Turbulent near solid walls

In the thermal conduction sublayer near solid walls, a linear law can be used. In the turbulent near-wall region, Reynolds analogy between momentum and energy transport allows to derive a logarithmic law for the mean temperature, similar to (12.5-8). In general, the thickness of the thermal conduction layer differs from the thickness of the viscous sublayer and depends on the physicochemical properties of the fluid. The thermal sublayer thickness can be estimated from the intersection between the linear law and the logarithmic law. 

Flow of the liquid past the electrode is found in electrochemical cells where a liquid electrolyte is agitated with a stirrer or by pumping. The character of liquid flow near a solid wall depends on the flow velocity v, on the characteristic length L of the solid, and on the kinematic viscosity (which is the ratio of the usual rheological viscosity q and the liquid s density p). A convenient criterion is the dimensionless parameter Re = vLN, called the Reynolds number. The flow is laminar when this number is smaller than some critical value (which is about 10 for rough surfaces and about 10 for smooth surfaces) in this case the liquid moves in the form of layers parallel to the surface. At high Reynolds numbers (high flow velocities) the motion becomes turbulent and eddies develop at random in the flow. We shall only be concerned with laminar flow of the liquid. 

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. 

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).

The presence of the solid wall has a considerable influence on the turbulence structure near the wall. Because there can be no flow normal to the wall near the wall, v decreases as the wall is approached and as a result the turbulent stress and turbulent heat transfer rate are negligible in the region very near the wall. This region in which the effects of the turbulent stress and turbulent heat transfer rate can be neglected is termed the sublayer or, sometimes, the laminar sublayer [1],[2], [26],[27],[28],[29]. In this sublayer ... 

Kasagi, N., Kuroda, A., and Hirata, M., Numerical Investigation of Near-Wall Turbulent Heat Transfer Taking Into Account the Unsteady Heat Conduction in the Solid Wall , J. of Heat Transfer, Vol. Ill, pp. 385-392, 1989. 

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. 

Free turbulence has a different experimental character from that of turbulence near a solid wall or a free jet. 

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 ... 

Here, the gas velocity is even higher than in the turbulent bed. What we have is a bottom-dense zone consisting of a mixture of bubbles with more solids in them than in the bubbling bed and clumps or packets of particles rising through most of the bed s cross-section, while some anulsion flows down at/near the wall. These packets naturally have a terminal velocity much higher than that of the particles and hence... 

Near the wall, the k-e model cannot be applied in the viscous sub layer. Wall functions are needed for the logarithmic layer [Launder and Spalding, 1972]. The turbulence variables near the solid wall are then calculated from ... 

Arundel, Bibb, and Boothroyd (1970) found agglomeration of solids to increase near the wall in their study of a 1- to 40-jum-diameter zinc particles flowing in a vertical tube. They also found that the turbulence was suppressed near the wall, contributing to the agglomeration phenomenon. 

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