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

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

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

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)

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

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!

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: 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 kblb = 1 x/d = 60 Scaling law for nonreacting jets 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 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

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)

Thermal Dissipation Length Scale in Flames lb (mm) 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 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

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 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

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

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 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)

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)

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).

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 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)

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