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Dynamic Characterization of Candle Flame

Article in International Journal of Spray and Combustion Dynamics · September 2010

DOI: 10.1260/1756-8277.2.3.267

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Suvojit Ghosh

McMaster University

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Sirshendu Mondal

National Institute of Technology, Durgapur


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Tanmoy Mondal

Motilal Nehru National Institute of Technology


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Achintya Mukhopadhyay

Jadavpur University

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Dynamic characterization of candle flameSuvojit Ghosh, Sirshendu Mondal, Tanmoy Mondal, Achintya Mukhopadhyay,

Swarnendu SenMechanical Engineering Department, Jadavpur University, Kolkata – 700032, India

Received August 18, 2009; In revised form on March 18, 2010 and June 30, 2010; Accepted on July 04, 2010

ABSTRACTThe present work focuses on studying the flickering of a candle placed in a hollow cylindricalglass tube. Variations in flame area and intensity have been studied as the oscillating parametersof the flame with a camera and a Photomultiplier tube (PMT), and results have been found to beindicative of the presence of some well defined peaks in the amplitude spectrum of the flameintensity. Tests have been carried out with a range of candle diameters for the same glass tube givingsimilar results. Fluctuations in fractal dimension of the flame structure have also been studied inthe course of the work. The time series data generated by processing camera images and alsothe PMT voltage output has been studied for existence of periodicity in the signal recorded. Thecorrelation dimension has been determined for a number of experiments to characterize thedynamics of the signal.

1. INTRODUCTIONFlickering is observable to the naked eye for most types of flames. However, whilethis observable part is mainly an oscillatory nature of the luminous intensity and tosome extent the geometric size of the flame as given by an oscillatory spatial shiftingof the flame front, other parameters of the flame such as the pressure [1] and flamestructure [2] have also been reported to show similar flickering. Mechanism ofgeneration of oscillatory patterns in flames has been described in great detail byWilson and Chapell [3] and by Kheskin [4]. Due to its close correlation withcombustion efficiency and pollutant emissions [4, 5] the frequency of flame oscillationhas been widely proposed and accepted as a parameter for evaluating the degree ofinstability in a particular flame [3, 6, 7].

Flickering in flames have been observed and studied extensively in a large numberof experiments reported in the existing literature, both recently and in the past. Theflames studied in such experiments range from industrial furnaces [6] to Bunsenburners [7] used in the laboratory, and almost exhaustively cover the nature of flickerobserved in such flames for a wide range of conditions. A brief survey of the availableliterature reveals how most researchers have attempted to correlate the frequency offlame flicker with other relevant parameters for the flame type under study. Some

International journal of spray and combustion dynamics · Volume .2 · Number . 3 .2010 – pages 267–284 267

researchers have also attempted to establish the parameters that control the oscillatorynature of a flame. However, most experimental studies regarding flame flicker havebeen done primarily using a particular type of burner and fuel, and the obviousparameters for controlling the flickering in such case have been the flow rate of fuels and air, for both premixed and non-premixed diffusion flames as well as tripleflames. In general, for a given burner and fuel type, oscillation has been noted to beginat a particular flow rate, although Maxworthy [8] has clearly established this ‘settingin point’ of oscillatory nature to be a small range of flow rates. This phenomenon hasmostly been associated with the heated jet flow or plume generated by the flame andthe subsequent formation of large vortices which cause a visible fluctuation in theflame height [9, 10]. Katta et al.[11] have presented an important summary paper onthe numerical computation of axisymmetric diffusion flames that exhibit oscillatorytrends of interest in this study.

However, a study involving such oscillatory response in a wick flame has not beenreported till date. It should be noted here that one of the main parameters of controllingflickering in flames, i.e. the fuel flow rate in a burner implies that a certain amount ofaxial momentum is imparted to the fuel before combustion. An investigation of theimpact of the same in flame oscillation would require that somehow the axialmomentum be controlled without hampering the fuel flow rate. Maxworthy [8] hasattempted to do away with such axial component of momentum in the fuel by aninnovative burner design where the outflow of fuel is radial, and has suggested that inthis case the axial momentum could only be produced by effects of buoyancy in theproducts of combustion and the ambient air in the immediate vicinity, which isundoubtedly true for any wick flame. A major difference between burner flames andcandle flame is that in case of a candle flame, the rate of fuel supply is controlled by therate of evaporation of the molten wax, which depends on the rate of heat supply. Sincethe major source of heat supply is the flame, fluctuations in fuel flow rate are coupledwith the fluctuations in heat release rate, producing a feedback loop. Thus, there is nodirect control over the fuel supply rate in a wick flame, as against a burner flame. Thishas provided a major motivation to investigate the dynamics of a candle flame. Thisstudy investigates oscillations in such a flame, followed by a non-linear dynamicanalysis of the same, leaving scope for further investigation of the origin of suchoscillatory patterns in a wick flame. These analysis tools have not been used in study offlame dynamics very widely. A further motivation of this study is to explore thesuitability of these tools for characterizing flame dynamics and correlating them withmore conventional analysis tools using this relatively simple configuration beforeextending the method to more complicated practical combustors. It should be noted atthis point that in case of such flames, a major controlling parameter is the wickgeometry and alignment. The effect of variations in the same on the behavior of theflame would present an interesting observation, which also remains to be investigated.However, in this study, efforts were made to use the same type of wick and candle forall observations noted, which can be justifiably said to have been validated by highlevels of consistency in the observations, while other flame conditions have been variedas presented in the later sections.

268 Dynamic characterization of candle flame

2. EXPERIMENTAL SETUPIn this experiment, the oscillatory response of a candle flame has been studied. Candlesof different diameters have been studied in two distinct conditions, the first being anopen flame condition where the flame is open to the ambient. Care was taken to ensurethat there were no other perturbations in the room so that oscillations in the candleflame were generated primarily due to the dynamics of the flame itself, and not due toany external interference. The second one included a hollow glass tube of 45 mm innerdiameter and 31 cm length in which candles of two different diameters were placed.This was done keeping in mind the generation of a high speed coaxial flow surroundingthe flame, which would imply a higher axial momentum imparted to the fuel therebyessentially giving variation in rate of fuel transport. The variation in candle diametercreates a difference in the inlet area for air for such coaxial flow in the glass tube.

The objective in this experiment was to record the oscillations in the variousmeasurable parameters of a flame. For this particular study the parameters observedwere flame intensity, the area of the flame (in square pixels) as mapped in the image ofthe flame acquired using a camera, and the box-counting dimension, which is a measureof the fractal dimension of the flame.

A Prosilica CMOS digital camera has been used to acquire image sequences of size100 × 350 pixels to generate the data necessary to study the same. The experimentalsetup (fig. 1) comprises the flame placed in a dark room. The flame is sampled by theProsilica digital camera at a high frame acquisition rate (315 frames per second). Aneutral density filter (ND filter) of optical density 1.0 is placed in front of the cameralens to ensure that the flame intensity does not saturate the camera sensors at any instantor any pixel. This is essential to ensure that variation of intensity within the flame canbe successfully sampled. The image acquired from the camera is used to determine boththe flame area and a fractal dimension of the flame, as discussed in the next section. Theimage is also simultaneously used to determine the intensity of the flame by summingover the intensity of each pixel in grayscale. The flame is also simultaneously sampledby a PMT which records the flame intensity in terms of a voltage signal, sampled at

International journal of spray and combustion dynamics · Volume .2 · Number . 3 . 2010 269

ND filter

CandlePMT

Prosilica digitalcamera

NI 9215 CRIOdata acquisitionsystem

Figure 1: Experimental setup.

375 Hz. The PMT is interfaced with a computer terminal using a data acquisition system(National Instruments 9215 CRIO). National Instruments LabView® is used to recordthe data acquired from the PMT.

The candle flame has been placed at different locations within the hollow glasscylinder. It has been observed that maximum fluctuations occur when the flame isapproximately l/4th length of the cylinder above the bottom. Results discussed in this study have all been recorded in this condition for different candle diameters exceptfor the open flame condition where the candle is not placed in any enclosure.

3. IMAGE AND DATA PROCESSINGThe images acquired from the camera have been processed using a MATLAB® code tostudy the nature of oscillation in the various parameters under study. The imageprocessing methods used have been discussed briefly later in this section. The timeseries data generated from image processing, and the time series voltage data recordedby the PMT are then processed to generate the amplitude spectrum for the variousoscillating parameters. A correlation dimension for each time series data has also beengenerated to study the degree of non-linearity in the series.

3.1. Noise elimination in the image The image acquired from the digital camera, when subjected to frequency analysis forthe parameter Is, resulted in peaks at certain frequencies which clearly do not match thereported characteristic of diffusion flames (fig. 2). An investigation of the cameraimages revealed that a certain apparently random intensity distribution was beingmapped outside the flame area (fig. 3-a). Such a random intensity distribution in theimage was found to be mapped over the entire image when images were acquired withthe lens cap closed, and therefore may be attributed to electronic noise. The usualtechnique of subtracting a single background image to filter out the noise is not possiblein this case as the noted distribution of intensity has been observed to be time varying.


0.07

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Figure 2: Frequency peaks due to image noise.

However, it was observed that the intensity mapped in these pixels were all below acertain threshold value which was much lower than the intensity mapped in pixels thatlay within the flame region. The images were therefore processed so as to render allpixels mapped with an intensity value less than that threshold as absolutely dark, i.e. 0(fig 3-b). This was efficient in significantly reducing the peaks at frequencies notedearlier in this paragraph and thus may be considered satisfactory. An investigation of thesurface plot of the intensity map within the flame area of the image reveals a perfectlysmooth surface as opposed to the region outside the flame area where the surface ishighly irregular. Thus, it may reasonably be assumed that the signal to noise ratio beinghigher in this region, the influence of noise can be neglected for these pixels.

3.2. Determination of flame areaThe flame area, for the sake of studying oscillations in the same, has been determinedin terms of square pixels. Each image of the flame has been first processed as describedby step (3.1) above. Then the boundary of the flame has been detected in the imageusing an edge detection method. The number of pixels that lie within this boundary hasthen been counted to give a measure of the projected area of the flame in the verticalplane in square pixels. It may be noted here that although this is not a measure of thetotal surface area of the flame which may be suggested as a measure of the reaction rate,


Figure 3a: Candle image and intensity map surface plot before processing.

Figure 3b: Candle image and intensity map surface plot after noise elimination.

160140120100

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analysis of the area projected in the vertical plane is a good approximation for studyingthe fluctuations in the total surface area of the flame in terms of its frequency ofoscillation as both the noted areas would understandably have a similar time period inexhibiting oscillatory behavior.

3.3. Determination of flame intensity from imagesEach grayscale image of the flame comprises a number of pixels, each recording ameasure of the intensity of the flame at the corresponding location. Each image in asequence records a distribution of the variable I(x, y) which represents the radiationintensity of the flame mapped onto the pixel (x, y). Thus, a sum of the grayscaleintensity values recorded at any instant is clearly a measure of the intensity of the flameat that instant. Defining Is as

(1)

This summation carried over the whole image of the flame at a particular instant,after suitable noise elimination, gives a time series data of the flame radiation intensity.The validity of the same has been examined and found satisfactory when the time seriesdata so obtained is compared with the PMT voltage data for the same interval, as notedlater in this article.

3.4. Determination of fractal dimension of flame structure from imagesMinkowski-Bouligand dimension [12], also known as Minkowski dimension or BoxCounting dimension is a measure of the fractal dimension of an object. The processedimage of flame acquired at each instant was processed to acquire a time series data forthe fractal dimension of of the flame structure. The estimation of box countingdimension is sensitive to the range of box lengths used primarily due to the limitedresolution of the flame images. Nevertheless, it yields a useful first approximation to thefractal dimension of the flame structure. While the limited resolution of the digitizedimages may result in an underestimation of counts for smaller boxes resulting in aconvex log–log plot in the course of computation of the box counting dimension, thiscan be avoided by the image correction procedures proposed by Taylor and Taylor [13].In the present experiment, however, the log-log plot has been observed to be a fairlystraight line and a straight line curve fit has shown very little scatter. Thus, it canconcluded that such filtering methods are not necessary for the sake of processing thepresent images.

A brief description of the method for determination of box counting dimension hasbeen included in this section. A detailed description can be found in [14–16]. Thecontour of the image of the flame mapped in each image is identified through asuitable edge detection method. Boxes (squares) of side A pixels are made to cover theentire space mapped within each image. The number of boxes N required to cover theentire geometric object (in this case the flame) is recorded. The number of boxes is thenincreased, i.e. each box reduced in size and the process is repeated. It is to be noted that

I I x ys y x= ∑ ∑ ( , )


the minimum size of A in this particular operation is 1 given that the images acquiredhere are all digital images where length scales are measurable only in terms of thediscrete spatial parameter, number of pixels. The number of boxes (N) is related to thebox counting dimension Db as

(2)

i.e., (3)

As A tends to zero, the last term in eq.(3) becomes negligible. Thus,

(4)

Thus, each image gives a value of Db , and a time series data of the fractal dimensionof the flame can be obtained from a sequence of images.

3.5. Estimation of flicker frequencyAs noted by Huang et al. [17], the flame flicker should reflect the contributions of allcomponents over the entire frequency spectrum. The term F as defined in [17], given byeq.(5) below has been therefore incorporated, which would serve as a quantification ofthe flickering in the flame.

(5)

This is necessary as some flame types typically show multiple dominant frequenciesand extends over a wide range of higher frequencies, while others have one or two suchdominant frequencies [18].

3.6. Determination of correlation dimensionOne difficulty of constructing phase plots for systems with high dimension is therequirement of different types of sensors for recording the time series data of differentvariables. A strategy commonly adopted in dynamic analysis to overcome thisdifficulty involves use of Takens Embedding Theorem [19]. The basic premise of thistheorem is that the dynamics of a multidimensional system can be reconstructedfrom the time series data of a single variable. For determination of correlationdimension using time series data of radiation intensity and flame area, the followingprocedure is adopted. First, the delay time is evaluated. The delay time has been

Fp f

p

i ii

n

ii

n==

=

∑

∑1

1

DN A

Ab A= −

→limlog ( )

log0

DN A

A

k

Ab A= − +

→limlog ( )

log

log

log0

N A kAADb( ) lim= →

−0


identified as the time when the autocorrelation function first crosses zero [20]. Theautocorrelation function adopted is as noted in [21]. After the determination of thedelay time, the embedding dimension is determined. The procedure is adopted fordetermination of the embedding dimension following the algorithm of Grassbergerand Proccacia [22]. The correlation dimension is equal to 1 for periodic orbits, andtakes on fractional values for strange attractors. The procedure in detail has beenpresented in Datta et al.[23]

4. RESULTS AND DISCUSSIONSThe results generated in this study are difficult to present given the vast number of datagathered and the even higher number of possible representations for the same. Forbrevity, data has been presented for typical cases of each flame type, i.e. an open flameand two particular examples of the flame generated from the candle being placed in ahollow glass tube, one being for a thick candle (diameter 22 mm), another for arelatively thinner one (diameter 17 mm). The separate subsections hereinafter deal withthe various flicker parameters and their dynamic behavior for these cases. The mainreason for choosing these particular cases for studying the oscillations have beenexplained in the course of the discussions included later in this section.

4.1. Oscillations in radiation intensityThe time domain signal for radiation intensity has been acquired from two differentsources, as noted earlier. The PMT voltage recorded is the first measure of the same,as represented in fig. 4a for a particular experiment with the thin candle in the hollowglass tube. The parameter Is obtained from processing the images of the flame acquiredin sequence, as described in Section 3.3 also gives an estimate of the time domainsignal for radiation intensity as recorded by the camera, and has been presented infig. 4b for the same duration of the experiment noted above. Each sequence lastsaround 19–20 seconds.

A comparative observation of fig. 4a and 4b is clearly indicative of similarity in thesignals. This is matched by a nearly identical amplitude spectrum generated from thetime series data acquired from each of these sources, as presented in fig. 5a and fig 5bfor the same case. Figure 5c presents the spectrogram obtained from the short timeFourier transform of the same signal, indicating that the fundamental frequency for this


Figure 4a: Time domain signal sampled by PMT.

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Figure 4b: Time domain signal for flame intensity Is obtained by processing camera images.

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Figure 5a: Amplitude spectrum of radiation intensity from PMT for thin candle inglass tube.

0.1

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Figure 5b: Amplitude spectrum of normalised Is for thin candle in glass tube.

case and its harmonics are observed to be fairly constant with time. The spectrogram hasbeen obtained by sliding a window having a temporal width of ~0.7 seconds over thetime series data obtained from the image sequences after processing, and therefore givesa fairly accurate idea of the time dependence of the oscillating frequencies of theradiation intensity. Since similar results are obtained from both the PMT and thecamera, subsequent results have been presented only in terms of the data acquired afterprocessing of the camera images.

Figure 6a represents the amplitude spectrum for Is for a flame open to the ambient,while fig. 6b is a spectrogram representing the same with an identical sliding windowwidth. It can be observed that the fundamental frequency and all the harmonics are seento shift slightly to the left. Figure 7a-b is an identical representation for a thick candle inthe glass tube. The fundamental frequency peak and its harmonics in this case are seento shift slightly to the right when compared to the thin candle in the hollow glass tube.1

Average values of flicker frequency (F) computed using eq. (5) from the imagesequences and PMT voltage have been tabulated below (Table. 1). It should however benoted here that the frequency band over which the weighted mean is taken has beentruncated suitably in each case to eliminate the impact of white noise in the flickerfrequency while including all oscillation peaks which are characteristic of the flame.2

The truncation window used for each case is however identical, thereby making theresults comparably.

It can be clearly observed here that as the annular flow area for the air entry path intothe glass tube is gradually reduced from the limit of an open flame to a thick candle


150

100

Fre

quen

cy (

Hz)

50

0

−20

−40

−60

−80

−100

−1205 10

Time

15

Figure 5c: Spectrogram for normalised Is for thin candle in glass tube.

1Variations in diameter of the candle is used as a control on the area for entry of air to the annular space atthe bottom of the glass tube, and the wick type used are essentially identical in all cases.2The F value presented here is averaged over 4–5 observations of the same flame condition with a satisfactorylevel of consistency.

obstructing a majority of the entry path, the flicker frequency increases slightly. Thefrequency peak from the amplitude spectra presented in fig. (5a–7a) also show similartrends, as is clearly observable in the fundamental frequency peaks. Another significantobservation from the amplitude spectra is that the amplitudes at the peak frequency andits harmonics are significantly reduced for the thick candle. A possible explanation ofthis phenomenon is as follows. The buoyancy generated by the flame entrains airvertically upward, the mass of air entrained being primarily determined by the strength


0.08

0.06

0.04N

orm

alis

ed I s

am

plitu

de

0.02

00 50

Frequency (Hz)

100 150

Figure 6a: Amplitude spectrum of normalised Is for open candle flame.

0

50

−20

−40

−60

−80

−100

−120

100

Fre

quen

cy (

Hz)

150

5 10

Time

15

Figure 6b: Spectrogram of normalised Is for open candle flame.


0.07

0.06

0.05

0.04N

orm

alis

ed in

tens

ity a

mpl

itude

0.03

0.02

0.01

00 50 100

Frequency (Hz)150 200 250

Figure 7a: Amplitude spectrum of normalised Is for thick candle in glass tube.

160

140

120

100

Fre

quen

cy (

Hz)

80

60

40

20

0

−20

−40

−60

−80

−100

−120

Time (s)5 10 15

Figure 7b: Spectrogram of normalised Is for thick candle in glass tube.

Table 1. Flicker frequency of candle flame radiation intensity at differentconditions.

Maximum percentage Flame condition Flicker frequency (F) Hz. variation about mean

Open flame 18.9617 0.8668Thin candle 20.3530 0.2781Thick candle 24.5115 3.0794

of the buoyant source (flame). A thick candle reduces the air flow passage leading to ahigher air velocity. The higher coflow velocity tends to damp out the oscillations.Significant weakening of gravity-induced oscillations due to increased coflow has alsobeen observed in coflow burners by Azzoni et al. [24]. They also observed that thefrequency of oscillation was relatively insensitive to the strength of coflow. Thisobservation further suggests that the flame dynamics observed herein is gravity-inducedrather than acoustic. However, further investigation of the changing flow pattern of thebuoyant air stream surrounding the flame and its impact on the flame are required.

4.2. Oscillations in flame areaThe time series data for flame area has been generated by processing the imagesequences, as described in section 3.2. The amplitude spectrum of normalized flamearea has been presented below to represent the oscillatory behavior in this flickerparameter (fig. 8) for the thin candle under study. It is interesting to note that thefrequency peaks obtained from the flame area and flame intensity are nearly identical,as observable when fig. 9 is compared with fig. 6a. Similar observations have beenmade for all the flame conditions under study. This illustrates that the fluctuations inflame intensity is caused by fluctuations in flame area, which is expected given that anincrease in flame area can be understandably inferred as an increase in reaction ratewhich would necessarily give an increase in intensity of flame.

4.3. Fractal dimension of the flameThe fractal dimension of the flame area has been determined using the box countingalgorithm [13–15], given by Eqn. (4). The fractal dimension of all flames under studyhere has been seen to lie within a very limited range. The time series signal of Db for a


0.09

0.08

0.07

0.06

0.05

Nor

mal

ised

flam

e ar

ea a

mpl

itude

0.04

0.03

0.02

0.01

0 50 100

Frequency (Hz)

150 2000

Figure 8: Amplitude spectrum of normalised flame area for thin candle flame.

particular sequence of images for the thin candle under study has been presented infig. 9, indicating that the range of fractal dimensions to be in the region of 1.15 −1.42.Similar values have been observed for other flame conditions as well. However, aninteresting observation was made when the time series data of flame area fractaldimension was analyzed for amplitude peaks in oscillation frequency of Db. The case ofthe thin candle under study has been presented as an example (fig. 10). It has beenobserved that the oscillation peaks are identical with flame area and intensity for thisparticular set of images. It should be noted that other conditions have also givenidentical results.


1.5

1.4

1.3Db

1.2

1.10 2 4 6 8

Time (s)

10 12 14 16 18

Figure 9: Time series of Db.

0.03

0.025

0.02

0.015

Db

0.01

0.005

00 50 100


Figure 10: Amplitude spectrum of Db.

4.4. Correlation dimension of radiation intensityThe time series data of radiation intensity has been used to determine the correlationdimension. One example for the flame of each thick and open candle has beenpresented here.

Figures 11 and 12 represent the variation of correlation dimension with embeddingdimension for the temporal change of flame intensity of open candle and thin candle in


00

0.2

0.4

0.6

Cor

rela

tion

dim

ensi

on

0.8

1

1.2

1.4

2 4

Embedding dimension

6 8 10

Figure 11: Correlation dimension of radiation intensity for open candle.

3.5

2.5

2

Cor

rela

tion

dim

ensi

on

1.5

1

0.5

00 2 4 6

Emdedding dimension8 10 12

3

Figure 12: Correlation dimension of radiation intensity for thick candle in glass tube.

glass tube respectively. It is clear from fig. 11 that for the case of open candle, thecorrelation dimension saturates at the value of 1.1, which is indicative of a high degreeof periodicity in the temporal signal for this case. This is also evident from theamplitude spectrum (fig. 6a) and time series data (fig. 13) of the same. For periodicsystems, the correlation dimension is unity. However, due to unavoidable noise inexperimentally obtained time series, the correlation dimension for periodic systemsexceeds unity slightly (~1.05 – 1.1). Similar values were obtained by Gotoda and Ueda[25] in the context of periodic Bunsen flames. On the other hand it should be noted thatfor the thin candle placed in the glass tube, the same saturates at a value slightly lessthan 3, indicating that the same degree of periodicity is not present when the flame isplaced in the enclosure. Correlation dimension has been typically observed to be muchhigher than unity for both the thin and thick candle under study. This is also evidentfrom the amplitude spectrums, which clearly indicate that amplitude peaks in this case(fig.7a) are not as sharp as in the case of the open flame.

5. CONCLUSIONAn experimental investigation of the oscillatory nature of the flicker parametersradiation intensity, flame area and fractal dimension has been carried out for a candleflame placed in the ambient and also in a hollow glass cylinder where the opening ofthe annular space inside the enclosure has been varied by variations in the candlediameter. In spite of its simplicity, the configuration investigated presents a veryimportant feature, namely, a coupling of heat release and fuel supply rates. Although theactual mechanisms are not identical, such coupling is common in many practicalcombustors like gas turbine combustors, where nonlinear coupling between fluctuationsin fuel supply (or equivalence ratio) and heat release rate have been observed.

The flicker frequency F of eq.(5) has been observed to increase as the inlet area isdecreased from the limit of the flame open to the ambient. Also the three parameters areshown to exhibit almost identical frequency peaks.

The correlation dimension has been determined as a chaos quantifier to study thenon-linearity in the dynamics of these parameters. It has been observed that the same


1.0

0.8

0.6I s

0.4

0.2

014 14.1 14.2 14.3 14.4 14.5

Time (s)14.6 14.7 14.8 14.9 15

Figure 13: Time series data of normalized flame intensity for open candle flame overa short duration of 1 s.

remains at a very low value (~1.1) for the flame open to the ambient, and is thusstrongly indicative of oscillatory behaviour of the flicker parameters. However, thecorrelation dimension evaluated for the flame conditions under study placed in thehollow glass tube typically show a much higher value, typically around 3.

The analysis tools used here are generic in nature, applicable for a wide range ofnonlinear dynamic problems. However, in spite of the presence of strong nonlinearities,such tools have not been widely used for investigating combustion dynamics. A majoroutput of the work is the correlation between conventional techniques like time seriesplots and FFT and tools like short time Fourier series, correlation dimension and fractalanalysis. The correlation observed between these in this simple configurationencourages one to apply the tools of nonlinear dynamics to more complex situationswhere techniques like FFT have been observed to be inadequate by many researchers.

REFERENCES[1] Cetegen, B.M., and Ahmed, T.A., 1993. “Experiments on the periodic instability

of buoyant plumes and pool fires”, Combust. Flames, 93, pp. 157–184. [2] Yilmaz, N., Donaldson, A.B., Gill, W., Lucero, R.E., 2009. “Imaging of flame

behavior in flickering methane/air diffusion flames”, J. Visualization 12(1) pp. 47–55.

[3] Wilson, P. M. and Chapell, T. E., 1985. “Pulverised fuel flame monitoring in utilityboilers”, Meas. Control 18(2) pp. 66–72.

[4] Khesin, M., 1996. “Demonstration of new frequency based flame monitoringsystem”. in Proc Amer. Power Conf., Chicago, IL, 58-II pp. 1010–1013.

[5] Hamins, A., Yang, J. C., and Kashiwagi, T., 1992 “ An experimental investigationof pulsation frequency of flames”. in Proc. 24th Symp. Combust., 1992, pp. 1695–1702.

[6] Jackson, P. and Bulger, J. 1987 ‘Enhancing techniques for flame monitoring’,Control Instrum., 19(9), Sep, pp. 73–75.

[7] Broadbend, J. A., 2000 “Fundamental flame flicker monitoring for power plantboilers”, in Proc. IEEE Semin. Adv. Sens. Instrum. Syst. Combus. Processes, June,pp. 4/1–4/4.

[8] Maxworthy, T., 1999. “The flickering candle: transition to a global oscillation ina thermal plume”. J. Fluid Mech, 390, pp. 297–323.

[9] Chen, L. D. and Roquemore, W. M., 1986 “Visualization of Jet Flames”, Combust.Flame, 66 pp. 81–86.

[10] Schoenbuecher, A., Arnold, B., Banhardt, K., Bieller, V., Kasper, H., Kaufmann,M., Lucas, R. and Schiess, N., 1986. “Simultaneous observation of organiseddensity structures and the visible field in pool fires” 21st Symp. (Intl) onCombustion, pp. 83–92. The Combustion Institute.

[11] Katta, V. R., Goss, L. P., Roquemore, W. M. and Chen, L. D., 1996. “Dynamicsof propane jet diffusion”, Atlas of Visualization III (ed. The Visualization Societyof Japan), CRC Press.


[12] Weisstein, Eric W. “Minkowski-Bouligand Dimension”. MathWorld - A WolframWeb Resource. On the WWW URL http://mathworld.wolfram.com/Minkowski-BouligandDimension.html.

[13] Taylor, C. C. and Taylor, S. J., 1991 “Estimating the dimension of a fractal”.Journal of the Royal Statistical Society Series, B-Methodological 53, pp. 353–364.

[14] Hilborn, R.C., 1994 Chaos and Non-linear Dynamics, An Introduction forScientists and Engineers. Oxford University Press, New York.

[15] Peitgen, Heinz-Otto, Jürgens, Harmut, and Saupe, Dietmar, 2004. Chaos andFractals, New Frontiers of Science, second ed,. Springer-Verlag.

[16] Satyamurthy, V., Banerjee, D., Sakamoto, H., Kim, J., 2008, “Measurement of thefractal order of wall void fraction during nucleate boiling”. Int. J. Heat FluidFlow, 29, pp. 207–218.

[17] Huang, Y., Yan, Y., Lu, Y. and Reed, A., 1999. “On-line measurement of gaseousflames by image processing and spectral analysis” Meas. Sci. Technol. 10,pp. 726–733.

[18] Xu, L. and Yan, Y., 2007 “An improved algorithm for the measurement of flameoscillation frequency” IEEE Trans. Instrum. Meas., 56(5), October, pp. 2087–2093.

[19] Takens, F., 1981, “Dynamical Systems and Turbulence”, Lecture Notes inMathematics, 898, Rand, D. A. and Young, L. S. (eds.), Springer-Verlag, Berlin.

[20] Hilborn, R. C.. 2000. Chaos and Nonlinear Dynamics, 2nd edition, OxfordUniversity Press, New York.

[21] Abarbanel, H.D.I., Brown, R., Sidorowich, J.J. and Tsimring, L.S., 1993. “TheAnalysis of Observed Chatioc Data”. Rev. Modern Phys., 65, pp. 1331–1392.

[22] Grassberger, P. and Procaccia, I., 1983. “Measuring the Strangeness of StrangeAttractors”. Physica D, 9, pp. 189–208.

[23] Datta, S., Mondal, S., Mukhopadhyay, A., Sanyal, D., and Sen, S., 2009, “Aninvestigation of nonlinear dynamics of a thermal pulse combustor”, CombustionTheory and Modelling, 13, pp. 17–38.

[24] Azzoni, R., Ratti, S., Puri, I.K. and Aggarwal, S.K., 1999. “Gravity effects ontriple flames: Flame structure and flow instability”, Physics of Fluids, 11, 3449– 3464.

[25] Gotoda, H. and Ueda, T., 2002. Transition from Periodic to Non-Periodic Motionof a Bunsen-Type Premixed Flame Tip With Burner Rotation, Proc. Combust.Inst., 29, 1503–1509.


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Dynamic characterization of candle flame...International journal of spray and combustion dynamics·...

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