Circular cylinder pressure distribution

Figure 10-3. A comparison of the pressure distribution on the surface of a circular cylinder according...

The cause of large drag in the case of a body like a circular cylinder is the asymmetry in the velocity and pressure distributions at the cylinder surface that results from separation. All bodies in laminar streaming flow at large Reynolds number are subjected to viscous stresses that boundary-layer analysis shows must be... 

The boundary-layer problem for the specific case of a circular cylinder is (10-40), (10 41), (10-43), and (10-47), with ue and 3p/dx given by (10-122) and (10-123). The first point to note is that a similarity solution does not exist for this problem. Furthermore, in view of the qualitative similarity of the pressure distributions for cylinders of arbitrary shape, it is obvious that similarity solutions do not exist for any problems of this general class. The Blasius series solution developed here is nothing more than a power-series approximation of the boundary-layer solution about x = 0. 

Experimental observations of the flow past a circular cylinder show that separation does indeed occur, with a separation point at 0S — 110 . It should be noted, however, that steady recirculating wakes can be achieved, even with artificial stabilization,24 only up to Re 200, and it is not clear that the separation angle has yet achieved an asymptotic (Re —> oo) value at this large, but finite, Reynolds number. In any case, we should not expect the separation point to be predicted too accurately because it is based on the pressure distribution for an unseparated potential flow, and this becomes increasingly inaccurate as the separation point is approached. The important fact is that the boundary-layer analysis does provide a method to predict whether separation should be expected for a body of specified shape. This is a major accomplishment, as has already been pointed out. 

An elastohydrodynamic problem customarily involves the calculation of the pressure distribution in the lubricant film, allowing for the effects of pressure on the properties of the fluid and on the geometry of the interface. The shape of the lubricant film and its thickness are functionally related to the pressure distribution. The technologically important solutions are for bounding surfaces of counterformal geometry, which in most cases can be approximated satisfactorily by two opposing circular cylinders. 

Achenbach, E. Distribution of local pressure and skm fiiction around a circular cylinder in crossflow up to Re = 5x 10 . Fluid Mechanics 34, 625-639, 1968. 

Fig. 9 Drying simulation of a circular cylinder containing a spherical solid particle. Shown is the liquid distribution for different saturations, as well as the vapor pressure isolines in the gas phase...

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