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In modeling turbulent combustion, decoupling the chemistry from the turbulence is of great practical significance. In cases in which the equilibrium chemistry model breaks down, laminar flamelet modeling (LFM) is a promising approach to decoupling. Here, the validity of this approach is investigated using direct numerical simulation of a simple chemical reaction in two-dimensional turbulence.
Statistical information required to support modeling of turbulent premixed combustion by laminar flamelet methods is extracted from a database of the results of Direct Numerical Simulation of turbulent flames. The simulations were carried out previously by Rutland (1989) using a pseudo-spectral code on a three dimensional mesh of 128 points in each direction. One-step Arrhenius chemistry was employed together with small heat release. A framework for the interpretation of the data is provided by the Bray-Moss-Libby model for the mean turbulent reaction rate. Probability density functions are obtained over surfaces of the constant reaction progress variable for the tangential strain rate and the principal curvature. New insights are gained which will greatly aid the development of modeling approaches.
We analyze results of a premixed constant density flame propagating in three-dimensional turbulence, where a flame model developed by Kerstein, et al. (1988) has been used. Simulations with constant and evolving velocity fields are used, where peculiar results were obtained from the constant velocity field runs. Data from the evolving flow runs with various flame speeds are used to determine two-point correlations of the fluctuating scalar field and implications for flamelet modeling are discussed.
The soot properties of round, nonbuoyant, laminar jet diffusion flames are described, based on experiments at microgravity carried out on orbit during three flights of the Space Shuttle Columbia, (Flights STS-83, 94 and 107). Experimental conditions included ethylene- and propane-fueled flames burning in still air at an ambient temperature of 300 K and ambient pressures of 35-100 kPa. Measurements included soot volume fraction distributions using deconvoluted laser extinction imaging, and soot temperature distributions using deconvoluted multiline emission imaging. Flowfield modeling based on the work of Spalding is presented. The present work explores whether soot properties of these flames are universal functions of mixture fraction, i.e., whether they satisfy soot state relationships. Measurements are presented, including radiative emissions and distributions of soot temperature and soot volume fraction. It is shown that most of the volume of these flames is bounded by the dividing streamline and thus should follow residence time state relationships. Most streamlines from the fuel supply to the surroundings are found to exhibit nearly the same maximum soot volume fraction and temperature. The radiation intensity along internal streamlines also is found to have relatively uniform values. Finally, soot state relationships were observed, i.e., soot volume fraction was found to correlate with estimated mixture fraction for each fuel/pressure selection. These results support the existence of soot property state relationships for steady nonbuoyant laminar diffusion flames, and thus in a large class of practical turbulent diffusion flames through the application of the laminar flamelet concept.
NASA Marshall Space Flight Center (MSFC) has embarked upon a joint project with the Air Force to improve the state-of-the-art of space application combustion device design and operational understanding. One goal of the project is to design, build and hot-fire test a 40,000 pound-thrust Oxygen/Rocket Propellant-2 (RP-2) Oxygen-Rich staged engine at MSFC. The overall project goals afford the opportunity to test multiple different injector designs and experimentally evaluate the any effect on the engine performance and combustion dynamics. To maximize the available test resources and benefits, pre-test, combusting flow, Computational Fluid Dynamics (CFD) analysis was performed on the individual injectors to guide the design. The results of the CFD analysis were used to design the injectors for specific, targeted fluid dynamic features and the analysis results also provided some predictive input for acoustic and thermal analysis of the main Thrust Chamber Assembly (TCA). MSFC has developed and demonstrated the ability to utilize a computationally efficient, flamelet-based combustion model to guide the pre-test design of single-element Gas Centered Swirl Coaxial (GCSC) injectors. Previous, Oxygen/RP-2 simulation models utilizing the Loci-STREAM flow solver, were validated using single injector test data from the EC-1 Air Force test facility. The simulation effort herein is an extension of the validated, CFD driven, single-injector design approach applied to single injectors which will be part of a larger engine array. Time-accurate, Three-Dimensional, CFD simulations were performed for five different classes of injector geometries. Simulations were performed to guide the design of the injector to achieve a variety of intended performance goals. For example, two GCSC injectors were designed to achieve stable hydrodynamic behavior of the propellant circuits while providing the largest thermal margin possible within the design envelope. While another injector was designed to purposefully create a hydrodynamic instability in the fuel supply circuit as predicted by the CFD analysis. Future multi-injector analysis and testing will indicate what if any changes occur in the predicted behavior for the single-element injector when the same injector geometry is placed in a multi-element array.
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This work provides an overview of the ongoing research to better estimate radiation and soot in large-scale pool fires. The core focus of this presentation is on improvements to models for novel physics at larger scales.
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Studies in the mathematical modeling of the high-speed turbulent combustion has received renewal attention in the recent years. The review of fundamentals, approaches and extensive bibliography was presented by Bray, Libbi and Williams. In order to obtain accurate predictions for turbulent combustible flows, the effects of turbulent fluctuations on the chemical source terms should be taken into account. The averaging of chemical source terms requires to utilize probability density function (PDF) model. There are two main approaches which are dominant in high-speed combustion modeling now. In the first approach, PDF form is assumed based on intuitia of modelliers (see, for example, Spiegler et.al.; Girimaji; Baurle et.al.). The second way is much more elaborate and it is based on the solution of evolution equation for PDF. This approach was proposed by S.Pope for incompressible flames. Recently, it was modified for modeling of compressible flames in studies of Farschi; Hsu; Hsu, Raji, Norris; Eifer, Kollman. But its realization in CFD is extremely expensive in computations due to large multidimensionality of PDF evolution equation (Baurle, Hsu, Hassan).
A simple, easy-to-evaluate, surrogate model was developed for predicting the particle emission source term in wildfire simulations. In creating this model, we conceptualized wildfire as a series of flamelets, and using this concept of flamelets, we developed a one-dimensional model to represent the structure of these flamelets which then could be used to simulate the evolution of a single flamelet. A previously developed soot model was executed within this flamelet simulation which could produce a particle size distribution. Executing this flamelet simulation 1200 times with varying conditions created a data set of emitted particle size distributions to which simple rational equations could be tuned to predict a particle emission factor, mean particle size, and standard deviation of particle sizes. These surrogate models (the rational equation) were implemented into a reduced-order fire spread model, QUIC-Fire. Using QUIC-Fire, an ensemble of simulations were executed for grassland fires, southeast U.S. conifer forests, and western mountain conifer forests. Resulting emission factors from this ensemble were compared against field data for these fire classes with promising results. Also shown is a predicted averaged resulting particle size distribution with the bulk of particles produced to be on the order of 1 μm in size.
The mean reaction rate in flamelet models for turbulent premixed combustion depends on two basic quantities: a mean chemical rate, called the flamelet speed, and the flame surface density. Our previous work had been primarily focused on the problem of the structure and topology of turbulent premixed flames, and it was then determined that the flamelet speed, when space-averaged, is only weakly sensitive to the turbulent flow field. Consequently, the flame surface density is the key quantity that conveys most of the effects of the turbulence on the rate of energy release. In flamelet models, this quantity is obtained via a modeled transport equation called the Sigma-equation. Past theoretical work has produced a rigorous approach that leads to an exact but unclosed formulation for the turbulent Sigma-equation. In the exact Sigma-equation, it appears that the dynamical properties of the flame surface density are determined by a single parameter, namely the turbulent flame stretch. Unfortunately, the turbulent flame stretch as well as the flame surface density is not available from experiments, and, in the absence of experimental data, little is known on the validity of the closure assumptions used in current flamelet models. Direct Numerical Simulation (DNS) is the alternative approach to get basic information on these fundamental quantities. In the present work, three-dimensional DNS of premixed flames in isotropic turbulent flow is used to estimate the different terms appearing in the Sigma-equation. A new methodology is proposed to provide the source and sink terms for the flame surface density, resolved both temporally and spatially throughout the turbulent flame brush. Using this methodology, our objective is to extract the turbulent flame stretch from the DNS data base and then perform extensive comparisons with flamelet models. Thanks to the detailed information produced by the DNS-based analysis, it is expected that this type of comparison will not only underscore the shortcomings of current models, but also suggest ways to improve them.
Although the different regimes of premixed combustion are not well defined, most of the recent developments in turbulent combustion modeling are led in the so-called flamelet regime. The goal of these models is to give a realistic expression to the mean reaction rate (w). Several methods can be used to estimate (w). Bray and coworkers (Libby & Bray 1980, Bray 1985, Bray & Libby 1986) express the instantaneous reaction rate by means of a flamelet library and a frequency which describes the local interaction between the laminar flamelets and the turbulent flowfield. In another way, the mean reaction rate can be directly connected to the flame surface density (Sigma). This quantity can be given by the transport equation of the coherent flame model initially proposed by Marble & Broadwell 1977 and developed elsewhere. The mean reaction rate, (w), can also be estimated thanks to the evolution of an arbitrary scalar field G(x, t) = G(sub O) which represents the flame sheet. G(x, t) is obtained from the G-equation proposed by Williams 1985, Kerstein et al. 1988 and Peters 1993. Another possibility proposed in a recent study by Mantel & Borghi 1991, where a transport equation for the mean dissipation rate (epsilon(sub c)) of the progress variable c is used to determine (w). In their model, Mantel & Borghi 1991 considered a medium with constant density and constant diffusivity in the determination of the transport equation for (epsilon(sub c)). A comparison of different flamelet models made by Duclos et al. 1993 shows the realistic behavior of this model even in the case of constant density. Our objective in this present report is to present preliminary results on the study of this equation in the case of variable density and variable diffusivity. Assumptions of constant pressure and a Lewis number equal to unity allow us to significantly simplify the equation. A systematic order of magnitude analysis based on adequate scale relations is performed on each term of the equation. As in the case of constant density and constant diffusivity, the effects of stretching of the scalar field by the turbulent strain field, of local curvature, and of chemical reactions are predominant. In this preliminary work, we suggest closure models for certain terms, which will be validated after comparisons with DNS data.
Examinations of flame fronts spreading over solid fuels in an opposed flow of oxidizer have shown that the flame front fragments into smaller (cellular) flames. These 'flamelets' will oscillate, recombine, or extinguish, indicating that they are in the near extinction limit regime (i.e., to one side of the quenching branch of the flammability map). Onset of unstable cellular flamelet formation for flame spread over thin fuels occurs when a heat-sink substrate is placed a small distance from the underside of the fuel. This heat-sink substrate (or backing) displaces the quenching branch of the flammability map in a direction that causes the instabilities to occur at higher air velocities. Similar near-limit behavior has been observed in other works using different fuels, thus suggesting that these dynamic mechanisms are fuel-independent and therefore fundamental attributes of flames in this near-limit flame spread regime. The objective of this project is to determine the contributions of the hydrodynamic and thermodiffusive mechanisms to the observed formation of flame instabilities. From this, a model of diffusion flame instabilities shall be generated. Previously, experiments were conducted in NASA drop towers, thereby limiting observation time to O(1-5 sec). The NASA tests exhibited flamelet survival for the entire drop time, suggesting that flamelets (i.e., small cellular flames) might exist, if permitted, for longer time periods. By necessity, experiments were limited to thermally thin cellulose fuels (approximately 0.001 in thick): instabilities could form by virtue of faster spread rates over thin fuels. Unstable behavior was unlikely in the short drop time for thicker fuels. In the International Space Station (ISS), microgravity time is unlimited, so both thin and thick fuels can be tested.
Predictive high-fidelity simulations of turbulent spray combustion must capture the combined effects of complex chemistry, multiphase evaporating flow and spray-flame interactions to achieve physical accuracy. Finite-rate chemistry (FRC) combined with a realistic chemical mechanism is a combustion model well-suited for this purpose, but has a high computational cost due to the large number and stiffness of transported chemical species. In contrast, flamelet-based models achieve lower cost by transporting a small number of quantities of reduced stiffness, but assumptions regarding local flame topology, boundary conditions and inter-phase coupling limit their physical accuracy. Recently, the Pareto-efficient combustion (PEC) framework was developed to dynamically assign combustion models based on local cost and accuracy metrics in gas-phase reacting flows. In this work, we extend this PEC framework to spray combustion through the rigorous analysis of the multiphase coupling terms in the governing equations. The derivation shows that spray evaporation causes errors in the prediction of species mass fractions for flamelet-based models due to the sensitivity of the local thermo-chemical state to changes in composition caused by fuel vaporization across combustion regimes present in practical spray combustion devices. Sub-model assignment is formulated as a multiple-choice knapsack problem, where computational cost is directly controlled through the fraction of the domain assigned to the FRC sub-model. The extended PEC formulation is applied to the simulation of a realistic rich-quench-lean gas turbine combustor at steady-state conditions, as well as transient operation resulting in lean blow-out (LBO). Analysis of transient simulations during LBO demonstrates the extended PEC formulation’s capacity to dynamically adapt to changing conditions within the combustor. Transient combustor dynamics are shown to approach convergence with limited increases in computational cost, while retaining substantial computational cost reduction compared to monolithic FRC simulations. Through PEC simulations with increasing fractions of the domain assigned to FRC, monolithic flamelet simulations are shown to over-predict flame stability during LBO. Finally, the extended PEC formulation is thus shown to overcome deficiencies of monolithic models by controlling modeling error for multiphase combustion modeling.