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Dynamic Characterization of aLaboratory-Scale Pulse CombustorSirshendu Mondal a , Achintya Mukhopadhyay a & Swarnendu Sen aa Mechanical Engineering Department , Jadavpur University ,Kolkata , IndiaAccepted author version posted online: 15 Oct 2013.Publishedonline: 21 Jan 2014.
To cite this article: Sirshendu Mondal , Achintya Mukhopadhyay & Swarnendu Sen (2014) DynamicCharacterization of a Laboratory-Scale Pulse Combustor, Combustion Science and Technology, 186:2,139-152, DOI: 10.1080/00102202.2013.851078
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DYNAMIC CHARACTERIZATION OF ALABORATORY-SCALE PULSE COMBUSTOR
Sirshendu Mondal, Achintya Mukhopadhyay, andSwarnendu SenMechanical Engineering Department, Jadavpur University, Kolkata, India
Pulse combustion is a self-sustained and self-oscillating process driven by combustion,
coupled with resonant oscillation of the flow in the tailpipe. This article describes the inves-
tigation of the effects of different parameters in a laboratory-scale pulse combustor and ana-
lyzes them using concepts of nonlinear dynamics. Two orientations of the fuel injection holes
were used. In one orientation, the fuel comes in vertically in parallel and counter-flow with
the air stream, while in the other orientation the fuel is injected horizontally at cross-flow
with the air stream. For the vertical orientation, the frequency slightly decreased with
decrease of global equivalence ratio and inlet flow rate. With change of lean to rich air/fuel
mixture, the dynamics changes from non-pulsating to pulsating combustion. The transition
from noise-dominated to periodic oscillation has also been verified by evaluating the corre-
lation dimension. In the horizontal orientation of the fuel inlet, the pulsating behavior has
been obtained even under fuel-lean conditions due to better mixing of air and fuel, and phase
and fast Fourier transform plots indicate quasi-periodic behavior.
Keywords: Correlation dimension; Pulse combustor; Quasi-periodicity
INTRODUCTION
Pulse combustors are a class of air-breathing engines in which pulsations incombustion are utilized to improve the performance. Pulse combustors provide severaladvantages over their steady flow counterparts, such as lower emissions, higher ratesof transfer, and higher efficiency. These advantages have been exploited in differentdesigns of pulse combustors, mainly for heating and drying applications. Pulsecombustors also have potential for propulsion applications, particularly micropropulsion vehicles. Depending on the presence of mechanical valves at the inlet, suchcombustors are classified as valved or valveless. In valveless combustors, self-sustainedcombustion oscillations are obtained, even with steady inflow of reactants. In spite of
Received 30 April 2013; revised 30 September 2013; accepted 30 September 2013.
Present address for Sirshendu Mondal is Lehrstuhl fur Thermodynamik, Technische Universitat
Munchen, 85748 Garching, Germany.
Address correspondence to Achintya Mukhopadhyay, Department of Mechanical Engineering and
National Centre for Combustion Research and Development, Indian Institute of Technology Madras,
Chennai 600 036, India (On lien from: Mechanical Engineering Department, Jadavpur University,
Kolkata 700032, India). E-mail: [email protected]
Combust. Sci. Technol., 186: 139–152, 2014
Copyright # Taylor & Francis Group, LLC
ISSN: 0010-2202 print=1563-521X online
DOI: 10.1080/00102202.2013.851078
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the advantages offered by pulse combustors, their applications have been ratherlimited because of the lack of understanding of the complex dynamics of the process.
Richards et al. (1993) developed a model of thermal pulse combustor thatproduces oscillatory combustion even with steady inflow of reactants. They usedunsteady well-stirred reactor models and coupled them with a lumped model for gasflow in the tailpipe. Their results showed pulsating combustion in the intermediateranges of operating parameters. Daw et al. (1995) developed a mathematical modelbased on the work of Richards et al. (1993) and also carried out experiments on alaboratory-scale combustor to demonstrate the existence of bifurcations in the com-bustor performance that ultimately led to chaos. Rhode et al. (1995) used the modelof Richards et al. (1993) to demonstrate that the flammable range of flow time canbe extended by controlling the chaos using friction factor as the control variable.Mukhopadhyay et al. (2008), Datta et al. (2009), andMondal et al. (2012) investigatedthe effects of different parameters on the nonlinear dynamics and possible transition tochaos in pulse combustors incorporating radiative heat loss according to the model ofRichards et al. (1993). Gupta et al. (2006), Datta et al. (2006), and Chakraborty et al.(2008) applied the tools of symbolic dynamics to the above model of pulse combustorsto predict extinction in pulse combustors. Xu et al. (2011) analyzed the effect of differ-ent parameters on combustion stability, both theoretically and experimentally.
Margolis (1994) analyzed the nonlinear dynamics of a Helmholtz-type pulsecombustor and showed that the nonlinear acoustic oscillations arise from thecombustion-driven instabilities exciting the acoustic modes. Tang et al. (1995) showedthe oscillations in a pulse combustor to be a consequence of coupling of severalacoustic and hydrodynamic factors. Bloom et al. (2005, 2010; Bloom and Patterson,2009) studied the nonlinear dynamics of a pulse combustor, but focused their studyon valved pulse combustors. With the exception of Daw et al. (1995), none of theabove works applied the tools of nonlinear dynamics systematically to experimentalresults. However, Daw et al. (1995) considered only premixed combustion and limitedtheir study to only parametric variations of operating conditions like flow time andequivalence ratio. The objective of the present work is to systematically investigatethe effects of different designs and operating parameters in laboratory pulse combus-tor and analyze them using concepts of nonlinear dynamics. The design parametershave been varied in a way to achieve both non-premixed and partially premixed com-bustion. Characterization of nonpremixed and partially premixed combustion inpulse combustors using tools of nonlinear dynamics has not been reported to the bestknowledge of the authors. This would improve the understanding of the intrinsicdynamics of the system and lead to better design.
EXPERIMENTAL SET-UP
The set-up (shown in Figure 1) consists of an upstream section, the combustor,and the tailpipe. All metal parts are made of SS316 stainless steel that withstandshigh temperatures. The combustor is designed to provide optically accessible flames.It consists of a 200mm long quartz tube of inner diameter 60mm and outer diameter65mm to allow optical access. The quartz tube is held between two grooved flangesby two long rods threaded to the flanges. At the base of the combustor and near thetop, provisions were made for mounting pressure transducers and spark plug for
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ignition. The lower flange of the combustor was fastened to the flange of the inletsection with six bolts. Fuel is admitted through 2mm diameter holes drilled in tworows 180� apart on a 6mm diameter hollow steel pipe that spanned almost the entirediameter of the combustor. Fuel was injected using two alternative orientations ofthe holes, as shown in Figures 1b and 1c. In one orientation (referred to in this articleas the vertical configuration), the fuel comes in vertically in parallel and counter-flowwith the air stream. In the other orientation (referred to as the horizontal configur-ation), the fuel is injected horizontally at cross flow with the air stream. Air is admit-ted axially at the bottom of the upstream section. The tailpipe consists of two pipesof diameter of 30mm and length 300mm each, flanged at the ends. The tailpipe isopen to the atmosphere. The tailpipe length can be varied by using one or both pipes.For the present study, both tail pipes have been used.
The direct exposure of the pressure transducer to hot combustible gases mayhamper the diaphragm of the piezoelectric pressure transducer. For acquiring thedynamic pressure from the combustor, a cooling jacket has been designed andfastened to the combustion chamber to cool the piezoelectric diaphragm.
Figure 1 Schematic of the (a) experimental set-up (b) air and fuel flow in vertical configuration (c) air and
fuel flow in horizontal configuration.
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The fuel [liquefied petroleum gas (LPG) used in the set of results reported here]is supplied from a pressurized cylinder while air is supplied by means of a com-pressor through a pressure regulator (upstream pressure was maintained at 3 bars).Fuel and air-flow rates are measured with high precision mass flow controllers madeby Aalborg. The mass flow controller for air has a maximum flow rate of 500Lpm,while that for fuel has a maximum flow rate of 70Lpm. The optical signal from theflame was measured with a photomultiplier tube (PMT) of (Hamamatsu, model931B). A bandpass filter that allows radiation of wavelength 430 nm� 10 nm wasplaced in front of the PMT to allow emissions from CH� radicals (431 nm) aloneto reach the PMT. The intensity of CH� emission is widely considered as a signatureof chemical reaction rate and hence of heat release rate from premixed flames. Fornon-premixed and partially premixed flames, the suitability of CH� emission is notas well established. However, Kim et al. (2011) found similarity in results usingCH�, OH�, and CO�
2 filters for partially premixed flames, particularly at lower fre-quencies, and used only CH� emission to characterize heat release rate. The photo-multiplier tube generates voltage signals proportional to the intensity of radiationincident on itself. The output of the PMT was fed to a National Instruments PXIdata acquisition system. The acquired data was processed using National Instru-ments Labview software. The pressure inside the combustion chamber was measuredwith a piezoelectric dynamic pressure transducer made by Kistler. The output of thepressure transducer was also fed to the National Instruments PXI data acquisitionsystem through an amplifier, which also converts the charge generated by the piezo-electric sensor to voltage. Data was acquired for both the sensors at a sampling rateof 2000Hz for 20 s. The high frequency of sampling ensures that no dynamics aremissed up to 1000Hz (Nyquist criterion). In the post-processing stage, the samplingfrequency is reduced by simply skipping intermediate data depending on the fre-quency range of combustion. The time series voltage data recorded by the PMTand pressure transducer are then processed to generate the amplitude spectrum.
LPG (40% C3H8þ 60% C4H10) is used as the fuel. In a particular experiment,the air flow is kept fixed while the fuel flow is progressively reduced to maintain aglobal equivalence ratio roughly between 1.9 and 0.7. This ensures that the mixtureflow rate was nearly constant (as the stoichiometric A=F ratio for LPG is 15.43) tokeep the flow time almost unchanged. Thus the differences in observed phenomenaare caused primarily by the difference in heat release rates. The air flow rate was alsovaried from 80Lpm to 170Lpm. The parameter ranges investigated (air flow rate:80–170Lpm and equivalence ratio 0.7–1.9) ensures investigations over a range ofthermal power spanning an order of magnitude (�1.5–15 kW).
RESULTS AND DISCUSSION
Experiments are conducted first by keeping the holes for the fuel inlet in thevertical plane. Results are obtained in terms of the time series data for the intensityof CH� emission obtained using the PMT with CH� filter and pressure intensityobtained with the pressure transducer. Fast Fourier transform (FFT) is computed onthe time series data to examine the existence of any dominant frequency of oscillation.
The FFT plots of the time series data for the intensity of CH� emission (thesignature of heat release) and the pressure intensity are shown in Figure 2 for the
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air flow rate 160Lpm and for different equivalence ratios. The peak frequency forboth CH
�intensity and pressure agree very well. This frequency matching is found
for other air flow rates also. This indicates that the heat release oscillation and press-ure oscillation occurs inside the combustor at the same frequency as expected. Forboth sensors, one sharp peak is obtained at the same frequency, though a frequencyband at low frequency was found in the FFT plots of PMT data. For identifying thereason behind the presence of this kind of low frequency band, an experiment wasconducted with an open flame (removing the quartz tube from the combustion cham-ber) and keeping the other conditions unaltered. The FFT plot of the unconfinedflame data has been presented in Figure 3. A similar frequency band at lowfrequency is still present in the open flame data (Figure 3), which can be identified
Figure 2 FFT plots of intensity (left-hand column) and pressure (right-hand column) data for equivalence
ratio (a) 0.835, (b) 1.125, (c) 1.32, and (d) 1.42 keeping air flow rate fixed at 160 Lpm.
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as being due to flickering of the diffusion flame. This kind of frequency band isunlikely to be related to pressure fluctuations, as the experiment was conducted withan open flame. So, for the analysis of coupling of heat release and pressure fluctua-tions, this frequency band at low frequency has been ignored.
Figure 4 shows the variation of dominant frequency with global equivalenceratio for different air flow rates. The frequency is slightly decreasing with decreaseof the global equivalence ratio. From Figure 4, it is obvious that the increasing trendof acoustic frequency with the increase of equivalence ratio is found for all air flowrates presented here. The humming sound becomes sharper with the increase of thefuel flow rate. The lowest equivalence ratios presented in the curves for all air flowrates are the limiting equivalence ratios below which no sharp peak in FFT plot hasbeen found. In other words, the lowest equivalence ratio shown for each flow rate isthe starting point of pulsating combustion (below which the combustion isnon-pulsating), though the highest equivalence ratios are not the limiting cases.
Figure 3 FFT plot of PMT data with open flame.
Figure 4 Variation of dominant frequency with low rate for different equivalence ratios for vertical
configuration.
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The experiments have been terminated at the respective equivalence ratios (higherend) due to the restriction of fuel flow rates due to fixed cylinder (LPG) pressure.So, as the curves in Figure 4 are shifted to the left with the increase of air flow rates,this indicates that pulsating combustion with leaner equivalence ratio can beachieved with higher air flow rate (or higher inlet flow). Moreover, the frequencyfor a particular equivalence ratio increases with the increase of inlet flow rate, whichis very clear from Figure 4. The total ignition delay time in the pulse combustor iscontributed by three different processes: (1) sspecies, the time required for air and fuelto mix; (2) smixing, the time required for the fresh cold reactants to mix with the hotcombustion products from earlier cycles, which act as the ignition source for theincoming mixture; and (3) skinetic, the post-mixing chemical ignition time (Kelleret al., 1989; Kushari et al., 1996). The total ignition delay time, signition, is then givenby signition¼ f(sspecies, smixing, skinetic). A low to moderate signition is necessary for pul-sating combustion such that the ignition delay results in a phase lag conducive tosatisfaction of Rayleigh criterion (Jones and Leng, 1994). A very low or very highignition delay would violate this criterion and would lead to unsatisfactory opera-tions in terms of pulsations.
With the decrease of global equivalence ratio, the overall flow rate is reducedslightly, which in turn slightly increases sspecies and smixing. On the other hand, theaverage temperature is reduced with the decrease of global equivalence ratio, whichalso increases skinetic. So, with the decrease of global equivalence ratio, signition increasesand pulsating frequency decreases (Jones and Leng, 1994). And with increase in airflow rate, sspecies and smixing decrease due to the increased turbulence, which eventuallyincreases the frequency. With lower equivalence ratio and higher flow rates, due toreduction in sspecies and smixing, the total ignition delay time (signition) is low, which com-pensates for the increased skinetic due to low equivalence ratio. This ensures a reason-ably low signition, and pulsating combustion is achieved with a leaner equivalence ratioat higher flow rates.
Figure 5 shows the time series data from pressure transducer and correspond-ing FFTs for three fuel flow rates (or global equivalence ratios) for the vertical orien-tation of the fuel holes. It is observed from both time series and FFT plots that atlow fuel flow rate (/¼ 0.71), the behavior is non-pulsating. As the fuel flow rateincreases, the behavior becomes first weakly pulsating (as seen at /¼ 1.01) andfinally strongly pulsating. The strength of the periodic behavior, though apparentfrom the sharper rise in the FFT peak, will be clearer from the phase plot discussedbelow.
Similar results for the horizontal orientation are presented in Figure 6. Incontrast with the vertical configuration, in this case, pulsating behavior is observedat much lower (globally lean) equivalence ratios also. The strong pulsations arealso evident from the much higher amplitudes of oscillations in the time seriesdata. The difference may be due to the difference in the mixing of air and fuelin the two cases. In the vertical configuration, particularly for the fuel comingout of the top holes, the mixing is rather poor as the fuel and air move in coflow-ing streams. On the other hand, for the horizontal configuration, the fuel is issuedin a cross-flow of air, which ensures much better mixing. Thus, even with the leanair fuel mixtures, with sspecies and smixing being lower, pulsating combustionfrequency is achieved.
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Moreover, from a purely hydrodynamic viewpoint, the fuel injecting rod actsas a cylindrical obstacle for the air flow. The blowing effects due to fuel jets, whichcan alter the hydrodynamics in the vicinity of the cylinder, are likely to be differentfor the two orientations.
The FFTs in Figure 6 also show a second set of peaks at frequency values,which are not multiples of the dominant frequencies. Such multiple peaks at incom-mensurate frequencies are characteristics of quasi-periodicity (Hilborn, 2000).Significant differences in the characteristic frequencies are also observed for thetwo orientations. As discussed previously, in the vertical configuration, increase in
Figure 6 Time series data for pressure fluctuations and FFT for horizontal configuration.
Figure 5 Time series data for pressure fluctuations and FFT for vertical configuration.
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global equivalence ratio leads to an increase in the frequency. However, in the hori-zontal case, the frequencies remain nearly constant with changes in global equival-ence ratio, as seen from Table 1. The fact that the frequency remains nearlyinvariant with change in global equivalence ratio indicates that the ignition delayis primarily controlled by the hydrodynamic phenomena, i.e., sspecies and smixing.Since the horizontal configuration ensures better mixing, even at low fuel flow rates,ignition delay is conducive to ensure pulsating combustion. This observation isfurther corroborated by the fact that even for the vertical configuration, the fre-quency is more sensitive to changes in air flow rate (affecting sspecies and smixing) thanchanges in global equivalence ratio.
Further insight into the system dynamics is obtained using phase plots. One dif-ficulty of constructing phase plots for systems with high dimension is the requirementof different types of sensors for recording the time series data of different variables. Astrategy commonly adopted in dynamic analysis to overcome this difficulty involvesuse of Takens’s embedding theorem (Takens, 1981). The basic premise of this theoremis that the dynamics of a multidimensional system can be reconstructed from the timeseries data of a single variable. Thus information about the system dynamics can beobtained by plotting values of scalar variables at two different instants of time againsteach other. The time delay s (i.e., the interval between the two time instants used forgenerating the phase plots) is obtained as the first zero of the autocorrelation functionof the scalar variable defined as (Abarbanel et al., 1993):
CL sð Þ ¼1N
PN
m¼1
x mþ sð Þ � �xx½ � x mð Þ � �xx½ �
1N
PN
m¼1
x mð Þ � �xx½ �2
where x(m) denotes the instantaneous pressure at t¼ t0 þmss, where t0 and ss are theinitial time and sampling time, respectively, for the pressure time series, m is an integer,and �xx ¼ 1
N
PNm¼1 xðmÞ and N are the total number of pressure data available. The time
delay is estimated as 0.015 s. The phase plots of different equivalence ratios for the airflow rate 160Lpm are shown in Figure 7 for both the configurations where p(t) standsfor the pressure data at the tth time instant. The effect of measurement noise was reduced
Table 1 Frequencies of oscillation obtained for different equivalence ratio for
horizontal and vertical orientation of fuel flow rate
Vertical configuration Horizontal configuration
Equivalence ratio Frequency (Hz) Equivalence ratio Frequency (Hz)
0.785 55.82
0.935 55.26
1.16 50.52 1.08 56.56
1.36 51.4 1.23 56.75
1.5 52.67 1.375 56.8
1.65 53.33 1.52 56.95
1.84 54.21 1.67 56.56
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by using singular spectrum analysis (SSA) (Noble et al., 2009) on the raw data. In SSA, acovariance matrix is generated from the time series, and eigenvalues of the matrix aredetermined. Since the largest few eigenvalues are contributed by the system dynamicsand the rest are due to noise, only a few of the largest eigenvalues are used to reconstructthe time series with reduced noise. In the present work, all eigenvalues less than 10% ofthe largest eigenvalue are discarded. The phase plots clearly reveal the non-pulsatingbehavior at /¼ 0.71 for the vertical configuration. Similarly, the banded nature ofthe phase plots reveals a periodic behavior with noise contamination for the higherequivalence ratios. The relatively large scatter of the points reveal a weak periodicityat /¼ 1.01. On the other hand, for the horizontal configuration, the phase plots takea lobed structure for all the cases. Similar phase plots were obtained by Subramanianet al. (2010) for quasi-periodic orbits. This corroborates our earlier observation ofquasi-periodicity for the horizontal configuration.
For quantitative characterization of the dynamics, correlation dimensions areused. For determination of correlation dimensions using time series data of thepressure transducers, the following procedure is adopted. First, the delay time isevaluated as the time when the autocorrelation function first crosses zero (Takens,1981). After the determination of the delay time, the embedding dimension is deter-mined. The procedure adopted for determination of the embedding dimension fol-lows the algorithm of Grassberger and Procaccia (1983). In this algorithm, aninitial dimension, m, of the reconstructed attractor is adopted. For every vectorx(i) in the reconstructed m-dimensional space, the neighboring vectors x(j) withina m-dimensional hypersphere of radius e are identified, and the correlation integralis calculated as
Cm eð Þ ¼ 1
N2
XN
i;j¼1i 6¼j
H e� xi � xj�� ��� �
ð2Þ
Figure 7 Time delay phase plots for (a) vertical and (b) horizontal configurations.
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kxi� xjk represents the Euclidean distance between the two vectors x(i) and x(j), andH(�) represents the Heaviside function. The correlation integral Cm(e), which basi-cally counts the number of neighboring vectors within a hypersphere of radius e,scales with the hypersphere radius, e, as Cm eð Þ � eDC mð Þ where DC(m) is the corre-lation dimension for the chosen dimension m. The correlation dimension is obtainedfrom the linear part of logCm(e) versus log(e) curve as
DC mð Þ ¼ lime!0
logCm eð Þlog eð Þ ð3Þ
The correlation dimension is equal to 1 for periodic orbits, and takes on frac-tional values for strange attractors. The procedure has been presented in detail inDatta et al. (2009). With the reconstructed time series data of various equivalenceratios, the correlation dimension has been calculated. The time series data consist
Figure 8 Correlation dimensions as functions of embedding dimensions for vertical configuration (top)
and horizontal configuration (bottom).
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of 4000 samples for 20 s. The time delay is found to be 0.015 s using the procedurementioned before. The embedding dimension has been taken 1 to 12 in general forthe algorithm of Grassberger and Procaccia (1983). The variation of correlationdimension with embedding dimension for different equivalence ratio has been shownin Figure 8. The value of the correlation dimension, which does not increase furtherwith increase of embedding dimension, is taken as the correlation dimension for thattime series data. The corresponding embedding dimension is also adopted as theembedding dimension of the system.
In Figure 8, it is clear from the top figure that the curve of correlation dimen-sion for equivalence ratio 0.715 does not saturate up to embedding dimension equalto 12. This kind of behavior is found in random data. This ensures that the temporalfluctuations for equivalence ratio 0.715 is entirely due to noise and confirms thenon-pulsating behavior observed earlier. For the weakly periodic behavior at equiv-alence ratio of 0.935, the intrinsic dynamics is relatively weak. Hence the effect ofnoise is significant, leading to saturation only at a high embedding dimension. Alter-natively, for equivalence ratios of 1.16 and 1.38, the strong pulsating dynamics leadsto early saturation. From the bottom part of Figure 8, it is observed that for thehorizontal configuration, the correlation dimension for equivalence ratio 0.39, doesnot saturate, again signifying the dominance of noise. The correlation dimensionsobtained for the pulsating cases for both the configurations, shown in Table 2, arein the range 1.5–2. These values are slightly lower than that of Daw et al. (1995). Thisis expected, as the fully premixed combustion in Daw et al. (1995) is expected to gen-erate more vigorous dynamics. This confirms the existence of low order dynamics,which is the characteristic feature of deterministic systems. The existence of suchlow order dynamics implies that the dynamic characteristics can be used for predic-tion and control of the combustor performance.
CONCLUSIONS
Dynamics of a thermal pulse combustor was investigated using a laboratoryscale thermal pulse combustor with different flow rates. For each flow rate, theequivalence ratios have been varied. The air was admitted axially through the baseof the combustor. Fuel was admitted through holes drilled on a pipe that spanned
Table 2 Correlation dimension obtained for different equivalence ratios for horizontal and vertical
orientation of fuel flow
Vertical configuration Horizontal configuration
Equivalence
ratio
Correlation dimension
(mean� std. dev.)
Equivalence
ratio
Correlation dimension
(mean� std. dev.)
1.085 1.80� 0.065 0.46 1.50� 0.033
1.16 1.69� 0.058 0.53 1.41� 0.058
1.235 1.64� 0.043 0.605 1.58� 0.056
1.305 1.67� 0.063 0.675 1.98� 0.048
1.38 1.63� 0.023 0.745 2.06� 0.083
1.45 1.74� 0.075
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the base of the combustor. Two orientations of the fuel injection holes were used. Inone case, the fuel was injected through the top and bottom of the fuel injection pipe(vertical configuration), while for the other case, the injection holes were on the sideof the pipe and fuel was injected horizontally. The optical signal from the flame wasmeasured with a photomultiplier tube (PMT) with a filter to capture the emission ofCH� radicals, and the pressure was measured with a piezoelectric pressure trans-ducer. The frequency for both CH� intensity and pressure showed very good agree-ment. For the vertical orientation, the frequency slightly decreased with decrease ofglobal equivalence ratio and inlet flow rate. With change of lean to rich air fuel mix-ture, the dynamics changes from non-pulsating to pulsating combustion. The tran-sition from noise-dominated to periodic oscillation has also been verified byevaluating the correlation dimension. In the horizontal orientation of the fuel inlet,the pulsating behavior has been obtained even under fuel lean conditions due tobetter mixing of air, and fuel and phase plots and FFTs indicate quasi-periodicbehavior.
FUNDING
This work has been partially supported by Council of Scientific and IndustrialResearch (CSIR), Government of India. The first author gratefully acknowledges theSenior Research Fellowship from CSIR.
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