**
Characterization of Fuel Injectors and Urea Dosers,**Open Technology Forum, Automotive Testing Expo, Stuttgart, Germany - June 2018

**Velocity Measurements of Spray **, Technology Forum, Automotive Testing Expo, Michigan, USA - Oct 2017.

Automotive Test Expo, Michigan

**Spray Characterization of Fuel Injectors & Urea Dosers**, Open Technology Forum, Automotive Engineering Exposition Nagoya , Japan - June 2016.

**Utilization of Combined X-Ray and Optical Extinction Tomography for Planar Drop Size Estimation in Fuel Injectors & Urea Dosers**, Open Technology Forum, Auomtive Test Expo, Chennai, India - April 2016

**Overview of SETScan Patternator**, Ohio State Univeristy, Woosier, OH- December 2015.

**
Extinction and emission Tomography in Turbulent Sprays and Flames**, Southern Aerocraft Engine Co. Ltd, China - September 2015.

**
Transient Characteristics of GDI Injectors using Statistical Extinction Tomography **, National Cheng Kung University, Taiwan - August 2015.

**
Characterization of Fuel Injectors and Urea Dosers**, Open Technology Forum, Automotive Test Expo, Stuttgart, Germany - June 2015.

**
Extinction Tomography for Sprays, Indian Space Research Organization**, Thiruvananthapuram, India.- June 2015.

**
Exinction and Emission Tomography in Turbulent Spryas and Flames**, Indian Institute of Science, Banglaore, India. - June 2015

**
X-Ray Tomography for Dense Sprays & GDI Test Protocols**, Open Technology Forum, Automotive Test Expo, Seoul, Korea- March 2015.

**
An Overview of Spray Capability**, at Doosan Heavy Industries Co Ltd, Seoul, Korea. - January 2015.

**
Mid-IR Spectroscopy for Flame and Surface Characterization**, at Reliance Industries Limited, India - January 2015.

**
Spray Characterization Methods**, at Enem Nostrum Remedies Pvt. Ltd. in Mumbai. - January 2015

**
Optical Analysis of Flat Spray Nozzles used in Coating Applications**, at Nordson Corportaion, Ohio. February 2015.

**
Characterization of Multiple Plume Injectors Using Extinction Tomography**, Open Technology Forum, Automotive Test Expo, Michigan - October 2014.

**
The SETScan Patternator: An Overview**, Tsinghua University, Institute of Engineering Thermo-physics, Department of Thermal Engineering, China - September 22, 23, 2014.

**
The SETscan Optical Patternator: An Overview**, Shanghai Jiaotong University, Xi'an Aero- Engine Co. Ltd, National Institute of Clean-and-Low-Carbon Energy, Beijing , China - June 2014.

**
Extinction Tomography for Sprays: An Overview**, Indian Space Research Organization, Thiruvananthapuram, India, March 2014.

**
Mapping Liquid Mass Fractions in Optically Dense Rocket Chambers**, Presented to the Department of Defense, January, 2013.

**
Quality Audit of Injectors: Best Practices**, Automotive Testing Expo, Stuttgart, Germany, June 2013.

**
Optical characterization of GDI Injectors**, Automotive Testing Expo, Novi, Michigan, October 2013.

**
Application of Extinction and Emission Tomography to Structure Determination in Aircraft and Rocket Engines**, Indian Space Research Organization, Thiruvananthapuram, India, March 2010.

**
Application of Extinction and Emission Tomography to Structure Determination in Turbulent Flows**, National Energy Technology Laboratory, Morgantown, WV, March 2008.

**
Industrial Process Tomography**, Gas Turbine Research Establishment, Banglore, India, March 2008.

**
Structure Determination in Large Scale Fires**, Sandia National Laboratories, Albuquerque, NM, August 2007.

**
The SETscan Patternator**, Pratt & Whitney, Ontario, Canada, May 2006.

**
Characterization of Aerosols using Optical Techniques**, Science and Engineering Council, SC Johnson Inc., Rancine, IA, April 2005.

**
SETScan Patternator, Nordson Corporation**, Westlake, OH, April 2004.

**
Optical Diagnostic Techniques for Aerosols: Liquid Sprays and Combustion Generated Particulates**, S.C. Johnson & Son Inc., Racine, WI, December 2003.

Fan beam emission tomography in the 1-5-μm band is used to estimate the structure of a solid rocket propellant plume. Fan beam emission tomography consists of two components. The first is a pair of orthogonal high-speed imaging spectrometers and scanners that measures the spectral radiation intensities from 1.3 to 4.8 μm at 256 view angles. The second is a robust deconvolution algorithm that estimates the structure of the plume from the spectral radiation intensity measurements. The deconvolution algorithm is based on the maximum likelihood estimation method in conjunction with a linearized radiative transfer equation. The radiation intensity measurements were completed in a series of burns using 2.5-cm-diam by 1.25-cm-long strands of aluminized solid rocket composite propellant. In general, the aluminum diffusion-flame particulate temperatures in the plume are much higher than the gas temperatures. The gaseous combustion product concentrations are much lower in the middle of the plume than at the outer edges. This indicates a diffusion-flame-type structure for the plume, caused by the fact that the composite solid rocket propellant is fuel-rich. The results indicate that reliable plume-structure measurements can be obtained using fan beam emission tomography.

**
Infrared Spectroscopy for High Temperature Estimation in Gases**,
Invited talk for the ASTM E-20 Committee on Temperature, Pittsburgh, May 2002.

**
Patternation of Transient Sprays**,
Calmar, Industrial City, CA, November, 2001.

A fast infrared array spectrometer (FIAS) with a thermoelectrically cooled 160-element PbSe detector was demonstrated using measurements of instantaneous infrared radiation intensities simultaneously over the 1.8-4.9 μm wavelength range at a sampling rate of 390 Hz. A three-point second-degree Lagrange interpolation polynomial was constructed to calibrate the FIAS because of the nonlinear response of the infrared array detector to the incident radiation beam. This calibration method gave excellent measurements of blackbody radiation spectra except for a narrow band at wavelength of 4.3 μm due to absorption by room carbon dioxide, which is one of the two major gas radiation peaks (2.7 and 4.3 μm) from the lean premixed hydrocarbon/air combustion products in the midinfrared spectrum. Therefore, the absorption coefficient of room carbon dioxide was conveniently measured on site with the blackbody reference source, and was used in the calibration of the FIAS and also in the calculations of the radiation spectra. Blackbody tests showed that this procedure was effective in correcting for the room carbon dioxide absorption in the radiation spectra measured by the FIAS. For an example of its application, the calibrated FIAS was used to measure spectral radiation intensities from three lean premixed laminar flames and a premixed turbulent jet flame for which reference data with a grating spectrometer were available for comparison. The agreement between the FIAS measurements and the reference data was excellent.

**
Patternation of Sprays**,
Proctor & Gamble, Cincinnati, OH, November, 2001.

A new method of estimating temperature, soot volume fraction, and gas species concentrations from spectral radiation intensity measurements is reported. The spectral radiation intensities emitted from a one-dimensional McKenna burner is measured at multiple wavelengths using a high-speed mid-infrared spectrometer. The spectrometer obtains the spectral radiation intensities from 1.3 to 4.8 μm at 1320 Hz. Radiation from the soot, H2O, and CO2 gas bands are used to estimate soot temperature, soot volume fraction, gas temperature, and mole fractions of CO2 and H2O gas. Because of high nonlinearity between the gas temperature and the emissivity of the gas molecules, temperature, and gas concentration estimation requires a robust nonlinear inversion algorithm. A linearized radiative transfer equation (LRTE) in conjunction with the maximum likelihood estimation (MLE) method is developed to deconvolute the spectral radiation intensities for temperatures and concentrations. The LRTE-MLE method is first verified using synthetic dataset. For the synthetic dataset, the LRTE-MLE method always converges to the exact solution from any reasonable initial guess. The LRTE-MLE method is found to be insensitive to random errors in radiation intensity measurements. However, the estimated gas temperature is sensitive to any potential errors in the wavelength calibration. The LRTE-MLE method is then applied to measurements from a one-dimensional premixed laminar flame. The estimated gas temperature and concentrations obtained using the LRTE-MLE method are very close to those obtained with thin filament pyrometry (TFP) and theoretical calculations. The computational cost for the LRTE-MLE method was found to be minimal when compared to other nonlinear methods.

**
Patternation of Aircraft Engine Nozzles**,
Woodward FST Inc., Zeeland, MI, July, 2001.

A new method of estimating temperature, soot volume fraction, and gas species concentrations from spectral radiation intensity measurements is reported. The spectral radiation intensities emitted from a one-dimensional McKenna burner is measured at multiple wavelengths using a high-speed mid-infrared spectrometer. The spectrometer obtains the spectral radiation intensities from 1.3 to 4.8 μm at 1320 Hz. Radiation from the soot, H2O, and CO2 gas bands are used to estimate soot temperature, soot volume fraction, gas temperature, and mole fractions of CO2 and H2O gas. Because of high nonlinearity between the gas temperature and the emissivity of the gas molecules, temperature, and gas concentration estimation requires a robust nonlinear inversion algorithm. A linearized radiative transfer equation (LRTE) in conjunction with the maximum likelihood estimation (MLE) method is developed to deconvolute the spectral radiation intensities for temperatures and concentrations. The LRTE-MLE method is first verified using synthetic dataset. For the synthetic dataset, the LRTE-MLE method always converges to the exact solution from any reasonable initial guess. The LRTE-MLE method is found to be insensitive to random errors in radiation intensity measurements. However, the estimated gas temperature is sensitive to any potential errors in the wavelength calibration. The LRTE-MLE method is then applied to measurements from a one-dimensional premixed laminar flame. The estimated gas temperature and concentrations obtained using the LRTE-MLE method are very close to those obtained with thin filament pyrometry (TFP) and theoretical calculations. The computational cost for the LRTE-MLE method was found to be minimal when compared to other nonlinear methods.

**
Evaluation of Effervescent Atomizer**,
Allison Advanced Research Corporation, Indianapolis, IN, July, 2001.

A new method of estimating temperature, soot volume fraction, and gas species concentrations from spectral radiation intensity measurements is reported. The spectral radiation intensities emitted from a one-dimensional McKenna burner is measured at multiple wavelengths using a high-speed mid-infrared spectrometer. The spectrometer obtains the spectral radiation intensities from 1.3 to 4.8 μm at 1320 Hz. Radiation from the soot, H2O, and CO2 gas bands are used to estimate soot temperature, soot volume fraction, gas temperature, and mole fractions of CO2 and H2O gas. Because of high nonlinearity between the gas temperature and the emissivity of the gas molecules, temperature, and gas concentration estimation requires a robust nonlinear inversion algorithm. A linearized radiative transfer equation (LRTE) in conjunction with the maximum likelihood estimation (MLE) method is developed to deconvolute the spectral radiation intensities for temperatures and concentrations. The LRTE-MLE method is first verified using synthetic dataset. For the synthetic dataset, the LRTE-MLE method always converges to the exact solution from any reasonable initial guess. The LRTE-MLE method is found to be insensitive to random errors in radiation intensity measurements. However, the estimated gas temperature is sensitive to any potential errors in the wavelength calibration. The LRTE-MLE method is then applied to measurements from a one-dimensional premixed laminar flame. The estimated gas temperature and concentrations obtained using the LRTE-MLE method are very close to those obtained with thin filament pyrometry (TFP) and theoretical calculations. The computational cost for the LRTE-MLE method was found to be minimal when compared to other nonlinear methods.

**
Infrared Spectroscopy in Gas Turbine Engine**,
GE Research Center, Cincinnati, OH, March 2000.

Tomographic reconstruction of local liquid surface areas per unit volume in a turbulent spray using path-integrated laser transmittance measurements is reported. Path-integrated transmittances from a turbulent spray were obtained using a newly developed six-axes optical patternator. A multiaxis maximum-likelihood estimation algorithm was developed to deconvolute for the local extinction coefficients from the path-integrated transmittances. The local extinction coefficients are identical to the local liquid surface area per un it volume within the spray. The algorithm was first evaluated using synthetic path-integrated data. The algorithm successfully recovered the local extinction coefficients from the synthetic path-integrated transmittances. The algorithm was then used to obtain local liquid surface areas per unit volume from the path-integrated transmittance measurements in the spray. The path-integrated extinction measurements were also compared with mass flux data obtained using a mechanical pattemator. The results suggest that the local velocity and size distribution of the spray field is highly correlated with the local surface area density in sprays.

**
The ES100 Spectrometer- Innovations in Quality Control**,
Purdue Technology Center, IN, July 2000.

Tomographic reconstruction of local liquid surface areas per unit volume in a turbulent spray using path-integrated laser transmittance measurements is reported. Path-integrated transmittances from a turbulent spray were obtained using a newly developed six-axes optical patternator. A multiaxis maximum-likelihood estimation algorithm was developed to deconvolute for the local extinction coefficients from the path-integrated transmittances. The local extinction coefficients are identical to the local liquid surface area per un it volume within the spray. The algorithm was first evaluated using synthetic path-integrated data. The algorithm successfully recovered the local extinction coefficients from the synthetic path-integrated transmittances. The algorithm was then used to obtain local liquid surface areas per unit volume from the path-integrated transmittance measurements in the spray. The path-integrated extinction measurements were also compared with mass flux data obtained using a mechanical pattemator. The results suggest that the local velocity and size distribution of the spray field is highly correlated with the local surface area density in sprays.

**
Infrared Spectroscopy in Reacting Flows**,
Course Lecture at Spectraline Inc., IN, August, 2000.

Tomographic reconstruction of local liquid surface areas per unit volume in a turbulent spray using path-integrated laser transmittance measurements is reported. Path-integrated transmittances from a turbulent spray were obtained using a newly developed six-axes optical patternator. A multiaxis maximum-likelihood estimation algorithm was developed to deconvolute for the local extinction coefficients from the path-integrated transmittances. The local extinction coefficients are identical to the local liquid surface area per un it volume within the spray. The algorithm was first evaluated using synthetic path-integrated data. The algorithm successfully recovered the local extinction coefficients from the synthetic path-integrated transmittances. The algorithm was then used to obtain local liquid surface areas per unit volume from the path-integrated transmittance measurements in the spray. The path-integrated extinction measurements were also compared with mass flux data obtained using a mechanical pattemator. The results suggest that the local velocity and size distribution of the spray field is highly correlated with the local surface area density in sprays.

**
Combination Smoke and Near-Infrared Flame Detector for Residential Applications**,
First Alert, Chicago, IL, September, 1997.

Experimental data are essential for the validation of radiation submodels, which have been found to be important for predicting pollutant formation in turbulent flames. Instantaneous radiation signals also provide fundamental information about scalar properties in turbulent combustion. Motivated by this, we report measurements of line-of-sight spectral radiation intensities from a non-premixed CH4/H2/N2 turbulent jet flame. The burner and the operating conditions are selected to take advantage of extensive scalar property and velocity measurements available in the literature. At three axial locations in the flame, a fast IR array spectrometer was used to capture the instantaneous radiation intensities for diametric radiation paths. Radiation intensities for the chord-like paths along various radial positions at one of the axial locations were also measured. By using stochastic time and space series (TASS) analysis, the instantaneous emission spectra were also simulated accounting for the turbulence/radiation interactions. In the simulations, the measurements of scalar statistics and mean velocity data were adopted to avoid uncertainties of a combustion model. The calculated mean and root mean square spectral radiation intensities are within 10% of the experimental data. Since the calculated root mean square values are strongly dependent on the integral length scales used in the TASS, these scales were estimated by fitting the calculation to the data. A tomography-like technique was also adopted to simulate the radiation intensities for chord-like paths from the flame edge to the center to examine the radial variation of the integral length scale. The results show factors of 3 variations in the integral length scale that have been ignored in the past work.

**
Temperature Measurements in Methane/Air Premixed Flames Using IR-Emission Spectroscopy**,
AMETEK Aerospace Products Inc., Wilmington, MA, March, 1997.

Experimental data are essential for the validation of radiation submodels, which have been found to be important for predicting pollutant formation in turbulent flames. Instantaneous radiation signals also provide fundamental information about scalar properties in turbulent combustion. Motivated by this, we report measurements of line-of-sight spectral radiation intensities from a non-premixed CH4/H2/N2 turbulent jet flame. The burner and the operating conditions are selected to take advantage of extensive scalar property and velocity measurements available in the literature. At three axial locations in the flame, a fast IR array spectrometer was used to capture the instantaneous radiation intensities for diametric radiation paths. Radiation intensities for the chord-like paths along various radial positions at one of the axial locations were also measured. By using stochastic time and space series (TASS) analysis, the instantaneous emission spectra were also simulated accounting for the turbulence/radiation interactions. In the simulations, the measurements of scalar statistics and mean velocity data were adopted to avoid uncertainties of a combustion model. The calculated mean and root mean square spectral radiation intensities are within 10% of the experimental data. Since the calculated root mean square values are strongly dependent on the integral length scales used in the TASS, these scales were estimated by fitting the calculation to the data. A tomography-like technique was also adopted to simulate the radiation intensities for chord-like paths from the flame edge to the center to examine the radial variation of the integral length scale. The results show factors of 3 variations in the integral length scale that have been ignored in the past work.

**
Non-Contact Temperature Measurement of the Stator and Rotor Coils Using Emission Spectroscopy**,
Caterpillar Inc., West Lafayette, IN, May, 1996.

The optical properties of particulate emitted from fires burning two distinct polydimethylsiloxane fluids (D4 and M2 or MM, where D=(CH3)2SiO and M=(CH3) 3SiO2) were obtained using a transmission cell-reciprocal nephelometer in conjunction with gravimetric sampling. The specific absorption coefficient of particulate ash from fires burning D4 and MM is significantly lower than that of particulate soot from an acetylene (hydrocarbon) flame. Scattering is the dominant part of extinction in fires burning the silicone fluids. This is very different from extinction by soot particles in hydrocarbon fires, where absorption is approximately five times greater than scattering. Temperatures and particulate volume fractions along the axis of a silicone fire (D4) were measured using multiwavelength absorption/emission spectroscopy. The structure of the D4 flames is markedly different from hydrocarbon flames. The temperatures and particulate volume fractions very close to the burner surface are much higher than in comparably sized hydrocarbon flames.

**
Emission/Absorption Spectroscopy in Luminous Turbulent Diffusion Flames**,
Invited Seminar, Sandia National Laboratories, Albuquerque, NM, April, 1995.

Thermal radiation properties of turbulent premixed flames have received little attention in the past perhaps because of the lower radiative heat loss compared with that for non-premixed flames. However, the high-temperature sensitivity of NO kinetics and the importance of radiation in near-limit laminar premixed flames provide fundamental reasons for studies of radiation properties of turbulent premixed flames. Reduced cooling airflows in lean premixed combustors, miniaturization of combustors, and the possible use of radiation sensors in combustion control schemes are some of the practical reasons for studying radiation heat transfer in these flames. Motivated by this, we report the first (to our knowledge) study of spectral radiation properties of turbulent premixed flames. Measurements of mean, root mean square (rms) and probability density functions (PDFs) of spectral radiation intensities leaving diametric paths at five heights in two turbulent lean premixed methane/air jet flames stabilized using small H2/air pilot flames in a coflow of air were completed. Measurements of spectral radiation intensities leaving three laminar flames were also completed. These data were used to evaluate narrowband radiation calculations independent of the treatment of turbulent fluctuations. Stochastic spatial series analysis was used to estimate instantaneous distributions of temperature. The analysis requires the specification of mean and rms temperature distributions, integral length scale distributions, and an assumption of exponential spatial correlation function. We specified the mean and rms temperature distributions measured by calibrated narrowband thin filament pyrometry. A simple flame and mixing model was used to relate the concentrations of CO2 and H2O to the temperature. We used scalar spatial series in conjunction with a radiation model to calculate the mean, rms, and PDFs of spectral radiation intensities.

**
Statistical Tomography of Path Integrated Measurements in Turbulent Flames**,
Statistical Engineering Division Seminar, NIST, Gaithersburg, February, 1995.

The first-principles-based analytical method for predicting drop size distributions in sprays developed in our previous study, and used to investigate the influence of separate fluctuations in liquid physical properties and gas-liquid relative velocity on the drop size distribution, is extended to study the impact of simultaneous fluctuations on the drop size distribution width. Fluctuations of two types are considered: those in gas-liquid relative velocity and those in liquid physical properties. These fluctuations are represented by joint probability distribution functions (pdfs) of velocity-viscosity, velocity-surface tension, and velocity-density. Results demonstrate that combined liquid physical property and velocity fluctuations can lead to drop size distributions significantly wider than those resulting from velocity fluctuations alone. For combined velocity-surface tension fluctuations, this widening is significant over a range of mean velocities, whereas for combined velocity-viscosity and velocity-density fluctuations, the widening is significant only at low mean velocities. Finally, it is observed that the drop size distribution remains almost unchanged for liquid physical property fluctuations less than 1% (RMS/mean) over wide ranges of mean velocities and velocity fluctuations. In such cases the drop size distribution can be predicted satisfactorily by considering velocity fluctuations alone and the expense of using joint pdfs can be avoided.

**
Statistical Methods in Engineering**,
Senior Research Fellowship Seminar, Center for Applied and Computational Mathematics, NIST, Gaithersburg, March 1994.

A first principles analytical method for predicting drop size distributions in sprays, where primary atomization is the dominant process, has been developed. The method is able to predict the effects of fluctuations in gas-liquid relative velocity at the atomizer exit, and variations in fluid physical properties, on the spray drop size distribution. The method is based on applying the discrete probability function (DPF) to a fluid mechanic instability model. The dispersion equation for growth of fluid mechanic disturbances in cylindrical liquid ligaments relates the magnitude of the liquid-gas relative velocity and liquid physical properties to the size of drops formed. Fluctuations in relative velocity and fluid physical properties are introduced into the dispersion equation in the form of probability density functions (pdfs). The solution of the dispersion equation over the range of the pdf yields a drop size distribution. Results demonstrate how fluctuations in gas-liquid relative velocity at the atomizer exit, and variations in fluid physical properties (density, surface tension, and viscosity) can lead to a distribution of drop sizes. The width of the drop size distribution is found to be strongly dependent on the level of gas-liquid relative velocity fluctuations at the exit of the injector. Furthermore, the width of the drop size distribution increases with the level of velocity fluctuations in a slightly nonlinear manner. Finally, a distinct upper limit is found to exist for the drop size distribution, which cannot be exceeded by any amount of velocity fluctuation. Fluctuations in physical properties have a lesser effect on the drop size distributions than fluctuations in relative velocity, with variations in viscosity having the greatest impact. It is concluded that typically observed fluctuations in fluid physical properties are too small to produce experimentally observed drop size distribution widths in most practical sprays.

**
A Radiation Coupled Kinetic and Transport Calculation of Soot in Laminar Diffusion Flames**,
Combustion, Energy Utilization and Thermodynamics Seminar, Purdue University, W. Lafayette, IN, February, 1993.

Multi-wavelength absorption/emission measurements of extinction coefficient, temperature, and soot volume fraction in a large (6 m by 6 m) JP8 pool fire using an in situ water-cooled fiber-optic probe are reported. These measurements provide the first in situ information on radiative properties, temperature, soot, and the associated time scales in large pool fires. Soot extinction coefficients on the order of 5 to 30 m-1 were measured in the visible regime, indicating paths lengths for radiative transport in the infrared of approximately 0.1 to 0.3m. Temperature measurements follow an approximately normal distribution with a mean of 1400K and a standard deviation of approximately 67 K. Integral length scales of approximately 0.25 m were deduced from the temperature data. This length scale corresponds to the size of the smaller combusting eddies visually observed in large fires. Soot concentration integral length scales of 1.4m were determined from the absorption measurements. Soot volume fractions ranging from 0 to 6.0 ppm were measured. In comparison to laboratory-scale flames, excellent agreement was observed between the volume fractions determined by extinction and emission measurements, indicating a uniform temperature distribution (and hence uniform flame coverage) within the 2.0cm long by 1.0cm diameter cylindrical sampling volume. Soot volume fractions determined by emission show a strong peak in the PDF just above 1.0 ppm. The same peak is observed on the soot volume fraction determined by absorption, but an additional maxima in the PDF is observed near 3.0ppm, indicating the occasional presence of thick, cold soot. The primary uncertainty in the results is due to uncertainty in the soot indices of refraction. Fortunately, the uniform flame volume observed in the results show that the environment is promising for the study of these refractive indices.

**
Stochastic Methods in Turbulent Combustion**,
Combustion Seminar, The University of Maryland, College Park, MD, August 1990.

Radiative heat transfer inside a cylindrical tube is modeled using a statistical method called the discrete probability function (DPF) method. The DPF method involves solution of the equation of radiative heat transfer using Lagrangian simulations of representative photon trajectories on a discrete spatial grid. The DPF method is different from the Markov Chain method in terms of associating a probability with each state of the photon rather than a transition from one state to another. The advantages and disadvantages of the DPF method in comparison to the Markov Chain method are demonstrated in this paper using two practical applications of the cylindrical tube radiative heat transfer problem. The cylindrical tube has a hot source at one end and a detector at the other end. The cylindrical wall absorbs and reflects (both diffusely and specularly) the radiation incident on it. The present calculations have applications in: (1) intrusive pyrometry with collimating light guides, and (2) measurement of the spectral absorption and reflection coefficients of coatings using two, coated cylindrical tubes as specimen. The results show that: (1) the effect of light guide surface properties on errors in pyrometry must be carefully assessed, and (2) the method can be used for a convenient evaluation of radiative properties of coatings.

**
Generalized State Relationships in Hydrocarbon Flames**,
Gas Dynamics Seminar, The University of Michigan, Ann Arbor, MI, September 1989.

An algorithm for the tomographic reconstruction of the individual moments of the probaility density functions describing the local transmittance of radiation through a turbulent flow field is advanced. The new method, which is based on Fourier inversion, is applicable to asymmetric (as well as, to axisymmetric) flows. The validity of the method is examined by comparing reconstructed moments of the local probability functions in a buoyant propene/air flame and an ethene/air jet flame to the corresponding values obtained from optical probe measurements..

**
Soot Volume Fraction and Temperature Correlations in Turbulent Acetylene/Air Diffusion Flames**,
Gas Dynamics Seminar, The University of Michigan, Ann Arbor, MI, February 1989.

An algorithm for the tomographic reconstruction of the individual moments of the probaility density functions describing the local transmittance of radiation through a turbulent flow field is advanced. The new method, which is based on Fourier inversion, is applicable to asymmetric (as well as, to axisymmetric) flows. The validity of the method is examined by comparing reconstructed moments of the local probability functions in a buoyant propene/air flame and an ethene/air jet flame to the corresponding values obtained from optical probe measurements..

**
Soot Properties in the Overfire Region of Turbulent Diffusion Flames**,
Gas Dynamics Seminar, The University of Michigan, Ann Arbor, MI, September 1988.

We consider a wide class of multistable systems perturbed by a dissipative term and coin-toss square-wave dichotomous noise. These systems behave like their harmonically or quasiperiodically driven counterparts: depending upon the system parameters, the steady-state motion is confined to one well for all time or experiences exits from the wells. This similarity suggests the application to the stochastic systems of a Melnikov approach originally developed for the deterministic case. The noise induces a Melnikov process that may be used to obtain a simple condition guaranteeing the nonoccurrence of exits from a well. For systems whose unperturbed counterparts have phase space dimension 2, if that condition is not satisfied, weak lower bounds can be obtained for (a) the mean time of exit from a well and (b) the probability that exits will not occur during a specified time interval.