Summary
The instability associated with the onset of motion in a toroidal natural-circulation loop has been studied theoretically. A one-dimensional model is used to investigate the problem of global flow initiation from a rest state. It is shown that a thermosyphonic flow is established when the modified Rayleigh number exceeds a critical value, R * c or R c , which depends on the modified Biot number B. For a loop heated by a uniform heat flux R * c is between the limits of 1/4 and 2.816 for small and large B, respectively. For a loop heated by a prescribed constant wall temperature, R c has a minimal value of 2 at B=1. These results were obtained by two methods: a direct solution of the steady-state problem and a stability analysis of the rest state. The latter shows that when R *>R * c there is a single monotonously growing perturbation and there are always additional monotonously decaying disturbance modes.
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Zvirin, Y. The onset of motion in a toroidal thermosyphon. J Eng Math 20, 3–20 (1986). https://doi.org/10.1007/BF00039319
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DOI: https://doi.org/10.1007/BF00039319