1. 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

2. 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)
Guanghua Wang

3. Background and Motivation
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 Pope’s model spectrum
Relationship between dissipation scales for T and mixture fraction
Conclusions

4. Turbulence–Chemistry Interaction: A Central Challenge
spray
pressure
scaling
particulates
complex
kinetics
geometry
turb/chem
practical
combustion
systems
instabilities
Simple Jet Piloted Bluff Body Swirl Lifted
Progression of well documented cases that address the fundamental science of turbulent flow, transport, and chemistry

5. Local Flame Extinction
CH4/H2/N2 jet flame
T (Rayleigh)
OH (PLIF)
Time series of planar OH LIF images, Dt = 125 ms Hult et al. (2000)
OH LIF marks reaction zone
velocity vectors from PIV
local flame
extinction
air
fuel
Bergmann et al. Appl. Phys. B (1998)

6. Mixture fraction quantifies the state of fuel-air mixing
Definitions for Nonpremixed Flames: Mixture Fraction
Mixture fraction:
“Fraction of mass in a sample that originated from the nozzle”
Definition proposed by Bilger, adopted by TNF Workshop
Fuel
x =1
Determined from mass fractions of species
Air
x =0
Mixture fraction quantifies
the state of fuel-air mixing 2 1
Mixture fraction, x

7. Scalar dissipation quantifies the rate of molecular mixing
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)
mixture diffusivity
Scalar dissipation quantifies
the rate of molecular mixing
Central concept in combustion theory and modeling
Hard to measure in turbulent flames!

8. 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)

9. 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)

10. Energy and Dissipation Spectra along Centerline (DLR-A)
Corrected energy/dissipation spectra collapse at all downstream locations when scaled by Batchelor frequency (f*=f/fB)
Good agreement with Pope model spectra using 50 < Rel < 60
Small separation of scales for this Red = 15,200 flame
Combust. Flame (2008)

11. 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

12. Model Energy and Dissipation Spectra
time series
1D imaging
k1* = kBlB = 1
Model 1-D dissipation spectrum (Pope, Turbulent Flows, 2000)
k*1 = 1 corresponds to ~2% of peak dissipation value, lB = 1/kB
Physical wavelength is 2plB

13. 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)

14. 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?

15. Dissipation Cutoff Scale in Nonreacting C2H4 Jets
kblb = 1
x/d = 60
Scaling law for nonreacting jets
Estimated using scaling law
Exp. Determined (2% cutoff)

16. 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

17. Normalized 1-D thermal dissipation spectra
Red=15,200
Red=22,400
2% level
noise
x/d = 10
x/d = 20
x/d = 40
Each spectrum normalized by its peak value
lb determined from 2% of the peak
4th-order implicit differencing stencil (Lele, 1992)

18. Thermal Dissipation Length Scale in Flames
lb (mm) determined experimentally from 2% cutoff in dissipation spectra
Red=15,200
Red=22,400
(mm)

19. Dissipation spectra in DLR-A flame at x/d=20
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

20. Thermal Dissipation vs. Mixture Fraction Dissipation
Single-shot profiles of T, x
Zero dissipation at T=Tmax
Double-peak in thermal dissipation
Higher spatial frequencies on average in T’ and grad(T’)

21. Determining the Mixture Fraction Cutoff Scale
Scale I-dissipation spectrum (from 1/Rayleigh) to align with the peak in x-dissipation spectrum
Alternatively, fit the model spectrum to the x-dissipation peak

22. Dissipation spectra in piloted CH4/air flames
laser
axis
laser axis
x/d =45
x/d =30
x/d =15
x/d =7.5
x/d = 2
Premixed Pilot Flame
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/d=1.1

23. 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/d=15
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/d=1.1

24. 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

25. 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)

26. Thermal Dissipation Structures in Jet Flame
Two-dimensional measurements used to determine radial and axial contributions to dissipation
Mean temperature field subtracted
Ignore diffusivity to capture structure and reduce noise
Opposing effects of noise and spatial averaging on dissipation
Adaptive smoothing
Range of scales (x/d = 5)
S.A. Kaiser, J.H. Frank, Proc. Combust. Inst. 31 (2007)
J.H. Frank, S.A. Kaiser, Exp. Fluids. (2008)

27. Resolving Dissipation Power Spectra
Interlacing for noise suppression
Image 1: odd lines
Apparent
dissipation
(from noise)
Noise
Suppression
Image 2: even lines
Average over 600 images
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).

28. 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).

29. Temperature Dependence of Dissipation Layer Widths
Probability density functions of layer width, lD, conditioned on temperature
x/d = 10
10% error due to adaptive smoothing
If no smoothing were required: relative error <10% for layers >60um
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)

30. Conclusions 1D Rayleigh scattering in non-reacting jet flow results:
2% of peak dissipation  cutoff length scale 2plB  local Batchelor scale
Consistent with the Pope’s model spectrum
Agrees with estimation based on scaling laws using local Reynolds number
Thermal dissipation spectra in jet flames:
Consistent with Pope’s 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