Wake shedding

The formation of an attached wake and the subsequent onset of wake shedding tend to be promoted by increasing oblateness (see Chapter 6) and by the tendency of surface-active contaminants to damp out internal circulation (see Chapter 5). Experiments have been conducted with dyes added to enable attached wakes and shedding phenomena to be visualized (H8, Ml, M2, S2) and wake volumes to be measured (H8, Y4) for drops and bubbles. Since dyes tend to be surface active, the results of these experiments are probably relevant... 

While other explanations have been proposed [e.g. (B6, El, H6)], secondary motions are most plausibly related to wake shedding. The onset of oscillations coincides with the onset of vortex shedding from the wake (El, E2, S5, W8). For high k or contaminated drops and bubbles, the onset of oscillations... 

In practice, this model is oversimplified since the exciting wake shedding is by no means harmonic and is itself coupled with the shape oscillations and since Eq. (7-30) is strictly valid only for small oscillations and stationary fluid particles. However, this simple model provides a conceptual basis to explain certain features of the oscillatory motion. For example, the period of oscillation, after an initial transient (El), becomes quite regular while the amplitude is highly irregular (E3, S4, S5). Beats have also been observed in drop oscillations (D4). If /w and are of equal magnitude, one would expect resonance to occur, and this is one proposed mechanism for breakage of drops and bubbles (Chapter 12). 

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). 

Free-fall experiments with Re >10 show that a sphere released from rest initially accelerates vertically, and then moves horizontally while its vertical velocity falls sharply (R3, S2, S3, V2). As for steady motion discussed in Chapter 5, secondary motion results from asymmetric shedding of fluid from the wake (S3, V2). Wake-shedding limits applicability of the equations given above. Data on the point at which wake-shedding occurs are scant, but lateral motion has been detected for in the range 4-5 (C7). Deceleration occurs for Re > 0.9 Re. The first asymmetric shedding occurs at much higher Re than in steady motion (Re = 200 see Chapter 5), due to the relatively slow downstream development, as shown in Fig. 11.12. 

The validity of the various simplifications has been the subject of considerable discussion [e.g. (A3, B2, H3, T4)]. Schoneborn (S4) showed that in the range where periodic wake shedding normally occurs (Re > 200 see Chapter 5), the effect of fluid oscillations depends on the relationship between the forced fluid frequency and the natural wake frequency ... 

In gas-solid fluidized beds wake shedding has also been observed. The shed wake fragments are banana-shaped and the shedding may occur at fairly regular intervals [Rowe and Partridge, 1965 Rowe, 1971],... 

Secondary motion associated with wake shedding occurs in the Newton s law regime, and is insensitive to (Re)p. In this regime the density ratio, X, plays an important role in determining the type of motion and the mean terminal velocity. For particles of arbitrary shapes,... 

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