A new concept of thermal design to optimize the operating temperature of HTS magnets is developed, aiming simultaneously for compactness and efficiency. The optimization procedure seeks the operating temperature to minimize the power consumption in steady state. This procedure includes the modeling of the critical properties of HTS conductors, the dimensions of HTS windings, the heat transfer analysis for cooling load estimate, the thermal interface between the HTS windings and cryocooler, and the thermodynamic evaluation of the required refrigeration. Finally, this method is applied to two specific cooling systems for HTS transformers: a liquid-cooled system with pancake windings and a conduction-cooled system with solenoid windings. The optimum temperature turns out to be slightly above 77 K, the normal boiling temperature of nitrogen, for both the liquid-cooled system and the conduction-cooled system, but could vary considerably by the magnitude of AC loss in the HTS conductors. Operation at a temperature below 77 K can be justified, if the amount of AC loss is substantially reduced or the savings in capital investment by the compactness is significant in comparison with the operational cost.
A new cryogenic design for cooling HTS transformers, the so called natural convection system, is proposed in accordance with the results of an optimization study and the considerations of liquid nitrogen as cooling media. In the natural convection system, HTS windings are immersed in a liquid nitrogen bath where the liquid is cooled simply by copper sheets vertically extended from the coldhead of a GM cryocooler above the windings. Liquid nitrogen in the gap between the windings and the copper sheets develops a circulating flow by the buoyancy force in the subcooled state. A comprehensive heat transfer analysis is performed to evaluate the proposed cooling system. The heat transfer coefficient for natural convection is predicted from the existing engineering correlations in which the temperatures of two surfaces are uniform, and then the axial temperature distributions of HTS windings, copper sheets, and liquid-vessel wall are calculated analytically and numerically, taking into account the distributed AC loss and the thermal radiation on the walls. The warm-end of the HTS windings is maintained at only 2~3 K above the freezing temperature of nitrogen (63 K) at atmospheric pressure with acceptable values for the height of HTS windings and the thickness of copper sheets. Such a system based on cooling by natural convection with subcooled liquid nitrogen could be an excellent option for HTS transformers, when considering all aspects of compactness, efficiency, and reliability.
In order to confirm the feasibility of the new design for cooling HTS transformers, a natural convection cooling experiment was designed and constructed. The primary purpose of the experiment, therefore, is to simulate the thermal environment as closely as possible to the proposed cooling system. The experimental apparatus is approximately 1:5 scale and has the same configuration as the cooling system for Korean HTS transformer, except that an electrical heater is used for simulate the AC loss and the vertical cavity between parallel plates replicates the narrow annular gap between HTS windings and the vertical copper sheets in the cooling system for an HTS transformer. A liquid nitrogen bath is cooled down to nearly the freezing temperature at atmospheric pressure by a vertical copper heat transfer plate thermally anchored to the coldhead of a single-stage GM cryocooler. A parallel copper plate generating a uniform heat flux is placed at a distance so that liquid between the two plates may develop a circulating flow by natural convection. The cold surfaces are continuously maintained below 66 K in subcooled liquid nitrogen for heat fluxes up to 100 W/m2. The vertical temperature distribution on both surfaces is measured in steady state, from which the heat transfer coefficient is calculated and compared with the existing correlations for a rectangular cavity where each vertical surface has a uniform temperature. When the heat flux is smaller than 40 W/m2 or the corresponding Rayleigh number is smaller than 1.6 x 10^8, good agreement is observed between the experiment and correlation because the plate temperatures are relatively uniform in the vertical direction. As the heat flux increases over 40 W/m2 or Rayleigh number exceeds 1.6 x 10^8, however, the heat transfer coefficients are approximately 20~30 % greater than the existing correlations. The thermal boundary conditions in the present experiment with surface temperature decreasing upwards may cause vertically segregated cellular flows in the cavity. These multi-cellular flow patterns can lead to the augmentation of wall-to-wall heat transfer by reducing the effective height of the cavity.