Abstract
The terminal orientation of a rigid body is a classic example of a system out of thermodynamic equilibrium and a perfect testing ground for the validity of the maximum entropy production principle(MEPP). A freely falling body in a quiescent fluid generates fluid flow around the body resulting in dissipative losses. Thus far dynamical equations have been employed in deriving the equilibrium states of such falling bodies, but they are far too complex and become analytically intractable when inertial effects come into play. At that stage, our only recourse is to rely on numerical techniques which can be computationally expensive. In our past work, we have realized that the MEPP is a reliable tool to help predict mechanical equilibrium states of free falling, highly symmetric bodies such as cylinders, spheroids and toroidal bodies. We have been able to show that the MEPP correctly helps choose the stable equilibrium in cases when the system is slightly out of thermodynamic equilibrium. In the current paper, we expand our analysis to examine bodies with fewer symmetries than previously reported, for instance, a half-cylinder. Using two-dimensional numerical studies at Reynolds numbers substantially greater than zero, we examine the validity of the MEPP. Does the principle still hold up when a sedimenting body is no longer isotropic or has three planes of symmetry? In addition, we also examine the relation between entropy production and dynamical quantities such as drag force to find possible qualitative relations between them.
Highlights
Homogeneous bodies of revolution around an axis, a, with fore-aft symmetry, when immersed in a quiescent liquid, orient themselves in certain ways with respect to the direction of gravity which depend upon the shape, size, density of the rigid body and the nature of the surrounding fluid [1,2,3]
Our study indicates that geometric effects are significant and allow us to test the validity of MEPP as a selection principle
What makes the case of the half cylinder challenging is that an analytical expression for the flow field is not available
Summary
Homogeneous bodies of revolution around an axis, a, with fore-aft symmetry, when immersed in a quiescent liquid, orient themselves in certain ways with respect to the direction of gravity which depend upon the shape, size, density of the rigid body and the nature of the surrounding fluid [1,2,3]. Experiments on terminal orientation have come in two forms: (i) sedimentation, where the body falls through a quiescent fluid under gravitational force or as (ii) a horizontal setup with the body being hinged at the center of a flow tank. In this latter case, the body is fixed in space, though allowed to rotate, while the fluid moves past it. The immense mathematical complexity of the problem and the advent of fast computing has resulted in more problems being solved numerically, where analytical arguments are no longer possible While these methods effectively capture the dynamical process, they are computationally expensive and often difficult to implement. Thermodynamics can reveal the underlying energetics of the system and provide more fundamental explanations for problems involving pattern formation/selection
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