Turbulence inner wall layer

Intuitively one could imagine that the boundary layer as a whole can be characterized in terms of the boundary layer thickness and related dimensionless groups. However, experimental data reveals that the laminar shear is dominant near the wall (i.e., in the inner wall layer), and turbulent shear dominates in the outer wall layer. There is also an intermediate region, called the overlap wall region, where both laminar and turbulent shear are important. 

Essentially, except for once-through boilers, steam generation primarily involves two-phase nucleate boiling and convective boiling mechanisms (see Section 1.1). Any deposition at the heat transfer surfaces may disturb the thermal gradient resulting from the initial conduction of heat from the metal surface to the adjacent layer of slower and more laminar flow, inner-wall water and on to the higher velocity and more turbulent flow bulk water. 

For the turbulent part of the inner boundary layer close to solid walls we usually adopt another closure for the Reynolds stresses and neglect the molecular diffusion term. The starting point for the boundary layer analysis, to be discussed shortly, is thus the fc-equation in the following form ... 

In this section the heat and mass transport coefficients for turbulent boundary layers are examined. In this case the model derivation is based on the governing Reynolds averaged equations. In these equations statistical covariances appear which involve fluctuating velocities, temperatures and concentrations. The nature of these terms is not known a priori and their effects must by estimated by semi-empirical turbulence modeling. The resulting parameterizations allow us to express the unknown turbulent fluctuations in terms of the mean flow field variables. It is emphasized that the Reynolds equations are not actually solved, merely semi-empirical relations are derived for the wall fluxes through the inner boundary layer. 

It has been shown that there exists a continuous change in the physical behavior of the turbulent momentum boundary layer with the distance from the wall. The turbulent boundary layer is normally divided into several regions and sub-layers. It is noted that the most important region for heat and mass transfer is the inner region of the boundary layer, since it constitutes the major part of the resistance to the transfer rates. This inner region determines approximately 10 — 20% of the total boundary layer thickness, and the velocity distribution in this region follows simple relationships expressed in the inner variables as defined in sect 1.3.4. 

The charts in this Chapter show how to estimate the optimum thickness of one layer of an insulator for both stagnant and turbulent air conditions. They are based on neglecting the resistances caused by both the metal and the inside film at the inner wall. 

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). 

In boundary-layer calculations, most workers simply use zonal models, with Eq. (9) in the inner region [which becomes Eq. (8) further from the wall] and something like Eq. (7) in the outer portion of the flow. Byrne and Hatton (B5) use a three-layer model as the basis for vt assumptions. Mellor and Herring (M2) have used concepts from the theory of matched asjTnptotic expansions to obtain composite representation for I valid across an entire turbulent boundary layer. A t j"pical distribution of 1 in a boundary layer is shown in Fig. 5. 

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). 

The viscous sub-layer is defined as the region next to the wall where the first term on the RHS of (1.362) is dominant. For larger values of y, the second term on the RHS of (1.362) will become dominant, and this region is usually referred to as the the inertial - or turbulent log-law sub-layer. Evidently there will be an intermediate region where the two stresses will be of equal magnitude, and this transition sub-layer is called the buffer layer. This boundary layer theory is based on the assumption that the effective shear stress is constant throughout the inner layer. 

In summary, experimental data indicates that the turbulent boundary layer can be subdivided into an inner constant wall stress layer for the approximate range 0 < < 0.1(5, and an outer non-constant stress layer bounded by... 

A common simplification adopted in many engineering CFD calculations is to neglect the influence of the deviating physics occurring in the buffer-layer. The inner part of the boundary layer is thus roughly subdivided into two more approximate sub-layers only, those are a viscous - and a turbulent sub-layer. The two sub-layers are separated at a certain distance from the wall... 

In this paragraph the wall function concept is outlined. The wall functions are empirical parameterizations of the mean flow variable profiles within the inner part of the wall boundary layers, bridging the fully developed turbulent log-law flow quantities with the wall through the viscous and buffer sublayers where the two-equation turbulence model is strictly not valid. These empirical parameterizations thus allow the numerical flow simulation to be carried out with a finite resolution within the wall boundary layers, and one avoids accounting for viscous effects in the model equations. Therefore, in the numerical implementation of the k-e model one anticipates that the boundary layer flow is not fully resolved by the model resolution. The first grid point or node used at a wall boundary is thus placed within the fully turbulent log-law sub-layer, rather than on the wall itself [95]. In effect, the wall functions amount to a synthetic boundary condition for the k-e model. In addition, the limited boundary layer resolution required also provides savings on computer time and storage. 

The irregularity in the color of the outer isosurface appears to indicate wave-like fluctuations in the near-wall pressure, i.e. near-wall turbulent boundary layer structures, consistent with what has been stated about the instability of the near-wall flow in Sect. 3.1.1. The low pressure in the inner part of the vortex and in the vortex finder is clearly to be seen. A very low pressure can be seen also to exist in the apex of the cone. Its location is consistent with what is seen experimentally when the vortex extends to the bottom of the cyclone, not terminating upon a vortex stabilizer or due to the natural... 

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