Turbulent flow near-wall region

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... 

Y. Nino, M.H. Garcia, Experiments on particle-turbulence interactions in the near-wall region of an open channel flow Implications for sediment transport, J. Fluid Mech. 326 (1996) 285-319. 

There are two main approaches to modeling the near-wall region. In one approach, the so-called wall function approach, the viscosity-affected inner regions (viscous and buffer layers) are not modeled. Instead, semi-empirical formulae (wall functions) are used to bridge the viscosity-affected region between the wall and the fully turbulent region. In another approach, special, low Reynolds number turbulence models are developed to simulate the near-wall region flow. These two approaches are shown schematically in Fig. 3.5(b) and 3.5(c). 

The near-wall region is composed of three layers as shown in Fig. 6.31. The layer immediately adjacent to the surface (y+ 5) is called the laminar sublayer where, because of the presence of the surface, the turbulence has been damped into a fluctuating laminar flow. In this layer, viscosity predominates over the eddy viscosity, and the velocity distribution may be approximated by... 

The behavior of the alternate forms of eM/v in the near-wall region of a turbulent boundary layer is shown in Fig. 6.35. The classical Prandtl-Taylor model assumes a sudden change from laminar flow (eM/v = 0) to fully turbulent flow (Eq. 6.173) at y = 10.8. The von Kftrman model [88] allows for the buffer region and interposes Eq. 6.174 between these two regions. The continuous models depart from the fully laminar conditions of the sublayer around y+ = 5 and asymptotically approach limiting values represented by Eq. 6.173. In finite difference calculations, eM/v is allowed to increase until it reaches the value given by Eq. 6.158 and then is either kept constant at this value or diminished by an intermittency factor found experimentally by Klebanoff [92]. 

Velocity measurements close to the wall or the velocity profile measurement in the near-wall region can be used to determine the wall shear stress. Clauser proposed an approach for shear stress measurement of turbulent flow [1]. Here, the mean velocity measurements away from the wall are used with the assumption that the mean velocity (u) varies with the logarithmic distance from the wall (y), i.e.. 

Experiments are reported in which.a concentrated polymer solution is injected into the centre of a turbulent pipe flow. Drag reduction is obtained even if the polymer forms a liquid thread which is conveyed in the core region of the flow, i.e. no significant part of the injected polymer is present in the near-wall region. This type of drag reduction differs from that found in homogeneous solutions and seems to be due to an interaction between the polymer thread and the large-scale structure. 

The results of an experimental study of the injection of concentrated polymer solutions into the near-wall region of a turbulent pipe flow are presented. Local drag reduction and friction behaviour was obtained by measuring pressure differences over a test section 13 m in length. 

In the elevated hot wire approach, the hot wire is mounted a small distance away from the wall. The velocity increases linearly with the wall distance in the near-wall region of both laminar and turbulent flow. For turbulent flow, this assumption is valid for the instantaneous velocity profile up to the wall normal location y" (y /v) < 5. The linear relationship between the shear stress (rw) and the velocity u at distance y from the wall is given as... 

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. 

Vfjp is the friction velocity and =/pVV2 is the wall stress. The friction velocity is of the order of the root mean square velocity fluctuation perpendicular to the wall in the turbulent core. The dimensionless distance from the wall is y+ = yu p/. . The universal velocity profile is vahd in the wall region for any cross-sectional channel shape. For incompressible flow in constant diameter circular pipes, = AP/4L where AP is the pressure drop in length L. In circular pipes, Eq. (6-44) gives a surprisingly good fit to experimental results over the entire cross section of the pipe, even though it is based on assumptions which are vahd only near the pipe wall. 

The application to pipe flow is not strictly valid because u (= fRjp) is constant only in regions close to the wall. However, equation 12.34 appears to give a reasonable approximation to velocity profiles for turbulent flow, except near the pipe axis. The errors in this region can be seen from the fact that on differentiation of equation 12.34 and putting y = r, the velocity gradient on the centre line is 2.5u /r instead of zero. 

In the absence of diffusion, all hydrodynamic models show infinite variances. This is a consequence of the zero-slip condition of hydrodynamics that forces Vz = 0 at the walls of a vessel. In real systems, molecular diffusion will ultimately remove molecules from the stagnant regions near walls. For real systems, W t) will asymptotically approach an exponential distribution and will have finite moments of all orders. However, molecular diffusivities are low for liquids, and may be large indeed. This fact suggests the general inappropriateness of using to characterize the residence time distribution in a laminar flow system. Turbulent flow is less of a problem due to eddy diffusion that typically results in an exponentially decreasing tail at fairly low multiples of the mean residence time. 

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. 

As developed by Dukler, Deissler s expression for e was used for the region near the wall, and, von Karman s relationship was used for highly developed turbulent flow. 

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