Separated flow past cylinder

Separated flow past a cylinder at moderate Reynolds numbers. If the Reynolds number becomes larger than the critical value Re = 2.5, the vortex counterflow with closed streamlines arises near the rear point, that is, separation occurs [486]. As the Reynolds number increases, the separation point gradually... 

Separated flow past a cylinder at high Reynolds numbers. With further increase of Re, the rear vortices become longer and then alternative vortex separation occurs (the Karman vortex street is formed). Simultaneously, the separation point moves closer to the equatorial section. The frequency Uf of vortex shedding from the rear area is an important characteristic of the flow past a cylinder. It can be determined from the empirical formula [117]... 

Fig. 3. Flow past a circular cylinder for (a). Re < 5 where no separation is evident (b) 5 < Re < 40 and fixed vortices exist in a separation bubble or wake ...

This separation point is indicated in Fig. 6-8. As the flow proceeds past the separation point, reverse-flow phenomena may occur, as also shown in Fig. 6-8. Eventually, the separated-flow region on the back side of the cylinder becomes turbulent and random in motion. 

In the moderate range of 10 < Re < 1 O . Ihe drag coefficient remains relatively constant. This behavior is characteristic of blunt bodies. Tlie flow in the boundary layer is laminar in this range, but the flow in the separated region past the cylinder or sphere is highly turbulent with a wide turbulent wake. 

Among references that discuss closed-streamline patterns and eddies in low-Reynolds-number flows, the reader may wish to refer to Ref. 13, Chap. 7, and D. J. Jeffrey and J. D. Sherwood, Streamline patterns and eddies in low-Reynolds-number flow, J. Fluid Mech. 96, 315-34 (1980) A. M. J. Davis and M. B. O Neill, The development of viscous wakes in a Stokes flow when a particle is near a large obstacle, Chem. Eng. Sci. 32, 899-906 (1977) A. M. J. Davis and M. B. O Neill, Separation in a slow linear shear flow past a cylinder and a plane, J. Fluid Mech., 81, 551-64 (1977). 

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. 

The problem of start-up flow for a circular cylinder has received a great deal of attention over the years because of its role in understanding the inception and development of boundary-layer separation. An insightful paper with a comprehensive reference list of both analytical and numerical studies is S. I. Cowley, Computer extension and analytic continuation of Blasius expansion for impulsive flow past a circular cylinder, J. Fluid Mech. 135, 389-405 (1983). 

These ideas are developed in more detail in the following paper L. G. Leal, Vorticity transport and wake structure for bluff bodies at finite Reynolds number, Phys. Fluids A Fluid Dynamics 1 124-131 (1989). Additional insight into the evolution of a separated wake for a solid, circular cylinder may be obtained at large, but finite, Reynolds number from numerical solutions such as those in W. M. Collins and S. C. R. Dennis, Flow past an impulsively started circular cylinder, J. Fluid Mech. 60, 105-127 (1973). 

Problem 10-2. Inviscid, Potential Flow Past a Half Cylinder. Consider inviscid, potential flow past the half cylinder depicted in the figure. Calculate the force (life and drag) on the object, assuming that the flow does not separate. If the flow does separate at 90°, what happens to the lift and drag ... 

Figure 1.7. Flow separation and the onset of a recirculation region in flow past a cylinder...

Particularly when fluids flow past immersed objects, the local mass-transfer coefficient varies with position on the object, due especially to the separation of the boundary layer from the downstream surfaces to form a wake. This phenomenon has been studied in great detail for some shapes, e.g., cylinders [8]. The average mass-transfer coefficient in these cases can sometimes best be correlated by adding the contributions of the laminar boundary layer and the wake. This is true for the second entry of item 5, Table 3.3, for example, where these contributions correspond respectively to the two Reynolds-number terms. 

For the flow of a viscous fluid past the cylinder, the pressure decreases from A to B and from A to C so that the boundary layer is thin and the flow is similar to that obtained with a non-viscous fluid. From B to D and from C to D the pressure is rising and therefore the boundary layer rapidly thickens with the result that it tends to separate from the surface. If separation occurs, eddies are formed in the wake of the cylinder and energy is thereby dissipated and an additional force, known as form drag, is set up. In this way, on the forward surface of the cylinder, the pressure distribution is similar to that obtained with the ideal fluid of zero viscosity, although on the rear surface, the boundary layer is thickening rapidly and pressure variations are very different in the two cases. 

Surface Force Measurements. Another method to measure the thickness of adsorbed layers is by the surface force apparatus (SFA) (17). In this method two freshly cleaved mica sheets are glued to the surfaces of two crossed cylindrical lenses. Polymer chains are then allowed to adsorb on the mica sheets. In order to measure the thickness of the adsorbed layers the two cylinders are brought in contact and the force between them is measured as a fimction of separation. The onset of the repulsive force associated with compression of the adsorbed layer can be related to the thickness of the adsorbed layer. On the other hand, in the event of bridging between the adsorbed layers the force will be attractive. Recent advances in the instrument have made it possible to probe the effect adsorption has on the flow of fluid past a surface (18). 

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