6] visualized the flame distribution and behavior when axial and swirl oxidizer injection was applied respectively to hybrid rocket combustion. Their results show that swirl injection induces helical velocity component near surface region whereas rotating component appears around the centerline. This helical velocity component enhanced convective heat transfer to solid fuel and increased regression rate. In recent studies, swirl oxidizer injection was found not only to increase the regression rate but also to stabilize combustion in a hybrid rocket. Bellomo et al. [7] reported that swirl injection could significantly reduce the amplitude of the combustion pressure oscillations compared to those with axial injection. Also, Pucci et al. [8] conducted an experimental study on the improvement of combustion stability by swirl injection. Their results show that the pressure fluctuations of 20 Hz and 600 Hz bands were amplified when the swirl intensity was less than a certain value or none. Messineo et al. [9] also performed similar study on the combustion instability using swirl injection. Their results showed that small-sized vortex generation and their shedding are reduced, when swirl injection is applied. And the reduction in vortex generation decreased the amplitude of the pressure fluctuations of 500 Hz band and to enhance combustion stabilization. Although many studies reported that swirl injection enhances combustion stabilization, detailed physics has not been investigated.
Corresponding author. E-mail addresses: [email protected] (J. Kim), [email protected] (C. Lee).
https://doi.org/10.1016/j.actaastro.2018.07.036 Received 25 January 2018; Received in revised form 12 June 2018; Accepted 21 July 2018 0094-5765/ © 2018 IAA. Published by Elsevier Ltd. All rights reserved.
Please cite this article as: Kim, J., Acta Astronautica (2018), https://doi.org/10.1016/j.actaastro.2018.07.036
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Meanwhile, Lee et al. [4] recently confirmed that the establishment of a positive coupling of p' and q' in 500 Hz band is the necessary condition for the LFI occurrence. Interestingly, it has been found that the establishment of a positive coupling occurs at specific O/F (oxidizer/fuel) ratios. However, no study has yet been reported on the coupling behavior of p' and q' in 500 Hz band with swirl injection. Generally, swirl motion in a pipe flow enhances the heat transfer to the wall [10]. However, convective heat transfer in hybrid rocket combustion seems to have more complicated behavior because the fuel evaporation flow inside the boundary layer makes more complex turbulence characteristics. Combustion flow visualization is an effective way to directly investigate changes of both flow and heat release dynamics in hybrid rocket combustion. By combustion visualization, Obata et al. [11] have observed that the diffusion flame in the hybrid rocket combustion moves further to the fuel surface as the swirl intensity increases. And the shift of flame location will increase the convective heat transfer to the surface. Therefore, swirl injection not only modifies the flow structure of the main combustion chamber, but the convective heat transfer and turbulent flow structures in post combustion chamber. However, the effect of swirl injection on flame position, near surface flow and convective heat transfer is not well known. In this regard, POD (Proper Orthogonal Decomposition) through flow visualization seems a very suitable tool for analyzing the flow structure. Choi et al. [12] have successfully done POD analysis by visualizing combustion flow in the post chamber. As a result, they reported that the occurrence of LFI was closely related to the appearance of rotational flow motion. Thus, the main objective of this study is to understand the change in flow structure by swirl injection using POD technics. In the analysis, flow structures were decomposed into several dominating low-dimensional modes. And each mode would provide temporal and spatial behavior of fluctuating flow component when swirl injection was applied. Also, CH* chemiluminescence was used to visualize the combustion flow. Analyzing flow structure by combustion visualization may not be accurate enough to resolve very sensitive changes in flow fluctuation. However, previous results in Ref. [12] already proved that CH* chemiluminescence technics would provide sufficient accuracy in analyzing flow structures with low frequency characteristics in hybrid rocket. The change of photon emission was additionally monitored by PMT (Photo-Multiplier Tube) to measure the heat release oscillation.
Table 1 Summary of test configurations of each case. Test
Test 1
Injector
Axial injector
Swirl angle (degree) Main chamber length (mm) Post chamber length (mm) Mass flow rate (g/s) Remarks
0 400 105 20 Stable
Test 2
Test 3
Test 4
Swirl injector 0 400 75 20 LFI
7 400 75 20 Weak LFI
10 400 75 20 Stable
50%. In the test, Casio Ex-1 camera and photomultiplier tube (PMT) H10722 by Hamamatsu were used. Camera and PMT have the same shooting area. The operation of both devices was synchronized by event-based synchronization technique. Using LED as trigger, it can start to synchronize pressure measurement and image capturing process. Visualization was made in complete darkroom in order to minimize the noise in the PMT measurement. In addition, a band pass filter for 430 nm wavelengths was placed at the camera lens and PMT to clearly capture the heat release oscillations. Since this filter only passes through the wavelength of CH*, combustion heat release can be estimated. The shooting speed of the camera is 1200 fps sufficiently enough to measure any events with frequency characteristics up to 600 Hz. Details of visualization technics and post processing method including extraction of the light intensity from the captured images are well documented in reference [12]. Kitagawa [13] claimed that the regression rate increases with increasing number of LOx (liquid oxygen) injection holes and the crosssectional area. They also reported that the combustion can be stabilized when the swirl intensity is above a certain value. Thus, number of injection holes and injection speed can be possibly two factors controlling the swirl intensity. In another experimental study, Potchara [14] also observed that as the swirl intensity increases, the fuel regression rate increases. Takashi et al. [15] were conducted a series of experimental tests using PMMA and GOx as fuel and oxidizer. They found that as the swirl intensity increases by increasing the number of holes, the fuel regression rate increases. However, the increase in the regression rate did not produce a uniform increase in the axial direction but a biased increase limited to the front part of the fuel. In this study, the tests were carried out only with varying the swirl intensity while keeping all other conditions unchanged. The swirl intensity was increased using the injection angle from 0°, 7° to 10°. Fig. 2 shows schematics of an axial (Test 1) and swirl injector of 10° (Test 4). Rayleigh criterion is generally a mathematical tool for determining the coupling correlation between p' and q', which states that if p' and q' are in positive coupling, the combustion pressure is amplified by the coupling process [12]. The phase difference of the two fluctuations is a critical factor determining the physical correlation defined by equation (1). Mathematical formulation of the criterion can be expressed as
2. Combustion tests with swirl injection 2.1. Experimental setup A series of combustion test was conducted with a lab scale hybrid rocket motor of GOx (Gaseous Oxygen) and PMMA (Poly Methyl Meth Acrylate) combination. Solenoid and check valves were used to control oxidizer feeding. Oxidizer mass flow rate was controlled up to 40 g/sec by the mass flow controller. Nitrogen gas was used to purge after the combustion by PLC (Programmable Logic Controller) control. Piezotype sensors were installed to measure the combustion pressure. Pressure sensor is located in pre chamber. DAQ board and LabVIEW program were also implemented for data acquisition process. Table 1 summarizes details of test configurations and remarks of each case. In the tests, both axial injectors (Test 1, 2) and swirl injectors (Test 3, 4) were adopted. Test 1 is a stable combustion case and Test 2 represents the case of LFI. In tests 3 and 4, swirl injectors were used under the same test condition of Test 2 in which combustion instability was observed. Swirl angle in Test 4 was increased from 7° to 10° to control the swirl intensity. Fig. 1 shows the test setup for visualizing the combustion flow. One side of the main chamber was modified with quartz window for visualizing the combustion flow. The light from the combustion chamber was divided into two directions using special glass with a reflectance of
R=
1 T
T
∫ p′ (x, t )⋅q′ (x, t ) dt 0
(1)
Rayleigh criterion can determine two kinds of correlation; positive and negative coupling. In a positive coupling, the amplitude of combustion pressure gradually increases over time leading to combustion instability. On the other hand, the negative coupling is the case where the amplitude gradually decreases. Coupling status can be determined by evaluating the sign of Rayleigh index (RI). A transfer function F(f) is an effective way of estimating the phase angle ∅pq between p' and q'. Equation (2) defines the transfer function in the frequency domain, which is obtained by using FFT (Fast Fourier Transform) results for combustion pressure and luminosity time signals.
2
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Fig. 1. Experimental setup for (a) hybrid rocket combustion and (b) visualization.
F(f) =
(p′ / p ) = G (f )exp(j∅ (f ) ⎞⎟ (L′/ L ) ⎠
of p' and q' in 500 Hz band. This is the detailed description of frequency characteristics of p' and q' in 20 Hz band and in 500 Hz band in stable combustion. Fig. 5 shows the comparison of combustion pressure and heat release oscillations in Test 2, 3 and 4 as swirl intensity increases. As mentioned, Test 2 is the reference case, where an axial injection was used and LFI occurred. In this case, the maximum amplitude of LFI was measured at about 23% of the average pressure. As the swirl intensity increases, the maximum amplitude gradually decreased to 14.4% in Test 3 and eventually became a stable combustion only with 2.3% of the average pressure in Test 4. Note that a sudden amplification of combustion pressure and heat release fluctuation was completely suppressed in Test 4 and a stable combustion was achieved. Test results confirmed that combustion became stable by increasing the swirl intensity. Even though detailed mechanism is not completely understood, previous studies suggested that the generation of p' and q' in 500 Hz band could be linked with turbulent flow structures entering the post chamber, and the additional combustion of unburned fuel along the shear layer [2,3]. Fig. 6 compares FFT results of the frequency waterfall for p' and q' in 500 Hz band measured in Test 2, 3 and 4, as the swirl intensity increases. In all cases, the location of peak frequencies of p' and q' remained nearly at the same range of 420–480 Hz, even if swirl intensity increased. Fig. 7 shows the overlay and the phase difference between p' and q' in 500 Hz band in Test 2, 3 and 4 with increasing the swirl intensity. Also, the behavior of Rayleigh index for two fluctuations was compared. This comparison may enlarge the basic understanding how the swirl injection affects to stabilize unstable combustion. In Test 2 with an axial injection, two fluctuations of p' and q' in 500 Hz band shows little phase difference of less than π/2, so that two fluctuations are in a very strong positive coupling. With slight increase in swirl intensity in Test 3, even if the swirl is applied, the phase difference of two fluctuations is still less than π/2 and maintains a strong positive coupling. As can be seen at the bottom of Fig. 7, the evaluation of Rayleigh index for Tests 2 and 3 produces about 14–16 peaks per second. The appearance of RI peaks means that the pressure and the heat release
(2)
Here, p′ / p is the Fourier transform of pressure and L′/ L is that of luminosity. G(f) is the modulus or the transfer function gain, while ∅pq is its phase angle. And the positive coupling is defined as the case where the phase angle ∅pq is less than π/2. And a negative coupling is the case where ∅pq is larger than π/2. 2.2. Coupling behavior of p', q' by swirl injection In a recent study, two types of frequency characteristics were observed in the stable combustion of a hybrid rocket. These include a frequency band of 14–18 Hz associated with thermal lag of the fuel and the frequency characteristic in 450–500 Hz band with very small amplitudes. Fig. 3 shows a trajectory of combustion pressure and FFT results for the stable combustion with an axial injector (Test 1). In FFT results, a frequency peak in 20 Hz band is observed, and frequency peaks in 500 Hz band with very weak amplitudes are also observed discontinuously. In hybrid rocket, the occurrence of LFI is the result of physical resonance between the thermal lag closely related to the heat transfer characteristics of the solid fuel and the pressure oscillation of less than 100 Hz. Moon et al. [5] investigated the phase difference of p' and q' in 500 Hz band by using the combustion images in post combustion chamber. In their results, the two fluctuations were in a negative coupling at stable combustion and a positive coupling was found in an unstable combustion. Therefore, the coupling status and the occurrence of LFI seem to be physically related to each other. Lee et al. [4] also observed that Rayleigh index (RI) for p' and q' in 500 Hz band displayed about 14–18 peaks per second, when the LFI occurs. Therefore, they suggested that this may act as external disturbances perturbing the boundary layer resulting in LFI occurrence by mutual resonance. Fig. 4 shows the overlay of p' and q' in 20 Hz band and 500 Hz band respectively in stable combustion. As can be seen, since the phase difference is almost π/2, there is no clear correlation between p' and q' in 20 Hz band. This feature can be found in the overlay of the fluctuations
Fig. 2. Schematics of top and cross-section view of (a) axial and (b) swirl injector. 3
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Fig. 3. Trajectory of (a) combustion pressure oscillation and (b) FFT results in stable combustion (Test 1).
flow, flow characteristics in hybrid rocket are expected different from those in pipe flow. Nonetheless, when swirl injection is applied, a helical flow structure near the fuel surface is observed, which results in an increase in heat transfer to the solid. Fig. 8 shows the transition of peak frequency of p' and q' of 20 Hz band with increasing swirl intensity. In Test 2, the frequency peak of p' and q' locates at approximately 20 Hz, which is consistent with thermal lag frequency of the solid fuel. However, as the swirl intensity increased (Test 3), the frequency peak was shifted from 20 Hz to 30 Hz. In Test 4, where the swirl intensity was the highest, it can be seen that the frequency peak further increases and shifted to about 50 Hz band. It is believed that the swirl injection increases the convective heat transfer, which affects the thermal lag characteristics of the solid fuel and increases thermal lag frequency. In summary, the swirl injection of proper intensity changes the phase difference between p' and q' of 500 Hz band and leads to the transition of coupling status from positive to negative coupling. Thus, the transition to negative coupling appears to be a critical modification contributed by swirl injection to stabilize combustion. Another noticeable change is the gradual shift of peak frequency of p' and q' up to 50 Hz band from the initial 20 Hz band representing thermal lag frequency, as the swirl intensity increases. The direct comparison of visualization images with and without the swirl injection shows the differences in the flow pattern in post chamber. Fig. 9 compares time-averaged flame images of combustion visualization with and without the swirl injection. For baseline case (Test 1), the flame image displays a steady structure stretched in the axial direction, exhibiting a chamber-axis symmetric distribution, and gradually expands in the radial direction shortly after the inlet. However, in Test 4, the flame image shows a rounded shape of gradually expanding in the radial direction due to the influence of centrifugal force. Thus, the change in momentum distribution due to swirl injection in the main chamber significantly affects flame shape and turbulence structure in post chamber. Therefore, it is necessary to understand the
oscillations in 500 Hz band coincide with each other about 14–16 times per second, leading to the amplification of pressure fluctuations. However, as the swirl intensity increases further in Test 4, the phase difference between p' and q' becomes larger than π/2, and the coupling status of two fluctuations changes to a negative coupling. And the evaluation of Rayleigh index does not produce any resonance peaks at all. Fig. 7 (c) shows details of the change in phase difference and coupling status in Test 4. However, interesting physical changes are found in the comparison of the results of Test 3 with Test 4. In Test 3, the swirl intensity was not sufficiently strong enough to change the phase difference larger than π/ 2 leading to a negative coupling. Details of physical processes that change the phase difference have not been revealed yet. On the other hand, if the swirl intensity becomes strong enough as in Test 4, the coupling status between p' and q' transitions from positive to negative coupling as the phase difference increases by more than π/2. Also, no peaks are observed in the evaluation of Rayleigh index. Therefore, applying swirl injection of sufficient intensity, rather than applying simple swirl injection, can be a crucial factor in combustion stabilization, with which the coupling status of p' and q' of 500 Hz band shifts from positive to negative coupling. However, the criterion for determining how much is sufficient swirl intensity to stabilize unstable combustion has not been proposed yet. From this point of view, studying the change of flow structure using POD technique is expected to be able to provide a practical criterion for determining the sufficient swirl intensity for combustion stabilization. As mentioned, the occurrence of p' of 20 Hz band is the result of the amplification of thermal time lag of solid fuel to external perturbations, even though the type of external perturbations is not specified. Note that thermal lag is the physical time scale determined by the heat transfer and the thermal inertia of solid fuel. Thus, an increase in heat transfer may result in a change in thermal lag characteristics. It is well known that increasing the swirl intensity in the pipe flow increases the convective heat transfer [10]. However, because of the fuel evaporative
Fig. 4. Overlay of p' and q' in (a) 20 Hz band and (b) 500 Hz band in stable combustion (Test 1). 4
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Fig. 5. Comparison of combustion pressure and heat release oscillations in Test (a) 2, (b) 3 and (c) 4.
change in the flow structure in the main chamber by the swirl injection with increasing swirl intensity. In this regard, POD technique is a suitable tool to analyze the change of flow structure by the swirl injection.
2.3. Flow characteristics in the main chamber 2.3.1. POD analysis It is well known that POD is one of the most efficient tools to investigate complex turbulent flows with varying sizes of flow structures. In particular, POD is widely applied to the system with multi-scale structures such as turbulent flows and the chemical reactions in order to
Fig. 6. Frequency characteristics of p' and q' in 500 Hz band in Test (a) 2, (b) 3 and (c) 4. 5
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Fig. 7. Overlay, phase difference and Rayleigh index of p', q' in 500 Hz band in Test (a) 2, (b) 3 and (c) 4.
Fig. 8. Transition of frequency peaks of p' and q' in 20 Hz band in Test (a) 2, (b) 3 and (c) 4 with swirl injection.
understand the flow dynamics and the combustion characteristics. This technic generates an orthogonal basis function that can effectively describe given data set, for example visualized images in the present study. The derived orthogonal basis function, called as modes, can be
used to decompose the data set both spatially and temporally. POD is attractable as it can capture the dominant features of the data set with first few basis functions. Orthogonal basis can be found by firstly describing the given physical quantity q (x,t) as described in Eq. (3). 6
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Fig. 9. Comparison of flame raw images in stable combustion in Test (a) 1 and (b) 4. M
q(x, t) ≅ q0 +
∑ ai (t ) ϕi (x ) i=1
(3)
Here q(x, t), q 0, ai (t) , and ϕi (x) represent snapshots, time-averaged field, time coefficients, and spatial distribution of the i-th mode of the data set, respectively. Fluctuation is consisted of the sum of temporal coefficient and spatial distribution of total number of the modes, M. The number of mode M corresponds to either the number of data points per each snapshot, or the number of snapshots. Physically, mode 1 represents the average flow. Two or more modes represent the flow characteristics including perturbations. A detailed description of the method of POD analysis using flame visualization data is well documented in Ref. [11].
Fig. 10. Distribution of energy contents of each mode in Test 2.
2.3.2. POD analysis for flow field in the main chamber with axial injection The flow field in the main chamber was analyzed by POD technique to the image data set of the combustion visualization. The combustion visualization does not accurately represent the actual flow field, but it is assumed that the streak lines in the combustion images can be sufficiently approximate the flow changes and fluctuations. And this method was already proved as a very simple and efficient one for analyzing the characteristics of the flow field if the flow velocity was not so fast as in the hybrid rocket combustion [12]. The swirl injection in the main chamber alters the flow structure in terms of the axial flow velocity, helical velocity component near the wall, and small-sized vortices generation by interfering with the fuel vaporization flow. All of these are related to the increase in convective heat transfer and are physically important parameters that determine the flow and combustion characteristics in post chamber as well. In particular, the swirl injection is expected to significantly affect the formation of small-sized vortices and their shedding into the post chamber. Therefore, although the flow is reconstructed only in mode 1–5, the mode used for reconstruction involves most physically significant changes in the flow structure, and the analysis using the reconstructed flow is expected to provide sufficient information about the flow characteristics induced by swirl injection. Reference 11 shows an example of reconstructing the complex flow with modes 1 to 5 and analyzing the flow characteristics by applying the POD technique. Fig. 10 shows the distribution of energy levels of each mode up to mode 25 of the flow structure in Test 2 (with LFI). The energy level of mode 1 is about 33%, and the sum of energy of modes 1 to 5 is larger than 50% of the total. To understand the basic features of the internal combustion flow in Test 1 (stable combustion with axial injection), first 5 spatial modes are displayed in Fig. 11. The most dominant mode shall be the axial flow represented by mode 1. Considering the basic behavior of turbulent flows and the orderly arrangement of POD modes, mode 2 or higher
Fig. 11. POD images of mode 1 to 5 in Test 1 (Mode (a) 1, (b) 2, (c) 3, (d) 4, (e) 5).
represent smaller flow characteristics such as small vortices generated near the surface region or small flow structures dissipated from large scale structures. Fig. 11 shows the chamber-axis symmetric structures are observed in all modes because it is the flow of Test 1 with axial injection. Mode 2, in particular, represents a flow mode that is closely related to convective heat transfer. In this regard, Obata et al. [11] claimed that mode 2 flow is related to the formation of small-sized turbulent structures near the fuel surface and is a crucial mode for determining turbulent heat transfer characteristics. And it is analyzed that the flow structure of mode 3 or more is a flow mode in which the large turbulent structure is dissipated. On the other hand, since the time coefficient represents the temporal characteristic of each spatial mode, FFT analysis on the time coefficient can provide the frequency characteristic of the spatial mode. 7
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Fig. 12. FFT of time coefficients of mode 1, 2 in Test 1 ((a) 0–100 Hz, (b) 400–600 Hz).
observed in Test 1 is still found weakly in the frequency domain of Mode 2 of Test 2 where unstable combustion occurs. At this moment, the generation mechanism of fluctuations of the frequency is not clearly understood. Presumably, the physical process triggering the frequency peaks of 60 Hz band is related to the frequency band shift that has been occurred with the swirl injection.
In particular, we expect that FFT analysis on the time coefficient of mode 2 provide better understanding how the flow mode near the fuel surface changes by swirl injection. First of all, to understand the frequency characteristics of each flow mode in stable combustion, FFT analysis was done for the time coefficients of mode 1–5 in Test 1. For simple analysis, the frequency was divided into two regions; 0–100 Hz and 400–600 Hz region. Fig. 12 summarizes the temporal characteristics of each mode of 1, 2 in the two frequency regions. In mode 1, two consecutive frequency peaks are firstly observed near at 17 Hz and 25 Hz in the frequency region less 100 Hz and distinctive frequency peaks are also observed at around 430 Hz. Compared with Fig. 3, which displays the FFT analysis of the combustion pressure in Test 1, Fig. 12 shows very similar results. In Fig. 3, dominant frequency peaks are shown near at 14–18 Hz and very weak frequency peaks are also found near at 450–500 Hz. Interestingly, in frequency analysis of mode 2, the frequency peak is observed very weakly at around 60 Hz as well as around 20 Hz. However, in mode 3 and above, no frequency peaks are observed in both frequency regions. Note that frequency peaks of 16–18 Hz represents a frequency exhibited by the thermal lag of the fuel. And the turbulent flow containing the small vortices generated in the boundary layer of the main chamber shows the frequency characteristics of 500 Hz band [3]. However, when the LFI occurs, new frequency characteristics appear because the flow structure changes. Fig. 13 shows the FFT results of the time coefficients of modes 1, 2 in Test 2, where the LFI occurred. First of all, the frequency peak in mode 1 is approximately 15–30 Hz, very similar to the frequency peak measured in test 1, but amplified over a much wider range. This is the typical example of the resonating amplification of the heat transfer fluctuation due to the boundary layer adjustment to external disturbances and the thermal lag of the fuel. Interestingly, when unstable combustion occurs, a very strong frequency peak of 470–530 Hz is observed in mode 2, which is not observed in stable combustion. Considering that Mode 2 represents the boundary layer flow, the appearance of strong frequency peak at 470–530 Hz in Mode 2 implies that external disturbances with this frequency characteristic is interfering with the boundary layer flow. No other frequency peaks are observed in modes other than mode 1 and mode 2. However, the frequency of the very weak 60 Hz band
2.3.3. High frequency characteristics of flow mode by swirl injection Swirl injection has been reported to improve not only the fuel regression rate but also stabilizing the combustion by simply changing the flow from axial to rotational structure. Nevertheless, much research has not been done on why the swirl flow stabilizes the combustion. In this regard, it is particularly valuable to see how swirl injections have changed the boundary layer flow near the fuel surface. Fig. 14 compares the high frequency characteristics of FFT results for the time coefficients of modes 1 and 2, as the swirl intensity increases. Here the swirl intensity was controlled by the variation of injection angle from 7(Test 3) to 10° (Test 4). In FFT results of test 3, where the swirl intensity is weak, the frequency peaks in 450–485 Hz band are clearly seen in both modes 1 and 2. As mentioned, test 3 is a case where the combustion is not stabilized due to insufficient swirl strength even though swirl injection is applied. However, the swirl injection of sufficient intensity changes the phase difference of the pressure and combustion fluctuation of high frequency band and leads to combustion stabilization. Test 4 is the case where the swirl angle was increased to 10° and swirl intensity shows the max among the cases. From FFT results, Fig. 14 shows that the high-frequency characteristics almost disappeared both in modes 1 and 2. Therefore, it is believed that the swirl injection could significantly eliminate flow fluctuations having a frequency around 450 Hz band by changing the flow structure, and the high frequency peak disappeared eventually in modes 1 and 2 as the swirl intensity increased. Nevertheless, there is still a lack of understanding how swirl injection affects to change the combustion chamber flow including mode 1 and 2. Fig. 15 shows the comparison of the images of the instantaneous combustion flow in the main chamber as swirl intensity increases. Note that the combustion visualization does not exactly represent the actual flow field, but it is assumed that the streak lines in the combustion flow 8
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Fig. 13. FFT of time coefficients of mode 1, 2 in Test 2 ((a) 0–100 Hz, (b) 400–600 Hz).
can be sufficiently approximate the flow change by swirl injection. Reviewing the trajectory of the streak lines of Test 2, the axial flows is obviously dominant. In the trajectory image of Test 3, the flow upstream of the main chamber shows spiral trajectories due to swirl injection. However, since the swirl intensity gradually decreases toward the downstream, the flow trajectories recover to the axial ones and then enter the post chamber. In the previous discussion of Fig. 7, it was suggested that the combustion stability was not achieved in Test 3 due to insufficient swirl injection intensity. Nevertheless, the physical explanation of what sufficient swirl intensity is has not been addressed. In Fig. 15, we could suggest the definition of sufficient swirl intensity simply by comparing streak line images of Test 3 and 4. In Test 3, the occurrence of the LFI seems to be closely related to the flow conditions entering the post chamber. Reference [3] claimed that the primary
Fig. 15. Instant images of flow streak lines in Test (a) 2, (b) 3 and (c) 4.
source of pressure fluctuations of 500 Hz band is the introduction of turbulent flow containing small vortices into the post chamber. Therefore, despite the swirl injection, it can be assumed that when the
Fig. 14. FFT of time coefficients of mode 1–2 in Test (a) 3 and (b) 4 (400–600 Hz). 9
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recovered axial flow enters into the post chamber, p' and q' of 500 Hz band maintain positive coupling, leading to the occurrence of the LFI. The basis for this assumption can be seen in Fig. 15 (c), which shows the streak lines of Test 4. In other words, the streak line of Test 4 enters the post chamber while maintaining the helical trajectories to the end of the main chamber. As discussed in Fig. 7, the swirl injection brought about combustion stabilization only when the swirl component survived until the end of the chamber and entered the post chamber. Therefore, if these flow conditions are satisfied, it is known that the phase difference between p 'and q' of 500 Hz band is changed by the turbulent flow structure modified by the swirl injection, and the combustion stabilization is achieved.
turbulence characteristics of mode 2, which represents the boundary layer flow near the fuel surface but also by generating rotational velocity component in mode 1 representing the axial flow. As discussed in Fig. 7, Rayleigh index (RI) shows resonance peaks 14 to 18 per a second in unstable combustion by establishing positive couplings between p' and q' of 500 Hz band. And the appearance of RI resonance peaks may act as external perturbations by disturbing the boundary layer flow near the solid fuel. In this regard, the application of swirl injection induces to shift phase difference and changes to negative coupling between p' and q' of 500 Hz band suppressing the occurrence of LFI. Therefore, the swirl injection seems to bring about two very important changes related to combustion stabilization. The first is the increase of the thermal lag frequency due to the enhancement of the convective heat transfer, and the second is to suppress the occurrence of the resonance peak of RI by changing the phase difference between high frequencies p 'and q'. However, it is very difficult to conclude which of the two effects contributes more to combustion stabilization. Rather, it is believed that two effects such as an increase in the thermal lag frequency and the shift in the phase difference of the high frequency fluctuations contribute to the combustion stabilization at the same time.
2.3.4. Low frequency characteristics of flow mode by swirl injection As mentioned, the swirl injection increases the convective heat transfer near the fuel surface in hybrid rocket combustion. Obata et al. [11] visualized the main combustion chamber and investigated flow and flame behavior using POD method in hybrid rocket. In the results, they claimed that as the swirl intensity increases, the thickness of the diffusion flame increases in the boundary layer and thereby enhances the convective heat transfer. They also performed a frequency analysis on the time coefficient of flow mode 2 and found that the frequency peaks gradually increase as the swirl intensity increased. Note that mode 2 represents a turbulent flow in the boundary layer containing small size vortices. Therefore, the amplification of the frequency peaks with increasing swirl intensity leads to the increase in the convective heat transfer. As shown in Fig. 8, frequency peaks of 14–17 Hz in pressure fluctuations were always measured in all cases with axial injection regardless of the occurrence of LFI. Note that low-frequency peaks of 14–18 Hz band represents the frequency bands of thermal lag characteristic of the solid fuel. However, when the swirl injection is used, the peaks of the low frequency band are shifted due to the enhancement of the heat transfer. Fig. 16 shows the shift of low frequency peaks of mode 1 and 2 in Test 3 and 4 respectively. In mode 1 of Test 3, two distinctive frequency peaks of 12 Hz and 38 Hz are observed. And, the frequency peak in Test 4 shifted to around 50 Hz as the swirl intensity increased. Thus, we can suggest that the application of the swirl injection increases the thermal lag frequency not only by changing the
3. Conclusion The occurrence of LFI in hybrid rocket combustion is the result of physical resonance between the thermal lag closely related to the heat transfer characteristics of the solid fuel and the pressure perturbations in response to external disturbances in the boundary layer. Recent studies have shown that swirl oxidizer injection not only increases the regression rate but also significantly stabilizes combustion. In this study, a series of experimental tests has been done to investigate the effect of swirl injection on flow changes near the fuel surface and combustion stabilization by using combustion visualization technique and POD method. To this end, tests were designed only with varying the swirl intensity while keeping all other experimental conditions unchanged. As a result, the application of the swirl injection seems to significantly modify the two major physical processes responsible for the initiation of LFI. First modification is the change of the coupling status between two fluctuations of p' and q' of 500 Hz band to a negative coupling from a
Fig. 16. FFT of time coefficients of mode 1–2 in Test (a) 3 and (b) 4 (0–100 Hz). 10
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References
positive coupling by shifting the phase difference. In the results, the swirl injection with proper intensity contributes to shift the phase difference between p' and q' of 500 Hz band, and transits to a negative coupling. Therefore, the transition of p' and q' to a negative coupling by swirl injection seems to be a critical modification for stabilizing combustion. Another noticeable effect of swirl injection is the steady increase in the pressure oscillation frequency from its initial value of 20 Hz up to 50 Hz band, which is caused by the thermal lag, as the swirl intensity increases. To understand the effect of the flow change on the combustion stabilization with increasing swirl intensity, POD technique was also used on the visualization image data. FFT analysis on the time coefficients of flow modes in each image data set provides temporal information in terms of peak frequency location. Results of POD analysis show a qualitatively good agreement with both low- and high-frequency behavior of pressure fluctuations. The analysis of temporal behavior of mode 1 and 2 confirmed that the swirl injection with proper intensity possibly suppress the generation of p' of 500 Hz band. Also, the swirl injection induces a frequency shift from around 20 Hz–50 Hz band both in mode 1 and mode 2. This frequency shift is the result of heat transfer increase due to swirl injection. And this seems to be another contributing factor for combustion stabilization.
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Acknowledgements This work was possible with financial supports by the National Research Foundation [NRF-2015R1D1A1A01058070] of the Republic of Korea.
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