W. Kollmann

Pdf Modeling of Turbulent Nonpremixed Methane Jet Flames

Abstract Anexpanded model of turbulent nonpremixed combustion is herein presented. In the model, the scalar mixing and reactions are described by a probability density function (pdf) submodel capable or handling five scalars, while the turbulent velocity field is described by a second-order moment closure. Two plausible chemical reaction models are considered: a five-scalar, four-step, reduced reaction mechanism and a four-scalar constrainted equilibrium model. Detailed comparisons of model predictions with laser Raman experimental data provide a valuable evaluation of the models ability in predicting nonequilibrium chemistry in turbulent nonpremixed flames. Overall, the model fails to predict greater departure from chemical equilibrium as mixing rates are increased. Interestingly, this failure is not due to the chemical model, both of which perform satisfactorily. Instead, the failure to predict greater departure from chemical equilibrium is a subtle artifact of the current Monte Carlo simulation of tur...

Surface density function in premixed turbulent combustion modeling, similarities between probability density function and flame surface approaches

To characterize the dynamics and the physical properties of isoconcentration surfaces of a random reactive scalar field, an instantaneous isosurface quantity and its transport equation are introduced. For turbulent flows, the mean area of isoconcentration surface per unit volume is studied through its transport equation derived by using the probability density function (pdf) formalism. This approach allows the value of the reactive scalar used to define the level surface to be treated as an independent variable. It also leads to the definition of a surface density function. The developed formalism is applied to premixed turbulent combustion and a bridge is built between modeling approaches based on pdf, and others based on the flame surface concept.

Conserved scalar fluxes measured in a turbulent nonpremixed flame by combined laser Doppler velocimetry and laser Raman scattering

Abstract This paper presents a new combined laser Doppler velocimetry-laser Raman scattering (LDV-Raman) apparatus which simultaneously measures velocity and scalars. Measurements in a ducted nonpremixed turbulent flame using this apparatus are presented and compared with previous LDV-Mie and LDV-Rayleigh measurements. A partial equilibrium numerical model of the hydrogen flame herein investigated predicts the major species to be at their equilibrium concentration while radical species, such as hydroxyl, can have mean concentrations that are three times greater than their equilibrium concentrations.

The pdf approach to turbulent flow

Probability density function (pdf) methods provide a complete statistical description of turbulent flow fields at a single point or a finite number of points. Turbulent convection and finite-rate chemistry can be treated in closed and exact form with pdfs in contrast to methods based on statistical moments. The equations for pdfs at a finite number of points are indeterminate due to molecular transport and pressure-gradient terms which require pdfs of higher order. The theoretical foundation of pdfs methods are developed in this paper starting from the exact and linear equations on the functional level. The closure problem for single-point pdf equations is treated in detail and several closure models are analyzed. Turbulent combustion at low Mach numbers constitutes an important area of application and selected results for a turbulent methane flame are presented as an example. The extension of pdf methods to supersonic turbulent flows with and without chemical reactions are outlined. Progress in the numerical solution of pdf equations is reviewed briefly. In the concluding remarks, both the advantages and disadvantages of pdf methods are evaluated.

A model for soot formation in a laminar diffusion flame

A simple model has been developed for the prediction of soot volume fractions in a laminar diffusion flame. Measurements and computations of a counterflow flame have been used to evaluate the correlation between soot surface growth rates and the mixture fraction or fuel atom mass fraction. An average particle number density was used to permit the determination of the aerosol surface area. Equations for the momentum, mixture fraction, and soot volume fraction were solved numerically for an axisymmetric laminar diffusion flame. Good agreement was obtained with the measurements for two different experimental conditions.

The mechanism of two-dimensional pocket formation in lean premixed methane-air flames with implications to turbulent combustion

Abstract The mechanism of unburnt pocket formation in an unsteady two-dimensional premixed lean methane-air flame is investigated using direct numerical simulations. Theoretical results for nonlinear diffusion equations combined with analytical examples are used to interpret some of the results. Flame structure and propagation show three distinct stages of pocket formation: (1) flame channel closing involving head-on quenching of flames, (2) cusp recovery, and (3) pocket burnout. The flame channel closing and subsequent pocket burnout are mutual annihilation events that feature curvature, diffusion normal to the flame front, unsteady strain rate effects, and singularities in flame propagation and stretch rate. The results show that during channel closing and pocket burnout thermo-diffusive and chemical interactions result in the acceleration of the flames prior to annihilation; the time scales associated with the final stage of mutual annihilation and the initial stage of cusp recovery are significantly smaller than diffusive and convective time scales. As in earlier one-dimensional studies, the acceleration is attributed to enhanced diffusion and reaction rates, modifications to species profiles leading to shifts in balance between diffusion and reaction, and vanishing species and thermal gradients at the location in the channel where the pocket pinches off. Flame propagation and stretch rate are singular at this location. Enhanced radical production is initiated by a reversal of diffusion of H 2 towards the reaction zone during the early stages of thermo-diffusive interactions. Peak radical concentrations resulting from flame channel closing and pocket burnout exceed peak laminar values by as much as 25%. After the merging of the fuel consumption layers, radical production and flame structure shifts more towards an H 2 /CO/O 2 system at the expense of hydrocarbon reactions. Species thermodiffusive interaction times are shorter than the unstrained one-dimensional counterpart due to unsteady strain and convection. Curvature effects on the flame propagation are prominent during pocket burnout and cusp recovery. The recovery stage shows strong dependence on diffusion of radicals left from the channel closing stage. This diffusion is amplified by the strong curvature of the flame cusp.

PDF modeling and analysis of thermal NO formation in turbulent nonpremixed hydrogen-air jet flames☆

Abstract A numerical model is developed based on the probability density function (pdf) approach to study the thermal NO formation in turbulent nonpremixed hydrogen jet flames. In particular, the effects of nonequilibrium chemistry and radiation heat loss on the thermal NO formation are examined. The numerical results indicate that when the NO x emission index is scaled with a properly defined flame residence time, it shows the negative one-half power dependence on the Damkohler number as observed by Chen and Driscoll [Twenty-Third Symposium (International) on Combustion]. An analysis is performed suggesting that the observed power dependence is due to the nonequilibrium chemistry effect, and it depends on the self-similar laws for jets. Comparisons of numerical results obtained with and without radiation heat loss show a significant impact on the thermal NO formation for jet flames with radiant franctions greater than 5%.

Multifield Visualization Using Local Statistical Complexity

Modern unsteady (multi-)field visualizations require an effective reduction of the data to be displayed. From a huge amount of information the most informative parts have to be extracted. Instead of the fuzzy application dependent notion of feature, a new approach based on information theoretic concepts is introduced in this paper to detect important regions. This is accomplished by extending the concept of local statistical complexity from finite state cellular automata to discretized (multi-)fields. Thus, informative parts of the data can be highlighted in an application-independent, purely mathematical sense. The new measure can be applied to unsteady multifields on regular grids in any application domain. The ability to detect and visualize important parts is demonstrated using diffusion, flow, and weather simulations.

Nonreacting turbulent mixing flows

Abstract This paper provides a comprehensive review of available data on turbulent nonreacting flows which could be of use in the evaluation of turbulence modeling schemes. The review is limited to parabolic, stationary shear flows with well-defined boundary conditions; these flows have many of the characteristics of flows found in combustion devices and are typical of laboratory flames for which model evaluation data are most likely to be available. This report is an outgrowth of a study conducted under the direction of the Air Force Office of Scientific Research. A bound volume containing, in detail, the results of that study will be available in the near future.

Conditional sampling of velocity and scalars in turbulent flames using simultaneous LDV-Raman scattering

The laser Doppler velocimeter (LDV) measures the velocity distribution of particles which is often an acceptable representation of the distribution of gas velocities. However, in turbulent two stream mixing flows, the particle velocity distribution will differ from the gas velocity distribution when the particle densities in the two streams are unequal. This bias is explored in a reacting and nonreacting turbulent jet which is surrounded by coflowing air. By adding seed particles to only the coflow air and then to only the jet fluid, the limits of this bias are established. Additional measurements with an LDV triggered laser Raman scattering system demonstrate that the bias in the LDV sampling is propagated to the Raman measurements. An analytical equation is presented which will generate unbiased velocity and scalar distributions from measurements obtained from seeding only one stream at a time.