DOE OSTI2017
The sodium thermal electrochemical converter (Na-TEC) is a heat engine that generates electricity through the isothermal expansion of sodium ions through a beta”-alumina solid-electrolyte. The Na-TEC is a closed system that can theoretically achieve conversion efficiencies above 45% when operating between thermal reservoirs at 1150 K and 550 K. However, thermal designs have confined previous single-stage devices to thermal efficiencies below 20%. To mitigate some of these limitations, we consider dividing the isothermal expansion into two stages; one at the evaporator temperature (1150 K) and another at an intermediate temperature (550 K – 950 K). This dual-stage Na-TEC takes advantage of regeneration and reheating, and could be amenable to better thermal management through a reduction of parasitic losses. These losses are comprised of (i) the heat input that does not participate in power production but simply bypasses the thermo-electrochemical process and is transferred to the condenser, and (ii) heat that is lost from the device directly to the surroundings due to poor insulation. Heat loss to the surroundings occurs from a lower average hot-side temperature given that a fraction of the power conversion occurs at an intermediate stage. Also, the condenser now directly interacts with the lower temperature of the intermediate stage, thereby reducing radiation loss. A simplified geometry is developed for this device to help guide its design from a heat transfer perspective. All thermal contact and boundary conditions are discussed, including the evaporation and condensation of sodium vapor, thermal leakage through the housing, and the thermal contact between the beta”-alumina and the housing. A ray tracing method assuming gray, diffuse surfaces is used to account for the internal radiation heat transfer within the device. Liquid sodium flows in a capillary wick between the condenser and the evaporator with Pe << 1, so only conduction heat transfer is considered within this liquid return path. For simplicity, natural convection between the sodium vapor and the device housing is neglected. A numerical linear resistance model (<5% error when compared to a finite element model) is used to determine the expected conversion temperatures of each stage for a range of candidate materials. Furthermore, a numerical model (<2% error) is developed to find the factor of increase in the thermal resistance for several designs of corrugated features for the device housing. By using an iterative scheme, efficiency vs. power curves are created for a number of material and size combinations. Finally, the fundamental tradeoff between the power and efficiency is explored in conjunction with the total system size.