Turbulent boundary layer eddy transport

The random eddy motion of groups of particles resembles the random motion of molecules in a gas—colliding with each other after traveling a certain distance and exchanging momentum and licat in the process. Therefore, momentum and beat transport by eddies in turbulent boundary layers is analogous to the molecular momentum and heat diffusion. Then turbulent wall shear stress and turbulent heat transfer can be expressed in an analogous manner as... 

The turbulent boundary layer model accounts for the transfer of a solute molecule A from a turbulent stream to a fixed surface. Eddy diffusion is rapid in the turbulent stream and molecular diffusion is relatively insignificant. It is supposed that the turbulence is damped out in the immediate vicinity of the surface. In the intermediate neighborhood between the turbulent stream and the fixed surface, it is supposed that transport is by both molecular and eddy diffusion which take place in parallel. The total rate of transfer (moles of A transferred per unit time per unit area) is given by an extended form of Fick s law... 

As mentioned previously, even when the flow becomes turbulent in the boundary layer, there exists a thin sub-layer close to the surface in which the flow is laminar. This layer and the fully turbulent regions are separated by a buffer layer, as shown schematically in Figure 7.1. In the simplified treatments of flow within the turbulent boundary layer, however, the existence of the buffer layer is neglected. In the laminar sub-layer, momentum transfer occurs by molecular means, whereas in the turbulent region eddy transport dominates. In principle, the methods of calculating the local values of the boundary layer thickness and shear stress acting on an immersed surface are similar to those used above for laminar flow. However, the main difficulty stems from the fact that the viscosity models, such as equations (7.13) or (7.27),... 

Mass and heat transfer to the walls in turbulent flows is a complex mixture of molecular transport and transport by turbulent eddies. The generally assumed analogy between mass and heat transfer by assuming Sh = Nu, is not valid for turbulent flows [26]. Simulations and measurements have shown that there is a laminar film close to the surface where most of the mass transfer resistance for high Sc liquids is located. This fUm is located below y+ = 1 and for low Sc fluids, and for heat transfer the whole boundary layer is important [27]. 

In summary, while most studies of atmospheric boundary layer flows have used local theories involving eddy transport coefficients, it is now recognized that turbulent transport coefficients are not strictly a local property of the mean motion but actually depend on the whole flow field and its time history. The importance of this realization in simulating mean properties of atmospheric flows depends on the particular situation. However, for mesoscale phenomena that display abrupt changes in boundary properties, as is often the case in an urban area, local models are not expected to be reliable. 

Particle deposition from a moving fluid involves two aspects. First the individual particles have to be transported to the surface by one or a combination of mechanisms, including Brownian motion, turbulent diffusion, and by virtue of the momentum possessed by the particle, as it is carried in the fluid stream. It will be appreciated that the size of the particle will exert a great influence on the dominant mechanism. Larger particles would be expected to move toward a surface, as a result of the momentum they possess. Finer particles with relatively low momentum can only approach the surface across the boundary layers, by Brownian or eddy diffusion. Having reached the surface to form a part of the foulant layer, the particle has to stick , but it may be removed from the surface by the shear forces produced by the flowing fluid [see Eq. (1)]. 

A simple conceptual model for turbulent flow deals with eddies, small portions of fluid in the boundary layer that move about for a short time before losing their identity [8], The transport coefficient, which is defined as eddy diffusivity for momentum transfer eM, has the form... 

While this calculation provides a sense of the effective thickness of the boimdary layer, conceptually it is the same as assuming transport through a stagnant film. At low wind speeds gas transfer likely occurs through diffusion into the boundary layer from the gas phase and then transport due to erosion of the boundary layer from below by small turbulence eddies. 

Turbulence in electrolytic cells is usually advantageous since the eddies both increase mass transport of the electroactive species to the electrode surface and promote the exchange of species between the bulk solution and the boundary layer, minimizing local pH and other concentration changes due to the electrode reaction. Indeed, it is not uncommon to introduce bars or other structural features into the cell to act as turbulence promoters. 

In laminar flows, the grid near boundaries should be refined to allow the solution to capture the boundary layer flow detail. A boundary layer grid should contain quadrilateral elements in 2D and hexahedral or prism elements in 3D, and should have at least five layers of cells. For turbulent flows, it is customary to use a wall function in the near-waU regions. This is due to the fact that the transport equation for the eddy dissipation has a singularity at the wall, where k [in the denominator in the source terms in eq. (5-14)] is zero. Thus, the equation for e must be treated in an alternative manner. Wall functions rely on the fact... 

Movement of a soluble chemical throughout a water body such as a lake or river is governed by thermal, gravitational, or wind-induced convection currents that set up laminar, or nearly frictionless, flows, and also by turbulent effects caused by inhomogeneities at the boundaries of the aqueous phase. In a river, for example, convective flows transport solutes in a nearly uniform, constant-velocity manner near the center of the stream due to the mass motion of the current, but the friction between the water and the bottom also sets up eddies that move parcels of water about in more randomized and less precisely describable patterns where the instantaneous velocity of the fluid fluctuates rapidly over a relatively short spatial distance. The dissolved constituents of the water parcel move with them in a process called eddy diffusion, or eddy dispersion. Horizontal eddy diffusion is often many times faster than vertical diffusion, so that chemicals spread sideways from a point of discharge much faster than perpendicular to it (Thomas, 1990). In a temperature- and density-stratified water body such as a lake or the ocean, movement of water parcels and their associated solutes will be restricted by currents confined to the stratified layers, and rates of exchange of materials between the layers will be slow. 

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