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Scalar Dissipation Measurements in Turbulent Jet Flames
Robert S. BarlowCombustion Research FacilitySandia National Laboratories
Livermore, CA, 94550
Supported by US Department of Energy, Office of Basic Energy Sciences,Division of Chemical Sciences, Biosciences and Geosciences
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
Scalar Spectra and Length Scales in Turbulent Jet Flames
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
Progression of well documented cases that address the fundamental science of turbulent flow, transport, and chemistry
Turbulence–Chemistry Interaction: A Central Challenge
spray
pressurescaling
particulates
complexkinetics
complexgeometry
turb/chem
practicalcombustion
systems
instabilities
Simple Jet Piloted Bluff Body Swirl Lifted
CH4/H2/N2 jet flame
Time series of planar OH LIF images, t = 125 s
Hult et al. (2000)
OH LIF marks
reaction zone
velocity vectors from
PIV
air
fuel
local flameextinction
Local Flame Extinction
T (Rayleigh) OH (PLIF)
Bergmann et al. Appl. Phys. B (1998)
Mixture fraction quantifies the state of fuel-air mixing
Mixture fraction:
“Fraction of mass in a sample that originated from the nozzle”
Fuel=1 Air
=0
Mixture fraction,
Definitions for Nonpremixed Flames: Mixture Fraction
OOOHHHCCC
OOOHHHCCC
wYYwYYwYY
wYYwYYwYY
/)(2/)(/)(2
/)(2/)(/)(2
2,1,2,1,2,1,
2,2,2,
Definition proposed by Bilger, adopted by TNF Workshop
Determined from mass fractions of species
12
Scalar dissipation quantifies the rate of molecular mixing
222 )/()/()/(2)(2 zyxDD
mixture diffusivity
Hard to measure in turbulent flames!
Central concept in combustion theory and modeling
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)
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)
Wang et al. (UT Austin)
High rep rate laser Time series of temperature
Thermal Dissipation by Rayleigh Thermometry
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 < Re < 60
Small separation of scales for this Red = 15,200 flameCombust. Flame (2008)
Turbulent Combustion Laboratory
8 laser5 cameras7 computers
Combined measurement: T, N2, O2, CH4, CO2, H2O, H2, CO 220-m spacing, 6-mm segment
(40-m spacing for Rayleigh) state of mixing (mixture fraction) progress of reaction rate of mixing (scalar dissipation) local flame orientation
Model Energy and Dissipation Spectra
Model 1-D dissipation spectrum (Pope, Turbulent Flows, 2000)
*1 = 1 corresponds to ~2% of peak dissipation value, B = 1/B
Physical wavelength is 2B
time series
1D imaging
=BB = 1
Challenge of Dissipation measurements in Flames
Over resolved measurement (40 m)
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
2/14/3Re3.2 ScB Scaling law for nonreacting jets
= 1
x/d = 60
Estimated using scaling lawExp. 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
Fluctuations in thermal diffusivity, , are at length scales of the energy spectrum
“Dissipation” spectrum = PSD of radial gradient in T’, determined from inverse of Rayleigh signal
noise
Normalized 1-D thermal dissipation spectra
Each spectrum normalized by its peak value
determined from 2% of the peak
4th-order implicit differencing stencil (Lele, 1992)
x/d = 10
x/d = 20
x/d = 40
Red=15,200
Red=22,400
2% level
noise
Thermal Dissipation Length Scale in Flames
(m) determined experimentally from 2% cutoff in dissipation spectra
Red=15,200
Red=22,400
(mm)
Dissipation spectra in DLR-A flame at x/d=20
DLR-A
Spectra for:• I = 1/(Rayleigh signal)• T = temperature• = mixture fraction
T spectra at Raman resolution,use species data for Ray
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
Thermal Dissipation vs. Mixture Fraction Dissipation
Single-shot profiles of T,
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-dissipation spectrum
Alternatively, fit the model spectrum to the -dissipation peak
Flame-D: Red = 22,400
Flame-E: Red = 33,600
x/d = 15, r/d=1.1
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
Dissipation spectra in piloted CH4/air flames
laseraxis laser
axis
x/d =45
x/d =30
x/d =15
x/d =7.5
x/d = 2
Premixed Pilot Flame
Flame-D: Red = 22,400
Flame-E: Red = 33,600
x/d = 15, r/d=1.1
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• ~ 86 2 ~ 540 m
• ~ 71 2 ~ 440 m
Applicable in more general flames(to be tested)
Dissipation spectra in piloted CH4/air flames
Resolution Curves: Temperature Variance and Dissipation
Resolution relative to fB
Variance curves:
• Depend on Re
• Range of Re consistent with local
T
Dissipation curves:
• Flame results agree well with
model
• Initial roll-off has little Re
dependence
Highly-Resolved Planar Rayleigh Imaging
DLR-A, CH4/H2/N2
Re = 15,200x/d = 10
S.A. Kaiser, J.H. Frank, Proc. Combust. Inst. 31 (2007)
J.H. Frank, S.A. Kaiser, Exp. Fluids. (2008)
Highly-resolved 2D Rayleigh imaging
Structure of dissipation layers
Thermal Dissipation Structures in Jet Flame
2 2 2( ) ( )T T r T x
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)
Resolving Dissipation Power Spectra
Interlacing, or dual detector, technique suppresses noise Power spectral density measured over three orders of
magnitude
NoiseSuppression
Image 1: odd lines
Image 2: even lines
Interlacing for noise suppression
*1 2radPSD FFT T r FFT T r
Apparentdissipation
(from noise)
S.A. Kaiser, J.H. Frank, Proc. Combust. Inst. 31 (2007).
Comparison of 1D and 2D Results
Cutoff at C = 2
Line results 10-20% higher S.A. Kaiser, J.H. Frank, Proc. Combust. Inst. 31 (2007).
Temperature Dependence of Dissipation Layer Widths
Adaptive smoothing used to reduce noise when determining layer thicknesses
Layer-widths scale approximately as (T/T0)0.75
x/d = 10
0.75*0D D T T
Probability density functions of layer width, D, conditioned on temperature
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 2 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 2
• 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