Turbulent viscous sublayer

In turbulent flow, the velocity profile is much more blunt, with most of the velocity gradient being in a region near the wall, described by a universal velocity profile. It is characterized by a viscous sublayer, a turbulent core, and a buffer zone in between. 

A review on drag-reducing polymers is given in the literature [1359]. It has been suggested that drag reduction occurs by the interactions between elastic macromolecules and turbulent-flow macrostructures. In turbulent pipe flow, the region near the wall, composed of a viscous sublayer and a buffer layer, plays a major role in drag reduction. 

When electrically insulated strip or spot electrodes are embedded in a large electrode, and turbulent flow is fully developed, the steady mass-transfer rate gives information about the eddy diffusivity in the viscous sublayer very close to the electrode (see Section VI,C below). The fluctuating rate does not give information about velocity variations, and is markedly affected by the size of the electrode. The longitudinal, circumferential, and time scales of the mass-transfer fluctuations led Hanratty (H2) to postulate a surface renewal model with fixed time intervals based on the median energy frequency. 

The near-wall region is conceptually subdivided into three layers, based on experimental evidence. The innermost layer is the viscous sublayer in which the flow is almost laminar, and the molecular viscosity plays a dominant role. The outer layer is considered to be fully turbulent. The buffer layer lies between... 

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). 

It is important to place the first near-wall grid node far enough away from the wall at yP to be in the fully turbulent inner region, where the log law-of-the-wall is valid. This usually means that we need y > 30-60 for the wall-adjacent cells, for the use of wall functions to be valid. If the first mesh point is unavoidably located in the viscous sublayer, then one simple approach (Fluent, 2003) is to extend the log-law region down to y — 11.225 and to apply the laminar stress-strain relationship U — y for y < 11.225. Results from near-wall meshes that are very fine using wall functions are not reliable. 

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... 

As the wall becomes rougher, the velocity profile in the turbulent zone changes as shown in Figure 2.5, and the viscous sublayer and generation zone eventually disappear. 

More recent experiments [62] concerning the viscous sublayer have shown a three-dimensional structure for turbulence near the wall. In a plane normal to the mean flow, counterrotating eddy pairs are involved (Fig. 6c), whereas in the direction of the mean flow, the motion is quasi-periodic (as described earlier). Since the wavelength along the mean flow is much larger than along the perimeter of the tube, a simplified bidimensional model may account only... 

For turbulence it is convenient to describe particle flux in terms of an eddy diffusion coefficient, similar to a molecular diffusion coefficient. Unlike a molecular diffusion coefficient, however, the eddy diffusion coefficient is not constant for a given temperature and particle mobility, but decreases as the eddy approaches a surface. As particles are moved closer and closer to a surface by turbulence, the magnitude of their fluctuations to and from that surface diminishes, finally reaching a point where molecular diffusion predominates. As a result, in turbulent deposition, turbulence establishes a uniform aerosol concentration that extends to somewhere within the viscous sublayer. Then molecular diffusion or particle inertia transports the particles the rest of the way to the surface. 

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. 

In turbulent flow, the velocity profile is nearly a straight line in the core region, and any significant velocity gradients occur in the viscous sublayer. 

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