Theoretical Model

5.4 Conclusions

5.4.5 Theoretical Model

We developed a theoretical model to explain how intruders rise or sink within the granular medium when oscillated horizontally at a specific amplitude and time period.

The model was able to identify a critical time period, below which an oscillating intruder will not rise. For all the intruder shapes, a point of no return was proposed; if the granular particle passes this point, it will reach the cavity’s surface layer. These particles settling at the surface of the cavity will help the intruder climb on it and rise.

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C

HAPTER

6

R OLE OF CONSTITUENTS OF A GRANULAR MEDIUM ON THE LIFT FORCE EXPERIENCED BY A TRANSLATING AND ROTATING INTRUDER .

6.1 Introduction.

G

ranular material is an assembly of discrete solid particles, and their interactions are dissipative [1, 2] in nature. There has been a lot of research on the rheology of spherical and almost spherical particles [3–6]. Food grains, catalyst pellets, and medicinal pills, for example, are generally non-spherical granular materials. Although many elements of the mechanics of non-spherical particles have been investigated in- depth, the rheology of such materials has not. The shape of the particles has an impact on the static and flow characteristics of granular materials. The understanding of flow behavior of shape heterogeneous mixture will be helpful in many industrial and natural processes such as mixing [7, 8], segregation [9, 10], advection and compaction [11, 12].

When a moving ball is spinning through the air, it gets deflected in the direction of spin due to the pressure difference on the opposite sides of the spinning ball. This phenomenon is known as the Magnus effect. It is believed that Newton was the first who gave explanation regarding this phenomenon in 1671 [13] while observing a tennis match in Cambridge college. Later, Benjamin Robins while working on the firing of a musket ball in the early part of 1742 [14] has explained the deviation of this musket ball

CHAPTER 6. ROLE OF CONSTITUENTS OF A GRANULAR MEDIUM ON THE LIFT FORCE EXPERIENCED BY A TRANSLATING AND ROTATING INTRUDER.

after firing in terms of the Magnus effect. After a century, in 1852, Heinrich Magnus gave a detailed explanation of the phenomena [15] and left his name to it.

The Bernoulli principle says that an increase in fluid speed happens concurrently with a drop in pressure for an inviscid flow and vice versa. The traditional Magnus effect on a spinning object has been explained in terms of a delayed separation on the retreating side when the spherical surface moves with the flow since the notion of the boundary layer was proposed by Prandtl in 1904 [16]. The flow separates further downstream on the advancing side (the spherical surface travels against the flow) than on the retreating side when the inverse Magnus effect occurs. Swanson using the boundary layer theory, described the circulation of airflow around the cylinder in his work [17]. He proposed that the top and lower boundary layers separate differently due to differing velocities and that this behavior causes circulation. With this, a friction-aware origin for the Magnus force was postulated, and the force’s direction was explained.

It has also been observed that at certain Reynolds number the spinning ball is deflected opposite the direction of the usual Magnus effect [18–20]. Kimet al.[19] stated that this capricious behavior arises when the boundary layer flow traveling against the surface of a spinning sphere transition to turbulence, but the flow moving with the revolving surface stays laminar. Turbulence vitalizes the flow, causing the primary separation to occur further downstream, resulting in higher flow velocity and negative lift force. Whereas a circular object rotated in granular media, regardless of the area fraction, the direction of lift is opposite the direction of the general Magnus effect seen in viscous fluid [21]. The primary reasons for this type of lift generation in the granular medium are the tangential forces operating around the rotating intruder and the change in relative motion between the surrounding granules and the intruder due to the spinning.

The present work focuses on elucidating the role of constituent granules in the medium that affects the lift generation on a rotating and translating circular intruder. A mixture of dumbbells and discs is considered as a shape heterogeneous mixture.