Chemical Engineering Science 59 (2004) 1473–1479www.elsevier.com/locate/ces

A study on fractal characteristics of aerodynamic %eld in low-NOxcoaxial swirling burner

Jiang Wua;b;∗, Ming-chuan Zhanga, Hao-Jie Fana, Wei-dong Fana, Yue-gui Zhoua

aDepartment of Energy Engineering, Shanghai Jiaotong University, Shanghai 200240, PR ChinabDepartment of Power Engineering, Shanghai University of Electric Power, Shanghai 200090, PR China

Received 30 December 2002; received in revised form 13 October 2003; accepted 1 December 2003

Abstract

The primary air of a low-NOx coaxial swirling burner is visualized by using glycol as smog tracer. The information of the visual 9ow%eld is input into a computer through image-capturing card with CCD camera as the image-capturing element. The boundary of the visualzone, i.e., the interface of the primary and secondary airs, is obtained by image processing. Fractal dimension (FD) of the boundary isexamined and found to change from 1.10 to 1.40 with S1, S2 and �1. When FD is small, the complex level of the interface is low, andmixture between the primary and secondary airs is weak near exit of the burner at the initial phase of combustion. This is strati%ed 9ow.When FD is big, mixture becomes strong near exit of the burner. It has been proposed that the 9ow with FD ranging from 1.10 to 1.20 isstrati%ed 9ow favoring the reduction of NOx yield and the 9ow with FD from 1.25 to 1.40 is mixed 9ow producing signi%cant amount ofNOx . The mechanisms of the formation of strati%ed 9ow and mixed 9ow are analyzed. The corresponding S1, S2 and �1 of these 9owsare given.? 2004 Elsevier Ltd. All rights reserved.

Keywords: Low-NOx burner; Aerodynamic %eld; Visual experiment; Image processing; Fractal characteristics; Strati%ed 9ow

1. Introduction

At present, combustion is the prevailing mode of fossilenergy utilization and coal is the principal fossil fuel of elec-tric power generation (Beer, 2000). Combustion-generatedpollution a?ects the environment seriously, therefore cleancombustion of coal has increasingly become a focal point ofresearch in the %eld of combustion science and technology.Staged combustion is an important combustion mode to

reduce NOx yield (Kurose et al., 2001), and many kindsof swirling burner with staged combustion have been de-veloped and applied. A low-NOx coaxial swirling burner isan original burner (Barta et al., 1999). Through appropri-ate disposition of swirling strength of the primary and sec-ondary air, the principle of centrifugal force strati%cation isapplied to control mixture velocity so as to realize stagedcombustion with low-NOx yield. This kind of burner is

∗ Corresponding author. Department of Energy Engineering, ShanghaiJiaotong University, Shanghai 200240, PR China. Tel.: 86-21-5474-2847;fax: 86-21-5474-2996.

E-mail address: wjcfd2002@sina.com (J. Wu).

fundamentally di?erent from traditional burners, whose jet9ows mix strongly at initial stage of combustion to producehigh-NOx emission. The strati%cation phenomenon of 9amewas found at %rst in the natural world. Emmons and Ying(1967) and their colleagues found that 9ame was strati%edwhen they studied forest %re disaster and they validated theirhypothesis with experiments. Beer et al. (1971) repeatedthat experiment replacing combustion 9ame with helium jetand got similar results.In the design of low-NOx burner, special provision is

made for the fuel to be injected into a fuel rich 9ame regionwhere nitrogen species are being converted to molecularnitrogen and hence rendered innocuous for NO formation.This requires suppression of air fuel mixing in this 9ameregion to allow suIcient time for the pyrolysis reactions torun their course. The rest of the combustion air is then mixedin to complete combustion. At the pyrolysis stage of the9ame, strati%cation, i.e. stable interface between the primaryand secondary airs, %nds useful application. Strati%cationthat can occur in constant density rotating 9ows is gettingfurther enhanced in burner 9ames by a strong positive radialdensity gradient: inertial forces keep the cooler air rotating at

0009-2509/$ - see front matter ? 2004 Elsevier Ltd. All rights reserved.doi:10.1016/j.ces.2003.12.027

1474 J. Wu et al. / Chemical Engineering Science 59 (2004) 1473–1479

larger radial distances from being drawn into the low-density9ame core.Studies on strati%cation mechanism is very important to

understand under what conditions low-NOx coaxial swirlingburner can lead to strati%cation at initial stage of combustionand mixture at later stage of combustion to achieve stagedcombustion. To study strati%cation mechanism, it is neces-sary to research aerodynamic characteristics. Aerodynamic%eld in outlet of the burner in consideration is studied byvisual experiment. When processing the visual images ofturbulent 9ow, it is noted that instantaneous image is ex-tremely complex because there exists pulsation in turbulentjet, which include much information about turbulent 9ow(Huang, 2000). To get information about turbulent 9ow,fractal theory can be used to analyze the observed data.Mandelbrot (1982) applied fractal theory to research the

structure of turbulent 9ame and studied fractal characteris-tics of turbulent 9ow on uniform surfaces. His paper pointedout that turbulent 9ame has fractal characteristics and thefractal dimension is 2.2–2.5. Subsequent researchers usedclassical stepping-scale-program method to verify fractalcharacteristics of turbulent 9ame (Goix and Lewis, 1993;Mantzaras, 1989).In this paper, we attained the boundary of the visual zone

by sequentially %xing pictures from the video and imageprocessing devices, and studied its fractal characteristics andfractal dimension. The range of fractal dimension of thestrati%ed 9ow’s visual zone boundary is computed and therelative parameters at exit of the burner are given. We alsoprovide a mechanism for the formation of strati%ed 9ow.

2. Experimental approach

2.1. Experimental system

The low-NOx coaxial swirling burner studied in thepresent paper is shown in Fig. 1. There is no central coolingair. The burner makes the 9ow swirl by a swirler with an ax-ially adjustable swirl vane. The ratio of direct 9owing air toswirling air changes with the vane’s varying axial position,which produces di?erent swirling intensity. When there isno swirler in the primary air tube, the swirling intensity willbe zero, i.e., direct 9ow. The proportion of the primary air isadjusted by changing 9ux of the primary and secondary air.The 9ow %eld is visualized by a smog tracer, Glycol of

analytical grade, with density of 1.111–1:115× 103 kg=m3and boiling point of 196–198◦C. The smog tracer is heatedby smog generator and spouted into the primary air tubeand 9ows out from the burner with the primary air. Thesmog generator, Antari.F-120, is made by Antari Lightingand E?ects Ltd. Information about the 9ow %eld is obtainedby taking visual images of the smog tracer with a cam-era. The dynamic pictures taken are input into a computerthrough image-capturing card for display, storage and pro-cessing. The image-capturing system is shown in Fig. 2. The

Fig. 1. The model of low-NOx coaxial swirling burner. 1. Primary airhand wheel, 2. Primary air vane wheel, 3. Secondary air worm cover, 4.Secondary air vane wheel, 5.Secondary air tube, 6. Primary air tube, 7.Primary air hand wheel, 8. Primary air worm cover.

image-capturing element is a 6310PD-type CCD (chargecoupled device) camera made in Taiwan with space resolu-tion of 352×286 pixels. Model of the mirror head is SE1616.To improve image-capturing e?ect and reduce image

noise, the experiments are done on cloudy day and the 9ow%eld to be photographed is illuminated with uniform lightfrom electric arc lamps. A blackened board perpendicularto the ground is used as background to increase the contrastbetween visual 9ow %eld and background. The electric arclamp is hung from the center of a horizontal board. Theboard is supported by six poles and the distance from theboard to axis of the burner is equal to the distance fromaxis of the burner to the ground. The board and the polesdo not a?ect 9ow %eld. Another electric arc lamp of samepower is put on the ground at the position symmetrical withthe position of the %rst lamp, with axis of the burner as thesymmetrical axis.

2.2. Experimental cases

The parameters of the primary and secondary air fromburner exit mainly include 9ux and swirling intensity. Theswirling intensity of the primary and secondary air and thefraction of the primary air are chosen as adjusting parametersto study their e?ect on aerodynamic %eld in outlet of theburner.The de%nitions of swirling intensities of the primary and

secondary airs are as follows:

S1 =

∫ R10 �uwr2 dr

R1∫ R10 �u2r dr

; (1)

S2 =

∫ R2R1�uwr2 dr

R2∫ R2R1�u2r dr

; (2)

J. Wu et al. / Chemical Engineering Science 59 (2004) 1473–1479 1475

Fig. 2. The system of the visual experiment. 1. Screen, 2. Smog generator, 3. Low-NOx coaxial swirling burner, 4. Ink-painted black board, 5. Electricarc light, 6. CCD camera, 7. Image-capturing card, 8. Computer.

where R1 is the radius of the primary air tube, R1=0:165 m;R2 is the radius of the secondary air tube, R2 = 0:265 m; uand w are axial air velocity and tangential air velocity at theexit of the burner, respectively, and they are measured byHWA (Hot Wire Anemometer).Fraction of the primary air is de%ned as

�1 = Q1=(Q1 + Q2); (3)

whereQ1 andQ2 are 9uxes of the primary and secondary air,respectively. �1 is changed by adjusting the opening of thevalves for the primary and secondary air. The ranges of S1and S2 are 0–0.75 and 0.80–1.85, respectively. �1 changesfrom 16% to 37.5%.

3. Image processing and fractal dimension measurement

The original pictures are strengthened to reduce noise. Thestrengthening curve is shown as Fig. 3. The dynamic range ofgray value at 0–g1 and g2–G − 1 in the original pictureis reduced to 0–t1 and t2–G − 1. The range of g1–g2 in

Fig. 3. The image strengthening curve.

Fig. 4. The original visual image of a typical case.

Fig. 5. The strengthened picture of the visual image.

the original picture is increased to t1–t2. An original pictureis shown as Fig. 4 and its strengthened picture is shown asFig. 5. Boundary of a picture is obtained by one-step di?er-ential sub-pixel boundary-checking method (Zhang, 2000).The boundary of the picture obtained by this method isshown as Fig. 6.It is observed that there are many wrinkles in the bound-

ary curve of the visual picture. These wrinkles contain much

1476 J. Wu et al. / Chemical Engineering Science 59 (2004) 1473–1479

Fig. 6. The boundary curve of the visual picture at a typical case.

information about the turbulent 9ow. To get such informa-tion by fractal theory will be useful in studying the mix-ing process between the primary and secondary air. Fractaldimension is a basic parameter in fractal theory. Its strictmathematical de%nition is as following: If D¿ 0, and if thenumber of the balls with diameter � covering a set S is N (�),then MD, the D dimension measure, can be expressed asfollows (Feder, 1988):

MD = lim�→0

�(D)N (�)�D; (4)

where �(D) is the geometrical factor. In the case of a square,�(D) equals 1. D is Hausdor?–Besicovitch dimension.There are a lot of methods to measure fractal dimension of

di?erent objects of interest (Mandelbrot, 1982). Based on thecharacteristics of the boundary curve of aerodynamic %eldin the burner outlet, the box-counting method is adopted.The boundary curve of the visual picture is discretized bysquares with side of � and N (�), the number of the squares iscomputed. N (�) changes with �. The fractal dimension canbe attained through the relationship as

N (�)˙ �−D: (5)

According to expression (5), let

N (�) = k�−D; (6)

where k is a positive constant. Length of the fractal curve is

L(�) = N (�)�; (7)

so

L(�) = k�1−D; (8)

or

log[L(�)] = (1− D) log(�) + log(k); (9)

i.e., length of the fractal curve is linear with the size ofthe measurement square at double logarithmical coordinate.Length of the boundary curve shown in Fig. 6 is measured,i.e., discretized by squares with some size, and the actualmeasured results are shown in Fig. 7 as circle points. It canbe found that when size of the square is small enough, lengthof the boundary curve will not change with size of the square,and the boundary curve is not fractal. This small size canbe called inner cuto?. On the other hand, when size of thesquare is big enough, the length attained by the measurementwill have no relation to the complexity of the boundary

-1 -0.5 0 0.5 1 1.5 2 2.5 3

Log (ε)

6.4

6.5

6.6

6.7

6.8

6.9

7

7.1

7.2

Log

[L(ε

)]

originalpolyfit

Fig. 7. The relation between length of boundary curve of the visual image.

curve and length of the boundary curve will not change withsize of the square. This large size can be called the outercuto?. The straight line in Fig. 7 is a %tting curve rangingfrom inner cuto? to outer cuto?. The boundary curve hasfractal characteristics between inner cuto? and outer cuto?,so slope of the %tting line is 1-D according to expression (9)and fractal dimension of the boundary curve of the visualpicture can be calculated.

4. Results and analyses

A series of visual pictures are attained under di?erent S1,di?erent S2, and di?erent �1. After strengthening these pic-tures and obtaining their boundary, fractal dimension of theboundary is measured. The fractal dimensions with varyingS1 and S2 with �1 at 37.5%, 29%, 26% and 16% are shownin Fig. 8(a)–(d). From Fig. 8 (a)–(d), it is found that frac-tal dimension ranges from 1.10 to 1.40 and show certainpatterns of distribution.Fig. 8(a)–(d) show that, when S1 and S2 are %xed, fractal

dimension decreases with the reduction of �1. Possibly dueto the e?ect of centrifugal force, vacant room arises near axisof the burner when the secondary air of strongly swirling9ow expands radially along the axis. When �1 is big, thevacant room is less than the primary air, which is weaklyswirling or without swirl, so the primary and secondary airmix strongly and there is violent exchange of momentumbetween them, giving rise to strong pulsation on interfacebetween the primary and secondary airs. The boundary of theprimary air is complex and its fractal dimension is high.With�1 decreasing, vacant room formed by swirling 9ow of thesecondary air can allow the primary air to 9ow directly forsome distance along axis of the burner before mixing withthe secondary air. The complexity of interface between theprimary and secondary air reduces, and its fractal dimensiondecreases.As shown in Fig. 8(a)–(d), under the same value of �1,

the relationship between changes in fractal dimension and

J. Wu et al. / Chemical Engineering Science 59 (2004) 1473–1479 1477

0

0.2

0.4

0.6S1

0.8

1.1

1.4

1.7S2

1

1.08

1.16

1.24

1.32

1.4

1

1.08

1.16

1.24

1.32

1.4

0

0.2

0.4

0.6

S1

0.8

1.1

1.4

1.7S2

1

1.08

1.16

1.24

1.32

1.4

1

1.08

1.16

1.24

1.32

1.4

0

0.2

0.4

0.6

S1

0.8

1.1

1.4

1.7

S2

1

1.08

1.16

1.24

1.32

1.4

1

1.08

1.16

1.24

1.32

1.4

0

0.2

0.4

0.6

S1

0.8

1.1

1.4

1.7S2

1

1.08

1.16

1.24

1.32

1.4

FD

FD F

DF

D

FD

FD

1

1.08

1.16

1.24

1.32

1.4

FD

(a)

(c) (d)

(b)

FD

Fig. 8. Fractal dimension changes with S1 and S2 under di?erent �1. (a) �1 = 37:5%, (b) �1 = 29%, (c) �1 = 26%, (d) �1 = 16%.

S1 and S2 is complex. In general, when %xing S2, fractal di-mension of the boundary of the primary air decreases withthe increase of S1. When S1 keeps constant and small, fractaldimension is high and almost not a?ected by S2. When S1keeps constant and big, fractal dimension decreases with theincrease of S2. This may due to strong swirling of the sec-ondary air. When S1 is small, there are large di?erences oftangential velocities between the primary and secondary airand strong exchanges of momentum between them. Hencethey mix strongly, the interface between them is complexand the fractal dimension is high. When S1 is big, undersuitable �1, di?erence of tangential velocities between theprimary and secondary air is not big and the distribution ofcentrifugal force makes pulsation between them moderate,so that exchange of momentum between them is weak with-out strong mixture, and the fractal dimension is low.The burner in practice can stably combust only when there

is a central recirculating zone in 9ow %eld, so the %nding has

the additional guiding value for burner development. It canbe applied to analyze fractal dimension of cases with centralrecirculating zone, and can identify cases with strati%ed 9ow.By measurement with HWA, it is found that the centralrecirculating zone is formed when the ranges of S1, S2 and�1 are 0.30–0.75, 1.20–1.85 and 16–29%, respectively.The complexity of the visual zone’s boundary is low

when its fractal dimension is small, and it can be regardedas strati%ed 9ow. According to distribution of fractal dimen-sion shown in Fig. 8(a)–(d), the cases with fractal dimen-sion from 1.10–1.20 are de%ned as strati%ed 9ow cases, andthe cases with fractal dimension ranging from 1.25–1.40 aremixed 9ow cases. From Fig. 8, it can be found that 9ows withS1, S2 and �1 ranging from 0.50–0.75, 1.50–1.85 and 16–26%, respectively has fractal dimension ranging from 1.10–1.20, and they are with central recirculating zone, there-fore, they are strati%ed 9ow cases with central recirculatingzone. Strati%cation of 9ow delays mixing between fuel and

1478 J. Wu et al. / Chemical Engineering Science 59 (2004) 1473–1479

oxygen and creates a reductive atmosphere with high fueland low oxygen concentrations, so it reduces the yield ofnitrogen oxide.At present, only fractal dimension of turbulent 9ow pic-

tures on two-dimensional plane can be measured. To getfractal dimension of real three-dimensional turbulent 9owimages, it’s required to apply residual dimension additivelaw (Huang, 2000). If fractal dimension of one-dimensional,two-dimensional and three-dimensional turbulent 9ow areD1; D2 and D3, then

D3 = D2 + 1 = D1 + 2: (10)

Its premise is that fractal dimension of every section indi?erent directions is same. Prasad and Sreenivasan (1990)examined residual dimension additive law by studying aone-dimensional line in a two-dimensional turbulent 9owimage. The results of measurement in two-dimensionalplane were similar to those in one-dimensional line, soresidual dimension additive law is valid in measurement ofturbulent 9ow.PLIF (Planar Laser Induced Fluorescence) technology

can be used to obtain two-dimensional time-average con-centration, instantaneous concentration, pulsating concen-tration, energy spectrum and other information about turbu-lent 9ow. But in practice, due to thickness of 9at light, theresults are overlapped results of the section with thickness�. Ideally, 9at light can be as thin as possible. Prasad andSreenivasan (1990) studied in9uence of �, the thickness ofthe section, on fractal dimension D2, and found that D2 rep-resented Guassian distribution along �=� (� is kolmogorovscale), thickness of the section, as follows:

D2 = 1:22 + 0:147 exp

[−0:01075

(��

)2]: (11)

In the present paper, the images obtained by CCD areprojection images, i.e., the overlap of multi-layer “cloud”,but not real two-dimensional pictures. It can be assumedthat �=� in projection images is very big, i.e., the exponentterm disappears in expression (11). Under ideal conditions,i.e., when �=� is small enough, fractal dimension of realtwo dimensional image can be obtained, so fractal dimen-sion of the visual pictures’ boundary can be attained byincreasing the range of 1.10–1.40 by 0.147. According tothe analysis of uncertainty of measurement (Yang, 1992),the uncertainty term is ±0:04, so the range of fractal dimen-sion can be expressed as 1.247–1:547 ± 0:04. Accordingto expression (10), fractal dimension of interface betweenthe primary and secondary air in three-dimensional spaceis 2.247–2:547± 0:04.Expression (11) was a regression equation attained by

least-square method in jet 9ow and tail 9ow with Reynoldsnumber of 4000. It required further study to determinewhether or not expression (11) %ts 9ow with other Reynoldsnumbers. However, that will not a?ect the distribution offractal dimension but only add a constant to each value offractal dimension distribution. Of course, the speci%c ex-

pression for the 9ow with other Reynolds numbers needsmore research. At this point, the range of fractal dimen-sion is given as 1.10–1.40 in the present paper. The rangesof fractal dimension of strati%ed 9ow and mixed 9ow aregiven as 1.10–1.20 and 1.25–1.40, respectively.

5. Conclusion

1. With Glycol as smog tracer and CCD camera asimage-capturing element, the primary air of a low-NOx

coaxial swirling burner is visualized. By image processing,contour of mixed boundary of the primary and secondaryair is attained and its fractal dimension is computed. Therange of fractal dimension is 1.10–1.40.2. Fractal dimension represents complexity of boundary

of the primary and secondary air. An original method is pro-posed to determine whether a 9ow is mixed 9ow or strati%ed9ow according to fractal dimension. The 9ow with fractaldimension ranging from 1.10 to 1.20 is strati%ed 9ow, whilethe 9ow with fractal dimension ranging from 1.25 to 1.40is mixed 9ow.3. As for the low-NOx coaxial swirling burner under in-

vestigation, strati%ed 9ow with central recirculating zone isformed when S1, S2 and �1 range from 0.50–0.75, 1.50–1.85 and 16–26%, respectively. In such 9ow, a large enoughcentral recirculating zone can guarantee stable ignition ofpulverized coal-gas 9ow and strati%ed 9ow can prohibit thesecondary air mixing into the primary air in the initial stageof combustion, therefore lead to the goal of reducing NOx

yield with staged combustion.

Notation

D Hausdor?–Besicovitch dimensionD1 fractal dimension of one-dimensional pictureD2 fractal dimension of two-dimensional pictureD3 fractal dimension of three-dimensional pictureE mathematical expected value of p(x)EH (g) gray-strengthening functionFD fractal dimensionf(x) function of a pictureg original gray coordinateh(x) one-step di?erential of f(x)k a positive constant coeIcientL(�) length of the fractal curveMD D dimensional measureN (�) number of the covering ballsp(x) probability function of g(x)Q1 9ux of the primary airQ2 9ux of the secondary airR1 radius of the primary air tubeR2 radius of the secondary air tuber radial coordinatesS1 swirling number of the primary airS2 swirling number of the secondary air

J. Wu et al. / Chemical Engineering Science 59 (2004) 1473–1479 1479

T a threshold for h(x)t strengthened gray coordinateu velocity component in axial directionw velocity component in tangential direction

Greek letters

�(D) geometrical factor� thickness of the 9at light� diameter of the covering ball�1 ratio of the primary air� kolmogorov scale

Acknowledgements

This work was partially supported by the Chinese Spe-cial Fund for National Key Fundamental Research (GrantNo. G1999022209-04) and China National Natural ScienceFoundation (Grant No. 59876019).

References

Barta, L.E., Lewis, P.F., Beer, J.M., 1999. Low-NOx combustionof pulverized coal using the radially strati%ed 9ame core burner.

FACT-Vol. 23, 1999 Joint Power Generation Conference, ASME, Vol.1, pp. 165–178.

Beer, J.M., 2000. Combustion technology developments in powergeneration in response to environmental challenges. Progress in Energyand Combustion Science 26, 301–327.

Beer, J.M., Chigier, N.A., Davies, T.W., Bassindale, K., 1971.Laminarization of turbulent 9ames in rotating environments.Combustion and Flame 16, 39–45.

Emmons, H.W., Ying, S.J., 1967. The 11th International Symposium onCombustion. Combustion Institute, Pittsburgh, pp. 475–481.

Feder, J., 1988. Fractals. Plenum Press, New York.Goix, P.J, Lewis, P.F., 1993. Number e?ects on turbulent premixed 9amestructure. Combustion Science and Technology 91, 191–206.

Huang, Z.L., 2000. Fractal nature in turbulence. Advances in Mechanics30 (4), 581–596 (in Chinese).

Kurose, R., Ikeda, M., Makino, H., 2001. Combustion characteristics ofhigh ash coal in pulverized coal combustion. Fuel 80, 1447–1455.

Mandelbrot, B.B., 1982. The Fractal Geometry of Nature. Freeman, NewYork.

Mantzaras, Z., 1989. Fractals and turbulent premixed engine 9ames.Combustion and Flame 77, 295–310.

Prasad, R.R., Sreenivasan, K.R., 1990. The measurement and interpretationof fractal dimension of the scalar interface in turbulent 9ows. Physicsof Fluids A 2 (5), 792–807.

Yang, G.W., 1992. The uncertainty in computing real fractal dimensionby using P(�) = P0�1−D. China Science Bulletin 10, 953–956.

Zhang, Y.J., 2000. Image Processing & Analysis. Tsinghua UniversityPress, Beijing.