Bluff body boundary layers

When a bluff body is interspersed in a fluid stream, the flow is split into two parts. The boundary layer (see Chapter 11) which forms over the surface of the obstruction develops instabilities and vortices are formed and then shed successively from alternate sides of the body, giving rise to what is known as a von Karman vortex street. This process sets up regular pressure variations downstream from the obstruction whose frequency is proportional to the fluid velocity, as shown by Strouai. 9. Vortex flowmeters are very versatile and can be used with almost any fluid — gases, liquids and multi-phase fluids. The operation of the vortex meter, illustrated in Figure 6.27, is described in more detail in Volume 3, by Gjnesi(8) and in a publication by a commercial manufacturer, Endress and Hauser.10 ... 

Figure 7-7. Mean thickness of the air boundary layer (a) adjacent to a flat leaf at various wind speeds indicated next to the curves and (b) adjacent to objects of three different shapes at a wind speed of 1 m s-1. The length for a flat leaf represents the mean distance across it in the direction of the wind the diameter is used for the bluff bodies represented by cylinders and sp heres. Values were determined using Equations 7.10 through 7.12. Note that 1.0 m s-1 equals 3.6 km hour-1 or 2.2 mile hour-1.

Although relatively flat leaves can be described by the boundary layer considerations just presented (Fig. 7-6 and Eq. 7.10), many plant parts, such as stems, branches, inflorescences, fruits, and even certain leaves (e.g., the tubular leaves of onion, Allium cepa), represent three-dimensional objects. Airflow is intercepted by such bluff bodies and forced to move around them. Here we will consider two shapes, cylinders and spheres. In the next subsection we will present heat flux equations for objects of cylindrical and spherical symmetry as well as for flat leaves. 

Boundary-layer theory finds wide application in analyses of flame stabilization. The simplest configuration is the stagnation-point boundary layer, studies of which provide information concerning stabilization of a flame ahead of a bluff body placed in the flow some analyses and ideas... 

The curve of Cj, versus for an infinitely long cylinder normal to the flow is much like that for a sphere, but at low Reynolds numbers, does not vary inversely with because of the two-dimensional character of the flow around the cylinder. For short cylinders, such as catalyst pellets, the drag coefficient falls between the values for spheres and long cylinders and varies inversely with the Reynolds number at very low Reynolds numbers. Disks do not show the drop in drag coefficient at a critical Reynolds number, because once the separation occurs at the edge of the disk, the separated stream does not return to the back of the disk and the wake does not shrink when the boundary layer becomes turbulent. Bodies that show this type of behavior are called bluff bodies. For a disk the drag coefficient Cj, is approximately unity at Reynolds numbers above 2000. 

For flow over a bluff body, the fluid elements are subjected to a rapid change in deformations near the frontal face hence elastic effects are likely to be important in this region and the simple boundary layer approximations shoifld not be apphed to visco-elastic materials in this region. However, if elastic effects are negligibly small, the previous approach is reasonably satisfactory for viscoelastic fluids. For instance, the normal stresses developed in visco-elastic fluids will give rise to additional terms in the vr-component of the momentum balance. 

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. 

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