Abstract
The stability of the flow between two vertical, infinite, rigid, coaxial cylinders held at different temperatures is analyzed by linear stability theory. For a Prandtl number of 22.8 and a radius ratio of 0.02, the flow is unstable to an axisymmetric perturbation at a critical Grashof number of 2150; the wave speed of the instability is comparable to the maximum velocity of the unperturbed flow. When the rigid outer cylinder-fluid interface is replaced by a crystal-melt interface which can change shape, two new modes of instability occur at lower Grashof numbers. There is an asymmetric instability with a critical Grashof number of 180 and an axisymmetric instability with a critical Grashof number of 460; for both of these modes the wave speed of the instability is several orders of magnitude smaller than the unperturbed flow velocity. These calculations were motivated by and are in general agreement with our recent experiments on succinonitrile. A long vertical cylindrical sample of succinonitrile was heated by an electrical current through a coaxial vertical wire so that a vertical melt annulus formed between the coaxial heater and the surrounding crystal-melt interface. Above a critical Grashof number of circa 200, a helical crystal-melt interface formed which rotated steadily about the cylinder axis; the wave speed was several orders of magnitude less than the base flow velocity.
Published Version
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