Statistical Mechanics of Turbulent Flows

About this book

The simulation of turbulent reacting flows, connected with environmental protection and the design of chemical and mechanical processes, is increasingly important. Statistical Mechanics of Turbulent Flows presents a modern overview of basic ways to calculate such flows. It discusses the fundamental problems related to the use of basic equations and their modifications. Special emphasis is placed on the discussion of very promising statistical methods which provide solutions to these problems by models for the underlying stochastic physics of turbulent reacting flows. Their foundations and important new developments up through current challenges are systematically explained. Students and researchers in atmospheric sciences and oceanography, mechanical and chemical engineering and applied mathematics and physics may use Statistical Mechanics of Turbulent Flows as a guide to solve many problems related, e.g. to the assessment of complex atmospheric chemistry, chemical reactor processes, turbulent combustion, and multi-phase flows.

Contents

Introduction: The basic equations; Turbulence models; Filter operations.- Stochastic variables: PDFs of one variable; The characterization of PDFs by moments; PDFs of several variables; Statistically most-likely PDFs; Examples for statistically most-likely PDFs; Examples for other PDFs; Theta and delta functions.- Stochastic processes: PDF transport equations; The Fokker-Planck equation; An exact solution to the Fokker-Planck equation; Stochastic equations for realizations; Stochastic modeling; The dynamics of relevant variables.- The equations of fluid and thermodynamics: The fluid dynamic variables; From the molecular to fluid dynamics; The closure of the fluid dynamic equations; The equations for multicomponent reacting systems; Direct numerical simulation; Reynolds-averaged Navier-Stokes equations; Second- and higher-order RANS equations.- Stochastic models for large-scale turbulence: A hierarchy of stochastic velocity models; The generalized Langevin model for velocities; A hierarchy of Langevin models; The Kolmogorov constant; A hierarchy of stochastic models for scalars; Compressible reacting flow: velocity models; Compressible reacting flow: scalar models; Stochastic models and basic equations; Consistent turbulence models; Nonlinear stochastic models.- Stochastic models for small-scale turbulence: The generalization of LES by FDF methods; The closure of the equation for filtered velocities; The closure of the scalar FDF transport equation; The closure of LES and FDF equations; The dynamic eddy length scale calculation; The scalar-conditioned convective flux; An assumed-shape FDF method.- The unification of turbulence models: The need for the unification of turbulence models; Unified turbulence models; Some unsolved questions. References.- Author index.- Subject index.

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