Models of turbulence

B. E. Launder and D. B. Spalding, Mathematical Models of Turbulence, Academic Press, Inc., New York, 1972. 

The physics and modeling of turbulent flows are affected by combustion through the production of density variations, buoyancy effects, dilation due to heat release, molecular transport, and instabiUty (1,2,3,5,8). Consequently, the conservation equations need to be modified to take these effects into account. This modification is achieved by the use of statistical quantities in the conservation equations. For example, because of the variations and fluctuations in the density that occur in turbulent combustion flows, density weighted mean values, or Favre mean values, are used for velocity components, mass fractions, enthalpy, and temperature. The turbulent diffusion flame can also be treated in terms of a probabiUty distribution function (pdf), the shape of which is assumed to be known a priori (1). 

In general, comprehensive, multidimensional modeling of turbulent combustion is recognized as being difficult because of the problems associated with solving the differential equations and the complexities involved in describing the interactions between chemical reactions and turbulence. A number of computational models are available commercially that can do such work. These include FLUENT, FLOW-3D, and PCGC-2. 

The Prandtl mixing length concept is useful for shear flows parallel to walls, but is inadequate for more general three-dimensional flows. A more complicated semiempirical model commonly used in numerical computations, and found in most commercial software for computational fluid dynamics (CFD see the following subsection), is the A — model described by Launder and Spaulding (Lectures in Mathematical Models of Turbulence, Academic, London, 1972). In this model the eddy viscosity is assumed proportional to the ratio /cVe. 

Patel, B. R. and Sheikoholeslami, Z., Numerieal modelling of turbulent flow through the orifiee meter. International Symposium on Fluid Flow Measurement, Washington, D.C., November 1986. 

Peng, S. H. Modeling of turbulent flow and heat transfer for building ventilation. Ph.D. thesis, Dept, of Thermo and Fluid Dynamics, Chalmers University of Technology, Gothenburg, 1998. 

Computational fluid dynamics (CFD) is the numerical analysis of systems involving transport processes and solution by computer simulation. An early application of CFD (FLUENT) to predict flow within cooling crystallizers was made by Brown and Boysan (1987). Elementary equations that describe the conservation of mass, momentum and energy for fluid flow or heat transfer are solved for a number of sub regions of the flow field (Versteeg and Malalase-kera, 1995). Various commercial concerns provide ready-to-use CFD codes to perform this task and usually offer a choice of solution methods, model equations (for example turbulence models of turbulent flow) and visualization tools, as reviewed by Zauner (1999) below. 

Magnussen, B. F., and B. H. Hjertager. 1976. On the mathematical modelling of turbulent combustion with special emphasis on soot formation and combustion. 16th Symp. (Int.) on Combustion, pp. 719-729. The Combustion Institute, Pittsburgh, PA. 

Wilson, K. C. and Puoh, F. ]. Can. Ji. Chem. Eng. 66 (1988) 721. Dispersive-force modelling of turbulent suspensions in heterogeneous slurry flow. 

The counterflow configuration has been extensively utilized to provide benchmark experimental data for the study of stretched flame phenomena and the modeling of turbulent flames through the concept of laminar flamelets. Global flame properties of a fuel/oxidizer mixture obtained using this configuration, such as laminar flame speed and extinction stretch rate, have also been widely used as target responses for the development, validation, and optimization of a detailed reaction mechanism. In particular, extinction stretch rate represents a kinetics-affected phenomenon and characterizes the interaction between a characteristic flame time and a characteristic flow time. Furthermore, the study of extinction phenomena is of fundamental and practical importance in the field of combustion, and is closely related to the areas of safety, fire suppression, and control of combustion processes. 

Vermorel, O., et al.. Numerical study and modelling of turbulence modulation in a particle laden slab flow. /. Turbulence, 2003. 4(25) l-39. 

Launder, B. E., and Spalding, D. B., Lectures in Mathematical Models of Turbulence . Academic Press, London p. 1 (1972). 

The divergence of (4.21) yields a Poisson equation for p. However, the residual stress tensor r6 is unknown because it involves unresolved SGS terms (i.e., UfiJfi). Closure of the residual stress tensor is thus a major challenge in LES modeling of turbulent flows. 

Besnard, D. C., F. H. Harlow, R. M. Rauenzahn, and C. Zemach (1990). Spectral transport model of turbulence. Report LA-11821-MS, Los Alamos National Laboratory. 

Biagioli, F. (1997). Modeling of turbulent nonpremixed combustion with the PDF transport method comparison with experiments and analysis of statistical error. In G. D. Roy, S. M. Frolow, and P. Givi (eds.), Advanced Computation and Analysis of Combustion. ENAS Publishers. 

Chen, J. Y., W. Kollmann, and R. W. Dibble (1989). PDF modeling of turbulent nonpremixed methane jet flames. Combustion Science and Technology 64, 315-346. 

Flagan, R. C. and J. P. Appleton (1974). A stochastic model of turbulent mixing with chemical reaction Nitric oxide formation in a plug-flow burner. Combustion and Flame 23, 249-267. 

Kerstein, A. R. (1988). A linear-eddy model of turbulent scalar transport and mixing. 

Linear-eddy modeling of turbulent transport. II Application to shear layer mixing. 

Linear-eddy modelling of turbulent transport. Part 3. Mixing and differential diffusion in round jets. Journal of Fluid Mechanics 216, 411 —4-35. 

An introduction to single-point closure methodology. In T. B. Gatski, M. Y. Hussaini, and J. L. Lumley (eds.), Simulation and Modeling of Turbulent Flows, chap. 6, pp. 243-310. New York Oxford University Press. 

McMurtry, P. A., S. Menon, and A. R. Kerstein (1993). Linear eddy modeling of turbulent combustion. Energy and Fuels 7, 817-826. 

Meneveau, C., T. S. Lund, and W. Cabot (1996). A Lagrangian dynamic subgrid-scale model of turbulence. Journal of Fluid Mechanics 319, 353-385. 

Schiestel, R. (1987). Multiple-time-scale modeling of turbulent flows in one-point closures. 

Ramaekers, W.J.S. The application of flamelet generated manifolds in modeling of turbulent partially-premixed flames, MSc thesis, Eindhoven University of Technology, Eindhoven, The Netherlands, (2005). 

Lumley, J. L., and Khajeh-Nouri, B. (1974). Computational modeling of turbulent transport. Adv. Geophys. 18A, 169-192. 

Kosaly, G. 1986. Theoretical remarks on a phenomenological model of turbulent mixing. Combustion Science Technology 49 227-34. 

Kosaly, G., and P. Givi. 1987. Modeling of turbulent molecular mixing. Combustion Flame 70 101-18. 

Launder, B.E., and D.B. Spalding. 1972. Lectures in mathematical modeling of turbulence. London, UK Academic Press. 

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