Author

# Forman A. Williams

Other affiliations: University of California, University of California, Berkeley

Bio: Forman A. Williams is an academic researcher from University of California, San Diego. The author has contributed to research in topics: Combustion & Diffusion flame. The author has an hindex of 59, co-authored 374 publications receiving 13119 citations. Previous affiliations of Forman A. Williams include University of California & University of California, Berkeley.

##### Papers published on a yearly basis

##### Papers

More filters

•

01 Jan 1981

TL;DR: In this paper, the MBL-model of premixed Turbulent Combustion is used for variable density and combusting flow prediction and measurement in non-premixed flames.

Abstract: 1. Fundamental Aspects, Paul A Libby and F A Williams 2. Laminar Flamelets in Turbulent Flames, K N C Bray and Norbert Peters 3. Recent Developments in MBL-Model of Premixed Turbulent Combustion, K N C Bray and Paul A Libby 4. Reduced Chemical Systems and Their Application in Turbulent Combustion, K Seshadri and Forman A Williams 5. Comparison of Prediction and Measurement in Nonpremixed Turbulent Flames, J Y Chen and W Kollmann 6. Turbulence Modeling and Numerical Solution Methods for Variable Density and Combusting Flows, W P Jones 7. Recent Development in PDF Methods, Cesar Dopazo 8. Spectral and Random Vortex Methods in Turbulent Reacting Flows, Peyman Givi 9. Flames in Stagnating Turbulence, K N C Bray, M Champion and Paul A Libby 10. High Speed Turbulent Combustion, K N C Bray, Paul A Libby and Forman A Williams.

980 citations

••

TL;DR: In this paper, the effects of flow inhomogeneities on the dynamics of laminar flamelets in turbulent flames, with account taken of influences of the gas expansion produced by heat release, were investigated.

Abstract: To study effects of flow inhomogeneities on the dynamics of laminar flamelets in turbulent flames, with account taken of influences of the gas expansion produced by heat release, a previously developed theory of premixed flames in turbulent flows, that was based on a diffusive-thermal model in which thermal expansion was neglected, and that applied to turbulence having scales large compared with the laminar flame-thickness, is extended by eliminating the hypothesis of negligible expansion and by adding the postulate of weak-intensity turbulence. The consideration of thermal expansion motivates the formal introduction of multiple-scale methods, which should be useful in subsequent investigations. Although the hydrodynamic-instability mechanism of Landau is not considered, no restriction is imposed on the density change across the flame front, and the additional transverse convection correspondingly induced by the tilted front is described. By allowing the heat-to-reactant diffusivity ratio to differ slightly from unity, clarification is achieved of effects of phenomena such as flame stretch and the flame-relaxation mechanism traceable to transverse diffusive processes associated with flame-front curvature. By carrying the analysis to second order in the ratio of the laminar flame thickness to the turbulence scale, an equation for evolution of the flame front is derived, containing influences of transverse convection, flame relaxation and stretch. This equation explains anomalies recently observed at low frequencies in experimental data on power spectra of velocity fluctuations in turbulent flames. It also shows that, concerning the diffusive-stability properties of the laminar flame, the density change across the flame thickness produces a shift of the stability limits from those obtained in the purely diffusive-thermal model. At this second order, the turbulent correction to the flame speed involves only the mean area increase produced by wrinkling. The analysis is carried to the fourth order to demonstrate the mean-stretch and mean-curvature effects on the flame speed that occur if the diffusivity ratio differs from unity.

452 citations

••

377 citations

••

TL;DR: In this article, a statistical formalism for describing the behavior of sprays is presented, which includes the effects of droplet growth, the formation of new droplets, collisions, and aerodynamic forces.

Abstract: A statistical formalism for describing the behavior of sprays is presented, which includes the effects of droplet growth, the formation of new droplets, collisions, and aerodynamic forces. Criteria for the efficiency of impinging jet atomization are developed. It is shown that if the incident jets have a size distribution of a generalized Rosin‐Rammler type, then the resulting spray belongs to the same class of distributions. The size history of evaporating sprays is also obtained from the theory. A spray combustion analysis given by Probert is extended to include more general size distributions and the effects of droplet interactions and the relative motion of the droplets and the fluid. It is shown that the over‐all spray evaporation rate is largest for uniform sprays.

364 citations

•

01 Jan 1993

TL;DR: In this paper, the authors present Premixed Flames, Diffusion Flames, Flammability, Explosions, and Detonations, and Turbulent Combustion, and the Future.

Abstract: Introduction. 1: Premixed Flames. 2: Diffusion Flames. 3: Flammability, Explosions, and Detonations. 4: Turbulent Combustion. 5: The Future

300 citations

##### Cited by

More filters

••

TL;DR: While the book is a standard fixture in most chemical and physical laboratories, including those in medical centers, it is not as frequently seen in the laboratories of physician's offices (those either in solo or group practice), and I believe that the Handbook can be useful in those laboratories.

Abstract: There is a special reason for reviewing this book at this time: it is the 50th edition of a compendium that is known and used frequently in most chemical and physical laboratories in many parts of the world. Surely, a publication that has been published for 56 years, withstanding the vagaries of science in this century, must have had something to offer. There is another reason: while the book is a standard fixture in most chemical and physical laboratories, including those in medical centers, it is not as frequently seen in the laboratories of physician's offices (those either in solo or group practice). I believe that the Handbook can be useful in those laboratories. One of the reasons, among others, is that the various basic items of information it offers may be helpful in new tests, either physical or chemical, which are continuously being published. The basic information may relate

2,493 citations

••

TL;DR: The optical properties of light-absorbing, carbonaceous substance often called "soot", "black carbon", or "carbon black" have been the subject of some debate as discussed by the authors.

Abstract: The optical properties of the light-absorbing, carbonaceous substance often called “soot,” “black carbon,” or “carbon black" have been the subject of some debate. These properties are necessary to model how aerosols affect climate, and our review is targeted specifically for that application. We recommend the term light-absorbing carbon to avoid conflict with operationally based definitions. Absorptive properties depend on molecular form, particularly the size of sp 2-bonded clusters. Freshly-generated particles should be represented as aggregates, and their absorption is like that of particles small relative to the wavelength. Previous compendia have yielded a wide range of values for both refractive indices and absorption cross section. The absorptive properties of light-absorbing carbon are not as variable as is commonly believed. Our tabulation suggests a mass-normalized absorption cross section of 7.5 ± 1.2 m2/g at 550 nm for uncoated particles. We recommend a narrow range of refractive indices for s...

2,312 citations

••

TL;DR: In this paper, the steady laminar counterflow diffusion flame exhibits a very similar scalar structure as unsteady distorted mixing layers in a turbulent flow field, and the conserved scalar model is interpreted as the most basic flamelet structure.

1,933 citations

••

TL;DR: Chandrasekhar et al. as mentioned in this paper used the internal constitution of the stars to give a classical account of his own researches and of the general state of the theory at that time.

Abstract: EDDINGTON'S “Internal Constitution of the Stars” was published in 1926 and gives what now ranks as a classical account of his own researches and of the general state of the theory at that time. Since then, a tremendous amount of work has appeared. Much of it has to do with the construction of stellar models with different equations of state applying in different zones. Other parts deal with the effects of varying chemical composition, with pulsation and tidal and rotational distortion of stars, and with the precise relations between the interior and the atmosphere of a star. The striking feature of all this work is that so much can be done without assuming any particular mechanism of stellar energy-generation. Only such very comprehensive assumptions are made about the distribution and behaviour of the energy sources that we may expect future knowledge of their mechanism to lead mainly to more detailed results within the framework of the existing general theory. An Introduction to the Study of Stellar Structure By S. Chandrasekhar. (Astrophysical Monographs sponsored by The Astrophysical Journal.) Pp. ix+509. (Chicago: University of Chicago Press; London: Cambridge University Press, 1939.) 50s. net.

1,368 citations

••

01 Jan 1988TL;DR: In this article, it is shown that the inner structure of the flamelets is one-dimensional and time dependent, and a new coordinate transformation using the mixture fraction Z as independent variable leads to a universal description.

Abstract: The laminar flamelet concept covers a regime in turbulent combustion where chemistry (as compared to transport processes) is fast such that it occurs in asymptotically thin layers—called flamelets—embedded within the turbulent flow field. This situation occurs in most practical combustion systems including reciprocating engines and gas turbine combustors. The inner structure of the flamelets is one-dimensional and time dependent. This is shown by an asymptotic expansion for the Damkohler number of the rate determining reaction which is assumed to be large. Other non-dimensional chemical parameters such as the nondimensional activation energy or Zeldovich number may also be large and may be related to the Damkohler number by a distinguished asymptoiic limit. Examples of the flamelet structure are presented using onestep model kinetics or a reduced four-step quasi-global mechanism for methane flames. For non-premixed combustion a formal coordinate transformation using the mixture fraction Z as independent variable leads to a universal description. The instantaneous scalar dissipation rate χ of the conserved scalar Z is identified to represent the diffusion time scale that is compared with the chemical time scale in the definition of the Damkohler number. Flame stretch increases the scalar dissipation rate in a turbulent flow field. If it exceeds a critical value χ q the diffusion flamelet will extinguish. Considering the probability density distribution of χ , it is shown how local extinction reduces the number of burnable flamelets and thereby the mean reaction rate. Furthermore, local extinction events may interrupt the connection to burnable flamelets which are not yet reached by an ignition source and will therefore not be ignited. This phenomenon, described by percolation theory, is used to derive criteria for the stability of lifted flames. It is shown how values of ∋ q obtained from laminar experiments scale with turbulent residence times to describe lift-off of turbulent jet diffusion flames. For non-premixed combustion it is concluded that the outer mixing field—by imposing the scalar dissipation rate—dominates the flamelet behaviour because the flamelet is attached to the surface of stoichiometric mixture. The flamelet response may be two-fold: burning or non-burning quasi-stationary states. This is the reason why classical turbulence models readily can be used in the flamelet regime of non-premixed combustion. The extent to which burnable yet non-burning flamelets and unsteady transition events contribute to the overall statistics in turbulent non-premixed flames needs still to be explored further. For premixed combustion the interaction between flamelets and the outer flow is much stronger because the flame front can propagate normal to itself. The chemical time scale and the thermal diffusivity determine the flame thickness and the flame velocity. The flamelet concept is valid if the flame thickness is smaller than the smallest length scale in the turbulent flow, the Kolmogorov scale. Also, if the turbulence intensity v′ is larger than the laminar flame velocity, there is a local interaction between the flame front and the turbulent flow which corrugates the front. A new length scale L G =v F 3 /∈ , the Gibson scale, is introduced which describes the smaller size of the burnt gas pockets of the front. Here v F is the laminar flame velocity and ∈ the dissipation of turbulent kinetic energy in the oncoming flow. Eddies smaller than L G cannot corrugate the flame front due to their smaller circumferential velocity while larger eddies up to the macro length scale will only convect the front within the flow field. Flame stretch effects are the most efficient at the smallest scale L G . If stretch combined with differential diffusion of temperature and the deficient reactant, represented by a Lewis number different from unity, is imposed on the flamelet, its inner structure will respond leading to a change in flame velocity and in some cases to extinction. Transient effects of this response are much more important than for diffusion flamelets. A new mechanism of premixed flamelet extinction, based on the diffusion of radicals out of the reaction zone, is described by Rogg. Recent progress in the Bray-Moss-Libby formulation and the pdf-transport equation approach by Pope are presented. Finally, different approaches to predict the turbulent flame velocity including an argument based on the fractal dimension of the flame front are discussed.

1,268 citations