THESIS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

Technical Report No. 414

Laser Sheet Imaging and Image Analysis for Combustion Research

by

RAFEEF ABU-GHARBIEH

Department of Signals and Systems School of Electrical and Computer Engineering

Chalmers University of Technology S-412 96 Göteborg, Sweden

Göteborg 2001

RAFEEF ABU-GHARBIEH

Laser Sheet Imaging and Image Analysis for Combustion Research ISBN 91-7291-081-X Copyright © 2001, Rafeef Abu-Gharbieh All rights reserved Doktorsavhandlingar vid Chalmers tekniska högskola Ny serie nr 1764 ISSN 0346-718X Technical report No. 414 School of Electrical and Computer Engineering Department of Signals and Systems Chalmers University of Technology S-412 96 Göteborg Sweden Telephone + 46 (0)31-772 1000 http://www.chalmers.se Cover: Image sequence of a diffusion flame obtained through simultaneous OH PLIF and PIV imaging. Printed in Sweden by Chalmers Reproservice Göteborg, September 2001

To my mother Fairouz, my father Hussein, and my husband Ghassan

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ABSTRACT

This Thesis presents techniques that aim at exploiting the potential of image analysis and processing in order to solve problems of data reduction, interpolation, quantification, and interpretation within the field of experimental laser imaging of combustion processes.

Combustion is the most important source of energy for power generation, heating, and transportation in the world today and its strong dominance is projected to continue in the foreseeable future. There are, however, many concerns regarding health effects and risks on humans, environmental pollution, climate changes, as well as availability of fuel resources, fuel cost, and competing markets. Therefore, a great interest in studying and better understanding the combustion processes emerged within the academic and industrial communities. Laser based optical diagnostics has been proven to be a valuable tool for characterizing combustion processes in great detail. These methods are appreciated for their ability to combine non-intrusiveness with sensitivity and selectivity for specific chemical species.

The first part of the Thesis deals with the analysis of spray images obtained through the application of tunable excimer lasers to spray diagnostics. The aim is to form a better understanding of the spray behavior, which may in turn lead to performance improvements in many applications of sprays in aerosols and combustion systems. The images of fuel sprays are experimentally produced by planar laser imaging where Mie scattered light from a cross section of the spray is imaged onto a CCD detector. Spray characterization then involves analyzing the resulting images by segmenting the sprays and investigating a number of their characteristics such as the cross sectional area, perimeter, and penetration length. Also, since the studied sprays are optically dense, a method for compensating laser attenuation based on the inversion of Beer Lambert’s law is developed. The second part of the Thesis deals with the analysis of flame images obtained through the application of time resolved laser imaging to turbulent combustion diagnostics. The data is produced by planar laser induced fluorescence (PLIF) imaging, where a laser diagnostic system for high speed spectroscopic imaging is

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used to record image sequences with very high frame rates (several kHz). Images reflecting the OH radical concentrations in flames are used to investigate the flame front structure in both non-premixed jet flames and spark ignited premixed flames. The aim is to study the influence of fluid motion and reaction chemistry on flame structure, velocity, topology etc. Image analysis methods for edge preserving smoothing, segmentation, tracking, frequency domain interpolation, and velocity estimation are developed for these purposes. Curve matching based on the computation of geodesic paths is used to track (interpolate) the flame motion. Implicit representations incorporating level set methods are deployed to allow proper handling of complex flame front curves with arbitrary topology present in high turbulence scenarios. Finally, a scheme which combines high speed PLIF imaging of OH with particle image velocimetry (PIV), is used to facilitate the separation of the effects of flow and chemistry on local flame front velocities and structures. In conclusion, the work presented in this Thesis, which applies image analysis techniques to laser sheet imaging data, represents novel approaches for analyzing time resolved combustion processes both qualitatively and quantitatively. This will provide insight into fundamental mechanisms of turbulent combustion and a better understanding of such processes.

Keywords: image (sequence) analysis, tracking, curve evolution/propagation, curve matching, level sets, geodesic paths, segmentation, non-linear diffusion filtering, flame propagation, flame fronts, laser, spectroscopy, laser induced fluorescence, LIF, particle image velocimetry, PIV, time resolved imaging, laser sheet imaging, laser attenuation, spray diagnostics, spray characterization, optically dense sprays, optical density, Mie scattering, combustion, combustion engines, combustion diagnostics.

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TABLE OF CONTENTS

ABSTRACT ................................................................................................................I

TABLE OF CONTENTS........................................................................................... III

LIST OF PAPERS .................................................................................................. VII

ACKNOWLEDGEMENT...........................................................................................IX

ACRONYMS AND ABBREVIATIONS ........................................................................XI

CHAPTER 1. INTRODUCTION ............................................................................... 1 1.1 Motivation ............................................................................................... 1 1.2 Image Analysis in Combustion Research................................................ 2

1.2.1 Morphological Operations and Filtering ......................................... 2 1.2.2 Segmentation ................................................................................... 2 1.2.3 Fractal Analysis ............................................................................... 2 1.2.4 Propagation Studies ......................................................................... 3

1.3 Thesis Contribution ................................................................................. 3 1.3.1 Spray Diagnostics Studies ............................................................... 3 1.3.2 Time Resolved Studies of Turbulent Flames .................................. 4

1.4 Thesis Outline.......................................................................................... 5

CHAPTER 2. BACKGROUND ................................................................................. 7 2.1 Combustion Engines................................................................................ 7 2.2 Combustion Flames................................................................................. 8 2.3 Lasers as Diagnostic Tools...................................................................... 8

2.3.1 Light .............................................................................................. 10 2.3.2 Light Scattering by Particles ......................................................... 10 2.3.3 Direct and Inverse Problems ......................................................... 11

2.4 Laser Diagnostic Techniques ................................................................ 11 2.4.1 Classification of Laser Diagnostic Methods ................................. 12 2.4.2 Advantages and Disadvantages ..................................................... 13

2.5 Charge Coupled Devices ....................................................................... 13

CHAPTER 3. SPRAY DIAGNOSTICS .................................................................... 15 3.1 Experimental Setup ............................................................................... 17

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3.2 Spray Image Sets ...................................................................................18 3.2.1 Low Magnification Dataset ...........................................................19 3.2.2 High Magnification Dataset...........................................................19

3.3 Non-Uniform Background Subtraction .................................................20 3.4 Compensation of Laser Attenuation ......................................................24

3.4.1 Scattering Model............................................................................24 3.4.2 Compensation Algorithm...............................................................26 3.4.3 Compensation Results....................................................................27

3.5 Segmentation and Labeling ...................................................................39 3.6 Global Spray Characterization...............................................................44

3.6.1 Spray Body Area............................................................................44 3.6.2 Spray Body Perimeter ....................................................................44 3.6.3 Penetration Length .........................................................................44 3.6.4 Objects Around Main Spray Body.................................................44

3.7 Discussion and Conclusion....................................................................47

CHAPTER 4. TIME RESOLVED FLAME IMAGING...............................................49 4.1 High Speed Imaging System..................................................................50

4.1.1 Nd:YAG Laser Cluster ..................................................................50 4.1.2 Dye Laser .......................................................................................51 4.1.3 High Speed CCD Camera ..............................................................51

4.2 Image Data Acquisition .........................................................................53 4.2.1 Premixed Data................................................................................53 4.2.2 Diffusion Flame Data.....................................................................56 4.2.3 Laser Beam Profile Measurement..................................................58

4.3 Simultaneous OH PLIF and PIV Measurements ...................................58

CHAPTER 5. FLAME FRONT TRACKING ............................................................63 5.1 Image Processing Stage .........................................................................64

5.1.1 Preprocessing Raw Image Data .....................................................64 5.1.2 Noise Reduction Using Non-Linear Diffusion Filtering ...............66

5.2 Image Analysis Stage.............................................................................68 5.2.1 Segmentation Using Active Contour Models ................................68 5.2.2 Temporal Interpolation of Flame Contours ...................................71

5.3 Flame Front Velocity Estimation...........................................................78 5.4 Discussion and Conclusion....................................................................81

CHAPTER 6. MATCHING FLAME FRONTS OF ARBITRARY TOPOLOGY ............83 6.1 Experimental Data .................................................................................83 6.2 Smoothing and Segmentation ................................................................84 6.3 Contour Matching Framework...............................................................91

6.3.1 Geodesic Distance..........................................................................91 6.3.2 Level Set Representation ...............................................................93

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6.3.3 Locating Optimal Paths ................................................................. 94 6.3.4 Matching With Point Correspondence .......................................... 96 6.3.5 Critical Point Detection ................................................................. 97

6.4 Flame Front Matching and Tracking Results ........................................ 97 6.5 Discussion and Conclusion ................................................................. 107

CHAPTER 7. RESOLVING CHEMISTRY AND TURBULENCE INTERACTION...... 109 7.1 OH PLIF Data Analysis ...................................................................... 110 7.2 PIV Data Analysis ............................................................................... 111 7.3 Velocity Measurement ........................................................................ 111

7.3.1 Flame Front Velocity Calculation ............................................... 111 7.3.2 Flow Field Calculation ................................................................ 112

7.4 Turbulence/Chemistry Interaction....................................................... 114

CHAPTER 8. FUTURE OUTLOOK...................................................................... 119 8.1 Spray Diagnostics Aspects .................................................................. 119 8.2 Multi Dimensional Diagnostics in Space and Time............................ 120 8.3 Comparing Models with Experimental Data....................................... 121 8.4 Large Scale Quantitative Studies ........................................................ 121

APPENDIX A ........................................................................................................ 123

BIBLIOGRAPHY ................................................................................................... 125

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LIST OF PAPERS

This Thesis is based on edited versions of the following publications:

• Abu-Gharbieh R., Persson J., Försth M., Rosén A., Karlström A., and Gustavsson T. “Compensation Method for Attenuated Planar Laser Images of Optically Dense Sprays”. Journal of Applied Optics, vol. 39(8), pp. 1260-1267, March 2000.

• Abu-Gharbieh R., Hamarneh G., Gustavsson T., and Kaminski C.

“Flame Front Tracking by Laser Induced Fluorescence Spectroscopy and Advanced Image Analysis”. Journal of Optics Express, vol. 8(5), pp. 278-287, February 2001.

• Abu-Gharbieh R., Kaminski C., Gustavsson T., and Hamarneh G.

“Flame Front Matching and Tracking in PLIF Images Using Geodesic Paths and Level Sets”. Proceedings of IEEE’s Workshop on Variational and Level Set Methods in Computer Vision, pp. 112-118, Vancouver, July 2001.

• Abu-Gharbieh R. and Kaminski C. “Flame Front Matching and

Particle Image Velocimetry for Resolving Interactions of Chemistry and Turbulence in Flames”. Submitted for publication.

• Abu-Gharbieh R. “Image Analysis Applied to Spray Characterization”.

Technical report R008/1998, Department of Signals and Systems, Chalmers University of Technology, September 1998.

Related Publications:

• Abu-Gharbieh R. “Laser Sheet Imaging and Image Analysis Applied to Spray Diagnostics”. Licentiate Thesis, technical report 317L, Department of Signals and Systems, Chalmers University of Technology, August 1999.

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• Abu-Gharbieh R., Persson J., and Försth M. “Compensating Laser Sheet Images of Optically Dense Sprays”. Proceedings of the Swedish Symposium on Image Analysis SSAB’99, pp. 1-4, Göteborg, March 1999.

• Abu-Gharbieh R., Hamarneh G., and Gustavsson T. “Review - Active

Shape Models - Part II: Image Search and Classification”. Proceedings of the Swedish Symposium on Image Analysis SSAB’98, pp. 129-132. Uppsala, March 1998.

• Hamarneh G., Abu-Gharbieh R., and Gustavsson T. “Review - Active

Shape Models - Part I: Modeling Shape and Gray Level Variation”. Proceedings of the Swedish Symposium on Image Analysis SSAB’98, pp. 125-128, Uppsala, March 1998.

• Gustavsson T., Abu-Gharbieh R., Hamarneh G., and Liang Q.

“Implementation and Comparison of Four Different Boundary Detection Algorithms for Quantitative Ultrasonic Measurements of the Human Carotid Artery”. IEEE Proceedings on Computers in Cardiology, vol. 24, pp. 69-72, Lund, September 1997.

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ACKNOWLEDGEMENT

I would like to express my sincere gratitude to all those who made this work possible. Special thanks to:

• My supervisor Prof. Tomas Gustavsson for introducing me to the field of

image analysis and for his continuous encouragement and support. • My co-supervisor Dr. Clemens Kaminski who worked with me first as a

member of the Lund Laser Center at Lund Institute of Technology and later as a member of the Department of Chemical Engineering at Cambridge University.

• Prof. Marcus Aldén and Johan Hult from the Combustion Physics group at Lund Institute of Technology.

• Prof. Arne Rosén, Dr. John Persson and Michael Försth from the Molecular Physics group at the Department of Experimental Physics at Chalmers for their fruitful collaboration in the spray diagnostics part of this work.

• Anders Karlström, Director of the Combustion Engine Research Center at Chalmers (CERC).

• Prof. Mats Viberg, Head of the Department of Signals and Systems who is always a source of inspiration.

• Prof. Demetri Terzopoulos, Prof. Tim McInerney and the Visual Modeling (Vision) Group at the Department of Computer Science at the University of Toronto for welcoming me as part of their group for many months.

• My current and former colleagues in the Image Analysis Group and in the Department of Signals and Systems in general for their friendship and the nice times we had together during the past years. Thanks also to all my friends who were always there for me when I needed them.

• My mother Fairouz, my father Hussein, my husband Ghassan and all my family. Thank you for all the love, support and patience throughout the years. I am finally leaving school!

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ACRONYMS AND ABBREVIATIONS

1, 2, 3, 4D One, Two, Three, Four Dimensional ACM Active Contour Models CARS Coherent Anti-Stokes Raman Spectroscopy CCD Charge Coupled Device CFL Courant-Friedrichs-Lewy CPD Critical Point Detection DCT Discrete Cosine Transform DFWM Degenerate Four Wave Mixing DNS Direct Numerical Simulations DWT Discrete Wavelet Transform FWHM Full Width Half Maximum IDCT Inverse Discrete Cosine Transform LASER Light Amplification by Stimulated Emission of Light LES Large Eddy Simulations LIF Laser Induced Fluorescence LII Laser Induced Incandescence LSD Laser Sheet Dropsizing Nd:YAG Neodymium Doped Yttrium Aluminum Garnet NLDF Non-Linear Diffusion Filtering PDA Phase Doppler Anemometry PDF Probability Density Function PIV Particle Image Velocimetry PLIF Planar Laser Induced Fluorescence RANS Reynold Averaged Navier Stokes SMD Sauter Mean Diameter

Chapter 1. INTRODUCTION

In this chapter we discuss the motivation behind the research presented in this Thesis and introduce its novel contributions.

1.1 Motivation Combustion is the most important energy source for power production, heating, and transportation in today’s world. This strong dominance of combustion will continue in the foreseeable future as the world energy production is projected to increase by 60% in the next 20 years [EIA 00]. Combustion has huge effects on the global environment through the emission of CO2, which is a greenhouse gas, NOx, SOx, CO and other particles, which leads to decreased air quality, acid rain and health hazards. The fact that combustion systems are so widespread thus dictates the need for improving their efficiency and decreasing their negative impact on the environment by the reduction of pollutant formation. To accomplish these goals improved understanding of the fundamental processes taking place during combustion is extremely necessary. This understanding is also needed for the prevention of accidental fires and explosions, and for increasing the reliability of combustion systems.

Laser based optical diagnostics has proven to be a valuable tool for characterizing combustion processes in great detail [Eckbreth 96][Taylor 93][Wolfrum 98]. They are appreciated for their ability to combine non-intrusiveness with sensitivity and selectivity for specific chemical species, which is of particular importance for combustion studies. Applications of laser diagnostics are used to improve combustion, which basically leads to increasing efficiency and minimizing pollutants. The work presented in this Thesis aims at amalgamating these exciting optical diagnostic capabilities with novel advanced image analysis and processing techniques. This type of interdisciplinary research is of interest to the combustion physics community since image analysis provides means for qualitative and quantitative studies of experimentally obtained measurements, which in turn allows for statistical interpretation and automated processing of huge amounts of data. This research is also of interest to the image analysis community since it allows for the development, incorporation, testing and enhancement of analysis techniques in an applicative ‘real world’ framework.

Chapter 1

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1.2 Image Analysis in Combustion Research In this section, we discuss some of the common image analysis and processing techniques that have been used in the literature for solving a number of combustion data analysis problems.

1.2.1 Morphological Operations and Filtering Many combustion research studies that involve imaging and image processing incorporate morphological operations for processing the image data for various purposes such as removing or reducing noise, eroding, dilating, closing or opening structures. Smoothing, median filtering etc. are also common [Smallwood 95][Malm 00][Ding 00].

1.2.2 Segmentation Segmentation plays a major role in image processing where images are basically divided into a set of parts with homogenous characteristics such as gray scale, texture etc. The quality of the segmentation results is determined by the accuracy of resulting edges and their connectivity and continuity.

For resolving segmentation problems in combustion related applications, many resort to deploying simple or adaptive thresholding to obtain flame structures. In [Smallwood 95] the threshold values are set by studying the intensity histograms in the images. Other alternatives include using spatial image gradients rather than intensities for setting the threshold values [Knikker 00]. Nonetheless, these rather simple approaches do not work well in complex cases often resulting in loss of details, the appearance of holes and contour gaps in the segmented structures, and the false detection of noise as signal.

The use of classical edge detectors for segmentation problems such as the Sobel, Marr-Hildreth, Canny and their variation is common. In [Malm 00] a Canny filter is used to segment flame boundaries in processed flame images for the purpose of determining the circumference-to-area ratios.

Clustering algorithms and morphological operations such as opening and closing can also be used. In [Baldini 00], for example, color images of flames are analyzed by first extracting regions of interest (by means of a clustering method) followed by eliminating irrelevant regions and applying morphological operations. In [Lopera 99] an edge detector that links unconnected edges, based on estimated directions, is applied to images of Diesel spray injection.

1.2.3 Fractal Analysis The use of Fractal geometry concepts for studying the properties of segmented flame contours or surfaces offers means for describing wrinkled flame fronts [Haslam 95] [Chen 99]. These methods have also been used to provide estimates of the turbulent flame velocities [Gulder 00]. They, however, introduce many

Introduction

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difficulties such as the determination of the correct fractal parameters like the fractal dimension.

1.2.4 Propagation Studies Beside standard image processing and analysis techniques, much work has been reported surrounding the stability and instability of flames. Attempts at understanding the turbulence or wrinkling of a flame front and its interaction with the flow field are examples. Pioneering work in this field started with the analysis of a plane flame front in which the flame speed along its normal is modeled to be constant. Later it was postulated that the flame speed depends on the curvature [Osher 88]. Since then many investigations of flame stability have been reported [Sethian 87].

Level set formulations in which a flame is modeled as a sharp interface propagating normal to itself with a certain speed function have been proposed to model combustion flames. The propagating reaction zone is then viewed as an infinitely thin flame front. In this view, the combustion reaction dynamics happen on a thin zone relative to the underlying fluid mechanics. Such level set methods are used to solve a number of combustion problems such as tracking the fluid mechanics and studying the shock dynamics [Sethian 99].

1.3 Thesis Contribution The Thesis presents image analysis and processing techniques for two different laser diagnostic frameworks. The first examines laser sheet images of spray injection while the second studies time resolved planar laser induced fluorescence image sequences of turbulent flames. The presented image analysis techniques, applied to laser sheet imaging data, represent new approaches for analyzing (time resolved) combustion processes both qualitatively and quantitatively with the potential of giving insight into fundamental mechanisms of (turbulent) combustion leading to better understanding of such processes.

1.3.1 Spray Diagnostics Studies This part of the Thesis represents collaboration between the Image Analysis Group at the Department of Signals and Systems and the Molecular Physics Group at the Department of Experimental Physics both at Chalmers University of Technology. The underlying project is part of the activities of the Combustion Engine Research Center (CERC), which is a competence center at Chalmers that serves as a forum for joint industrial and academic research. CERC performs research of industrial interest and focuses on the transfer of knowledge between the academic and industrial communities in an interdisciplinary way.

Chapter 1

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In this part of the work we present techniques for analyzing image data obtained through the application of laser sheet imaging to combustion diagnostics, more specifically, to spray diagnostics. The images reflect Mie Scattering arising from particles or droplets in fuel sprays and are used to study the fuel injection stage of combustion. The analysis of the images comprises background removal, spray segmentation, edge detection, as well as measurement of a number of spray characteristics such as the cross sectional area, perimeter length, and penetration length.

On the other hand, since the studied sprays are optically dense, a method for compensating laser attenuation is developed. The scheme is based on Beer-Lambert’s law, which is used to sum up the light loss along the laser path in the image and to compensate for this loss. Further studies of the spray characteristics via its cross sectional profiles, which reflect the optical density, are obtained after correcting for laser attenuation using the aforementioned compensation scheme.

1.3.2 Time Resolved Studies of Turbulent Flames This part of the Thesis represents collaboration between the Image Analysis Group at Chalmers University of Technology, the Department of Chemical Engineering at Cambridge University, and the Combustion Physics Group at Lund University (the latter being part of the Lund Laser Center, an organization for coordinating research and teaching in lasers, optics and spectroscopy at Lund University).

In this part of the work we present techniques for analyzing image sequences obtained through the application of time resolved laser imaging for turbulent combustion diagnostics. The analyzed data comprise image sequences produced by planar laser induced fluorescence (PLIF) imaging of turbulent flames which are used to investigate flame front structures in both non-premixed jet flames and spark ignited premixed flames. Image analysis methods for edge preserving smoothing, segmentation, tracking, frequency domain interpolation, and velocity estimation are developed in order to study the influence of fluid motion and reaction chemistry on flame structure, velocity, topology etc. Curve matching based on the computation of geodesic paths is used to track (interpolate) the flame motion where implicit representations incorporating level set methods are deployed to allow proper handling of complex flame front curves with arbitrary topology present in high turbulence scenarios. Finally, a scheme where high speed PLIF imaging of OH is combined with particle image velocimetry (PIV) is used to facilitate the separation of the effects of flow and chemistry on local flame front velocities and structures.

Introduction

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1.4 Thesis Outline Chapter 2 presents a short discussion over a number of background topics that are useful for the understanding of the combustion research issues related to this Thesis.

Chapter 3 deals with spray diagnostics in combustion systems where image analysis of data produced using laser sheet imaging is employed for the purposes of characterizing sprays in engines equipped with direct fuel injection. This chapter is based on the following publications:

• Abu-Gharbieh R., Persson J., Försth M., Rosén A., Karlström A., and Gustavsson T. “Compensation Method for Attenuated Planar Laser Images of Optically Dense Sprays”. Journal of Applied Optics, vol. 39(8), pp. 1260-1267, March 2000.

• Abu-Gharbieh R. “Image Analysis Applied to Spray Characterization”.

Technical report R008/1998, Department of Signals and Systems, Chalmers University of Technology, 1998.

Chapter 4 provides a description of the high speed laser diagnostic system used to produce image data sequences to be analyzed for the purposes of conducting studies on turbulent flame phenomena. The system has the capability of recording rapid sequences of up to eight images with a temporal resolution ranging from microseconds to milliseconds. Chapter 5 presents a number of advanced image analysis methods for extracting information about the structure and dynamics of turbulent flame images such as edge preserving smoothing, contour segmentation, interpolation and tracking in time. This chapter is based on the paper:

• Abu-Gharbieh R., Hamarneh G., Gustavsson T., and Kaminski C. “Flame Front Tracking by Laser Induced Fluorescence Spectroscopy and Advanced Image Analysis”. Journal of Optics Express, volume 8(5), pp. 278-287, February 2001.

Chapter 6 treats the problem of tracking complex flame contours of arbitrary topology. A curve matching approach is proposed where the concepts of shortest paths (geodesics) and implicit level set representations are used. This chapter is based on the paper:

• Abu-Gharbieh R., Kaminski C., Gustavsson T., and Hamarneh G. “Flame Front Matching and Tracking in PLIF Images Using Geodesic

Chapter 1

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Paths and Level Sets”. Proceedings of IEEE’s Workshop on Variational and Level Set Methods in Computer Vision, pp. 112-118, Vancouver, July 2001.

Chapter 7 presents methods for studying image data sequences obtained using a scheme where high speed PLIF imaging of OH radical concentrations is combined with PIV in turbulent flames. The techniques facilitate the separation of flow and chemistry effects on local flame front structures. This chapter is based on the paper:

• Abu-Gharbieh R. and Kaminski C. “Flame Front Matching and Particle Image Velocimetry for Resolving Interactions of Chemistry and Turbulence in Flames”. Submitted for publication.

In Chapter 8 a number of future research directions are discussed.

Chapter 2. BACKGROUND

Our deep dependence in modern day civilization on combustion processes in almost all fields of life such as propulsion, heating, manufacturing, energy conversion etc. creates great demands on fuel resources while at the same time introduces many environmental and health concerns. As a result, there exists a clear need for increasing our knowledge and understanding of combustion processes in order to enhance their efficiency and reduce their negative environmental effects. For those reasons, combustion research continues to be an important research topic that essentially aims at designing better machines that are safe, efficient and clean. This chapter briefly discusses some related background topics in this area.

2.1 Combustion Engines An engine is a machine that converts some form of energy into mechanical power (motion). Heat engines refer to devices that produce mechanical power from chemical energy contained in the fuel by deriving power directly or indirectly from exothermic reactions such as those occurring during combustion. The two principal classes of heat engines are internal combustion engines and external combustion engines. External combustion engines employ a secondary working fluid that comes in between the combustion chamber and the power producing elements. An example of such engine is the steam engine. Internal combustion engines are those in which the mixture of fuel and air is burned in the engine so that the hot gaseous products of combustion act directly on the surface of its moving parts, such as the piston. These engines are the most widely used of all present day power generating systems. They date back to 1876 when Otto developed the spark ignition engine and 1892 when Diesel invented the compression ignition engine [Heywood 88].

Internal combustion engines can be divided into two major subclasses, namely the continuous combustion engines and non-continuous combustion engines. In the first type, a stable flame is maintained for continuous combustion by a steady flow of fuel and air into the engine. An example of such engine is the jet engine. In the second type, combustion is done in cycles with periodical ignition of the mixture of fuel and air. An example of such engine is the gasoline reciprocating piston engine. The basic principle of these engines is that the ignited

Chapter 2

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fuel/air mixture pushes a piston located in the combustion chamber that is connected to a crank causing it to rotate thus generating the output mechanical power.

Many internal combustion engine designs exist nowadays. Classification of different designs depends on aspects such as the type of fuel used which could be anything from Gasoline to diesel to natural gas to alcohols. The designs also vary depending on their use i.e. whether they are generating power for a car, a truck or an aircraft. Another aspect is the ignition which can either be generated using a spark or by compression as in diesel engines. The diesel engine gains its energy by burning fuel injected or sprayed into the compressed, hot air within the cylinder. The air must be heated to a temperature greater than the temperature at which the injected fuel can ignite. Fuel sprayed into air that has a temperature higher than the “auto ignition” temperature of the fuel spontaneously reacts with the oxygen in the air and burns. The most outstanding feature of the diesel engine is its efficiency. The principal drawback though is the emission of air pollutants. These engines typically discharge high levels of particulate matter (soot), reactive nitrogen compounds (commonly designated NO), and odor compared to spark ignition engines.

2.2 Combustion Flames Combustion problems can be classified according to their flame types: diffusion, premixed, or partially premixed. In diffusion flames, the fuel and oxidizing species enter the combustion zone as discrete streams. Subsequent chemical reaction and heat release take place when the processes of molecular and/or turbulent diffusion bring the reactants together. Flames of this type are typically found in gas turbine combustion chambers, open fires, and many power station and industrial furnaces.

In premixed flames, the fuel and oxidizer are mixed at a given ratio before they enter the combustion device. Subsequent reaction takes place in a combustion region that separates unburnt reactants and completely burnt combustion products. Flames of this type are seen in many designs of natural gas burners, and in problems of hazard analysis where a gas/air mixture may be accidentally ignited.

Partially premixed flames exhibit the properties of both premixed and diffusion flames. They often result when an additional oxidizer stream enters a premixed system, or when a diffusion flame becomes lifted off the burner so that some premixing takes place prior to combustion.

2.3 Lasers as Diagnostic Tools Recent years have witnessed a huge growth in the use of lasers and computers for measuring the detailed performance of combustion systems. Laser diagnostic methods allow direct measurement in a non-invasive way while computational

Background

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power allows the development of modeling and analysis approaches for the measured data. New methods that use lasers for diagnostic probing of combustion processes introduce new capabilities for performing accurate measurements that are instantaneous as well as spatially and temporally precise, which were impossible to perform earlier.

Lasers produce coherent beams of light of a very pure single color that can be intense enough to vaporize the hardest and most heat resistant materials. The word laser is an acronym derived from “Light Amplification by Stimulated Emission of Radiation”. Nowadays, there a large number of different lasers exist, but some of the important ones for diagnostics purposes include YAG, organic dye, and excimer lasers.

The fundamental principles of lasers are based on the fact that atoms and molecules may exist at low and high energy levels. Exciting those at low levels to higher levels causes them to emit light when they return to the lower levels. The decay of the stimulated electrons to a lower energy state yields emission of light, which is contained within the lasing medium between two mirrors. The reflections back and forth amplify the stimulating wave and, with sufficient multiplication, results in an intense, coherent, narrow beam of monochromatic light that is tremendously powerful. This is what is usually referred to as LASER (in ordinary light sources, the atoms and molecules emit light of many different colors –wavelengths- independently).

Lasing takes place in various media, including glasses and single crystal ceramics. The first laser, operated by Theodore H. Maiman in 1960, consisted of a rod of synthetic ruby (single crystal Al2O3 doped with chromium) that was excited by a flash lamp. Excitation, or pumping, involves promoting electrons within the dopant centers to higher energy levels by optical or electronic means. Two well known ceramic lasing materials are the chromium doped Al2O3 known as ruby and the neodymium doped yttrium aluminum garnet known as Nd:YAG.

Certain organic dyes are capable of fluorescing i.e. re-radiating light of a different color. Though the excited state of their atoms lasts only a small fraction of a second and the light emitted is not concentrated in a narrow band, many such dyes have been made to exhibit laser action, with the advantage that they can be tuned to a wide range of frequencies. Dyes such as Rhodamine 6G, which emits orange-yellow light, can be made to lase (provide laser action) through excitation by another laser. Rhodamine 6G was the first dye for which continuous, rather than pulsed, operation was achieved, making possible the production of a continuous beam of tunable laser light. Another dye, methylumbelliferone, with the addition of hydrochloric acid, can be made to lase at wavelengths varying across the light spectrum from ultraviolet to yellow, producing laser light of almost any desired frequency within this range.

Chapter 2

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2.3.1 Light Light is an electromagnetic radiation. Electromagnetic radiation refers to the flow of energy at the “speed of light” in the form of electric and magnetic fields that make up an electromagnetic wave. Electromagnetic waves are characterized by their frequency f or wavelength � . The quantities f , measured in Hz (cycle/sec), and � , measured in meters, are related through c f�� where c is the speed of light in vacuum, and is equal to ca 300 000 km/sec.

Electromagnetic radiation can occur over an extremely wide range of wavelengths ranging from gamma rays with wavelengths in the order of 10-14 cm to long radio waves measured in millions of kilometers (see the electromagnetic spectrum in Figure 2.1). Quantum theory describes this radiation as the flow of photons (light quanta) through space. Photons are packets of energy that move with the speed of light c . This energy E is usually expressed in units of electron volts and is given as E hf� where h is Planck’s constant and is equal to 6.6260755e-34 joule sec (its dimension is the product of energy multiplied by time, a quantity called action).

The term ‘light’ usually refers to the electromagnetic radiation that can be detected by the human eye. This covers a narrow band of the electromagnetic spectrum with corresponding wavelengths extending from 7e-5 cm (red) to 4e-5 cm (violet). Nevertheless, the spectral regions adjacent to the visible band, namely the infrared and ultraviolet regions, are often referred to as light also. The different frequency bands with their corresponding wavelengths are illustrated in Figure 2.1.

2.3.2 Light Scattering by Particles The underlying physics of scattering comes from the composition of matter. Matter is composed of electrically charged particles, electrons, and protons which when illuminated by an electromagnetic wave, are excited and set into motion. The electric field in the electromagnetic wave accelerates the electrons in the molecules of the medium which causes each accelerating electron to produce it’s own secondary electromagnetic wave (scattered wavelet) which propagates spherically outwards.

When the scattering particles are very small compared to the wavelength of light, the intensity of the scattered light is related to that of the incident light by the inverse fourth power of the wavelength. This is called Rayleigh scattering. If the size of the scattering particles approaches the wavelength of light or exceeds it, the complex Mie scattering theory applies. In this case, the scattered light is a complicated function of the droplet shape, size, scattering angle and wavelength. In cases where the medium is absorbing, the energy coupled into the electron from the incident photon is dissipated and thus the photon energy will be absorbed and converted to thermal energy. This is called “light absorption”.

Background

11

2.3.3 Direct and Inverse Problems When an electromagnetic wave interacts with a particle, one could consider two sets of problems. In the first, the direct problem, one wants to determine the field everywhere given all the information about the particle’s size, shape, composition as well as the characteristics of the illuminating beam. On the other hand, in the second set of problems, the inverse problem, one wants to deduce information about the particle or particles giving rise to an observed scattering. Usually, the second problem is the one of interest and is the harder task.

Figure 2.1: The Electromagnetic Spectrum [EB].

2.4 Laser Diagnostic Techniques Various laser diagnostic techniques exist. The high brightness, pure color, and directionality of laser light make it ideally suited for experiments on light scattering. Even a small amount of light that is scattered with a change of wavelength or direction can be readily identified and used to constitute a signal that can be studied and analyzed.

Chapter 2

12

2.4.1 Classification of Laser Diagnostic Methods Laser diagnostic implementations can be either incoherent or coherent. In incoherent scattering processes, a signal is generated by the scattering that is radiated in all directions from each point in the path of a single laser (i.e. the signal is essentially radiated into 4� str). A fraction of the scattered signal is

collected at some angle to the incident beam, usually 90º. Back scattering (collecting at angle 180º) can also be utilized which means incoherent methods can be single port, that is, only a single observation window needs to be added to the engine or combustion system.

Incoherent scattering includes elastic and inelastic scattering. In elastic scattering, the incident light photons and the target particles do not exchange energy. This way, no frequency shift occurs for the scattered light, i.e. the scattered light has the same frequency as the incident light. An example of elastic scattering is Rayleigh scattering, which occurs when the particles scattering the light quanta have a much smaller diameter d than the light wavelength � (d ��� ). Rayleigh scattering is inversely proportional to the fourth power of the light frequency, 4

RayleighS ��

� , and hence the higher frequencies are the most scattered. This kind of scattering is the reason why the sky appears blue during daytime. The light from the sun is scattered by dust particles and clusters of gas molecules, and the scattered blue rays seen against the dark background of outer space cause the sky to appear blue. At sunrise and sunset, when sunlight travels the farthest, almost all of the blue rays are scattered and the light that reaches the earth directly is seen as predominantly red or orange. Another example of elastic scattering is Mie scattering, which refers to the case when the relation d ��� does not hold. In these cases, the Mie scattering theory that explains colors other than blue such as white, which is scattered at the largest sizes as in fog and clouds, applies.

In inelastic scattering processes, an energy exchange between the light quanta and the particles occurs and thus the scattered frequency is changed from that of the incident light frequency. Examples include instantaneous Raman scattering and laser induced fluorescence (LIF). In LIF photons from a laser beam are absorbed by molecules so that their valance electrons are excited into a higher electron state. After a short time, depending on such factors as pressure and temperature, the electrons fall back into the lower energy state thereby emitting photons. This florescence is collected and constitutes the LIF signal.

By contrast to incoherent methods, coherent approaches are two-port (always require two observation ports). These methods are more complex and require line of sight optical access and result in a laser like signal beam. Examples of coherent scattering processes are coherent anti-stokes raman spectroscopy (CARS) and degenerate four wave mixing (DFWM).

Background

13

Two dimensional laser imaging is a very important diagnostic technique. The basic concept is that a laser beam is formed into a thin sheet that illuminates a thin plane while the scattered light is imaged into a two dimensional detector, which is typically an array detector such as a CCD camera.

2.4.2 Advantages and Disadvantages Many limitations restrict the experimental probing of combustion processes. Although these processes are very harsh and hostile, in terms of high temperatures for example, they can nevertheless be easily disturbed. Hence, employing any physical probes will introduce perturbations that might change the processes under investigation. Optical techniques on the other hand have the potential to overcome these limitations. Techniques such as laser diagnostic methods enable non-intrusive in-situ measurements, which even means that there are no upper temperature limits for their applicability. Pulsed laser make it possible to perform instantaneous measurements in what could be seen as freezing any rapid changes in the processes under investigation. A typical pulsed laser has a pulse duration of ~10 ns, but also ultra fast lasers can be used with pico second and femto second pulse lengths.

Nonetheless, a major limitation of laser techniques is that they require optical access to the test volume, which often means that windows to the enclosure where the process under investigation is taking place have to be available. On the other hand, measurements can also become impossible to perform if the fuel or gases absorb the laser light. Another limitation for many laser techniques is that they only give relative data while we often need quantitative measurements. Other limitations include high cost and the need for a skilled expert to carry out the experiments and measurements.

2.5 Charge Coupled Devices Boyle and Smith invented charge coupled devices (CCDs) in 1970 [Holst 98]. This technology is based on a semiconductor architecture in which charge is collected in storage areas, then transferred from there to be converted into measurable voltage. CCDs can be thought of as films for electronic cameras, although they are also found in video cameras and desktop scanners. They consist of thousands or even millions of cells, each of which is light sensitive and capable of producing varying amounts of charge in response to the amount of light they receive. CCDs use a light sensitive material on a silicon chip to electronically detect photons. The chip contains integrated microcircuitry to transfer the detected signal along a row of discrete picture elements (or pixels) and thereby scan an object or objects very rapidly. The CCD’s photosensitive elements (usually a high purity silicon layer) are located between a silicon dioxide layer on one side and a low resistivity silicon substrate on which the device is fabricated, on the other side. They operate by measuring the photon induced charge which is created,

Chapter 2

14

stored and read out by shifting the charge from pixel to pixel by changing the gate potentials, see Figure 2.2. When individual pixels are simply arranged in a single row, the detector is referred to as a linear array. When the pixels are arranged in rows and columns, the assemblage is a two dimensional array.

CCDs are very sensitive and possess large dynamic ranges and low noise characteristics. However, when CCD arrays operate in warm conditions, they produce an output signal even if no light is incident on them [Eckbreth 88]. This signal is known as the dark current, which introduces noise to the real detected signal. To reduce this noise, the CCD array should be cooled so that thermal excitation is reduced. Usually this is achieved by electrical or chemical cooling. In combustion imaging applications CCDs are ideal due to their high sensitivity, image fidelity and large dynamic range.

Figure 2.2: Basic structure of a charge coupled device.

Chapter 3. SPRAY DIAGNOSTICS

The work covered in this chapter is based on joint collaboration between the Image Analysis Group at the Department of Signals and Systems and the Molecular Physics Group at the Department of Experimental Physics, both at Chalmers University of Technology. The underlying project was initiated by the Combustion Engine Research Center (CERC), a competence center at Chalmers where joint industrial and academic combustion research is performed.

In this chapter1 we present analysis methods for image data obtained through the application of laser sheet imaging to combustion diagnostics for the purpose of characterizing sprays in engines employing direct fuel injection. Examples of targeted combustion systems include gasoline engines and diesel engines. Understanding the spray behavior aims at enhancing the performance of combustion systems equipped with a spray injector. This involves finding means to disperse the fuel into the smallest possible droplets that are well mixed with the air in the combustion chamber.

The overall shape of a spray and its penetration length into the receiving media, can be measured by photography, either direct or backlit by flash lamps or laser [Sjöberg 96]. The extent of the vapor cloud surrounding the spray can be visualized using Schlieren imaging [Siebers 98] or laser induced fluorescence (LIF) of the fuel vapor [Hodges 91]. However, measuring the internal properties of a spray, such as its breakup from solid liquid into smaller droplets, their size and number density, is quite difficult. Methods that are used to measure droplet distributions include phase doppler anemometry (PDA) [Koo 91], interferometric laser imaging [Glover 95], extinction measurements [El-Beshbeeshy 92] [Kamimoto 89], and polarization ratio light scattering measurements [Cavaliere 88] [Presser 90]. PDA and laser interferometry measure the size and the number of droplets passing through a measurement point, but the results become unreliable when the methods are applied to the core of the spray, close to the spray nozzle where the number density of droplets is highest, and their size and shape vary the most. Extinction methods measure the integrated (line of sight) mean droplet diameter but can also be used to measure a local mean droplet diameter. The polarization ratio method measures a local mean droplet diameter too. A recently developed technique that offers more promise for measurements in 1 Parts of this chapter appeared in [Abu-Gharbieh 98] and [Abu-Gharbieh 00].

Chapter 3

16

dense sprays is laser sheet dropsizing (LSD). In LSD the same imaging system is used to capture a PLIF image of a sprayed liquid as well as another Mie scattered image. The ratio of the intensity at a certain pixel in the PLIF image to the corresponding intensity in the Mie image is proportional to the Sauter mean diameter (SMD) of the spray [Le Gal 99][Jermy 00][Jeong 00].

The image data analyzed in this chapter depict the spray injection stage. These images of fuel sprays (ethanol) are experimentally produced by planar laser imaging where time evolutions of the spray are observed by capturing images at different laser delays. Laser sheet imaging of a spray works by sending a laser beam shaped into a thin sheet through it with the plane of the laser defining the cross section of the spray that is imaged. Imaging can be based on several different optical principles [Eckbreth 88] one of which is Mie scattering, such as light scattering from liquid droplets [Ossler 95]. The scattered intensity from a small droplet is a complicated function of the droplet shape, size, scattering angle and wavelength [Bohren 83]. The Mie scattered light from cross sections of the fuel sprays is imaged onto a CCD camera. This technique works well in media that are optically thin, that is where the laser is only attenuated by 10% or less after passing through the spray. When the medium is not optically thin, as in the core of a fuel spray, the quality of the images is degraded and interpretation becomes difficult.

Two data sets are studied here. The first consists of low magnification images while the second consists of high magnification images. The raw image data are preprocessed in preparation for performing the characterization study. The sprays in the first image dataset are segmented and some of their characteristics, such as the spray’s cross sectional area, perimeter length and penetration length, investigated. The sprays in the second set are used to further study the spray characteristics after being corrected for laser attenuation as we describe next. Since the studied sprays are optically dense, a method for compensating laser attenuation in optically dense sprays is developed. The scheme is based on Beer-Lambert’s law, which is used to sum up the loss of light along the path of the laser in the image and to compensate progressively, pixel by pixel, for this loss. The spray images from the high magnification set are corrected using the aforementioned compensation scheme. The compensated images are then used to further study the characteristics of the spray by gaining information about the spray core. For that purpose, the cross sectional profile of the spray, which reflects the optical density, is analyzed.

Spray Diagnostics

17

3.1 Experimental Setup An overview of the experimental setup2 used to produce the image data analyzed in this chapter is shown in Figure 3.1. The light source is an XeCl excimer laser with wavelength 308 nm, a pulse energy of 80 mJ, and a pulse length of about 20 ns.

Figure 3.1: An overview of the experimental setup. Excimer lasers have a relatively low directionality, which is a problem when a tight focus is necessary. For this reason the laser beam is filtered. The beam is focused by a cylindrical quartz lens. This focuses the beam in the horizontal plane but leaves the vertical height unaffected. As a result of the imperfect directionality of the beam rays, the cylindrical lens does not focus all rays to a tight focal point. This necessitates the use of a slit of 0.02 mm width that is placed in the focus of the laser beam. In this way, the rays that deviate much from the mean direction of the laser beam do not pass through the slit but instead hit its edges, which consists of reflecting razorblades. Finally, the remaining rays, which do pass the slit, continue as if they originate from a highly directional beam. The beam is then passed through a second cylindrical lens and is focused to a point corresponding to the centerline of the spray. As a result of the described beam filtering, a laser sheet with a waist of 30 µm can be created.

The spray is generated using a Bosch fuel injector equipped with a single hole nozzle, with a hole diameter of approximately 0.2 mm. The opening pressure of the injector is set for 245 bar with ethanol injected into air at atmospheric

2 The experiments were carried out at the Department of Experimental Physics at Chalmers.

Chapter 3

18

pressure and at temperature 295 K, which are the operating conditions for this study. The duration of the injection is 1 ms, measured with a needle lift gauge, which is also used to synchronize the laser with the spray start. The injector is mounted vertically on a translation table with the spray injected downward, as shown in Figure 3.2. The translation table is movable in the direction perpendicular to the laser beam, thus making it relatively easy to direct the laser sheet to the middle of the spray, that is, to enter along a diameter of the spray.

The laser is focusedto a thin sheet,0.03 mm thick

Light scattered from liquidsurfaces, drops and bubbles

Laserbeam

0.02 mm slit

CCD camera

Lens

The nozzle opening,0.2 mm diameter

The spray surface,expanding down (into the paper)

Figure 3.2: The top view of the experimental setup with the beam optics included.

Part of the light scattered by the spray is collected with a Nikon quartz telephoto lens and imaged onto a thermo-electrically cooled CCD camera (Spectra Source, model Teleris 2, with a CCD array of fabricate Kodak KAF 1400). The CCD chip has 1317 pixels by 1035 pixels with a pixel size of 6.8 µm by 6.8 µm and a dynamic range of 12 bits. A band pass filter (Schott UG11) centered on the laser wavelength (308 nm) is mounted on the telephoto lens to suppress stray light. The FWHM (full width half maximum) bandwidth of the filter is 110 nm. This experimental setup enables only one image per spray cycle to be recorded and not multiple images of the same spray, which would be needed for a detailed study of the spray dynamics. The long readout time (1-2 sec) of the used CCD chip does not allow multiple exposures during a single spray cycle (which lasts ca 1 ms).

3.2 Spray Image Sets Two sets of images are studied, one set with higher resolution while the other with a low magnification factor.

Spray Diagnostics

19

3.2.1 Low Magnification Dataset The first spray image dataset contains low magnification images with each pixel representing a 35 µm by 35 µm area. These overview images show the evolution of the spray and are used to segment the spray body in order to determine its overall shape and size, or in other words, to determine its global characteristics, as we will describe later. Example images from this set are shown in Figure 3.3 where the captured spray is shown at two time instants. Note that in the figures the laser beam (sheet) is impinging on the spray from the bottom.

(a)

(b)

Figure 3.3: Examples of overview low magnification images at two time instants. (a) captured prior to (b) relative to the injection cycle.

3.2.2 High Magnification Dataset The second image dataset consists of high magnification spray images with each pixel representing a 2.5 µm by 2.5 µm area. These images show only parts of the spray and thus reflect its structure in more detail. The images are corrected for laser attenuation and then used for studying and analyzing the core of the spray as we describe later in this chapter. Example images from this set are shown in Figure 3.4.

Chapter 3

20

(a)

(b)

Figure 3.4: Examples of high magnification images at two time instants. (a) captured prior to (b) relative to the injection cycle.

3.3 Non-Uniform Background Subtraction Due to a variety of reasons such as leakage of light into the system and CCD array dark counts, the background intensity of the spray images is not uniform. In order to avoid bringing this pattern into the image characterization procedure, a preprocessing step to remove this non-uniform background is applied.

The non-uniform background can be approximated by fitting a function, � �,B x y , to a number of points that are part of the background in the original raw

image. Different functions can be used for the fitting procedure; a bicubic polynomial interpolation function is used here.

For a bicubic polynomial, the functional form of the background is expressed as:

� � 2 250 1 2 3 4

2 2 3 36 7 8 9

,

B x y a a x a y a xy a x a y

a x y a xy a x a y

� � � � � �

� � � �

. (3.1)

Using the known locations and brightness values of selected image points, least squares fitting of the function � �,B x y can be performed by evaluating its value at

Spray Diagnostics

21

each point. This means that we have to solve the following set of equations for the polynomial coefficients:

2 250 1 2 3 4

2 2 3 36 7 8 9

( , )

i i i i i i i i

i i i i i i

B x y a a x a y a x y a x a y

a x y a x y a x a y

� � � � � �

� � � � (3.2)

for 1,2, ,i N� � which can be rewritten as ( , ) for 1,2, ,Ti i i iB x y b i N� � �a v � (3.3)

where 2 2 2 2 3 31T

i i i i i i i i i i i i ix y x y x y x y x y x y� �� � �� �v (3.4)

0 1 9T a a a� �� � �� �a � (3.5)

and N is the number of the selected image points. The polynomial � �,B x y has ten unknown coefficients 0 1 9a a a� , and

could, in principle, be fitted with only that number of marked points, (i.e. with 10N � ). However, in order to get a good fit and diminish sensitivity to minor

fluctuations in individual pixels, and to have enough points to sample the entire image area properly, it is usual to require several times this minimum number of points.

By arranging the N equations in (3.3) we get �b Va where

1 2T

Nb b b� �� � �� �b � and 1 2

TN

� �� � �� �V v v v� .

Solving for the fitted coefficients a gives �

�a V b where � �1T T��

�V V V V . The fitted background � �,B x y can now be subtracted from the original image,

� �,oI x y , just as a physically acquired background image would be. The resulting image with the non-uniform background removed, ( , )nbI x y , is then expressed as:

� � � �( , ) , ,onbI x y I x y B x y� � (3.6)

To locate the selected image points used in the background fitting procedure, we subdivide the image into a grid of smaller regions and sample the background (the darkest pixels in our case) in each sub-region. In summary, the background subtraction algorithm constitutes the following:

1. Dividing the raw spray images into small sub-images of size M�N pixels. The choice of M and N depended on the size of the images in different data sets as well as the specific existing background pattern.

Chapter 3

22

2. For each sub-image, the minimum intensity value is determined and then considered to be the background value for that sub-image.

3. An approximate model of the background is formed by generating a

background surface with the same dimensions of the original image. This is implemented here using Bi-cubic interpolation between the background intensity values of all of the different sub-images obtained in step 2.

4. The resulting background surface is subtracted from the original image.

An example result is shown in Figure 3.5. It illustrates how the proposed algorithm successfully removes the non-uniform background from the spray images.

Spray Diagnostics

23

(a)

(b)

(c)

Figure 3.5: Non-uniform background subtraction. (a) Original image. (b) After background subtraction. (c) Background image.

Chapter 3

24

3.4 Compensation of Laser Attenuation Laser sheet imaging techniques work well in media which are optically thin, that is, where the laser is only attenuated by less than 10% after passing through the whole spray. When the medium is not optically thin but instead is optically dense, as in the core of a fuel spray, the quality of the images is seriously degraded and interpretation becomes difficult. Optical density ρ refers to the transmittance T of the medium that the light traverses. T and ρ are related according to

101logT

ρ � �= � �� �

(3.7)

which for example means that a medium of optical density ρ =1.0 has a transmittance T of 0.1 (10%). Generally, optically dense matters are defined as those that have their molecules separated with a distance less then the wavelength of the incident light.

Most of the raw images studied in this chapter suffer from strong asymmetry. This is reflected in a much stronger light scattering in the lower half of the image (where the laser beam enters the sample). This is due to the attenuation of the laser beam as it traverses the spray. As the spray got denser, more light is scattered from the laser beam and thus the beam gets attenuated faster.

3.4.1 Scattering Model The optical density ( )x� is defined as the density of scattering cross section � per unit volume. The scattering cross section can, through the theory of Mie scattering, be related to the droplet surface area and quantitative measurements can then be realized. Note that here we assume that an incoming laser ray can either be reflected or transmitted, that is, absorption is assumed to be negligible.

In an infinitesimal volume we have by definition: d dV Adx� � �� � where dV is an infinitesimal volume and A is the area. This gives

0

( ) ( )x

x A x dx C� � � �� �� (3.8)

where C is an integration constant. Here 0x � corresponds to the point where the laser beam enters the spray, which will be denoted by 0x from now on. The power scattered from an infinitesimal cross section d� is given by: dP Id�� � . The intensity of the laser beam I after this scattering will be decreased by /dP A , therefore

IdI dA

�� � (3.9)

and hence

Spray Diagnostics

25

exp( )I CA�

�� � (3.10)

where C � is an integration constant. With equation (3.8) inserted we obtain

0

( ) exp ( )x

CI x C x dxA

�

� ��� �� � ��� � � �� ��� � (3.11)

Finally, using the boundary condition 0 0( )I x I� gives

00

( ) exp( ( ) )x

I x I x dx� � �� �� (3.12)

which is the Beer-Lambert’s law. In order to relate the scattered light captured by the CCD array to the optical density in the spray, which is responsible for the laser attenuation, we make an assumption relating the scattering cross section, ( )x� , to the signal observed at the CCD chip, ( )s x . The geometry of our setup means that we are only measuring the light scattered through 90°, and not detecting any light scattered into other directions. Our assumption comes here in that the light detected at 90°, for each droplet, is proportional to the total scattering cross section � for that droplet, that is

� �90 totalconst� �� � � . (3.13) This approximation is quite good for the majority of spherical droplets, with the exception being the set of droplets where destructive interference gives rise to extinction of the light scattered at 90° [Bohren 83] [Hirleman 84]. We are thus assuming that the set of droplet sizes that gives rise to (near) extinction is not sufficiently prevalent in the spray to affect our measure of d dV� �� . The

assumption of equation (3.13) could also be violated when too much light is scattered into the 90° angle. In the geometrical optics limit, where for example the laser hits an extended liquid surface, the orientation of this air/liquid interface becomes important. Properly oriented, the entire � for the surface could be scattering at 90°, rather than a small percentage.

With the assumption discussed above, the signal ( )s x on the CCD array coming from a position x in the spray can be related to ( )x� by

0( ) ( ) ( )s x C x I x�� (3.14) where 0C is a constant (consisting of the constant from equation (3.13), multiplied by the detection efficiency of the optical system and the width of the laser sheet) and ( )I x is the intensity of the laser beam at position x.

Chapter 3

26

Inserting equation (3.12) in equation (3.14) gives

0 00

( ) ( ) exp( ( ) )x

s x C x I x dx� � � �� �� . (3.15)

Denoting 0( )s x by os and 0( )I x by oI in equation (3.14) enables us to replace

0 0C I by 0 0/s � and thus equation (3.15) can be rewritten as

0 00

( )(exp( ( ) ))/

xd s xx dxdx s

��

�� �� �� (3.16)

Integrating, we get

01

00 0

exp( ( ) )) ( )x x

x dx s x dx Cs�

��

� � � �� � �� � (3.17)

Solving for the case 0x � gives 1 1C � , and therefore

0

00 0

( ) ln(1 ( ) )x x

x dx s x dxs�

� � � � �� � �� � (3.18)

which finally gives the scattering model

0

0 0

( )( )( )

xs xx

ss x dx

�

�

�

� �� � (3.19)

To conclude our scattering model discussion, we reiterate on the assumptions made in that model. First, it is assumed that an incoming laser ray can either be reflected or transmitted, that is, absorption is assumed to be negligible. Secondly, it is assumed that the scattered light that is detected at 90° from each droplet is proportional to the total cross section for that droplet. The third assumption is that only single scattering occurs, that is, multiple scattering is neglected.

3.4.2 Compensation Algorithm Here we summarize the algorithm practically used. Since -refer to equation (3.15)-

00

0 0

( ) ( ) ( ) ( )exp( ( ) )x

ss x C x I x x x dx� � �

�� �� � �� (3.20)

can be written as

� �0

00

( )exp( ( ) )x

ss x x dx x� �

�� � �� (3.21)

and denoting 0

0( ) ( )new s

s x x��

� (3.22)

Spray Diagnostics

27

we obtain the continuous compensation equation

0

0 0

( ) ( )exp( ( ) )x

new news x s x s x dxs�

� �� � (3.23)

For discretization, the integration in equation (3.23) is replaced by a summation and thus the following algorithm is used for discrete image compensation

1

0

j inewj

jK Snew old

i iS S e

� �

�

�� � (3.24)

where oldiS is the observed pixel intensity, new

iS is the compensated value for that pixel and K is a constant corresponding to 0 0/s� in equation (3.23).

The unknown constant K has to be determined in order to perform compensation according to equation (3.24). Since the spray is injected from a cylindrically symmetric nozzle, it will be symmetric around the centerline (the line passing through the center of the nozzle). Thus K is determined such that both sides of the spray image around its centerline become balanced. Specifically, we chose the criteria for optimizing the K factor to be minimizing the difference between the upper and lower halves of the average profile in each image. This average profile represents the mean of all the profiles across the spray throughout one image (see the related figures in the next section).

3.4.3 Compensation Results The compensation algorithm is first tested on some synthetic images and then on simplified experimental images. Finally, the compensation scheme is applied on real spray images where the high resolution image dataset is used since it reflects details of the spray core with a much better resolution.

Testing on Synthesized and Test Images

Figure 3.6-a shows a synthetic image reflecting a single exponential decay from left to right. Figure 3.6-b shows the result of applying our compensation algorithm on this image. It is clear that the compensated image is of a constant intensity, which is equal to the starting intensity at the left side of the exponentially attenuated one. The optimal K factor that the algorithm finds is the one that maximize the symmetry of the profiles across the image around its centerline (which meant flattening the exponential to a line with constant level). Figure 3.6-c shows a profile across both images (from left to right). The compensation factor used is obviously the one we used to synthesize the image.

Figure 3.7-a shows a synthetic image illustrating the case when the laser beam passes through three media each having a different optical density. The optical density in the first region is double that in the second and quadruple that in the third region. Note that the exponential fall off factor K is related to the starting intensity, that is, if the optical density in a region is reduced by a factor F

Chapter 3

28

then the attenuation factor is reduced by the same factor and the scattered light intensity is also reduced accordingly. Figure 3.7-b shows the result of applying the compensation algorithm on the synthetic image discussed above where successful restoring of the piecewise constant optical density is achieved. Finally, in Figure 3.7-c, the profiles along one horizontal pixel row for the original and compensated images are presented. The algorithm is successful in restoring the constant optical density of the different optical density regions.

The algorithm is applied now on images of simplified experimental situations. Figure 3.8-a shows the attenuation of the laser sheet traversing an aqueous mono-disperse suspension of 0.5mm diameter polystyrene latex micro spheres (Duke Scientific Corporation) contained between two thin glass plates. The spheres are homogeneously distributed and thus are suitable for the purpose of testing the algorithm on a homogeneous medium with (almost) a constant optical density. Figure 3.8-b shows the result of applying the compensation algorithm on the aforementioned experimental image. Figure 3.8-c shows the profiles along one horizontal pixel row for the original and compensated images. The algorithm is successful in restoring the constant optical density of the micro sphere suspension, except for local fluctuations that were already present in the original profile.

Spray Diagnostics

29

(a) (b)

(c)

Figure 3.6: Compensating a synthetic image reflecting a single exponential decay: (a) Original image (of size 200×150 pixels). (b) Compensated image. (c) Horizontal profiles (x-axis: pixel location, y-axis: pixel intensity).

Chapter 3

30

(a) (b)

(c)

Figure 3.7: Compensating a synthetic image with three different optical densities: (a) Original image (b) Compensated image. (c) Horizontal profiles (x-axis: pixel location, y-axis: pixel intensity).

Spray Diagnostics

31

(a) (b)

(c)

Figure 3.8: Compensating an experimental test image with an aqueous mono-disperse suspension of polystyrene latex micro spheres (which approximately has a constant optical density): (a) Original image (of size 100×150 pixels). (b) Compensated image. (c) Horizontal profiles (x-axis: pixel location, y-axis: pixel intensity).

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Before we illustrate how the algorithm works on real spray images, we first discuss an aspect of the spray images that has to be handled prior to applying the compensation algorithm. Parts of the spray images show some very bright regions with intensities much higher than the rest of the spray. Probably this happens because the scattering angular distribution at these locations does not follow our assumption of being uniform but instead there is a very strong scattering towards the direction of the camera. This could happen if the spray contains big droplets behaving like mirrors, instead of the more uniform Mie scattering behavior assumed in our model. Since this behavior does not follow our model, we filter out these “hotspots” (HS) before compensation. The filtering procedure removes any pixel HSP with intensity ( )HSI P that exceeds nine times the standard deviation of the distribution of the spray body S and replaces it by a local average of its ‘non-hotspot’ neighbors.

Application on High Magnification Spray Images

The proposed compensation method is finally applied on the captured high magnification spray images. Figure 3.9 shows an original spray image with the laser penetrating the spray from the bottom side. Figure 3.10 shows the average intensity profile, which we described earlier, for that image both before (thick line) and after (thin line) compensation. Figure 3.11 shows the same average profile, before compensation, but with its left half (side) flipped horizontally by 180° (mirrored horizontally) and overlaid on its right half. The bars show the average values for the corresponding left and right halves (sides). Figure 3.12 on the other hand is similar to Figure 3.11 but shows the two halves (sides) of the average profile after compensation. Figure 3.13 shows the final result, which is the spray image after compensation. Finally, Figure 3.14 shows example intensity profiles taken at certain locations in the spray image both before (thick line) and after (thin line) compensation.

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Figure 3.9: Original high magnification spray image.

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Figure 3.10: Average intensity profile for the spray image shown in Figure 3.9, before compensation (thick line) and after compensation (thin line).

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Figure 3.12: The average intensity profile for the spray image shown in Figure 3.9, after compensation, with its left half (side) flipped horizontally by 180° and overlaid on its right half. The bars show the average value for the corresponding left and right sides.

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Figure 3.13: The spray image shown in Figure 3.9 after compensation.

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We show the results of applying the proposed compensation scheme on another high magnification spray image (see Figure 3.15 through Figure 3.19). This image differs from the first example in that it is captured at an earlier time within the injection cycle (ca 20 µs earlier).

Figure 3.15: Original high magnification spray image.

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Figure 3.16: Average intensity profile for the spray image shown in Figure 3.15, before compensation (thick line) and after compensation (thin line).

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Figure 3.18: The average intensity profile for the spray image shown in Figure 3.15, after compensation, with its left half (side) flipped horizontally by 180° and overlaid on its right half. The bars show the average value for the corresponding left and right sides.

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Figure 3.19: The spray image shown in Figure 3.15 after compensation.

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The compensated, final images shown in Figure 3.13 and Figure 3.19 now represent pictures of the scattering cross sections encountered by the laser beam at each point inside the spray, and a qualitative understanding of the internal structure of the spray can be extracted from them. The first five profiles in Figure 3.20 show a very clear double peak structure, with low intensity in the middle, between the peaks. We interpret this as a solid liquid column exiting from the nozzle, with droplets only forming a thin layer around this liquid jet. The image in Figure 3.9 is taken at a slightly later time in the spray cycle and when we study the profiles in Figure 3.14, we see the double peak structure only in the first profile while it is basically washed out in the second profile. This disappearance could correspond to a fast breakup of the central liquid core. A possible reason for the breakup appearing to be stronger in this case is increased pressure in the nozzle, since this image is from a slightly later time, when a higher pressure will have built up in the nozzle.

3.5 Segmentation and Labeling In order to segment spray structures, the images are thresholded resulting in binary images. The segmented sprays in the binary images are then labeled to identify the different components in their structures, i.e. to identify the main spray body (the largest object corresponding to the core of the spray) from the rest of the spray consisting of smaller objects (droplets) surrounding the main body. During labeling, objects are considered connected using the 8-connectivity criterion.

In Figure 3.21 through Figure 3.28 we show a sequence of images, from the low magnification set with their detected boundaries overlaid in white. The images illustrate the evolution of the spray. They are part of a larger sequence, where images are recorded every 10 µs during the evolution of the spray from repeated spray cycles. The resolution is low considering that the droplets in the images are predominantly in the size range of 5-50 µm, but the aim here is to capture the whole spray in each image and thus visualize its evolution.

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Figure 3.21: Example spray image sequence: at 100µs.

Figure 3.22: The spray at 200µs.

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Figure 3.23: The spray at 300µs.

Figure 3.24: The spray at 400µs.

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Figure 3.25: The spray at 500µs.

Figure 3.26: The spray at 600µs.

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Figure 3.27: The spray at 700µs.

Figure 3.28: The spray at 800µs.

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3.6 Global Spray Characterization A number of different global spray characteristics are studied. These include spray body cross sectional area, perimeter, penetration length, and number of objects surrounding the main body.

3.6.1 Spray Body Area The area of the spray body is proportional to the total number of pixels within the main body in the binary image. The time evolution of this measure for the sequence shown in Figure 3.21 through Figure 3.28 is shown in Figure 3.29.

3.6.2 Spray Body Perimeter A pixel is considered on the perimeter if it is white (1-valued) with at least one black (zero-valued) pixel in its neighborhood. The neighborhood could be defined using 4- or 8-connectivity criteria. Here we use the average of the two since the first tends to underestimate the true perimeter value and the second tends to overestimate it. The time evolution of the spray perimeter length is shown in Figure 3.30.

3.6.3 Penetration Length The spray penetration length is defined as the difference between the index of the first and last object in the main spray body. The time evolution of the spray penetration length is shown in Figure 3.31.

3.6.4 Objects Around Main Spray Body The number of separate objects surrounding the main spray body in each image is counted. The time evolution of this measure is shown in Figure 3.32.

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Cross sectional area of main spray body

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3.7 Discussion and Conclusion Laser sheet imaging of spray cross sections and the development of routines that can correct for laser attenuation in these images is aimed at gaining information about the spray core in applications such as high pressure fuel injection systems. The compensation method described in this chapter is based on an algorithm for progressive inversion of the Beer-Lambert law for the spray system. It is shown to work well for the test case of an aqueous suspension of polystyrene spheres. When applied to spray images, the whole image is successfully compensated with a single compensation factor used everywhere in the image.

The main use of the method lies in interpretation of the cross section profiles of the spray. One example is to measure the breakup length, the distance from the nozzle where the liquid column is shattered into droplets. A second example is the study of cavitation in the spray nozzles, and the question whether or not the cavitation bubbles can be detected in the liquid outside the nozzle. However, to make the method quantitative, calibration studies of how the scattered light intensity depends on droplet size and number density are needed.

Equation (3.19) can be used to estimate the optical density from the observed signal on the CCD camera. This will solve the problem of compensating the attenuation suffered by the laser beam as it passes through the spray. This compensation, however, adjusts for the laser being attenuated on its path into the spray, but in fact neglects the attenuation of the scattered light on its way to the detector. This attenuation due to multiple scattering could be treated in an average fashion based on the cylindrical symmetry of the problem, thus it can be approximated in much the same way as the scattering along the path of the laser and added to the solution.

One problem to point out is that the image quality in the compensated images is in part negatively affected by the process in that the image appears streaky in some areas. This problem arises because the spray system is in reality three dimensional, with multiple scattering carrying photons starting out traveling along one row into an entirely different row, where they are registered on the CCD chip. Our model does not take this into account since it is strictly one dimensional. However, the numerical variation caused by the streakiness is not very significant in the sense that single profiles from the images do not significantly deviate from the local average.

The equation for the CCD signal, namely equation (3.15), is similar to the expressions found for Planar LIF (PLIF) measurements in [Versluis 97]. Using a bi-directional setup with counter propagating laser sheets, the quenching and attenuation terms could be eliminated for the PLIF case. If this could be realized experimentally, the same approach could work for spray measurements, but the micrometer precision needed to overlap very thin laser sheets, and the much stronger attenuation encountered in the spray would make this quite difficult.

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Concerning global spray characteristics, we showed that laser sheet imaging along with the image analysis methods presented in this chapter are well suited for measurements of the spray evolution such as spray cross sectional area, spray perimeter length and spray penetration length. We believe that if these techniques are applied in more difficult environments, such as in a cell with combustion or in an engine, these measures can still be extracted.

Though the work has so far dealt with the spray injection stage, we believe that they can be equally successful if applied on images from other stages within the combustion cycle or on images from real combustion environments (i.e. from a real combustion chamber in a commercial engine).

Chapter 4. TIME RESOLVED FLAME IMAGING

Time resolved measurements require the use of high repetition rate lasers. For these laser diagnostic techniques, laser systems that produce a short but fast burst of two or more pulses can be used. Such systems may consist of a number of individual low repetition rate lasers that are fired in series, or a single laser that is operated in a multiple pulse mode.

All turbulent combustion processes are time dependent. Experiments performed with high time resolution are needed to reveal the dynamics of the turbulent reacting flow. Such time resolved measurements, with which the evolution of structures can be studied, are valuable to deepen the understanding of interactions between turbulence and chemistry.

A few number of time resolved 2D imaging data have been reported in the past due to the high demands on lasers and detectors. However, time resolved 2D imaging of fuel concentration has been demonstrated using Mie scattering of aerosols seeded to the fuel [Winter 89]. Time resolved velocity field measurements using particle image velocity (PIV) based on Mie scattering have also been reported [Oakley 96]. Double pulse imaging of OH [Dyer 84] [Atakan 93], CH [Schefer 94] and Acetone [Seitzman 94] concentrations has been performed using LIF. Longer sequences of OH and O2 LIF at comparatively low repetition rates (250 Hz) have been reported [Kychakoff 87]. Double pulse temperature imaging has been performed using Rayleigh scattering [Komiyama 96]. Detailed time resolved studies in perturbed non-premixed flames of OH concentrations [Mueller 97], OH concentrations and velocities [Mueller 95] and OH and CH2O concentrations [Paul 98] have been reported.

In this chapter we describe the setup used for producing time resolved image sequences depicting turbulent flames. LIF is used as the diagnostic technique, which has the sensitivity to provide spatially and temporally resolved information on species in gas flows. The measurement principle in this technique involves electronic excitation of the molecules of interest by laser radiation and the detection of the induced fluorescence. By using a thin sheet of laser light and recording the fluorescence with a CCD camera in a direction perpendicular to the plane of the light sheet, one can obtain two dimensional fluorescence distributions of the species of interest (planar LIF).

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4.1 High Speed Imaging System The turbulent flame image data analyzed in the next three chapters were produced through experiments conducted using a high speed laser diagnostic system at the Department of Combustion Physics at Lund Institute of Technology. The system has the capability of recording rapid sequences of up to eight images with a temporal resolution ranging from microseconds to milliseconds. It consists of an Nd:YAG laser cluster and a high speed camera. A dye laser can be optionally pumped by the Nd:YAG laser cluster if tunable laser radiation is needed.

4.1.1 Nd:YAG Laser Cluster The laser source of the high speed laser diagnostic system is a cluster consisting of four standard flash lamp pumped Nd:YAG lasers (BMI, France), see the photo in Figure 4.1.

Figure 4.1: Photograph of the laser cluster.

The multiple laser design is needed because the repetition rate of a single high power Nd:YAG laser is much slower than typical flame time scales which are in the kHz to MHz range. The beams from the four lasers, which is combined using a scheme patented by BMI which is illustrated in Figure 4.2. The four individual lasers can be fired in series with time delays ranging from 0 up to 100 ms. Each of the Nd:YAG lasers can be fired two times with a short separation between pulses. The time separation can be adjusted from 25 µs to 145 µs. By interleaving the double pulses from the four lasers the time separation between pulses can be reduced down to 6.25 µs (= 25 µs /4).

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Figure 4.2: Diagram of the laser cluster.

4.1.2 Dye Laser To convert the 532 nm output from the Nd:YAG laser cluster to other wavelengths a dye laser pumped by the Nd:YAG laser cluster is used. For exciting the OH radical, laser light with a wavelength close to 283 nm is used. This wavelength is generated using a Rhodamine 590 dye solution in methanol, with subsequent frequency doubling of the dye laser.

4.1.3 High Speed CCD Camera The detector of the high speed diagnostic system is a modified high speed framing camera (Imacon 468, DRS Hadland, UK), see the photo in Figure 4.3.

The high framing speed, up to 100 MHz, is achieved by exposing eight individual CCDs in series using short exposure times. Additional features facilitating extra triggering and incorporating an extra image intensifier are used to modify the commercially available Imacon camera, see the diagram in Figure 4.4.

Individual CCD modules consist of an image intensifier and a CCD image sensor. When used in combination with an image intensifier, very short exposure times (ns) can be reached. The image intensifiers can be switched on or off in less than 2 ns, allowing exposures as short as 10 ns. The intensifiers are fiber-optically coupled to the CCD to ensure maximum coupling efficiency. Each CCD has 576�385 pixels, with a pixel size of 22�22 µm. The signals from the CCDs are digitized to 8 bits and then stored in digital frame stores within the camera, and transferred to the controlling computer via a fiber optic link. An extra image intensifier can be fit at the front of the optical system. This intensifier increases the sensitivity of the high speed camera.

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Figure 4.3: Photograph of the high speed CCD camera.

Exposure times, gains and trigger delays for each CCD are individually programmable. The minimum time between consecutive images is 10 ns, which is increased to 1 µs when the extra intensifier is used due to the decay time of the intensifier’s phosphor. The shortest time interval between two consecutive 8-image sequences is governed by the transfer rate to the mass storage device and is limited to about 2 seconds. The possibility of using different gains for different CCDs allows events where the signal intensities varies strongly in time to be captured, as the dynamic range between images is increased in this way.

Figure 4.4: Diagram of the high speed CCD camera.

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4.2 Image Data Acquisition Using the described high speed diagnostic system, image data sequences are obtained through controlled experiments using planar laser induced florescence (PLIF) imaging of OH radicals in combustion processes. The principle of PLIF is to form a light sheet from a laser beam, using suitable optics, which traverses the flame. If the wavelength is tuned to match a molecular resonance line of OH then light from the sheet is inelastically scattered from the OH radicals present in the interaction region. This scattered light (fluorescence) is captured at right angles using a camera which is focused to image the illuminated flame cross section. The local intensity in the recorded image is a function of the local OH concentration in the flame. Since OH is formed in the reaction zone of the flame and is rapidly quenched by cold unreacted gases, it is a good indicator of the flame front position in flames where the reaction zone is thin. In hot combusted gases, OH is removed more slowly, and a certain equilibrium concentration prevails depending on local temperatures and burnt gas composition. Different types of data are analyzed including diffusion (non premixed) flames as well as premixed flames subjected to varying degrees of turbulence.

4.2.1 Premixed Data The multiple Nd:YAG laser cluster is used to pump a frequency doubled dye laser providing tunable radiation around 283 nm. The laser output is passed through sheet forming optics before traversing the combustion system of interest. A combustion cell featuring two opposing tungsten electrodes is used to ignite mixtures of methane and air, see the photo in Figure 4.5. Controlled degrees of turbulence can be imposed on the mixture via four high speed rotating fans. Figure 4.6 shows a schematic diagram of the setup used. An example sequence of the premixed combustion data captured with the described experimental setup is shown in Figure 4.7.

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Figure 4.5: Photo of the combustion cell.

Figure 4.6: Schematic setup for time resolved PLIF of turbulent spark ignition (premixed) flames.

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(a) (b)

(c) (d)

Figure 4.7: Image sequence of a premixed combustion process. (a-d) The flame progress framed every 1.7 milliseconds.

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4.2.2 Diffusion Flame Data The diffusion flames are stabilized on a co-flow burner as illustrated in Figure 4.8. Figure 4.9 illustrates the optical setup used for capturing the diffusion flame data.

Figure 4.8: Schematic diagram of the burner.

The frequency doubled output from the Nd:YAG laser cluster, λ=532 nm, is used to pump the dye laser. The dye laser radiation of ca 566 nm is then frequency doubled to 283 nm and the laser beam is focused into a sheet. This laser sheet intersects the flame generating the LIF signal at the intersection region. The LIF signal is detected at a right angle by the high speed camera. Two filters are used in front of the camera lens transmitting the LIF signal and rejecting the scattered residual dye laser light at 566 nm. An example sequence of (non-premixed) diffusion combustion data captured with the described experimental setup is shown in Figure 4.10 where one can observe a flame re-ignition event.

Figure 4.9: Schematic setup for time resolved PLIF of diffusion flames.

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(a) (b)

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Figure 4.10: Image sequence of a diffusion combustion process (non-premixed). (a-d) The flame progress framed every 125 microsecond.

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4.2.3 Laser Beam Profile Measurement The laser sheet intensity profiles are recorded online to enable the compensation of laser intensity fluctuations of the dye laser. The online laser profile measurements are performed using the setup illustrated in Figure 4.11.

Figure 4.11: Schematic diagram of the optical setup used for online laser beam profile measurement.

A portion (few percent) of the sheet intensity is split at right angles and the reflected sheet is focused into a cell containing a dye solution. The resulting dye fluorescence from the cell is imaged onto one edge of the camera’s CCDs, using a second quartz plate positioned at 45º in front of the camera lens. This plate transmits the LIF signal and reflects a few percent of the dye fluorescence on top of the PLIF image.

4.3 Simultaneous OH PLIF and PIV Measurements Another flame image dataset is obtained by a novel measurement technique where simultaneous time resolved measurements of the OH radical distribution evolution and the instantaneous velocity field are made in turbulent flames so as to study the dynamics of turbulence/chemistry interactions in real time. High speed planar laser induced fluorescence (PLIF) of OH radicals is used to track the response of the flame front to the turbulent flow field. Instantaneous velocity field measurements are simultaneously performed using particle image velocimetry (PIV) in which small particles are seeded in fluid flows in order to trace their

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motion. Measurements of both velocity and species concentrations (captured at the same time) allow detailed studies of the interaction between flow and chemistry in turbulent flames.

A commercially available Dantec PIV system is used (Dantec PIV2000 processor and Dantec Flow Manager software). It consists of a double Nd:YAG laser unit, a sheet optics module, a frame transfer CCD camera (positioned at right angles to the laser) and control and data evaluation software. The PIV laser sheet is overlapped with the OH PLIF laser sheet in the measurement region, coming from the opposite direction as illustrated in Figure 4.12. The two laser systems are synchronized so that the PIV image pair is acquired shortly after the second image in the OH PLIF sequence. An example of the captured image sequences is shown in Figure 4.13 and example images of the seeded particles are shown in Figure 4.14.

Figure 4.12: Experimental setup used for the simultaneous measurement of time resolved OH concentrations and flow fields. The OH PLIF system is shown to the upper left corner and the PIV system is shown to the lower right corner.

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(a) (b)

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Figure 4.13: Example sequence of images captured using the simultaneous OH PLIF and PIV measurement setup shown in Figure 4.12. (a-d) The flame progress framed every 125 microsecond. The PIV vectors are overlaid on the second OH frame.

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(a)

(b) Figure 4.14: (a, b) Example images of seeded particles obtained using the PIV imaging system.

Chapter 5. FLAME FRONT TRACKING

The influence of fluid physics on the development of flames is of fundamental importance for the design of more efficient and environmentally friendly combustion devices [Warnatz 96]. Turbulence, for example, has a major effect on the shape of the flame surface, which is defined as the interface between reacted and unreacted components of the combustible mixture. Turbulence can wrinkle and stretch this surface, thus steepening concentration gradients and increasing the rate of diffusive mixing across this interface.

The higher efficiency of mixing afforded by turbulence in turn leads to an increase of the burning rate of the mixture. This is often a desirable feature. Turbulent mixing, for example, has a direct effect on the efficiency of an automotive engine. However, excessive turbulence can wrinkle and stretch the flame boundary to such an extent that molecular transport starts to compete with chemical reactions. At very high strain, the heat released by reactions does not suffice to support the strong gradients and as a result the flame may become extinct. A detailed understanding of these processes is both of fundamental and practical interest and, despite much progress over recent years, is far from complete.

Recently, useful tools have emerged which allow the study of flame front development in a direct way by comparing experimental data to numerical simulations. One of the most widely used and advanced experimental techniques in this respect is planar laser induced fluorescence (PLIF) imaging which allows images of thin cross-sectional slices through the flame to be obtained. In particular, by imaging flame generated chemical radicals, which are directly produced in the reaction zone, PLIF can provide very accurate data on the flame front topology. Such data can be used to provide input for advanced theoretical descriptions of the same processes. Direct numerical simulations (DNS) and large eddy simulations (LES) are particularly promising approaches in this respect, since data generated by these techniques is directly comparable to data provided by PLIF. Model assumptions that have to be made in these two approaches can thus be tested or developed based on PLIF imaging data.

In the past PLIF flame visualizations have mostly been limited to two dimensions and/or single events in time, which do not resolve the true dynamic nature of turbulent reactive flows. Recently however, the application of high repetition rate PLIF imaging has been reported [Kaminski 00a]. This technique

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has been applied for the quantitative study of spark ignition and for performing detailed comparisons to model simulations [Dreizler 00]. Time resolved imaging of the type described in [Kaminski 00a] [Dreizler 00] offers the possibility to track the velocity and the development of flame front topology in time thus offering a more complete characterization of the process. In a variant of the technique, where the flame is rapidly sliced in space, even three dimensional reconstructions of the reaction front can be made [Hult]. However, the resulting image data create large demands on image processing and analysis and data reduction techniques.

In this chapter3, we present a number of advanced image analysis methods for extracting information about the structure and dynamics of the turbulent flame images obtained using the high speed PLIF setup described in Chapter 4. The application of non-linear anisotropic diffusion filtering and of active contour models is described to isolate flame boundaries. In a subsequent step, the detected flame boundaries are tracked in time using a frequency domain contour interpolation scheme. The implementations of the methods are described and possible applications are discussed.

5.1 Image Processing Stage As described earlier, the image data contains sequences of PLIF images reflecting OH concentrations in turbulent flames. Each sequence comprises four frames corresponding to the four consecutive laser pulses. The images are first preprocessed to correct for some experimental factors and then enhanced to reduce existing noise.

5.1.1 Preprocessing Raw Image Data Three steps are performed to correct experimental defects found in the raw recorded images. Geometrical transformations are used to correct small shifts and rotations between images recorded with different CCD channels. These effects, which cause the imaged regions not to overlap perfectly, are a result of the imperfect alignment of the individual CCD modules with respect to the optical axis. By imaging a grid pattern with all eight CCDs, the displacements can be measured and corrected by means of a geometrical transform that maps the images from the different CCDs to a common reference image (see Figure 5.1).

3 Parts of the work reported in this chapter appeared in [Abu-Gharbieh 01a].

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Figure 5.1: Correcting small shifts between images recorded with different CCD channels. Left: Alignment image as captured by two different CCDs. Middle: Magnification of the encircled areas before correction. Right: After correction.

The raw images are also processed to remove existing background levels, which are determined by experimentally capturing a zero illumination image and subtracting it from the raw image.

Finally, laser profile referencing is done, using the laser beam profile that is monitored online and saved with each PLIF image (as explained in Section 4.2.3) thus allowing subsequent compensation for beam profile non-uniformities and shot to shot fluctuations, see Figure 5.2.

Figure 5.2: Laser profile referencing. Left: Original image with the recorded laser beam intensity profile to the left and the PLIF data to the right. Right: PLIF data after dividing by beam profile.

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5.1.2 Noise Reduction Using Non-Linear Diffusion Filtering To improve the signal to noise ratio and simplify the segmentation of OH boundaries, image smoothing is used where image datasets are processed using non-linear diffusion filtering (NLDF). Mathematically, in NLDF, one treats the problem like a diffusion process where the diffusion coefficient is locally adapted to the effect that diffusion stops or becomes negligible as object boundaries are approached resulting in efficient noise reduction and object contour enhancement.

Adaptive diffusion filtering techniques were originally formulated by Perona and Malik [Perona 90] and offer several advantages. On one hand they smooth noise locally within regions defined by object boundaries whereas little or no smoothing occurs across objects. On the other hand, they also enhance local edges.

Linear Diffusion (in N dimensions) smoothes by convolving with a Gaussian kernel G such as

� �

� �� � � �� �11 1exp

22T

NG

�

�

� � � � �

�

x x m x m (5.1)

where x is a vector containing the N variables (for a two dimensional image N=2). � is the covariance matrix of the variables, and m is the mean of x .

Diffusion can be thought of as the physical process that equilibrates concentration differences without creating or destroying mass. Mathematically, this is described by Fick’s law

j D I� � �� (5.2) where the flux j is generated to compensate for the concentration gradient I� and D is a tensor that describes the relation between the two [Weickert 98]. Using the continuity equation (conservation of mass)

� � � �t I div j� � � (5.3) we get

� � � �t I div D I� � � � . (5.4) The solution of the linear diffusion equation with a scalar diffusivity D d� ,

� �tI div d I� � � , is exactly the same operation as convolving the image I with a Gaussian kernel of width 2 .t Perona and Malik proposed to exchange the scalar diffusion constant d with a scalar valued function g of the gradient of the gray levels in the image. The diffusion equation then becomes

� �� �tI div g I I� � � � . (5.5) The length of the gradient I� is a good measure of the edge strength of the current location, which is dependent on the differential structure of the image. This dependence makes the diffusion process nonlinear. In our case the imaged data is filtered using the equation

� �� �� �*tI div g G I I�

� � � � (5.6)

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where I represents the intensity of the image under consideration, and � �� �*g G I

�� represents a locally adaptive diffusive strength. The latter is

made proportional to the gradient I� in the image itself after smoothing with a Gaussian kernel G

� of width � , which is done for stability reasons [Catté 92].

As a diffusivity function we use a function originally proposed in [Weickert 96] which is

� �

� �1 exp

/mm

Cg ss �

� �� ��� � �� ��� � (5.7)

where m is a positive integer. Cm>0 is a constant whose value determines the direction of the flux function. � >0 acts as a contrast parameter that separates regions where forward diffusion occurs from those where backward diffusion takes place. The numerical implementation of the scheme used is described in [Malm 00].

An example illustrating the results of applying NLDF on flame images is shown in Figure 5.3. It clearly shows how the noise is suppressed and structural information is enhanced which greatly simplifies subsequent image segmentation of the flames.

Figure 5.3: NLDF applied to an OH PLIF image. Left: Raw data. Right: Data after 30 iterations. In the lower section of the figure, cross sectional profiles corresponding to the horizontal line crossing the images are shown. See animation at http://www.opticsexpress.org/opticsexpress/v8n5cvr.htm.

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5.2 Image Analysis Stage In order to segment the flames in the measurement series active contour models are used, which results in the identification of flame front boundaries. These contours are then interpolated in time and the interpolation results are used to estimate the flame front velocities.

5.2.1 Segmentation Using Active Contour Models Active contour models (known as ACM or snakes) refer to a segmentation technique that guarantees continuity and smoothness of detected contours and boundaries [Kass 87]. In this technique a contour model (snake) is initialized on the image and then deformed in a way that minimizes its total energy by, for example, the application of forces on the contour in an iterative manner. The energy minimization process corresponds to moving the snake towards desired image features (e.g. edges) while maintaining its smoothness.

A snake in the continuous spatial domain is represented by a 2D parametric contour curve � � � � � �� �,v s x s y s� where � �0,1s � . In a discrete setting the snake is defined as a set of N nodes, � � � � � �� �,i i iv n x n y n� where

� �ix n and � �iy n are the x- and y-coordinates of node n at iteration i, 1,2,...,n N� . Various forces act on the nodes yielding the following equation

for updating their position4 � � � � � � � �

� � � �

1 1 2

3 4

tens flexi i ii

ext infi i

v n v n w F n w F n

w F n w F n�

� � �

� �

(5.8)

where 1w , 2w , 3w and 4w are scalar factors weighting the different forces that are incorporated to deform the snake during its iterations [McInerney 00].

� �tensiF n is a tensile force, which resists stretching of the snake, acting on node n

at iteration i and is given in discrete form as � � � � � � � �2 1 1tens

i i i iF n v n v n v n� � � � � . (5.9) � �

flexiF n is a flexural force which resists bending of the snake and is given as

� � � � � � � �2 1 1flex tens tens tensi i i iF n F n F n F n� � � � � . (5.10)

� �infiF n is an inflation force designed to move the snake nodes in a direction

normal to the contour they form. In cases where the snake is a closed contour, as in our application images, this means the nodes will move inwards or outwards. Hence, the snake will either inflate or deflate towards the target boundary, which enables the initialization (of the snake) at locations far from the target object to be segmented. 4 In static image segmentation scenarios, the mass is set to zero resulting in simplified equations of motion [McInerney 00].

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69

� �infiF n is defined as

� � � � � �� �� � � �,infisi i iF n f I x n y n n n�

�� (5.11) where in

�� is the unit vector in the direction normal to the contour at node n and � � � �� �,s i iI x n y n is the intensity of the pixel � � � �� �,i ix n y n in a smoothed

version of the image. The binary function

� �� �� �1, ,

,1,

I x y Tf I x y

otherwise

� ����� �����

(5.12)

links the inflation force to the image data by determining if the snake is to be deflated or inflated and T is an image intensity threshold. � �

extiF n is an external

force that is derived from the image data in a way that causes the snake nodes to move towards regions of higher intensity gradient (mainly edges) in the image and is defined as

� � � � � �� �,exti i iF n P x n y n� � (5.13)

where P is the image gradient reflecting high intensity changes commonly present at boundary points.

Our implementation of the discrete active contour model also incorporates an adaptive inflation reversal and damping. In addition, it incorporates an adaptive subdivision scheme where snake nodes are resampled to give the snake an appropriate resolution (node separation) thus allowing it to latch onto varying levels of detail in the target’s boundary [Abu-Gharbieh 01a]. The resampling decision (whether nodes are inserted, removed, or unaltered) is not only based on the distance between the nodes along the snake, as in [Lobregt 95] for example, but is also dependent on the local curvature. More points are added when high snake curvature is detected whereas nodes are removed when low curvature is detected so as not to clutter the snake with nodes that might cause problems like self crossing. In other words, our subdivision method is based on the distance between neighboring nodes and also on the angle between neighboring snake segments. Equation (5.8) is used to deform the snake nodes iteratively until the solution converges. This is achieved when the changes in the snake node locations between subsequent iterations become very small (i.e. below a certain predetermined threshold).

An example showing results of using ACM for segmenting flame contours in an OH PLIF image is shown in Figure 5.4. The example illustrates how the segmentation process results in the identification of continuous and smooth flame boundaries that fit the data perfectly thus eliminating classical edge detection problems of non-smooth and open contours. These obtained flame boundaries can

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be used for reducing the flame image data to single curves that will be used for further analysis.

(a) (b)

(c) (d)

(e) (f)

Figure 5.4: Progress of snake iterations. (a) Original raw image. (b) Initial snake initialized on the non-linear diffusion filtered image. (c)-(e) Snake after 1, 25, and 85 iterations, respectively. (f) Final result overlaid on the original raw image. See animation at http://www.opticsexpress.org/oevideo/915.mov.

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5.2.2 Temporal Interpolation of Flame Contours The detected flame contours can be used to study the flame front dynamics in time. In particular, we are interested in the extraction of local flame front velocities from discretely sampled data. However, the small number of frames available in each sequence (four only) does not allow for accurate estimation of flame motion. One solution lies in the development of contour interpolation techniques where intermediate contours can be obtained and further used for estimating flame front velocities. To facilitate this task we interpolate between discrete contours in time as described below.

To reiterate, after applying the active contour segmentation to a PLIF frame, we end up with a single snake contour locating the flame boundary in that frame. Thus for each frame j we have a snake contour

� � � � � �� �� �, , , , , 1,2,...,v n j x n j y n j n N� � for 1,2,...,j F� where F is the number of frames (which in the present case is four). In order to interpolate, we start by reparameterizing each of the original flame contours with a new shape representation. This is efficiently done by transforming from the spatial into the frequency domain. An advantage is that the need for a node-to-node correspondence between different contours (snakes) is avoided.

The one dimensional discrete cosine transform (DCT) of the sequence of � �,x n j contour coordinates (and similarly for the � �,y n j coordinates),

1,2,...,n N� , is defined as follows [Jain 89]

� � � � � �� �� �

1

2 1 1, , cos2

N

n

n kX k j w k x n jN

�

�

� �

� � (5.14)

where

� �

1 1

2 2

kNw k

k NN

��� ����� ��� � �����

(5.15)

and 1,2,...,k N� . Using the DCT as a new frequency domain shape parameterization has many advantages: It produces real coefficients, has excellent energy compaction properties, as well as having coefficients that correspond (opposed to spatial contour points with no point-to-point correspondence).

Now using these frequency coefficients � �,X k j and � �,Y k j as new curve parameters, we can directly perform the actual interpolation. In our implementation cubic spline interpolation between corresponding frequency coefficients is utilized. It is worth noting that the DCT coefficients of the curves are normalized with respect to similarity transformation parameters utilizing only corresponding starting points.

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Finally the inverse discrete cosine transform (IDCT) is used to transform the interpolated components back into the spatial domain

� � � � � �� �� �' '

1

2 1 1, , cos2

N

k

n kX n j w k X k jN

�

�

� �

� � (5.16)

where 1,2,...,n N� and 'j spans the interpolated frames (which include the original ones).

The proposed interpolation method is tested on synthetically generated data for validation purposes. A single synthetic example consists of a shape sequence represented by a set of coordinates. Both the x and y coordinates of each node move throughout the sequence (in time) according to sinusoidal functions with different amplitudes and frequencies, which causes spatial shape deformation in time. The coordinates are also scaled differently between frames according to sinusoidal functions in order to produce dynamic shapes that temporally shrink or expand. To quantify the error (difference) between the original (known) synthetic sequences and the interpolated ones, we define the following error measure for each shape in the sequence

o oi i

o

A A A AA

�

� � �� (5.17)

where oA and iA are the areas enclosed within the original and interpolated shapes, respectively.

Figure 5.5 through Figure 5.7 illustrate some of the test examples and report the corresponding average error values (over all frames in each test sequence) between the original and the interpolated sequences. Figure 5.8 shows some further qualitative testing examples. The test examples illustrate how the frequency based interpolation scheme manages to reconstruct intermediate curves with good accuracy.

The described interpolation scheme is finally applied to PLIF image data sequences. An example is shown in Figure 5.9 where ten contours are interpolated between each pair of the original four contours (resulting in 34 contours in total). The results are very plausible and would enable accurate measurement of flame front velocities as we will describe in the next section.

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73

-30-20

-100

1020

30

-30-20

-100

1020

300

5

10

15

X

Original Sequence

Y

Tim

e

(a)

(b)

-30-20

-100

1020

30

-30-20

-100

1020

300

5

10

15

X

Interpolated Sequence

Y

Tim

e

(c)

Figure 5.5: Validating the temporal interpolation scheme. Example 1: Elliptical shapes, Error=3.53% (see text). (a) Original synthetic sequence comprising 16F � shapes (generated by evolving a shape in time using predetermined controlled deformations). (b) Four original shapes extracted from the synthetic sequence and fed into the interpolation algorithm. (c) The interpolation result; reconstruction of 16 frames from 4 only.

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-40

-20

0

20

40

60

-40-30-20

-10010

2030400

5

10

15

X

Original Sequence

Y

Tim

e

(a)

(b)

-40

-20

0

20

40

60

-40-30-20

-10010

2030400

5

10

15

X

Interpolated Sequence

Y

Tim

e

(c)

Figure 5.6: Validating the temporal interpolation scheme. Example 2: Star shapes, error=5.25% (see text). (a) Original synthetic sequence comprising

16F � . (b) Four original shapes extracted from the synthetic sequence and fed into the interpolation algorithm. (c) Interpolation result.

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-100

-500

50100

-150-100

-500

50100

1500

5

10

15

X

Original Sequence

Y

Tim

e

(a)

(b)

-100-50

0

50100

-150-100

-500

50100

1500

5

10

15

X

Interpolated Sequence

Y

Tim

e

(c)

Figure 5.7: Validating the temporal interpolation scheme. Example 3: Shapes based on deforming a real flame boundary: Error=0.75% (see text). (a) Original synthetic sequence comprising

16F � . (b) Four original shapes extracted from the synthetic sequence and fed into the interpolation algorithm. (c) Interpolation result.

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(a) (b)

(c) (d)

(e) (f)

Figure 5.8: Temporal interpolation: (a-f) Different validation tests on synthetic examples. The original 4 contours are displayed in black and the interpolated ones in gray.

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77

Figure 5.9: Temporal interpolation on the PLIF data sequence shown in Figure 4.7. Four original contours are shown in thick black and the curves interpolated in between are shown in gray colors. See animation at http://www.opticsexpress.org/oevideo/916.mov.

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5.3 Flame Front Velocity Estimation One of the most important quantities for the characterization of turbulent combustion is the flow velocity and its fluctuations in the reactive flow field. The high relative velocities of gaseous fuel versus air leads to turbulent mixing and complicated subsequent chemistry. Turbulence in the flow also strongly affects the flame speed. Gas exchange processes between hot and cold areas yield a complicated turbulence/chemistry interaction.

As previously discussed, once flame contours are temporally interpolated they can be used to estimate the flame front velocities. The direction of the velocity vector at each snake node in a particular contour (frame) is locally perpendicular to the contour curve at that node. Subsequently, the intersection of this normal vector with the contour in the next frame defines the target location to which the node in question has moved within the time elapsed between the two frames. Results of applying our velocity estimation method on the time interpolated frames illustrated in Figure 5.9 are shown in Figure 5.10 and Figure 5.11. Note how local velocities are affected by turbulence with a wide range of velocities present.

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Figure 5.10: Flame front motion and velocity estimation based on temporal interpolation of the four flame contours. The calculated velocity vectors are overlaid on the original contours.

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0

0.5

1

1.5

2

2.5

3

Figure 5.11: Color map representation of the flame velocity values. The image shows the magnitude (in m/s) of the flame front velocity at each boundary point in each frame using the color map shown to the right.

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5.4 Discussion and Conclusion The capability to track flame contours in time as shown here for the first time provides a unique way to study turbulent flame dynamics. A related application lies in the rendering of three dimensional flame contour data obtained from discrete data slices through the flame [Hult] where the interpolation is in the spatial rather than the temporal domain.

The methods outlined in this chapter present efficient data reduction techniques where flame images can be represented through the extraction of flame front contours in large experimental datasets. This is useful in several ways for comparisons with numerical data. For example, the degree of flame wrinkling can be extracted from the flame contour. This is defined as the ratio of the flame surface area of the turbulent flame to the corresponding area of a laminar flame and can be directly obtained by integration of the flame contours evaluated with the presented methods. The degree of flame wrinkling is in turn related to local reaction rates [Warnatz 96].

The reaction boundary can also be used to define a reaction progress variable c which is defined as c=0 for fresh gases (which corresponds to the region outside the detected flame boundaries in the examples presented here) and c=1 for burnt gases (inside the boundaries). The conservation equations for premixed flames may be directly expressed in terms of such a progress variable.

In summary, the presented techniques are fast and efficient methods for reducing the large amounts of data obtained by sequential imaging of turbulent reactive flows with limited contrast and signal to noise ratios. The described interpolation scheme enables the estimation of flame motion and the extraction of flame front velocity data from discretely (sparsely) sampled image sets.

The discussed active contour model implementation segments single objects. However, at high turbulence levels where the flame becomes corrugated to an extent that isolated features appear, the need arises for incorporating modifications that enable the active contours to handle multiple objects. One solution is to initialize multiple independent snakes. Other methods include, for example, using topology adaptive snakes [McInerney 00] or geodesic active contours [Caselles 95].

The discussed interpolation technique works well in low to medium turbulence premixed flames where the flame contours remain singly connected. It might though be of interest to investigate the use of discrete wavelet transform (DWT) as opposed to DCT for representation of snake contours since DWT coefficients contain more spatially localized information.

In the next chapter, we describe a more sophisticated approach which can be used even at large turbulence intensities, where several separated objects may appear in the image, and is capable of dealing with flame fronts of arbitrary topology.

Chapter 6. MATCHING FLAME FRONTS OF ARBITRARY TOPOLOGY

In the previous chapter we presented a flame front tracking technique that employs a frequency domain interpolation scheme for estimating flame motion. The proposed technique is nevertheless unable to handle complex front structures where sharp edges, cusps, and topological changes occur. In this chapter5 we treat the problem of tracking flame contours of arbitrary topology. Image sequences of combustion processes captured from the controlled experiments discussed in Chapter 4 are first processed for enhancement and noise reduction. Smoothing using non-linear diffusion filtering then segmentation using active contour models is used to obtain the curves that most accurately describe the flame boundary.

The resulting curves are subsequently matched using the concept of shortest path (geodesic) computation on a cost surface. Level Set representation is employed so that complex curve evolutions including those with topological changes in their structure could be handled. A critical point detection algorithm is used to identify important curve landmarks that are then used to modify the cost surface so as to improve the quality and stability of the matching.

Accordingly, the propagation of curves representing successive flame contours within a sequence is obtained and used for studying the flame dynamics by tracking flame movements (between subsequent frames) within each sequence. The interpolated data is also used to calculate local flame front displacement velocities.

6.1 Experimental Data The image data sequences analyzed in this chapter fall into two categories that are both time resolved. The first category comprises premixed combustion flame cases obtained as described in Section 4.2.1, an example is shown in Figure 6.1. The second category contains diffusion (non-premixed) combustion flames obtained as described in Section 4.2.2, an example is shown in Figure 6.2.

5 Parts of this chapter appeared in [Abu-Gharbieh 01b].

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84

6.2 Smoothing and Segmentation To improve the signal to noise ratio and simplify the segmentation of the OH boundaries, the images are first smoothed using non-linear diffusion filtering or edge preserving filtering as discussed in detail in Section 5.1.2. In a nutshell, the principle of the method is to smooth out noise locally by diffusive flow while at the same time prevent flow across boundaries. By a proper choice of the diffusion kernel, object boundaries may be enhanced and physical gradients sharpened thus simplifying the determination of object boundaries. The data is basically filtered using the equation

� �� �� �*I div g G I It �

�� � �

� (6.1)

where I represents the image intensity and � �� �*g G I�

� represents a locally adaptive diffusive strength. The latter is chosen to be inversely proportional to the image gradient I� . For stability reasons [Catté 92], the image is convolved with a Gaussian kernel G

�of width � . Figure 6.3 shows the results of applying non-

linear diffusion filtering on the data shown in Figure 6.1 while Figure 6.4 shows the results on the data shown in Figure 6.2. It is clearly seen how the noise is suppressed and the flame edges enhanced which facilitates the segmentation stage that follows.

For flame segmentation in different measurement series, ACM (snakes) is used (as described in Section 5.2.1). This results in the identification of flame front boundaries, which are fed to the curve matching algorithm described in the next section. Multiple snakes are initialized in the cases where topological changes of the flame structure occur producing multiple flame fragments. Figure 6.5 and Figure 6.6 show the results of flame segmentation where it is clearly seen that the obtained flame contours accurately fit the data.

Matching Flame Fronts of Arbitrary Topology

85

(a) (b)

(c) (d) Figure 6.1: Premixed flame sequence. (a-d) Four frames captured with a 1.7 millisecond interframe interval.

Chapter 6

86

(a) (b)

(c) (d)

Figure 6.2: Diffusion flame sequence. (a-d) Four frames captured with a 125 microsecond interframe interval. The sequence depicts a flame extinction event (note the lower left side of the frames in b and c).

Matching Flame Fronts of Arbitrary Topology

87

(a)

(b)

(c) (d) Figure 6.3: Smoothing the images of Figure 6.1 using non-linear diffusion filtering.

Chapter 6

88

(a) (b)

(c) (d)

Figure 6.4: Smoothing the images of Figure 6.2 using non-linear diffusion filtering.

Matching Flame Fronts of Arbitrary Topology

89

(a) (b)

(c) (d) Figure 6.5: Segmenting the images of Figure 6.3 using ACM. The results are overlaid on the original images.

Chapter 6

90

(a) (b)

(c) (f)

Figure 6.6: Segmenting the images of Figure 6.4 using ACM. The results are overlaid on the original images.

Matching Flame Fronts of Arbitrary Topology

91

6.3 Contour Matching Framework The local intensity in the recorded images is a function of the local OH concentration in the flames. Since OH is formed in the reaction zone of the flame and is rapidly quenched by cold un-reacted gases, it is a good indicator of the flame front position. This fact makes the task of studying flame structures and deformations possible through the evolution of OH (flame) boundaries. If these boundaries are matched, the results can then be used to study the dynamics of the flame in a number of ways. For example, intermediate curves can be interpolated between the experimentally obtained curves and velocities of the boundary points can be estimated.

In the previous chapter, we discussed a frequency domain based interpolation technique that proved to work well in low to medium turbulence scenarios where the flame contours remain connected. In this chapter, we describe a more sophisticated approach which can be used even at large turbulence intensities, where several separated objects may appear in the image, and is capable of dealing with flame fronts of arbitrary topology.

The nature of high turbulent flame data necessitates the use of a curve matching algorithm that is accurate, robust, and can handle a wide variety of curve structures including those with sharp edges, cusps and arbitrary topology. To achieve these requirements, we employ a technique based on point wise tracking of structures, inspired by the work of Cohen et al [Cohen 98a][Cohen 98b]. The method is based on the computation of a set of geodesic paths connecting two curves, namely, the source and the destination curves, S and D , respectively, on a cost function. In our case the source and destination curves are two flame front contours at two consecutive time instances (frames). The curves can be implicitly represented using level sets, which facilitates handling complex curves and allows for topological changes in their structure.

The curve matching results are improved by incorporating a term in the cost function that steers certain pairs of points to correspond (match). These corresponding pairs of points can either be manually marked by the user or automatically detected. Here, a critical point detection algorithm is used to automatically identify these landmarks whose incorporation improves the quality and stability of the matching results.

6.3.1 Geodesic Distance Given two points on a surface � �� �, , ,Z x y z x y� , the computation of the shortest path between the two points is equivalent to locating the minimal geodesic on that surface [Do Carmo 76]. This computation can be performed using various methods. In [Kimmel 95] it is shown that geodesic curves are the points of constant curve parameter s of a parameterized curve � � � � � � � �� �, ,s x s y s z s� �

Chapter 6

92

evolving according to the equal distance contour evolution (at a specific parameter value s s� ) given as

� �,t s t N T� � �

� ���� (6.2)

where x y

x y

Z ZN

Z Z�

�

�

� �

�

� � is the normal to the surface and s

sT �

�

�

�

�

� is the tangent

(at a specific t t� ) to the curve � �,s t� .

� �1,0,xzZ px

�� �

�

�

and 0,1,yzZ qy

�� ���� � �� ��� ��

�

are the partial derivatives of the

surface Z with respect to x and y , respectively. Rewriting N

�

and T�

we get � �

2 2

, ,11

x y

x y

Z Z p qNZ Z p q

� � �� �

� � �

� �

�

� � (6.3)

and � �

2 2 2

, ,s s s

s s s

x y zTx y z

�� �

�

(6.4)

where sx , sy , and sz are the derivatives of the coordinates of � �s� . The solution on general 3D surfaces is quite difficult, but Kimmel et al

showed that if restricted to graph surfaces only, the solution can be characterized through the projection of the curve � �,s t� on the � �,x y plane.

Since the tangential component only affects the curve’s parameterization, the evolution of a shape thus depends only on the normal component of the curve.

The propagation for the projection ��

along its normal � �

2 2

,s s

s s

y xnx y�

�

�

�

��

can be

given as

� �,s t Vn� �

� �

�� ��

(6.5) where

� �� � � �

2 2 2 2 2

, ,1 , ,,

1s s s

ts s s

p q x y zV s t n np q x y z

�

� �� � � � �

� � � �

� �

�� ��

��� . (6.6)

Using the chain rule, sz can be substituted by x s y s s sz x z y px qy� � � since the curve � is on the surface sz . By inserting the expressions for the normal

1 22 2 2 2,s s

s s s s

y xn n nx y x y

� �� �� �� � �� �� ��� �

�

��

(6.7)

the propagation equation of the curve � �,t s t�

�

���

becomes

� � 2 21 2 1 2, t s t an bn cn n n� � � �

� �

��� ��

(6.8)

Matching Flame Fronts of Arbitrary Topology

93

where 2

2 21

1qa

p q�

�� �

, 2

2 21

1pb

p q�

�� �

, and 2 22

1pqcp q

�� �

.

Equation (6.8) represents the evolution of the equal geodesic distance contour on the surface � �� �, , ,Z x y z x y� .

6.3.2 Level Set Representation In the previous section, it is shown that the curve evolution scheme of a curve � �,s t�

�

depends on the curve’s parameterization. Since estimating the normal components using derivatives becomes inaccurate and unstable in complex curves, a non-parametric representation of the curve is needed. In a level set representation, the curve can be implicitly presented as the zero level set of a two dimensional function � defined on the � �,x y plane [Sethian 99], namely

� � � �1, 0t s t� ��

�

�

���

. (6.9) A major advantage for using this representation is the ability to model curves undergoing arbitrary topological changes, see Figure 6.7.

t3

t2

t1

Figure 6.7: Topological changes with level set surfaces. Two curves (fronts) are initially separate (t1) but they merge later in time (t3).

Deploying this level set representation, and using the chain rule and equation

� �,tx yt t

�

� ��

� �

�

���

(6.10)

yields

tx y

t x t y t� � �

� �� � � � �

� � � � �� � � � �

�

���

��

. (6.11)

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94

Using equation (6.5) and the fact that the planar unit normal to any level set of � can be written as

n �

�

��

�

�

����

�� , (6.12)

we get

Vn V Vt� �

� � �

�

� �� � � � � � � �

� �

�

����

�� �� ��

�� (6.13)

Finally, by replacing

1 2, yxn n n��

� �

� ��� ��� � � �� �� �� �� �� �

�

��

�� �� (6.14)

in the velocity function V given by equation (6.8), we can express the curve propagation equation through the level set curve � �1 0�

� with � evolving as (see Figure 6.8)

2 2x y x yt a b c� � � � �� � � . (6.15)

Figure 6.8: Level set representation. Two dimensional curves are defined as zero level sets of a three dimensional surface.

6.3.3 Locating Optimal Paths The curves to be matched are defined as two sets of source and destination contour points S and D, respectively. The matching routes between S and D are defined as those that minimize a certain cost function � �,f x y along their path. This cost function must characterize the similarity between the two curves S and D and also enable the matching to be symmetric, i.e. the optimal paths obtained

Matching Flame Fronts of Arbitrary Topology

95

using this function should be the same whether S is matched to D or vice versa. One such cost function can be defined as

� �, S Df x y D D� (6.16) where SD and DD are the geodesic distance maps of S and D respectively and will be defined later.

Since the minimal paths are orthogonal to the equal distance contours, they can be reconstructed by starting on a point on the source contour and moving in the direction of the gradient of the cost function � �, S Df x y D D� until reaching the destination curve. The optimal path is thus defined by a parameterized curve ( )p s such that

� �,p f x ys

�� ��

�. (6.17)

In our implementation, the gradient of the cost function is smoothed using a 2D Gaussian kernel resulting in more plausible and robust results.

The two distance maps DS and DD are defined by solving the equal geodesic distance contour propagation equation (6.15) on a graph surface Z twice, once for S and once for D, such that � �,SD x y�� and � �,DD x y�� . The signed Euclidian distance maps [Borgefors 84] 0� and 0� of the curves S and D , respectively, are used as initial estimates. Details on the numerical approximations used for the solution are discussed in Appendix A.

The graph surface Z on which these geodesic distance maps are computed has to be the same for the computation of both maps in order to define a similarity measure between S and D . Z should also have both S and D as zero level sets. One such surface is

0 0( , , ) min( , )Z x y z � �� . (6.18) Modifications to the graph surface can be incorporated, for example, to allow for geometrical properties of the curves to be taken into account. This is helpful when geometric similarities exist between the matched curves [Cohen 98b]. A graph surface can be defined such that it adapts to large and small deformations in order to preserve geometric similarities in the case of small deformations and loosen these geometric constrains when large deformation occur. Such surface can be defined as

� � � �� �0 0min ,Z A A� �� (6.19) where

� �� �

� �0 0

0 0

2

22 2

k kA

k k W

� �

� �

� �

�

� ���� �� ��� � �� �� �� �� ����

11

(6.20)

and

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96

� � � �

2Kk�

� �� �� . (6.21)

W defines the neighborhood size on which the geometric properties are considered. � and K are the mean curvature and Gaussian curvature of the surface, respectively, and are defined as

� � � �

� �

2 2

3 22 2

2( ) xx y x y xy yy x

x y

� � � � � � ��

� �

� � � �� �

� �

1 11

(6.22)

� �

2 2

3 22 2

2( ) xx y x y xy yy x

x y

K� � � � � � �

�

� �

� ��

�

. (6.23)

In summary, the introduced function � �A � will strengthen the similarity measure when small deformations are present and the distance is small.

6.3.4 Matching With Point Correspondence To improve the quality and stability of the matching results when geometrically similar feature points on the curves have moved over a wide range (large distance), we propose adding another term CD to the cost function � �,f x y . This term steers the algorithm into matching certain distinctive landmark pairs when their correspondence can be accurately identified. We define CD as

� � � � � � � �� �1 2

1, , , ,

i i

N

p piCi

D x y w x y D x y D x y�

� �� (6.24)

where � � � �1 2 1 1 2 2, , , ,i i i i i ip p x y x y� is the thi pair of landmark points to be matched and

1ipD and 2ipD are their Euclidean distance maps. N is the number of

pairs used and � �,iw x y is a weighting factor that is incorporated to localize the effect of the matching term, i.e. to attenuate its effect as the distance to 1 2,i ip p increases and is defined as

� � � � � �� �1 2

, , ,i ip piw x y d x y d x y

��

�

� � (6.25) where � and � are positive constants, and

� � � � � �2 2

,ijp ij ijd x y x x y y� � � � , 1,2j � .

CD adds components to the cost function that act as a field steering corresponding landmark pairs to each other, see Figure 6.9. Accordingly, the cost function becomes

� �, S D Cf x y D D D� � � . (6.26) The pairs of points to be matched can be identified either manually or automatically. In the next section we describe an algorithm we use for critical

Matching Flame Fronts of Arbitrary Topology

97

point detection (CPD) on a simple closed 2D object boundary. The algorithm does not require curvature estimation or Gaussian filtering [Zhu 95].

6.3.5 Critical Point Detection A set of pseudo critical points (candidates from the original boundary curve) oC is generated. This is done by first transforming the curve points to polar coordinates thus obtaining two one dimensional curves, � �s� and � �s� . Pseudo critical points are chosen to be those at which local minima and maxima exist in � and � . Assigned to each point in oC is a critical level that depends on the shape of the triangle formed by that point and its two pseudo critical neighbors. The points with the lowest critical level are then deleted recursively until only the true critical points with critical levels higher than a specified level remain. An example illustrating this CPD scheme is shown in Figure 6.10.

6.4 Flame Front Matching and Tracking Results The described curve matching algorithm is applied to match the boundary curves of the experimentally obtained PLIF flame data (i.e. match the flame fronts in the images). Figure 6.11-a through Figure 6.13-a show the results on the sequence shown in Figure 6.1. Figure 6.11-b through Figure 6.13-b show intermediate (temporally interpolated) curves that are generated using the obtained matching paths between consecutive experimentally captured frames.

Figure 6.14 shows an example of matching fronts in a diffusion non-premixed flame. The results clearly show how the flame front is moving as an extinction process is taking place. The source curve shows a connected flame front that is heavily stretched until it is topologically altered. The example illustrates how the algorithm manages to handle the topology change (the flame split in the lower left side). Figure 6.15 illustrates the improvements on the matching results when the proposed point correspondence term CD is incorporated in the matching cost function. The corresponding pairs of points are acquired using the CPD algorithm discussed earlier. In Figure 6.16 resulting intermediate (interpolated) frames are illustrated. Another example is shown in Figure 6.17 and Figure 6.18. The results again clearly illustrate how the matching is successful in tracking flame movement correctly even as it undergoes under topology changes. The extinction event seen in this particular flame sequence can thus be reconstructed.

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pi1

pi2

(a) (b)

Figure 6.9: Matching a pair of corresponding points. (a) CD in the vicinity of

1 2,i ip p . (b) The gradient CD� , which acts as a field steering 1ip to 2ip .

(a) (b)

Figure 6.10. CPD applied to the flame boundary contours of (a) Figure 6.5-d(b) Figure 6.6-c. Original curves (dashed) and the critical points (connected dots).

Matching Flame Fronts of Arbitrary Topology

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(a)

(b)

Figure 6.11: Curve matching of flame fronts extracted from Figure 6.1-a and Figure 6.1-b. (a) Matching paths. (b) Interpolated curves (thin) between the original (thick) flame fronts segmented using snakes.

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(a)

(b)

Figure 6.12: Curve matching of flame fronts extracted from Figure 6.1-b and Figure 6.1-c. (a) Matching paths. (b) Interpolated curves (thin) between the original (thick) flame fronts segmented using snakes.

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(a)

(b)

Figure 6.13: Curve matching of flame fronts extracted from Figure 6.1-c and Figure 6.1-d. (a) Matching paths. (b) Interpolated curves (thin) between the original (thick) flame fronts segmented using snakes.

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Figure 6.14: Matching paths of flame contours extracted from the two frames in the diffusion flame sequence shown in Figure 6.2-b and c.

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Figure 6.15: Improving the matching results shown in Figure 6.14 by incorporating two pairs of corresponding points (marked as black dots).

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Figure 6.16: Intermediate curves obtained via the matching paths shown in Figure 6.15. The visualization shows interpolated flame contours (gray colors) between the original flame fronts (black) segmented using snakes.

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(a) (b) (c) (d)

Figure 6.17: Diffusion flame sequence. (a-d) Four frames captured with a 75 microsecond interframe interval.

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(a) (b)

Figure 6.18: Curve matching of flame fronts extracted from Figure 6.17-b and c. (a) Matching paths. (b) Interpolated curves (gray colors) between the original flame fronts (black) segmented using snakes.

Matching Flame Fronts of Arbitrary Topology

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6.5 Discussion and Conclusion The capability of tracking flame contours of arbitrary topology in time as shown here for the first time facilitates the study of turbulent flame dynamics. Once the contours are matched by this novel approach, the matching paths can be used to interpolate and visualize intermediate frames within the experimentally sampled image sequences and flame front velocities can also be estimated.

The curve matching method presented here provides alternative methods to study the movement of flame fronts subjected to high turbulent flow fields. This can be used for model development and validation of technical combustion processes. In combination with standard flow velocimetry techniques such as particle imaging velocimetry (PIV), the present techniques provides a unique way to track the response of the flame front in the presence of turbulence. Applications range from aero- and automobile engine research to the design of technical combustors used in industry and for heating. This aspect will be the topic of the next chapter.

Chapter 7. RESOLVING CHEMISTRY AND TURBULENCE INTERACTION

Understanding the stability of turbulent non-premixed flames is both of fundamental and practical importance because of their widespread appearance in technical applications. To increase the understanding of turbulence and chemistry interaction phenomena such as local flame extinction, flame stabilization and liftoff, experimental studies have to be performed in well characterized turbulent flames.

In the past, turbulent combustion research has mostly focused on the measurement of temporally uncorrelated events. Such data can be used for the construction of PDFs (probability density functions) and comparisons with RANS (Reynold averaged Navier Stokes) modeling approaches. However, since turbulence is inherently a time dependent phenomenon, model construction will ultimately benefit from the provision of time correlated measurement data. Very few experiments have been done in this respect owing to the extreme complexity of the measurements and subsequent data evaluation.

Point measurements of time correlated quantities in turbulent flames have recently been reported by Renfro et al [Renfro 00] using an 80 MHz repetition rate Ti:Sapphire laser system. Double pulse line images of majority species and temperature in turbulent jet flames have been recorded by Brockhinke et al [Brockhinke 96]. Two dimensional double pulse imaging techniques have also been employed, for example to measure the temporal development of OH concentration fields from which turbulent fluctuation time scales could be measured [Dyer 84][Atakan 93]. Longer sequence recordings of turbulent reactive flow structures have been reported by Winter and Long using Mie scattering of aerosols seeded into the fuel [Winter 89]. Similarly OH and O2 were imaged at low repetition frequencies (250 Hz) by Kychakoff et al [Kychakoff 87]. High quality high repetition rate planar laser induced fluorescence (PLIF) image sequences of flame produced radicals can nowadays be recorded at repetition rates exceeding tens of kHz [Kaminski 00][Dreizler 00]. Combination of PLIF and particle image velocimetry (PIV) measurements that are simultaneously performed on a single shot basis have also been demonstrated [Frank 96][Watson 99].

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Combined OH PLIF and PIV techniques can be used to separate the effects of flow and chemistry on the local flame front structure. From OH PLIF sequences the velocity of the local flame front movement can be extracted. This velocity is a function of both global flow and chemistry effects, but as the flow component alone can be measured from PIV measurements, the chemistry effects may be isolated. In other words, the pure flow velocities obtained by the PIV measurements can be subtracted from the flame front velocities thus allowing the chemistry part to be isolated.

Experimentally obtained PIV and OH PLIF image data create large demands on data reduction, image processing and image analysis techniques. In this chapter6 we present image analysis methods for studying image data sequences obtained using the scheme described in Section 4.3 where high speed PLIF imaging of OH radical concentrations is combined with PIV in turbulent flames. The presented techniques facilitate the separation of the effects of flow and chemistry on local flame front structures. We focus on computational methods for extracting flame front velocities from the OH PLIF data and quantitatively comparing them with flow field velocities extracted from the PIV measurements. The techniques can be used to study the dynamics of turbulence and chemistry interactions in real time.

OH image sequences are analyzed to extract the flame front velocity, which is a function of both global flow and chemistry effects. The flame images are first smoothed using non-linear diffusion filtering to reduce noise levels. They are then segmented using ACM (snakes) with the resulting boundary curves subsequently matched in order to reconstruct the flame’s motion between successive experimental frames. We employ the technique proposed in Chapter 6 where flame front matching is based on the calculation of geodesic paths between curves represented with level sets. This enables successful handling of sharp edges and cusps as well as topological changes in the flame structure that were difficult to accomplish previously. The matching paths are then used to estimate the flame front velocities. Finally, the flow velocities obtained through the PIV measurements are subtracted from the flame front velocities thus allowing chemical effects to be isolated.

7.1 OH PLIF Data Analysis The first steps in the analysis start by filtering the image data by non-linear diffusion filtering to reduce noise effects followed by flame segmentation to identify the flame fronts as described in Chapter 5. The curve matching algorithm described in Chapter 6 is then employed to track the evolving flame fronts in the OH PLIF image datasets [Abu-Gharbieh 01b]. Figure 6.15 is an example.

6 Parts of this chapter’s content appeared in [Abu-Gharbieh].

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111

7.2 PIV Data Analysis PIV methods have developed rapidly over the past years as recording and evaluation techniques moved from analog to digital platforms. Fast digital cameras have replaced the initial analog methods that use photographic films and optical correlation methods.

In PIV the velocity is calculated from the measured displacement of fluid elements in a known time. In order to accomplish this, the flow is seeded with small particles (~µm) that trace the motion of the fluid (TiO2 particles in our case). A pulsed laser is used to obtain images of the seed particles by firing it twice with a suitable time interval in between. This way, two images are acquired with a CCD camera (as described in Section 4.3), which are then processed to find the velocity vector map of the flow field.

The processing starts by first dividing the two images, 1Im and 2Im , into small areas called interrogation regions, then the displacement of groups of particles within each interrogation region is measured using a correlation technique. The cross correlation function determines the match between local regions at different time steps and is discretely defined by

� � � � � �

2 2

/2 /2

1 2, , ,M N

M N

i jR x y Im i j Im i x j y

�� ��

� � �� � (7.1)

where M and N determine the size of the interrogation region and are usually equal. The positions of the peaks in R are then used to determine the displacements. From these displacements the velocity vectors are calculated in each region and the complete 2D velocity vector map is determined. An alternative method is to transform the correlation problem to a multiplication problem in the frequency domain, which reduces the required computational operations.

7.3 Velocity Measurement At this point, it is possible to extract the flame front and the flow field velocities for conducting quantitative comparisons.

7.3.1 Flame Front Velocity Calculation As the matching paths between flame contours in OH PLIF images are traced, the flame motion can be reconstructed between the experimentally captured frames and the flame front velocities can be estimated. This is achieved by dividing the distance traveled by each node of the flame contour by the time it takes to move that distance (which is the original inter-frame interval used when conducting the experiments). Figure 7.1 illustrates the flame front velocities obtained for the sequence shown in Figure 6.2 (see also the matching paths in Figure 6.15).

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112

0

5

10

15

20

25

30

Figure 7.1: Flame front velocities estimated from the matching paths shown in Figure 6.15. The color bar to the right shows the velocity values in m/s.

7.3.2 Flow Field Calculation

The PIV images are divided into interrogation areas of 32×32 pixels. Velocity vectors are produced with a 50% overlap between regions. A validation process is performed to discard erroneous vectors in the raw instantaneous velocity fields. Finally the OH images are remapped to the coordinate system of the PIV images and the velocity vectors are plotted on top of the corresponding OH image. Details on this are reported in [Hult 00]. An example of the resulting velocity vectors is shown in Figure 7.2.

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113

20 m/s

Figure 7.2: Flow field vector map estimated from the PIV image data corresponding to the sequence of Figure 6.2 after mean subtraction of a 9 m/s vertical velocity for better visualization. The arrow in the top left illustrates the scale.

Now that both the two dimensional flow field (from the PIV images) and the flame front velocities (from the OH PLIF images) are separately measured, it is possible for the first time to make direct comparisons between the two.

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114

7.4 Turbulence/Chemistry Interaction Turbulence can greatly enhance the rate at which chemical species proceed to react by increasing the mixing rates of reactants. However excessive strain on the flame front, caused by turbulent convection can also have the opposite effect: The flame front thins, and radiative losses can lead to flame extinction. The event witnessed in the sequence of Figure 6.2 is precisely of that nature. Although it is clear that flame extinction is taking place in this sequence, it is interesting to compare the physical mechanisms leading to this event in more detail.

The techniques discussed in the preceding sections allow a more precise interpretation of the physics behind turbulent flame extinction than has been possible before. Figure 6.15 clearly shows how the flame front is moving as the extinction process is taking place. The source curve shows a connected flame front that is heavily stretched. This can be observed from the solid lines that show the estimated trajectories of points within the flame front as it proceeds through the extinction event towards the topologically altered destination curve. This stretching thins the flame front at a rapid rate as can be seen from the color coded map in Figure 7.1.

Since the flame front velocity values reflect the global flame motion, which is a consequence of both turbulent convection and chemical reactions, one way to compare the results is to subtract the fluid flow velocity (obtained from PIV) from the local flame front velocity (obtained by the geodesic path analysis). The result of doing that for the sequence of Figure 6.2 is shown in Figure 7.3. The directional variations between the flame front velocity vectors and the difference vectors (i.e. the flame front velocities from which the fluid flow is subtracted) give an indication of the effect of convection on the flame front. Near the region of the extinction event, it can be seen that the two sides of the ‘OH braid’ are rapidly approaching each other, leading to the flame front thinning effect. In this region the fluid flow and the flame front movement are carrying combustible mixture into an ever more thinning region. Further results are illustrated using the sequence of Figure 6.17. Figure 6.18-a shows the matching geodesic paths. Figure 7.4 and Figure 7.5 show the various velocity measurements obtained: flame front (overall), flow field (turbulence) and the difference between the two (chemistry effects).

It is worth noting that although the presented techniques provide extensive information on flow/chemistry interactions, it must be remembered that they are confined to a single measurement plane and thus cannot give consideration to 3D effects such as vortex motion in and out of the measurement planes. It is however possible to extend our analysis techniques to 3D if three dimensional measurements (for example PLIF coupled with stereo PIV techniques) are available. For example, the curve matching can be extended to flame surface matching, which means that the cost function in equation (6.16) will become a hypersurface in four dimensional (4D) space [Huot 00].

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115

25 m/s

Flame front (OH)

Turbulence (PIV)

Difference

Figure 7.3. OH PLIF vs. PIV velocity vector comparisons at the flame front. The thick black curve is the source and the dotted curve is the destination. The white arrows are the flow field vectors, the dotted arrows are the flame front velocity vectors, and the solid black arrows are the difference of the two. The arrow in the lower right corner illustrates the scale of the velocity vectors.

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116

0

5

10

15

20

20 m/s

(a) (b)

Figure 7.4: (a) Flame front velocities estimated from the OH PLIF image sequence. The color bar to the right shows the velocity values in m/s. (b) Flow field vector map estimated from the PIV image after the subtraction of a 24 m/s mean vertical velocity for better visualization. The white arrow illustrates the scale.

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20 m/s

20 m/s 20 m/s

(a) (b) (c) Figure 7.5: Velocity measurements for the sequence of Figure 6.17. (a) Flame front velocity vectors. (b) PIV vectors. (c) Difference vectors.

Chapter 8. FUTURE OUTLOOK

This Thesis presents a framework where various imaging, image processing and image analysis techniques are designed, developed and used for the purposes of characterizing and studying combustion processes. Although significant progress have been accomplished, surely many possibilities for further research in this area remain open for future studies and analysis. A number of these research possibilities are discussed in this chapter.

8.1 Spray Diagnostics Aspects In the model of laser attenuation in optically dense sprays, multiple scattering is assumed to be negligible. For example, any attenuation of the laser beam caused by the re-scattering it suffers on its way to the CCD camera after its first reflection is not considered. More accurate compensation necessitates that this problem be taken into consideration by including its effects in the attenuation model.

Another interesting aspect lies in investigating the possibilities of extending the spray analysis by relating the scattering cross section to the droplets’ surface area in the spray. The argument is that for droplets in a limited size range (say from 0.1 µm to tens of µm in diameter) the scattering cross section for 90-degree angle scattering can be simply approximated to be proportional to the projected surface area of the droplets. If this approximation could be validated, it should be possible to extract information about the total surface of the droplets present at each point in the spray.

Other aspects that remain to be investigated in the future include the expansion of the stages in which the spray is studied. So far we dealt with spray injection while evaporation, ignition and combustion are not investigated. It is planned that the methods presented in this Thesis will be tested on more data from real combustion environments. For these purposes, different experiments where laser measurements are used for characterizing the combustion processes are being built at the department of Thermo and Fluid Dynamics at Chalmers University. These include building a new high pressure cell (100 bar) for spray combustion studies (no moving parts) and also modifying a one cylinder Volvo Diesel truck engine (complete with the moving parts and piston) so that it can be used for optical measurements.

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120

8.2 Multi Dimensional Diagnostics in Space and Time Continuing technological advancements in multidimensional measurements in flames such as in laser sources, detectors, and computers enable the production of high dimensional data that can include two and three spatial dimensions, time, as well as multiple species and velocity. Though measurements are challenging, they provide unique possibilities to visualize and interpret the relationships between various quantities, which can be invaluable for the deeper understanding of extremely complex combustion systems.

As turbulence is an intrinsically three dimensional phenomenon, 3D measurements of relevant flow and flame quantities are quite important. For example, such measurements reveal the exact topology of turbulent flames and facilitate the calculation of 3D gradients. The high speed laser diagnostic system described in this Thesis can be used for 3D measurements by rapidly sweeping the laser sheet through the measurement volume using a rotating mirror resulting in a set of eight closely spaced planar images as shown in Figure 8.1. The entire measurement of all eight planes must of course be performed at repetition rates higher than the characteristic time scales of the studied flow. A first demonstration of the feasibility of 3D measurements using such a system has already been performed [Hult]. The 3D soot volume fraction is measured in both laminar and moderately turbulent non-premixed C2H4/air flames. The absolute soot volume fraction is measured using laser induced incandescence (LII).

Figure 8.1: Schematic setup of a 3D imaging experiment where laser beams are spatially displaced by means of a rapidly rotating mirror.

Once 3D flame data is available, it is possible for the image analysis and processing methods described in this Thesis to be extended to three dimensions. For example deformable surfaces [McInerney 99] or other methods [Delingette 99][Terzopoulos 91] can be used for segmentation. Also the application of the discussed curve matching technique can be extended to flame surface matching

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121

which means that the cost function will become a hypersurface in four dimensional space [Huot 00].

8.3 Comparing Models with Experimental Data In parallel to the progress in diagnostic techniques, computational capabilities have also advanced to the point where some reasonably detailed comparisons between models and experiments are now possible as illustrated in Figure 8.2 for example.

Figure 8.2: Comparison of a high speed PLIF sequence reflecting the OH concentration field during turbulent spark ignition. (a) Measured OH mole fraction with time. (b) OH mole fraction calculated by DNS with time.

However, a direct detailed comparison of multidimensional measurements and computations of fully turbulent flames remain beyond current capabilities. Rather, it is likely that comparisons will need to rely on statistical characterizations, which require the generation and analysis of extremely large data sets of both experimental and computational data.

8.4 Large Scale Quantitative Studies There still remains a need for conducting statistical and quantitative studies which require the processing and analysis of large amounts of data with minimal user interactivity.

In a recent campaign with the German Aerospace center, the University of Cambridge and the Lund Institute of Technology have conducted experiments where large numbers of simultaneous 3D PIV data, OH images, as well as Rayleigh temperature images and OH time sequences were obtained. It is planned to conduct large scale quantitative studies on this experimental data utilizing the techniques developed in this Thesis.

APPENDIX A

In this appendix we briefly describe the numerical approximations used in the solution for the propagation equation (6.15). The spatial gradients x� and y� are estimated as

� � � � � �� �, minmod , , ,x x y x x y x x yih jh D ih jh D ih jh� � �� �

� (A.1) and

� � � � � �� �, minmod , , ,y x y y x y y x yih jh D ih jh D ih jh� � �� �

� (A.2) where xh and yh are the spatial steps, xD� and xD� (or yD� and yD� ) are the forward and backward derivatives defined as

� � � �1, ,x

x

i j i jDh

� ��

� � �� (A.3)

and � � � �, 1,

xx

i j i jDh

� ��

�� �

� . (A.4)

and the minmod function is defined by

� �

� � � �min , if >0minmod a,b

0

sign a a b ab

otherwise

���

� ����

. (A.5)

On the other hand, the squared derivative is estimated by [Sethian 99]

� �22 max ,0,x x xD D� � �

� �� � . (A.6)

The parameters a , b , and c representing the geometry of the graph surface Z in equation (6.15) are computed using the central finite estimation of p and q

1, 1,, 2

i j i ji j

x

z zp

h� �

�

� (A.7)

and , 1 , 1

, 2i j i j

i jy

z zq

h� �

�

� (A.8)

124

Using these schemes, the following discrete approximation for the propagation equation can be obtained

� �

� �

� � � �

12 2

21

max ,0,

max ,0,

minmod , minmod ,

n nx xij ij ij

n n n ny yij ij ij ij ij

n n n nx x y yij ij ij ij ij

a D D

t b D D

c D D D D

� �

� � � �

� � � �

� �

� � �

� � � �

� �� � �� �� �� �� �� �� � � � �� �� ��� �� �� �� ���� �

. (A.9)

This explicit scheme is conditionally stable and the convergence to a solution is achieved when the time step t� and the space steps xh and yh satisfy the Courant-Friedrichs-Lewy (CFL) condition [Courant 67]

� �1

min ,x yt

h h� � . (A.10)

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[Abu-Gharbieh 01a] Abu-Gharbieh R., Hamarneh G., Gustavsson T., and Kaminski C. “Flame Front Tracking by Laser Induced Fluorescence Spectroscopy and Advanced Image Analysis”. Optics Express, vol. 8(5), pp. 278-287, February 2001.

[Abu-Gharbieh 01b] Abu-Gharbieh R., Kaminski C., Gustavsson T., and Hamarneh G. “Flame Front Matching and Tracking in PLIF Images Using Geodesic Paths and Level Sets”. Proceedings of IEEE’s Workshop on Variational and Level Set Methods in Computer Vision. Vancouver, July 2001.

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[Abu-Gharbieh 98b] Abu-Gharbieh R. “Image Analysis Applied to Spray Characterization”. Technical report R008/1998, Department of Signals and Systems, Chalmers University of Technology, 1998.

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