Boundary layers viscous sublayer

However, the molecules percolating up into the boundary layer from beneath the soil surface tend to become trapped in the stagnant laminar sublayer of the boundary layer. This sublayer is usually much thinner than the overall turbulent boundary layer, since it is dominated by viscous and surface tension forces, rather than by velocity. Phelan and Webb call this the chemical boundary layer and state categorically that there will generally be no chemical signature above this chemical boundary layer [1, p. 52],... 

As the fluid s velocity must be zero at the solid surface, the velocity fluctuations must be zero there. In the region very close to the solid boundary, ie the viscous sublayer, the velocity fluctuations are very small and the shear stress is almost entirely the viscous stress. Similarly, transport of heat and mass is due to molecular processes, the turbulent contribution being negligible. In contrast, in the outer part of the turbulent boundary layer turbulent fluctuations are dominant, as they are in the free stream outside the boundary layer. In the buffer or generation zone, turbulent and molecular processes are of comparable importance. 

Equation 2.40 is an empirical equation known as the one-seventh power velocity distribution equation for turbulent flow. It fits the experimentally determined velocity distribution data with a fair degree of accuracy. In fact the value of the power decreases with increasing Re and at very high values of Re it falls as low as 1/10 [Schlichting (1968)]. Equation 2.40 is not valid in the viscous sublayer or in the buffer zone of the turbulent boundary layer and does not give the required zero velocity gradient at the centre-line. The l/7th power law is commonly written in the form... 

Consider a fully developed turbulent flow through a pipe of circular cross section. A turbulent boundary layer will exist with a thin viscous sublayer immediately adjacent to the wall, beyond which is the buffer or generation layer and finally the fully turbulent outer part of the boundary layer. 

Conditions in the fully turbulent outer part of the turbulent boundary layer are quite different. In a turbulent fluid, the shear stress f is given by equation 1.95. As illustrated in Example 1.10, outside the viscous sublayer and buffer zone the eddy kinematic viscosity e is much greater than the molecular kinematic viscosity v. Consequently equation 1.95 can be written as... 

The changing character of the flow in the different regions of the turbulent boundary layer explains certain aspects of the friction factor chart. If the absolute roughness of the pipe wall is smaller than the thickness of the viscous sublayer, flow disturbances caused by the roughness will be damped out by viscosity. The wall is subject to a viscous shear stress. Under these conditions, the line on the friction factor chart... 

While the viscous sublayer may be important for momentum transport, it is everything for mass and heat transport through liquids. Virtually the entire concentration boundary layer is within the viscous sublayer This difference is important in our assumptions related to interfacial transport, the topic of Chapter 8, where mass is transported through an interfacial boundary layer. 

The penetration theory is attributed to Higbie (1935). In this theory, the fluid in the diffusive boundary layer is periodically removed by eddies. The penetration theory also assumes that the viscous sublayer, for transport of momentum, is thick, relative to the concentration boundary layer, and that each renewal event is complete or extends right down to the interface. The diffusion process is then continually unsteady because of this periodic renewal. This process can be described by a generalization of equation (E8.5.6) ... 

Figure 6.8 Conceptual diagram of the different scales of the components of the benthic boundary layer (BBL). In bottom water above the sediment-water interface where the Eckman layer occurs as flow is affected by the rotation of the Earth and bottom friction, where w = friction velocity and / = Coriolis parameter the logarithmic layer predominates when the velocity profile is well described using a logarithmic function a viscous sublayer is formed by molecular viscosity a diffusive boundary layer forms, whereby solute transport is controlled by molecular diffusion. (Modified from Boudreau and Jprgensen, 2001.)...

The zones where these gradients occur are often called boundary layers. For example, the aerodynamic boundary layer is the region near a surface where viscous forces predominate. Boundary layers exist with both laminar and turbulent flow and may be either solely laminar or turbulent with a laminar sublayer themselves (Landau and Lifshitz, 1959). 

A turbulent boundary layer is actually made up of three zones, a viscous or laminar sublayer immediately adjoining the wall, a buffer zone, and finally a turbulent zone making up the main boundary layer (Schlicting, 1968). Generally speaking, turbulent boundary layers are thicker than laminar boundary layers. 

Turbulent flow over a flat plate is characterized by three re-gions f l (a) a viscous sublayer often called the laminar sublayer, which exists right next to the plate, (b) an adjacent turbulent boundary layer, and (c) the turbulent core. Viscous forces dominate inertial forces in the viscous sublayer, which is relatively quiescent compared to the other regions and is therefore also called the laminar sublayer. This is a bit of a misnomer, since it is not really laminar. It is in this viscous sublayer that the velocity changes are the greatest, so that the shear is largest. Viscous forces become less dominant in the turbulent boundary layer. These forces are not controlling factors in the turbulent core. 

The thin fluid layer in the immediate neighborhood of the solid surface is called the fluid film [32]. In this connection, there are instances where the fluid film is referred to as the laminar film, the boundary layer or the viscous sublayer. 

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. 

Farther away from the surface the fluid velocities, though less than the velocity of the undisturbed fluid, may be fairly large, and flow in this part of the boundary layer may become turbulent. Between the zone of fully developed turbulence and the region of laminar flow is a transition, or buffer, layer of intermediate character. Thus a turbulent boundary layer is considered to consist of three zones the viscous sublayer, the buffer layer, and the turbulent zone. The existence of a completely viscous sublayer is questioned by some, since mass transfer studies suggest that some eddies penetrate all the way through the boundary layer and reach the wall. 

The viscous sublayer occupies only a very small fraction of the total cross section. It has no sharp upper boundary, and its thickness is difficult to define. A transition layer exists immediately adjacent to the viscous sublayer in which both viscous shear and shear due to eddy diffusion exist. The transition layer, which is sometimes called a buffer layer, also is relatively thin. The bulk of the cross section of the flowing stream is occupied by entirely turbulent flow called the turbulent core. In the turbulent core viscous shear is negligible in comparison with that from eddy viscosity. 

Surface Roughness. Up to this point, the turbulent boundary layer has been assumed to form on a surface that is aerodynamically smooth, namely, a surface whose roughness elements are small compared with the thickness of the viscous sublayer. As many surfaces in practical appli-... 

A viscous boundary layer adjacent to the surface of some obstacle on which deposition is occurring is an impediment to all depositing species, regardless of the orientation of the target surface. Molecular (and Brownian) diffusion occurs independently of direction molecular diffusion can occur to the underside of a leaf just as easily as it can to the top surface. The flux across the quasi-laminar sublayer adjacent to the surface is expressed in terms of a dimensionless transfer coefficient, B, multiplying the concentration difference across the layer, C2 — Cj. Since, under steady-state conditions, this flux is equal to that across each layer, we write... 

The border diffusion layer model was introduced as an amendment to the film model to present a more realistic description. It accounts for an undefined film thickness, turbulence effects, and the role of molecular diffusion. When the flow is turbulent, the flow around the bubble is split into four sections the main turbulent stream, the turbulent boundary layer, the viscous sublayer, and the diffusion sublayer. Eddy turbulence accounts for mass transfer in the main turbulent stream and the turbulent boundary layer. The viscous sublayer limits eddy turbulence effects so that the flow is laminar and mass transfer is controlled by both molecular diffusion and eddy turbulence. Microscale eddy turbulence is assumed to be dominant in the viscous sublayer. Mass transfer in the diffusion sublayer is controlled almost completely by molecular diffusion (Azbel, 1981). 

The basic turbulence structure is assumed to be similar to that in Newtonian boundary layers, in that there exist three regions the viscous sublayer, which is the closest to the wall, and where the dissipative forces dominate a logarithmic region and the buffer layer between the two. Large eddies... 

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