Numerical study on natural convection of liquid nitrogen used to cool the high-temperature superconducting cable in a new combined energy transmission system

In a new high-temperature superconducting (HTS) electricity transmission system, natural convection of liquid nitrogen in the annular channel is caused by the inside wall heating and outside wall cooling. Two-dimensional numerical simulation of the natural convection is conducted using a finite volume method. The dimensionless eccentricity, ε∗, in the range of −1.0 to 1.0 is considered when the Rayleigh numbers (Ra) varied from 2 × 10⁵ to 1 × 10⁷. A bifurcation map of flow pattern is obtained by many numerical simulations. It is found that there are three typical flow regions in the fully developed stage, i.e. steady flow, periodic flow and chaotic flow. When the Ra is relatively low, the flow is steady and uniform. As the Ra increases, the reinforced natural convection approaches a time-dependent periodic flow and further a strongly chaotic flow. Furthermore, when the ε∗ is up to 0.6, a cluster of Rayleigh-Bénard convection cells appears on the top of the flowing channel, and enhances the heat transfer slightly. The effect of the ε∗ and Ra on the heat transfer of natural convection is analyzed quantitatively. It is demonstrated that the most suitable region for the vertical position of the HTS cable is for a dimensionless eccentricity in the range of −0.8 to −0.6 to enhance the heat transfer while guaranteeing the safety of the HTS system.