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## Über dieses Buch

Turbulent reactive flows are of common occurrance in combustion engineering, chemical reactor technology and various types of engines producing power and thrust utilizing chemical and nuclear fuels. Pollutant formation and dispersion in the atmospheric environment and in rivers, lakes and ocean also involve interactions between turbulence, chemical reactivity and heat and mass transfer processes. Considerable advances have occurred over the past twenty years in the understanding, analysis, measurement, prediction and control of turbulent reactive flows. Two main contributors to such advances are improvements in instrumentation and spectacular growth in computation: hardware, sciences and skills and data processing software, each leading to developments in others. Turbulence presents several features that are situation-specific. Both for that reason and a number of others, it is yet difficult to visualize a so-called solution of the turbulence problem or even a generalized approach to the problem. It appears that recognition of patterns and structures in turbulent flow and their study based on considerations of stability, interactions, chaos and fractal character may be opening up an avenue of research that may be leading to a generalized approach to classification and analysis and, possibly, prediction of specific processes in the flowfield. Predictions for engineering use, on the other hand, can be foreseen for sometime to come to depend upon modeling of selected features of turbulence at various levels of sophistication dictated by perceived need and available capability.

## Inhaltsverzeichnis

### Measurement of the Topology of Large-Scale Structures in Turbulent Reacting Flows

Turbulent combustion involves a complex interplay between fluid motion and chemistry. A widely held view is that large-scale structures play an important role in this interaction. Experimental work that concentrates on providing new information on the spatial characteristics of large-scale structures in flames has been done. Laser imaging techniques that can provide two-, and more recently, three-dimensional data on quantities such as species concentrations, temperatures, and densities in turbulent flames have been developed.

Marshall B. Long, Brandon Yip, Michael Winter, Joseph K. Lam

### Finite Chemical Kinetics Effects in a Subsonic Turbulent Hydrogen Flame

Departures from chemical equilibrium appear in nonpremixed turbulent flames at very high mixing rates, as shown by dimensional analysis based on Damköhler number (characteristic time of mixing over characteristic time of chemical reaction). This paper presents an experimental study that shows departures from chemical equilibrium in a hydrogen-air flame, which is often erroneously considered to have an infinitely fast chemical rate and therefore to be at chemical equilibrium.These departures from chemical equilibrium are measured with nonintrusive laser diagnostics. Instantaneous and spatially resolved measurements of major combustion species (H2, O2, H2O, and N2), density, and temperature are performed by means of Raman and Rayleigh scattering in a turbulent jet flame with a fuel of 22 mole percent argon in hydrogen. From these measurements we infer the local fuel mixture fraction f. Departures from chemical equilibrium are manifested by the comparison between the measured temperature and the equilibrium temperature deduced from the value of f.We vary the Damköhler number by adjusting either the aerodynamic conditions or the chemical rate. In the first case, a range of Reynolds numbers is explored: Re=8,500, Re=17,000, and Re=20,000, using the same fuel. The experimental results show a dramatic effect of the Reynolds number on the extent of departure from the limit of chemical equilibrium. Differences between the measured temperature and the inferred equilibrium temperature are as large as 450K as the flame approaches blow-off conditions. In the second case, we hold the aerodynamic conditions constant, and alter the chemical reaction rate by diluting the fuel with increasing amounts of nitrogen. These last experiments also show a difference between measured temperature and the inferred equilibrium temperature. Consequently, departures from the limit of chemical equilibrium are achieved through increasing the rate of mixing or by decreasing the rate of chemical reaction.

P. Magre, R. Dibble

### Cars Study of Premixed Turbulent Combustion in a High Velocity Flow

Premixed turbulent flames offer interesting possibilities to study turbulent combustion and permit confrontation between experiments and calculations. In addition, there is direct application to the design of afterburners for turbojet engines, if the flow veloCity is fast enough. For both reasons ONERA have undertaken continously over the last ten Years an experimental and theoretical study of such a turbulent flame, stabilized either by a planar hot jet parallel to the main stream, or by a sudden enlargment. The studies began with shadowgraphic visualizations and wall pressure measurements, followed by gas sampling and analysis by chromatography in order to know the mean concentration profile inside the flame. The veloCity profile was studied in detail later, with veloCity and turbulence measurements by laser Doppler anemometry. An attempt to measure some aspects of the temperature profile was made also by means of a pneumatic probe and emission-absorption spectroscopy. Very recently, a programme of measurements by CARS (Coherent anti-Stokes Raman Spectroscopy) has led to measurements of the fluctuating temperature. These results are presented here.

P. Magre, P. Moreau, G. Collin, R. Borghi, M. Péalat, J. P. Taran

### The Structure of Jet Diffusion Flames

This paper presents the structural characteristics of free, round, jet diffusion flames as obtained using a new 2D laser sheet lighting visualization technique referred to as the RMS (Reactive Mie Scattering) method. The results of analyzing photographs and high speed movies of flames using the RMS method are discussed in terms of the visible flame structure. The fuel veloCity is varied from 0.16 to 17 m/s. The presence of large toroidal vortices formed outside the visible flame zone have been known for many Years but their importance in determining the dynamic structure of free jet diffusion flames has not been fully appreciated. The influence of the outer vortices on flame structure is prevalent for near laminar and transitional flames and diminishes for near turbulent flames. They are believed to result from a Kelvin-Helmholtz type instability formed by a buoyantly driven shear layer. They appear to be responsible for flame flicker defined by the separation of the flame tip or the oscillations of the flame surface and for determining the shape of the mean, rms, and pdf radial profiles of temperature. Vortex structures have also been observed inside the visible flame zone. In transitional flames established by a contoured nozzle, these structures are shown to be on the scale of the 10 mm diameter nozzle, toroidal, and coherent for a long distance downstream. However, they may have only a minimal impact on the mean temperature characteristics of transitional flames. Their impact on the visible flame structure of near turbulent flames is large. At high fuel velocities, coalescence of the large vortices appear to be correlated with the formation of small 3D vortices which are randomly distributed in size and space. Collisions of the small vortices with the visible flame front produce small localized flamelets which are responsible for the wrinkled appearance of the visible flame surface. The localized stretching of the flame surface is believed to invoke finite rate chemistry effects. Indeed, collisions are observed where the flame stretch is large enough to cause localized holes to form in the flame surface. This appears to occur when the radial velocities of the inner vortices are large. Holes formed near the lip of the jet are postulated to be one mechanism that induces flame lift-off.

W. M. Roquemore, L.-D. Chen, L. P. Goss, W. F. Lynn

### Instantaneous Radial Profiles of OH Fluorescence and Rayleigh Scattering Through a Turbulent H2- Air Diffusion Flame

We have obtained instantaneous radial profiles of OH fluorescence and then Rayleigh scattering through a turbulent hydrogen-air diffusion flame by imaging a pulsed laser beam onto a gated linear diode array. Such data are helpful to determine what kind of flame front structure [1] can be expected in the flow : either a wrinkled flapping flame front if the turbulence scale is larger than the flame front thickness or a thickened flame front due to an internal micromixing by the small turbulence scales. Although turbulent flames must have one of the two structures above, the turbulence scale spectrum is spread over a considerable range and can be modified by combustion so that both structures may be alternatively found in a given flame.

D. Stepowski, K. Labbaci, R. Borghi

### Flame Structure in Spark Ignited Engines, from Initiation to Free Propagation

Flame visualization techniques, Schlieren and tomography, are used in experimental engines running with lean propane- air mixtures. They reveal that engine flames are turbulent as soon as created, and that this turbulence favors initiation. At very low engine speed, the engine flames are of wrinkled type. When going to higher rpm, the turbulent overall flame thickness increases, being around 1 cm at 1500 rpm. The study of the inner structure of the turbulent flame brush shows that the combustion zone is made of a very corrugated flame fronts, with peninsula and pockets. The distribution of the wrinkle scales widens when increasing engine speed, ranging from a few millimeters to tenth of mm.

T. A. Baritaud

### Comparison Between Two Highly Turbulent Flames Having Very Different Laminar Burning Velocities

Stationary jet burners, with Bunsen or V-shaped type flame are widely used for the study of premixed gas combustion. Since they are supposed to be simple configurations, they appear to the modeler scientist as a good test case to validate turbulent combustion equations closure assumptions. Modern diagnostic tools, such as laser Doppler anemometry /1/ or fine wire thermocouple temperature measurements /2/ have pointed out two essential features: a turbulence increase when crossing the combustion region and a counter-gradient diffusion. This helped to build the concept of “flamelet” combustion, where the combustion zone is seen as a region where a moving thin front, more or less corrugated, separates the fresh from burnt gas. To get a better knowledge of this flame front displacement, along with turbulence-combustion interaction, a statistical data processing involving the probability density function of the variables (PDF) was introduced /3,4,5,6/, and taken into account by the models, the most famous being the BLM model /7/.

D. Durox, T. Baritaud, J. P. Dumont, R. Prud’Homme

### Structure of Turbulent Premixed Flames as Revealed by Spectral Analysis

Although spectral analysis has proved a powerful tool for studying non-reacting turbulent flows, its application in turbulent reacting flow investigations has been limited. With the development of recent theoretical models which place more emphasis on the temporal characteristics of the scalar and veloCity fluctuations/1/, experimental investigation of their spectral behaviour would be useful to further the development of turbulent combustion models and to infer the physics of the turbulence-combustion interaction mechanisms which control the overall reaction rate.

I. Gökalp, A. Boukhalfa, R. K. Cheng, I. G. Shepherd

### Turbulent Flow Field and Front Position Statistics in V-Shaped Premixed Flame With and Without Confinement

Premixed turbulent flames have received considerable attention during the past few Years both from an experimental and theoretical point of view. However our understanding of the mutual interaction of combustion and turbulence is still incomplete due to the large number of mechanisms involved in such a problem.

Ph. Goix, P. Paranthoën, M. Trinité

### Two-Component Velocity Probability Density Measurements During Premixed Combustion in a Spark Ignition Engine

A two-component laser Doppler velocimeter is used to investigate turbulence during confined premixed combustion in an internal combustion engine. Of particular interest is the effect of unidirectional compression on the turbulence structure of the preflame gas, and the effect of the density jump across the flame on the turbulence in the burned gas. Measurements are presented for two components of turbulence intensity and their probability density functions, the correlation coefficient, and the joint probability density function. It is concluded that for low levels of preflame turbulence, both compression in front of the flame and expansion through it cause an increase in the turbulence intensity. For high initial levels of turbulence, however, compression has a negligible effect on the preflame turbulence, and expansion across the flame actually results in reduced turbulence levels.

Peter O. Witze, David E. Foster

### On the Accuracy of Laser Methods for Measuring Temperature and Species Concentration in Reacting Flows

During the past decade, following the improvements of both the lasers and the detectors and associated processors, a number of studies have been devoted to temperature and species concentration measurements by laser-based methods. In their prospective paper (1) in the 1975 Project Squid Workshop on Combustion Measurements in Jet Propulsion Systems, R. GOULARD., A.M. MELLOR and R.W. BILGER presented the type of measurements needed in combustion studies as following: -A)Discrete (but simultaneous) Measurements of Temperature, Velocity and ConcentrationSpatial resolution to 0.1mm, temporal resolution to 10φs (1OOKHz), and accuracy to 5 percent or better are desirable. Data accumulation at each point sufficient so that means, variances, convariances, p.d.f.s and joint p.d.f.s can be determined to better than 5 percent. Sufficient simultaneous information must be obtained so that instantaneous density can be computed and temperature or other corrections applied. Good coverage (mapping) of the combustion field is required.

M. J. Cottereau, J. J. Marie, P. Desgroux

### Structure of Flamelets in Turbulent Reacting Flows and Influences of Combustion on Turbulence Fields

Attention is focused on the reaction-sheet regime of turbulent reacting flows. In this regime the chemistry occurs in thin sheets convected and distorted by turbulent motions. Consideration is given to structures of reaction sheets, to their stability, and to influences of these sheets on the turbulence in turbulent combustion. These considerations are pursued separately for premixed and nonpremixed combustion.In the past, analyses of reaction-sheet structures have been based largely on activation-energy asymptotics. These analyses have addressed influences of strain and curvature on sheet structures and extinction. More recently there have been reaction-sheet analyses that account for more detailed chemistry, including hydrocarbon-air chemistry. These analyses are reviewed and evaluated with respect to their utility in turbulent-flame calculations.To address influences of reaction-sheet combustion on turbulence fields, attention is restricted mainly to large-scale, low-intensity turbulence and to premixed systems. It is then possible to calculate adjustments to the turbulence that occur in the preheat zone and in larger hydrodynamic zones of essentially constant-density fluid dynamics outside the flame. The adjustments in the hydrodynamic zones are significant and affect measured turbulence characteristics appreciably. The nature of the modifications introduced by the hydrodynamic zones is discussed.

F. A. Williams

### Flamelet Library for Turbulent Wrinkled Flames

The characteristics of a turbulent combustion in premixed gases are depending on the physico chemical properties of the reactive mixture and on the scales of the approaching turbulent flow compared to the thickness d and the speed uL of the laminar flame. All the properties of the reactive mixture that are necessary to characterize the turbulent wrinkled flame regime are included in few parameters such as the gas expansion parameter γ, the Markstein number Ma (describing stretch and curvature effects upon the local combustion rate) and the Froude number (when gravity effects are important). The theory of this regime is reviewed with a special emphasis on derivations of local laws and expressions of the Markstein number. Both stable and unstable flame fronts are considered in the wrinkled flame regime. New experimental data concerning the Markstein number are reported.

Paul Clavin, Guy Joulin

### Diffusion Flame Attachment and Flame Spread Along Mixing Layers

An analysis is presented for the description of the diffusion flame attachment region to the splitter plate separating the fuel and air, which should provide the flame lift-off speed of the fuel Jet in laminar and turbulent diffusion flames.The region of flame attachment and the flow veloCity there are small enough to allow for a balance of convection and upstream diffusion, so that the complete quasi-steady Navier-Stokes equations must be used to describe the flow in this region. The problem that must be solved is posed and it is conjectured that for the typical values of the overall activation energy there is a diffusion controlled solution with a flame attached close to the splitter plate, only for values of the Jet flow veloCity below a critical value; otherwise the flame is lifted-off.For those small values of the Jet veloCity there is a second unstable solution, which may also be attached to the wake region of the plate, and a third nearly frozen solution. The transition from the nearly frozen solution to the stable attached flame solution is only possible after flame ignition by a hot source in the mixing layer and subsequent flame propagation along the local laminar mixing layers or vortex cores. The problem of flame propagation along the local laminar mixing layers is also posed.

Amable Liñàn

### Length and Time Scales in Turbulent Combustion

The different regimes of premixed turbulent combustion may well be illustrated in a diagram, initially proposed by R. Borghi, where the ratio of the turbulence intensity to the laminar flame speed is plotted over the ratio of the turbulence integral length scale to the flame thickness. In this diagram four different regimes of turbulent combustion are specified: 1.the regime of wrinkled flamelets,2.the regime of corrugated flamelets,3.the regime of distributed reaction zones and4.the regime of the well-stirred reactor.While the first and fourth regime, representing limiting conditions, have been analysed in the past rather successfully, the second and third regime describe a more intense interaction between turbulence and combustion. Using arguments based on Kolmogorov’s energy cascade, a new length scale is identified in each of these two intermediate regimes.In the regime of corrugated flamelets, the Gibson scale $${{\rm{L}}_{\rm{G}}} = {\rm{v}}_{\rm{F}}^{3/{\rm{\varepsilon }}}$$ is derived. Here vF is the flame veloCity which by definition is equal to the characteristic turn-over veloCity of the eddy of size LG. Eddies much larger than LG which have a larger turn-over veloCity than vF will convect the flame front within the flow field as if it was a passive surface. Eddies much smaller than LG, having a smaller turn-over veloCity than vF, are consumed by the flame front very rapidly and therefore cannot corrugate the front. The Gibson scale therefore is the lower cut-off of all scales that appear in the corrugated flame surface.In the regime of distributed reaction zones the mean turbulent flame thickness is of the order of the quench scale δq, which is predicted to be proportional to $${\left( {{\rm{\varepsilon t}}_{\rm{q}}^3} \right)^{1/2}}$$, where tq=1/aq is the quench time, aq is the stretch rate at quenching of a premixed flame and ε the dissipation of turbulence. The quench scale presents the largest eddy within the inertial range, which is still able to quench the thin inner reaction zone of a premixed flame. Smaller eddies, inducing a larger stretch, will quench this thin layer more readily and therefore will try to homogenize the scalar field locally. Therefore a thickened flame front will appear. Larger eddies, inducing a weaker stretch that will not be able to quench the inner reaction zones, will only wrinkle this thickened flame front.

N. Peters

### A Model for Reactions in Turbulent Jets: Effects of Reynolds, Schmidt, and Damköhler Numbers

Data from several recent experiments on mixing and chemical reactions in turbulent shear layers and jets is discussed in detail and used to formulate a picture of the path from the freestream to the molecularly mixed State. A model is proposed which incorporates the essential steps in this path and which appears to provide a framework for understanding the major effects of Reynolds, Schmidt, and Damköhler numbers on the chemical reaction. A simplified version of the model reproduces the observed Reynolds number dependence of nitric oxide production in turbulent fuel jets.

### A Fractal Description of Flamelets

Under appropriate conditions, reaction in premixed turbulent flames is known to occur in thin sheets called flamelets. For weak turbulence the local structure of these flamelets approaches that of unperturbed steady laminar flames. It has been hypothesized that the geometry of flamelets may be described by the techniques of fractals, and combustion models based on this hypothesis have been proposed.In this paper fractal based combustion models for burning veloCity and chemical closure are reviewed. Evidence for the fractal behavior of surfaces in turbulent flow and of flamelets is reviewed, and new experimental data on the fractal character of premixed flamelets obtained by laser tomography and related techniques are presented and discussed.Several conclusions regarding the fractal description of flamelets are reached. These include: 1) If valid a fractal description of flamelets can be extremely useful in modeling turbulent combustion rates. 2) While the evidence is not conclusive it appears that flamelet surfaces can be represented by fractal surfaces and that this fractal wrinkling is related to turbulent veloCity fluctuations in the inertial subrange. 3) Additional experiments are need to confirm the fractal behavior of flamelets, to determine the fractal dimension and its dependency on conditions and to study the cutoffs to fractal behavior.

F. C. Gouldin

### Some Results on the Structure of the Tempertature Field in Low Damkohler Number Reaction Zones

Low Damköhler number premixed gaseous reaction zones, either thickened flame fronts or distributed reactions regimes, are much less investigated than high Damköhler number flames. Nevertheless, there are several reasons, ranging from the most fundamental ones to those of applied nature, which should motivate their study. Concerning the formers, low Damköhler number reaction zones constitute turbulent reacting flow situations where the chemistry, mixing and turbulence are the most profoundly intermingled due to the comparability of their respective time scales. They constitute then a challenging configuration to look for the interactions between chemical reactions and turbulence, as the combustion reactions are distributed throughout the volume occupied by the turbulent reaction zone /l/. Furthermore, due to their low exothermiCity, the low Damköhler number reaction zones are most suitable from the perspective of a systematic comparison between the turbulence structure in reacting and non-reacting but strongly variable density flows.

F. Gaillard, I. Gökalp

### Interaction of a Flame Front with Vortices : An Experiment

When chemical reactions occur in turbulent flows turbulence plays an important role along with thermodynamics and chemistry. This results in complex problems involving the interaction of turbulent motions with combustion. Many analytical and numerical analyses have been carried out to gain an understanding of the turbulent combustion and to predict the structure of turbulent reacting flows. However, progress has been impeded by the lack of experimental results due in a large part to the difficulties to provide accurate time-resolved veloCity, density, temperature and concentration fields in combustion environment. But new developments In optical diagnostic techniques, and particularly the visualization techniques, now allowed us to examine the interaction of turbulence and combustion at a fundamental level.

D. Escudié

### Experimental Studies in Vortex Pair Motion Coincident with a Liquid Reaction

An experimental examination of the coincidence of a liquid reaction (acid-base) with the formation of a vortex pair structure is described, in which emphasis is placed on the evolution of the strained diffusion layer and reacted core structures. Flow visualization of the reaction process is achieved via the technique of chemically sensitive laser-induced fluorescence. The observed growth of reacted core structures, associated with each vortex, is compared with theoretically predicted behavior published recently (Marble, Adv. in Aero. Sci., 395 (1985) and Karagozian and Manda, Comb. Sci. and Tech., 49, 185 (1986)). Vortex pair separation is also compared with theoretical correlations, and the relevance of the analogy between a fast liquid reaction (Sc » 1) and a gaseous reaction (Sc z 1) is discussed.

A. R. Karagozian, Y. Suganuma, B. D. Strom

### On an Attempt to Measure the Decay of Concentration Fluctuations in a Quasi-Isotropic Grid by Use of the Fluorescence of the Solution

A main characteristic of turbulence is its ability to mix transported scalar fields such as temperature or concentration. In chemical engineering the different species having to be mixed are often diluted in liquids, and the Schmitt number SC = v/D where v is the kinematic viscosity and D the molecular diffusivity of one species, is much greater than in a mixture of gases. A typical value of this number for diluted species in water is about 103. As the molecular diffusivity is much smaller than v , the turbulent concentration field exhibits much smaller “dissipative” scales than the veloCity field. The classical measurement method of concentration fluctuations of ionic species in water uses a conductimetric probe whose measurement volume is too large to give satisfactory information about the smallest scales of the concentration field. Such a method was used by Gibson (1962) to study the evolution of a concentration field of Nacl in a quasi-isotropic grid turbulence. BENNANI, GENCE and MATHIEU (1985) used the conductimetric method to study the evolution of a slow chemical reaction in the same conditions.

J. L. Lievre, J. N. Gence

### Turbulent Reactive Flows of Liquids in Isothermal Stirred Tanks

Reactive flows in the liquid phase are of major interest for the chemical engineers, but also for the scientist from a theoretical point of view.

René David

### Turbulent Shear Layer Mixing With Fast Chemical Reactions

A model is proposed for calculating molecular mixing and chemical reactions in fully developed turbulent shear layers, in the limit of infinitely fast chemical kinetics and negligible heat release. The model is based on the assumption that the topology of the interface between the two entrained reactants in the layer, as well as the strain field associated with it, can be described by the similarity laws of the Kolmogorov cascade. The calculation estimates the integrated volume fraction across the layer occupied by the chemical product, as a function of the stoichiometric mixture ratio of the reactants carried by the free streams, the veloCity ratio of the shear layer, the local Reynolds number, and the Schmidt number of the flow. The results are in good agreement with measurements of the volume fraction occupied by the molecularly mixed fluid in a turbulent shear layer and the amount of chemical product, in both gas phase and liquid phase chemically reacting shear layers.

Paul E. Dimotakis

### The Use of Direct Numerical Simulation in the Study of Turbulent, Chemically-Reacting Flows

At the present time the role of direct numerical simulation as applied to turbulent, chemically-reacting flows is twofold: to understand the physical processes involved, and to develop and test theories. In this paper we present and example of the former. We employ full turbulence simulations to study the effects of chemical heat release on the large-scale structures in turbulent mixing layers. This work not only aids in understanding this phenomena, but also gives insight into the strengths and limitations of the methodology.We find, in agreement with previous laboratory experiments, the heat release is observed to lower the rate at which the mixing layer grows and to reduce the rate at which chemical products are formed. The baroclinic torque and thermal expansion in the mixing layer are shown to produce changes in the flame vortex structure that act to produce more diffuse vortices than in the constant density case, resulting in lower rotation rates of the large scale structures. Previously unexplained anomalies observed in the mean veloCity profiles of reacting jets and mixing layers are shown to result from vortiCity generation by baroclinic torques. The density reductions also lower the generation rates of turbulent kinetic energy and the turbulent shear stresses, resulting in less turbulent mixing of fluid elements.Calculations of the energy in the various wave numbers shows that the heat release has a stabilizing effect on the growth rates of individual modes. A linear stability analysis of a simplified model problem confirms this, showing that low density fluid in the mixing region will result in a shift in the frequency of the unstable modes to lower wave numbers (longer wavelengths). The growth rates of the unstable modes decrease, contributing to the slower growth of the mixing layer.Finally, we find that this methodology can be confidently applied for Reynolds numbers less than several hundred and for Damköhler numbers less than about ten. With some modification it is possible to treat the infinte Damköhler number case using a conserved scalar.

J. J. Riley, P. A. McMurtry

### Direct Numerical Simulation and Simple Closure Theory for a Chemical Reaction in Homogeneous Turbulence

The direct numerical simulation of turbulent flows serves as a useful test of simple closure theories, since one can examine the dynamics of the concentration and veloCity fields in more detail than in laboratory experiments and learn how the interaction of turbulent motion and molecular diffusion affects the overall reaction rate. A brief review of the most popular methods available for full turbulence simulations is presented, and a demonstration of the usefulness of direct numerical simulation is given for simple single-point closure theories (viz., those of Toor and of Patterson) applied to the irreversible, second-order chemical reaction of initially unmixed reactants.

Andy D. Leonard, James C. Hill

### The Interaction Between Turbulence and Chemistry in Premixed Turbulent Flames

Recent studies of turbulent premixed combustion by the authors and their coworkers are reviewed with emphasis on two topics, related to the interaction between turbulence and chemistry. The first is the use of conditional averaging techniques to describe terms in the transport equations for Reynolds stress and flux components. Secondly a laminar flamelet description of the mean reaction rate terms is presented. Some problems which remain to be solved are identified.

K. N. C. Bray, M. Champion, Paul A. Libby

### On the Problem of Modelling Time or Length Scales in Turbulent Combustion

All the existing methods for turbulent reaction rates modelling need the knowledge of time or length scales characterizing the reacting turbulent medium. The old (but usefull) Eddy Break Up model assumes that a characteristic time for the destruction of the fluctuation of the progress variable is proportional to the integral Eddy Turn over time of the turbulence [1]; a similar assumption has been used with the presumed pdf approach, when the chemistry is not infinitely fast [2]. The conserved scalar approach for diffusion flames needs an assumption relating X» the mean scalar dissipation rate, to ɛ, the mean dissipation rate for the turbulence kinetic energy [3]. A similar hypothesis has to be involved also in approaches using modelled equations for the joint probability function of the veloCity and species mass fraction [A]. The coherent flame model of [5] involves a different quantity : the mean flame surface by unit of volume; but this quantity is nothing but a length scale of the turbulent medium. The flamelets approaches [6] are something more detailed: they need a full distribution of stretch rates, that means a range of turbulent times scales, instead of a single one.

R. Borghi, A. Picart, M. Gonzalez

### Statistical Modelling of Turbulent Reactive Flows

Turbulent combustion occurs in many engineering applications: spark-ignition engines, gas-turbine combustors, and furnaces, for example. In each of the applications cited the design process is lengthy and expensive. The industries involved are attempting to improve their design procedures by using computer models of turbulent reacting flows.Since the fundamental governing partial differential equations are known, the direct approach is to solve them numerically. However, because of the wide range of length and time scales involved, this direct approach is computationally impracticable, now and in the foreseeable future. The alternative is to use a statistical approach. Such approaches face a formidable challenge: superimposed on the difficulties of calculating inert, constant-density turbulent flows, are those associated with reaction and heat release. The reaction rates are typically highly nonlinear functions of the composition variables, which are subject to large turbulent fluctuations. Often reaction takes place in laminar flamelets that are thin compared to turbulent scales. Due to heat release the specific volume of the mixture can increase by a factor of ten which, as may be expected, is found to have a large effect on the turbulence. For example, due to heat release, the turbulence energy can increase by an order of magnitude, and new transport process become dominant and can lead to countergradient diffusion.

S. B. Pope

### Coherent Flame Description of Turbulent Premixed Ducted Flames

This paper describes some aspects of our effort to analyze turbulent combustion on the basis of an extension of the coherent flame model initially proposed by Marble and Broadwell.At this stage the model comprises a local description (flamelets) and a global representation of the turbulent flow-field including a balance equation for the mean flame area per unit volume.The flamelets are non-adiabatic premixed strained flames, a model suggested by Libby, Linan and Williams. Complex chemistry calculations have been carried out for a large number of propane-air flames and a large data-base of flamelets is being constructed. These calculations provide consumption rates, extinction and ignition characteristics which ere used in the global turbulent calculation to model the mean reaction terms. Numerical results obtained for turbulent premixed flames stabilized in a duct are discussed.Experiments performed on a model combustor provide distributions of the mean heat release rate. These distributions are compared with those determined numerically. This comparison indicates that the coherent flame description accounts for important features found in the experiment.

N. Darabiha, V. Giovangigli, A. Trouvé, S. M. Candel, E. Esposito

### Turbulence-Combustion Interactions in a Reacting Shear Layer

Turbulence-combustion interactions are analyzed using results of a numerical simulation of a reacting shear layer. Premixed combustion at finite activation energy, moderate chemical kinetic rates and finite diffusivities is considered. The transport element method, a numerical scheme based on the accurate discretization of the vortiCity and the scalar gradient fields into Lagrangian finite elements, is used to perform the numerical simulation. Processes that lead to burning enhancement, flame deceleration or possible extinction are analyzed. We find that the rollup of the shear layer accelerates burning by stretching the reaction surface. However, by comparing the local burning velocities within the shear layer to that of a laminar flame, we find that stretch, which accompanies the rollup, decelerates the rate of burning per unit area. This is due to the local cooling effects associated with the enhanced heat flux out and mass flux into the reaction zone. Both phenomena are strong functions of the turbulence field and the Damkohler number.

Ahmed F. Ghoniera, Ghassem Heidarinejad, Anantha Krishnan

### A PDF Method for Turbulent Recirculating Flows

A novel approach for the application of probability density function (PDF) methods to multidimensional turbulent recirculating flows is presented. The method is applicable to turbulent recirculating and reacting flows such as in gas turbine combustors. The method is based on a judicious combination of the conventional finite-volume technique for the solution of the Reynolds-averaged equations and the Monte Carlo technique for the solution of the transport equation for the veloCity-scalar joint PDF. An important aspect of the approach is that the use of conventional turbulence closure models is avoided. The method is applied to the flow over a backward-facing step investigated experimentally by Pronchick and Kline [1]. The results predicted using the present approach are in good agreement with data.

M. S. Anand, S. B. Pope, H. C. Mongia

### Dyanmics of Cold and Reacting Flows on Backward Facing Step Geometry

Aerodynamic of recirculating flow is one of the most difficult problem encountered in fluid mechanics. Particulary, classical turbulent closure of equations and finite difference treatment are handicaped by several drawbacks and does not work so well in view to prediction on these flows.

A. Giovannini

### PDF — Transport Equations for Chemically Reacting Flows

The analysis and the computation of turbulent flows with chemical reactions can be carried out by means of probability density functions (pdf’s) or characteristic functions. Pdf’s and characteristic functions offer several advantages over moment methods: Finite-rate chemistry can be dealt with rigorously as well as turbulent diffusion. The transport equations for pdf and characteristic functions require closure assumptions for the effects of viscosity and pressure on the pdf. this closure problem is the central part of the paper. It will be analyzed in terms of pdf’s and characteristic functions. First the properties of the linear and closed equations for the characteristic functional for Eulerian and Lagrangian variables will be established. Then the closure problem for the finite-dimensional case will be discussed for pdf and characteristic function. It will be shown for instance that the closure for the scalar dissipation term in the pdf equation developed by Dopazo [18] and Kollmann et al. [15] results in terms of characteristic functions in a single integral in contrast to the pdf, where double integration is required. Finally some recent results using pdf methods, which were obtained for turbulent flows with combustion including effects of chemical non-equilibrium, will be discussed.

W. Kollmann

### Modelling the Effects of Combustion on a Premixed Turbulent Flow : A Review

Combustion modifies the turbulent flow where it occurs through large density fluctuations due to heat release and through large variations in the molecular properties of the reactive fluid : viscosity and diffusivities. Interaction between these effects and pressure or velocity gradients leads to new or, at least, strongly modified mechanisms of production and destruction of turbulence. Following a modeller’s point of view and using the moment approach of turbulent combustion, these interaction mechanisms are represented by various production and dissipation terms in the second order balance equations for mean quantities such as turbulent kinetic energy K, Reynolds stress tensor components and mass and energy turbulent fluxes. General features of such an unclosed set of equations are given by Libby and Williams /1/ 12/ and Bray /3/. In the absence of a unified model for turbulent reactive flows the closure equations depend on the chemical and dynamical characteristic of the particular flow investigated.

M. Champion

### The Numerical Simulation of Compressible and Reactive Turbulent Structures

Computational research on the simulation of compressible and reactive turbulent structures in the Laboratory for Computational Physics and Fluid Dynamics requires the development of algorithms to exploit parallel and vector processing, the application of these techniques to simulate compressible, turbulent reactive flow structures, and the initiation of laboratory experiments to calibrate and complement the simulations.Our algorithmic research includes the development of explicit and implicit monotone methods for compressible convection, techniques for coupling disparate timescales which do not involve inverting matrices, variable, adaptive and unstructured gridding in multidimensions suitable for turbulent flows, realistic models for inflow and outflow boundary conditions in bounded domain problems, and the use of triangular grids in two dimensions and tetrahedronal grids in three dimensions to adapt the solution automatically to evolving flow structures. This paper will review recent important contributions in each of these areas and will discuss the practical limits attainable by finite resolution detailed modeling techniques.Our applications of these advances in simulation technology include research into the turbulent structure, propagation and extinction of detonations and flames using detailed chemistry models and multispecies diffusion coefficients, strong shock and transonic flows in complex geometries, and the study of turbulence and boundary layer phenomena in subsonic and supersonic shear layers and jets.A brief review will be given using illustrative simulations from the Naval Research Laboratory Cray and the Graphical and Array Processing System (GAPS), a multitasking, low cost hardware and software system assembled to provide a parallel processing capability to perform and analyze turbulent reactive flow simulations interactively. The GAPS approaches Cray performance on spatially evolving, compressible transition-to-turbulence simulations.

Jay Boris, Elaine Oran, Kazhikathra Kailasanath

### Turbulent Multiphase Flows

Recent measurements and predictions concerning turbulent multiphase flows are considered, emphasizing findings of the author and his associates. The properties of both dense sprays (comparable phase volume fractions) and dilute dispersed multiphase flows (dispersed-phase volume fractions less than 1–10 percent) are considered.Results for dense sprays are limited to the near-injector region of noncombusting, combusting monopropellant, and combusting bipropellant sprays from pressure-atomizing injectors. The results suggest that these flows approximate locally-homogeneous flow properties in the atomization regime, but exhibit much slower mixing rates as the first wind-induced breakup regime is approached, in a manner which is not anticipated by predictions. Flow properties for the atomization regime are strongly influenced by the degree of flow development and turbulence levels at the injector exit. However, existing measurements of the structure of dense sprays are very limited: more work is required to assess the appropriate flow regimes and the effectiveness of locally homogeneous flow analysis for these flows.Contemporary stochastic analysis of dilute multiphase flows has provided encouraging predictions of the mean structure and mixing properties (turbulent dispersion) of a variety of dilute dispersed flows. However, effects of turbulence modulation (the modification of turbulence properties by the dispersed phase) have been observed, which existing theoretical methods cannot treat effectively, due to inadequate consideration of the response of the dispersed phase to various wave numbers of the turbulence spectrum. Interphase transport phenomena associated with high relative turbulence intensities, virtual mass forces, Basset history forces, and the existence of envelope flames around drops, are also not sufficiently understood to provide reliable predictions of the properties of the dilute portions of combusting sprays.

G. M. Faeth

### Lagrangian Simulation of Particle Dispersion

Eulerian and Lagrangian approaches have been studied at Rouen for the prediction of particle dispersion in turbulent flows. A first computer code DISCO (Dispersion computing) has been developed during the past Years for predicting turbulence and the dispersion of discrete particles in the framework of an Eulerian approach. In that method, the particles are considered as a continuum and satisfy a transport equation which involves a dispersion tensor linked to particles and fluid characteristics. The Tchen theory (on discrete particle displacement) and the Batchelor theory (for diffusion of fluid particles) are used to determine the dispersion tensor, and a correction factor is defined to take into account for the crossing trajectories effects.

A. Berlemont, G. Gouesbet, P. Desjonqueres

### Numerical Modelling of Devolatilization in Pulverised Coal Injection Inside a Hot Coflowing Air Flow

A two-dimensional separated flow model has been developed for predicting fluid-particles turbulent recirculating two-phase flows. Thus, separate conservation equations are formulated for both phases including interphase transfer terms (mass, momentum and enthalpy). Turbulence is modeled by means of a q2- ɛ eddy viscosity model in the continuous phase which does not, at the present, take account for the interaction between the two phases.The model, including pyrolysis of coal and combustion of volatile matter, is used to compute an axisymetric injection of pulverised coal in a hot coflowing air flow, for two different particle sizes and two different inlet temperatures of the coflowing air flow. A first attempt is made to model the heterogeneous gaseous combustion process due to the local distribution of matter around particles.

O. Simonin, P. L. Viollet

### Flame Stabilization in a Supersonic Combustor

The combustors using supersonic combustion are characterized by two fundamental problems: the stabilization of the flame in a supersonic air flow,the maximum combustion efficiency.

M. Barrère

### Mixing Problems in Supersonic Combustion

The attainment of satisfactory supersonic combustion requires that the fuel and air be mixed to a sufficient extent at the molecular level, at a high enough temperature, so that the combustion reaction is largely complete before the gases leave the combustor. The macro-mixing must be achieved through turbulence, and molecular diffusion effects are only significant within the dimensions of the viscous eddies. The effects of macro-mixing only extend for the dimensions of the macro-scale eddies, hence the fuel injectors must be separated by a distance not exceeding twice the macro-scale. Since the turbulence is produced at the expense of the kinetic energy of the flow, there is an engine thrust penalty as the level of turbulence is increased. On the other hand, combustion efficiency and therefore thrust is limited by the degree of mixing. Hence there is an optimum level of turbulence, mixing and combustion efficiency in a scramjet engine.The design of practical supersonic combustors entails arranging the geometry so that this optimum can be achieved. Various systems have been investigated experimentally at Sheffield University and it should be noted that interaction between the pressure gradients due to heat release and the flow must be taken into account since there may be large differences between the flows with and without combustion. Thus calculation procedures are required to accurately predict the supersonic (or mixed supersonic-subsonic) turbulent reacting flows. One of the most successful practical geometries which we have tested involves the generation of vortices within the flow by injectors spanning the stream, with their trailing edges swept back behind the local Mach angle. These produce multiple vortices within the flow, and in common with other vortex flows will have turbulence which is highly anisotropic. We have already developed a very successful Reynolds stress code for subsonic swirling flow calculations and this technique may be extended to supersonic flows.(NB Parts of this paper were covered in Ref. 10. However, since that document is of very limited availability, is was considered that its inclusion here would be helpful).

J. Swithenbank, F. Boysan, B. C. R. Ewan, L. Shao, Z. Y. Yang

### Morphology of Flames Submitted to Pressure Waves

The influence of pressure waves on the mean structure of a turbulent flame is described. Two cases are presented : (1)When the pressure wave is generated by the flame itself, the system is submitted to combustion instability. In some extreme circumstances, the coupling between combustion and acoustics can lead to a flame structure characterized by the shedding of large vortices behind the flame holders; for this regime, the mean flame structure definition is a result of a cyclic formation and destruction of the reactive pattern at the frequency of the pressure oscillation. The characteristics of this cycle are studied by a phase average imaging method of the local reaction rate. This low frequency combustion instability is described in the first part of this paper.(2)Pressure waves can also be externally imposed to the flame. Arrays of driver units (loudspeakers) can be used to excite the flame at a chosen frequency and with a predetermined acoustic structure. With this technique it is possible to excite the flame in the transverse sloshing mode. In the case of a multiple flame combustor, this excitation induces strong modifications of the flame pattern : small vortices generated by the sloshing motion interact and set the jets of fresh mixture into a flapping motion. The flame structure appears as the result of the nonlinear interaction between small vortices generated by high frequency excitation and a low frequency induced flapping motion of the jets. Phase average measurements cannot be used in such circumstances because the fluctuations are the result of the superposition of many different modes. A spectral imaging method is developed to analyse these nonlinear coupling effects and its application is described in the second part of the paper.

T. Poinsot, A. Trouve, D. Veynante, S. M. Candel, E. Esposito

### Control of Turbulence in Combustion

Passive shear-flow control methods are being investigated to enhance turbulence for subsonic combustion. In this paper, two control methods are discussed. These methods were developed in subsonic nonreactlng flows and verified in subsonic combustion processes to avoid combustion Instabilities in a dump combustor. Both methods, which are based on the detailed understanding of flow instability mechanisms in shear layers, were used to change the initial conditions of the air flow (Jet) issued from the Inlet duct into dump combustor, in an attempt to decouple combustion from the large-scale structures In the flow. Two different Jet nozzles located at the dump plane are discussed: jet nozzles having sharp corners (these jets are characterized by large azimuthal variations of the flow field), and a multi-step nozzle with numerous sources for turbulence production yielding highly turbulent homogeneous incoherent flow fields. These nozzles augment turbulence or fine-scale (molecular) mixing and, at the same time, reduce large-scale mixing. Both methods were shown to be able to modify the flow field mixing pattern and inner eddy structure and to provide the potential for minimizing combustion instabilities.

K. C. Schadow, E. Gutmark, T. P. Parr, D. M. Parr, K. J. Wilson

### Progress Toward Shock Enhancement of Supersonic Combustion Processes

In air breathing propulsion systems for flight at Mach numbers 7 to 20, it is generally accepted that the combustion processes will be carried out at supersonic velocities with respect to the engine. The resulting brief residence time places a premium on rapid mixing of the fuel and air. To address this issue we are investigating a mechanism for enhancing the rate of mixing between air and hydrogen fuel over rates that are expected in shear layers and jets.The mechanism rests upon the strong vortiCity induced at the interface between a light and heavy gas by an intense pressure gradient. The specific phenomenon under investigation is the rapid mixing induced by interaction of a weak oblique shock with a cylindrical jet of hydrogen embedded in air. The status of our investigations is described in three parts: a) shock tube investigation of the distortion and mixing induced by shock waves impinging on cylindric of hydrogen embedded in air, b) the molecular mixing and chemical reaction in large vortices, periodically formed in a channel, and c) two-dimensional non-steady and three-dimensional steady numerical studies of shock interaction with cylindrical volumes of hydrogen in air.

Frank E. Marble, Gavin J. Hendricks, Edward E. Zukoski

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