Potentialities of TEC topping: a simplified view of parametric effects

An examination of the benefits of thermionic-energy-conversion (TEC)-topped power plants and methods of increasing conversion efficiency are discussed. Reductions in the cost of TEC modules yield direct decreases in the cost of electricity (COE) from TEC-topped central station power plants. Simplified COE, overall-efficiency charts presented illustrate this trend. Additional capital-cost diminution results from designing more compact furnaces with considerably increased heat transfer rates allowable and desirable for high temperature TEC and heat pipes. Such improvements can evolve of the protection from hot corrosion and slag as well as the thermal expansion compatibilities offered by silicon-carbide clads on TEC-heating surfaces. Greater efficiencies and far fewer modules are possible with high-temperature, high-power-density TEC: This decreases capital and fuel costs much more and substantially increases electric power outputs for fixed fuel inputs. In addition to more electricity, less pollution, and lower costs, TEC topping used directly in coal-combustion products contributes balance-of-payment gains.


EXECUTIVE SUMMARY
High-temperature, high-power-density thermionic energy conversion (TEC) offers more power, lower costs, and less pollution from toppingcycle generation: High temperatures enable substantial Carnot gains, hence more power and less pollution from a given fuel input. And high power densities allow great reductions in numbers of converters for a given fuel input, hence much lower capital investments.
For a TEC-topped steam power plant the net overall efficiency with 0.15 bypass (K) is n^oP ~ 0.34 + 0.38 HTEC °^ with zero bypass ^NOP ^ 0.34 + 0.45 rixEC» where nxEC ^^ ^^^ efficiency with optimized leads. The corresponding 30-year levelized cost of electricity in 1975 dollars is for K = 0.15 COE30 ^ 4.9 + (17.6 + 0.064 C^^^ + 0.5 nr,,j.c •*" 17.9N)/(0.9 + n^g(.) or for K = 0 COE73 "=• 4.9 + (14.7 + 0.063 C^g^, + 0.5 Tirpgf, + 15. IN)/O. 75 + n,p£(,), where C^g^, is $/kW^ for the TEC system and N is $/10^ Btu for fuel. Thus, with a 0.15 bypass 10% HTEC V^^'^^^ 11% more electric power than steam alone; 20% n'j;£Qi 22% more power; 30% ^TEC ^^^ more power; and 40% n^pg^j 45% more power. Also increasing rijgp with constant C^gc ($100/kWj. for example) and N ($1/10° Btu and $4/10^ Btu) effects substantial changes in COE^^ relative to that for steam alone: ^75 These numbers indicate parametric effects of TEC and fuel costs as well as TEC efficiency. But they fail to imply the great cost saving possible with fully matured high-temperature, high-power-density TEC: For negligible interelectrode losses and 10% back emission, using 1800 K, 30A/cm2 TEC rather than 1600 K, 5A/cm2 TEC produces the same power output 25-to-31% more efficiently with one-seventh the number of converters. Such gains are certainly worth striving to attain through TEC applied research and development.
Recent findings on hot-corrosion protection, slag resistance, and thermal-expansion compatibilities of silicon-carbide-clad heat receivers predict successful TEC service in high-temperature coal-combustion products. And new compact furnace designs with much greater heat-transfer-' rates optimized for TEC with emitter as well as collector heat pipes should allow further significant cost reductions.
Thus, high-temperature, high-power-density TEC topping not only offers more power, lower costs, and less pollution but also promises contributions toward balance-of-payment equity and national energy independence.
TEC TOPPING-CYCLE CONSIDERATIONS Thermionic energy conversion (TEC) brings significant advantages to topping-cycle power generation: Substantially increased outputs and decreased costs of electricity are possible through camot-ef flciency gains inherent with TEC. But, its true potential remained veiled until recently (refs. 1 to 4) because of the apparently defensive avoidance of the high temperatures and great power densities attainable with TEC (refs. 5 to 18). These TEC characteristics are strengths not weaknesses. And to amplify that observation this paper further indicates the potentialities of "high-temperature, high-power-density thermionic energy conversion" (ref. 1).
Reference 4 adapts partially optimized results for TEC topping of a steam plant (ref. 3) to the cost-of-electricity (COE), overallefficiency chart from reference 19. This adaptation allows the compatible comparison of "thirty-year leverlized costs in mid-1975 dollars" with "fuel cost assumed constant in fixed dollars" at $1/10^ Btu for coal ( fig. 1). The "partial optimization of steam-plant topping with > 20 A/cm2 TEC yields overall efficiencies near those for the mostefficacious advanced systems and COE's between the best and those for conventional steam plants. And as reference "3 concludes, 'we expect that further significant improvements can be made by optimizing the overall system design.' Such results should place TEC, STEAM among the best systems on figure" 1 (ref. 4).
In the present paper, corrected and reduced reference -3 equations imply influences of TEC efficiency (10 to 40%) and cost (100 to 400 $/kWt) as well as fuel cost (1 to 4 $/106 Btu) on overall efficiency and COE for TEC topping of central-station steam plants. In turn plots of TEC efficiency and power density reveal the striking performance gains possible with the hotter emitters at 30 A/cm2 as opposed to 5 A/cm .
Equations (2), (10), (2A), and (lOA) for the variables composing figure 1 emphasize the importance of TEC performance: n,,r.p varies directly with IXEC* ^^'^ ^^^ predominant n^EC offset on COE^c derives from the denominator ("^ %0P^ °^ ^^^ second term in (10) or (lOA); the numerator HJEC effect is nearly negligible. Much stronger influences result from TEC power densities, which subsequent sections discuss. Those discussions cover results from converter-performance equations presented in the next section.

TEC-PERFORMANCE EQUATIONS
The appropriate converter outputs are the current density, the voltage at optimum-lead terminals, the electrode power density, PQ = ^OVQ (1^) and the effective power density with optimum leads attached to the converter, PQL = -JQVOL (15) Here 0E and 0Q are emitter and collector work functions, Vj) is the interelectrode voltage drop, Vg = 0^ + Vp is the barrier index or total internal loss, VA is the equivalent auxiliary input voltage (not used in the present calculations), and V^ is the voltage loss required for optimum leads.
The current-density components correspond to emitter saturation, which has a collector-saturation counterpart, 2 Jcs = A(l -R^) TQ exp (-0c/kTc) (17) and to the reverse flow J-^, which includes reflections, backscattering, back emission, and other effects that diminish the output current density. In equations (16) and (17) A and K are RicharJson and Boltzmann constants, Tg and TQ are emittor and collector temperatures, and Rg and RQ are emitter and collector reflection coefficients.
An important theoretic detail relates Lo a common inconsistency in the treatment of back emission (refs. 1, 20 and 21): In generalized TEC terminology back emission subt racts from the emitter current in obtaining the net output current. This usual definition of bad' emission requires it to be only that part of the collector emission that reaches the emitter and thereby diminishes the output current according in a netflow balance at the converter boundaries. Thus, back emission is not the saturated collector emission given by equation (17), regardless of RQ modification, because the emission barrier is incorrect: This observation derives from the fact that, in the generally cited TEC powerproducing mode, the emitter electron barrier (motive maximum) is a few tenths of a volt (the interelectrode voltage drop) above its collector counterpart. So during steady-state operation the preponderance of collector saturated emission cannot clear the emitter sheath, even in the absence of other deflecting encounters. Therefore, most of the collector saturated emission must return to its source nullifying to a large extent its effect on the diminution of the net output current.
Unless the interelectrode loss is much closer to zero than to its currently common value of about a half volt, only a small fraction of the collector emission, the true back omission Jgg, will ^each the emitter: Jgg = A(l -Rgg) Tc exp (-Vg/kTc) (18) In this equation the effective back-emission reflection coefficient RgE comprises RQ and similar coefficients for all interelectrode mechanisms that return collector-emitted electrons to their source -except those for noncollisional repulsion by the emitter sheath. Thus, using equation (18) without RRE produces a conservative estimate of the converter output current. Such an approximation seems reasonable for low cesium concentrations, reduced enhanced-mode pressures, and small interelectrode gaps. Of course, with zero interelectrode losses assumed (ref. 6 for FY 81) as well as negligible interelectrode-reflection effects, equations (17) and (18) Here the last term of the denominator approximates nonelectronic thermal transport while the factor following the first 2 in the numerator represents the optimum-lead loss V^. Deleting 2VL from equation (19) transforms that expression into one for the TEC electrode efficiency riEC used here to compute the optimum-lead loss. Of course, the electrode efficiency is the true converter evaluation analogous to other power-generator performance ratings. But because of relatively high TEC current densities and low voltages the optimum-lead efficiency seems more pragmatic. A discussion of results from (19) as well as (15) (2) and (10) offer additional perspective on COE^O n^np trends for variations of C,pgp and TTpEC" Incidentally the steam-plant basis for equations (2) and (10) at 34% HNOP ^'^^ 44.3-mills/kWhr COE^^ differs slightly from its figure-1 counterpart.

TEC-PERFORMANCE INFLUENCES
The importance of converter-performance improvements in TEC topping of power plants (TOPP) stands out in figures 1 to 5. However, figures 6 and 7 emphasize a far more important characteristic of the results for TEC with 10% back emission and negligible interelectrode losses: Changing from low emitter temperatures and low power densities to allowable high-temperature, high-power-density TEC not only significantly increases converter efficiency but also greatly reduces the number of TEC modules, hence the cost, required for a given thermal input or a desired power output.
Reference 1 indicated this effect in 1977 for space nuclear electric power utilizing TEC with 925 K collectors. Those results parallel or analogize TEC-TOPP implications: These underlined values also reveal the significant output and efficiency gains for TEC operation at 1800 K and 30 A/cm2 as compared with 1650 K and 5 A/cm2 (refs. 5 to 8): The 28.5% increase in optimum-lead efficiency means lighter radiators and either more output power or smaller nuclear reactors and lighter shield-dependent weights for NEP. The 10.8% higher optimum-lead voltage requires less power conditioning capability and results in lower transmission-line losses for a given quantity of output power. The 560% gain in effective output power density allows many fewer converters and associated current-collecting bus bars for a given output-power level. And of course the higher emitter temperature (coupled with greater efficiency) enables the use of substantially fewer and/or smaller emitter heat pipes. This reduction in turn should produce significant decreases in shielding-related as well as reactor weights. The higher emitter temperature can also make possible considerably increased collector temperatures if parametric studies indicate the need for lower radiator weights (the T^ influence).
"Less power conditioning ... fewer converters and associated currentcollecting bus bars ... fewer and/or smaller, emitter heat pipes" all relate directly to the TEC-TOPP application.
Similarly, in a comparison of figures 6 and 7 results, using 1800 K, 30 A/cm2 TEC rather than 1600 K, 5 A/cm2 TEC (1) for a given power output requires about one-seventh the number of converters and yields 25-to-31%-more efficiency, (2) for a given thermal input produces 25-to-31%-more power output with less than one-fifth the number of converters. In fact figures 6 and 7 indicate that using 1600 K, 30 A/cm2 TEC rather than 1600 K, 5 A/cm2 TEC generates -12% more output power within -79% fewer converters for a given thermal input. These potentially great cost savings are in no way implied by equations (3) and (10) or figures 2 to 5.
But are the advantages of high-temperature, high-power-density TEC attainable? The DOE TEC program aims at approaching converter capabilities represented by figures 6 and 7. Figure 15 of reference 4 shows the definite progress in that direction. For the fully matured TEC technology, figures 6 and 7 reveal that the higher efficiencies at 30 A/cm2 are available for emitter temperatures down to 1300 K. Furthermore reference 3 predicts much lower costs for converter modules with the higher power densities in TEC TOPP even with emitters at 1500 K. However TEC service at much higher temperatures in coalcombustion products appears feasible: References 24 to 28 support this observation with gratifying findings on silicon-carbide protection against hot corrosion and slag as well as workable thermal-expansion compatibilities. And TEC with suitable silicon-carbide cladding appears substantially more economical than with lower-temperature super alloy protection (private communication with F. N. Huffman, Thermo Electron Corporation).
In addition to the preceding potentialities high-temperature, highpower-density TEC should encourage designs of more compact furnaces with significantly greater heat-transfer rates. In turn high-temperatureemitter heat pipes can collect outputs from optimum-cost furnaces and transform them to TEC-input thermal-power densities. Such increased degrees of design freedom should facilitate overall-plant optimization, which could yield even lower relative costs. This capability is important because curves for CXEC ~ 0 fall essentially on the dashed lines representing figure-1 points.
Thus high-temperature, high-power-density TEC promises greater efficiencies, far fewer topping modules, and improved overall-plant optimization -decreasing capital and fuel costs as well as increasing power outputs. And with lower costs, more electricity, and less pollution, TEC topping in coal-combustion products will also contribute to balance-of-payment gains and national energy independence.
The potentialities of TEC topping alone warrant the appliedresearch and development efforts required for their attainment.