Quantitative scattering measurements of condensed phase material

1. Quantitative scattering measurements of condensed phase material Terry Parker, Manfred Geier, and Jennifer Labs Engineering Division Colorado School of Mines Presented at: Laser Applications to Chemical and Environmental Analysis Annapolis, Maryland February 9-11, 2004

2. Acknowledgements • NASA Center for Commercial Applications of Combustion in Space • Biodiesel directed studies supported by NREL, Shaine Tyson, Contract Monitor • Facility development supported by a National Science Foundation Career Award, Dr. Farley Fisher, Contract Monitor • Ongoing research support by NSF, Dr. Farley Fisher, Contract Monitor • Graduate student support, GANN award, Dept. of Ed. • Custom drilling of injector nozzle, Raycon Corporation • New injection system, Sturman Industries • CSM contributors • Dr. Tom Grover, Eric Jepsen, Dr. Heather McCann, Dr. Jon Filley, Dr. Tony Dean, Dr. Patrick Earhart

3. A range of instruments have been developed to monitor droplets and particulate • Polar nephelometers • Acquire angular scattering signature • Very well controlled sample conditions • Typically report particle diameter • Diffraction based instruments • Ensemble measurement based on line-of-sight diffraction, collects scattering in the forward direction • Quoted diameter range quite large (0.1 to 3500 mm), tradeoff between dynamic range and resolution within the distribution, proprietary inversion methods • Refractive index insensitive, maximum optical depth approximately 0.7 • Single particle measurements • PDPA, LDA, monitor single droplet/particle in probe volume • Diameter range 0.5 to 2.0 mm (typical), can provide velocity and number density (time averaged)

4. Diesel sprays are transient and optically thick Silica forming flames produce small particulate in a luminous environment Classic measurements do not address optically thick sprays or silica formation in a flame

5. Diesel sprays Experimental systems Measurement details Results Silica formation in flames Experimental systems Measurement details Results Overview of today’s discussion

6. Optical Measurements Are Made in a Unique Combustion Chamber • Capable of operation up to1000 K and 50 atm • Operated at 873 K and 12.5 atm • Orthogonal optical access via BaF2 windows • Simulator is a cold-wall pressure vessel with a heated air core • System includes central air flow and side arm nitrogen flows • 3-D translation capabilities • Data rates are 500 kHz in order to capture spray transients

7. The Fuel Injection System Provides Realistic Diesel Injection Events • Single Shot Pressure Amplifier • Peak injection pressure ~150 MPa (22,000 psi) • Standard Fuel Injector • Custom Lucas CAV Nozzle • (D ~ 0.16 mm, L/D ~ 4) Trigger chamber Drive chamber Injection chamber To Injector

8. Infrared lasers replace the more classic visible light sources • To decrease optical thickness effects, the optical “probe” wavelengths have been shifted into the infrared • Lower Attenuation Levels • System must avoid hydrocarbon absorption features near 10.6 mm • Extinction and angular scattering techniques are used to determine droplet sizes and volume fraction as a function of position and time in the near field spray region

9. The governing scattering equation produces as a function of measured signal A ratio of two signals produces the droplet size Number density cancels out for common probe volume Number density is calculated using the diameter from corrected scattering signals (which gives the differential scattering cross section) and the 9.27 mm signal This signal is used because thickness correction is smaller and well known Result is the average volume fraction over the probe volume Scattering signals are proportional to number density and optical cross section

10. Scattering Measurements Provide Spatial Resolution and an Increased Sizing Range • Ratio of Scattering Measurements at Different Wavelengths and Angles Can Be Used to Produce Spatially Resolved Droplet Size Measurements • Modeling Indicates Reported Diameters are Sauter Mean • Insensitive to Distribution Width • Diameter values greater than 16 mm cannot be uniquely sized due to multiple roots

11. Laser scattering measurements Nd:Yag (1.06 mm) at 90° Tunable CO2 (9.27 mm) at 11° Scattering detectors calibrated for absolute measurements Beam power monitored to compensate for power fluctuations Lasers are focused to an experimentally verified diameter of 150 mm Galilean beam expander Diffraction limit Measurements Utilize a Well-Defined Optical System

12. Attenuation from the spray decreases scattering signal Extinction measurement gives synchronous attenuation across total spray field Optical thickness correction “k” value is based upon location in spray k = 1 for all 9.27 mm measurements 0.5 < k < 1.0 for 1.06 mm measurements Extinction Measurement Provides an Optical Thickness Correction

13. Extinction and scattering probe volumes similar at the spray edge Agreement for results confirm validity of measurements Optical thickness correction is small, as expected Data plotted are 100 point averages with time zero at the spray onset Results from Extinction and Scatteringfor Droplet Sizes at Spray Edge Agree

14. System is Absolutely Calibrated and Errors Quantified • Each detector is calibrated over the range of expected signal levels using a blackbody • The uncertainty in the calibration can be calculated and is used to determine overall error level in system • Error in calibration is the dominant error • Asymmetric errors are calculated using a classic error propagation format • Total error is quadrature sum of uncertainty contributions from each measured quantity

15. Steady State Axial Position Dependence at Centerline (1.55 ms) • Axial Dependence • Smaller droplets produced by combusting spray • Steeper fall off of liquid volume fraction for combusting spray

16. Spray Exhibits Radial Dependencies During Steady State • Radial dependencies during spray development • Similar to axial trends, combusting droplets are smaller • Combusting spray is thinner at centerline • Volume fraction fall off is similar for cold and combusting sprays

17. Penetration Length and Spray Angle for Combusting Case • Liquid Penetration Length • Predicted* ~32 mm • Measured ~35 mm • Spray Half Angle • Predicted** 2.8-4.3° • Measured ~5.0° *Higgins, B.S., C.J. Mueller, and D.L. Siebers, SAE Paper No. 1999-01-0519. **Wu, K.-J, C.-C. Su, R. L. Steinberger, D. A. Santavicca, and F. V. Bracco, Journal of Fluids Engineering 105:406-413 (1983).

18. Dodecane Time averaged over 0.1 ms per frame  43 frames Look for: Spray development Steady state spray  high volume fraction area visible Injection shut-off  loss of any structure Combusting Volume Fraction Movie (t = 0  4.3 ms)

19. Dodecane Time averaged over 0.1 ms per frame  43 frames Look for: Spray development  more obvious here Steady state spray  small droplets near centerline Injection shut-off  loss of any structure Combusting Droplet Diameter Movie (t = 0  4.3 ms)

20. Existing models Rely on an imposed initial size distribution Assume droplet size determined by primary and secondary breakup Do not capture the proper droplet size dependence on injection pressure Little focus on transient nature of spray, entrainment and mixing What do the measurements add? Validation data set Indicate the breakup physics assumed cannot produce the droplet sizes measured Turbulence and/or cavitation should be considered Droplet lifetime estimates indicate the spray is nearly saturated in terms of fuel vapor Air entrainment is therefore critical to evaporation A beginning on tracking fuel evolution through the system The spray measurements illustrate that existing spray models do not capture spray behavior

21. Flame synthesis is another system where elastic light scattering can be applied • Flame Synthesis (FS) • Conversion of Gaseous or Liquid Precursors to Solid Nanoparticles in Flames • Attractive in Industrial Production of Nanosized Powder (Carbon black, Silica, Alumina, etc…) • Complex, Chemically Reactive, Multiphase Flow Field • Elastic Light Scattering Measurements (ELSM) • Non-intrusive • Spatial and Temporal Resolution • Allow Monitoring of Particle Formation and Growth (Growth Mechanisms and Rate) • Enable More Reliable Predictive Models (Particle Size and Morphology) for Process Control

22. Issues Specific to ELS in Flame Synthesis • Flame • Background Emission  Pulsed Signals, Gated Detectors • Flow Field Instability  Temporal Resolution, Large Sample Size • Flow Field Heterogeneity  Alignment and Sizes of Probe Volumes • Particle Flow Field • Particle Sizes Range From Molecular Size up to about 500nm • Dilute Flow Field (Volume Fraction smaller than 10E-6) • Narrow to Wide Particle Size Distribution Functions (PSDF) to Be Expected • Particle Properties • Morphology  Spherical or agglomerated • Refractive Index at Flame Temperature

23. Experimental system uses multiple angles, wavelengths, and polarizations states • Q-Switched Nd:YAG • 2 Probe Wavelengths • 70ns pulses, 1kHz • Linearly Polarized Beams, 45° • 5 Scattering Tubes • Stray Light Rejection • Arrangement Based on Simulations (Numerical Optimization) • Power Measurements • Calibrated Coherent Power Meter • Pin-Diode (In-House Calibrated) • 0.55mm Beam Waist

24. Accurate and robust data reduction relies on a fit based on residual minimization • Signal Ratios • Eliminate Number Density • Good for Narrow PSDF • Larger Uncertainties • Direct Inversion (Fitting) • Larger Dynamic Range • Over determined system provides a better estimate of the model parameters • Method of Least Squares: use χ2 for Goodness-of-Fit and Error Statements • Requires Absolute Calibration • For Assumed Lognormal PSDF: 3 Unknowns • Volume Median Diameter (VMD) • Geometric Standard Deviation (sg) • Volume Fraction (Φ)

25. Inversion Relies on Maximizationof Fit Between Data and Model • Least Squares Method for Nonlinear Parametric Regression • Minimize χ2 • χ2 is Nonlinear in VMD and sg • χ2minAllows Statistical Inference on Model Adequacy or Error Specification • Numerical Methods (applicable to many 4000+ data point sets) • Simplification Due to Linearity in Volume Fraction • Marquardt Algorithm • Iterative, Gradient Based Parameter Search • Inefficient • Sensitive to Initial Guess • Grid Search • Pre-calculated Integrals for Large Number of (VMD, sg) Table • Search Entire Table to Obtain (VMD, sg) That Minimizes χ2

26. Simulations Are Used To Estimate Performance of Data Analysis • Sizing Performance Is degraded for very small particulate • “true” Rayleigh scattering cannot be used to determine size • “quoted” minimum diameter that can be found is l/3 • Noise and calibration errors complicate analysis • Error Estimates • Perturbation of Synthetic Signals Gives Uncertainties in VMD, sg, and Φ • Estimates ignore covariance between parameters

27. Monte Carlo methods provide an accurate estimate of sizing performance • Gaussian errors produce a non-gaussian distribution in diameter • Error propagation that ignores covariance terms under predicts error • Data analysis must include monte carlo error analysis to accurately determine errors

28. Multi-Element Diffusion Burners Do NOT Provide Homogeneous Flow Field • Heterogeneous Particle Flow Field • Fluctuations Cause Large Temporal Variations in Signals • Size and Alignment of Probe Volumes Become Crucial For Minimum Additional Error • May Have Impact on Particle Growth Path 100mm Above Burner Surface

29. For colder temperatures collisions will produce agglomerates instead of coalescence • Agglomerates are NOT spherical • Least Mean Squares fitting will produce a result but c2 will indicate poor correlation between the model and the fit • Signature for an agglomerate • Side scattering of very small particulate (from the primary particles) • Forward scattering typical of a large particulate

30. Overall system provides a stream of data at known heights above the burner • Data averaging produces plots of particle growth as a function of residence time • Growth rate is a function of seed concentration and flame temperature

31. Volume fraction growth rate is a function of temperature and SiCl4 concentration

32. Elastic scattering can be used to successfully probe material synthesis flames • Results indicate an ability to monitor growth rates as a function of system operating conditions • Minimum sizing capability is dependent on error tolerance • Over determined system (multiple measurements) increases the dynamic range of the system • Data reduction techniques and careful error analysis are critical to success

33. Diesel sprays Shifting to Infrared wavelengths used to provide quantitative measurements where other measurements fail Silica formation in flames Wavelengths chosen to provide smallest possible minimum resolvable particle Both measurements require close attention to measurement and data reduction details Scattering measurements can investigate systems where turnkey instruments are not available