Yudaya R. Sivathanu, Jongmook Lim, Bill Wallace, and Roger Seei, A Comparison of Spray Angle Measurements using Optical and Mechanical Methods, Atomization and Sprays, vol. 20, pp. 85-92.
A comparison of spray angle measurements obtained using optical and mechanical methods is presented. The optical method used extinction tomography at two axial locations for obtaining surface area density contours. These surface area density contours were used to define the spray angle. The method is similar to that proposed by the Society of Automotive Engineers for defining spray angles from gasoline direct injection (GDI) injectors. The mechanical method used a protractor to directly measure angles from front-illuminated sprays. Three types of fuel atomizers were used to obtain spray angles. The results obtained are analyzed to provide a consistent approach to spray angle measurements using extinction.Buy full text here.
Ariel R. Muliadi, Paul E. Sojka, Yudaya R. Sivathanu, and Jongmook Lim, A Comparison of Particle Dynamics Analyzer (dual-PDA) and Optical Patternator Data for Twin-fluid and Pressure-swirl Atomizer Sprays, ASME Journal of Fluids Engineering 132(6) 061402-1.
The goal of this study was to determine when patternation information derived from Phase Doppler Analyzer (Dantec Dynamics, Skovlunde, Denmark, dual-PDA) measurements of volume flux, drop velocity, and mean size agreed with corresponding values measured using an optical patternator (Enurga, Inc., West Lafayette, IN, SetScan OP-600). To achieve this, data from each instrument were transformed into spatially resolved absorptances (equivalent to drop surface area per unit spray volume) and compared. Key conclusion is absorptance agreement to within 20% in many cases. However, discrepancies between phase Doppler analyzer (PDA)-calculated and optical patternator-measured absorptances become larger as the drop arrival rate increases, as the mean drop size decreases, and when a significant drop size-velocity correlation is present. These discrepancies are attributed to an underestimation of the volume flux (which becomes more important with increasing droplet arrival rate), an over-reporting of the mean drop diameter (which is the result of the restrictive data acquisition scheme applied when ensuring mass closure for the PDA measurements), the limited PDA dynamic range (which can preclude simultaneously accounting for both the largest and smallest drops in the spray), and by the optical patternator's number-density based measurement scheme (which will not yield the same results as the flux-based PDA when a drop size-velocity correlation is present).Buy full text here.
Y. Sivathanu, J. Lim, L. E. Reinhart, and R. C. Bowman, Structure of Plumes from Burning Aluminized Propellant Estimated using Fan Beam Emission Tomography, AIAA Journal, vol. 45, No. 9, pp. 2259-2266.
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.Buy full text here.
Jongmook Lim and Yudaya Sivathanu, Optical Patternation of a Multi-Orifice Spray Nozzle, Atomization and Sprays, vol. 15, pp. 687-698.2.
Patternation of a multi-orifice nozzle with an extinction tomography based optical patternator is reported. Path integrated transmittances were obtained from a six-orifice nozzle at 1000 Hz. The path-integrated transmittances were deconvoluted using the Maximum Likelihood Estimation method in conjunction with a novel grid scheme. The optical patternator obtains path-integrated extinction measurements at only six view angles due to the limitation in the physical size of the instrument, and the optical arrangement. An old grid scheme would therefore provide an angular resolution of only 30 degrees for the deconvolution method. However, a theoretical study with the new grid scheme showed that the angular resolution could be increased significantly by compromising on the radial resolution. This increase of angular resolution results in more uniform segment size distribution so that the method is less prone to deconvolution errors. The deconvolution method in conjunction with the new grid scheme was applied to the path-integrated measurements from the six-orifice nozzle. The method successfully resolved the spatial distribution of surface area per unit volume of drops in a horizontal plane within the spray.Buy full text here.
J. Ji, J. P. Gore, Y. R. Sivathanu, and J. M. Lim, Fast infrared array spectrometer with a thermoelectrically cooled 160- element PbSe detector, Review of Scientific Instruments, Vol. 75, Issue 2, pp. 333-339.
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.Buy text here or here.
J. Lim, Y. Sivathanu, J. Ji, and J. Gore, Estimating Scalars from Spectral Radiation Measurements in a Homogeneous Hot Gas Layer, Combustion and Flame, vol. 137, pp. 222-229.
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.Buy full text here.
J. Lim, Y. Sivathanu, V. Narayanan, and S. Chang, Optical Patternation of a Water Spray Using Statistical Extinction Tomography, Atomization and Sprays, vol. 13, pp. 27-43.
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.Buy full text here.
Y. Zheng, Y. R. Sivathanu, and J. P. Gore, Measurements and Stochastic Time and Space Series Simulations of Spectral Radiation in a Turbulent Non-premixed Flame, Proceedings of The Combustion Institute, The Combustion Institute, Pittsburgh, 29: 1957-1963.
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.Buy full text here.
Y. Sivathanu, A. Hamins, G. Mulholland, T. Kashiwagi, and R. Buch, Characterization of Particulate from Fires Burning Silicone Fuels, J. Heat Trans,. vol. 123, pp. 1093-1097.
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.Buy full text here.
Jun Ji, Y. R. Sivathanu, and J. P. Gore, Thermal Radiation Properties of Turbulent Lean Premixed Methane Air Flames, Proceedings of the Combustion Institute, vol. 28, pp. 391-398.
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.Buy full text here.
S. D. Sovani, P. E. Sojka, and Y. R. Sivathanu, Prediction of Drop Size Distributions from First Principles: Joint PDF Effects, Atomization and Sprays, vol. 10, pp. 587-602.
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.Buy full text here.
Y. R. Sivathanu, J. M. Lim, and R. K. Joseph, Statistical Absorption Tomography for Turbulent Flows, J. Quant. Spec. & Rad. Trans., vol. 68, pp. 611-623.
A Monte-Carlo method for the tomographic reconstruction of the mean and the RMS of local transmittance of radiation through a correlated turbulent Gaussian field is derived. Previous statistical reconstruction of turbulent flow fields have neglected spatial correlation resulting in very low spatial resolution. The present method provides for very high spatial resolution since the spatial correlation of local transmittance is considered. The validity of the method is examined using synthetically generated path-integrated transmittance data. If spatial correlations are neglected, the tomographic reconstruction method yielded local transmittances that are substantially different from the synthetic data. If spatial correlation is considered, the tomographic reconstruction method provided the mean and RMS of local transmittances within 5% and the local spatial integral length scale within 20% of the synthetic data.Buy full text here.
S. D. Sovani, P. E. Sojka, and Y. R. Sivathanu, Prediction of Drop Size Distributions from First Principles: The Influence of Fluctuations in Relative Velocity and Liquid Physical Properties, Atomization and Sprays, vol. 9, pp. 133-152.
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.Buy full text here.
C. Hagwood, Y. Sivathanu and G. Mulholland, The DMA Transfer Function with Brownian Motion: A Trajectory/Monte-Carlo Approach, Aerosol Sci. and Tech., vol. 30, pp. 40-61.
The transfer function for the Differential Mobility Analyzer (DMA) is derived based on particle trajectories for both nondiffusing particles and diffusing particles. The effect of particle diffusion is assessed by using a Monte-Carlo method for particles of sizes 1,3,10,30, and 100 nm. This approach includes both the effect of wall losses and axial diffusion. The range of validity of the Stolzenburg analysis is assessed by comparing his transfer function, the peak of his transfer function, and its dimensionless width with similar calculations based on the Monte-Carlo. For particle sizes smaller than 10 nm, the Monte-Carlo method indicates large wall losses, which result in a reduction in the peak of the transfer function by as much as a factor of 10 to 30, sensitivity to the flow-field, and skewness of the transfer function. It is shown that Stolzenburg's approximate formula for the standard deviation of the width of the transfer function agrees with Monte-Carlo simulations for particle sizes of 3 nm and larger.Click here for full text.
.O.S. Prasad, R. N. Paul, Y. R. Sivathanu, and J. P. Gore, An Evaluation of Combined Flame Surface Density and Mixture Fraction Models for Non-isenthalpic Premixed Turbulent Flames, Combustion Flame, vol. 117, pp. 514-528.
A computational study of a nonisenthalpic premixed turbulent jet flame is described. The flame burns a homogeneously premixed stoichiometric methane-air mixture injected into a coflow of air. The enthalpy (chemical + sensible) varies because of mixing between the jet fluid and the coflow. The performance of the Bray-Moss (BM) model and three flame surface density (FSD) models is evaluated by comparing the predictions of mean velocity and temperature profiles with recent experimental data. The reaction progress variable approach, which is established for isenthalpic flames, is extended to the present nonisenthalpic flames by including mean and mean square mixture fraction equations. The joint probability density function (PDF) of the reaction progress variable and the mixture fraction is modeled in terms of two statistically independent PDFs. The time-averaged reaction rate term is modeled using the BM and the FSD models. The effects of mixing with the coflow air were found to be unimportant in the evaluation of the flame speed required for modeling the mean reaction rate term. All models yielded reasonable predictions of mean velocity. Predictions of time-averaged temperatures agree better with the thin filament pyrometry data than those of Favre-averaged temperatures. The BM and MB models provided the best agreement with the mean temperature data but the other FSD models with slight tuning of the constants could provide similar agreement as well. The results show that a simple extension of the FSD models is promising for the treatment of nonisenthalpic flames. It appears that the differences in the conceptual framework of the FSD models disappear in their implementation using basically the same turbulence properties of kinetic energy and dissipation rates.Buy full text here.
L. A. Gritzo, Y. R. Sivathanu and W. Gill, Transient Measurements of Radiative Properties, Soot Volume Fraction and Soot Temperature in a Large Pool Fire, Combust. Sci. Tech., vol. 139, pp. 113-136.
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.Click here for full text.
M. J. Zimberg, S. H. Frankel, J. P. Gore and Y. R. Sivathanu, A Study of Coupled Turbulent Mixing, Soot Chemistry and Radiation Effects Using the Linear Eddy Model, Combust. Flame, vol. 113, pp. 454-469.
Transient simulations of strongly radiating, acetylene-air, nonpremixed flames in stationary, homogeneous turbulence are conducted in order to study coupled turbulence, soot chemistry, and radiation interactions. The linear eddy model is used to simulate turbulent advection. A laminar flamelet state relationship combustion model is employed along with two different soot models. The first soot model involves an extension of the laminar flamelet concept to soot using a soot volume fraction state relationship. The second soot model involves transport equations for soot mass fraction and soot number density, which include finite rate source terms to account for soot nucleation, surface growth, agglomeration, and oxidation. Radiation effects are accounted for by including the appropriate source/sink terms in the conservation of energy equation. The effects of a presumed surrounding large scale field which radiates with the spectral properties of soot at an assumed effective temperature are also included. Simulations are conducted for two values of the surrounding temperature and the model large eddy turnover time. The results capture several unique aspects of strongly radiating turbulent flames. In particular, an inflection point in the temperature versus mixture fraction profile is observed near the soot region which highlights the effects of radiative cooling. The large difference between radiation source terms calculated using mean properties and those calculated using instantaneous properties highlights the important interactions between turbulence and radiation.Buy full text here.
Y. R. Sivathanu and L. K. Tseng, Fire Detection Using Time Series Analysis of Source Temperature, Fire Safety Journal, Vol. 29, pp. 301-315.
The evaluation of a near-infrared fire detector using standard test fires is presented. The spectral radiation intensities incident on the fire detector are continuously measured at two near-infrared wavelengths (900 and 1000 nm), and a time series of apparent source temperatures is obtained from these measurements. The power spectral density and the probability density function of the apparent source temperatures are sufficient to determine the presence of a fire in the vicinity of the detector. The detector can also indicate the presence of a fire in an adjoining room from the radiation which is incident on it due to reflections from common building materials.Buy full text here.
M.W. Renfro, Y.R. Sivathanu, J.P. Gore, G.B. King, and N.M. Laurendeau, Time-series analysis and measurements of intermediate-species concentration spectra in turbulent non-premixed flames, Symposium (International) on Combustion, Vol. 27, pp. 1015-1022.
The ability to make frequency-resolved measurements of minor-species concentrations in turbulent flames has recently been demonstrated by picosecond time-resolved laser-induced fluorescence (PITLIF). However, few previous studies have focused on the power spectral density (PSD) of minor species in reacting flows. What little information is available suggests that strong interactions between velocity fluctuations and scalar distributions complicate the PSD, making interpretation of flame data difficult. In this work, time-series analysis, previously applied in flame-radiation studies, is extended to the study of temporal fluctuations in minor-species concentrations. In particular, an assumed PSD model for mixture fraction (Z) is used to simulate its time series. State relationships for narrowly distributed minor species as a function of mixture fraction are applied to develop concentration time series. Extension of this laminar-flamelet approach to minor species requires additional consideration of the effect of flame strain rate on the width of a minor-species profile in Z space as well as its peak concentration. The resulting minor-species concentration PSDs are computed and studied as a function of profile width (in Z) and fluctuation intensity (Z'RMS). These simulations compare favorably to previously reported CH and OH PSDs in a low-Reynolds-number, methane diffusion flame. Similarly, new PITLIF measurements of OH time series in a hydrogen diffusion flame at several Reynolds numbers also demonstrate favorable comparisons to the PSD simulations.Buy full text here.
Y. R. Sivathanu and J. P. Gore, Effects of Surface Properties on Radiative Transfer in a Cylindrical Tube with Non-participating Media, J. of Heat Transfer, vol. 119, pp. 495-501.
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.Click here for full text.
Y. R. Sivathanu and J. P. Gore, Effects of Gas-Band Radiation on Soot Kinetics in Laminar Methane/Air Diffusion Flames, Combust. Flame, vol. 110, pp. 256-263.
A coupled radiation and soot kinetics calculation of laminar methane/air diffusion flame properties is described. Transport equations for mass, momentum, mixture fraction, enthalpy (sensible + chemical) including gas-band radiation, soot mass fraction, and soot number density are solved. A simplified soot kinetics model incorporating nucleation, growth, oxidation, and agglomeration processes is used. The reaction rates in the simplified kinetics model depend on the temperature and the local concentrations of C2H2, O2, and OH. The major gas species and the C2H2 and OH concentrations are obtained using state relationships. The local temperature is obtained by solving the energy equation, taking radiation loss and gain from gas species and soot particles into consideration. The radiative source/sink term in the energy equation is obtained using a multiray method in conjunction with the narrow-band algorithm RADCAL. The results of the soot kinetics model are compared with existing laser-induced incandescence (LII) measurements of soot volume fractions. Reasonable comparison can be obtained only with an arbitrary downstream shift of 20 mm in the origin of the predictions from the burner exit. This highlights the need for improved chemical kinetics, but does not affect the following conclusions: 1) the contribution of participating gas (CO2 and H2O) radiation dominates that of soot radiation by an order of magnitude in the present methane/air flames, and 2) even for the present weakly radiating flames, the local radiative heat loss/gain strongly influences the soot nucleation, formation, and oxidation rates.Buy full text here.
P. Dutta, Y. R. Sivathanu, and J. P. Gore, Discrete Probability Function Method for the Calculation of Turbulent Particle Dispersion, AIAA Journal, vol. 35, No. 1, Technical Notes, pp. 200-202.
Dispersion of liquid drops in spray combustion systems is a critical parameter for high combustion efficiency. In modern lean-premixed-prevaporized (LPP) low NO* combustors, the design of premixers to achieve complete drop evaporation and fuel-air mixing prior to combustion is crucial to the success of such systems. Drop dispersion determines the residence time of the drop in the premixer, prescribes local boundary conditions for drop heat and mass transfer processes, and enhances interface area and fuel vapor concentration gradients to promote faster evaporation and molecular mixing. Thus, the performance of premixers in LPP combustion systems seems to be dispersion limited. Most dispersion calculations involve separated flow trajectory models, which require the simulation of a large number of particle trajectories to obtain statistically significant results and to reduce shot noise. Even with a large number of computational parcels, events with lower probability may not be adequately represented. These events can be important in LPP combustion systems that depend on burning everywhere at overall lean conditions. For example, excursions in the equivalence ratio due to the presence of a relatively small number of large drops can lead to large variations in global NO* emissions. These events, though rare, are responsible for almost all of the NO formation. In this Note, a discrete probability density (DPF) method is applied to drop dispersion calculations to provide accurate simulations with reduced statistical noise and to simulate the occurrence of rare events.Buy full text here.
M. R. Nyden, P. Vallikul, and Y. R. Sivathanu, Tomographic Reconstruction of the Moments of Local Probability Density Functions in Turbulent Flow Fields, J. Quant. Spec. & Rad. Trans., vol. 55, pp. 345-356.
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..Click here for full text.
Y. R. Sivathanu, C. Hagwood, and E. Simiu, Exits in Multistable Systems Excited by Coin-toss Square-wave Dichotomous Noise: A Chaotic Dynamics Approach, Physical Review E, vol. 52, no. 5, pp. 4669-4675.
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.Buy full text here.
L. G. Blevins, Y. R. Sivathanu, M. A. Shahien, and J. P. Gore, Radiometric Measurements of Wall Temperatures in the 800 K to 1150 K Range for a Quartz Radiant Heating Tube, J. Heat Transfer, vol. 117, pp. 653-658.
Many industrial applications require heat transfer to a load in an inert environment, which can be achieved by using gas-fired radiant tubes. A radiant tube consists of a flame confined in a cylindrical metal or ceramic chamber. The flame heats the tube wall, which in turn radiates to the load. One important characteristic of radiant heating tubes is wall temperature uniformity. Numerical models of radiant tubes have been used to predict wall temperatures, but there is a lack of experimental data for validation. Recently, Namazian et al., Singh and Gorski, and Peters et al. have measured wall temperature profiles of radiant tubes using thermocouples.Click here for full text.
P. Dutta, J. P. Gore, Y. R. Sivathanu and P. E. Sojka, Global Properties of High Liquid Loading Turbulent Crude Oil + Methane/Air Spray Flames, Combust. Flame, vol. 97, pp. 251-260.
Measurements of atomization quality, flame heights, radiative fractions, emission temperatures, and transmittance for Alberta sweet crude oil/methane flames established on a novel burner for simulating well-blowout fires are reported. The results show the effects of two-phase flow on flame heights. The measurements of radiative fractions and the optical properties suggest relatively low soot loading. The measured high temperatures suggest almost complete combustion of crude-oil. However, larger-scale tests as well as information concerning the physical processes in the present atomizer and burner are essential for the application to practical fires and combustion devices.Buy full text here.
Y. R. Sivathanu and J. P. Gore, Coupled Radiation and Soot Kinetics Interaction in Laminar Acetylene/Air Diffusion Flames,, Combust. Flame, vol. 97, pp. 161-172.
Radiation heat transfer from flames depends on the instantaneous soot volume fractions and temperatures. A coupled radiation and soot kinetics calculation in laminar acetylene/air and acetylene-methane/air diffusion flames is described. Transport equations for mass, momentum, gas-phase mixture fraction, enthalpy (sensible + chemical), soot mass fraction, and soot number density are solved. A simplified soot kinetics model incorporating nucleation, growth, oxidation, and agglomeration processes is used. The reaction rates in the simplified kinetics model depend on the temperature and the local concentrations of acetylene and oxygen. The major gas species concentrations are obtained from state relationships. The local temperature is obtained by solving the energy equation, taking radiation loss and gain and the energy exchanges associated with soot formation and oxidation into consideration. The radiative source/sink term in the energy equation is obtained using a multiray method. Since these flames radiate a substantial part of their energy, the kinetic rates associated with soot processes are strongly coupled to the energy equation. This strong coupling between radiation, and soot formation and oxidation processes is modeled for the first time. The results of the soot kinetics model are compared with measurements of soot volume fractions obtained using laser tomography. The agreement between measurements and predictions of soot volume fractions supports the present method. The predicted temperature profiles support the structure of strongly radiating flames discovered earlier.Buy text here.
Y. R. Sivathanu and J. P. Gore, A Tomographic Method for the Reconstruction of Local Probability Density Functions, J. Quant. Spec. & Rad. Trans., vol. 50, pp. 483-492.
A method of obtaining the probability density function (PDF) of local properties from path integrated measurements is described. The approach uses a discrete probability function (DPF) method to infer the PDF of the local extinction coefficient from measurements of the PDFs of the path integrated transmittance. The local PDFs obtained using the method are compared with those obtained from direct intrusive measurements in propylene/air and ethylene/air diffusion flames. The results of this comparison are good.Click here for full text.
Y. R. Sivathanu, J. P. Gore, J. Jenssen, and D. W. Senser, A Study of Insitu Specific Absorption Coefficients of Soot Particles in Laminar Flat Flames, J. Heat Trans., vol. 115, pp. 653-658.
Simultaneous measurements of absorption at 632 nm and emission at 800 nm and 900 nm along diametric paths are used to infer soot volume fractions based on both absorption and emission and temperatures based on emission in laminar, premixed flat flames. Agreement between soot volume fractions based on emission and absorption is used as an indicator of homogeneity of the optical path. Emission measurements at the gas band-free wavelengths of 2300 nm and 4000 nm for homogeneous paths are used to infer the specific absorption coefficients of soot particles. The results for methane, propane, and ethylene mixed with nitrogen and oxygen show insensitivity of the specific absorption coefficients to fuel type and weak dependence on temperatureBuy full text here.
Y. R. Sivathanu and J. P. Gore, A Discrete Probability Function Method for the Equation of Radiative Transfer,, J. Quant. Spec. & Rad. Trans., vol. 49, pp. 269-280.
A discrete probability function (DPF) method for the equation of radiative transfer is derived. The DPF is defined as the integral of the probability density function (PDF) over a discrete interval. The derivation allows the evaluation of the DPF of intensities leaving desired radiation paths including turbulence-radiation interactions without the use of computer intensive stochastic methods. The DPF method has a distinct advantage over conventional PDF methods since the creation of a partial differential equation from the equation of transfer is avoided. Further, convergence of all moments of intensity is guaranteed at the basic level of simulation unlike the stochastic method where the number of realizations for convergence of higher order moments increases rapidly. The DPF method is described for a representative path with approximately integral-length scale-sized spatial discretization.Click here for full text.
Y. R. Sivathanu and J. P. Gore, Total Radiative Heat Loss in Jet Flames from Single Point Radiative Flux Measurements, Combust. Flame, vol. 94, pp. 265-270.
A method for estimating total radiant output of turbulent jet flames based on the measurement of radiative heat flux at a single location is reported. The radiative flux from a variety of jet flames was measured and plotted in normalized coordinates to establish the feasibility of this approach. In addition, the radiative flux from acetylene-air diffusion flames to representative detector locations, for two different burner geometries and flow conditions, was calculated using the Planck-averaged equation of transfer coupled with a multiray technique. The local temperature and soot volume fractions for the calculations were obtained from emission/absorption measurements. The normalized calculated heat flux for the two flames also collapse with the experimental data. This result shows that scalar property distributions combined with the appropriate view factor for the single location are the basis for the single point technique.Click here for full text.
M. K. Klassen, Y. R. Sivathanu, and J. P. Gore, Simultaneous Emission Absorption Measurements in Toluene Fired Pool Flames, Combust. Flame, vol. 90, pp. 34-44.
Local measurements of mean and RMS emission intensities, transmittances, emission temperatures, and soot volume fractions based on emission and absorption in toluence flames burning in a pool configuration are reported. Radial profiles of these quantities at six axial stations within the flame are selected for discussion. The results show large fluctuations in temperatures and soot volume fractions at all locations including those near the liquid surface. Differences between the soot volume fractions based on emission and those based on absorption indicate the presence of large quantities of relatively cold soot at all positions. This work is supported by the Building and Fire Research Laboratory of the National Institute of Standards and Technology, Grant Nos. 60NANB9D0944 and 60NANB1D1169, with Dr. Takashi Kashiwagi serving as NIST Scientific Officer.Buy full text here.
Y. R. Sivathanu and J. P. Gore, Transient Structure and Radiation Properties of Strongly Radiating Buoyant Flames, J. Heat Transfer, vol. 114, pp. 659-665.
Measurements of instantaneous temperature and soot volume fractions based on absorption and emission in highly buoyant turbulent acetylene/air and propylene/air flames are reported. These measurements are used to predict mean, rms, probability density functions, and power spectral densities of spectral radiation intensities along a representative horizontal chord in the flame. The results show the presence of large quantities of relatively cold soot in the vicinity of smaller amounts of hot soot particles.Buy full text here.
J. P. Gore, U. S. Ip, and Y. R. Sivathanu, Coupled Structure and Radiation Analyses of Acetylene/Air Flames, J. Heat Transfer, vol. 114, 487-493.
A coupled radiation-structure analysis of turbulent, non-premixed, strongly radiating acetylene/air flames is described. The analysis extends the laminar flamelet concept to include the effects of local radiative heat loss/gain. A new method for the calculation of the radiative source term is presented. New measurements of mean and fluctuating emission temperatures and radiation intensities, and previous data concerning flame structure are used to evaluate the predictions.Buy full text here.
M. K. Klassen, J. P. Gore, Y. R. Sivathanu, A. Hamins, and T. Kashiwagi, Radiative Heat Feedback in a Toluene Pool Fire, Twenty-Fourth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, PA, p. 1713-1719.
A purged radiometer was used to measure directional heat flux incident on the fuel surface in a 30cm diameter toluene fire. A new approximate method for the treatment of the effects of turbulence on radiation was evaluated using these data. The average emissive power and the average transmittance are the two local properties needed for the approximate method. These quantities were obtained from transient local measurements of temperatures and soot volume fractions based on emission at two wavelengths. Soot volume fractions based on absorption were also measured for comparison. The results showed that a large fraction of the soot particles observed by the absorption probe were at relatively low temperatures. The predictions of direction heat fluxes showed systematic errors with angle when compared to measurements. These errors are related to the absorption of energy by fuel vapor in the central core and the higher spatial resolution needed in the necking-in region of the fire. The directional total flux data and predictions were integrated to obtain total radiative heat feedback to the surface. Comparisons between measurements and predictions of total heat flux were reasonably good.Buy full text here.
Y. R. Sivathanu and J. P. Gore, Simultaneous Multiline Emission and Absorption Measurements in Optically Thick Turbulent Flames, Comb. Sci. & Tech., vol. 80, pp. 1-21.
Simultaneous transient emission/absorption measurements at five wavelengths in strongly radiating, optically thick, turbulent diffusion flames burning acetylene in air were completed. The data were processed to obtain CO2, mole fractions, temperatures and soot volume fractions spatially resolved to the estimated local integral length scale of mixture fraction fluctuations. Temperatures and soot volume fractions based on emission intensities showed strong negative correlation due to radiative cooling effects. Probability density functions of soot volume fractions conditioned on CO2, mole fractions showed similarities with position. However, probable effects of negligible diffusivity of soot particles were observed. Probability density functions of soot volume fractions conditioned on both CO2, concentrations and temperature illustrate the important role of radiative heal transfer in determining the flame structure. A multivariate stochastic analysis resulted in good predictions of radiation intensities.Click here for full text.
M. E. Kounalakis, Y. R. Sivathanu, and G. M. Faeth, Infrared Radiation Statistics of Non luminous Turbulent Diffusion Flames, J. Heat Transfer, vol. 113, pp. 437-445.
Mixture fraction and radiation statistics were studied for radiation paths through turbulent carbon monoxide/hydrogen diffusion flames burning in still air. Measurements included Mie scattering for mixture fraction statistics and fast-response infrared spectroscopy for radiation statistics. Measured mixture fraction statistics also were used to predict radiation statistics based on stochastic time series methods, the laminar flamelet approximation, and a narrow-band radiation model. Measured intensities of radiation fluctuations were in the range 10-40%, which causes mean radiation levels to be 1.1-4.2 times larger than estimates based on mean scalar properties in the flames. In contrast, stochastic predictions of mean and fluctuating radiation properties were generally in excellent agreement with measurements. An exception was the temporal integral scales of radiation fluctuations, where differential diffusion errors of the Mie scattering measurements were identified as the source of the discrepancies.Buy full text here.
Y. R. Sivathanu, J. P. Gore, and J. Dolinar, Transient Scalar Properties of Strongly Radiating Jet Flames, Comb. Sci. & Tech., vol. 76, pp. 45-67.
An experimental and a theorietical study of transient radiation properties of strongly radiating turbulent diffusion flames is described. Simultaneous transient measurements of temperatures and volume fractions of soot obtained using a three wavelength emission-absorption probe are reported. Soot volume fractions inferred from absorption measurements are significantly higher than those inferred from emission data suggesting the presence oflarge quantities of relatively cold soot within the flames. The results show effects of progressive radiative cooling with distance from the injector exit. Reasonably good predictions of monochromatic intensities were obtained using a new bivariate stochastic analysis.Click here for full text.
G. M. Faeth , M. E. Kounalakis, and Y. R. Sivathanu, Stochastic aspects of Turbulent Combustion Processes, Journal of Chemometrics and Intelligent Laboratory Systems, vol. 10, pp. 199-210.
Methods of using stochastic simulations to treat nonlinear interactions in turbulent combustion processes are described -- emphasizing the use of statistical time-series techniques to analyze the turbulence--radiation interactions of nonpremixed flames. Three aspects of the problem are considered, as follows: the statistics of scalar properties in turbulent flames, the formulation of algorithms to stimulate flame radiation based on flame statistics, and evaluation of the methodology using recent measurements for nonluminous flames. It is shown that the process becomes tractable through the laminar flamelet approximation whereby all scalar properties are taken to be solely functions of a conserved scalar like the mixture fraction. Thus, the simulations are designed to generate realizations of mixtures fractions along radiations path with the radiation properties of each realization found using a narrow-bond radiation model. An autoregressive process that reproduces probability density functions and spatial and temporal correlations of mixture fraction was found to yield reasonably good predictions of the statistical properties of spectral radiation intensities measured for turbulent carbon monoxide and hydrogen jet flames burning in still air. Although the approach appears to be promising, additional development is needed in order to treat some of the unique statistical features of turbulence that are not encountered during conventional use of statistical time-series techniques.Buy text here.
Y. R. Sivathanu and G. M. Faeth, State Relationships for Major Gas Species in Non-premixed Hydrocarbon/Air Flames, Combust. Flame, vol. 82, pp. 211-230.
Generalized state-relationship correlations giving the mass fractions of major gas species (N_2 , O_2 , fuel, CO_2 , H_2 O, CO, and H_2 ) and temperature as functions of local fuel-equivalence ratios were studied for hydrocarbon-air diffusion flames. The data base included existing measurements in laminar methane, propane, /n/-heptane, acetylene, and ethylene flames burning in air (or N_2 /o_2 mixtures) with burner configurations involving porous cylinders in crossflow, coflowing round jet flames, and flat-laminar diffusion flames. Reasonably good generalized state-relationship correlations were found for major gas species over the available data base, which included molar fuel H/C ratios in the range 1-4 and fuel-equivalence ratios in the range 10^-2 - 10^2 . Typical of state relationships for particular fuels, the generalized state relationships approximated thermodynamic equilibrium for fuel-lean conditions and departed from equilibrium in a relatively universal manner for near-stoichiometric and fuel-rich conditions. Temperature state-relationship correlations were also reasonably good, over the more limited available data base, in view of uncertainties concerning radiative heat losses from the test flames and thermocouples. The results should be useful for estimating the scalar properties and the infrared gas-band radiation properties of laminar and turbulent hydrocarbon/air diffusion flames - the latter in conjunction with the laminar flamelet concept.Buy full text here.
Y. R. Sivathanu and G. M. Faeth, Temperature/ Soot Volume Fraction Correlations in Fuel-rich Region of Buoyant Turbulent Diffusion Flames, Combust. Flame, vol. 81, pp. 150-165.
Instantaneous soot volume fractions and temperatures were measured in the fuel-rich (underfire) region of turbulent nonpremixed acetylene, propylene, ethylene, and propane flames burning in still air. Large-scale, highly buoyant, pool-like flames were considered, having characteristic residence times greater than 250 ms and burner exit Richardson numbers greater than 18. Measurements were made using an optical probe than involved laser extinction for soot volume fractions and two-wavelength pyrometry for temperatures. Strong correlations were found between soot volume fractions and temperatures for each fuel-relatively independent burner operating conditions and position in the underfire region. This behavior is supportive of the existence of nearly universal relationships between soot volume and mixture fractions in the underfire region of turbulent nonpremixed flames having large characteristic residence times. Underfire soot is largely confined to a narrow range of mixture fractions (yielding a soot spike) and temperatures. The latter observation supports approximations of constant-temperature soot layers that have been proposed in teh past for estimates of continuum radiation from soot-containing diffusion flames.Buy full text here.
Y. R. Sivathanu and G. M. Faeth, Soot Volume Fractions in the Overfire Region of Turbulent Diffusion Flames, Combust. Flame, vol. 81, pp. 133-149.
Overfire soot volume fractions and mixture fractions, flame heights, and characteristic flame residence times, were measured for turbulent acetylene, propylene, ethylene and propane diffusion flames burning in still air. Test conditions ranged from highly buoyant pool-like flames to buoyant jet flames, using three burners (with exit diameters of 5, 50, and 234 mm) and a wide range of fuel flow rates. Soot generation efficiencies (the percentage of fuel carbon converted to soot and emitted from the flame) were uniform throughout the overfire region for a given flame condition. Soot generation efficiencies increased with increasing flame residence times but tended to approach asymptotic values for residence times roughly ten times longer than residence times at the normal smoke point. Within the asymptotic region, soot volume fractions are directly related to mixing levels, analogous to the laminar flamelet concept for nonpremixed flames, which offers substantial simplifications for analysis of the continuum radiation properties of the overfire region.Buy full text here.
Y. R. Sivathanu, M. E. Kounalakis, and G. M. Faeth, Soot and Continuum Radiation Statistics of Luminous Turbulent Diffusion Flames, Twenty-third Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, pp. 1543-1550.
The statistics of soot and spectral radiation intensities in the continuum were measured for horizontal radiation paths through the axis of highly-buoyant propylene flames burning in still air. Radiation statistics were also analyzed using a stochastic simulation of soot properties that matched soot statistics along the radiation path. Predictions and measurements of radiation statistics were generally in good agreement, aside for difficulties in predicting spikes of the measured PDF's and temporal power spectra due to release of coherent structures near the source for low burner Reynolds numbers. Radiation fluctuation intensities up to 100 percent were observed while temporal power spectra decayed proportional to the - 5/3 power of frequency at high frequencies, suggestion strong turbulent/radiation interactions and a close relationship between turbulent mixing and continuum radiation statistics in turbulent flames.Buy full text here.
Y. R. Sivathanu, J. P. Gore, and G. M. Faeth, Scalar properties in the Overfire Region of Sooting Turbulent Diffusion Flames, Combust. Flame, vol. 73, pp. 315-329.
The scalar structure of the overfire (fuel-lean) region of sooting turbulent diffusion flames was investigated, considering ethylene and acetylene burning in air. Measurements and predictions are reported of the mean concentrations of major gas species and mean soot volume fractions. Predictions were based on the conserved-scalar formalism in conjunction with the laminar flamelet approximation. The comparison between predictions and measurements was encouraging, suggesting that state relationships for major gas species, found in laminar diffusion flames, were preserved in the overfire region of the turbulent flames. Measurements also indicated nearly constant soot generation efficiencies from point to point in the overfire region for sufficiently long characteristic residence times to yield nearly universal soot volume fraction state relationships at the same conditions. However, effects attributed to finite-rate chemistry were observed at shorter characteristic residence times, causing spatial variations of soot generation efficiencies in the overfire region, with associated loss of universal soot volume fraction state relationships.Buy full text here.