Scalar Dissipation Measurements in Turbulent Jet Flames

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Scalar Dissipation Measurements in Turbulent Jet
Flames Robert S. Barlow Combustion Research
Facility Sandia National Laboratories Livermore,
CA, 94550 Supported by US Department of
Energy, Office of Basic Energy Sciences, Division
of Chemical Sciences, Biosciences and Geosciences
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Scalar Spectra and Length Scales in Turbulent Jet
Flames

• Rayleigh scattering time series measurements (UT
  Austin)
• Guanghua Wang, Noel Clemens, Philip Varghese
  Proc. Combust. Inst. 29 (2005) Meas. Sci.
  Technol. 18 (2007) Combust Flame 152 (2008)
• Line-imaging of Rayleigh/Raman/CO-LIF (Sandia)
• Guanghua Wang, Rob Barlow Proc. Comb. Inst. 31
  (2007) Combust. Flame 148 (2007) Exp.
  Fluids 44 (2008)
• High-resolution planar Rayleigh imaging (Sandia)
• Sebastian Kaiser, Jonathan Frank Proc. Comb.
  Inst. 31 (2007) Exp. Fluids 44 (2008)

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Outline

• Background and Motivation
• Turbulence-chemistry interaction in flames
• Importance of scalar dissipation
• Experimental methods and challenges
• Results
• Measured scalar energy and dissipation spectra in
  jets and flames
• Comparisons with Popes model spectrum
• Relationship between dissipation scales for T and
  mixture fraction
• Conclusions

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TurbulenceChemistry Interaction A Central
Challenge

• Progression of well documented cases that address
  the fundamental science of turbulent flow,
  transport, and chemistry

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Local Flame Extinction
CH4/H2/N2 jet flame
T (Rayleigh)
OH (PLIF)
Time series of planar OH LIF images, Dt 125
msHult et al. (2000)
velocity vectors from PIV
local flame extinction
OH LIF marks reaction zone
Bergmann et al. Appl. Phys. B (1998)
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Definitions for Nonpremixed Flames Mixture
Fraction
Fuel x 1
Determined from mass fractions of species
Air x 0
Mixture fraction quantifies the state of
fuel-air mixing
1
2
Mixture fraction, x
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Definitions for Nonpremixed Flames Scalar
Dissipation

• Reactants must be mixed at the molecular level by
  diffusion
• Molecular mixing occurs mainly at the smallest
  scales, dissipation range
• Scalar dissipation rate (s-1)

Scalar dissipation quantifies the rate of
molecular mixing
Central concept in combustion theory and modeling
Hard to measure in turbulent flames!
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Experimental Approach

• Use Rayleigh scattering to investigate scalar
  structure of turbulent flames
• High SNR
• Good spatial resolution
• CH4/H2/N2 jet flames DLR-A (Red
  15,200) DLR-B (Red 22,400)
• Nearly constant Rayleigh cross section throughout
  flame
• Measure energy and dissipation spectra of
  temperature fluctuations
• Compare to model spectra (Pope, Turbulent Flow,
  Ch 6.5)
• Mixture fraction (Raman scattering ? lower SNR
  and resolution)

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Thermal Dissipation by Rayleigh Thermometry

• Wang et al. (UT Austin)
• High rep rate laser ? Time series of temperature

• 10 kHz sampling rate
• Optical resolution, 0.3 mm
• Redundant measurement
• CH4/H2/N2 jet flame
• Re 15,200
• d 7.8 mm

Wang, Clemens, Varghese, Proc. Combust. Inst. 29
(2005) Wang, Clemens, Varghese, Barlow, Combust.
Flame (2008)
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Energy and Dissipation Spectra along Centerline
(DLR-A)

• Corrected energy/dissipation spectra collapse at
  all downstream locations when scaled by
  Batchelor frequency (ff/fB)
• Good agreement with Pope model spectra using 50
  lt Rel lt 60
• Small separation of scales for this Red 15,200
  flame

Combust. Flame (2008)
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Turbulent Combustion Laboratory
8 laser 5 cameras 7 computers

• Combined measurement
• T, N2, O2, CH4, CO2, H2O, H2, CO
• 220-mm spacing, 6-mm segment(40-mm spacing for
  Rayleigh)
• state of mixing (mixture fraction)
• progress of reaction
• rate of mixing (scalar dissipation)
• local flame orientation

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Model Energy and Dissipation Spectra
time series
1D imaging
k1 kBlB 1

• Model 1-D dissipation spectrum (Pope, Turbulent
  Flows, 2000)
• k1 1 corresponds to 2 of peak dissipation
  value, lB 1/kB
• Physical wavelength is 2plB

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Challenge of Dissipation measurements in Flames

• Over resolved measurement (40 mm)
• Noise contributes to apparent dissipation
• Spatial filtering reduces noise, can also reduce
  true dissipation
• Cannot evaluate accuracy without knowing the
  local dissipation cutoff scale (local Batchelor
  scale)

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Questions

• Can we determine the local dissipation cutoff
  scale from ensembles of short 1D measurements?
• Nonreacting jets
• Jet flames
• How do scalar dissipation spectra behave in
  flames?
• Temperature, mixture fraction, reactive species
• Can we use spectral information to determine
  local resolution requirements in complex flames
  and develop methods for accurate measurement of
  mixture fraction dissipation?

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Dissipation Cutoff Scale in Nonreacting C2H4 Jets
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Energy and Dissipation Spectra in CH4/H2/N2 Jet
Flames

• Energy spectrum
• Flat noise floor in each energy spectrum
  (uncorrelated)
• Dissipation spectrum
• Fluctuations in thermal diffusivity, a , are at
  length scales of the energy spectrum
• Dissipation spectrum PSD of radial gradient
  in T, determined from inverse of Rayleigh signal

noise
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Normalized 1-D thermal dissipation spectra

• Each spectrum normalized by its peak value
• lb determined from 2 of the peak
• 4th-order implicit differencing stencil (Lele,
  1992)

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Thermal Dissipation Length Scale in Flames
lb (mm) determined experimentally from 2 cutoff
in dissipation spectra
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Dissipation spectra in DLR-A flame at x/d20

• Spectra for
• I 1/(Rayleigh signal)
• T temperature
• x mixture fraction
• T spectra at Raman resolution,use species data
  for sRay
• Spectra for T and I yield the same cutoff length
  scale
• Thermal dissipation cutoff length scale is
  smaller than or equal to that for mixture
  fraction dissipation

DLR-A
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Thermal Dissipation vs. Mixture Fraction
Dissipation

• Single-shot profiles of T, x
• Zero dissipation at TTmax
• Double-peak in thermal dissipation
• Higher spatial frequencies on average in T and
  grad(T)

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Determining the Mixture Fraction Cutoff Scale

• Scale I-dissipation spectrum (from 1/Rayleigh) to
  align with the peak inx-dissipation spectrum
• Alternatively, fit the model spectrum to the
  x-dissipation peak

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Dissipation spectra in piloted CH4/air flames

• Partially premixed CH4/air jet flames
• Rayleigh cross section is not constant
• Variations in Rayleigh cross section occur at
  larger length scales
• Measured at radial location of max scalar
  variance

• Flame-D Red 22,400
• Flame-E Red 33,600
• x/d 15, r/d1.1

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Dissipation spectra in piloted CH4/air flames

• Each spectrum normalized by its peak value and
  the cutoff determined from the I spectrum
• Rayleigh cross section is not constant
• Variations in Rayleigh cross section occur at
  larger length scales
• Surrogate dissipation length scale at x/d15
• lb 86 2plb 540 mm
• lb 71 2plb 440 mm
• Applicable in more general flames(to be tested)

• Flame-D Red 22,400
• Flame-E Red 33,600
• x/d 15, r/d1.1

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Resolution Curves Temperature Variance and
Dissipation

• Resolution relative to fB
• Variance curves
• Depend on Rel
• Range of Rel consistent with local T
• Dissipation curves
• Flame results agree well with model
• Initial roll-off has little Re dependence

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Highly-Resolved Planar Rayleigh Imaging

• Highly-resolved 2D Rayleigh imaging
• Structure of dissipation layers

DLR-A, CH4/H2/N2 Re 15,200 x/d 10
S.A. Kaiser, J.H. Frank, Proc. Combust. Inst. 31
(2007) J.H. Frank, S.A. Kaiser, Exp. Fluids.
(2008)
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Thermal Dissipation Structures in Jet Flame

• Two-dimensional measurements used to determine
  radial and axial contributions to dissipation

S.A. Kaiser, J.H. Frank, Proc. Combust. Inst. 31
(2007) J.H. Frank, S.A. Kaiser, Exp. Fluids.
(2008)
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Resolving Dissipation Power Spectra
Interlacing for noise suppression
Image 1 odd lines
Apparent dissipation (from noise)
Noise Suppression
Image 2 even lines

• Interlacing, or dual detector, technique
  suppresses noise
• Power spectral density measured over three orders
  of magnitude

S.A. Kaiser, J.H. Frank, Proc. Combust. Inst. 31
(2007).
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Comparison of 1D and 2D Results

• Cutoff at lC 2plb
• Line results 10-20 higher

S.A. Kaiser, J.H. Frank, Proc. Combust. Inst. 31
(2007).
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Temperature Dependence of Dissipation Layer Widths
Probability density functions of layer width, lD,
conditioned on temperature
x/d 10

• Adaptive smoothing used to reduce noise when
  determining layer thicknesses
• Layer-widths scale approximately as (T/T0)0.75

S.A. Kaiser, J.H. Frank, Proc. Combust. Inst. 31
(2007) J.H. Frank, S.A. Kaiser, Exp. Fluids.
(2008)
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Conclusions

• 1D Rayleigh scattering in non-reacting jet flow
  results
• 2 of peak dissipation ? cutoff length scale 2plB
  ? local Batchelor scale
• Consistent with the Popes model spectrum
• Agrees with estimation based on scaling laws
  using local Reynolds number
• Thermal dissipation spectra in jet flames
• Consistent with Popes model spectrum, noise
  easily identified
• Dissipation cutoff length scale 2plb
• Simple diagnostic to determine scalar length
  scales, resolution requirements
• Mixture fraction cutoff scale may be determined
  if dissipation peak is resolved ? methods for
  accurate determination of mean dissipation
• Proper binning proper differentiation scheme
  significantly reduce noise without affecting true
  dissipation rate