Layer flow Reynolds number

Figure 6.16 illustrates how the stagnation flow is altered with increasing surface rotation. In all cases the flow Reynolds number is Rey = 100, but the rotation Reynolds number varies from 100 to 2000. At low rotation, such as W = 1 at the surface, there is very little effect of rotation. The axial and radial velocities and the temperatures are weakly affected at low rotation rate. As the rotation increases, however, the boundary layer is thinned and the shape of the profiles changes significantly. 

Fig. 6.16 Nondimensional velocity and temperature profiles in a finite gap with a rotating surface. In all cases the Prandtl number is 0.7 and the forced-flow Reynolds number is Rey = 100. The profiles are illustrated for four values of the rotation Reynolds number Re = G1L2/v. The viscous boundary layers are close to the surface. With the exception of the axial velocity, the plots show the range 0 < z < 0.2, with the small insets illustrating the entire gap 0 < z < 1.

Transition from laminar to turbulent flow Reynolds number. The factors that determine the point at which turbulence appears in a laminar boundary layer are coordinated by the dimensionless Reynolds number defined by the equation... 

To avoid concentration polarization, an improved mass transfer should be realized in the feed compartment. Determining parameters are feed flow velocity (modified through the hydraulic diameter of the feed cell or the pump characteristics), solute diffusion (changed via the feed temperature), feed viscosity (idem), shape and dimensions of the module (introduction of turbulence promoters, use of pulsating flows to break the boundary layer, increased Reynolds numbers,...). 

The skin friction decreases in the flow direction as the boundary layer thickness increases in the downstream x-direction. The wall shear stress and hence the skin friction can be obtained from the known velocity field, which is defined by the continuity and momentum equations of fluid motion. The skin frictions are generally expressed in the form of a correlation as a function of characteristics flow Reynolds number as... 

See also -> convection, -> Grashof number, -> Hagen-Poiseuille, -> hydrodynamic electrodes, -> laminar flow, -> turbulent flow, -> Navier-Stokes equation, -> Nusselt number, Peclet number, Prandtl boundary layer, -r Reynolds number, -> Stokes-Einstein equation, -> wall jet electrode. 

It is essential for the rotating-disc that the flow remain laminar and, hence, the upper rotational speed of the disc will depend on the Reynolds number and experimental design, which typically is 1000 s or 10,000 rpm. On the lower lunit, 10 s or 100 rpm must be applied in order for the thickness of tlie boundary layer to be comparable to that of the radius of the disc. 

Flat Plate, Zero Angle of Ineidenee For flow over a wide, thin flat plate at zero angle of incidence with a uniform free-stream velocity, as shown in Fig. 6-47, the eritieal Reynolds number at which the boundaiy layer becomes turbulent is normally taken to be... 

Continuous Flat Surface Boundaiy layers on continuous surfaces drawn through a stagnant fluid are shown in Fig. 6-48. Figure 6-48 7 shows the continuous flat surface (Saldadis, AIChE J., 7, 26—28, 221-225, 467-472 [1961]). The critical Reynolds number for transition to turbulent flow may be greater than the 500,000 value for the finite flat-plate case discussed previously (Tsou, Sparrow, and Kurtz, J. FluidMech., 26,145—161 [1966]). For a laminar boundary layer, the thickness is given by... 

Friction loss The pressure energy loss that takes place in duct or pipe flow. It is related to the Reynolds number, boundary layer growth, and the velocity distribution. 

Thus for turbulent flow at high Reynolds numbers, where the thickness of the laminar sub-layer may be neglected, a 1. 

For flow in an open channel, only turbulent flow is considered because streamline flow occurs in practice only when the liquid is flowing as a thin layer, as discussed in the previous section. The transition from streamline to turbulent flow occurs over the range of Reynolds numbers, updm/p = 4000 — 11,000, where dm is the hydraulic mean diameter discussed earlier under Flow in non-circular ducts. 

That the flow may be considered essentially as unidirectional (2f-direction) and that the effects of velocity components perpendicular to the surface within the boundary layer may be neglected (that is, uy Reynolds numbers where the boundary layer thickens rapidly. 

In addition to momentum, both heat and mass can be transferred either by molecular diffusion alone or by molecular diffusion combined with eddy diffusion. Because the effects of eddy diffusion are generally far greater than those of the molecular diffusion, the main resistance to transfer will lie in the regions where only molecular diffusion is occurring. Thus the main resistance to the flow of heat or mass to a surface lies within the laminar sub-layer. It is shown in Chapter 11 that the thickness of the laminar sub-layer is almost inversely proportional to the Reynolds number for fully developed turbulent flow in a pipe. Thus the heat and mass transfer coefficients are much higher at high Reynolds numbers. 

The quantity a, which is the ratio of the velocity at the edge of the laminar sub-layer to the stream velocity, was evaluated in Chapter 11 in terms of the Reynolds number for flow over the surface. For flow over a plane surface, from Chapter 11 ... 

Because of fhe planar nafure of the cormterflow flame and the relatively high Reynolds number associated with the flow, the flame/flow configuration can be considered to be "aerodynamically clean," where the quasi-one-dimensional and bormdary-layer simplifications can be implemented in either analytical or computational studies. Useful insights into the thermochemical structure... 

Fluid flow and reaction engineering problems represent a rich spectrum of examples of multiple and disparate scales. In chemical kinetics such problems involve high values of Thiele modulus (diffusion-reaction problems), Damkohler and Peclet numbers (diffusion-convection-reaction problems). For fluid flow problems a large value of the Mach number, which represents the ratio of flow velocity to the speed of sound, indicates the possibility of shock waves a large value of the Reynolds number causes boundary layers to be formed near solid walls and a large value of the Prandtl number gives rise to thermal boundary layers. Evidently, the inherently disparate scales for fluid flow, heat transfer and chemical reaction are responsible for the presence of thin regions or "fronts in the solution. 

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