PDF methods for turbulent reactive flows

Turbulent jet diffusion flames

Counterflow diffusion flames

An approach to the autoignition of a turbulent mixture

A Langevin model appropriate to constant property turbulent flows is developed from the general equation for the fluid particle velocity increment proposed by Pope in an earlier paper [Phys. Fluids 26, 404 (1983)]. This model can be viewed as an analogy between the turbulent velocity of a fluid particle and the velocity of a particle undergoing Brownian motion. It is consistent with Kolmogorov’s inertial range scaling, satisfies realizability, and is consistent with second‐order closure models. The objective of the present work is to determine the form of a second‐order tensor appearing in the general model equation as a function of local mean quantities. While the model is not restricted to homogeneous turbulence, the second‐order tensor is evaluated by considering the evolution of the Reynolds stresses in homogeneous flows. A functional form for the tensor is chosen that is linear in the normalized anisotropy tensor and in the mean velocity gradients. The resulting coefficients are evaluated by matching the modeled Reynolds stress evolution to experimental data in homogeneous flows. Constraints are applied to ensure consistency with rapid distortion theory and to satisfy a consistency condition in the limit of two‐dimensional turbulence. A set of coefficients is presented for which the model yields good agreement with available data in homogeneous flows.

A generalized Langevin model for turbulent flows

The electrical behavior of weakly ionized, compressible gases flowing along a solid boundary is studied. Analysis is made for flows wherein the range of electrical effects, such as the sheath thickness, is much greater than the mean free path between the charged and the neutral‐gas particles. The relationships between the surface potential, currents, and the boundary‐layer flow parameters are analyzed.

Electrical Characteristics of Couette and Stagnation Boundary‐Layer Flows of Weakly Ionized Gases

The simplified statistical theory developed previously is employed to analyze the equilibrium and near‐equilibrium combustion of initially unmixed reactants. It is found that the flame zone in the limit of large Damkohler numbers is very thick and is of the order of the local integral scale of turbulence. This is in contrast to the existing phenomenological theories which predict the infinitesimally thin flame sheet, in the same limit, as it is with the laminar diffusion flame. Qualitative agreements with the available experimental results are shown. It is found that singularities exist at the edges of the flame which are removed as Damkohler number is reduced. Also, it is found that the heat transfer may take place against the local mean temperature gradient in certain regions within the flame.

Diffusion flame in homologous turbulent shear flows.

A simplified statistical theory is developed which describes the chemically reacting, turbulent shear flows in a tractable manner. This theory, which is based on the concept of the generalized Brownian motion, instead of Navier‐Stokes equation, is completely self‐containing provided that the molecular Schmidt number is of order one and that the local turbulence Reynolds number is sufficiently large. The latter requirement restricts the theory to the flow region outside of the laminar sublayers. The homologous flow and concentration fields are first analyzed for the chemically frozen case. From the analyses, the relationships between the mean velocity and concentration gradients, and the Reynolds stress, turbulence energy, turbulent transport of chemical species, and the mean square fluctuation of the species concentration are established. Comparison of the present results with the available experimental data is made, which shows a satisfactory agreement. The nonequilibrium chemical reaction is then analyzed and is found to create an inhomogeneity in the concentration field which, among other things, causes the mean square fluctuation to vary nonuniformly with respect to the Damkohler number and the flow region.

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Chemical reaction in a turbulent flow field with uniform velocity gradient

The paper examines the mathematical and physical foundations for the kinetic theory of reactive turbulent flows, discussing the differences and relation between the kinetic and averaged equations, and comparing some solutions of the kinetic equations obtained by the Green's function method with those obtained by the approximate bimodal method. The kinetic method described consists essentially in constructing the probability density functions of the chemical species on the basis of solutions of the Langevin stochastic equation for the influence of eddies on the behavior of fluid elements. When the kinetic equations are solved for the structure of the diffusion flame established in a shear layer by the bimodal method, discontinuities in gradients of the mean concentrations at the two flame edges appear. This is a consequence of the bimodal approximation of all distribution functions by two dissimilar half-Maxwellian functions, which is a very crude approximation. These discontinuities do not appear when the solutions are constructed by the Green's function method described here.

A kinetic-theory approach to turbulent chemically reacting flows

The simplified statistical theory developed earlier is extended to the wall shear flows. This is accomplished by formulating the contribution of the smaller eddies to the observable properties, which becomes significant very close to the wall, from an available stochastic analysis of the Navier‐Stokes equation. Turbulent Couette flow is then analyzed by the use of the theory. Comparison of the Couette flow solutions obtained with the available experimental results shows that the present theory satisfactorily describes the rather detailed turbulence structure of the flow field as well as the mean velocity profile and the surface shear.

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Paul M. Chung

Papers

Electrical Characteristics of Couette and Stagnation Boundary‐Layer Flows of Weakly Ionized Gases

Diffusion flame in homologous turbulent shear flows.

Chemical reaction in a turbulent flow field with uniform velocity gradient

A kinetic-theory approach to turbulent chemically reacting flows

Turbulence description of Couette flow