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