Sodium Vapor Pressure Losses in a Multitube, Alkali-Metal Thermal-to-Electric Converter

Abstract

A model was developed to calculate the vapor pressure losses and characterize the vapor flow regimes on the cathode side of a multitube, vapor-anode, alkali-metal thermal-to-electric converter (AMTEC) cell, with internal chevron's radiation shields. The dusty gas model was used to predict the vapor flow over a wide range of pressures, including the free-molecular, transition, and continuum flow regimes. Results showed that the vapor flow on the cathode side of a multitube AMTEC cell is typically in the transition regime, and that the pressure loss in the chevron's shield accounts for about 50% of the total pressure losses. An analysis is also performed to optimize the conical chevron's geometry for minimum pressure loss. Nomenclature A= surface area, m 2 a cc = accommodation coefficient, Eqs. (1) and (25), 1 b = perpendicular distance between chevrons, m D = flow diffusion coefficient, m 2 /s D a = diameter of centerline liquid-return artery, m, 3.18 mm D B = BASE tubes outer diameter, m, 6.35 mm D e = equivalent hydraulic diameter, m D w = inner diameter of AMTEC cell wall, m, 33.2 mm d = separation distance between chevrons, m F = Faraday's constant, 96,485 C/mol / = laminar friction coefficient G -dimensionless geometric factor for pressure loss, Eq. (5) / = total cell electrical current, A J r = electrode current density, A/m 2 Kn -Knudsen number of sodium vapor L = effective flow path through chevrons, m L B = distance between bottom of electrode and top of BASE tube, m L c = distance between BASE tubes top and chevrons, m L s = height of chevron's shield, m L T = distance between chevrons and condenser, m M = molecular weight of sodium, kg/mol, 23 gm/mol Ma = vapor Mach number, w"A/ypP Wp 0re = vapor mass flux in electrode pores, kg/m 2 s m z -vapor axial mass flow rate, kg/s m" = vapor axial mass flux, kg/m 2 s N = number of conical chevrons N B = number of (seried-connected) BASE tubes, 7 P = sodium vapor pressure, Pa Re = vapor Reynolds number, D e m"/jji R g = perfect gas constant, 8.314 J/mol K R p -average hydraulic radius of electrode pores, m, 10 jam T = temperature, K t E = thickness of cathode electrode, m, 5 ^m z = axial coordinate, m a = chevrons packing factor, Fig. 3 a 2= coefficient for advection of axial momentum y = specific heat ratio of sodium vapor, 5/3 AP = pressure loss through conical chevron's shield, Pa APcd = pressure loss due to condensation of sodium, Pa AP £ = pressure loss through cathode electrode, Pa APevap = pressure loss as a result of evaporation of sodium at BASE surface, Pa e £ = volume porosity of cathode electrode, 0.9 £ = correction factor for laminar flow in annulus 0 = angle of conical chevrons, Fig. 3 IJL = dynamic viscosity of sodium vapor, kg/m s £ = resistance coefficient for sudden expansion, Eqs. (13) and (14) p = vapor density (kg/m 3 ), PMI(R S T) 9 = compressible factor, Eq. (26) X = flow conductance of chevron's shield, m 2 /s Subscripts B = beta"-alumina solid electrolyte (BASE) c = cathode electrode/BASE interface cd = condenser ev = evaporator E = catho...

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

“…The evaporator wick and LSRA model calculates 1 P wick , whereas 1 P cell is calculated by APEAM. 3 The present analysis assumes that, up to incipient dryout of the evaporator wick, the Creare-type condenser structure is saturated with liquid sodium, and the liquid-vapor (L-V) interface is highly re ective (effective emissivity of »0.05). This assumption is reasonable, particularly at high electric current (or high condensation mass ux).…”

“…The latter is calculated by the vapor pressure loss model in APEAM. 3 The pressure drop across the cathode electrode is typically expressed in terms of an empirical dimensionless factor G E , which is determined experimentally (see Table 1). …”

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

“…For converters that do not contain remote condensers and vapor condenses on a surface adjacent to the tubes, the pressure loss due to vapor flowing to the condenser after moving through the porous cathode electrode is simply approximated as the result of a sudden expansion, and any other pressure loss prior to condensing is assumed negligible. The sodium flow pressure losses on the cathode side of a multi-tube AMTEC cell with internal chevrons radiation shields can be found from [31,32]. The flow diffusion coefficients in the free-molecular regime were calculated using the Dushman formulas, while those in the continuum regime were determined by using an exact analytical solution (when available) or the equivalent hydraulic diameter approximation [38,39].…”

“…This integrated cell model consists of four submodels: (a) a sodium vapor pressure loss model [31,32]; (b) a radiation/conduction heat transfer model [33,34]; (c) a cell electrochemical model [35]; and (d) a two-dimensional cell electric circuit model [35]. The fully integrated cell model (APEAM) has been benchmarked successfully using experimental data of single-and multi-tube cells ground tested in vacuum at the Air Force Research Laboratory/ Phillips Laboratory (AFRL/PL).…”

“…The sodium flow pressure losses on the cathode side of a multi-tube AMTEC cell with internal chevrons radiation shields can be found from [31,32]. The flow diffusion coefficients in the free-molecular regime were calculated using the Dushman formulas, while those in the continuum regime were determined by using an exact analytical solution (when available) or the equivalent hydraulic diameter approximation [38,39].…”