Turbulent region, fully

For Reynolds numbers > 1000, the flow is fully turbulent. Inertial forces prevail and becomes constant and equal to 0.44, the Newton region. The region in between Re = 0.2 and 1000 is known as the transition region andC is either described in a graph or by one or more empirical equations. 

In the fully turbulent region, / is independent of /VRe, so the Colebrook equation reduces to... 

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... 

To save computational effort, high-Reynolds number models, such as k s and its variants, are coupled with an approach in which the viscosity-affected inner region (viscous sublayer and buffer layer) are not resolved. Instead, semiempiri-cal formulas called wall functions are used to bridge the viscosity-affected region between the wall and the fully turbulent region. The two approaches to the sublayer problem are depicted schematically in Fig. 2 (Fluent, 2003). 

It is important to place the first near-wall grid node far enough away from the wall at yP to be in the fully turbulent inner region, where the log law-of-the-wall is valid. This usually means that we need y > 30-60 for the wall-adjacent cells, for the use of wall functions to be valid. If the first mesh point is unavoidably located in the viscous sublayer, then one simple approach (Fluent, 2003) is to extend the log-law region down to y — 11.225 and to apply the laminar stress-strain relationship U — y for y < 11.225. Results from near-wall meshes that are very fine using wall functions are not reliable. 

In the fully turbulent flow region DE, the curve becomes horizontal and the power function is independent of the Reynolds number for mixing ReM. For the region ReM > 10000... 

At still greater Reynolds numbers the boundary layer itself becomes turbulent and separation occurs at the rear of the sphere and closer to the particle. In this fully turbulent region, beyond Re = 2x 10 the drag coefficient falls further to a value of about 0.10. 

Several of these investigators have quoted an upper and lower critical value, enclosing a transition region, and Schoklitsch (S3) has given three values, the lowest, Nr = 144, at which turbulence could be first detected, the second, Nr0 = 389, at which the turbulent part of the flow became important, and an upper value, NRe = 900, at which the film became fully turbulent. ... 

I aminar flow, transition, and fully turbulent regions. 

Lastly, consider the outer, fully turbulent region which is assumed to exist when y+ >30. In this region it is assumed that e v and ew v, i.e., that in this region ... 

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). 

In reality the laminar sublayer is continuously transformed into the fully turbulent region. A transition region exists between the two, known as the buffer layer, so that the wall law of velocity can be split into three areas, whose boundaries are set by experimentation. The laminar sublayer extends over the region... 

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