PERIODIC VORTICES

At a particular range of Reynolds Number ( 2,500), vortices are shed alternately from opposite sides of a body at a definite frequency as shown in Fig. 6.9. The vortices in one row are staggered with respect to those in the other. Vortex shedding may also occur at high values of Reynolds Number. 

Such vortices were apparently first observed by Leonardo da Vinci about 1480 in a river behind a bridge pier. They were found to be spaced a distance s about four times the diameter of the bridge pier (actually sId = 4%). In the middle of the 19 century, these vortices were 

Strouhal foimd the Strouhal Niunber (Sj) to be about %. Actually the constant varies between 0.2 and 0.5 depending on the shape of the body, but has a constant value for a given shape. In 1911, von Karman showed anal5 ically lhat the only stable vortex configuration was that given by the Strouhal Niunber. These vortices are, therefore, sometimes called the Karman Vortex Street. 

When a vortex leaves, the body is subjected to a reactive force. If the frequency of vortex formation corresponds to the natural frequency of the body (the frequency with which it will vibrate if bumped) large amplitudes of vibration may result. 

Structures other than bridges are often subjects for potential Strouhal-Karman difficulties. These include high smokestacks and tall buildings. The St. Louis Arch (the Gateway to the West) was questioned from this point of view. Model tests and calculations performed by den Hartog at MIT revealed that the arch would be in trouble at wind velocities of 60 10 mph when the wind blows from due north or south 5°. As a matter of safety, the arch has been instrumented to monitor its vibration and people are not allowed to go up into the arch if the wind velocity exceeds 40 mph. 

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If all the lengths are non-dimensionalized by the displacement thickness and the velocity by then the periodic vortices impose a time scale on the flow given by oiq = 2Kcja The periodicity of the vortices excites the shear layer at circular frequencies wq, 2o o, 3o o.etc. Thus, the distur-... 

In this study, the relationship between oscillatory heat release and large vortex structure was systematically examined as a function of flow and chemistry scaling. Figure 16.3 shows the experimental setup used for producing vortex flames. A premixed propane-air jet was ignited, and the flame was stabilized at the exit downstream of a sudden-expansion flameholder. A 75-watt compression driver was used to apply controlled disturbance and to produce periodic vortices into a jet flame. The frequency response of actuation was evaluated separately to maintain a similar amplitude of acoustic disturbance at the exit plane. The objectives were to identify the location for active fuel injection in the general case and to establish a scaling criterion. 

Figure 16.4 Phase-lock Schlieren images of periodic vortices convecting inside a turbulent jet-flame structure during a cycle. The spacing between images is 30° Re = 7200 and

Often a periodic vortical structure typical of EOl bifurcates from a time-dependent quiescent conduction state, prior to the onset of steady state. In this case, the width of the depletion front at the charge-selective interface first develops in time with the typical diffusion similarity scaling, /i. Subsequently, this evolution slows down, with some typical width selected, which further develops at a rate much slower than For a review of these time-dependent aspects of EOl, the reader is referred to [9] and references therein. 

Yu, K.H., T. P. Parr, K. J. Wilson, K.C. Schadow, and E. J. Gutmark. 1996. Active control of liquid-fueled combustion using periodic vortex-droplet interaction. 26th Symposium (International) on Combustion Proceedings. Pittsburgh, PA The Combustion Institute. 

Incubate at room temperatutre for 2 hr with periodic vortexing. 

Extract the DNA from the gel using the MinElute gel extraction kit following the instructions. Use 6 volumes of Buffer QC per volume of gel and incubate the gel slices at room temperature with periodic vortexing until the gel slices are dissolved see Note 21). Add 2 volumes of isopropanol, and follow the kit instructions. Elute in 25 pL of buffer EB. 

As the Reynolds number rises above about 40, the wake begins to display periodic instabiUties, and the standing eddies themselves begin to oscillate laterally and to shed some rotating fluid every half cycle. These still laminar vortices are convected downstream as a vortex street. The frequency at which they are shed is normally expressed as a dimensionless Strouhal number which, for Reynolds numbers in excess of 300, is roughly constant ... 

The periodic shedding produces lateral forces of the same period on the cylinder. Should the cylinder be weakly supported and have a natural frequency close to the shedding frequency, it oscillates strongly in concert with the vortex street. Such behavior is responsible for the singing of power lines, the oscillation of tall smokestacks, and, most spectacularly, for the coUapse in 1940 of the newly built Tacoma Narrows suspension bridge, in Washington state, under the influence of a steady 65 km/h wind. 

FIG. 6-56 Computational fluid dynamic simulation of flow over a square cylinder, showing one vortex shedding period. (From Choudliuty, et al., Trans. ASME Fluids Div, TN-076[1994].)... 

The discovery of ozone holes over Antarctica in the mid-1980s was strong observational evidence to support the Rowland and Molina hypothesis. The atmosphere over the south pole is complex because of the long periods of total darkness and sunlight and the presence of a polar vortex and polar stratospheric clouds. However, researchers have found evidence to support the role of CIO in the rapid depletion of stratospheric ozone over the south pole. Figure 11-3 shows the profile of ozone and CIO measured at an altitude of 18 km on an aircraft flight from southern Chile toward the south pole on September 21, 1987. One month earlier the ozone levels were fairly uniform around 2 ppm (vol). 

The pressures on the sides and roof of the structure build up to the incident overpressure as the blast wave traverses the structure. Traveling behind the blast wave front there is a short period of low pressure caused by a vortex formed at the front edge during the diffraction process (Figures A. 8c and A. 9c). After the vortex has passed, the pressure returns essentially to that in the incident blast wave. The air flow causes some reduction in the loading to the sides and roof, because the drag pressure has a negative value for these surfaces. 

Fig. 2. Mixing in the vortex mixing flow with increasing periods of flow (P). The flow is time periodic with each cylinder rotating alternately for a fixed time period (Jana, Metcalfe and Ottino, 1994).

At Re = 130, a weak long-period oscillation appears in the tip of the wake (T2). Its amplitude increases with Re, but the flow behind the attached wake remains laminar to Re above 200. The amplitude of oscillation at the tip reaches 10% of the sphere diameter at Re = 270 (GIO). At about this Re, large vortices, associated with pulsations of the fluid circulating in the wake, periodically form and move downstream (S6). Vortex shedding appears to result from flow instability, originating in the free surface layer and moving downstream to affect the position of the wake tip (Rll, R12, S6). 

Few observations have been reported on wakes of ellipsoidal bubbles and drops at Re > 1000. Yeheskel and Kehat (Y4) characterized shedding in this case as random. However, Lindt (L7, L8) studied air bubbles in water and distinguished a regular periodic component of drag associated with an open helical vortex wake structure. Strouhal numbers (defined as 2af/Uj, where / is the frequency and 2a is the maximum horizontal dimension) increase with Re, to level off at about 0.3 as bubbles approach the transition between the ellipsoidal and spherical-cap regimes. 

Support for the importance of aerosols in maintaining chlorine in an active form during the maintenance period is found in Fig. 12.34. This shows the satellite-derived average total O, in the vortex as a function of... 

All determinations are performed in duplicate. Prepare samples by dissolving the lyo-philized residue carefully in 60 pi of distilled water keep on ice. Take a 20-pl sample and add 20 pi periodate mix and incubate for 30 min at 37°C. Add 20 pi thiosulfate and vortex (a brown color will develop and disappear by vortexing). 

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