Study Of Granular Convection In Quasi-two-dimensional Vertically Vibrated Cuneal Granular Beds

This thesis studies the granular convection in quasi-two-dimensional cunealparticle beds subjected to the vertical vibration by experiment and discrete elementmethod. Convective patterns are found to vary with the inclined angle of the sidewalls as well as the vibration acceleration. Experimental observations show thereversed granular convection in the particle beds confined between two side wallsslanted outward, namely particles stream up along the side walls, then converge to thecenter along the slope of the surface, and then flow downward in the central channel,finally diverge towards the corners in the bottom.With the same vibration acceleration, the particle bed confined between the sidewalls with the inclined angle of65displays the strongest convection. More deviatesthe inclined angle of the side walls from65, weaker the granular convection.Extrapolating the relationship between the convective velocity and the inclined angleof the side walls, it’s found that the cease of the reversed granular convection occursat86.5, beyond which the transition to the normal convection takes place. Theconvective velocity largely increases linearly with the vibration acceleration with theconstant inclined angle of the side walls. An exception was found for the case of theconvention confined between two side walls with the inclined angle of65, whosevelocity jumps117%with the acceleration increasing from10g to12g, wellexceeding the average strength growth rate with the acceleration of other studiedcases which is around10%. The convective center lowers with the increase of theacceleration. The experimental observations above agree well with the results of thediscrete element simulation.The granular convection mainly occurs during the expansion of the particle bedwings subjected to the gravity wave. At the moment the particles adjacent to the sidewalls collide with the side walls at an increased height, the particles within the innerside of the particle bed wings still remains outward expansion while falling downward,and then fill into the voids below the outmost layer of particles which since stick to the side walls. The entrainment of the inner side of the particle bed wings into thebottom corners forms the outward flow at the bottom of the convection rolls. Theparticle bed expansion is initiated by the release of the transversely aligned forcechains, which get momently activated at the initial stage of the particle bed beingflung into the air. Due to the inertia of particles, the expansion of the particle bedbecomes discernable only when the bed begins to fall down.With the consistent extent of the expansion, the particle bed would hit the sidewalls with larger inclined angle at a lower position, leading to a reduced convectivevelocity. Meanwhile an increased inclined angle of the side walls corresponds toweaker force chains which in turn are responsible for a weaker particle bed expansion,resulting in further reduced convective velocity. Nevertheless, when the inclined sidewalls approach the vertical position, the downward wall friction exerted on theparticle bed wings becomes increasingly nontrivial during the transient contactbetween them at the initial stage of the particle bed being flung up into the air. Theupward velocity of the particle bed wings thus get reduced and so does the flight time,the development of the particle bed expansion then being suppressed. These twoopposite influences on the particle bed expansion by the side wall inclined angle getbalanced at the inclined angle of65, at which the convection velocity is the fastest.