A New Look at Closed Brayton Cycles

8/13/2019 A New Look at Closed Brayton Cycles

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F. David Doty & J. Dewey Jones

ncorporated & Simon Fraser University


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The MTS heat exchanger achieves these goals by taking ad-vantage of the properties of modern alloys and automatedmanufacturing techniques. Mass-produced sub-millimeter-diameter stainless-steel tubes are finished to the requiredlength, then automatically inserted into spacer forms. Theyare held rigidly by encapsulation in a low-melting-point fusiblealloy, and die-cut tube strips are pressed onto each end of thearray of tubes. Given the right degree of interference fit be-tween the tubes and the die-cut holes in the tube strips (0.4- 3 ), the assembly can then be heated to 1100 O C for afew minutes to effect diffusion welding between the tubesand header strips. We have assembled heat-exchanger mod-ules containing over 100 tubes by this method and foundthe welds to be 100 leak-tight - within l o - & mm3/s tohydrogen a t one atmosphere.A sketch of a single module is shown in Figure 1.

FiTure 1In a typical application, many modules would be manifoldedtogether into banks (Figure 2.)

Figure 2We have so far built and tested a three-module, 327-tubebank, and believe the current limit of technology is an 800-tube module.In the companion paper, we calculate the dimensions thatwould be appropriate for an MTS heat exchanger designedto exchan e 3 MW between helium streams flowing at 1kg/s,for a totaf frictional loss of 30 kW. This corresponds to anMTS design employing 200,000 tubes of length 0.3 m andinternal diameter 0.5 mm. This is a theoretically based cal-culation;. practical considerations, including the losses asso-ciated with manifolding and baffling, would certainly com-promise this performance. However, we believe the quotedfigures are of the correct order, and that a heat exchanger ofthese dimensions can be manufactured with currently avail-able technology at a reasonable price.

The heater and cooler must exchange heat with the environ-mental air. Because of the acknowledged sensitivity of theMTS heat exchangers to fouling, high efficiency in filtrationis of crucial importance, both for cooling and for combus-tion. While air filtrat ion is a very mature and well developedtechnology, the stringent requirements of the MTS exchang-ers warrant a careful evaluation of the available technologyand the development of some innovative designs.Advantages of the Closed Bravton CvcleIf the MTS heat exchanger can reduce the cost penalty as-sociated with the closed cycle, does that cycle have any dis-tinctive advantages to recommend it?The most important advantage of any closed cycle is theflexibility it affords in establishing non-polluting combustionconditions with littIe adverse afect on efficiency. Clean fueIsspecially alcohol an be used to virtually eliminateNO,, CO, and unburned hydrocarbon air pollution.A second advantage of the closed Brayton cycle is its abilityto achieve high efficiencies over a wide range of power de-mand by adjusting the gas pressure, fuel burning rate, andgenerator control parameters[3]. The typical demand condi-tions for utilities between midnight and 5 0 0 A M is aboutone fourth of peak demand. Efficiency of the closed Braytoncycle will generally be maximum at about half power andwill drop to about 96 of maximum at full power and atquarter power. The efficiency of open Brayton cycles andclosed Rankine cycles, on the other hand, decreases rapidlyunder off-design load conditions. Their efficiency is usually amaximum at full power, and it typically drops to about 80%of maximum at half power and 50 at quarter power[4].A further advantage of the CBC is that it separates the hotcorrosion resistance and hot strength requirements: hot corrosion resistance is required only in the heater, and hot spe-cific strength only in the turbine. Uncoated high-strength su-peralloys are well-suited for high-efficiency turbine designs,and the new highly corrosion-resistant ductile superalloysare adequate in the heater. There have been intensive ef-forts over the past two decades to develop high-performanceceramics such as ransformation-toughened zirconia and hot-pressed silicon nitride/carbide. However, these ceramics arestill two to five times as expensiveas most superalloys in fin-ished products, and are therefore not expected to see wideuse in the near future.An engine designed around the LPR CBC also has the advan-tage of simplicity. High-performance heat exchangers allowhigh system efficiencywithout the complications of combinedcycles, turbine-blade cooling, turbine interstage reheat, com-pressor interstage cooling and complex high-compression tur-bine designs. The system is only slightly more complex thana modern internal-combustion engine, allowing it to be scaleddown below 100 kW (135 HP) without major sacrifices inperformance.Finally, the high-working-pressure LPR CBC results in moreefficient utilization of turbine materials, for two fundamentalreasons. First, the ratio of the radial to tangential turbineblade forces is greatly reduced. The specific power of theturbine is greatly increased, even though the pressure ratiohas been reduced, owing to the high pressure and the highvelocity of sound in helium. Second, the subsonic flow con-ditions simplify airfoil design for high polytropic efficiencyin the turbines. State-of-the-art polytropic efficiencies forcompressors and turbines are 83% and 90 respectively at

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3a compression ratio of 13 (as in a typical open cycle). At acompression ratio of 2, these respective efficiencies are 94and 94.5 .CBC DesignWe now derive analytic expressions for the efficiency andpower density of the CBC as a function of the fundamentalsystem parameters. We also consider ease of manufacture.Efficiencv

1 0 1.5 2.0 2.5 3.0 3.5 4 . 0 4.5 5.0 5 5P

Figure 3Fig. 3shows theoretical efficiency curves for the ideal closedBrayton cycle, using helium as a working fluid, with perfectheat exchange for several temperature ratios r = T TI =TH/Tc) as a function of pressure ratio (pr = p2/pi l5]. Atvery low pressure ratio, the efficiency approaches the Carnotlimit. The easiest conceptual explanation of the advantageof low pressure ratio (LPR) in the closed regenerative Bray-ton Cycle is that it increases turbine exhaust temperatureand decreases compressor outlet temperature. This is obvi-ously the opposite of what is desired without heat recovery,but with heat recovery it means that the average tempera-ture of heat injection is higher and the average temperatureof heat rejection is lower. Hence, th e theoret ical efficiencyis increased. (This is not a novel concept. It has been wellunderstood for decades [5,6].) Very high efficiencies can beobtained at moderate temperature ratios by using a low pres-sure ratio. Reducing the pressure ratio tends to reduce thepower density of the engine, but this can be compensatedfor by increasing the mean cycle pressure. Such a desi nhas not been optimum in the past because the heat-transkrrequirements in the recuperator are increased at least five-fold and the pressure requirements in the heater are similarlyincreased. Using MTS heat exchangers for the recuperatorand heater makes it possible to meet these requirements atreasonable cost.The efficiency q of the ideal cycle (isentropic compression andexpansion, 100 recuperator effectiveness, zero pressure lossin ducts and exchangers) is given by:

where r is the compressor pressure ratio, r = Th/Tl, and7= p/.v.

Deriving an expression for the efficiency of a real cycle be-comes very complicated if many effects are considered sepa-rately. The only way to approach theproblem is by computer modelling. Howevlook at major losses analytically andeffects.

Wilsons results to the CBindependent of temperature (valid within 0.1% for He overthe range of interest), and correcting a typographical errorin his final equation (Eq. 3.2, p. 109) yields the followingexpression for the overall system efficiency qs in generatingelectricity.

where r l ~s the heater efficiency, qe is the generator effi-ciency, 7 s the recuperator effectiveness,and C = T2-Tl)/Tl.Assuming an idealE = 1- r- )(-Y)ttc/Yc = r y-l)/yttc - 1 (4)

where r is the compression ratio, qc is the compressor poly-tropic efficiency, qe is the expander polytropic efficiency and6, is the normalized pressure drop in the ducts and recuper-ator.Typical recuperator effectiveness will be 0.9 to 0.97; typi-cal electrical generator efficiency will be 0.96; typical heaterefficiency will be 0.85 to 0.95. Eq. 2 above ignores bear-ing friction losses and assumes that all ducting heat losses and viscous heating are properly considered in VX. Poly-tropic efficiencies for small, low-pressure-ratio, atmosphericcompressor and expander turbines are typically in the 0.85-0.90 range, while larger turbines can exceed 0.96. Efficiencyis primarily a funct ion of number of stages, precision, andReynolds number (size). It is somewhat improved by in-creasing the mean pressure and reducing the pressure ratio.

0 5 . 5 , [ 11.00

a45 E l l E

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7 5 00 2 5 1 I I I t 8 1 6.00089 090 0.91 0.92 0.93 0.93 0.94 O S 0 097 0.53

Renrperator EffectivenesS-

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A short program has been written, based on Eq. 2 , to calcu-late i s as a function of system parameters and componentefficiencies. Figure 4 shows system efficiency and specificmass for a range of values of recuperator effectiveness, andfor high and low component efficiencies; curves A correspondto expander, compressor and generator efficiencies of 0.778,0.756 and 0.886 respectively, while curves B correspond tothe values of 0.9, 0.86 and 0.95 for the same parameters.Specific conductances of recuperator, heater, cooler and pre-heater for this figure are taken to be 150, 70 , 40 and 100W/kg.K respectively; our companion paper reports an ex-perimentally measured specific conductance of 50 W/kg.Kfor a prototype MTS heat exchanger, and we believe theseperformances to be achievable in the short term.

054 5.50055.p 052

3 0bi5 051

0.49a40

5.205.x)5.00 .g4.90 54.804.70

0.46 0.89 as0 031 092 033 034 M5 095 037 OS 0.99Recuperator EffectFveneSs

Figure 5Figure 5shows an optimization curve based on a longer-term extrapolation of currently available technologies. Theassumed figures for expander, compressor and generator ef-ficiencies are 0.95, a.92 and 0.95 respectively, while the as-sumed values for specific conductance in recuperator, heater,cooler and pre-heater are 800 ,70 ,60 and 140 W/kg.K respec-tively.Svecific PowerAn important parameter in the open Brayton cycles usedfor jet propulsion is the ratio of output power to gas flow.Hence, it is customary t o define specific power as the dimen-sionless ratio Po/(rizcpTI),where Po is the power output, mthe mass flow rate, cp the gas specific heat and TI the maxi-mum cycle temperature. In the CBC, this parameter is of noconsequence. An extremely significant parameter, however,is the specific power P' as frequently defined for the Ottoand Diesel internal combustion engines:

P' = Po/ms ( 5 )where m S is the tota l system mass. For the CBC,

The number of microtubes for the cooler and heater may becalculated from the equations presented in the companionpaper. The equation for the heater may also be applied tothe recuperator, and the number of tubes in the preheater,n p , may be calculated fromPOn p w 2.0-LT6 ( 7 )

where the coefficient, 2.0 , depends to some extent on thechoice of fuel.A 10,000-hour design life with standard safety margins cor-rosion allowances plus creep-limited stress at hi h temper-atures, or 0.7 yield stress at low temperatures? for pa =50 MPa requires the following exchanger masses, includingbank manifolding, (short) main manifolds, thermal insula-tion, recuperator containment vessel, and heater combusior.mC w 1.2nd2Lp = 3d2pPo/TamH w 3.0ndlLp B 6d2pPo/Tamp w l.On&Lp w 2&pPo/TbmR w 3 . 0 n 8 L p w 6 & p P 0 / ( ( l - 71x) T3- 2))

[m.K/W][m.K/W][m.K/W]

[m.K/W(2 6 in the recuperator has been expressed in terms of itseffectiveness.)The above expressions are believed to be accurate withinabout 25 for systems between 20 kW and 100 MW. Forillustration, we substitu te the following values, typical for ahigh efficiency (55 ) design:Metal density: 9000 kg/m3 for the high-tungsten heater alloyand 8000 kg/m3 for the other alloys;Microtube I.D.: 0.8 m m for the heater, 0.6 mm for the pre-heater, and 0.5 mm for the recuperator and cooler;T6: 10 K for the cooler, 20 K for the preheater, and 75 Kfor the heater; 0.97 for the recuperator effectiveness, withThen,(T3- Tz) = 550 K.

mC w 1.3Po [kg/kW] (8)mH w 0.4Po [kg/kW] (9)m p w 0.3P0 Fg/kW] (10)m c w 0.25Po [kg/kW] 1 1 )

For applications where specific power is more important thanefficiency, the exchanger masses can be reduced significantlyby allowing a larger Tb. If mC and m p are reduced by afactor of four and mH and mR by a factor of two, it is stillpossible to achieve a system efficiency of 45 .m S = mC +mH i p +mR +mM f mE f m ~6)

where the above subscripts refer to cooler, heater, preheater,recuperator, miscellaneous, electric generator, and turbinemasses respectively. They are listed in order of decreasingsize.Preliminary results from computer modeling indicate thatthe mass of the MTS bank manifolding and cages will becomparable to th e mass of the microtubes. The mass of thehigh-pressure containment vessel for the recuperator will becomparable to the total mass of the enclosed MTS banks.

The importance of using a gas with low molecular weight,M, follows from the fact that thermal conductivity is ap-proximately proportional to 1 / ( 7 M ) .The selection of the optimum mean cycle pressure involvesa trade-off between pumping losses and creep stress limits.Pumping loss Wp n any one of the heat exchangers is givenby

( 1 2 )

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Swhere p is the gas density (kg/m3) and 1 1 is the dynamicviscosity (kg/ms). W can be reduced by increasing n, henumber of tubes in t i e heat exchanger, or d i , the tube in-ternal diameter; both these strategies lead to an undesirableincrease in heat-exchanger mass. Reducing W, by decreas-ing L extracts penalty in increased conduction losses alongthe heat exchanger. T he only remaining option is to increasep by increasing the mean pressure. This requires the mass,and hence cost, of the heater to increase to meet creep stressrequirements. Sample calculations suggest that the optimumvalue of mean cycle pressure lies in the range of 0.4-6 MPa.While the heat exchangers easily scale to any size from 1kW to 100 MW, the turbine ex ander is difficult to scalebelow 200 kW with very high effkiency, owing to the highmean pressure. Partial-admittance turbines can be scaledsmaller, but they perform poorly. Highest efficiency is ob-tained for full-admittance, 50% reaction, axial-flow, multi-stage expanders. For such expanders operating at low pres-sure ratios with inlet pressure p 2 , it can be shown that theideal shaft power PE is given by

PE = Ap2(r - )l.'J= (13)where A is the frontal area of the nozzles. For helium gas at2 MPa, 1250 K, this is

pE 3.2 x 1 0 9 ~ ( ~1 p [w/m2] (14)Thus at a pressure ratio of 2, a 2-MPa, 300-kW helium ex-pander (for a 200-kW CBC system) requires an inlet area ofabout 100 mm2. The high velocity of sound (2000 m/s) inhelium at these temperatures requires about 10 stages if un-cooled superalloy blades are used. While such designs havebeen proposed in the 100-MW range, they are impractical forsmall systems. Expander and compressor efficiencies above92% may be achieved in small systems with three-stage su-perallo turbines if the sonic velocity can be reduced to 700m/s. (Single-stage ceramic impulse turbines have demon-strated efficiencies above 80 ' at shaft power below 5 kWwith sonic velocities near 700 m/s.) Changing the workinggas from helium to argon will reduce the sonic velocity by afactor of 3.1, but the thermal conductivity drops by factorof 8.6. This would require an increase in recuperator mass bythe same factor and a doubling of heater and cooler masses.A notable improvement in system performance per cost canbe achieved by using a gas mixture rather than a pure gassince the sonic velocity is determined by bulk properties -(7p/pdo,' - while the thermal conductivity is primarily deter-mine by the volume fractions of the constituents. Holland[8] gives the following expression for a reasonably accurateestimate of the thermal conductivity k of a mixture of gasesfar below the critical pressure:

where y i is the volume fraction of com onent and Mi is itsmolecular weight. A mixture of 8% ( mass) helium and92% argon gives a sonic velocity m/s at 1200 K, ther-mal conductivity being reduced ctor of 2.7 comparedwith pure helium. If the alloys used in the system have suf-ficient carburization resistance, it is possible to use carbondioxide in the mixture: replacing argon by carbon dioxidereduces the sonic velocity to 700 m/s and slightly increasesthe thermal conductivity. For aerospace applications, xenon

about $50/kW in lower-efficiency mobile applications and$100/kW in higher-efficiency stationary power plants. Thecost of larger systems is dominated by the cost of the heatexchangers and it becomes p t i c a l to employ six or moreturbine stages to allow sma ler recuperators. The optimummixture in CBCs above several megawatts is likely to com-prise equal fractions of helium and argon, giving y abouteanmolecular weight of about 8, a thermal CO20 below that of pure helium, and sonic of 1500m/s at 1200 K.The CBC en 'ne can greatly extend the load range overwhich high eg ien cy is obtained. Optimum turbine design isessentially independent of mean pressure. The design is pri-'marily determined by t he turbine materials, gas pressure ra-tio, and speed of sound, which depends only on temperature.Reducin the compressor outlet pressure from 2 MPa to 0.2MPa an reducing the combustion rate by an order of mnitude will reduce output preduce the TS's in the exchaincrease relative conductionorder of magnitude, and increase relativetwo orders of magnitude. Th e net effectin efficiency of about 30 . (For cwill be down 30% in efficiency a

an order of magnit

face speed 40 m/s) with a shear shigh torque generated by a high-pressure turbine necessi-tates larger relative shaft diameter. We have considered us-ing high-speed silicon nitride ball-bearings and accepting thenecessity for oil-stream lubrication. However, the contami-

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6speeds. Total compressor power drain plus bearing frictionwill be about 0.02% of shaft power for high-stiffness bearingsat surface speeds under 100 m/s. Some degree of bearing gaspressure control will be required to achieve stabil ity over thewide range of mean cycle gas pressures needed to achieveflexible output power.FabricationEase of fabrication is a key factor in cost. Blade-coolingducts a re not necessary in the CBC owing to its lower tur-bine inlet temperature. This simplifies blade manufactureand eliminates the associated cooling losses. While 83%efficiency may be possible with a single row of blades, a tleast four rows of blades will be required to achieve 95% ef-ficiency. Small turbines would be machined from solid disksfor reduced cost, although this eliminates directionally solidi-fied materials from consideration. The inert atmosphere andlower T4 in the CBC allows considerable freedom in turbinematerials selection. A number of alloys are available thatwill perform very well here, although it is likely that betteralloys can be developed for these inert atmosphere condi-tions. The compressor will be made from a high-strengthtitanium-based alloy such as IMI 550.Hieh-SDeed GeneratorsThe mass and cost of the heat exchangers are expected toexceed those of the turbine and compressor. This impliesthe use of low-molecular-weight gases and small, high-speedturbines. Finding a generator to match these high rotationalspeeds is difficult. For turbines in the 10-1,000 kW range, wewould like to operate at rotational speeds between 30,000 and200,000 rpm, the higher speeds corresponding to the lowerpowers.There have been several experimental generators which liein the power and speed range of interest. One such is theRice synchronous generator, a switched-reluctance machinewhich has been used with 25-kW CBCs for space power.Hyperconducting and superconducting induction generatorshave been used in the multi-megawatt range, and homopolargenerators have been used for large DC welding supplies, rail-guns, and tokamak plasma heating.We are currently exploring three technologies which we be-lieve hold promise: inherently stable liquid-metal current col-lectors for homopolar generators; whisker-reinforced ferritesfor high-speed permanent-magnet rotors; and efficient DCexcitation for high-frequency variablereluctance generators.Detailed comment on this work will be deferred to a laterreport.AdicationsStationarv Power GenerationOne of the more attract ive applications of the CBC engine isthe stat ic generation of electrical power. Existing non-hydroutility power-generating plants cost from $800 to 4,000 perkW of capacity, and most plants a re in the 150 to 1,000MW range, averaging $1,50O/kW, or about 900 million perplant. At present about 250 plants are being designed or areunder construction in the States, with construction times of3 to 10 years. Utility power plant growth and replacement ofobsolete plants is expected to continue to average more than10 GW per year during the next 25 years. This represents a$15 billion annual market at current prices.

The advantage of the CBC engine in this application is itscombination of low capital costs with high efficiency, andhence low running costs. It also has the advantage that i tcan combine high efficiencies with clean operAtion. Whilecombined-c cle power plants have been built with efficienciesof about 46&, these plants cost around $4,00O/kW, and theirhigh operating temperatures lead to NO, emissions whichare far above environmental standards, necessitating the ad-dition of costly catalytic converters.Nuclear Power ConversionAlthough nuclear energy has been quite unpopular since theThree Mile Island accident in March of 1979, nuclear en-ergy research continues to be funded, especially for very longrange tokamak fusion concepts and for inherently-safe High-Temperature-Gas-Cooled (HTGC) fast spectrum reactors.The MTS heat exchangers and LPR CBC are an ideal matchfor HTGC reactors, and MTS surface exchangers provide aviable solution to tokamak first-wall cooling problems.

ConclusionAdvances in heat-exchanger technology justify a re-examinationof the closed Brayton cycle. Guidelines for engine designhave been developed, and the areas requiring further researchhave been identified. Some of the more promising applica-tions have been reviewed.

NomenclatureA Frontal area of nozzles (m2Temperature ratio T2- Tl{/Tlc, Specific heat of gas at constant pressure(J/kg.K)c Specific heat of gas at constant volume J/kg.K)d i Heat-exchanger tube inner diameter (m\E Temperature ratio T4- T5)/T4Spinning frequency (Hz)f Conductivity (W/m.K)L Length of tubes in heat exchanger (m)mC Mass of cold heat exchanger (kg)mE Mass of electric generator (k )mH Mass of hot heat exchanger fkgm p Mass of the pre-heater (kg)m R Mass of the recuperator(kg)mS Mass of the CBC engine-plus-generator system (kg)Mass of the CBC turbine (kg)Mass flow rate (kg/s)M Molecular weight (amu)n Number of microtubes in a heat exchangernp Number of microtubes in the preheaterp Pressure (Pa)P Specific system power (W/kg)PE Ideal shaft power W)Po Output Power (w\r Pressure ratio (Dimensionless)P, Actual shaft power (W)

p2 Compressor outlet pressure (Pa)T Compressor pressure ratior Shaft radiusS Shear strengthT Hoop stress (Pa)Tc Sink temperature (KTN Source temperature /K)

mM Mass of miscellaneous system e1ements (kg)

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TsU Gas velocity (m/s)v Circumferential speed (m/s)yiy Ratio of specific heatsNormalized pressure dropr] Efficiency of ideal cycleqc Compressor efficiencyq Electrical generator efficiency9~ Heater efficiencyq5qz Recuperator efficiencyp Gas viscosity (kg/m.s)p Density (kg/m3)Ratio of turbine inlet temperature t o compressorinlet temperature

Mean temperature difference between entering hotgas stream and leaving cold gas stream

Mole fraction of a constituent of a mixture

System efficiency of real system

References1 L.M. Lidsky e t al., A Direct-Cycle Gas TurbinePower Plant for Near-Term Applications: MGR-GTpresented at the 10th International HTGR Confer-

ence, San Diego, CA September 19-20, 1988.2 2. P. Tilliette, J. Engin. as Tur. and Power 109,92, 1987.

M. Berchtold and C. Keller, U. S. Patent #3,218,807,M. R. Erbes et al, Science 237, 379 (1987).

5 H. Cohen, G. F. C. Rogers, H. I. H. Saravanamuttoo,

1965.

Gas Turbine Theory, Longman, London, 1974.6 A. H. Shapiro, Compressible Fluid Flow, Vol. I, Wi-ley, NY, 1953.7 D. G. Wilson, The Design of High Efficiency Tur-bomachinery and Gas Turbines, MIT Press, Cam-

bridge, Mass., 1984.8 F. A. Holland t al., Heat Transfer, Hunemann Ed-ucational Books, pp. 336, 339, London, 1970.

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A New Look at Closed Brayton Cycles

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