Turbulence and boundary layers

Most examples of flow in nature and many in industry are turbulent. Turbulence is an instability phenomenon caused, in most cases, by the shearing of the fluid. Turbulent flow is characterized by rapid, chaotic fluctuations of all properties including the velocity and pressure. This chaotic motion is often described as being made up of eddies but it is important to appreciate that eddies do not have a purely circular motion. 

The word eddy is simply a convenient term to denote an identifiable group of fluid elements having a common motion, whether that motion be shearing, stretching or rotation. 

The properties of the turbulence are different at the two extremes of the scale of turbulence. The largest eddies, known as the macroscale turbulence, contain most of the turbulent kinetic energy. Their motion is dominated by inertia and viscosity has little direct effect on them. In contrast, at the microscale of turbulence, the smallest eddies are dominated by viscous stresses, indeed viscosity completely smooths out the microscale turbulence. 

Owing to the complexity of turbulent flow, it is usually treated as if it were a random process. In addition, it is usually adequate to calculate mean values of flow quantities, but as will be seen these are not always as simple as might be expected. The instantaneous value of the velocity 

For turbulent flow near the axis of a pipe, the fluctuation v x will not exceed about 10 per cent of the mean value. 

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Form drag for bluff bodies can be minimized by streamlining the body (Fig. 3.1-lc), which forces the separation point toward the rear of the body, which greatly reduces the size of the wake. Additional discussion of turbulence and boundary layers is given in Section 3.10. 

Chien, K. Y. Predictions of channel and boundary layer flows with a low-Reynolds-nuraber turbulence model. AIAA J., vol, 20, pp. 33-18, 1982. 

Cherry and Papoutsakis [33] refer to the exposure to the collision between microcarriers and influence of turbulent eddies. Three different flow regions were defined bulk turbulent flow, bulk laminar flow and boundary-layer flow. They postulate the primary mechanism coming from direct interactions between microcarriers and turbulent eddies. Microcarriers are small beads of several hundred micrometers diameter. Eddies of the size of the microcarrier or smaller may cause high shear stresses on the cells. The size of the smallest eddies can be estimated by the Kolmogorov length scale L, as given by... 

Fig. 3. Numerical values of A and a for the solution of turbulent flow boundary layer on a rotating hemisphere. The value of meridional angle, 9, is given in degrees. From [22].

The Reynolds number is the ratio of inertial to viscous forces and depends on the fluid properties, bulk velocity, and boundary layer thickness. Turbulence characteristics vary with Reynolds number in boundary layers [40], Thus, variation in the contributing factors for the Reynolds number ultimately influences the turbulent mixing and plume structure. Further, the fluid environment, air or water, affects both the Reynolds number and the molecular diffusivity of the chemical compounds. 

Kestin, J. and Richardson, P.D., Heat Transfer across Turbulent. Incompressible Boundary Layers , J. Heat Mass Transfer, Vol. 6, pp. 147-189,1963. 

Prevention or minimization of fouling and concentration polarization represents one of the main challenges that confronts membrane processing in general and membrane filtration of beer in particular. Various approaches have been developed to control membrane fouhng and increase the permeate flux in CMF, including membrane selection and modification, boundary layer control, use of turbulence inducers, or pretreatment of the feed. The two main strategies that are currently used in beer CMF are proper membrane selection and boundary layer control. 

Note the similarity with the intermittent behaviour of the turbulent boundary layer with polymers. This may be relevant to the flow over very flexible plant canopies (Ptasinski et al., 2003 [511]). There is a finite jump in velocity across this fluctuating layer. The external turbulence is blocked by the vorticity of the layer (Hunt and Durbin, 1999 [292]). This is why there is only a very weak effect of large eddies moving above the canopy. The layer is analogous to that at the outer edge of jets, wakes and boundary layers (Bisset et al., 2002 [63]). 

Carlotti, P., and Hunt, J.C.R. (2000) Spectra of turbulence in boundary layers near the ground. In Proceedings of 8th European Turbulence Conference, Barcelona, Kluwer. Submitted to Journal of Flow Turbulence and Combustion, 307-310. 

Raupach, M.R., Coppin, P.A., and Legg, B.J. (1986) Experiments on Scalar Dispersion Within a Model Plant Canopy. Part I The Turbulence Structure, Boundary-Layer Meteorol. 35, 21-52. 

The particle velocity associated with the shallow water wave is elliptic ally with the major axis aligned parallel to the bottom and the minor axis perpendicular to it. The amplimde of the particle velocity decays with depth but remains finitely by close to the bottom where the minor axis of the particle motion approaches to zero. This implies that particle motions of shallow water waves are quite capable of resuspending sediments as well as to develop a turbulent bottom boundary layer. 

Taylor GI (1935) Distribution of velocity and temperature between concentric rotating cylindres. Proc Roy Soc London A151(874) 494-512 Taylor GI (1936) Statistical Theory of Turbulence. V. Effect of turbulence on boundary layer. Proc Roy Soc London A156(888) 307-317 Taylor GI (1937) The Statistical Theory of Isotropic Turbulence. Journal of the Aeronautical Sciences 4(8) 311-315... 

It has been shown that there exists a continuous change in the physical behavior of the turbulent momentum boundary layer with the distance from the wall. The turbulent boundary layer is normally divided into several regions and sub-layers. It is noted that the most important region for heat and mass transfer is the inner region of the boundary layer, since it constitutes the major part of the resistance to the transfer rates. This inner region determines approximately 10 — 20% of the total boundary layer thickness, and the velocity distribution in this region follows simple relationships expressed in the inner variables as defined in sect 1.3.4. 

In practice, however there could be differences between the observed and estimated flux. The mass transfer coefficient is strongly dependent on diffusion coefficient and boundary layer thickness. Under turbulent flow conditions particle shear effects induce hydrodynamic diffusion of particles. Thus, for microfiltration, shear-induced difflisivity values correlate better with the observed filtration rates compared to Brownian difflisivity calculations.Further, concentration polarization effeets are more reliably predicted for MF than UF due to the fact diat macrosolutes diffusivities in gels are much lower than the Brownian difflisivity of micron-sized particles. As a result, the predicted flux for ultrafiltration is much lower than observed, whereas observed flux for microfilters may be eloser to the predicted value. 

T. H. Okiishi, and G. K. Serovy, An Experimental Study of the Turbulent Flow Boundary Layer Development in Smooth Annuli, J. Basic Eng., (89) 823-836,1967. 

W. C. Reynolds, W. M. Kays, and S. J. Kline, Heat Transfer in the Turbulent Incompressible Boundary Layer, I—Constant Wall Temperature, NASA Mem. 12-1-58W, 1958. 

Box (1981) classified all of the different plant species into 16 different structural types (trees, small trees, etc.) and in turn into a total of 77 plant forms (e.g., evergreen tropical rainforest trees, mediterranean dwarf shrubs, etc.). This latter classification combines form, geographical distribution, and to a certain extent function (evergreen, deciduous, ephemeral). So fundamentally there are not too many different structural types of plants, as Theophrastus noted several millennia ago. These basic forms, when coalesced into communities, certainly have an influence on land surface/atmospheric models through turbulent transfer and boundary-layer effects that are often incorporated into atmospheric exchange models. 

The design and development of aerodynamic vehicles require precise measurements of shear stress and boundary layer for turbulence control. The application of MEMS sensors has enabled the localization of flow separation where drastic variation in shear stress develops on the air foils. Ho and Tai [11] have... 

Fig. X.1. Structure of laminar (a) and turbulent (b) boundary layers and velocity distribution in these layers (c) (1) laminar layer (2) laminar sublayer (3) buffer layer (4) turbulent core.

In Section 3.10 an approximate integral analysis was made for the laminar hydrodynamic and also for the turbulent hydrodynamic boundary layer. This was also done in Section 5.7 for the thermal boundary layer. This approximate integral analysis can also be done in exactly the same manner for the laminar and turbulent concentration boundary layers. 

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