MIT 22 33 - Calculated Efficiency for Thermionic Systems

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Calculated Efficiency for Thermionic SystemsAustin Roach11/10/041 ObjectiveWe will develop a model for estimating the efficiency of a thermionic system based on severalparameters, includingits emitter temperature, collector temperature, electrical characteristics,diode spacing, and cesium gas pressure. 2 Energy Conservation AnalysisThe calculated efficiency for a high-pressure cesium diode thermionic system is given by (1)where V is the voltage at the electrodes, is the voltage drop across the leads, J is themeasured current density, and is the input heat-rate density.The term is itself the sum of several terms, (2)where is the energy flux from the current J leaving the emitter, is the heat conductionrate through the thermionic structure, is the heat conduction rate through the vapor, is theenergy flux associated with thermal radiation into the inter-electrode space, and isthe heat rate through the leads.The term is the term describing the electron cooling of the emitter, and can be expressed as(3)where is given by (4)The heat conduction rate through the vapor can be determined by (5)where and are the emitter and collector temperatures in Kelvin, is the cesiumpressure in torr, d is the diode spacing in centimeters, and is the thermal conductivity of thecesium vapor in watts per degree Kelvin per centimeter, evaluated at the mean vapor temperaturegiven by (6)The interelectrode thermal radiation rate per unit area is given by (7)For refractory metal electrodes, it is reasonable to assume a value .Thermal conduction through the supports and through the electrical leads and the supports isdifficult to calculate theoretically, but as a convservative approximation can be taken to be 30%of the other thermal loss mechanisms.3 Analysis of Efficiency for the Proposed Thermionic SystemThe calculated efficiency will be determined for a system with a rhenium emitter at 1800K, amolybdenum collector at 950K, a diode spacing of 5 mils, and a cesium pressure of 10 torr.The electron cooling of the emitter is taken as an experimentally determined value.Extrapolating data from systems similar to the proposed system, the system can be expected toproduce of electric power . For and , the mean vapor temperature . Atthis value, . The interelectrode spacing, d, is specified in thedesign to be 5 mils, or 0.0127 centimeters. The cesium vapor pressure will ber taken to be10 torr as a conservative estimate. These numbers produce a heat conduction rate through thecesium vapor of .For the given electrode temperatures and an estimated emissivity of 0.3, the thermal radiationloss is determined to be . The thermal losses through the leads and otherstructure and approximated to be .The calculated efficiency of the electrical system is therefore determined to be 24.8%. Thiscalculation does not take into account the voltage drop across the leads of the system. This lossmechanism and other inefficiencies within the system could easily bring this number down, butthe efficiency will almost certainly stay above the 10% demanded by the project’s goals.All formulas and parameters from:Hatsopoulos, H.N., & Gyftopoulos, E.P. (1973). Thermionic energy conversion volume I:processes and devices. Cambridge, MA: MIT Press.Figure 1: Thermionic convertor conceptual drawing. The horizontal scaling is exaggerated toshow


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MIT 22 33 - Calculated Efficiency for Thermionic Systems

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