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Analysis of air inlet and fuel plenum behavior in a rotating detonation combustor
Accepted Manuscript Analysis of Air Inlet and Fuel Plenum Behavior in a Rotating Detonation Combustor Vijay Anand, Andrew St. George, Robert Driscoll, Ephraim Gutmark PII: DOI: Reference:
S0894-1777(15)00283-6 http://dx.doi.org/10.1016/j.expthermflusci.2015.10.007 ETF 8597
To appear in:
Experimental Thermal and Fluid Science
Received Date: Revised Date: Accepted Date:
14 July 2015 5 October 2015 6 October 2015
Please cite this article as: V. Anand, A. St. George, R. Driscoll, E. Gutmark, Analysis of Air Inlet and Fuel Plenum Behavior in a Rotating Detonation Combustor, Experimental Thermal and Fluid Science (2015), doi: http:// dx.doi.org/10.1016/j.expthermflusci.2015.10.007
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Analysis of Air Inlet and Fuel Plenum Behavior in a Rotating Detonation Combustor Vijay Anand, Andrew St. George, Robert Driscoll, Ephraim Gutmark Gas Dynamics and Propulsion Laboratory Department of Aerospace Engineering University of Cincinnati, OH 45221
Abstract The behavior of the oxidizer inlet and the fuel injection plenums during the operation of a Rotating Detonation Combustor (RDC) is studied using pressure sensors in the air injection gap, the fuel plenum, and in the combustor. Significant pressure feedback from the rotating detonation wave is observed in the air injection gap. Pressure feedback into the fuel plenum is relatively weaker. The average normalized cross-correlation between the pressure-time series in the air injection gap and within the combustor is greater than 0.3. The air injection gap has a considerable base sinusoidal oscillation in the same frequency range as a previously discovered waxing-and-waning instability in the combustor. The fundamental frequency in the air injection gap is the same as the RDC operation frequency for almost all test cases, indicating the high efficacy of the sensors in the air inlet to attain the operating frequency. Frequency analysis reveals notable spatial variation in the fuel plenum dynamics. The low frequency oscillation in the air injection gap is found to be constant at 235 (+/- 2.5) Hz for all the air flow rates and equivalence ratios tested. Nomenclature f Φ t R x y n N PC PA PF PRA PRF ff σ
frequency (Hz) equivalence ratio Time Normalized cross-correlation arbitrary first pressure-time series (bar) arbitrary second pressure-time series (bar) sample number maximum number of samples in a time series averaged combustor pressure during operation averaged air plenum pressure during operation (bar) averaged fuel plenum pressure during operation (bar) air injection pressure ratio during operation fuel injection pressure ratio during operation fundamental frequency (Hz) standard deviation
1
1. Introduction Detonation is a supersonic combustion wave distinguished by the coupling between a shock wave with the exothermic reaction zone behind it. This is in contrast to a deflagration wave which only travels at subsonic speeds. Across a detonation wave there is always a pressure rise due to the presence of the shock wave, while a deflagration wave always produces a slight pressure loss across it. This property of a detonation to produce an increase in pressure renders it useful in detonation combustors due to the theoretical increase in thermal efficiency that can be achieved [1]. Detonation combustors are mainly classified into Pulsed Detonation Combustors (PDC) and Rotating Detonation Combustors (RDC). RDCs are relatively more compact in size, and mechanically simpler than a PDC. Additionally, unlike PDCs, RDCs do not require valving to inject the fuel and the oxidizer. The reactant supply is continuous, and is combusted by an azimuthally travelling detonation wave inside the combustor. By virtue of the high frequency rotating detonation and the relatively lower pressure amplitude, the exit flow of an RDC is quasisteady and hence more amenable to turbine-integration, as opposed to the PDC which produces large fluctuations in pressure at the exit [2]. The above-mentioned advantages of an RDC over a PDC have been responsible for the increased scientific interest in an RDC in recent years. However, comparatively, the RDC is less developed than the PDC technologically. While several factors like the overall RDC geometry [3], combustor channel width variation [3], homogenous [3-7] and heterogeneous reactant mixtures [3,6,7], subcritical (un-choked) air injection [5,8], and back-pressurization [5,9] have been studied, there are significant facets of RDC operation that are yet to be investigated. Of considerable interest is the effect of the rotating detonation waves on the air and the fuel plenum. Numerical simulations by Schwer et al. [10] determined the presence of pressure feedback into the mixture plenum by the detonation wave, but mass feedback was not observed. Mixture plenum dynamics was found to be minimally affected by the height of the plenum. Fotia et al. [11] used shadowgraph in a two-dimensional RDC analogue to observe the effect of a detonation wave on the fuel plenum. Significant pressure feedback was observed from the detonation wave into the fuel plenum which was sufficient to temporarily disturb the fuel plenum dynamics by 200 microseconds. In addition to the original pressure wave manifested due to the detonation wave propagation, secondary pressure waves were also found to occur in the opposite direction in the two-dimensional setup. It was postulated that in an actual RDC, these secondary reflected pressure waves may cause significant interactions with the next detonation lap. Naples et al. [12] estimated the fuel injection velocity in an RDC by utilizing hot film anemometers and observed a noticeable decrease in velocity as the detonation wave passed through, indicating periodic local un-choking of the fuel supply by the detonation. While these studies confirm the pressure feedback exerted by the detonation on the fuel injection plenum, the three-dimensional spatial variation in fuel plenum dynamics has not been investigated. Rankin et al. [13] used pressure sensors in the air plenum to determine that higher air injection pressure ratios caused lower periodic pressure fluctuations in the plenum by the detonation wave. However, since the effect of 2
the detonation wave would be lesser in the air plenum when compared to the actual air injection gap, a better understanding of the detonation pressure feedback can be attained by instrumenting the actual air inlet. In this study, the pressure feedback by the detonation wave on the air injection gap, instead of the air plenum, is studied using three azimuthally-distributed piezoelectric sensors in the air inlet. Directly flush-mounted pressure sensors are prone to permanent failure due to the very high-temperature RDC environment [5], and hence recent research has concentrated on using Infinite Tube Pressure (ITP) [5,14] setups to evaluate the RDC operation. Hence, the sensors in the air inlet are also investigated for their efficacy in determining the RDC operating frequency. Three pressure sensors are also integrated into the fuel plenum to analyze the spatial variation in fuel plenum dynamics. In addition to the sensors in the air injection gap and the fuel plenum, the combustor annulus is also instrumented with three flush-mounted pressure sensors to evaluate the correlation between the sensors in different locations.
2. Experimental methodology The current study utilizes data collected from hydrogen-air RDC tests performed at the Gas Dynamics and Propulsion Laboratory (GDPL) at the University of Cincinnati. The facility is shown in Fig. 1. The modular RDC has radially inward air-injection and axial fuel injection (Fig. 2). Ignition is achieved with a pre-detonator tube filled with ethylene and oxygen [15], which exhausts tangentially into the annulus. Detonation develops briefly after the ignition event through a Deflagration-to-Detonation transition (DDT) mechanism [15]. The air injection width and the fuel injection scheme are varied with interchangeable combustor components. A detailed description of the different fuel injection schemes are dealt in [5]. For this study, the fuel plate with the highest number of orifices is used [5]. The combustor and air plenum are instrumented with a Capillary Tube Averaged Pressure (CTAP) sensor setup [16] to estimate the injection pressure drop from the air and fuel plenum to the RDC combustion annulus. A total of 9 PCB pressure sensors are instrumented in the RDC with a data acquisition rate of 1 MHz. The facility (Fig. 1) is described in detail by St. George et al. [16].
3
Figure 1: RDC facility at University of Cincinnati The general location of the piezoelectric sensor in the air injection gap (blue) and the fuel plenum (violet) is shown in Fig. 2. A schematic of the RDC instrumentation ports is given in Fig. 3. The combustor has 3 PCB (red) sensors (1, 2 and 3), separated by 120o and flush-mounted in the three stations in the first row of instrumentation port. To analyze the pressure feedback into the air inlet, 3 PCB sensors (4, 5 and 6) are instrumented in the air injection gap, ≈ 2.54 cm from the combustor. To study fuel plenum dynamics, 3 more PCB sensors (7, 8 and 9) are integrated at the base of the plenum (Fig. 3). The individual air inlet and fuel plenum PCB sensors are displaced by approximately 21o from the corresponding flush-mounted combustor PCB sensor (Fig. 3). Finally, a CTAP pressure sensor (orange circle) is placed in station 3, row 4 (Fig. 3) to get absolute pressure variations.
Figure 2: RDC schematic with the injection scheme
4
Figure 3: RDC instrumentation schematic The air flow rates and equivalence ratios tested are given in Table 1. In the remainder of the paper, individual tests will be denoted by the test number. For instance, test number II-B denotes an air flow rate of 0.3 kg/s and an equivalence ratio of Φ = 1.03. All testing is limited to t ≈ 0.3 second (hence a frequency resolution of 2.5 Hz) to avoid damage to the flush-mounted sensors due to prolonged exposure to the high temperature, high pressure environment. In addition to the qualitative study of the pressure-time traces, Fast-Fourier Transformation (FFT) is used to study the frequency of pressure feedback into the air inlet and fuel plenum. Crosscorrelation is also used to estimate the similarity of the pressure-time series obtained from sensors in different locations. Series
Air flow rate, kg/s
I II III
0.2 0.3 0.4
Equivalence ratios, Φ A B C 0.874 1.0 1.21 0.871 1.03 1.22 0.917 0.997 1.2
Table 1: Test Matrix
3. Results and Discussion 3.1. Pressure feedback into the air inlet and fuel plenum A study of the pressure feedback into the air injection gap and the fuel plenum can be done by juxtaposing the pressure-time trace with the associated flush-mounted combustor sensors. Fig. 4 shows the pressure-time traces in the flush mounted PCB sensor, air gap sensor, and the fuel plenum sensor respectively, for an arbitrary time interval for tests I-B and III-B. Fig. 4a and 4b shows the similarity between pressure magnitude (for test I-B) seen in the flush mount due to the detonation wave and the magnitude of pressure feedback experienced by the air injection gap 5
area due to the detonation wave in the combustor. It is to be noted that the reason behind the apparent higher pressure in the air inlet when compared to the combustor at certain time instances is due to the inherent property of the piezoelectric sensors to only record dynamics pressures while neglecting the steady component. The air inlet exhibits sinusoidal low-frequency pressure oscillations of significant magnitude (up to 0.5 bar fluctuation in Fig. 4b). For the same test point, the fuel plenum sensors record relatively lower pressure fluctuations, not exceeding 0.2 bar. This highlights the heightened impact of the detonation wave on the air inlet in comparison to the fuel plenum. Test III-B exhibits similar trends in pressure-time traces for the fuel plenum (Fig. 4f). While the pressure oscillations exceed to 0.4 bar now, they are consistently below the pressure fluctuations in the air inlet which extend up to 1 bar (Fig. 4e) for the 0.4 kg/s case. Fig. 4e shows the pressure-time trace at the air inlet and once again there are significant sinusoidal oscillations with frequency close to the prior condition, at f ≈ 230 Hz. Two features can be inferred about RDC operation from the above discussion. One, the air inlet experiences much higher pressure feedback when compared to the fuel plenum. Two, there is a strong low-frequency oscillation in the air inlet, even when the combustor has almost no oscillation at the same time.
(a)
(d)
(b)
(e)
6
(c)
(f)
Figure 4: Pressure-time traces of sensors 3 and 6 for I-B (left) and III-B (right)
3.2. Correlation of pressure-time traces The prior section is instrumental in deciphering easily observable trends in the pressure-time series. However, to get at the general pattern of air inlet and fuel plenum behavior at different air flow rates and equivalence ratios the method of cross-correlating the individual sensors with the respective flush-mounted combustor sensors is done using the following equation: R ,
∑ಿషభ సబ ಿషభ మ √ ∑సబ మ ∑ಿషభ సబ
(1)
Here, and are the pressure-time series from the combustor sensors and the air inlet/ fuel plenum sensors respectively, each having n discrete samples, amounting to a maximum number of N. Fig. 5a shows a plot of the cross-correlation between sensors 3 and 6, for test III-C. It is a known fact that cross-correlation peaks when the two signals under consideration are identical to each other which is the case when one directly influences the other. Hence, from Fig. 5b, since the correlation coefficient is maximum at time, t ≈ 119 μs, it implies an almost instantaneously pressure feedback from the detonation wave into the air inlet.
(a)
(b)
Figure 5: Cross-correlation plot of sensors 3 and 6 for test III-C (a) and magnified plot (b)
7
A typical pressure trace from the CTAP sensor in the air and fuel plenum, and the combustor before and during RDC operation is shown in Fig. 6. The air supply (green line) is continuous, but the fuel supply (blue line) starts only at time t ≈ -1.7 s. Ignition from the pre-detonator is initiated at t = 0 s, and the increase in pressure in the combustor during operation can be seen (red line). The combustor pressure during operation (PC) is defined as the average pressure in the RDC for 0.3 s after initiation. The air plenum pressure during operation (PA) and the fuel plenum pressure during operation (PF) are defined similarly. The air injection pressure ratio and the fuel injection pressure ratio can thus be acquired from CTAP sensors using PC, PA and PF. PRA = PA / PC PRF = PF / PC
(2) (3)
The combustor pressure during operation reaches a maximum of 1.2 bar (+/- 0.028) for test III-A, but is relatively low for all the other tests (Fig. 7). Uncertainty is calculated from 1σ value of the pressure-time series. The pressure rise due to detonation in the combustor is higher at the higher flow rate of 0.4 kg/s and decreases to around 1.05 bar (+/- 0.027) and 1.02 bar (+/0.02) for the lower flow rates of 0.3 kg/s and 0.2 kg/s, respectively, as seen in Fig. 7. There is also a slight increase in pressure with an increase in equivalence ratio with the exception of test III-A. The above two observations infer that the combustor pressure during operation (Pc) has a strong dependence on air flow rate and a lower dependence on equivalence ratio. Air plenum Fuel Combustor P PF
PC
Fuel supply Air supply
Figure 6: Correlation coefficient for air inlet - sensors 3 and 6 (left) III-C
8
Combustor pressure during operation, Pc (bar)
1.25 1.2 1.15 1.1 1.05 1 0.95 0.8
0.9
1
1.1
1.2
1.3
Equivalence ratio, Φ 0.2 kg/s
0.4 kg/s
0.3 kg/s
Figure 7: Combustor pressure during operation vs. equivalence ratio
3.5 3 2.5 2 1.5 0.8
0.9
1
1.1
1.2
1.3
Equivalence ratio, Φ 0.2 kg/s
0.3 kg/s
0.4 kg/s
Fuel injection pressure ratio
Air injection pressure ratio
The air injection pressure ratio, PRA (Fig. 8) remains relatively unaltered with equivalence ratio for test points other than test III-A. The fuel injection pressure ratio, PRF, has a stronger dependence on equivalence ratio and increases notably for higher equivalence ratios. Error in injection pressure ratios is calculated by linear sensitivity analysis of the obtained PC, PA and PF, for 1σ, and is found to be negligible. 3.5 3 2.5 2 1.5 1 0.8
0.9
1
1.1
1.2
1.3
Equivalence ratio, Φ 0.2 kg/s
0.3 kg/s
0.4 kg/s
Figure 8: Air injection pressure ratio (left), and fuel injection pressure ratio (right) When the combustor flush-mounted sensors 2 and 3 are cross-correlated among themselves, they show poor correlation despite being in the same generic location of the RDC annulus. The correlations are, on an average, 0.24 for all 9 tests, which is very low. This indicates a considerable spatial variation in the strength of detonation wave, the exact reasons to which are currently unknown. The correlation coefficients for the sensor pairs 1 and 4, 2 and 5, and 3 and 6 (combustor sensor with the air inlet sensor) have similar trends. Hence, for brevity, only the 9
Correlation coefficient
sensor pair of 3 and 6 is going to be discussed, since it consistently has a higher correlation. Overall, the cross-correlation coefficient for the pair of 3 and 6 does not exceed 0.55 which may be a result of the high-amplitude low frequency oscillation in the air inlet skewing the correlation. It is to be noted that this value is still considerably higher than the correlation among different sensors in the combustor itself. At higher flow rates, the pressure ratio across the air injection gap increases. Hence, it makes sense for correlation between the air inlet and the combustor to reduce with increase in air flow rate since a higher air plenum pressure would act against the pressure feedback from the detonation wave (Fig. 9). Like the air inlet analysis, fuel plenum analysis only deals with the sensor pair of 3 and 9 (combustor sensor with the fuel plenum sensor). The correlation coefficient is higher at increased PRF for flow rates of 0.2 kg/s and 0.3 kg/s (Fig. 10) which could be attributed to the higher plenum pressure acting against the pressure feedback from the detonation wave. However, for 0.4 kg/s the correlation increases with increased PRF which may be suggestive of the detonation wave being strong enough to counteract the higher fuel plenum pressure. 0.6 0.5 0.4 0.3 0.2 0.1 0 1.5
2
2.5
3
3.5
Air injection pressure ratio
0.2
0.3
0.4
Correlation coefficient
Figure 9: Correlation coefficient for air inlet - sensors 3 and 6 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 1.5
2
2.5
3
3.5
Fuel injection pressure ratio
0.2
0.3
0.4
Figure 10: Correlation coefficient for fuel plenum - 3 and 9
10
3.3. Frequency analysis 3.3.1. Comparative study Frequency analysis of the pressure-time traces has the potential to reveal interesting characteristics of the different sensors that cannot be observed from pressure-time traces and correlations. The fundamental frequencies obtained from the FFT analysis are assembled for the combustor, air inlet and fuel plenum sensors (Table. 2). If the fundamental frequency, ff, in the air inlet or the fuel plenum is different from the operating frequency in the combustor by 10% or more, the cell is colored yellow in contrast to the green-colored cells of the table which indicate a lesser than 10% difference from the ff obtained from the combustor. It can be seen that the ff is the same as the operating frequency for most of the air inlet and fuel plenum sensors. Only test III-A has a different fundamental frequency in the air inlet and fuel plenum in comparison to the combustor. However, it is to be noted that, for certain tests, one or two of the fuel plenum sensors out of the three had a different ff from the operating frequency of the RDC. This suggests a spatial variation in fuel plenum dynamics. But, all the air inlet sensors always registered the same ff irrespective of the operating point. Since the ff in the air inlet sensors and the combustor matches exactly for the eight of the nine tests conducted, the strong efficacy of the air inlet sensors in determining the operating frequency of the RDC at all regions except at the lean operating boundary is established.
Test I-A
Combustor ff (Hz) 2942
Air inlet ff (Hz) 2942
Fuel plenum ff (Hz) 2942
I-B
3042
3042
3042
I-C
3100
3080
3100
II- A
2935
2935
2935
II- B
3045
3045
3045
II- C
3143
3055
3122
III- A
1705
235
2705
III- B
3643
3645
3642
III- C
3755
3755
3760
Table 2: Fundamental frequencies in the combustor, air inlet and the fuel plenum
3.3.2. Fuel plenum 11
The frequency response of the RDC fuel plenum has been studied previously by Naples et al. [12]. But, that study only used one sensor in the plenum which precludes spatial analysis of the plenum. Since the current study uses three piezoelectric sensors in the fuel plenum, an FFT analysis could further the study on fuel plenum by observing the spatial response in the plenum to the rotating detonation wave in the combustor. Fig. 11 shows the FFT plot for the fuel plenum sensors 8 and 9 for tests I-B (Fig. 11a, 11b), II-B (Fig. 11c, 11d) and III-B (Fig. 11e, 11f). The plots show a notable difference in the ff experienced by each sensor, which is an indicant of considerable spatial variation in the fuel plenum dynamics. This may be due to the detonation wave varying in strength as it propagates through the annulus (as inferred previously by the poor correlation between two combustor sensors for all tests), or a complex pressure wave interaction due to reflection within the fuel plenum, or a combination of both. A similar hypothesis was arrived at by Fotia et al. due to the fuel jet being deflected in a direction opposite to the detonation wave propagation direction, in their 2D setup [11]. It is unclear at present if the spatial variation in plenum dynamics causes a detonation wave of varying strength in the combustor, or vice versa.
(a)
(b)
(c)
(d)
(e)
(f) 12
Figure 11: FFT plots for fuel plenum sensors 8 (left) and 9 (right) for test I-B, II-B and III-B
3.3.3 Air inlet oscillations Pressure-time traces from the prior section led to the discovery of low-frequency oscillations of considerable amplitude in the air inlet. A similar low-frequency component was experimentally discovered in the combustor annulus by the authors [17], but that instability did not have any notable trend with changes in air flow rate or equivalence ratio. It is thus desirable to try to analyze the oscillation in the air inlet and compare it to the previously discovered oscillation in the combustor. This led to an investigation of the oscillation for all the tests. Fig. 12a, 12b and 12c show the FFT plot for three stoichiometric test cases, i.e. tests I-B, II-B and IIIB. While the ff (also the operation frequency as discussed in the previous section) is easily observable from the three plots at f ≈ 3 kHz, f ≈ 3 kHz and f ≈ 3.8 kHz respectively, there is also considerable activity in all three test cases at f ≤ 0.5 kHz. The secondary dominant frequency is identified to be f ≈ 235 Hz (shown by red circle) and is the same for all the three tests which have different air flow rates. When all the tests are analyzed for the oscillation frequency, it is found that the frequency of oscillation in the air inlet always centered on f ≈ 235 Hz for all the 9 tests. This is an interesting discovery since it implies that irrespective of the air flow rate or the equivalence ratio of the operating point, the inlet of the RDC in use for the current study always oscillates at f ≈ 235 Hz. The f ≈ 235 Hz oscillation (black arrow) does not extend throughout the test, but rather is sporadically occurring with time as shown by the spectrogram of tests I-B, II-B and III-B, in Fig. 12d, Fig. 12e and Fig. 12f respectively. To confirm that the oscillation is caused by the detonation wave and not due to an inherent oscillation in the air supply, the RDC was operated under cold-flow conditions without ignition of the reactants, which revealed the lack of any activity in the 235 Hz region. Since the cold flow RDC testing did not produce any oscillation at the same frequency, it can be understood that the oscillation in the air gap is linked to detonation wave propagation in the annulus. The Helmholtz frequency for the air plenum under study is estimated to be ≈ 355 Hz for all flow rates since the speed of sound is relatively unaltered due to an almost constant supply temperature. But, the complex geometry of the plenum would skew the resonance frequency obtained from the basic Helmholtz equation considerably [18]. For instance, a ≈ 15% error is incurred between the calculated and the experimentally obtained frequency when the basic Helmholtz equation is used to calculate the resonance frequency for a cylindrical prism with a long neck [18]. Hence, to get an accurate resonance frequency value, geometry-specific equations need to be developed, even for simple geometries. Despite these unknown variables, since the approximately estimated resonance frequency is different from the oscillation frequency in the inlet by only 33%, it is a strong indication of the air plenum’s functioning as a Helmholtz resonator due to the excitation produced by the high-frequency detonation wave in the combustor. It is hypothesized that the
13
detonation wave excites the air inlet to a resonance frequency which manifests as the waxing and waning detonation instability [17] in the combustor, due to the fluctuating air supply.
(a)
(d)
(b)
(e)
(c)
(f)
Figure 12: FFT plot (left) showing the fundamental low-frequency oscillation for I-B, II-B, III-B, and spectrogram (right) of the respective test points
4. Conclusion Rotating Detonation Combustor operation is analyzed at three air flow rates and three equivalence ratios for each of the air flow rate to study the pressure feedback from the rotating detonation wave onto the air inlet and fuel plenum. A total of nine dynamic piezoelectric sensors are used for the analysis, three each in the combustor, the air inlet and the fuel plenum. Pressuretime traces are studied for the air inlet and the fuel plenum and compared with the flush-mounted combustor sensors. For the most part, the pressure fluctuation in the air inlet is between 45% and 70% of the pressure fluctuation due to detonation passage in the combustor annulus. Pressure 14
fluctuations in the fuel plenum are significantly lower than that experienced by the air inlet, and is usually around 20% of the pressure fluctuation in the combustor. Additionally, low-frequency pressure oscillations of high amplitude are discovered in the air plenum. These oscillations are similar, and occur around the same time scale as the waxing and waning detonation instability observed in the same RDC in a prior study [17]. Cross-correlation between sensors in the combustor reveals very poor conformity of signal shape for all the tests run, thereby indication significant changes in detonation wave strength as it propagates azimuthally around the annulus. Cross-correlation reaches a maximum of 0.55 between air inlet sensors and the corresponding flush-mounted combustor sensors. The crosscorrelation coefficient does not exceed 0.35 for the fuel plenum sensors, indicating that the pressure feedback into the air inlet is higher in comparison to the fuel plenum. As a general trend, correlation decreases with increasing injection pressure ratios. Thus, higher injection pressure is required to reduce pressure feedback from the detonation wave, especially for the air inlet. It is found that the fundamental frequency recorded by all the air inlet sensors is exactly the same as the operating frequency of the RDC, found by the flush-mounted combustor sensors. Only at the very lean limits of operation do the air inlet sensors fail to pick up RDC operating frequency. This finding is of significant importance as it establishes that air inlet sensors are an extremely viable substitute to flush-mounted sensors in the actual combustor. Traditionally, pressure sensors used in the actual combustor have been prone to mechanical disintegration due to the high-pressure and high-temperature environment of the RDC [5]. Hence, some studies have used an Infinite Tube Pressure (ITP) setup [5,14] to analyze the RDC operating mode to avoid sensor damage. However, implementing pressure sensors in the air inlet can be an easier method to ascertain RDC operating modes without risking the destruction of the sensor. The three sensors in the fuel plenum have different fundamental frequencies for many of the test cases indicating strong spatial non-uniformity in the fuel plenum dynamics. The spatial nonuniformity may be a result of a change in the detonation wave strength as it propagates through the annulus, or may be due to complex interaction of the pressure wave from the detonation with already existing, reflected pressure waves from the walls of the plenum. Finally, the low frequency oscillation in the air gap is investigated for all the tests, and it’s found that the fundamental oscillation frequency in the air inlet is always ≈ 235 Hz. There is strong evidence to suggest that this is a manifestation of Helmholtz resonance in the air inlet. Further experimentation is required to clearly investigate the linkage, if any, between this low frequency oscillation in the air inlet and the waxing-and-waning detonation instability in the combustor.
References
15
[1]
[2]
[3] [4]
[5]
[6]
[7] [8]
[9]
[10]
[11]
[12]
[13]
Heiser, W., and Pratt, D., “Thermodynamic Cycle Analysis of Pulse Detonation Engines” Journal of Propulsion and Power, Vol. 18, No. 1, January-February 2002. Yi, T., Lou, J., Turangan, C., Choi, J., Wolanski, P., “Propulsive Performance of a Continuously Rotating Detonation Engine,” J. Propulsion and Power, Vol. 27, 2011, pp. 171-182. Bykovskii, F. A., Zhdan, S. A., Vedernikov, E. F., “Continuous Spin Detonations,” Journal of Propulsion and Power, 22(6), 2006, pp. 1204-1216. Shank, J., King, P., Karnesky, J., Schauer, F., Hoke, J., “Development and Testing of a Modular Rotating Detonation Engine,” 50th Aerospace Sciences Meeting, Nashville, Tennessee, AIAA 2012-0120. Anand, V., St. George, A., Driscoll, R., Gutmark, E., “Experimental Investigation of H2-Air Mixtures in a Rotating Detonation Combustor,” ASME Turbo Expo 2015, GT2015-43614, Canada, 2015. Falempin, F., Naour, B. L., “R&T Effort on Pulsed and Continuous Detonation Wave Engines,” 16th International Space Planes and Hypersonic Systems and Technologies Conference, AIAA 2009-7284. Wolanski, P., “Detonative propulsion,” Proceedings of the Combustion Institute, Vol. 34, 2013, pp. 125-158. Bykovskii, F. A., Vedernikov, E. F., “Continuous Detonation of a Subsonic Flow of a Propellant,” Combustion, Explosion, and Shock Waves, Vol. 39, No. 3, 2003, pp. 323-334. Tellefsen, J. R., King, P. I., Schauer, F., Hoke, J., “Analysis of an RDE with Convergent Nozzle in Preparation for Turbine Integration,” 50th Aerospace Sciences Meeting, Nashville, Tennessee, AIAA 2012-0773. Schwer, D. A., Kailasanath, K., 2012, “Feedback into Mixture Plenums in Rotating Detonation Engines,” 50th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, Nashville, TN, AIAA 20120617. Fotia, M. L., Hoke, J., 2014, “Propellant Plenum Dynamics in a Two-dimensional Rotating Detonation Experiment,” 52nd Aerospace Sciences Meeting, National Harbor, Maryland, AIAA 2014-1013. Naples, A., Hoke, J., Schauer, F., “Experimental Investigation of a Rotating Detonation Engine Fuel Injector Temporal Response,” 53rd Aerospace Sciences Meeting, Kissimmee, Florida, AIAA 2015-1104. Rankin, B. A., Fotia, M. L., Paxson, D. E., Hoke, J. L., Schauer, F. R., “Experimental and Numerical Evaluation of Pressure Gain Combustion in a Rotating Detonation Engine,” 53rd Aerospace Sciences Meeting, Kissimmee, Florida, AIAA 2015-0877.
16
[14]
[15]
[16]
[17]
[18]
Naples, A., Hoke, J., Schauer, F., “Rotating Detonation Engine Interaction with an Annular Ejector,” 52nd Aerospace Sciences Meeting, National Harbor, Maryland, AIAA 2014-2087. St. George, A., S. Randall, V. Anand, R. Driscoll, E. Gutmark, “Characterization of Initiator Dynamics in an RDC,” 9th U. S. National Combustion Meeting, Cincinnati, 2015. St. George, A., Driscoll, R., Anand, V., Randall, S., Munday, D., Gutmark, E., “Development of a Rotating Detonation Combustor Facility at the University of Cincinnati,” 53rd AIAA Aerospace Sciences Meeting, Kissimmee, FL, 2015. Anand, V., St. George, A., Driscoll, R., Randall, S., Gutmark, E., “Statistical Treatment of Wave Instability in Rotating Detonation Combustors,” 53rd AIAA Aerospace Sciences Meeting, AIAA 2015-1103, Kissimmee, FL, 2015. Alster, M., “Improved calculation of resonant frequencies of Helmholtz resonators.” Journal of Sound and Vibration, Vol. 24, No. 1, 1972, pp-63-85.
17
Highlights: 1. Pressure fluctuations in the air inlet and fuel plenum of the Rotating Detonation Combustor are analyzed comprehensively for the first time, experimentally. 2. A low frequency sinusoidal base oscillation is discovered in the air inlet for the tested operating conditions. 3. This low frequency is found to occur at 235 Hz irrespective of the air flow rate, or the equivalence ratio, and is shown to be probable case of Helmholtz resonance in the air inlet due to the detonation wave passage. 4. This in turn in conjectured to cause the waxing and waning instability in the combustor distinguished by periodic waxing and waning of detonation wave strength. 5. A novel way to determine the operating frequency of the RDC by integrating the sensors in the air inlet is established. This avoids sensor destruction due to the extreme environment in the actual chamber. 6. Even for the same test cases, the three sensors in the fuel plenum exhibit different fundamental frequencies indicating the different spatial dynamics inside the fuel plenum.
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S0894-1777(15)00283-6 http://dx.doi.org/10.1016/j.expthermflusci.2015.10.007 ETF 8597
To appear in:
Experimental Thermal and Fluid Science
Received Date: Revised Date: Accepted Date:
14 July 2015 5 October 2015 6 October 2015
Please cite this article as: V. Anand, A. St. George, R. Driscoll, E. Gutmark, Analysis of Air Inlet and Fuel Plenum Behavior in a Rotating Detonation Combustor, Experimental Thermal and Fluid Science (2015), doi: http:// dx.doi.org/10.1016/j.expthermflusci.2015.10.007
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Analysis of Air Inlet and Fuel Plenum Behavior in a Rotating Detonation Combustor Vijay Anand, Andrew St. George, Robert Driscoll, Ephraim Gutmark Gas Dynamics and Propulsion Laboratory Department of Aerospace Engineering University of Cincinnati, OH 45221
Abstract The behavior of the oxidizer inlet and the fuel injection plenums during the operation of a Rotating Detonation Combustor (RDC) is studied using pressure sensors in the air injection gap, the fuel plenum, and in the combustor. Significant pressure feedback from the rotating detonation wave is observed in the air injection gap. Pressure feedback into the fuel plenum is relatively weaker. The average normalized cross-correlation between the pressure-time series in the air injection gap and within the combustor is greater than 0.3. The air injection gap has a considerable base sinusoidal oscillation in the same frequency range as a previously discovered waxing-and-waning instability in the combustor. The fundamental frequency in the air injection gap is the same as the RDC operation frequency for almost all test cases, indicating the high efficacy of the sensors in the air inlet to attain the operating frequency. Frequency analysis reveals notable spatial variation in the fuel plenum dynamics. The low frequency oscillation in the air injection gap is found to be constant at 235 (+/- 2.5) Hz for all the air flow rates and equivalence ratios tested. Nomenclature f Φ t R x y n N PC PA PF PRA PRF ff σ
frequency (Hz) equivalence ratio Time Normalized cross-correlation arbitrary first pressure-time series (bar) arbitrary second pressure-time series (bar) sample number maximum number of samples in a time series averaged combustor pressure during operation averaged air plenum pressure during operation (bar) averaged fuel plenum pressure during operation (bar) air injection pressure ratio during operation fuel injection pressure ratio during operation fundamental frequency (Hz) standard deviation
1
1. Introduction Detonation is a supersonic combustion wave distinguished by the coupling between a shock wave with the exothermic reaction zone behind it. This is in contrast to a deflagration wave which only travels at subsonic speeds. Across a detonation wave there is always a pressure rise due to the presence of the shock wave, while a deflagration wave always produces a slight pressure loss across it. This property of a detonation to produce an increase in pressure renders it useful in detonation combustors due to the theoretical increase in thermal efficiency that can be achieved [1]. Detonation combustors are mainly classified into Pulsed Detonation Combustors (PDC) and Rotating Detonation Combustors (RDC). RDCs are relatively more compact in size, and mechanically simpler than a PDC. Additionally, unlike PDCs, RDCs do not require valving to inject the fuel and the oxidizer. The reactant supply is continuous, and is combusted by an azimuthally travelling detonation wave inside the combustor. By virtue of the high frequency rotating detonation and the relatively lower pressure amplitude, the exit flow of an RDC is quasisteady and hence more amenable to turbine-integration, as opposed to the PDC which produces large fluctuations in pressure at the exit [2]. The above-mentioned advantages of an RDC over a PDC have been responsible for the increased scientific interest in an RDC in recent years. However, comparatively, the RDC is less developed than the PDC technologically. While several factors like the overall RDC geometry [3], combustor channel width variation [3], homogenous [3-7] and heterogeneous reactant mixtures [3,6,7], subcritical (un-choked) air injection [5,8], and back-pressurization [5,9] have been studied, there are significant facets of RDC operation that are yet to be investigated. Of considerable interest is the effect of the rotating detonation waves on the air and the fuel plenum. Numerical simulations by Schwer et al. [10] determined the presence of pressure feedback into the mixture plenum by the detonation wave, but mass feedback was not observed. Mixture plenum dynamics was found to be minimally affected by the height of the plenum. Fotia et al. [11] used shadowgraph in a two-dimensional RDC analogue to observe the effect of a detonation wave on the fuel plenum. Significant pressure feedback was observed from the detonation wave into the fuel plenum which was sufficient to temporarily disturb the fuel plenum dynamics by 200 microseconds. In addition to the original pressure wave manifested due to the detonation wave propagation, secondary pressure waves were also found to occur in the opposite direction in the two-dimensional setup. It was postulated that in an actual RDC, these secondary reflected pressure waves may cause significant interactions with the next detonation lap. Naples et al. [12] estimated the fuel injection velocity in an RDC by utilizing hot film anemometers and observed a noticeable decrease in velocity as the detonation wave passed through, indicating periodic local un-choking of the fuel supply by the detonation. While these studies confirm the pressure feedback exerted by the detonation on the fuel injection plenum, the three-dimensional spatial variation in fuel plenum dynamics has not been investigated. Rankin et al. [13] used pressure sensors in the air plenum to determine that higher air injection pressure ratios caused lower periodic pressure fluctuations in the plenum by the detonation wave. However, since the effect of 2
the detonation wave would be lesser in the air plenum when compared to the actual air injection gap, a better understanding of the detonation pressure feedback can be attained by instrumenting the actual air inlet. In this study, the pressure feedback by the detonation wave on the air injection gap, instead of the air plenum, is studied using three azimuthally-distributed piezoelectric sensors in the air inlet. Directly flush-mounted pressure sensors are prone to permanent failure due to the very high-temperature RDC environment [5], and hence recent research has concentrated on using Infinite Tube Pressure (ITP) [5,14] setups to evaluate the RDC operation. Hence, the sensors in the air inlet are also investigated for their efficacy in determining the RDC operating frequency. Three pressure sensors are also integrated into the fuel plenum to analyze the spatial variation in fuel plenum dynamics. In addition to the sensors in the air injection gap and the fuel plenum, the combustor annulus is also instrumented with three flush-mounted pressure sensors to evaluate the correlation between the sensors in different locations.
2. Experimental methodology The current study utilizes data collected from hydrogen-air RDC tests performed at the Gas Dynamics and Propulsion Laboratory (GDPL) at the University of Cincinnati. The facility is shown in Fig. 1. The modular RDC has radially inward air-injection and axial fuel injection (Fig. 2). Ignition is achieved with a pre-detonator tube filled with ethylene and oxygen [15], which exhausts tangentially into the annulus. Detonation develops briefly after the ignition event through a Deflagration-to-Detonation transition (DDT) mechanism [15]. The air injection width and the fuel injection scheme are varied with interchangeable combustor components. A detailed description of the different fuel injection schemes are dealt in [5]. For this study, the fuel plate with the highest number of orifices is used [5]. The combustor and air plenum are instrumented with a Capillary Tube Averaged Pressure (CTAP) sensor setup [16] to estimate the injection pressure drop from the air and fuel plenum to the RDC combustion annulus. A total of 9 PCB pressure sensors are instrumented in the RDC with a data acquisition rate of 1 MHz. The facility (Fig. 1) is described in detail by St. George et al. [16].
3
Figure 1: RDC facility at University of Cincinnati The general location of the piezoelectric sensor in the air injection gap (blue) and the fuel plenum (violet) is shown in Fig. 2. A schematic of the RDC instrumentation ports is given in Fig. 3. The combustor has 3 PCB (red) sensors (1, 2 and 3), separated by 120o and flush-mounted in the three stations in the first row of instrumentation port. To analyze the pressure feedback into the air inlet, 3 PCB sensors (4, 5 and 6) are instrumented in the air injection gap, ≈ 2.54 cm from the combustor. To study fuel plenum dynamics, 3 more PCB sensors (7, 8 and 9) are integrated at the base of the plenum (Fig. 3). The individual air inlet and fuel plenum PCB sensors are displaced by approximately 21o from the corresponding flush-mounted combustor PCB sensor (Fig. 3). Finally, a CTAP pressure sensor (orange circle) is placed in station 3, row 4 (Fig. 3) to get absolute pressure variations.
Figure 2: RDC schematic with the injection scheme
4
Figure 3: RDC instrumentation schematic The air flow rates and equivalence ratios tested are given in Table 1. In the remainder of the paper, individual tests will be denoted by the test number. For instance, test number II-B denotes an air flow rate of 0.3 kg/s and an equivalence ratio of Φ = 1.03. All testing is limited to t ≈ 0.3 second (hence a frequency resolution of 2.5 Hz) to avoid damage to the flush-mounted sensors due to prolonged exposure to the high temperature, high pressure environment. In addition to the qualitative study of the pressure-time traces, Fast-Fourier Transformation (FFT) is used to study the frequency of pressure feedback into the air inlet and fuel plenum. Crosscorrelation is also used to estimate the similarity of the pressure-time series obtained from sensors in different locations. Series
Air flow rate, kg/s
I II III
0.2 0.3 0.4
Equivalence ratios, Φ A B C 0.874 1.0 1.21 0.871 1.03 1.22 0.917 0.997 1.2
Table 1: Test Matrix
3. Results and Discussion 3.1. Pressure feedback into the air inlet and fuel plenum A study of the pressure feedback into the air injection gap and the fuel plenum can be done by juxtaposing the pressure-time trace with the associated flush-mounted combustor sensors. Fig. 4 shows the pressure-time traces in the flush mounted PCB sensor, air gap sensor, and the fuel plenum sensor respectively, for an arbitrary time interval for tests I-B and III-B. Fig. 4a and 4b shows the similarity between pressure magnitude (for test I-B) seen in the flush mount due to the detonation wave and the magnitude of pressure feedback experienced by the air injection gap 5
area due to the detonation wave in the combustor. It is to be noted that the reason behind the apparent higher pressure in the air inlet when compared to the combustor at certain time instances is due to the inherent property of the piezoelectric sensors to only record dynamics pressures while neglecting the steady component. The air inlet exhibits sinusoidal low-frequency pressure oscillations of significant magnitude (up to 0.5 bar fluctuation in Fig. 4b). For the same test point, the fuel plenum sensors record relatively lower pressure fluctuations, not exceeding 0.2 bar. This highlights the heightened impact of the detonation wave on the air inlet in comparison to the fuel plenum. Test III-B exhibits similar trends in pressure-time traces for the fuel plenum (Fig. 4f). While the pressure oscillations exceed to 0.4 bar now, they are consistently below the pressure fluctuations in the air inlet which extend up to 1 bar (Fig. 4e) for the 0.4 kg/s case. Fig. 4e shows the pressure-time trace at the air inlet and once again there are significant sinusoidal oscillations with frequency close to the prior condition, at f ≈ 230 Hz. Two features can be inferred about RDC operation from the above discussion. One, the air inlet experiences much higher pressure feedback when compared to the fuel plenum. Two, there is a strong low-frequency oscillation in the air inlet, even when the combustor has almost no oscillation at the same time.
(a)
(d)
(b)
(e)
6
(c)
(f)
Figure 4: Pressure-time traces of sensors 3 and 6 for I-B (left) and III-B (right)
3.2. Correlation of pressure-time traces The prior section is instrumental in deciphering easily observable trends in the pressure-time series. However, to get at the general pattern of air inlet and fuel plenum behavior at different air flow rates and equivalence ratios the method of cross-correlating the individual sensors with the respective flush-mounted combustor sensors is done using the following equation: R ,
∑ಿషభ సబ ಿషభ మ √ ∑సబ మ ∑ಿషభ సబ
(1)
Here, and are the pressure-time series from the combustor sensors and the air inlet/ fuel plenum sensors respectively, each having n discrete samples, amounting to a maximum number of N. Fig. 5a shows a plot of the cross-correlation between sensors 3 and 6, for test III-C. It is a known fact that cross-correlation peaks when the two signals under consideration are identical to each other which is the case when one directly influences the other. Hence, from Fig. 5b, since the correlation coefficient is maximum at time, t ≈ 119 μs, it implies an almost instantaneously pressure feedback from the detonation wave into the air inlet.
(a)
(b)
Figure 5: Cross-correlation plot of sensors 3 and 6 for test III-C (a) and magnified plot (b)
7
A typical pressure trace from the CTAP sensor in the air and fuel plenum, and the combustor before and during RDC operation is shown in Fig. 6. The air supply (green line) is continuous, but the fuel supply (blue line) starts only at time t ≈ -1.7 s. Ignition from the pre-detonator is initiated at t = 0 s, and the increase in pressure in the combustor during operation can be seen (red line). The combustor pressure during operation (PC) is defined as the average pressure in the RDC for 0.3 s after initiation. The air plenum pressure during operation (PA) and the fuel plenum pressure during operation (PF) are defined similarly. The air injection pressure ratio and the fuel injection pressure ratio can thus be acquired from CTAP sensors using PC, PA and PF. PRA = PA / PC PRF = PF / PC
(2) (3)
The combustor pressure during operation reaches a maximum of 1.2 bar (+/- 0.028) for test III-A, but is relatively low for all the other tests (Fig. 7). Uncertainty is calculated from 1σ value of the pressure-time series. The pressure rise due to detonation in the combustor is higher at the higher flow rate of 0.4 kg/s and decreases to around 1.05 bar (+/- 0.027) and 1.02 bar (+/0.02) for the lower flow rates of 0.3 kg/s and 0.2 kg/s, respectively, as seen in Fig. 7. There is also a slight increase in pressure with an increase in equivalence ratio with the exception of test III-A. The above two observations infer that the combustor pressure during operation (Pc) has a strong dependence on air flow rate and a lower dependence on equivalence ratio. Air plenum Fuel Combustor P PF
PC
Fuel supply Air supply
Figure 6: Correlation coefficient for air inlet - sensors 3 and 6 (left) III-C
8
Combustor pressure during operation, Pc (bar)
1.25 1.2 1.15 1.1 1.05 1 0.95 0.8
0.9
1
1.1
1.2
1.3
Equivalence ratio, Φ 0.2 kg/s
0.4 kg/s
0.3 kg/s
Figure 7: Combustor pressure during operation vs. equivalence ratio
3.5 3 2.5 2 1.5 0.8
0.9
1
1.1
1.2
1.3
Equivalence ratio, Φ 0.2 kg/s
0.3 kg/s
0.4 kg/s
Fuel injection pressure ratio
Air injection pressure ratio
The air injection pressure ratio, PRA (Fig. 8) remains relatively unaltered with equivalence ratio for test points other than test III-A. The fuel injection pressure ratio, PRF, has a stronger dependence on equivalence ratio and increases notably for higher equivalence ratios. Error in injection pressure ratios is calculated by linear sensitivity analysis of the obtained PC, PA and PF, for 1σ, and is found to be negligible. 3.5 3 2.5 2 1.5 1 0.8
0.9
1
1.1
1.2
1.3
Equivalence ratio, Φ 0.2 kg/s
0.3 kg/s
0.4 kg/s
Figure 8: Air injection pressure ratio (left), and fuel injection pressure ratio (right) When the combustor flush-mounted sensors 2 and 3 are cross-correlated among themselves, they show poor correlation despite being in the same generic location of the RDC annulus. The correlations are, on an average, 0.24 for all 9 tests, which is very low. This indicates a considerable spatial variation in the strength of detonation wave, the exact reasons to which are currently unknown. The correlation coefficients for the sensor pairs 1 and 4, 2 and 5, and 3 and 6 (combustor sensor with the air inlet sensor) have similar trends. Hence, for brevity, only the 9
Correlation coefficient
sensor pair of 3 and 6 is going to be discussed, since it consistently has a higher correlation. Overall, the cross-correlation coefficient for the pair of 3 and 6 does not exceed 0.55 which may be a result of the high-amplitude low frequency oscillation in the air inlet skewing the correlation. It is to be noted that this value is still considerably higher than the correlation among different sensors in the combustor itself. At higher flow rates, the pressure ratio across the air injection gap increases. Hence, it makes sense for correlation between the air inlet and the combustor to reduce with increase in air flow rate since a higher air plenum pressure would act against the pressure feedback from the detonation wave (Fig. 9). Like the air inlet analysis, fuel plenum analysis only deals with the sensor pair of 3 and 9 (combustor sensor with the fuel plenum sensor). The correlation coefficient is higher at increased PRF for flow rates of 0.2 kg/s and 0.3 kg/s (Fig. 10) which could be attributed to the higher plenum pressure acting against the pressure feedback from the detonation wave. However, for 0.4 kg/s the correlation increases with increased PRF which may be suggestive of the detonation wave being strong enough to counteract the higher fuel plenum pressure. 0.6 0.5 0.4 0.3 0.2 0.1 0 1.5
2
2.5
3
3.5
Air injection pressure ratio
0.2
0.3
0.4
Correlation coefficient
Figure 9: Correlation coefficient for air inlet - sensors 3 and 6 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 1.5
2
2.5
3
3.5
Fuel injection pressure ratio
0.2
0.3
0.4
Figure 10: Correlation coefficient for fuel plenum - 3 and 9
10
3.3. Frequency analysis 3.3.1. Comparative study Frequency analysis of the pressure-time traces has the potential to reveal interesting characteristics of the different sensors that cannot be observed from pressure-time traces and correlations. The fundamental frequencies obtained from the FFT analysis are assembled for the combustor, air inlet and fuel plenum sensors (Table. 2). If the fundamental frequency, ff, in the air inlet or the fuel plenum is different from the operating frequency in the combustor by 10% or more, the cell is colored yellow in contrast to the green-colored cells of the table which indicate a lesser than 10% difference from the ff obtained from the combustor. It can be seen that the ff is the same as the operating frequency for most of the air inlet and fuel plenum sensors. Only test III-A has a different fundamental frequency in the air inlet and fuel plenum in comparison to the combustor. However, it is to be noted that, for certain tests, one or two of the fuel plenum sensors out of the three had a different ff from the operating frequency of the RDC. This suggests a spatial variation in fuel plenum dynamics. But, all the air inlet sensors always registered the same ff irrespective of the operating point. Since the ff in the air inlet sensors and the combustor matches exactly for the eight of the nine tests conducted, the strong efficacy of the air inlet sensors in determining the operating frequency of the RDC at all regions except at the lean operating boundary is established.
Test I-A
Combustor ff (Hz) 2942
Air inlet ff (Hz) 2942
Fuel plenum ff (Hz) 2942
I-B
3042
3042
3042
I-C
3100
3080
3100
II- A
2935
2935
2935
II- B
3045
3045
3045
II- C
3143
3055
3122
III- A
1705
235
2705
III- B
3643
3645
3642
III- C
3755
3755
3760
Table 2: Fundamental frequencies in the combustor, air inlet and the fuel plenum
3.3.2. Fuel plenum 11
The frequency response of the RDC fuel plenum has been studied previously by Naples et al. [12]. But, that study only used one sensor in the plenum which precludes spatial analysis of the plenum. Since the current study uses three piezoelectric sensors in the fuel plenum, an FFT analysis could further the study on fuel plenum by observing the spatial response in the plenum to the rotating detonation wave in the combustor. Fig. 11 shows the FFT plot for the fuel plenum sensors 8 and 9 for tests I-B (Fig. 11a, 11b), II-B (Fig. 11c, 11d) and III-B (Fig. 11e, 11f). The plots show a notable difference in the ff experienced by each sensor, which is an indicant of considerable spatial variation in the fuel plenum dynamics. This may be due to the detonation wave varying in strength as it propagates through the annulus (as inferred previously by the poor correlation between two combustor sensors for all tests), or a complex pressure wave interaction due to reflection within the fuel plenum, or a combination of both. A similar hypothesis was arrived at by Fotia et al. due to the fuel jet being deflected in a direction opposite to the detonation wave propagation direction, in their 2D setup [11]. It is unclear at present if the spatial variation in plenum dynamics causes a detonation wave of varying strength in the combustor, or vice versa.
(a)
(b)
(c)
(d)
(e)
(f) 12
Figure 11: FFT plots for fuel plenum sensors 8 (left) and 9 (right) for test I-B, II-B and III-B
3.3.3 Air inlet oscillations Pressure-time traces from the prior section led to the discovery of low-frequency oscillations of considerable amplitude in the air inlet. A similar low-frequency component was experimentally discovered in the combustor annulus by the authors [17], but that instability did not have any notable trend with changes in air flow rate or equivalence ratio. It is thus desirable to try to analyze the oscillation in the air inlet and compare it to the previously discovered oscillation in the combustor. This led to an investigation of the oscillation for all the tests. Fig. 12a, 12b and 12c show the FFT plot for three stoichiometric test cases, i.e. tests I-B, II-B and IIIB. While the ff (also the operation frequency as discussed in the previous section) is easily observable from the three plots at f ≈ 3 kHz, f ≈ 3 kHz and f ≈ 3.8 kHz respectively, there is also considerable activity in all three test cases at f ≤ 0.5 kHz. The secondary dominant frequency is identified to be f ≈ 235 Hz (shown by red circle) and is the same for all the three tests which have different air flow rates. When all the tests are analyzed for the oscillation frequency, it is found that the frequency of oscillation in the air inlet always centered on f ≈ 235 Hz for all the 9 tests. This is an interesting discovery since it implies that irrespective of the air flow rate or the equivalence ratio of the operating point, the inlet of the RDC in use for the current study always oscillates at f ≈ 235 Hz. The f ≈ 235 Hz oscillation (black arrow) does not extend throughout the test, but rather is sporadically occurring with time as shown by the spectrogram of tests I-B, II-B and III-B, in Fig. 12d, Fig. 12e and Fig. 12f respectively. To confirm that the oscillation is caused by the detonation wave and not due to an inherent oscillation in the air supply, the RDC was operated under cold-flow conditions without ignition of the reactants, which revealed the lack of any activity in the 235 Hz region. Since the cold flow RDC testing did not produce any oscillation at the same frequency, it can be understood that the oscillation in the air gap is linked to detonation wave propagation in the annulus. The Helmholtz frequency for the air plenum under study is estimated to be ≈ 355 Hz for all flow rates since the speed of sound is relatively unaltered due to an almost constant supply temperature. But, the complex geometry of the plenum would skew the resonance frequency obtained from the basic Helmholtz equation considerably [18]. For instance, a ≈ 15% error is incurred between the calculated and the experimentally obtained frequency when the basic Helmholtz equation is used to calculate the resonance frequency for a cylindrical prism with a long neck [18]. Hence, to get an accurate resonance frequency value, geometry-specific equations need to be developed, even for simple geometries. Despite these unknown variables, since the approximately estimated resonance frequency is different from the oscillation frequency in the inlet by only 33%, it is a strong indication of the air plenum’s functioning as a Helmholtz resonator due to the excitation produced by the high-frequency detonation wave in the combustor. It is hypothesized that the
13
detonation wave excites the air inlet to a resonance frequency which manifests as the waxing and waning detonation instability [17] in the combustor, due to the fluctuating air supply.
(a)
(d)
(b)
(e)
(c)
(f)
Figure 12: FFT plot (left) showing the fundamental low-frequency oscillation for I-B, II-B, III-B, and spectrogram (right) of the respective test points
4. Conclusion Rotating Detonation Combustor operation is analyzed at three air flow rates and three equivalence ratios for each of the air flow rate to study the pressure feedback from the rotating detonation wave onto the air inlet and fuel plenum. A total of nine dynamic piezoelectric sensors are used for the analysis, three each in the combustor, the air inlet and the fuel plenum. Pressuretime traces are studied for the air inlet and the fuel plenum and compared with the flush-mounted combustor sensors. For the most part, the pressure fluctuation in the air inlet is between 45% and 70% of the pressure fluctuation due to detonation passage in the combustor annulus. Pressure 14
fluctuations in the fuel plenum are significantly lower than that experienced by the air inlet, and is usually around 20% of the pressure fluctuation in the combustor. Additionally, low-frequency pressure oscillations of high amplitude are discovered in the air plenum. These oscillations are similar, and occur around the same time scale as the waxing and waning detonation instability observed in the same RDC in a prior study [17]. Cross-correlation between sensors in the combustor reveals very poor conformity of signal shape for all the tests run, thereby indication significant changes in detonation wave strength as it propagates azimuthally around the annulus. Cross-correlation reaches a maximum of 0.55 between air inlet sensors and the corresponding flush-mounted combustor sensors. The crosscorrelation coefficient does not exceed 0.35 for the fuel plenum sensors, indicating that the pressure feedback into the air inlet is higher in comparison to the fuel plenum. As a general trend, correlation decreases with increasing injection pressure ratios. Thus, higher injection pressure is required to reduce pressure feedback from the detonation wave, especially for the air inlet. It is found that the fundamental frequency recorded by all the air inlet sensors is exactly the same as the operating frequency of the RDC, found by the flush-mounted combustor sensors. Only at the very lean limits of operation do the air inlet sensors fail to pick up RDC operating frequency. This finding is of significant importance as it establishes that air inlet sensors are an extremely viable substitute to flush-mounted sensors in the actual combustor. Traditionally, pressure sensors used in the actual combustor have been prone to mechanical disintegration due to the high-pressure and high-temperature environment of the RDC [5]. Hence, some studies have used an Infinite Tube Pressure (ITP) setup [5,14] to analyze the RDC operating mode to avoid sensor damage. However, implementing pressure sensors in the air inlet can be an easier method to ascertain RDC operating modes without risking the destruction of the sensor. The three sensors in the fuel plenum have different fundamental frequencies for many of the test cases indicating strong spatial non-uniformity in the fuel plenum dynamics. The spatial nonuniformity may be a result of a change in the detonation wave strength as it propagates through the annulus, or may be due to complex interaction of the pressure wave from the detonation with already existing, reflected pressure waves from the walls of the plenum. Finally, the low frequency oscillation in the air gap is investigated for all the tests, and it’s found that the fundamental oscillation frequency in the air inlet is always ≈ 235 Hz. There is strong evidence to suggest that this is a manifestation of Helmholtz resonance in the air inlet. Further experimentation is required to clearly investigate the linkage, if any, between this low frequency oscillation in the air inlet and the waxing-and-waning detonation instability in the combustor.
References
15
[1]
[2]
[3] [4]
[5]
[6]
[7] [8]
[9]
[10]
[11]
[12]
[13]
Heiser, W., and Pratt, D., “Thermodynamic Cycle Analysis of Pulse Detonation Engines” Journal of Propulsion and Power, Vol. 18, No. 1, January-February 2002. Yi, T., Lou, J., Turangan, C., Choi, J., Wolanski, P., “Propulsive Performance of a Continuously Rotating Detonation Engine,” J. Propulsion and Power, Vol. 27, 2011, pp. 171-182. Bykovskii, F. A., Zhdan, S. A., Vedernikov, E. F., “Continuous Spin Detonations,” Journal of Propulsion and Power, 22(6), 2006, pp. 1204-1216. Shank, J., King, P., Karnesky, J., Schauer, F., Hoke, J., “Development and Testing of a Modular Rotating Detonation Engine,” 50th Aerospace Sciences Meeting, Nashville, Tennessee, AIAA 2012-0120. Anand, V., St. George, A., Driscoll, R., Gutmark, E., “Experimental Investigation of H2-Air Mixtures in a Rotating Detonation Combustor,” ASME Turbo Expo 2015, GT2015-43614, Canada, 2015. Falempin, F., Naour, B. L., “R&T Effort on Pulsed and Continuous Detonation Wave Engines,” 16th International Space Planes and Hypersonic Systems and Technologies Conference, AIAA 2009-7284. Wolanski, P., “Detonative propulsion,” Proceedings of the Combustion Institute, Vol. 34, 2013, pp. 125-158. Bykovskii, F. A., Vedernikov, E. F., “Continuous Detonation of a Subsonic Flow of a Propellant,” Combustion, Explosion, and Shock Waves, Vol. 39, No. 3, 2003, pp. 323-334. Tellefsen, J. R., King, P. I., Schauer, F., Hoke, J., “Analysis of an RDE with Convergent Nozzle in Preparation for Turbine Integration,” 50th Aerospace Sciences Meeting, Nashville, Tennessee, AIAA 2012-0773. Schwer, D. A., Kailasanath, K., 2012, “Feedback into Mixture Plenums in Rotating Detonation Engines,” 50th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, Nashville, TN, AIAA 20120617. Fotia, M. L., Hoke, J., 2014, “Propellant Plenum Dynamics in a Two-dimensional Rotating Detonation Experiment,” 52nd Aerospace Sciences Meeting, National Harbor, Maryland, AIAA 2014-1013. Naples, A., Hoke, J., Schauer, F., “Experimental Investigation of a Rotating Detonation Engine Fuel Injector Temporal Response,” 53rd Aerospace Sciences Meeting, Kissimmee, Florida, AIAA 2015-1104. Rankin, B. A., Fotia, M. L., Paxson, D. E., Hoke, J. L., Schauer, F. R., “Experimental and Numerical Evaluation of Pressure Gain Combustion in a Rotating Detonation Engine,” 53rd Aerospace Sciences Meeting, Kissimmee, Florida, AIAA 2015-0877.
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[14]
[15]
[16]
[17]
[18]
Naples, A., Hoke, J., Schauer, F., “Rotating Detonation Engine Interaction with an Annular Ejector,” 52nd Aerospace Sciences Meeting, National Harbor, Maryland, AIAA 2014-2087. St. George, A., S. Randall, V. Anand, R. Driscoll, E. Gutmark, “Characterization of Initiator Dynamics in an RDC,” 9th U. S. National Combustion Meeting, Cincinnati, 2015. St. George, A., Driscoll, R., Anand, V., Randall, S., Munday, D., Gutmark, E., “Development of a Rotating Detonation Combustor Facility at the University of Cincinnati,” 53rd AIAA Aerospace Sciences Meeting, Kissimmee, FL, 2015. Anand, V., St. George, A., Driscoll, R., Randall, S., Gutmark, E., “Statistical Treatment of Wave Instability in Rotating Detonation Combustors,” 53rd AIAA Aerospace Sciences Meeting, AIAA 2015-1103, Kissimmee, FL, 2015. Alster, M., “Improved calculation of resonant frequencies of Helmholtz resonators.” Journal of Sound and Vibration, Vol. 24, No. 1, 1972, pp-63-85.
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Highlights: 1. Pressure fluctuations in the air inlet and fuel plenum of the Rotating Detonation Combustor are analyzed comprehensively for the first time, experimentally. 2. A low frequency sinusoidal base oscillation is discovered in the air inlet for the tested operating conditions. 3. This low frequency is found to occur at 235 Hz irrespective of the air flow rate, or the equivalence ratio, and is shown to be probable case of Helmholtz resonance in the air inlet due to the detonation wave passage. 4. This in turn in conjectured to cause the waxing and waning instability in the combustor distinguished by periodic waxing and waning of detonation wave strength. 5. A novel way to determine the operating frequency of the RDC by integrating the sensors in the air inlet is established. This avoids sensor destruction due to the extreme environment in the actual chamber. 6. Even for the same test cases, the three sensors in the fuel plenum exhibit different fundamental frequencies indicating the different spatial dynamics inside the fuel plenum.
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