Wakes cylinders

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 ...

For flow past a cyhnder, the vortex street forms at Reynolds numbers above about 40. The vortices initially form in the wake, the point of formation moving closer to the cylinder as Re is increased. At a Reynolds number of 60 to 100, the vortices are formed from eddies attached to the cylinder surface. The vortices move at a velocity slightly less than V. The frequency of vortex shedding/is given in terms of the Strouhal number, which is approximately constant over a wide range of Reynolds numbers. 

For 40 < Re < 200 the vortices are laminar and the Strouhal number has a nearly constant value of 0.2 for flow past a cylinder. Between Re = 200 and 400 the Strouhal number is no longer constant and the wake becomes irregular. Above about Re = 400 the vortices become turbulent, the wake is once again stable, and the Strouhal number remains constant at about 0.2 up to a Reynolds number of about 10. ... 

Pressure Fluctuation Turbulent pressure fluctuations which develop in the wake of a cylinder or are carried to the cylinder from upstream may provide a potential mechanism for tube vibration. The tubes respond to the portion of the energy spectrum that is close to their natural frequency. 

The Reynolds number, which is directly proportional to the air velocity and the size of the obstacle, is a critical quantity. According to photographs presented elsewhere, a regular Karman vortex street in the wake ot a cylinder is observed only in the range of Reynolds numbers from about 60 to 5000. At lower Reynolds numbers, the wake is laminar, and at higher Reynolds numbers, there is a complete turbulent mixing. 

However, one should be cautious when comparing the Reynolds number from regular Karman vortex streets with the Reynolds number calculated from factual situations in clean benches as the airflow from behind an obstacle is usually not the typically formed Karman vortex street predicted for an indefinitely long circular cylinder. The wake situations during actual conditions often seem to have a three-dimensional stmcnire. 

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. 

So far, the flow patterns around bluff bodies in combustible flows are not understood completely. However, a recirculation zone in the immediate wake of the stabilizer which takes the form of a pair of eddies, similar to isothermal flows, is known to exist. The length Lrz of the recirculation zone differs for 2D and axisymmetric bluff bodies. For 2D bodies (V-gutters, rods, prisms), the measured values of Trz/H range from 3 to 6 depending on the operating conditions of combustor [11], which is considerably larger than for isothermal flows, where Lrz/H 2 [11]. For axisymmetric bluff bodies (discs, cones, cylinders), at low-blockage ratio Lrz/H 2 [32], which is similar to isothermal flows [32, 33], or Lrz/H 2.b-A [34], or even Lrz/H 10-11 [35]. 

Experimental data are available for large particles at Re greater than that required for wake shedding. Turbulence increases the rate of transfer at all Reynolds numbers. Early experimental work on cylinders (VI) disclosed an effect of turbulence scale with a particular scale being optimal, i.e., for a given turbulence intensity the Nusselt number achieved a maximum value for a certain ratio of scale to diameter. This led to speculation on the existence of a similar effect for spheres. However, more recent work (Rl, R2) has failed to support the existence of an optimal scale for either cylinders or spheres. A weak scale effect has been found for spheres (R2) amounting to less than a 2% increase in Nusselt number as the ratio of sphere diameter to turbulence macroscale increased from zero to five. There has also been some indication (M15, S21) that the spectral distribution of the turbulence affects the transfer rate, but additional data are required to confirm this. The major variable is the intensity of turbulence. Early experimental work has been reviewed by several authors (G3, G4, K3). 

Namer, I., Agrawal, Y., Cheng, R. K., Robben, F., Schefer, R., and Talbot, L., "Interaction of a Plane Flame Front with the Wake of a Cylinder," presented at Fall Meeting, Western States Section of the Combustion Institute, Stanford, CA, October 1977. 

The flow in the wake of the cylinder will, in general, be unsteady due to the shedding of vortices from the rear portion of the cylinder as shown schematically in Fig. 3.30. This shedding causes the wake flow to be asymmetric about an axis that is parallel to the upstream flow and drawn through the center of the cylinder as shown in Fig. 3.30. 

Nishioka, M. and Sato, H. (1973). Measurements of velocity distributions in the wake of a circular cylinder at low Re3mold numbers. J. Fluid Mech. 65, 97-112. 

Williamson, C.H.K. (1989). Oblique and parallel modes of vortex shedding in the wake of a circular cylinder at low Reynold numbers. J. Flmd Mech. 206, 579-627. 

FIGURE 716 Laminar boundary layer separation witli a turbulent wake flow over a circular cylinder at Re = 7.000. 

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. 

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