Near-wall region

The near-wall region is conceptually subdivided into three layers, based on experimental evidence. The innermost layer is the viscous sublayer in which the flow is almost laminar, and the molecular viscosity plays a dominant role. The outer layer is considered to be fully turbulent. The buffer layer lies between... 

The viscosity-affected region is not The near-wall region is resolved... 

The turbulence models ought to be valid throughout the near-wall region. 

The second picture in Fig. 18 shows a temperature map for a vertical plane in the middle of the WS. The tube wall is to the right of the picture, and the scale has been chosen to emphasize the temperature gradients in the near-wall region. 

However, at low Reynolds number (e.g., the near-wall region), the dissipation tensor can be highly anisotropic and other models are required (Pope 2000). For example, a simple extension of (4.53) yields (Rotta 1951)... 

Owing to these unique characteristics, additional wall-reflection terms are required in the pressure redistribution model in order to obtain satisfactory agreement with data for the impinging jet flow. A detailed discussion of RANS models that employ a more physically realistic description of the pressure fluctuations in the near-wall region can be found in Pope (2000). However, one obvious shortcoming of current wall models is that they typically depend explicitly on the unit normal to the wall, which makes it very difficult to apply them to complex geometries. 

Y. Nino, M.H. Garcia, Experiments on particle-turbulence interactions in the near-wall region of an open channel flow Implications for sediment transport, J. Fluid Mech. 326 (1996) 285-319. 

As the gas velocity increases, the solids holdup decreases and, thus, hgc begins to become as important as hpc. In the center region of the riser, hgc is dominant, and its influence decreases with an increase in the solids holdup along the radial direction toward the wall. In the near-wall region, hpc dominates the heat transfer. The contribution of hpc decreases with a decrease in the particle concentration toward the bed center. As a result, a minimum value of h appears at r/R of about 0.5-0.8, as indicated in Fig. 12.16(b). 

Derive the radial profile of the particle convective heat transfer coefficient in a circulating fluidized bed of fine particles using the information given in 10.4.2, and simplify the expression for the center region and the near-wall region, respectively. 

Numerous experiments have shown that the near-wall region can be divided into three layers (Fig. 3.5(a)). 

There are two main approaches to modeling the near-wall region. In one approach, the so-called wall function approach, the viscosity-affected inner regions (viscous and buffer layers) are not modeled. Instead, semi-empirical formulae (wall functions) are used to bridge the viscosity-affected region between the wall and the fully turbulent region. In another approach, special, low Reynolds number turbulence models are developed to simulate the near-wall region flow. These two approaches are shown schematically in Fig. 3.5(b) and 3.5(c). 

Since ample experimental analyzes support the Prandtl h3q)othesis, it is evident that close to the wall the viscosity, i/, and the wall shear stress, Cw, are important parameters. Prom these quantities one can define viscous scales that are appropriate velocity scales and length scales in the near-wall region. Dimensional analysis confirmed by experiments indicates that the relevant velocity scale for the inner region is the friction velocity, given by ... 

Let us then reconsider the near-wall region, beginning again with Eq. (4-16). Before proceeding, it is convenient to introduce a change of variables,... 

Rather than starting with the original dimensional equations and searching for an appropriate characteristic length scale for the near-wall region, we can determine the correct form by simply rescaling the previously nondimensionalized equation, (4-21). To do this, let us introduce a new independent spatial variable,... 

The coefficient a and the relevant form of the governing equations in the near-wall region are determined by substitution of (4-22) into (4-21), which thus becomes... 

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