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DNS of Turbulent Nonpremixed Ethylene Flames

DNS of Turbulent Nonpremixed Ethylene Flames

DNS of Turbulent Nonpremixed Ethylene

DIRECT NUMERICAL SIMULATION OF SOOT FORMATION AND TRANSPORT IN TURBULENT NONPREMIXED ETHYLENE FLAMES by David Owen Lignell A dissertation submitted to the faculty of The University of Utah in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Chemical Engineering The University of Utah May 2008

  • Page 2 and 3: Copyright c○ David Owen Lignell 2
  • Page 4 and 5: THE UNIVERSITY OF UTAH GRADUATE SCH
  • Page 6 and 7: To my wife Jennifer and to our sons
  • Page 8 and 9: 2.5.4.1 Monodispersed Size Distribu
  • Page 10 and 11: LIST OF TABLES 2.1 First-order deri
  • Page 12 and 13: CHAPTER 1 INTRODUCTION Combustion o
  • Page 14 and 15: towards or away from a flame, the t
  • Page 16 and 17: the accuracy of the chemical mechan
  • Page 18 and 19: ¯f(x) = f(x D ′ )G(x − x ′ )
  • Page 20 and 21: Instead, for a given chemical state
  • Page 22 and 23: Figure 1.2. Flamelet model schemati
  • Page 24 and 25: ∂Y ′′ eY = − ρ ∂t + ρv
  • Page 26 and 27: 1.3 Review of Turbulent Simulations
  • Page 28 and 29: mechanism with PAH formation (2005)
  • Page 30 and 31: complex boundary conditions, high-o
  • Page 32 and 33: eflecting boundaries in the other.
  • Page 34 and 35: CHAPTER 2 DNS FORMULATION, MODELS,
  • Page 36 and 37: equal to zero. This inconsistency i
  • Page 38 and 39: the dimensionless numbers contain t
  • Page 40 and 41: Table 2.1. First-order derivative f
  • Page 42 and 43: Signal 1 0.5 0 -0.5 -1 0 0.2 0.4 0.
  • Page 44 and 45: are lower; hence both flames and so
  • Page 46 and 47: as bimodal extinction/ignition beha
  • Page 48 and 49: computational savings make realisti
  • Page 50 and 51: Ignition Delay Time (s) 0.1 0.01 0.
  • Page 52 and 53:

    approach the flame. This configurat

  • Page 54 and 55:

    Mole Fraction Mole Fraction (a) Gas

  • Page 56 and 57:

    to uncertainties in current soot me

  • Page 58 and 59:

    This figure is only intended to sho

  • Page 60 and 61:

    Figure 2.12. Schematic of soot evol

  • Page 62 and 63:

    CO: SCO = WCO · R3. (2.45) With th

  • Page 64 and 65:

    where Mr is the r th moment, and mi

  • Page 66 and 67:

    which carbon atoms are added to par

  • Page 68 and 69:

    −1 r = γ M k k+2/3m r−k 1 .

  • Page 70 and 71:

    integration increments these lines

  • Page 72 and 73:

    C5 = 10 + 5 61 ∞ ∞ m 0 0 2 µ

  • Page 74 and 75:

    Logarithmic interpolation for a fra

  • Page 76 and 77:

    The moments of the lognormal distri

  • Page 78 and 79:

    2/3 6 G2 = π · 2 · ksM ρsπ 5/3

  • Page 80 and 81:

    69 M2 = x 2 1w1 + x 2 2w2, (2.160)

  • Page 82 and 83:

    not be needed; or, in other words,

  • Page 84 and 85:

    The soot model implemented is from

  • Page 86 and 87:

    Moment Values (arb. units) Moment V

  • Page 88 and 89:

    M 0 (#/m -3 ) 2E+17 1.8E+17 1.6E+17

  • Page 90 and 91:

    no soot at time zero. However, unli

  • Page 92 and 93:

    CHAPTER 3 ONE-DIMENSIONAL SIMULATIO

  • Page 94 and 95:

    equations to steady state using the

  • Page 96 and 97:

    χ (1/s) 1 0.8 0.6 0.4 0.2 χ erf

  • Page 98 and 99:

    T (K) Y O2 Y OH 2500 2000 1500 1000

  • Page 100 and 101:

    to the variation of the diffusivity

  • Page 102 and 103:

    turbulent convective scales. 3.2.1

  • Page 104 and 105:

    Velocity (m/s) 1 0.8 0.6 0.4 0.2 0

  • Page 106 and 107:

    The reaction rate peak is more stat

  • Page 108 and 109:

    indicating the tradeoff between the

  • Page 110 and 111:

    this species directly contributes t

  • Page 112 and 113:

    Number Density (#/cm^3) 1.4E+11 1.2

  • Page 114 and 115:

    Figure 4.1. Typical experimental mi

  • Page 116 and 117:

    Figure 4.2. Initial velocity profil

  • Page 118 and 119:

    Table 4.1. Simulation parameters of

  • Page 120 and 121:

    Case 1 Case 2 Case 3 Figure 4.5. Pr

  • Page 122 and 123:

    • dilatation of the flame pushing

  • Page 124 and 125:

    1424 K and a mixture fraction of 0.

  • Page 126 and 127:

    Table 4.2. Comparison of bulk sooti

  • Page 128 and 129:

    CHAPTER 5 TWO-DIMENSIONAL TURBULENT

  • Page 130 and 131:

    the tip. Multidimensional effects o

  • Page 132 and 133:

    The turbulence parameters were set

  • Page 134 and 135:

    premixed flames. By applying the ch

  • Page 136 and 137:

    as above and computed as follows. M

  • Page 138 and 139:

    and acetylene mass fraction are. In

  • Page 140 and 141:

    versus mixture fraction. The mean s

  • Page 142 and 143:

    velocity as the two solid lines at

  • Page 144 and 145:

    Ysoot # Density (#/cm3) 0.003 0.002

  • Page 146 and 147:

    the flame; hence the profile is lim

  • Page 148 and 149:

    (a) (b) Figure 5.9. Alternate simul

  • Page 150 and 151:

    the DNS calculations highlights an

  • Page 152 and 153:

    etween the level of soot and the lo

  • Page 154 and 155:

    unity magnitude, we would not expec

  • Page 156 and 157:

    v ξ (cm/s) ξ* Fraction v ξ > 0 -

  • Page 158 and 159:

    P ρYs (v ξ ) (cm/s) 0.15 0.1 0.05

  • Page 160 and 161:

    and 4.5 cm/s at ξ = 0.2 at positio

  • Page 162 and 163:

    long timescales, downstream flames

  • Page 164 and 165:

    CHAPTER 6 THREE-DIMENSIONAL ETHYLEN

  • Page 166 and 167:

    fluid in the domain (for soot growt

  • Page 168 and 169:

    Figure 6.1. Isocontours of temperat

  • Page 170 and 171:

    Figure 6.2. Scatter plots of combus

  • Page 172 and 173:

    unsteady soot growth and strong dif

  • Page 174 and 175:

    are in agreement with those previou

  • Page 176 and 177:

    Pφ = 165 〈φ|ξ〉P (ξ) , (6.2)

  • Page 178 and 179:

    mass starts out lean at a mixture f

  • Page 180 and 181:

    smaller, and the soot was not stron

  • Page 182 and 183:

    terms in the figure indicates that

  • Page 184 and 185:

    at 16τj but then increases steadil

  • Page 186 and 187:

    v ξ , v thm × 10, (cm/s) 400 200

  • Page 188 and 189:

    the flame and burned out. Computati

  • Page 190 and 191:

    ρ ∂ξ ∂ξ ∂ + ρv − ρDξ

  • Page 192 and 193:

    where, in the first term, Eq. (7.8)

  • Page 194 and 195:

    Y soot 0.0025 0.002 0.0015 0.001 0.

  • Page 196 and 197:

    C/χ max 0.6 0.4 0.2 0 -0.2 -0.4 -0

  • Page 198 and 199:

    Before this equation is transformed

  • Page 200 and 201:

    peak temperature difference was 271

  • Page 202 and 203:

    One of the major challenges of CMC

  • Page 204 and 205:

    The resulting equation is averaged

  • Page 206 and 207:

    In this equation, a subscript η is

  • Page 208 and 209:

    P(η) 1.25 1 0.75 0.5 0.25 t=25τ j

  • Page 210 and 211:

    (kg/m 3 s)*1000 (kg/m 3 s)*1000 40

  • Page 212 and 213:

    CHAPTER 8 CONCLUSIONS AND FUTURE WO

  • Page 214 and 215:

    the flame moves towards the soot.

  • Page 216 and 217:

    The three-dimensional DNS were used

  • Page 218 and 219:

    APPENDIX A FINITE DIFFERENCE PROGRA

  • Page 220 and 221:

    APPENDIX B PRODUCT DIFFERENCE ALGOR

  • Page 222 and 223:

    Clearly, ci acts as an amplificatio

  • Page 224 and 225:

    c i α 0.1 0.08 0.06 0.04 0.02 0 0

  • Page 226 and 227:

    φ 1.25 1 0.75 0.5 0.25 0 0 2 4 6 8

  • Page 228 and 229:

    y > 3 : 217 φr(y) = 1.231697 exp(

  • Page 230 and 231:

    APPENDIX D DERIVATION OF THE CMC EQ

  • Page 232 and 233:

    − ∂ (ψωi) . ∂Zi The first t

  • Page 234 and 235:

    where Π represents the sample spac

  • Page 236 and 237:

    − ˆZ ZY s ZY s ∂ ∂ ˆ ∂ (

  • Page 238 and 239:

    [14] A. Coppalle, D. Joyeux, Temper

  • Page 240 and 241:

    [47] M. Balthasar, A. Heyl, F. Mau

  • Page 242 and 243:

    [76] S. Sreedhara, K. N. Lakshmisha

  • Page 244 and 245:

    [108] H. M. Hulburt, S. Katz, Some

  • Page 246:

    [139] J. Nagle, R. F. Strickland-Co

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