Turbulent flow near solid boundary

Also, laminar flows are dominated by viscosity and are independent of the fluid density, whereas fiilly turbulent flows are dominated by the fluid density and are essentially independent of the fluid viscosity at high turbulence levels. For fluids flowing near solid boundaries (e.g. inside conduits) viscous forces dominate in the immediate vicinity of the boundary, whereas for turbulent flows (high Reynolds numbers) inertial forces dominate in the region far from the boundary. 

Table 5.1 shows that, with the boundary conditions present in most environmental flows (i.e., the Earth s surface, ocean top and bottom, river or lake bottom), turbulent flow would be the predominant condition. One exception that is important for interfacial mass transfer would be very close to an interface, such as air-solid, solid-liquid, or air-water interfaces, where the distance from the interface is too small for turbulence to occur. Because turbulence is an important source of mass transfer, the lack of turbulence very near the interface is also significant for mass transfer, where diffusion once again becomes the predominant transport mechanism. This will be discussed further in Chapter 8. 

Eddy size decreases near boundaries to the flow field. Because the eddy size is zero at a solid boundary, and often close to zero at a fluid density interface (like an air-water interface), the turbulent eddy size has to decrease as one approaches the boundaries. In addition, because the flow cannot go through a boundary, the largest eddy size cannot be greater than the distance from the center of the eddy to the boundary. 

Constant-Stress Layer in Flowing Fluids. In the boundary layer of a fluid flowing over a solid wall. Ihe shear stress varies with distance from Ihe wall bul ii may be considered nearly constant within a small fraction of the layer thickness. The concept is of particular importance in turbulent flow where it leads lo a theoretical derivation of the law of ihe wall," the logarithmic distribution of mean velocity. The constant stress layer is ihe best-known example of the equilibrium flow s near a wall. 

LAMINAR AND TURBULENT FLOW IN BOUNDARY LAYERS. The fluid velocity at the solid-fluid interface is zero, and the velocities close to the solid surface are, of necessity, small. Flow in this part of the boundary layer very near the surface therefore is essentially laminar. Actually it is laminar most of the time, but occasionally eddies from the main portion of the flow or the outer region of the boundary layer move very close to the wall, temporarily disrupting the velocity profile. These eddies may have little effect on the average velocity profile near the wall, but they can have a large effect on the profiles of temperature or concentration when heat or mass is being transferred to or from the wall. This effect is most pronounced for mass transfer in liquids. 

From a model of turbulent flow dynamics near a solid boundary it can be shown that drag reduction means that the scale of the dissipation is increased relative to that for the non-drag reducing fluid. The increase in the scale of the small eddies near the wall can arise in several ways. Among these are the following ... 

The behavior of the boundary layer discussed in Section 2.2 can be used to obtain a quantitative expression for iV, the diffusional flux of solute 0 to the electrode surface. Let us use again the example from Section 2.2, namely that of a channel formed by two parallel solid electrodes. Figure 2.5 replaces the velocity profile of Fig. 2.1 by a concentration profile at the same location of the electrode for a fully developed turbulent flow. There are three regions a near horizontal portion corresponding to the fully mixed turbulent bulk ... 

For the velocity components parallel to the wall the calculation of the wall boundary conditions, i.e., the apparent bulk source term, for turbulent flows starts with the estimation of yp, the dimensionless distance of the near wall node, P, to the solid surface. For turbulent flows where yp < 11.63, the value of the laminar wall shear stress is determined from ... 

Boundary layer flows are a special class of flows in which the flow far from the surface of an object is inviscid, and the effects of viscosity are manifest only in a thin region near the surface where steep velocity gradients occur to satisfy the no-slip condition at the solid surface. The thin layer where the velocity decreases from the inviscid, potential flow velocity to zero (relative velocity) at the sohd surface is called the boundary layer The thickness of the boundary layer is indefinite because the velocity asymptotically approaches the free-stream velocity at the outer edge. The boundaiy layer thickness is conventionally t en to be the distance for which the velocity equals 0.99 times the free-stream velocity. The boundary layer may be either laminar or turbulent. Particularly in the former case, the equations of motion may be simphfied by scaling arguments. Schhchting Boundary Layer Theory, 8th ed., McGraw-HiU, New York, 1987) is the most comprehensive source for information on boundary layer flows. 

Figure 13 plots an example of the processed PIV frame. The turbulent velocity field and its boundaries, solid wall, and liquid-free surface are simultaneously shown in Figure 13. The turbulence structures such as the coherent vortical structure near the bottom wall and its modification after release from the no-slip boundary condition near the free surface of the open-channel flow, and the evolvement of the free-surface wave can be seen in Figure 13. This simultaneous measurement technique for free-surface level and velocity field of the liquid phase using PIV has been successfully applied to the investigation of wave-turbulence interaction of a low-speed plane liquid wall-jet flow (Li et al., 2005d), and the characteristics of a swirling flow of viscoelastic fluid with deformed free surface in a cylindrical container driven by the constantly rotating bottom wall (Li et al., 2006c).

---