Capillary Limit of Evaporator Wick in Alkali Metal Thermal-to-Electric Converters

Abstract

Vapor anode, multitube alkali metal thermal-to-electric converters are being developed for potential use in space and terrestrial electric power generation. In these converters, the capillary pressure head produced in the evaporator wick circulates the sodium working uid. A two-dimensional, thermal-hydraulic model of the porous evaporator wick and of the liquid sodium return artery is developed and thermally coupled to an integrated model of a ve-beta 0 0 -alumina solid electrolyte (BASE) tube, stainless-steel sodium converter (PX-3A), and an eight-tube, Mo-41%Re sodium converter. Results showed that the capillary limit in the evaporatorwick of the PX-3A converter is reached at zero electrical current, when the thermal input power to the converter exceeds 16 W, or the hot-side temperature exceeds 1136 K. For the Mo-41%Re converter, these values are 22 W and 1150 K, respectively. Before reaching the capillary limit, however, two or more of the following temperature limits occurred in both converters: 1) the TiNi metal-ceramic braze joints' temperature exceeded 1123 K, 2) the evaporator wick surface temperature exceeded 1023 K, or 3) the temperature difference between the cold end of the BASE tubes and the evaporator wick surface was less than +20 K. (16b) and (17) C p = speci c heat, J/kg ¢ K D = thermal conductance, W/m 2 ¢ K F = Faraday's constant, 96,485 C/mol G E = geometric factor for pressure losses in electrode g = gravity acceleration, 9.81 m/s 2 h = enthalpy, J/kg I = electrical current, A K = permeability, Eqs. (16b) and (17), m 2 k = thermal conductivity, W/m ¢ K M = molecular weight of sodium, 23 g/mole P m 00 ev = vaporization mass ux, kg/m 2 ¢ s P m I = sodium ow rate in the converter, kg/s N B = number of beta 00 -alumina solid electrolyte (BASE) tubes P = pressure, Pa P e = electrical power output, W e P sat = sodium saturation pressure, Pa q = area-averaged velocity in wick, m/s Q = conduction heat ow rate, W Q in = input thermal power, W Q rad = net rate of radiant heat loss, Eq. (2), W R c = radius of curvature, m R g = perfect gas constant, 8.314 J/mol ¢ K R L = external load resistance, Ä R p = effective pore radius of evaporator wick, m .Associate Fellow AIAA. r = radial coordinate, m T = temperature, K t = time, s V L = external load voltage, V Vol = volume, m 3 z = axial coordinate, m ® p = vapor volume fraction in porous wick 0 = conduction/advection heat ux, W/m 2 1P = pressure head/drop, Pa 1R i = radial width of numerical mesh, m 1T = temperature margin (T B ¡ T ev ), K 1t = discretization time step, s 1Z j = axial width of numerical mesh, m " = wick volume porosity µ = apex half angle of cone ¹ = dynamic viscosity, kg/m ¢ s ¹ c = cosine of contact angle, R p =R c ½ = density, kg/m 3 ¾ L = liquid surface tension, N/m  i; j = evaporation coef cient, Eq. (6), a cc .M=2¼ R g T i; j / 1=2 Subscripts/Superscripts a = anode side of BASE B = cold end of BASE tubes c = cathode side of BASE cap = capillary pressure cd = condenser eff = effective ev = evaporator wick surface hot = hot side of co...

A review on advances in alkali metal thermal to electric converters (AMTECs)

“…In fact, the current two problems with regard to the performance There are some unsolved technological problems that confront the AMTEC development efforts, such as the long-term stability and reliability of critical components (BASE, electrode, etc. ), high reliable braze seals between BASE and structural components, electric issues, such as electrical shunts that reduce power output and electrical breakdown, which limits the number of connected BASE, and the constrained operation by capillary limit [109,110]. Since the evaporator wick is the driving source in thermal to electric conversion process, it is important to ensure its stable and reliable operation.…”