Mixing and Chemical reactions under turbulent flow conditions are a basic feature of the energy release processes in many combustion and propulsion systems. The development of predictive calculation procedures for these systems requires the understanding and modeling of coupling between turbulence and various physical and chemical processes. Second-order closure modeling of turbulent flows provides a rational framework for studying these interactions. Models for the scalar probability density function (pdf) have to be developed to achieve closure of turbulent transport equations for mixing and reacting flows. A delta function 'typical eddy' pdf model for two species flows has been developed and incorporated into a complete second-order closure computer program. The program has been used to study uniform and variable density flowfields and the model predictions have been compared to experimental measurements. The modeling of turbulence dynamics for variable density flows requires further improvement. However, the importance of modeling the higher-order scalar correlations has been demonstrated. A number of statistical constraints on three species flowfields have also been derived. These will be useful in the development of the 'typical eddy' pdf modelfor reacting flows. (Author).

The first part aims at providing the physical and theoretical framework of the analysis of density variations in fully turbulent flows. Its scope is deliberately educational. In the second part, basic data on dynamical and scalar properties of variable density turbulent flows are presented and discussed, based on experimental data and/or results from direct numerical simulations. This part is rather concerned with a research audience. The last part is more directly devoted to an engineering audience and deals with prediction methods for turbulent flows of variable density fluid. Both first and second order, single point modeling are discussed, with special emphasis on the capability to include specific variable density / compressibility effects.

Turbulent flows involving chemical reactions are a basic feature of many combustion and propulsion systems. The development of calculation procedures for turbulent reacting flows requires the understanding and modeling of the coupling between turbulence and combustion. Second-order closure modeling of turbulent flows provides a convenient framework for studying these interactions between turbulence and chemical reactions. Models for the scalar probability density function (pdf) have to be developed to achieve closure of turbulent transport equations for mixing and reacting flows. A delta function 'typical eddy' model has been developed for the joint pdf of the scalar variables. It has been demonstrated that delta functions are a necessary part of pdf's in order to attain the extremums of the statistical constraints on the moments. The statistical bounds on a number of moments of interest have been derived. It has been proven that a rational pdf composed of a set of delta functions alone can always be constructed at any point within the statistically valid moment space. The model provides a good representation of actual pdf's in two-species, variable-density mixing flows. The model has been directly compared to experimental pdf measurements and good agreement for higher-order moments has been demonstrated. It can be shown that the delta function pdf model is significantly simpler than other proposed pdf models and is more than adequate for the closure of the transport equations. (Author).

Focuses on the second-order turbulence-closure model and its applications to engineering problems. Topics include turbulent motion and the averaging process, near-wall turbulence, applications of turbulence models, and turbulent buoyant flows.

This title provides the fundamental bases for developing turbulence models on rational grounds. The main different methods of approach are considered, ranging from statistical modelling at various degrees of complexity to numerical simulations of turbulence. Each of these various methods has its own specific performances and limitations, which appear to be complementary rather than competitive. After a discussion of the basic concepts, mathematical tools and methods for closure, the book considers second order closure models. Emphasis is placed upon this approach because it embodies potentials for clarifying numerous problems in turbulent shear flows. Simpler, generally older models are then presented as simplified versions of the more general second order models. The influence of extra physical parameters is also considered. Finally, the book concludes by examining large Eddy numerical simulations methods. Given the book’s comprehensive coverage, those involved in the theoretical or practical study of turbulence problems in fluids will find this a useful and informative read.

A second order closure turbulence model for compressible flows is developed and implemented in a 2D Reynolds-averaged Navier-Stokes solver. From the beginning where a kappa-epsilon turbulence model was implemented in the bidiagonal implicit method of MACCORMACK (referred to as the MAC3 code) to the final stage of implementing a full second order closure in the efficient line Gauss-Seidel algorithm, numerous work was done, individually and collectively. Besides the collaboration itself, the final product of this work is a second order closure derived from the Launder, Reece, and Rodi model to account for near wall effects, which has been called FRAME model, which stands for FRench-AMerican-Effort. During the reporting period, two different problems were worked out. The first was to provide Ames researchers with a reliable compressible boundary layer code including a wide collection of turbulence models for quick testing of new terms, both in two equations and in second order closure (LRR and FRAME). The second topic was to complete the implementation of the FRAME model in the MAC5 code. The work related to these two different contributions is reported. dilatation in presence of stron shocks. This work, which has been conducted during a work at the Center for Turbulence Research with Zeman aimed also to cros-check earlier assumptions by Rubesin and Vandromme. Haminh, Hieu and Kollmann, Wolfgang and Vandromme, Dany Unspecified Center...

The General Assembly of the International Union of Theoretical and Applied Mechanics in its meeting on August 28, 1994, selected for 1996 only four Mechanics Symposia, of which ours is the only one related to Fluid Mechanics: Variable Density Low Speed Turbulent Flows. This IUTAM Symposium, organized by the Institut de Recherche sur les Phenomenes Hors Equilibre (Marseille), is the logical continuation of the meetings previously organized or co-organized - on the French or European level, such as Euromech 237, Marseille, 1988 - by the same research group ofMarseille. This meeting focused specifically on the structure of turbulent flows in which density varies strongly : the effect of this variation on the velocity and scalar fields is in no sense negligible. We were mainly concerned with low-speed flows subjected to strong local changes of density as a consequence of heat or mass transfer or of chemical reactions. Compressible turbulent flows - such a!" supersonic ones - were also considered in order to underline their similarities to and their differences from low-speed variable density flows.