Greg Smallwood

Deconvolution of axisymmetric flame properties using Tikhonov regularization

We present a method based on Tikhonov regularization for solving one-dimensional inverse tomography problems that arise in combustion applications. In this technique, Tikhonov regularization transforms the ill-conditioned set of equations generated by onion-peeling deconvolution into a well-conditioned set that is less susceptible to measurement errors that arise in experimental settings. The performance of this method is compared to that of onion-peeling and Abel three-point deconvolution by solving for a known field variable distribution from projected data contaminated with an artificially generated error. The results show that Tikhonov deconvolution provides a more accurate field distribution than onion-peeling and Abel three-point deconvolution and is more stable than the other two methods as the distance between projected data points decreases.

Non-grey gas radiative transfer analyses using the statistical narrow-band model☆

Abstract Nongrey gas radiation analyses were conducted using the statistical narrow-band model and four implementation methods: the exact or the correlated formulation, the noncorrelated expression, greyband approximation based on global absorption coefficient, and a new approximate method. The new method is also a grey-band approximation but utilizes the local absorption coefficient. Using results of the correlated formulation as benchmark solution, accuracy of the three approximate narrow-band implementation methods was investigated for several one-dimensional non-grey gas radiation problems in parallel plate enclosure containing radiating gases of both uniform and non-uniform temperatures and/or concentrations. Radiative source term and wall heat flux predicted by the noncorrelated expression and the new method are in very close agreement with each other and in fair to good agreement to benchmark solutions. Radiative source term calculated from the grey-band approximation based on global absorption coefficient is in serious error. CPU time saving of two orders of magnitude can be achieved by using the three approximate implementation methods, relative to the correlated formulation. The new method provides slightly better accuracy than the noncorrelated approach with additional advantages that an arbitrary solution method can be employed and less CPU time is required.

Effective density and mass-mobility exponent of aircraft turbine particulate matter

A centrifugal particle mass analyzer and a modified differential mobility spectrometer were used to measure the mass and mobility of particulate matter emitted by CFM56-5B4/2P, CFM56-7B26/3, and PW4000-100 gas turbine engine sources. The mass-mobility exponent of the particulate matter from the CFM56-5B4/2P engine ranged from 2.68 to 2.82, whereas the effective particle densities varied from 600 to 1250  kg/m3, depending on the static engine thrust and sampling methodology used. The effective particle densities from the CFM56-7B26/3 and PW4000-100 engines also fell within this range. The sample was conditioned with or without a catalytic stripper and with or without dilution, which caused the effective density to change, indicating the presence of condensed semivolatile material on the particles. Variability of the determined effective densities across different engine thrusts, based on the scattering about the line of best fit, was lowest for the diluted samples and highest for the undiluted sample without a catalytic stripper. This variability indicates that the relative amount of semivolatile material produced was engine thrust dependent. It was found that the nonvolatile particulate matter, effective particle density (in kilograms per cubic meter) of the CFM56-5B4/2P engine at relative thrusts below 30% could be approximated using the particle mobility diameter (dme in meters) with 11.92d(2.76−3)me.

A robust and accurate algorithm of the β-pdf integration and its application to turbulent methane–air diffusion combustion in a gas turbine combustor simulator

The β-pdf has been widely assumed for the probability distribution of the mixture fraction in many turbulent mixing and turbulent nonpremixed combustion models in the literature. The numerical integration of the β-pdf often encounters the singularity difficulties and only few publications have addressed this issue. An efficient, accurate and robust numerical treatment of the β-pdf integration was proposed. The present treatment of the β-pdf integration was implemented into a flamelet model to calculate turbulent methane–air combustion in a model gas turbine combustor. Numerical results obtained using the present β-pdf integration method and those based on the properties of the beta and gamma functions were compared to illustrate the accuracy of the present method. Effect of assuming the β-pdf to the mass-weighted pdf and unweighted pdf of the mixture fraction on the calculated density field was also investigated.  2002 Editions scientifiques et medicales Elsevier SAS. All rights reserved.

Methodology for quantifying the volatile mixing state of an aerosol

ABSTRACT Mixing state refers to the relative proportions of chemical species in an aerosol, and the way these species are combined; either as a population where each particle consists of a single species (‘externally mixed’) or where all particles individually consist of two or more species (‘internally mixed’) or the case where some particles are pure and some particles consist of multiple species. The mixing state affects optical and hygroscopic properties, and quantifying it is therefore important for studying an aerosols climate impact. In this article, we describe a method to quantify the volatile mixing state of an aerosol using a differential mobility analyzer, centrifugal particle mass analyzer, catalytic denuder, and condensation particle counter by measuring the mass distributions of the volatile and non-volatile components of an aerosol and determining how the material is mixed within and between particles as a function of mobility diameter. The method is demonstrated using two aerosol samples from a miniCAST soot generator, one with a high elemental carbon (EC) content, and one with a high organic carbon (OC) content. The measurements are presented in terms of the mass distribution of the volatile and non-volatile material, as well as measures of diversity and mixing state parameter. It was found that the high-EC soot nearly consisted of only pure particles where 86% of the total mass was non-volatile. The high-OC soot consisted of either pure volatile particles or particles that contained a mixture of volatile and non-volatile material where 8% of the total mass was pure volatile particles and 70% was non-volatile material (with the remaining 22% being volatile material condensed on non-volatile particles).

Particle Emission Characteristics of a Gas Turbine with a Double Annular Combustor

The total climate, air quality, and health impact of aircraft black carbon (BC) emissions depend on quantity (mass and number concentration) as well as morphology (fractal dimension and surface area) of emitted BC aggregates. This study examines multiple BC emission metrics from a gas turbine with a double annular combustor, CFM56-5B4-2P. As a part of the SAMPLE III.2 campaign, concurrent measurements of particle mobility, particle mass, particle number concentration, and mass concentration, as well as collection of transmission electron microscopy (TEM) samples, allowed for characterization of the BC emissions. Mass- and number-based emission indices were strongly influenced by thrust setting during pilot combustion and ranged from <1 to 208 mg/kg-fuel and 3 ×× 1012 to 3 ×× 1016 particles/kg-fuel, respectively. Mobility measurements indicated that mean diameters ranged from 7 to 44 nm with a strong dependence on thrust during pilot-only combustion. Using aggregation and sintering theory with empirical effective density relationships, a power-law relationship between primary particle diameter and mobility diameter is presented. Mean primary particle diameter ranged from 6 to 19 nm; however, laser-induced incandescence (LII) and mass-mobility-calculated primary particle diameters demonstrated opposite trends with thrust setting. Similarly, mass-mobility-calculated aggregate mass specific surface area and LII-measured surface area were not in agreement, indicating both methods need further development and validation before use as quantitative indicators of primary particle diameter and mass-specific surface area. Copyright 2015 American Association for Aerosol Research

Sequential signal detection for high dynamic range time-resolved laser-induced incandescence

A new method for collecting time-resolved laser-induced incandescence (TiRe-LII) signals with high dynamic range is presented. Gated photomultiplier tubes (PMT) are used to detect temporal sections of the LII signal. This helps to overcome the limitations of PMTs caused by restricted maximum signal current at the strong initial signal and poor signal-to-noise ratios when the signal intensity approaches the noise level. We present a simple method for increasing the accuracy of two-color pyrometry at later decay times and two advanced strategies for getting high accuracy over the complete temperature trace or even achieve single-shot capability with high dynamic range. Validation measurements in a standardized flame show that the method is sensitive enough to even resolve the local increase in gas temperature as a consequence of heating the soot particles with a laser pulse.

Effective density and volatility of particles sampled from a helicopter gas turbine engine

ABSTRACT The effective density and size-resolved volatility of particles emitted from a Rolls-Royce Gnome helicopter turboshaft engine are measured at two engine speed settings (13,000 and 22,000 RPM). The effective density of denuded and undenuded particles was measured. The denuded effective densities are similar to the effective densities of particles from a gas turbine with a double annular combustor as well as a wide variety of internal combustion engines. The denuded effective density measurements were also used to estimate the size and number of primary particles in the soot aggregates. The primary particle size estimates show that the primary particle size was smaller at lower engine speed (in agreement with transmission electron microscopy analysis). As a demonstration, the size-resolved volatility of particles emitted from the engine is measured with a system consisting of a differential mobility analyzer, centrifugal particle mass analyzer, condensation particle counter, and catalytic stripper. This system determines the number distributions of particles that contain or do not contain non-volatile material, and the mass distributions of non-volatile material, volatile material condensed onto the surface of non-volatile particles, and volatile material forming independent particles (e.g., nucleated volatile material). It was found that the particulate at 13,000 RPM contained a measurable fraction of purely volatile material with diameters below ∼25 nm and had a higher mass fraction of volatile material condensed on the surface of the soot (6%–12%) compared to the 22,000 RPM condition (1%–5%). This study demonstrates the potential to quantify the distribution of volatile particulate matter and gives additional information to characterize sampling effects with regulatory measurement procedures. Copyright

Demonstration of the CPMA-Electrometer System for Calibrating Black Carbon Particulate Mass Instruments

In an effort to improve regulations for particulate emissions from aircraft engines, the Aircraft Exhaust Emissions Measurement Committee, SAE E-31, is investigating instruments to measure black carbon mass concentration in real time. The current candidates are a laser-induced incandescence instrument (LII 300) and a photo-acoustic Micro-Soot Sensor (MSS). However, both of these instruments use indirect techniques, measuring parameters other than the actual mass of particulate in the exhaust, and therefore require calibration. Previously, it has been shown that a centrifugal particle mass analyzer (CPMA) can be used in conjunction with an aerosol electrometer to traceably generate an aerosol with known mass concentration. This system can be used to rapidly calibrate particle mass instruments (on the order of minutes), without the time-consuming process of filter sampling, which is often used for calibration and prone to sampling artifacts. Here, we demonstrate the feasibility of the CPMA-electrometer system for calibrating two LII 300 instruments and two MSS instruments, which were calibrated to the NIOSH 5040 standard. The correlations between the CPMA-electrometer system and the challenge instrument were highly linear for both the LII and the MSS, and agreed well with the previous calibration. All four instruments were found to correlate with the CPMA-electrometer system with R2 values of 0.993 to 0.999. The standard uncertainty in the CPMA-electrometer system averaged 4.3% and was as low as 2.6% for some measurements. With a simple improvement to the aerosol electrometer, we estimate this average uncertainty would be less than 3%. This lower uncertainty and much higher speed of measurement support the use of the CPMA-electrometer system as a mass measurement calibration method for black carbon instruments. Copyright 2015 American Association for Aerosol Research

Determining Aerosol Particle Size Distribution Using Time-Resolved Laser-Induced Incandescence

Time-resolved laser-induced incandescence is a powerful tool for determining the physical characteristics of aerosol dispersions of refractory nano-particles. In this procedure, particles within a small aerosol volume are heated with a nano-second laser pulse, and the temporal incandescence of the particles is then measured as they return to the ambient gas temperature. It is possible to infer particle size distribution from the temporal decay of the LII signal since the cooling rate of an individual particle depends on its area-to-volume ratio. This requires solving a mathematically ill-posed inverse problem, however, since the measured LII signal is due to the incandescence contributed by all particle sizes within the aerosol volume. This paper reviews techniques proposed in the literature for recovering particle size distributions from time-resolved LII data. The characteristics of this ill-posed problem are then discussed in detail, particularly the issues of solution stability and uniqueness. Finally, the accuracy and stability of each method is evaluated by performing a perturbation analysis, and the overall performance of the techniques is compared.Copyright