Turbulent boundary layer nature

Apart from the nature of the bulk flow, the hydrodynamic scenario close to the surfaces of drug particles has to be considered. The nature of the hydrodynamic boundary layer generated at a particle s surface may be laminar or turbulent regardless of the bulk flow characteristics. The turbulent boundary layer is considered to be thicker than the laminar layer. Nevertheless, mass transfer rates are usually increased with turbulence due to the presence of the viscous turbulent sub-layer. This is the part of the (total) turbulent boundary layer that constitutes the main resistance to the overall mass transfer in the case of turbulence. The development of a viscous turbulent sub-layer reduces the overall resistance to mass transfer since this viscous sub-layer is much narrower than the (total) laminar boundary layer. Thus, mass transfer from turbulent boundary layers is greater than would be calculated according to the total boundary layer thickness. 

In this section the heat and mass transport coefficients for turbulent boundary layers are examined. In this case the model derivation is based on the governing Reynolds averaged equations. In these equations statistical covariances appear which involve fluctuating velocities, temperatures and concentrations. The nature of these terms is not known a priori and their effects must by estimated by semi-empirical turbulence modeling. The resulting parameterizations allow us to express the unknown turbulent fluctuations in terms of the mean flow field variables. It is emphasized that the Reynolds equations are not actually solved, merely semi-empirical relations are derived for the wall fluxes through the inner boundary layer. 

So the calculation done by assuming a completely turbulent boundary layer gives a drag force which is too high by 4.4 —1.3 = 3.1 Ibf. This error is small compared with the uncertainties introduced by the approximate nature of Eq. 11.37. 

From Eq. (X.51) it follows that the particle detachment depends on the properties of the medium (p, t ), the force of adhesion the particle size d, and the flow velocity v. Particle detachment, under otherwise equal conditions (P, ad> and d = const) will be determined by the flow velocity, which in turn depends on the conditions of flow around the objects or plates of different sizes. Hence, in order to create identical conditions of particle detachment from the model (small plate) and the object in nature (larger plate), the process of flow around the object must be modeled. Such modeling should bring about the establishemnt of an identical drag for the detachment of adherent particles under the model conditions and natural conditions in the case of laminar and turbulent boundary layers. 

Ounis et al. " and Shams et al. " studied dispersion and deposition of nano and microparticles in turbulent boundary layer flows. A sample simulated Brownian force for a 0.01-p.m particle is shown in Fig. 21. Here, the wall units with v/u and v/u being, respectively, the length and the time scales are used. Note that the relevant scales and the wall layer including the viscous sublayer are controlled by kinematic viscosity v and shear velocity u. The random nature of Brownian force is clearly seen from Fig. 21. 

Lee et al. (2003) presented the effectiveness of microsynthetic jet for modification of turbulent boundary layer under adverse gradient. They showed significant mixing enhancement of the boundary layer when the foreing frequency is closer to the natural instability frequency. The... 

The irregularity in the color of the outer isosurface appears to indicate wave-like fluctuations in the near-wall pressure, i.e. near-wall turbulent boundary layer structures, consistent with what has been stated about the instability of the near-wall flow in Sect. 3.1.1. The low pressure in the inner part of the vortex and in the vortex finder is clearly to be seen. A very low pressure can be seen also to exist in the apex of the cone. Its location is consistent with what is seen experimentally when the vortex extends to the bottom of the cyclone, not terminating upon a vortex stabilizer or due to the natural... 

The phenomenon of free convection results in nature, primarily from the fact that when the fluid is heated, the density (usually) decreases the warmer fluid portions move upward. This process is dramatically evident in rural areas on sunny days with low to no-wind when the soil surface is significantly hotter than the air above. The air at the soil surface becomes heated and rises vertically, producing velocity updrafts that carry the chemical vapor and the fine aerosol particles, laden with adsorbed chemical fractions, upward into the atmospheric boundary layer. When accompanied by lateral surface winds, the combined processes produce a very turbulent boundary layer and numerically large MTCs. This section will outline the major aspects of the theory of natural convection using elementary free convection concepts. Details are presented in Chapter 10 of Transport Phenomena (Bird et al., 2002). 

I. Turbulent, local flat plate, natural convection, vertical plate Turbulent, average, flat plate, natural convection, vertical plate Nsk. = — = 0.0299Wg=Ws = D x(l + 0.494W ) )- = 0.0249Wg=W2f X (1 + 0.494WE )- [S] Low solute concentration and low transfer rates. Use arithmetic concentration difference. Ncr > 10 " Assumes laminar boundary layer is small fraction of total. D [151] p. 225... 

The probability density function of u is shown for four points in Fig. 11.16, two points in the wall jet and two points in the boundary layer close to the floor. For the points in the wall jet (Fig. 11.16<2) the probability (unction shows a preferred value of u showing that the flow has a well-defined mean velocity and that the velocity is fluctuating around this mean value. Close to the floor near the separation at x/H = I (Fig. 11.16f ) it is hard to find any preferred value of u, which shows that the flow is irregular and unstable with no well-defined mean velocity and large turbulent intensity. From Figs. 11.15 and 11.16 we can see that LES gives us information about the nature of the turbulent fluctuations that can be important for thermal comfort. This type of information is not available from traditional CFD using models. 

It may be noted that no assumptions have been made concerning the nature of the flow within the boundary layer and therefore this relation is applicable to both the streamline and the turbulent regions. The relation between ux and y is derived for streamline and turbulent flow over a plane surface and the integral in equation 11.9 is evaluated. 

Let us just consider the piloted ignition case. Then, at Tpy a sufficient fuel mass flux is released at the surface. Under typical fire conditions, the fuel vapor will diffuse by turbulent natural convection to meet incoming air within the boundary layer. This will take some increment of time to reach the pilot, whereby the surface temperature has continued to rise. 

Now let us consider the mixing time, t. This will be estimated by an order of magnitude estimate for diffusion to occur across the boundary layer thickness, <5Bl- If we have turbulent natural conditions, it is common to represent the heat transfer in terms of the Nusselt number for a vertical plate of height, , as... 

Search strategies that exploit the natural tendency of the molecules to remain adsorbed on surface particles and to become trapped in the boundary layers near the surface are likely to be most productive. If odor plumes from buried sources do develop, they are likely to remain close to the surface until they dissipate from turbulence. 

In the seventies, the growing interest in global geochemical cycles and in the fate of man-made pollutants in the environment triggered numerous studies of air-water exchange in natural systems, especially between the ocean and the atmosphere. In micrometeorology the study of heat and momentum transfer at water surfaces led to the development of detailed models of the structure of turbulence and momentum transfer close to the interface. The best-known outcome of these efforts, Deacon s (1977) boundary layer model, is similar to Whitman s film model. Yet, Deacon replaced the step-like drop in diffusivity (see Fig. 19.8a) by a continuous profile as shown in Fig. 19.8 b. As a result the transfer velocity loses the simple form of Eq. 19-4. Since the turbulence structure close to the interface also depends on the viscosity of the fluid, the model becomes more complex but also more powerful (see below). 

Now return to a view of the nature of flow in the boundary layer. It has been called laminar, and so it is for values of the Reynolds number below a critical value. But for years, beginning about the time of Osborne Reynolds experiments and revelations in the field of fluid flow, it has been known that the laminar property disappears, and the flow suddenly becomes turbulent, when the critical VUv is reached. Usually flow starts over a surface as laminar but after passing over a suitable length the boundary layer becomes turbulent, with a thin laminar sublayer thought to exist because of damping of normal turbulent components at the surface. See Fig. 6. 

Available analyses of turbulent natural convection mostly rely in some way on the assumption that the turbulence structure is similar to that which exists in turbulent forced convection, see [96] to [105]. In fact, the buoyancy forces influence the turbulence and the direct use of empirical information obtained from studies of forced convection to the analysis of natural convection is not always appropriate. This will be discussed further in Chapter 9. Here, however, a discussion of one of the earliest analyses of turbulent natural convective boundary layer flow on a flat plate will be presented. This analysis involves assumptions that are typical of those used in the majority of available analyses of turbulent natural convection. 

Equation (8.166) cannot be directly applied to natural convective boundary layer flows because in such flows the velocity is zero at the outer edge of the boundary layer. However, Eq. (8.166) should give a good description of the velocity distribution near the wall. It is therefore assumed that in a turbulent natural convective boundary layer ... 

To proceed further, relationships for the wall shear stress, tw> and the wall heat transfer rate, qw, must be assumed. It is consistent with the assumption that the flow near the wall in a turbulent natural convective boundary layer is similar to that in a turbulent forced convective boundary layer to assume that the expressions for tw and qw that have been found to apply in forced convection should apply in natural convection. It will therefore be assumed here that the following apply in a natural convective boundary layer ... 

Solution. The following integrals arise in the approximate solution for turbulent natural convective boundary layer flow over a flat plate discussed above ... 

Some of the more commonly used methods of obtaining solutions to problems involving natural convective flow have been discussed in this chapter. Attention has been given to laminar natural convective flows over the outside of bodies, to laminar natural convection through vertical open-ended channels, to laminar natural convection in a rectangular enclosure, and to turbulent natural convective boundary layer flow. Solutions to the boundary layer forms of the governing equations and to the full governing equations have been discussed. 

Henkes, R.A.W.M. and Hoogendoom. C.J., Comparison of Turbullence Models for the Natural Convection Boundary Layer Along a Heated Vertical Plate , Int. J. Heat Mass Transfer, Vol. 32, pp. 157-169, 1989. 

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