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«A Dissertation Presented to The Academic Faculty by Alberto Amato In Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in ...»

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LEADING POINTS CONCEPTS IN TURBULENT PREMIXED

COMBUSTION MODELING

A Dissertation

Presented to

The Academic Faculty

by

Alberto Amato

In Partial Fulfillment

of the Requirements for the Degree

Doctor of Philosophy in the

School of Mechanical Engineering

Georgia Institute of Technology

August 2014

Copyright 2014 by Alberto Amato

LEADING POINTS CONCEPTS IN TURBULENT PREMIXED

COMBUSTION MODELING

Approved by:

Dr. Tim Lieuwen, Advisor Dr. Yuri Bakhtin School of Aerospace Engineering School of Mathematics Georgia Institute of Technology Georgia Institute of Technology Dr. Jerry Seitzman Dr. P. K. Yeung School of Aerospace Engineering School of Aerospace Engineering Georgia Institute of Technology Georgia Institute of Technology Dr. Caroline Genzale School of Mechanical Engineering Georgia Institute of Technology Date Approved: May 8, 2014 To my parents Carlo and Teresa iii

ACKNOWLEDGEMENTS

“[The discovery of the Higgs boson] certainly shows to us the value of just imagining… and try to follow the leads that you get from simple ideas… that is worthwhile doing this and see where you come out.” Gerald Guralnik, co-discoverer of the Higgs boson July 4, 2012, www.youtube.com/cerntv This thesis would be incomplete without mentioning several people who assisted, supported and encouraged me during the course of my study. First and foremost, I would like to thank my advisor, Prof. Tim Lieuwen, for his guidance and continuous support during the long and challenging years spent at Georgia Tech. I am neither the first nor I will be the last person to acknowledge Tim’s leadership: he truly has inspired our group to be better thinkers and persons. In a similar vein, I would like to thank Prof. Jerry Seitzman for many insightful comments on my work. His lucid mind and scientific curiosity are infectious and constantly challenge us students to be and do our best. I am also profoundly indebted to Dr. Marcus Day for providing me with many of the data utilized in this thesis and for patiently explaining the many subtleties involved in their analysis. Likewise, I am very appreciative of all the assistance that Prof. Yuri Bakhtin provided to help me understand many mathematical details of this thesis. I would also like to express my gratitude to my committee members, Prof. Caroline Genzale and Prof.

P.K. Yeung, for agreeing to serve on my committee in spite of their extremely busy schedules, and for offering constructive and valuable critiques regarding my research work.

The Ben T. Zinn Combustion Laboratory provided me with the perferct home duringall the years of my doctorate. Andrew Marshall and Prabhakar Venkateswaran, with the late

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them many highs and lows, so frequent in turbulent combustion research, and this work would not have been possible without their help. I am very grateful to Vishal Acharya, Dong-Hyuk Shin, Shreekrishna and Jack Crawford for helping me understand many aspects of combustion theory and numerical computations. I will always cherish the memory of the time spend shoulder to shoulder in our office with also Jordan Blimbaum.

Our “legacy” is in good hands with Nick Magina and Luke Humprey. The “experimentalists” (in no particular order) Jacqueline O’Connor (“Lab-mom”), Chris Foley, Ben Emerson, Ben Wilde, Bobby Noble, Brandon Sforzo, Ianko Chterev, Mike Aguilar, Michael Malanoski, Ryan Sullivan, Sai Kumar, Yash Kochar, Benjamin Knox and Gina Magnotti, were always kind to me and a true source of inspiration.

Here I would also like to acknowledge the many “slivers” of Italy that I befriended in Atlanta and helped me miss less my home. In August 2008 I arrived in the United States with Daniele Bertolotti and Paolo Manenti; for the first few months, before they moved back to Italy, they were my roomates and travelmates, without them I would have not enjoyed as much this experience. Matteo Senesi and Luca Airoldi shared with me the choice of staying longer in the US to pursue a PhD. Our summer trip to Savannah with Alice Sacchetti and Andrea Trimarco will always remain one of my funniest memories.

Martina Baroncelli shared with me one year of life at the Combustion Lab. When she arrived at the lab from Florence, I immediately started to appreciate the pleasure of hearing a familiar “buongiorno” in a Tuscan accent first thing in the morning.

Finally, I would like to thank my family for its unfailing support during these years. To my parents Carlo and Teresa goes all my affection. My uncle Roberto with his wife Sara

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phonecall. My cousins Pierluigi and Silvia with my grandmother Elisabetta, my uncle Guido and aunts Manuela and Giovanna were always the first people that I wanted to see when traveling home for Christmas and have been always a source of strength for me.

Unfortunately, my uncle Davide passed away at a very young age while I was in the middle of my graduate studies. He had been enthusiastic and encouraging about my studies since day one. To him goes my deepest graditude.

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Acknowledgements

List of Tables

List of Figures

Symbols and Abbreviations

Summary

CHAPTER 1: Introduction

1.1 Motivation

1.2 Molecular transport effects on turbulent premixed flame propagation and structure: experimental evidence

1.3 Scope and organization of the thesis

CHAPTER 2: Background

2.1 Preferential diffusion and Lewis number effects

2.1.1 Flame speed definitions

2.1.2 Nonlinear and unsteady effects

2.2 Turbulent premixed combustion modeling

2.3 Lewis number and preferential diffusion effects: direct numerical simulations of turbulent premixed flames

2.4 Leading points concept

2.4.1 Leading points burning rates

2.4.2 Dynamical significance of leading points

CHAPTER 3: LeadingIPointsIBurningIRates

3.1 Numerical procedures

3.2 Definitions

3.3 One dimensional numerical simulations

3.4 Turbulent flame front structure

3.4.1 Local flame front curvatures, shapes and strain rates

3.4.2 Case A31

vii 3.4.3 Case B31, C31 and D31

3.4.3.1 Cylindrical and spherical flamelets

3.4.3.2 Flamelets with low curvature

3.5 Flame front structure at the leading edge

3.6 Conclusions

CHAPTER 4: LeadingIPointsIDynamics

4.1 G-equation

4.2 Problem formulation and mathematical background

4.2.1 One dimensional problem formulation

4.2.2 Hopf-Lax formula and Huygens propagation

4.2.3 Aubry-Mather theory

4.2.4 Definition of Aubry-Mather Leading Points

4.3 Example problem

4.4 Curvature effects

4.5 Conclusions

CHAPTER 5: ConclusionsIandIRecommendations

5.1 Conclusions

5.2 Recommendations for future work

APPENDIX A

A.1. Numerical convergence and validation of the 1D numerical simulations.........143 A.2. Quasi-steady response and ignition transients of expanding cylindrical flames147 A.3. Tubular flames with an inner wall and spherical flames

APPENDIX B

B.1. Sensitivity to the choice of Tref

B.2. Sensitivity to the definition of leading edge

B.3. Joint PDFs at the leading edge

APPENDIX C

References

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Table 1. Methods and conditions of DNS of turbulent premixed flames associated with Lewis number and preferential diffusion effects.

.................. 53 Table 2. Turbulent flame properties for the four simulations at equivalence ratio φ = 0.31. The Reynolds number Re is evaluated utilizing the kinematic viscosity of the reactants νu = 0.175 cm2/s (viscosity of the adiabatic equilibrium products is ten times higher νb= 1.74 cm2/s)............... 68 Table 3. Procedure used to calculate the front displacement speed, sT, for the model problem considered in Section 4.3.

–  –  –

Figure 1-1. Dependence of turbulent flame speed sT on turbulence intensity u’ measured in the turbulent Bunsen burner facility of Venkateswaran et al. [11]. Different symbols refer to different H2/CO/Air mixtures with equal laminar flame speed sL0 = 34cm/s: molar concentrations (by percentage) of hydrogen/carbon monoxide in the fuel and equivalence ratios φ of the different mixtures are listed in the legend on the right. Different colors refer to different mean flow exit jet velocities U0 in the Bunsen burner.

Figure 1-2. sT as a function of the turbulent intensity u’ for CH4/H2/O2/N2 mixtures measured in spherical bombs experiments. Laminar flame speed sL0 is kept equal to 15cm/s across the different mixtures with constant equivalence ratio φ = 0.8 by varying the O2/N2 ratio in the oxidizer [15]. Different symbols refer to different CH4/H2 fuel blends: molar concentration of hydrogen and methane in the fuel are equal to 1-δ and δ, respectively.

Figure 1-3. Experimentally measured values of laminar and turbulent flame speeds vs equivalence ratio φ for C3H8/Air (a) and H2/Air (b).

Turbulent flame speeds are measured at constant turbulent intensity u’ = 2.5m/s in spherical bomb experiments. Flame speed data are normalized by the maximum value. Data adapted from Ref. [4]

Figure 1-4. OH PLIF images of C3H8/Air at φ = 0.7 (a), CH4/Air at φ = 0.8 (b) and H2/Air at φ = 0.27 (c) turbulent premixed flames taken in a LSB burner at turbulent intensity u’=18.5cm/s and integral length scale lt =3.0mm (corresponding to u’/sL0~1 and lt/δT0~5) [16]. Fresh reactants are flowing upward from below. The image width corresponds to 3cm in physical dimensions.

Figure 1-5. Instantaneous grayscale images of the temperature-based combustion progress variable, CT = (T-Tu)/(Tb,0-Tu), and the mole fraction, XOH, of OH radicals in a lean (φ = 0.325) hydrogen–air turbulent Bunsen flame [18]. The CT image is overlaid with isocontours of CT = 0.1, 0.2, 0.3, 0.5, 0.7, and 0.9. The XOH image is overlaid with isocontours of XOH = 0.0005, 0.0010, 0.0015, and 0.0020.

Figure 2-1. Schematic illustrating the typical structure of a methane/air laminar premixed flame. Adapted from Ref. [19]

Figure 2-2. Schematic showing flame coordinate system used to derive flame stretch expressions. Adapted from Ref. [26].

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Figure 2-4.. Illustration of the internal structure of a curved flame and a planar flame showing focusing/defocusing of diffusive fluxes in curved flames.

Figure 2-5. Prism shaped volume, Ω, constructed using curves locally normal to the temperature isotherms. The inset plot shows a typical variation of ɺ ωF normal to the flame surface. Reproduced from Day and Bell [28]........... 20 Figure 2-6. The mass burning rate m = ρsL for stationary spherical flames of different radii r, with burnt gasses at the center. CH4/Air, Tu = 300K, p=1atm: temperature at the inner layer is 1640K. Reproduced from Ref. [37]

Figure 2-7. Theoretical dependence of normalized flame speed U = sd sd,0 on b b Karlovitz number Ka = 2U R for expanding spherical flames (of radius R ) with different Lewis number, obtained by asymptotic analysis in Ref. [41]. “LM” refers to the linear model of equation (2.10), “DM” is a more detailed model taking into account nonlinearities and “SM” refers to a simplified version of “DM”................... 28 Figure 2-8. (a) Sketch of a planar counterflow premixed flame (left) and tubular counterflow premixed flame (right), where V is the inflow velocity of the incoming reactants. (b) Numerical computations [52] of flame temperature (temperature calculated at the axis of symmetry) dependence on stretch rate (κ = 2V/R and κ = 2V/L for planar and tubular counterflow flame, respectively [53]) for H2/Air flames, φ = 0.175, Tu = 298K, p=1atm, L = 1.26cm, R = 1.5cm

Figure 2-9. Dependence of instantaneous flame consumption speed, sc,P, on the instantaneous stretch rate, κ, at several frequencies of oscillation from 0Hz (Steady curve) to 1000Hz. Here δF0 = 0.1mm and sL0 =

22.15cm/s Image reproduced from Ref. [56] (H2/Air flame φ = 0.4 with reactants at standard temperature and pressure)

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Figure 2-12. Single step chemistry numerical simulation of normalized consumption speed sc, P sL 0 versus normalized time tsL 0 δ F 0 for spherical expanding H2/Air flames (with φ = 0.26, and reactants at standard temperature and pressure) ignited by pockets of adiabatic product gasses with initial radius ri [3, 42]. The maximum consumption speed for the spherical flame is indicated by an arrow and represents the critically stretched value.

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Figure 2-14. Schematic illustrating the various terms in equation (2.24), adapted from Ref. [7]. AT represents the wrinkled area, while AL is the area of the c = 0.5 contour. Also labeled are the flamelet consumption speed sc and the turbulent brush local consumption speed sT.

Figure 2-15. Scatter plot of local consumption speed sc, P dependence on flame curvature K C (a) strain rate KS (conditioned on K C being smaller than 10% of its maximum value) (b) and stretch rate κ (c) from the 2D DNS of Chen and Im [93] (H2/air, φ = 0.4, Tu=300K, p=1atm, sL0=22.4cm/s, δT0 = 0.61mm, δF0 = DO2 /sL0 = 0.1mm, u’/sL0 = 5.0, lt/δT0 = 3.18).

Figure 2-16. Isocontours of H2 consumption rate (red corresponds to zero consumption rate, blue corresponds to the maximum calculated consumption rate) from the DNS of Chen and Im [93], corresponding to the data shown in Figure 2-15. Reactants are on the left, products on the right.

Figure 2-17. Scatter plot of the three contributions (see equation (2.18)) to the displacement speed sd as a function of the curvature normalized by flame thickness KCδT 0 for the lean CH4/air flame of Ref. [94] (φ = 0.7, Tu = 800K, p = 1atm, u’/sL0 = 10, lt/δT0 = 2.77, δT0 = 0.31mm)................ 43 Figure 2-18.

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