Turbulent flow modeling mixing length model

As mentioned above, numerical computations were carried out [5, 6] based on a k-e model by Jones-Launder. This model has a more general description for turbulence than the mixing length models. Effects of buoyancy force and fluid expansion on the heat transfer to normal fluids are successfully analyzed by the k-e model. Thermophysical properties are treated as variables in the governing equations and evaluated from a steam table library. Thus, extremely nonlinear thermophysical properties of supercritical water are evaluated directly and correctly. This approach is applicable to a wide range of flow conditions of supercritical water. Many cases of different inlet temperatures can be calculated and the relation between the heat transfer coefficient and the bulk enthalpy can be obtained in a wide range. 

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. 

As seen in Chapter 2 for turbulent flow, the length-scale information needed to describe a homogeneous scalar field is contained in the scalar energy spectrum E k, t), which we will look at in some detail in Section 3.2. However, in order to gain valuable intuition into the essential physics of scalar mixing, we will look first at the relevant length scales of a turbulent scalar field, and we develop a simple phenomenological model valid for fully developed, statistically stationary turbulent flow. Readers interested in the detailed structure of the scalar fields in turbulent flow should have a look at the remarkable experimental data reported in Dahm et al. (1991), Buch and Dahm (1996) and Buch and Dahm (1998). 

The last term in the momentum equation, i.e., Eq. (9.78). represents the affect of the buoyancy forces on the mean momentum balance. However, these buoyancy forces also affect the variation of e and e in the flow. To illustrate how the buoyancy forces can effect e and e, consider again the simple mixing length model discussed in Chapter 5. Lumps or eddies of fluid are assumed to move across the flow through a transverse distance, lm, while retaining their initial velocity and temperature. They then interact with the local fluid layer giving rise to the fluctuations in velocity and temperature that occur in turbulent flow. 

A numerical procedure for calculating the heat transfer rate with turbulent boundary layer flow was discussed in Chapter 5. This procedure used a mixing length-based turbulence model. Discuss the modifications that must be made to this procedure to apply it to mixed convective flow over a vertical plate. 

Turbulent flows with simple closure models (eddy viscosity, mixing length, k-e) or complex closure models (ASM, RSM, RNG) for the Reynolds stresses... 

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