Boundary layer, turbulent forced

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. 

For a turbulent boundary layer, the total drag may be roughly estimated using Eqs. (6-184) and (6-185) for finite cylinders. Measured forces by Kwon and Prevorsek ]. Eng. Jnd., 101, 73-79 [1979]) are greater than predicted this way. 

Water flows at a velocity of 1 m/s over a plane surface 0.6 m wide and 1 m long. Calculate the total drag force acting on the surface if the transition from streamline to turbulent flow in the boundary layer occurs when the Reynolds group ReXc = 105. 

On increasing the Reynolds number further, a point is reached when the boundary layer becomes turbulent and the point of separation moves further back on the surface of the sphere. This is the case illustrated in the lower half of Figure 9.1 with separation occurring at point C. Although there is still a low pressure wake, it covers a smaller fraction of the sphere s surface and the drag force is lower than it would be if the boundary layer were laminar at the same value of Rep. 

When Re exceeds about 2 x 105, the flow in the boundary layer changes from streamline to turbulent and the separation takes place nearer to the rear of the sphere. The drag force is decreased considerably and ... 

However, the molecules percolating up into the boundary layer from beneath the soil surface tend to become trapped in the stagnant laminar sublayer of the boundary layer. This sublayer is usually much thinner than the overall turbulent boundary layer, since it is dominated by viscous and surface tension forces, rather than by velocity. Phelan and Webb call this the chemical boundary layer and state categorically that there will generally be no chemical signature above this chemical boundary layer [1, p. 52],... 

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. 

The effect increased with penetration of the wave front into the electric field. Addition of a magnetic field decreased the total current across the slug, by about 40% when the j x B force was in the direction of wave propagation, but by about 25% when the force was against this direction. There was no effect on the wave speed unless the j x B force was against the flow, in which case the wave speed was lowered by up to 10% on account of an increase of turbulence in the boundary layer. The changes in wave structure observed were attributed to the "Hall Effect ... 

A.M. Mollinger, F.T.M. Nieuwstadt, Measurement of the lift force on a particle fixed to the wall in the sublayer of a fully developed turbulent boundary layer, J. Fluid. Mech. 316 (1996) 285-306. 

The shearing stress, r, exerted by the wind on the ground entails a downwards flux of momentum. In the aerodynamic boundary layer above the surface, the momentum is transferred by the action of eddy diffusion on the velocity gradient. The friction velocity is defined by w = t/pa and is a measure of the intensity of the turbulent transfer. Near to a rough surface, the production of turbulance by mechanical forces... 

Saltation of solids occurs in the turbulent boundary layer where the wall effects on the particle motion must be accounted for. Such effects include the lift due to the imposed mean shear (Saffman lift, see 3.2.3) and particle rotation (Magnus effect, see 3.2.4), as well as an increase in drag force (Faxen effect). In pneumatic conveying, the motion of a particle in the boundary layer is primarily affected by the shear-induced lift. In addition, the added mass effect and Basset force can be neglected for most cases where the particle... 

In the present chapter and in the following two chapters, which are concerned with turbulent boundary layer flows and with turbulent duct flows, respectively, consideration will be restricted to forced flows, i.e., the effect of buoyancy forces on the mean flow and on the turbulence structure will be assumed to be negligible. Some discussion of the effect of buoyancy forces on turbulent flows will be given in Chapter 9. 

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. 

In using these equations, the forms of the velocity and temperature profiles in the boundary layer are assumed. Now, in turbulent forced convective boundary layer flows it has been found that the velocity profile is well described by ... 

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 ... 

In forced convective turbulent boundary layer flow over a plate the velocity and temperature distributions are approximately given by ... 

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