Vortex precession

Vortex precession meters feature no moving parts and a relatively high frequency digital output. They are used in the measurement of gas and Hquid flows, generally in pipe sizes 80 mm and smaller. 

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While fishing in Transylvania, Theodore von Karman noticed that downstream of the rocks the distance between the shed vortices was constant, regardless of flow velocity (Figure 3.104). From that observation evolved the three types of vortex meters the vortex shedding, the vortex precession, and the fluidic oscillation (Coanda) versions. All three types detect fluid oscillation. They have no moving components and can measure the flow of gas, steam, or liquid. 

Construction of a typical vortex precession (swirl meter). 

Another explanation is that the end of the vortex attaches to the side wall (i.e. the vortex core bends), and turns around or processes around the wall at a high rate see Fig. 9.2.1. Such a phenomenon, known as vortex precession can be observed, perhaps most easily, in liquid cyclones, where the core can be visualized with air bubbles see Fig. 9.2.2. 

Fig. 17. Mixing of floating soHds in agitated tanks (a) no surface movement, full baffles width = T/12 (b) deep vortex, no baffles need high energy which causes tank to sway (c) precessing vortex, partial baffles width = T/50 and (d) submerged partial baffles.

The vortex of a cyclone will precess (or wobble) about the center axis of the cyclone. This motion can bring the vortex into close proximity to the wall of the cone of the cyclone and pluck off and reentrain the collected solids flowing down along the wall of the cone. The vortex may also cause erosion of the cone if it touches the cone wall. Sometimes an inverted cone or a similar device is added to the bottom of the cyclone in the vicinity of the cone and dipleg to stabilize and fix the vortex. If it is placed correctly, the vortex will attach to the cone and the vortex movement will be stabilized, thus minimizing the efficiency loss due to plucking the solids off the wall and erosion of the cyclone cone. 

As Re increases beyond about 400, vortices are shed as a regular succession of loops from alternate sides of a plane which precesses slowly about the axis (A4, K6, MU). As shown in Fig. 5.9, the Strouhal number Sr for vortex shedding increases. At the same time, the point at which the detached shear layer... 

The examples presented in this chapter [308 320] are illustrations of the concepts presented in the previous chapters. They correspond to recent numerical analysis of burners which are typical of most modern high-power combustion chambers, especially of gas turbines the flame is stabilized by strongly swirled flows, the Reynolds numbers are large, the flow field sensitivity to boundary conditions is high, intense acoustic/combustion coupling can lead to self-sustained oscillations. Flames are stabilized by swirl. Swirl also creates specific flow patterns (a Central Toroidal Recirculation Zone called CTRZ) and instabilities (the Precessing Vortex Core called PVC). 

Coexistence of Acoustic Modes and Precessing Vortex Core... 

Figure 10.8. Left Precessing vortex core. Right Backflow line...

Instead of using swirl generators, another method of generating vortex shedding, which has been found to increase radiant heat transfer, is by precessing the jet stream. A precessing jet flow can be generated either by an axisymmetric nozzle which utilizes a natural fluid... 

Vortex core bending and precessing around wall... 

Fig. 9.2.2. Water model exibiting vortex core precession...

Although the vortex may attach to, and process around, the lower walls of the cyclone as in Fig. 9.2.1, vortex motion does not completely cease in the axial direction at this point or, more correctly, plane of attachment. This primary vortex induces a secondary vortex just downstream of it. This is a type of fluid coupling . The induction of the secondary vortex is probably related to the precession of the primary vortex. This precession is always in the same rotational sense as the swirl in the bulk of the vortex, as sketched in Fig. 9.2.1. 

Fig. 9.2.3. A stroboscopic image of the eye of the vortex core precessing along the cyclone wall...

If we perform a simplified analysis of the gas velocity near the wall in a cyclone operating with the vortex end precessing around the wall, an interesting result emerges with respect to the near-wall velocities. The illustration below attempts to show the vortex end precessing around the entire inner wall of a cyclone while, at the same time, displaying a snapshot of its characteristic rotational imprint ( eye of the hurricane) at any given point in time. 

We notice first that the end of the vortex is precessing around the inner wall of the separator at some precessional frequency / and precessional velocity vector Vp. For the case illustrated, this motion is counterclockwise (ccw) as viewed from above. However, superimposed on this motion is the vortex core spin or rotational velocity vector, vcs- This core spin velocity adds to the precessional velocity Vp at its top-most position (position A in illustration) producing the resultant velocity v. On the other hand, the core spin vector opposes the precessional velocity at the bottom-most position (position B). 

Fig. 9.2.4. Vortex end in contact with, and precessing around, inner wall...

The intense velocity resulting from the aforementioned processional motion also can be expected to significantly impair separation performance as some fraction of the collected dust spiraling down the walls becomes abruptly re-entrained by the action of the precessing vortex. Furthermore, particles of dust in this region of the cyclone may attrite at a rate greater than what one might expect from considerations of inlet velocity or even the core spin velocity alone. 

It has furthermore been claimed that the position of the vortex end is related to the sharpness of the cyclone cut (Abrahamsen and Allen, 1986). In support of this, the writers have observed considerable mixing of the solids originating in the plane where the precessing vortex tail attaches to the lower walls of model cyclones. This has been observed in both dedusting and demisting cyclones. 

As one might expect, the frequency of rotation of the vortex core around the inner walls of the cyclone (or swirl tube) has been observed to be directly proportional to the gas flow rate. Interestingly, for any given gas flow rate, this precession frequency is also foimd to be approximately equal to the core s maximum spin velocity divided by the circmnference of the inner wall at the plane of attachment. We will illustrate this below. 

In Fig. 9.2.7 we plot the velocity at which the vortex end or core trans-verses around the inside wall of the hopper (from Eq. 9.2.1) versus the estimated maximum tangential velocity of the vortex core (from Eq. 9.2.2). This plot strongly suggests that the precessional velocity is directly related to the maximum spin velocity. Thus, as stated earlier, precession frequency can be estimated by simply dividing the core s maximum spin velocity by the circumference of the inner wall to which it is attached. If this is true, then the end of the vortex acts much like a rubber wheel that rotates around the inner walls at a velocity equal to the maximum spin velocity of the vortex core. 

Where the vortex ends can have a significant bearing on cyclone performance. We ll try to illustrate this by examining two scenarios for vortex attachment, as shown in Fig. 9.2.8. The frame on the left has the vortex ending, and precessing around, the lower cone walls. Here, the pressure at the bottom of the cyclone (or top of the dipleg) can be expected to equal the inlet pressure minus the pressure loss due, primarily, to wall friction. (The latter typically... 

The results of the erosion study with cyclone a, when processing corundum particles, and with cyclone d, processing both the ash and corundum, are very interesting in that the erosion is observed to peak within the lower cones and to then fall off abruptly below these peaks. In the writers judgment these peaks were created by a type of vortex instability that caused the end of the inner vortex to attach to, and precess around, the lower cone walls. Such behavior is schematically illustrated in Fig. 12.1.2, and is often referred to as the natural end of the vortex . This phenomenon is discussed in Chap. 9. Thus, the physical length of a cyclone does not necessarily represent its active or effective length if it were to short circuit as described above. 

Fig. 12.1.2. Vortex tail attached to and precessing along lower cone wall...

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