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TitleTurbulent Reacting Flows
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Topics in Applied Physics Volume 44


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Topics in Applied Physics Founded by Helmut K. v. Lotsch 1 2 3 4 5 6 I 8 9 10 11 12 13 14 15 16 17 18 1 Dye Lasers 2nd Ed. Editor: F. P. Schlfer Laser Spectroscopy of Atoms and Molecules. Editor: H. Walther Numerical and Asymptotic Techniques in Electromagnetics Editor: R. Mittra Interactions on Metal Surfaces Editor: R. Gomer Miissbauer Spectroscopy Editor: U. Gonser Picture Processing and Digital Filtering 2nd Edition. Editor: T. S. Huang Integrated Optics 2nd Ed. Editor: T. Tamir Light Scattering in Solids Editor: M. Cardona Laser Speckle and Related Phenomena Editor: .I. C. Dainty Transient Eleclromagnetic Fields Editor: L. B. Felsen Digital Picture Analysis Editor: A. Rosenfeld Turbulence 2nd Ed. Editor: P. Bradshaw High-Resolution Laser Spectroscopy Editor: K. Shimoda Laser Monitoring of the Atmosphere Editor: E. D. Hinkley Radiationless Processes in Molecules and Condensed Phases. Editor: F. K. Fong Nonlinear Infrared Generation Editor: Y.-R. Sben Electroluminescence Editor: J. I. Pankove Ultrashort Light Pulses Picosecond Techniques and Applications Editor: S. L. Shapiro 19 Optical and Infrared Detectors 2nd Ed. Editor: R. J. Keyes 20 Holographic Recording Materials Editor: H. M. Smith 21 Solid Electrolytes Editor: S. Geller 22 X-Ray Optics. Applications to Solids Editor: H.-J. Queisser 23 Optical Data Processing. Applications Editor: D. Casasent 24 Acoustic Surface Waves Editor: A. A. Oliner 25 Laser Beam Propagation in the Atmosphere Editor: J. W. Strohbehn 26 Photoemission in Solids I. General Principles Editors: M. Cardona and L. Ley 21 28 29 30 31 32 33 34 35 36 31 38 39 40 41 42 43 44 45 46 47 48 Photoemission in Solids II. Case Studies Editors: L. Ley and M. Cardona Hydrogen in Metals I. Basic Properties Editors : G. Alefeld and J. Vijlkl Hydrogen in Metals II Application-Oriented Properties Editors: G. Alefeld and J. V6lkl Excimer Lasers Editor: Ch. K. Rhodes Solar Energy Conversion. Solid-State Physics Aspects. Editor: B. 0. Seraphin Image Reconstruction from Projections Implementation and Applications Editor: G. T. Herman Electrets Editor: G. M. Sessler Nonlinear Methods of Spectral Analysis Editor: S. Haykin Uranium Enrichment Editor : S. Villani Amorphous Semiconductors Edilor: M. H. Brodsky Thermally Stimulated Relaxation in Solids Editor: P. Brlunlich Charge-Coupled Devices Editor: D. F. Barbe Semiconductor Devices for Optical Communication Editor: H. Kressel Display Devices Editor: J. I. Pankove Computer Application in Optical Research Editor: B. R. Frieden Two-Dimensional Digital Signal Processing I. Linear Filters Editor: T. S. Huang Two-Dimensional Digital Signal Processing II. Transforms and Median Filters. Editor: T. S. Huang Turbulent Reacting Flows Editors: P. A. Libby and F. A. Williams Hydrodynamic Instabilities and the Transition to Turbulence Editors: H. L. Swinney and J. P. Gollub Glassy Metals I Editors: H.-J. Gijntherodt and H. Beck Sputtering by Particle Bombardment I Editor: R. Behrisch Optical Information Processing Fundamentals Editor: S. H. Lee


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116 K.N.C. Bray under which mixing occurs, so that mixing can be accomplished before significant reaction begins. Assuming that the relevant diffusion coefficients are all approximately equal, the subsequent reaction will then occur in a mixture of almost constant and uniform elemental composition. For the present study, premixed combustion provides the most important example. The chemical reaction time under ambient conditions can often be extremely large so that premixed reagents may be stored indefinitely. However, this time falls rapidly with increasing temperature and, at temperatures typical of combustion, it can become small in comparison with the characteristic times of other contributing processes. In practice, premixed combustion is almost always turbulent. Well-known examples include combustion in spark-ignition engines, in jet engines with reheat or with premixing and prevaporization to reduce pollutant emissions, and in tunnel burners in industry. Another important example is provided by vapor cloud explosions resulting from the leakage of fuel into the atmosphere where it mixes with air and can sub- sequently ignite. In all of these cases, the velocity field is closely coupled to the composition and temperature fields, so that turbulent motion and combustion interact strongly with each other. Isothermal premixed turbulent flows involving homogeneous chemical reactions in liquids, for example, are generally less complex; see Sect. 1.2. If mixing is essentially complete before the commencement of the reaction, then the subsequent chemistry takes place in a uniform isothermal mixture, and the reaction is independent of the turbulent flow. There are exceptions, particularly if reactions are allowed to occur at surfaces. Examples may be found in electrochemistry involving premixed liquid reagents flowing over electrodes; situations can arise where reaction intermediates, which are produced in reactions at the electrodes, must diffuse into the bulk liquid before the reaction can reach completion (see, for example, [4.1]). The turbulent velocity field then strongly influences the progress of the chemical reaction. It is, however, unlikely that the reaction will have any significant effect on the turbulence. Scientific investigation of turbulent premixed flames is generally recognized to have begun in 1940 with Damk6hler's classical theoretical and experimental study [4.2]. Reviews of knowledge concerning turbulent flames, emphasizing premixed reactants, were published in 1961 by Lewis and yon Elbe [4.3] and in 1965 by V~lliams [-4.4]. More recent reviews of the subject may be found in the work of Andrews et al. [4.5], Abdel-Gayed and Bradley [4.6], and Libby and I4411iams [4.7], while turbulent combustion in spark-ignition engines has been reviewed by Tabaezynski [4.8]. Damk6hler [4.2] first put forward the idea that sufficiently large-scale turbulence merely wrinkles a premixed laminar flame without significantly modifying its internal structure, while sufficiently small-scale turbulence pri- marily affects the transport processes inside the flame. Limiting regimes are thus identified in which the microscale of the turbulence is either very large or very small in comparison with the thickness of a laminar flame, and these concepts have influenced almost all later work on the subject.


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Turbulent Flows with Premixed Reactants 117 There is much indirect experimental evidence to support the existence of a wrinkled laminar flame regime in premixed turbulent combustion. Within this regime, thin laminar flames separate zones of unburned and fully burned mixture. Passage of such zones past a fixed point in the flow field causes large fluctuations to occur in the temperature, density, and composition of the gas and, for the reasons explained in Sect. 1.14, the time-averaged reaction rates are strongly affected. However, sufficiently intense turbulence tears the wrinkled flame sheet into pieces and can also quench the combustion in some of the resulting flame fragments. The laminar flame is known to be unstable to a broad spectrum of disturbances. It is, therefore, possible that in the presence of strong turbulence, instantaneous burning zones bear little or no resemblance to laminar flames. For example, Chomiak [4.9] suggested that these zones are associated with a fine vortex structure whose transverse dimension is compara- ble to the Kolmogorov microscale of the turbulence. Conditions under which such complications may arise are not yet firmly established. In Damk6hler's other limiting regime, where the turbulence scale is smaller than the laminar flame thickness, the turbulent fluctuations in temperature, etc., are expected to be relatively weak. A related problem concerns the influence of heat release and combustion- generated fluctuations in density on the structure and properties of the turbulent velocity field. The existence of so-called flame-generated turbulence has long been a topic of controversy and it is not yet clear whether conventional empirical descriptions of turbulence production and turbulent transport in cold nonreacting flows can be applied without modification in flames. The combustion-turbulence interaction is discussed in a recent review by the present author I-4.101. We shall look first at experimental information about the structure and propagation of premixed turbulent flames. Although, these flames have been studied in the laboratory for many years, so that a vast body of experimental data on them exists, there are still serious gaps and inconsistencies in the description which emerges. Section 4.3 discusses the premixed laminar flame which is relevant, both as a simpler flow resembling the turbulent flame and, more importantly, because it appears in wrinkled laminar flame models of turbulent flames. Since the laminar flame is subject to instabilities which influence its behavior in a turbulent flow, a rigorous and general treatment of this subject is difficult. Accordingly, the instability mechanisms are briefly reviewed in Sect. 4.3. Theoretical studies of premixed turbulent flames are reviewed in Sect. 4.4, starting with wrinkled laminar flame theories and continuing with combustion controlled by turbulent transport. Section 4.5 then presents a unified analysis of the subject, based on the work of Bray and Moss [4.11,121, which is capable of describing both wrinkled laminar flames and regimes of combustion dominated by turbulent transport. The chapter ends with a discussion of outstanding problems and possible approaches to them.


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242 Subject Index recombination 7 reversible 71 second-order 32 one-step irreversible exothermic 211 sequential 174 single, globalcombustion 176 surfaces 31 two-step 176 zone narrow 166 structure 86, 87 Reactor, homogeneous 211 plug-flow 179 stirred 179 model 178 Recirculation 48, 108 Relaxation model 204 Reynolds number 12, 37, 69 number similarity hypothesis 68 stress 158, 186 shear 120, 123 see also Stress, turbulent Scalar field, conditioned 213 field, passive nonreacting 186 Schmidt number 5,10, 38,59,140, 141,212,225 Scramjet 224 Secondary air 53 Self-turbulization 136 see also Laminar flame Shvab-Zeldovich coupling function 67, 68 relations 89 Similarity numbers 37-40 Simulation, direct numerical 191 Skewness 17 Smoke 48, 51 Soot 66, 88 Soret effect 4,8 Specific heat at constant pressure 5, 10, 141, 170 Spectral transfer 24, 104 Spectroscopy, laser spark 67 Spectrum 24, 38, 101-106 of kinetic energy 24 negative scalar intensity 206 of the radiation 221 Spectrum function 208 function, negative energy 206 Stabilization, method of 126 see also Flame State, equation of 12, 141,142, 171 thermochemical 143 Stationarity, statistical 190 Statistical independence 83 Stoichiometric coefficient 6 contour 48, 53, 85 mixture 106, 141,169 ratio 188 system 82 value of conserved scalar 70, 71 Stratification 221 Stress, turbulent (Reynolds) 16, 18, 25, 36 viscous 4, 8 Stretch factor 128 Structure functions 75 Superlayer, viscous 78 Swirl 48,49, 109 burner 109 Taylor length 39, 47 microscale 105, 125, 180 Temperature 7 Tensor, velocity correlation 23,24 Thermalconduction 115 conductivity coefficient 5 Thermochemistry 170 Time, chemical 53, 152 residence 205 scales 47 series 17, 18 turbulence eddy turnover 186 Transition ofalaminar flame 178 Transport equation 27, 29 molecular 3,4,5, 16 theory, nonreacting scalar 186 Tunnel burners 116 Turbine afterburners 46 Turbulence 12, 13 conditioned 36 energy, decay of 138 final-period 208 homogeneous 210 intensity 37, 38, 122, 130, 157 isotropic 24, 81,135,206 isotropic, small structure of 214 large scale 135 length scale 125, 130, 136, 157 modeling techniques 186 quasi-homogeneous 180, 215 Reynoldsnumber 38,68,96,98,101,125,126, 152, 155, 159 stationary 14, 22 structures, energy-containing 186 variable density 50 velocity, root mean square 125 wind tunnel, grid-generated 215


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l'urbulent combustion 157 combustion, premixed 129, 132, 141, 149, 166 exchange coefficient 137 flame confined oblique 159 diffusion 95 normal 159 premixed 116, 117, 180 planar 159 oblique 121,122 speed 123-126, 132, 135, 160, 229 local 124 propagation 151 flow, intermittent 213 theories of 129-139 thickness 151 unconfined oblique 159 see also Flame, Turbulent flame speed kinetic energy 37, 107, 138, 144 kinetic energy equation 107 energy, Favre 28,84 mixing time 53 mass flux 180 mixing 136 scalar transport theory 202 see also Mixing transport 3, 16, 117, 136, 137, 157 coefficient, negative 136 flux 180 model 157-159 processes 137, 140 Subject Index 243 Two-phase flows 48, 213, 219, 221,222 turbulent flows 223, 224 Unburned gas 166 mode 167 see also Fully burned Unmixedness integral 74 Variable-density flows 108 Variance 17 Velocity 3, 4, 8 characteristic 88 conditioned 164 correlation 188 fields, advecting 187 fluctuation, root mean square 130 gradient, mean 122, 123 Viscosity 4 kinematic 101 yon Neumann series 202 Vortex, dissipative 176 filaments, dissipation 151 Wake 76, 77 Wave number 103, 104, 206 number, Corrsin 104 Well-mixed limit 138 Wrinkledlaminar flame 39, 117, 129, 131,132, 134, 136, 137, 139, 140, 151,166, 176, 229 laminar flame, theories of 133-136 see also Laminar flame Zeldovich chain reactions 87

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