Transcript Slide 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
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
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
Turbulence–Chemistry Interaction: A Central Challenge
Simple Jet
Piloted
Bluff Body Swirl
Lifted
complex
kinetics
complex
geometry
practical
combustion
systems
turb/chem
spray
instabilities
pressure
scaling
particulates
 Progression of well documented cases that address the
fundamental science of turbulent flow, transport, and chemistry
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
fuel
air
Bergmann et al. Appl. Phys. B (1998)
velocity vectors
from PIV
local flame
extinction
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
x
2(YC  YC , 2 ) / wC  (YH  YH , 2 ) / 2wH  (YO  YO , 2 ) / wO
2(YC ,1  YC , 2 ) / wC  (YH ,1  YH , 2 ) / 2wH  (YO ,1  YO , 2 ) / wO
Determined from mass fractions of species
Mixture fraction quantifies
the state of fuel-air mixing
Fuel
x =1
Air
x =0
2
1
Mixture fraction, x
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)

  2Dx (x  x )  2Dx (x / x)2  (x / y) 2  (x / z )2

mixture diffusivity
Scalar dissipation quantifies
the rate of molecular mixing
Central concept in combustion
theory and modeling
Hard to measure in
turbulent flames!
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)
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)
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)
Turbulent Combustion Laboratory
8 laser
5 cameras
7 computers
Combined measurement:
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

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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
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
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)
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?
Dissipation Cutoff Scale in Nonreacting C2H4 Jets
x/d = 60
Scaling law for nonreacting jets
lB  2.3 Re3/ 4 Sc1/ 2
kblb = 1
Estimated using scaling law
Exp. Determined (2% cutoff)
Energy and Dissipation Spectra in CH4/H2/N2 Jet Flames
 Energy spectrum
 Flat noise floor in each energy
spectrum (uncorrelated)
 Dissipation spectrum
noise
 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
Normalized 1-D thermal dissipation spectra
10
0
-1
10
-2
10
-3
D*1(klb)
10
10
-4
DLR-A
Red=15,200
noise
2% level
DLR-B
Red=22,400
10
0
10
-1
10
-2
1-D model
r/d = 0
r/d = 1.0
r/d = 1.5
r/d = 0
r/d = 1.4
r/d = 2.0
r/d = 2.6
r/d = 0
r/d = 1.6
r/d = 3.6
r/d = 4.4
x/d = 10
x/d = 20
x/d = 40
-3
10
-4
10
-3
10
-2
10
klb
-1
10
0
10  Each spectrum normalized by its
peak value
-4
1 10
10
 lb determined from 2% of the peak
 4th-order implicit differencing stencil
(Lele, 1992)
Thermal Dissipation Length Scale in Flames
lb (mm) determined experimentally from 2% cutoff in dissipation spectra
(mm)
Red=15,200
Red=22,400
Dissipation spectra in DLR-A flame at x/d=20
10
0
10
-1
10
-2
r/d=2.6
10
0
r/d=2.0
-1
10
-2
D*1(klb)
10
-3
100
10
r/d=1.4
-1
10
-2
10
-3
-3
10 0
10
10
10
-1
 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
r/d=0
x
10
-2
10
-3
DLR-A
10
-3
10
T
I
1-D model
-2
10
-1
klb
10
0
10
1
 Thermal dissipation cutoff length
scale is smaller than or equal to
that for mixture fraction dissipation
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’)
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
Dissipation spectra in piloted CH4/air flames
 Partially premixed CH4/air jet flames
x/d =45
 Rayleigh cross section is not constant
x/d =30
 Variations in Rayleigh cross section
occur at larger length scales
Premixed Pilot Flame
Flame-D: Red = 22,400
x/d =15
Flame-E: Red = 33,600
x/d =7.5
x/d = 15, r/d=1.1laser
x/d = 2
axis
laser axis
 Measured at radial location of max
scalar variance
Dissipation spectra in piloted CH4/air flames
10
 Each spectrum normalized by its
peak value and the cutoff
determined from the “I” spectrum
0
Flame-E
-1
10
-2
10
-3
D*1(klb)
10
10
10
0
10
-1
10
-2
10
1
10
-3
Flame-D
 Rayleigh cross section is not
constant
x
T
I
1-D model
-3
10
-2
10
-1
klb
10
0
Flame-D: Red = 22,400
Flame-E: Red = 33,600
x/d = 15, r/d=1.1
 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)
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
Highly-Resolved Planar Rayleigh Imaging
 Highly-resolved 2D Rayleigh imaging
 Structure of dissipation layers
S.A. Kaiser, J.H. Frank, Proc. Combust. Inst. 31 (2007)
J.H. Frank, S.A. Kaiser, Exp. Fluids. (2008)
DLR-A, CH4/H2/N2
Re = 15,200
x/d = 10
Thermal Dissipation Structures in Jet Flame
 Two-dimensional measurements used to determine radial
and axial contributions to dissipation
T   (T  r ) 2  (T  x ) 2
2
S.A. Kaiser, J.H. Frank, Proc. Combust. Inst. 31 (2007)
J.H. Frank, S.A. Kaiser, Exp. Fluids. (2008)
Resolving Dissipation Power Spectra
Interlacing for noise suppression
Apparent
dissipation
(from noise)
Image 1: odd lines
Noise
Suppression
Image 2: even lines
PSDrad  FFT  T1 r  FFT *  T2 r 
 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).
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).
Temperature Dependence of Dissipation Layer Widths
Probability density functions of layer width, lD, conditioned on temperature
x/d = 10
lD*  lD T T0 
0.75
 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)
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