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All sourcesNASA NTRSDOE OSTI
NASA NTRS2016

Correlation of Normal Gravity Mixed Convection Blowoff Limits with Microgravity Forced Flow Blowoff Limits

The axisymmetric rod geometry in upward axial stagnation flow provides a simple way to measure normal gravity blowoff limits to compare with microgravity Burning and Suppression of Solids - II (BASS-II) results recently obtained aboard the International Space Station. This testing utilized the same BASS-II concurrent rod geometry, but with the addition of normal gravity buoyant flow. Cast polymethylmethacrylate (PMMA) rods of diameters ranging from 0.635 cm to 3.81 cm were burned at oxygen concentrations ranging from 14 to 18% by volume. The forced flow velocity where blowoff occurred was determined for each rod size and oxygen concentration. These blowoff limits compare favorably with the BASS-II results when the buoyant stretch is included and the flow is corrected by considering the blockage factor of the fuel. From these results, the normal gravity blowoff boundary for this axisymmetric rod geometry is determined to be linear, with oxygen concentration directly proportional to flow speed. We describe a new normal gravity 'upward flame spread test' method which extrapolates the linear blowoff boundary to the zero stretch limit in order to resolve microgravity flammability limits-something current methods cannot do. This new test method can improve spacecraft fire safety for future exploration missions by providing a tractable way to obtain good estimates of material flammability in low gravity.

microgravity↗
DOE OSTI2024

Temperature effect on turbulent burning velocity of lean premixed hydrogen/air flames

Hydrogen has drawn great attention in recent years as a carbon-free fuel. The turbulent burning velocity (S T ) is an important parameter for the design and modeling of hydrogen-fueled engines given the high propagation speed of hydrogen flames. It has been well documented that S T of hydrogen flames can be dramatically increased by thermo-diffusive effects which are sensitive to thermodynamic conditions. Previous studies have mainly focused on the pressure effect on S T of lean hydrogen flames, while the temperature effect has been largely ignored. Here, in the present study, the turbulent burning velocity for a lean hydrogen/air mixture over a wide range of temperatures (300–641 K) and pressures (1–15 atm) is investigated through direct numerical simulations of statistically planar turbulent premixed flames. Results show that the variation of normalized turbulent burning velocity (S T /S L , where S L is the laminar flame speed) with temperature and pressure is mainly controlled by the variation of the stretching factor I 0 . While S T /S L is only marginally dependent on temperature at the atmospheric pressure, it exhibits a decreasing trend with temperature at an elevated pressure (10 atm). This is associated with different temperature dependencies of flame surface area enlargement at the two different pressures, despite the monotonically decreasing trends of I 0 with temperature at both pressures. In addition, under engine-relevant conditions where the temperature and pressure increase simultaneously, the promotion effect of pressure is found to be largely canceled out by the suppression effect of temperature, leading to only a slight increase in I 0 and S T /S L . The observed trends are further explained through detailed flame dynamic analysis. Furthermore, I 0 at different temperatures and pressures is found to correlate very well with the enhancement of fuel consumption rate in the critically strained laminar flames. The present study elucidates the strong impact of temperature on S T of lean premixed hydrogen/air flames at elevated pressures and provides new insights into the modeling of S T , especially for engine-relevant conditions.

Wang, Yiqing [Argonne National Laboratory (ANL), A↗
NASA NTRSDate not supplied

Extinction of the Stagnation Point Diffusion Flame: Effect of Conductive Heat Loss into Solid Interior

The flammability boundary of a solid is U-shaped with the ordinate as ambient oxygen percentage (or total pressure) and the abscissa represents flow velocity, gravity level, stretch rate, etc. The left side of the flammability boundary is the quenching branch, and the right side is the blow-off branch. Quenching is due to a weak flame whose heat release from combustion cannot overcome the excessive heat losses from, for example, radiation. Blow-off is due to a short gas residence time that is smaller than the chemical reaction time (traditionally referred to as the small Damköhler number effect). For thick solids, the heat conduction into the solid interior has a long transient after ignition before the solid temperature reaches the steady state. During this slow transient, there is excessive (i.e. more than that at the steady state) gas phase heat conduction into the solid interior. From the viewpoint of the quasi-static gaseous flame, this is an additional heat loss that will affect the gas flame's flammability. In this work, a previously developed one-dimensional axisymmetric stagnation-point diffusion flame model is extended to account for the excessive heat loss into the solid beyond the steady burning state. A non-dimensional excessive conductive heat loss parameter Ψ is defined in the paper to account for the transient solid effect. For each Ψ, the gas phase is considered reaching a quasi-steady state. Extensive numerical computations have been performed to determine the extinction boundary and the characteristics of near-limit flames. The U-shaped flammability boundary is now a series of boundaries with Ψ as a parameter. Flame structures under the same environment condition but with different Ψ are compared. For a given oxygen ambient, the extinction boundary Ψ vs stretch rate is an inverted U-shape. The boundary consists of a blowoff branch and a radiative quenching branch. Extensive computed data including flame and pyrolysis temperatures, burning rate, flame standoff distance, species concentration, and reaction rate are presented along the extinction boundaries. Heat balance analysis is performed for both the gas phase and the gas-solid interface. Along the extinction boundary, the relative importance of conduction, convection, radiation, and chemical reaction are analyzed in detail.

Stagnation point diffusion flame↗
NASA NTRS1995

Coupled Monte Carlo Probability Density Function/ SPRAY/CFD Code Developed for Modeling Gas-Turbine Combustor Flows

The success of any solution methodology for studying gas-turbine combustor flows depends a great deal on how well it can model various complex, rate-controlling processes associated with turbulent transport, mixing, chemical kinetics, evaporation and spreading rates of the spray, convective and radiative heat transfer, and other phenomena. These phenomena often strongly interact with each other at disparate time and length scales. In particular, turbulence plays an important role in determining the rates of mass and heat transfer, chemical reactions, and evaporation in many practical combustion devices. Turbulence manifests its influence in a diffusion flame in several forms depending on how turbulence interacts with various flame scales. These forms range from the so-called wrinkled, or stretched, flamelets regime, to the distributed combustion regime. Conventional turbulence closure models have difficulty in treating highly nonlinear reaction rates. A solution procedure based on the joint composition probability density function (PDF) approach holds the promise of modeling various important combustion phenomena relevant to practical combustion devices such as extinction, blowoff limits, and emissions predictions because it can handle the nonlinear chemical reaction rates without any approximation. In this approach, mean and turbulence gas-phase velocity fields are determined from a standard turbulence model; the joint composition field of species and enthalpy are determined from the solution of a modeled PDF transport equation; and a Lagrangian-based dilute spray model is used for the liquid-phase representation with appropriate consideration of the exchanges of mass, momentum, and energy between the two phases. The PDF transport equation is solved by a Monte Carlo method, and existing state-of-the-art numerical representations are used to solve the mean gasphase velocity and turbulence fields together with the liquid-phase equations. The joint composition PDF approach was extended in our previous work to the study of compressible reacting flows. The application of this method to several supersonic diffusion flames associated with scramjet combustor flow fields provided favorable comparisons with the available experimental data. A further extension of this approach to spray flames, three-dimensional computations, and parallel computing was reported in a recent paper. The recently developed PDF/SPRAY/computational fluid dynamics (CFD) module combines the novelty of the joint composition PDF approach with the ability to run on parallel architectures. This algorithm was implemented on the NASA Lewis Research Center's Cray T3D, a massively parallel computer with an aggregate of 64 processor elements. The calculation procedure was applied to predict the flow properties of both open and confined swirl-stabilized spray flames.

Source record↗
NASA NTRS1978

A Roof for the Lion's House

Fans of the National Football League's Detroit Lions don't worry about gameday weather. Their magnificent new Pontiac Stadium has a domed, air-supported, fabric roof that admits light but protects the playing field and patrons from the elements. The 80,000-seat "Silverdome" is the world's largest fabric-covered structure-and aerospace technology played an important part in its construction. The key to economical construction of the Silverdome-and many other types of buildings-is a spinoff of fiber glass Beta yarn coated with Teflon TFE fluorocarbon resin. The big advance it offers is permanency. Fabric structures-tents, for example have been around since the earliest years of human civilization. But their coverings-hides, canvas and more recently plastics-were considered temporary; though tough, these fabrics were subject to weather deterioration. Teflon TFE-coated Beta Fiberglas is virtually impervious to the effects of weather and sunlight and it won't stretch, shrink, mildew or rot, thus has exceptional longevity; it is also very strong, lightweight, flame resistant and requires no periodic cleaning, because dirt will not stick to the surface of Teflon TFE. And to top all that, it costs only 30 to 40 percent as much as conventional roofing.

Source record↗
NASA NTRS2003

An Earth-Based Equivalent Low Stretch Apparatus to Assess Material Flammability for Microgravity and Extraterrestrial Fire-Safety Applications

The objective of this project is to modify the standard oxygen consumption (cone) calorimeter (described in ASTM E 1354 and NASA STD 6001 Test 2) to provide a reproducible bench-scale test environment that simulates the buoyant or ventilation flow that would be generated by or around a burning surface in a spacecraft or extraterrestrial gravity level. This apparatus will allow us to conduct normal gravity experiments that accurately and quantitatively evaluate a material's flammability characteristics in the real-use environment of spacecraft or extra-terrestrial gravitational acceleration. The Equivalent Low Stretch Apparatus (ELSA) uses an inverted cone geometry with the sample burning in a ceiling fire configuration that provides a reproducible bench-scale test environment that simulates the buoyant or ventilation flow that would be generated by a flame in a spacecraft or extraterrestrial gravity level. Prototype unit testing results are presented in this paper. Ignition delay times and regression rates for PMMA are presented over a range of radiant heat flux levels and equivalent stretch rates which demonstrate the ability of ELSA to simulate key features of microgravity and extraterrestrial fire behavior.

Olson, S. L.↗
DOE OSTI2023

Data reduction considerations for the burning velocity of spherical constant volume flames of R32 (CH 2 F 2 ) with air

Here, the present work explores data reduction techniques for the measurement of the laminar burning velocities of R32(CH 2 F 2 )-air mixtures using a constant volume combustion device, in which the pressure-time history is the only measured parameter. To allow clear assessment of the accuracy of the data reduction methods, the pressure-time histories used for analysis are synthetically generated via a detailed numerical simulation employing full kinetics and with and without an optically-thin radiation model. Various data reduction models are employed, including a two-zone model and two multi-zone models, and these are compared with the results from the burning velocity obtained from the output of the numerical simulation. The data reduction schemes are shown to be accurate if the same radiation model is employed in the data reduction as was used in the flame simulation to generate the pressure trace used for post-processing. If the incorrect radiation model is employed, however, the errors can be quite large. The effects of stretch, radiation, and different data post-processing methodologies are explored and the errors quantified. Stretch is shown to be important for the early stages and the selected data range that is used for extrapolation has a significant effect on the extrapolated burning velocity. However, with an appropriate choice of data considered for extrapolation, the prediction of the unstretched burning velocity can be quite accurate.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2004

A New Test Method for Material Flammability Assessment in Microgravity and Extraterrestrial Environments

The standard oxygen consumption (cone) calorimeter (described in ASTM E 1354 and NASA STD 6001 Test 2) is modified to provide a bench-scale test environment that simulates the low velocity buoyant or ventilation flow generated by or around a burning surface in a spacecraft or extraterrestrial gravity level. The Equivalent Low Stretch Apparatus (ELSA) uses an inverted cone geometry with the sample burning in a ceiling fire (stagnation flow) configuration. For a fixed radiant flux, ignition delay times for characterization material PMMA are shown to decrease by a factor of three at low stretch, demonstrating that ignition delay times determined from normal cone tests significantly underestimate the risk in microgravity. The critical heat flux for ignition is found to be lowered at low stretch as the convective cooling is reduced. At the limit of no stretch, any heat flux that exceeds the surface radiative loss at the surface ignition temperature is sufficient for ignition. Regression rates for PMMA increase with heat flux and stretch rate, but regression rates are much more sensitive to heat flux at the low stretch rates, where a modest increase in heat flux of 25 kW/m2 increases the burning rates by an order of magnitude. The global equivalence ratio of these flames is very fuel rich, and the quantity of CO produced in this configuration is significantly higher than standard cone tests. These results [2] demonstrate the ELSA apparatus allows us to conduct normal gravity experiments that accurately and quantifiably evaluate a material s flammability characteristics in the real-use environment of spacecraft or extra-terrestrial gravitational acceleration. These results also demonstrate that current NASA STD 6001 Test 2 (standard cone) is not conservative since it evaluates materials flammability with a much higher inherent buoyant convective flow.

Olson, S. L.↗
NASA NTRS1984

Numerical modeling of turbulent flow

Three dimensional combustor calculations are currently stretching the computer hardware capabilities and the computing budgets of gas turbine manufacturers. One of the main reasons for this relates to the large number of complex physical processes occurring in the combustor. Airflow, fuel spray, reaction kinetics, flame radiation, and not the least of which, turbulence must be modeled and the related differential equations solved. Discussions in this conference will address methods to improve the accuracy of combustor flow field calculations and methods to speed the convergence of the modeled equations. This report will focus on aspects of merging these two new technologies. The improved accuracy discretization schemes have a negative impact on the speed of convergence of the modeled equations that the improved solution algorithms may not overcome. A description of the causes of this problem and potential solutions will be examined.

Claus, R. W.↗
NASA NTRS2010

Spontaneous Raman Scattering Diagnostics: Applications in Practical Combustion Systems

In this chapter, the recent advancements and practical aspects of laser SRS diagnostics have been reviewed wi til regards to applications in practical combustion systems. Clearly, SRS represents a theoretically and experimentally mature diagnostic technology that has become an essential tool for multiscalar measurements in turbulent combustion at elevated pressures. Today, time-, space-, spectrally, and even polarization-resolved S RS diagnostics is at hand, with aid from recent innovations in theoretical and technological developments on electro-optical or electromechanical devices. Whilst a linear increase in SRS signals can be expected in high-pressure systems (this is perhaps one of the most important advantages for using SRS in high-pressure systems), there are practical (often severe) restrictions associated with pressurized vessels, due mainly to the limited degree of optical access. This narrows ti,e available choice of diagnostics that can be employed at any given time. Point-wise SRS diagnostics provides the highest accuracy on the chemical species and temperature measurements, and will continue to remain a vital approach for the study in such harsh environments. The practical design considerations and hands-on set-up guide for SRS diagnostics provided in this chapter are rarely presented elsewhere. Although the second-harmonic Nd:YAG pulsed laser (532 nm), combined with pulse-stretching optics or the recently introduced White Cell-based laser, seems to be the most favored excitation source of choice by the research community, UV excitation will undoubtedly continue to be used on many occasions, and especially in sooting flames. Detection methods may be divided into ICCD-based nanosecond-gate detection or a rotary-chopper electromechanical shutter-based CCD array detection, and the levels of background flame emission in individual cases would determine this critical design choice. Here, a process of Raman signal calibration based on ti,e crosstalk matrix formalism was explained step-by-step. As tI,is process may be very time-consuming and expensive, a well-planned experimental approach (01' building a transferable calibration database or library (at least with in a user's own facility over a series of different testing and runs) is vitally important. Hands on advice on the design and construction of flow control systems for high pressure burner facilities were also presented.

Kojima, Jun↗
DOE OSTI2022

Conversion of Phenolic Oil from Biomass Pyrolysis into Phenyl Esters

Bio-oil is among the most economical approaches for advanced biofuel production. However, bio-oil faces several challenges including high acidity and viscosity, poor storage, and thermal stability. This study focuses on the upgradation of lignocellulosic (corn stover and yellow pine) bio-oil derived phenolic oil (PO), produced by the autothermal fast pyrolysis, through acid-catalyzed esterification reaction. Our strategy exploits a little recognized chemistry: the Fischer esterification of PO and carboxylic acids into carboxylic acid phenyl esters (CAPE) using Dean Stark distillation. Analyses by the Folin–Ciocalteu method, Karl Fischer titration, gas chromatography flame ionization detector, and the molecular weight determination by gel permeation chromatography suggest the conversion of 50 wt% added phenolics to their corresponding CAPE. The Fourier transform infrared spectroscopy analysis confirmed the formation of new C=O and two C–O stretching bands and decrease in the intensity of phenolic-OH bands in the CAPE. The 13 C NMR analysis supports the formation of CAPE together with some unreacted precursors. A base-catalyzed ester hydrolysis experiment and mass balance calculation show an excellent agreement (within 5% range) of the equivalent weight between the produced ester and the phenyl hexanoate. Brookfield analysis indicates that CAPE has 330-fold lower viscosity than starting PO. Heating values of CAPE were higher than PO, from which they were derived (42.2 and 43.6%, respectively, for PO from pyrolysis of corn stover and yellow pine), while moisture content decreased by 98.3 and 98.7%, respectively. The CAPE, which is a phenolic analogue of methyl esters used in biodiesel, has improved stability compared to PO from which it was derived.

42 ENGINEERING↗
NASA NTRS2003

Measurement and Simulation of Spontaneous Raman Scattering Spectra in High-Pressure, Fuel-Rich H2-Air Flames

Rotational vibrational spontaneous Raman spectra (SRS) of H2, N2, and H2O have been measured in H2-air flames at pressures up to 30 atm as a first stem towards establishing a comprehensive Raman spectral database for temperatures and species in high-pressure combustion. A newly developed high-pressure burner facility provides steady, reproducible flames with a high degree of flow precision. We have obtained an initial set of measurements that indicate the spectra are of sufficient quality in terms of spectral resolution, wavelength coverage, and signal-to-noise ratio for use in future reference standards. The fully resolved Stokes and anti-Stokes shifted SRS spectra were collected in the visible wavelength range (400-700 nm) using pulse-stretched 532 nm excitation and a non-intensified CCD spectrograph with a high-speed shutter. Reasonable temperatures were determined via the intensity distribution of rotational H2 lines at stoichiometry and fuel-rich conditions. Theoretical Raman spectra of H2 were computed using a semi-classical harmonic-oscillator model with recent pressure broadening data and were compared with experimental results. The data and simulation indicated that high-J rotational lines of H2 might interfere with the N2 vibrational Q-branch lines, and this could lead to errors in N2-Raman thermometry based on the line-fitting method. From a comparison of N2 Q-branch spectra in lean H2 low-pressure (1.2 atm) and high-pressure (30 atm) flames, we found no significant line-narrowing or -broadening effects at the current spectrometer resolution of 0.04 nm.

Kojima, Jun↗
NASA NTRS1993

Multigrid methods for numerical simulation of laminar diffusion flames

This paper documents the result of a computational study of multigrid methods for numerical simulation of 2D diffusion flames. The focus is on a simplified combustion model, which is assumed to be a single step, infinitely fast and irreversible chemical reaction with five species (C3H8, O2, N2, CO2 and H2O). A fully-implicit second-order hybrid scheme is developed on a staggered grid, which is stretched in the streamwise coordinate direction. A full approximation multigrid scheme (FAS) based on line distributive relaxation is developed as a fast solver for the algebraic equations arising at each time step. Convergence of the process for the simplified model problem is more than two-orders of magnitude faster than other iterative methods, and the computational results show good grid convergence, with second-order accuracy, as well as qualitatively agreement with the results of other researchers.

Liu, C.↗
NASA NTRS2015

Microgravity Flammability of PMMA Rods in Concurrent Flow

Microgravity experiments burning cast PMMA cylindrical rods in axial flow have been conducted aboard the International Space Station in the Microgravity Science Glovebox (MSG) facility using the Burning and Suppression of Solids (BASS) flow duct, as part of the BASS-II experiment. Twenty-four concurrent-flow tests were performed, focusing on finding flammability limits as a function of oxygen and flow speed. The oxygen was varied by using gaseous nitrogen to vitiate the working volume of the MSG. The speed of the flow parallel to the rod was varied using a fan at the entrance to the duct. Both blowoff and quenching limits were obtained at several oxygen concentrations. Each experiment ignited the rod at the initially hemispherical stagnation tip of the rod, and allowed the flame to develop and heat the rod at a sufficient flow to sustain burning. For blowoff limit tests, the astronaut quickly turned up the flow to obtain extinction. Complementary 5.18-second Zero Gravity Facility drop tests were conducted to compare blowoff limits in short and long duration microgravity. For quenching tests, the flow was incrementally turned down and the flame allowed to stabilize at the new flow condition for at least the solid-phase response time before changing it again. Quenching was observed when the flow became sufficiently weak that the flame could no longer provide adequate heat flux to compensate for the heat losses (conduction into the rod and radiation). A surface energy balance is presented that shows the surface radiative loss exceeds the conductive loss into the rod near the limit. The flammability boundary is shown to represent a critical Damkohler number, expressed in terms of the reaction rate divided by the stretch rate. For the blowoff branch, the boundary exhibits a linear dependence on oxygen concentration and stretch rate, indicating that the temperature at blowoff must be fairly constant. For the quenching branch, the dominance of the exponential nature of the Arrhenius kinetics reaction rate indicates that the temperature is critical.

flammability↗
NASA NTRS1993

Efficiency and reliability enhancements in propulsion flowfield modeling

The implementation of traditional CFD algorithms in practical propulsion related flowfields often leads to dramatic reductions in efficiency and/or robustness. The present research is directed at understanding the reasons for this deterioration and finding methods to circumvent it. Work to date has focussed on low Mach number regions, viscous dominated regions, and high grid aspect ratios. Time derivative preconditioning, improved definition of the local time stepping, and appropriate application of boundary conditions are employed to decrease the required time to obtain a solution, while maintaining accuracy. A number of cases having features typical of rocket engine flowfields are computed to demonstrate the improvement over conventional methods. These cases include laminar and turbulent high Reynolds number flat plate boundary layers, flow over a backward-facing step, a diffusion flame, and wall heat-flux calculations in a turbulent converging-diverging nozzle. Results from these cases show convergence that is virtually independent of the local Mach number and the grid aspect ratio, which translates to a convergence speed-up of up to several orders of magnitude over conventional algorithms. Current emphasis is in extending these results to three-dimensional flows with highly stretched grids.

Buelow, Philip E. O.↗
NASA NTRS2017

Low Pressure Flame Blowoff from the Forward Stagnation Region of a Blunt-Nosed Cast PMMA Cylinder in Axial Mixed Convective Flow

Low-pressure blowoff experiments were conducted with a stagnation flame stabilized on the forward tip of cast PMMA rods in a vertical wind tunnel. Pressure, forced flow velocity, gravity, and ambient oxygen concentration were varied. Stagnation flame blowoff is determined from a time-stamped video recording of the test. The blowoff pressure is determined from test section pressure transducer data that is synchronized with the time stamp. The forced flow velocity is also determined from the choked flow orifice pressure. Most of the tests were performed in normal gravity, but a handful of microgravity tests were also conducted to determine the influence of buoyant flow velocity on the blowoff limits. The blowoff limits are found to have a linear dependence between the partial pressure of oxygen and the total pressure, regardless of forced flow velocity and gravity level. The flow velocity (forced and/or buoyant) affects the blowoff pressure through the critical Damkohler number residence time, which dictates the partial pressure of oxygen at blowoff. This is because the critical stretch rate increases linearly with increasing pressure at low pressure (sub-atmospheric pressures) since a second-order overall reaction rate with two-body reactions dominates in this pressure range.

flammability↗
DOE OSTI2023

On the evolution of scalar iso-surface area density in a turbulent mixing layer

In this paper, the transport equation for scalar iso-surface area density (Σ) in a turbulent, temporally developing mixing layer is examined. Exploring the spatial and temporal evolution of the terms in the Σ transport equation is vital to improving our understanding of turbulent flows characterized by distinct interfaces, e.g. the flame surface or the turbulent/non-turbulent interface. Previous work reported by the authors identified that Σ exhibits self-similar behaviour consistent with the development of the temporal mixing layer. Accordingly, each of the terms in the Σ transport equation is found to behave in a self-similar manner, though there are notable differences in the self-similar behaviours for each term. Based on the results presented herein, it is suggested that the rate of change of Σ (∂Σ/∂t) and the advection term scale with hλ Φ /ΔU, where h is the width of the mixing layer, λ Φ is the scalar Taylor length scale and ΔU is the velocity difference. The production and destruction terms are found to scale with an additional factor (ReSc) 1/2 . In contrast, the molecular diffusion term is found to scale with a factor (ReSc) –1/2 compared to ∂Σ/∂t. Importantly, it is found that the difference between the production and destruction terms, or net surface ‘stretch’, scales with the same factor as ∂Σ/∂t and the advection term, which may have a significant impact on how the evolution of Σ is understood and modelled in turbulent flows.

42 ENGINEERING↗
NASA NTRS1993

A transport equation for the scalar dissipation in reacting flows with variable density: First results

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.

Mantel, T.↗