Study the effect of magnetic field on gaseous flames using digital speckle pattern interferometry

Study the effect of magnetic field on gaseous flames using digital speckle patterninterferometryManoj Kumar, Shilpi Agarwal, Varun Kumar, Gufran S. Khan, and Chandra Shakher Citation: AIP Conference Proceedings 1620, 273 (2014); doi: 10.1063/1.4898253 View online: http://dx.doi.org/10.1063/1.4898253 View Table of Contents: http://scitation.aip.org/content/aip/proceeding/aipcp/1620?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Experimental study of vibraphone pitch bending using electronic specklepattern interferometry. J. Acoust. Soc. Am. 129, 2615 (2011); 10.1121/1.3588685 Study of Phaseshifting Techniques in Digital Speckle Pattern Interferometry for Deformation Measurement AIP Conf. Proc. 1236, 57 (2010); 10.1063/1.3426168 Digital Holographic Interferometry and Speckle Correlation AIP Conf. Proc. 1236, 46 (2010); 10.1063/1.3426163 Speckle interferometry experiments with a digital photocamera Am. J. Phys. 72, 906 (2004); 10.1119/1.1643375 A modal analysis of submerged composite plates using digital speckle pattern interferometry J. Acoust. Soc. Am. 91, 1180 (1992); 10.1121/1.402594

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 103.27.8.43

On: Sat, 25 Oct 2014 04:51:02

Study the Effect of Magnetic Field on Gaseous Flames using Digital Speckle Pattern Interferometry

Manoj Kumar a), Shilpi Agarwal, Varun Kumar, Gufran S. Khan and Chandra Shakher

Instrument Design Development Centre, Indian Institute of Technology Delhi Hauz Khas, New Delhi – 110016, India.

a) Corresponding author: [email protected]

Abstract. An experimental investigation on the behavior of gaseous flames in the presence of magnetic field by using digital speckle pattern interferometry is presented. Premixed, partially premixed and diffusion flames generated by butane torch burner were exposed to the magnetic field of 0.35 Tesla. Phase has been extracted from a single DSPI fringe pattern by the application of Riesz transform and the monogenic signal and from which refractive index and the temperature were calculated. Experimental results show that the temperature and the width of the flames are increased under the influence of magnetic gradient.

Keywords: Magnetic field, Temperature, Butane flames, Riesz transform, Monogenic signal, Digital speckle pattern interferometry. PACS: 42.30.Ms, 42.40.Kw, 42.40.My, 42.30.Rx, 42.30.Va, 42.30.Wb.

INTRODUCTION

Gaseous flames are fundamental to combustion and are encountered in many combustion devices such as combustion burner and combustion turbines. The gaseous combustion phenomenon comprises of both chemical reaction and physical process of heat transfer and mass movements [1]. Therefore much interest has been brought to study their characteristics. The combustion process is influenced by magnetic field because of paramagnetic and diamagnetic nature of constituent gases. The paramagnetic gases (for which magnetic susceptibility, χ > 0) are attracted towards the increasing direction of magnetic field while diamagnetic gases (χ < 0) pushed towards the decreasing direction of magnetic field. Oxygen is paramagnetic while butane, injected (CH4, N2) and burned gases (CO2, CO and H2O) are diamagnetic [2]. Therefore, the magnetic force originating from magnetic field gradient induces the changes in flame temperature and flame dimensions.

Optical methods have been used for many years for flame diagnostics and combustion research because of their numerous advantages such as full field, non-contact, non-invasive etc. Digital speckle pattern interferometry (DSPI) is an optical interferometric technique, implemented in almost real time, has been widely used for fluid flow visualization [3], measurement of deformation [4], vibration analysis [5], contouring of defocused objects [5], and temperature measurement [7] etc. DSPI is faster in operation, can cover a large size objects and less sensitive to environmental perturbations.

The objective of this paper is to obtain information on combustion characteristics of butane torch burner flames under the influence of magnetic field gradient by using DSPI. The paper is organized as follows. Section 2, 3, 4 and 5 present the description of formation of fringes by DSPI technique, description of phase extraction from a single fringe pattern by using Riesz transform and monogenic signal and temperature measurement, description of experimental procedure and results of magnetic field gradient on the flames of butane torch burner respectively. Finally a conclusion and discussion is presented in section 6.

Light and Its Interactions with MatterAIP Conf. Proc. 1620, 273-281 (2014); doi: 10.1063/1.4898253

© 2014 AIP Publishing LLC 978-0-7354-1257-6/$30.00

273 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 103.27.8.43

On: Sat, 25 Oct 2014 04:51:02

THEORY

In this technique, two speckle interferograms are recorded: one in absence of flame and other in presence of flame. These two speckle interferograms are subtracted to get the fringes corresponding to the change in refractive index. This process of fringe formation is shown mathematically below.

The intensity distribution on the CMOS sensor without burning of the flame can be expressed as [8]

)],(cos[),(),(2),(),( 2121 yxyxIyxIyxIyxIIbefore 1 where, ),(1 yxI and ),(2 yxI are the intensities of the reference and object beams respectively and ),( yx is the

random phase. The intensity distribution beforeI represents a speckle pattern rather than a fringe pattern. The intensity distribution of the second exposure corresponding to the flame can be expressed as

)],(),(cos[),(),(2),(),( 2121 yxyxyxIyxIyxIyxIIafter 2

where, ),( yx is the phase change corresponding to the temperature field. Again the intensity distribution

afterI represents a speckle pattern. The fringes are obtained from the two intensities beforeI and afterI by subtracting and taking modulus i.e.

2/),(sin2

),(),(sin4),( 21 yxyxyxIIyxI 3

The term 2

),(),(sin yxyx represents the high frequency speckle noise, while 2/),(sin yx is a

variable term. Since ),( yx varies inside the flame, the intensity would show variation and this intensity distribution would be termed as the DSPI fringe pattern.

Phase Extraction by using riesz transform and monogenic signal

Phase has been extracted from the single DSPI fringe pattern by the application of Riesz transform method and the monogenic signal [9]. The monogenic signal is characterized by local amplitude, local orientation and local phase and it is useful in several applications [10-12].

The Riesz transform is the 2D extension of Hilbert transform. It is a type of singular integral operator, i.e. it is given by convolution of one function having a singularity at the origin. For an image, I(x, y) it is defined by

),(*),(),(),(*),(),(

)),((2

1

yxIyxRyxQyxIyxRyxQ

yxIRy

x 4

where, * stands for convolution. Q1 and Q2 are the Riesz transform components on x- and y- axis. Rx and Ry are

spatial representation of the Riesz kernel respectively and given by

2/322

2/322

)(2/),(

)(2/),(

yxyyxR

yxxyxR

y

x 5

The monogenic signal for an image is defined as the combination of the image and its Riesz transform

components, i.e.

274 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 103.27.8.43

On: Sat, 25 Oct 2014 04:51:02

TM yxQyxQyxIyxS )),(),,(),,((),( 21 6

Equation (6) shows that the monogenic signal is 3D vector and one can get the local amplitude, local orientation,

local phase and phase vector. The phase vector is defined by

),)((2tan).)/(( 2/122

21

2/122

21 IQQaQQQ 7

where, ),( 21 QQQ

Temperature Measurement

The unwrapped phase is related to variation of refractive index inside the flame by

nl2 8

where, l is the diameter of the flame, λ is the wavelength of the laser light and Δn (= n-n0) is the change in

refractive index inside the flame. The refractive index variation is related to the temperature by Lorentz-Lorenz formula [13] given by

1

001

3231

TT

PARTPA

nn 9

where, T0 is the temperature at the reference condition at which refractive index is n0, P is the pressure, R is the

universal gas constant and A is the molar refractivity of air at 632.8 nm.

EXPERIMENTAL SETUP

Figure 1. shows the schematic of DSPI setup for measurement of temperature of gaseous flames in the presence of magnetic field gradient. He-Ne laser (wavelength 632.8nm) beam was divided into object and reference beams by a beam splitter (BS). The object beam after passing through the beam splitter has passed through the spatial filter and was collimated by the collimator (C1). The collimated light beam was reflected by the mirror (M6) and transmitted through the diffuser plate and hence produces the speckle field. The light beam modulated by speckles passes through the flame under study and is imaged by the imaging lens. The focused image by the imaging lens was transmitted through the relay lens and reached at the beam combiner where the object image and reference were interfering. The reference beam was spatially filtered (by SF2) and collimated (by C2) before interfering to the object beam at beam combiner. The interference pattern formed by the superposition of the object and reference beam was recorded by CMOS sensor.

The pixel size of the CMOS sensor was 6.7μm×6.7μm, the total number of pixels on CMOS chip were 1280×1022. The sensor chip has an area of 8.6mm× 6.9mm. The computer used in this experiment has a 32-bit Intel Pentium IV microprocessor with the CPU clock rate of 3.4 Ghz.

In this experiment, permanent magnets of rare earth (magnetic strength of 0.35 Tesla) were used. Two magnets of rectangular shape with dimensions 49mm×49mm×12mm were fixed at both sides of the flame and produce a magnetic field.

275 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 103.27.8.43

On: Sat, 25 Oct 2014 04:51:02

FIGURE 1. Schematic of DSPI set-up for measurement of temperature in the presence of magnetic field

A speckle interferogram was first recorded without a burning flame and stored as a reference speckle

interferogram and then another speckle interferogram was recorded corresponding to the flame. The DSPI fringes are obtained by subtraction of these two speckle interferograms.

Experiments were conducted on premixed, partially premixed and diffusion flames generated by butane torch burner in the absence of magnetic field and in the presence of magnetic field gradient (upward decreasing magnetic field). Figure 2(a), 2(b) and 2(c) show the DSPI fringes of premixed, partially premixed and diffusion flames in the absence of magnetic field respectively. Figure 3(a), 3(b), and 3(c) show the DSPI fringes of premixed, partially premixed and diffusion flames respectively in the presence of magnetic field gradient.

(a)

(b)

(c)

FIGURE 2. DSPI fringe pattern of (a) premixed, (b) partially premixed and (c) diffusion flames of butane torch burner in the absence of magnetic field.

276 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 103.27.8.43

On: Sat, 25 Oct 2014 04:51:02

(a)

(b)

(c)

FIGURE 3. DSPI fringe pattern of (a) premixed, (b) partially premixed and (c) diffusion flame of butane torch burner in the presence of magnetic field gradient.

RESULTS AND DISCUSSION

The optical phase distribution from the DSPI fringe pattern is extracted by the application of Riesz transform and monogenic signal. The Riesz components on x- and y-axis of the DSPI fringe pattern of premixed flame corresponding to figure 2(a) are shown in figure 4(a) and 4(b) respectively. Figure 5 shows the retrieved wrapped phase of premixed flame and figure 6 shows the unwrapped phase for half width of the flame along line AB.

(a)

(b)

FIGURE 4. Riesz component corresponding to figure 2(a) on x-axis and Riesz component corresponding to figure 2(a) on y-axis.

FIGURE 5. The retrieved wrapped phase of premixed flame by monogenic signal.

A B

277 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 103.27.8.43

On: Sat, 25 Oct 2014 04:51:02

FIGURE 6. The unwrapped phase of half width of premixed flame.

The relation between unwrapped phase and the variation of the refractive index is given by equation (8). The

calculated values of refractive index distribution along the line AB are plotted as shown in figure 7. These calculated values of refractive index distribution are then used to find out the temperature distribution

inside the flame by using Lorentz-Lorenz formula given by equation (9). Figure 8 shows the calculated values of temperature along the line AB of premixed flame.

FIGURE 7. Refractive index profile corresponding to figure 6. FIGURE 8. Temperature distribution of premixed flame in the

absence of magnetic field corresponding to figure 7.

278 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 103.27.8.43

On: Sat, 25 Oct 2014 04:51:02

Same procedure is applied to calculate refractive index variation and temperature for partially premixed and

diffusion flames in both the situations i.e. in the absence of magnetic field and in the presence of magnetic field gradient.

The retrieved wrapped phase of premixed flame in the presence of magnetic field gradient and the calculated temperature along a line A1B1 are shown in figures 9 and 10.

FIGURE 9. The retrieved wrapped phase of

premixed flame in the presence of magnetic field gradient by monogenic signal.

FIGURE 10. Temperature distribution of premixed flame in the

presence of magnetic field gradient corresponding to figure 9. Figures 11 and 12 show the wrapped phase of partially premixed and diffusion flames respectively in both the

situations. Figures 13 and 14 shows the temperature profiles corresponding to figures 11 and 12 respectively.

(a)

(b)

(a)

(b)

FIGURE 11. The retrieved wrapped phase of partially premixed flames (a) in the absence of magnetic field and (b) in

the presence of magnetic field gradient.

FIGURE 12. The retrieved wrapped phase of diffusion flames (a) in the absence of magnetic field and (b) in the presence of

magnetic field gradient.

A1 B1

279 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 103.27.8.43

On: Sat, 25 Oct 2014 04:51:02

(a)

(b)

FIGURE 13(a). Temperature distribution of partially premixed flame in the absence of magnetic field corresponding

to figure 11(a).

FIGURE 13(b). Temperature distribution of partially premixed flame in the presence of magnetic field gradient

corresponding to figure 11(b).

(a)

(b)

FIGURE 14(a). Temperature distribution of diffusion flame in the absence of magnetic field corresponding to figure 12(a).

FIGURE 14(b). Temperature distribution of diffusion flame in the presence of magnetic field gradient corresponding to figure

12(b).

280 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 103.27.8.43

On: Sat, 25 Oct 2014 04:51:02

CONCLUSION

In this work, effect of magnetic field gradient on temperature profile of different kinds of butane torch burner flames is investigated experimentally. Riesz transform method is applied for phase extraction from a single fringe pattern. This method provides phase distribution with a good accuracy. Experimental results reveal that the temperature is increased for diffusion and partially premixed flames, but a small effect on premixed flame. This is due to the fact that flame shape and the flow directions of combustion products and oxygen are changed due to the magnetic forces originating from magnetic gradient fields. Therefore we can conclude that the flow field in a flame can be controlled by the application of magnetic field and also to improve the combustion characteristics.

REFERENCES

1. T. Aoki, Japanese J. of Appl. Phys. 29, 181-190 (1990). 2. M. Chahine, P. Gillon, B. Sarh, J. N. Blanchard, and V. Gilard, “Magnetic Field Effect on Methane/Air

Diffusion Flame Characteristics,” in Proc. European Combustion Meeting, 2011. 3. N. Andres, M. P. Arroyo, H. Zahn and H. Hinrichs, Exp. Fluids 30, 562-567 (2001). 4. R. Kumar, I. P. Singh and C. Shakher, Opt. Lasers Engg. 41, 81–93 (2004). 5. S. Mirza, P. Singh, R. Kumar, A. L. Vyas and C. Shakher, Opt. Lasers Engg. 44, 41-55 (2006). 6. B. Bhaduri, N. K. Mohan, M. P. Kothiyal, Opt. Lasers Engg. 44, 637-644 (2006). 7. M. Kumar, V. Kumar and C. Shakher, “Measurement of temperature and temperature distribution in diffusion

flames using digital speckle pattern interferometry,” in Eleventh International Conference on Correlation Optics, Proceedings SPIE 9060, edited by Oleg V. Angelsky (Chernivtsi National University, Chernivtsi, Ukraine, 2013).

8. B. Lu, X. Yang, H. Abendroth, H. Eggers and E. Ziolkowski, Opt. Comm. 69, 6-10 (1988). 9. S. Zada, S. Darfi, V. Dembele, S. Rachafi and A. Nassim, ISRN Opt. 2013, 1-10, (2013). 10. M. Felsberg and G. Sommer, IEEE Trans. Signal Proc. 49, 3136–3144 (2001). 11. M. Felsberg and G. Sommer, J. of Math. Imag. Vision 21, 5–26 (2003). 12. S. Held, M. Storath, P. Massopust and B. Forster, IEEE Trans. Signal Proc. 19, 653–667 (2010). 13. C. Shakher and A. K. Nirala, Opt. Lasers Engg. 31, 455-499 (1999).

281 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 103.27.8.43

On: Sat, 25 Oct 2014 04:51:02