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suchabucketmightliealongalinesuchasE—F. The shape of line E——F is determined by the distribution of the mass of bucket material radially outward of each selected radius r moving from root to tip and upon the cross-sectional area at the same radius, according to the formula ' ‘F .S—AN 10 exit warps and bucket entrance warps which are reversed from those of the conventional tree vortex bucket based on constant temperature over the bucket height. ' The bucket is additionally constructed to e?ect opera tion at radial temperature gradients, by causing the actual local stress in the bucket to conform closely to the curve representing maximum allowable stress with varying tem peratureforaparticularbucketmaterial. Thisisaccom plished by causing the net area to ?rst increase with and tangent to curve 35. Bymeansofthespecialbucketshapeshown,however, 20 fromroottotip. 3,135,496 whereSisthecentrifugalstress,Fistheforceexertedon 10radiusandthentodecreasewithradius. Thisallowsthe the bucket cross-section due to the mass of material radial lyoutwardatthegivenradius,andAN isthenetcross sectionalareauponwhichforceFisexerted. Foracon ventional bucket with a linear variation of area, i.e., area increasinglinearlywithradius,curveE—F willbeslightly 15 concavedownwardasshown. Itwillbeapparentthatthe maximum stress curve permissible for a conventional bucketisasshown atI——K,whichisparalleltocurveEF actual stress distribution from root to tip to follow an approximation of a curve which is concave upward as in FIG.10. Thereductionofstresstakesplaceatamore rapid rate near the root than near the tip. This actual stress curve, determined by the net area variation with respect to radius, is caused to approximate the allowable stress curve for the particular bucket mate rialatvariabletemperatures. Thus,optimumuseismade of the bucket material along the entire temperature range the actual stress in the bucket may be caused to follow a curve such as EGF, which can be made to rather closely approximate the allowable stress/temperature curve 35. Curves EF and curve EGF are for a bucket of the same mass,buttheactualstresscurveEGF iscausedtovary 25 stresstoconformtothesecurvesmay sometimeshave as a more complex function of the radius, and to approxi matetheallowablestress/temperaturecurvebymeansof the special bucket shape of FIGS. 8 and 9, which varies innetareasuchasseeninFIG.12. Sincemostofthe massofthebucketisconcentratedintheroot,thestress30 however,designoftheblade,withthetangentialMach drops rapidly at ?rst along curve EG, which corresponds tothedistancefromcross-section23inFIG.9toacross sectionalongline36atthebottomofpocket28. There after,thestressisreducedmovingtowardthetipataless rapidratealonglineGF,whichcorrespondstothedis 35 temperaturepro?lemaybeadjusted,asdesired,inorder to simplify the blade shape for ease of manufacture. Numerous modi?cations of the arrangement described here will be apparent to those acquainted with gas turbine design. Forinstance,manyotherwayscanbefoundto horizontalscaleofFIG.10islaidoutforauniformvaria 40 achievethedesiredradialtemperaturegradient,suchas tance from cross-section 36 to cross-section 22 on FIG. 9. The allowable temperature TA at each local bucket cross-section at radius r can then be plotted as shown in FIG.11,fromtheinformationcontainedinFIG.10.The tion of stagnation temperature from root to'tip, although othertemperaturedistributionscouldbeemployed. Ata given radius r, one moves vertically in FIG. 10 to the actual stress of the bucket (on curve EG), horizontally to theallowablestress(oncurve35),andverticallytothe 45 allsuchmodi?cationsasfallwithinthetruespiritand allowabletemperatureTAat‘thatallowablestress. This processisshownbythedottedpath35ainFIG.10. r isplottedonthehorizontalaxisinFIG. 11andTAonthe verticalaxisastakenfromFIG.10. Iftheactualstress curveEGFonFIG.10conformedexactlytocurve35,the 50 resulting curve 36 on FIG. 11 would be a straight line. However, since there is merely a straight line approxima tion to curve 35, the resulting curve 36 of FIG. 11 has cusps 36a, 36b, which nevertheless cause curve 36 to roughly approximate a straight line. 55 It can be seen in FIG. 11 that the mean temperature, indicated by line 37, is signi?cantly higher than the tem perature on a conventional-shaped bucket with uniform temperature,indicatedbythehorizontalline38. Since themeantemperature37issubstantiallyhigher,therewill 60 be corresponding higher thermal ef?ciency and speci?c power output achieved through use of the radial tempera turegradientconceptofthisinvention. Thus itwill be seen that this improved design for axial ?ow turbine blades raises the e?iciency by deliberately 65 creating a preselected radial temperature gradient giving temperatures at the bucket tip which are much in excess ofthetemperatureswhichcouldbewithstoodbythehigh lystressedrootportionofthebucket. Thenozzleand bucket are then designed according to the relationship that the tangential‘Mach number varies inversely as the radius, which enables blade angles to be calculated for radialequilibriumconditions,independentlyoftheactual temperatureateachradius. Theresultingbladeangles, where temperature variation is substantial, give nozzle 75 It will be apparent to those skilled in the art that dif ferent materials will have different curves for allowable stress vs. temperature, and that the precise variation of gross and net areas required to cause the bucket actual to be resolved by solutions which are highly empirical in nature. Thereisalsothepossibilityofusingtemperature variation which is not exactly linear with radius, rather thanthesimplecurveofFIG.2.Regardlessofthisfact, number inversely. proportional to radius, is completely independentoftheactuallocaltotaltemperature. Itin cludescorrectionforthetemperaturevariation,whichis notaccountedforinthefreevortexdesign. Thus,the providing multiple sources of ?uid at di?erent tempera tures,conveyedtothebucket-wheelbyconcentricannu lar passages supplied from the various sources. It is of course desired to cover in the appended claims scope of the invention. What I claim as new and desire to secure by Letters Patent of the United States is: 1. In an axial ?ow turbine having at least one rotary bucket-wheel, the combination of means de?ning a ?ow passage of arcuate cross-section with inner and outer radii from centers at the axis of the bucket-wheel and supplying high-temperature elastic ?uid to said bucket-wheel, means creating a radial temperature gradient in the ?uid in said ?ow passage whereby the temperature is higher toward the outer radius of said flow pas sage, and a plurality of radially extending nozzle partitions dis posed at the end of said ?ow passage and imparting varyingtangentialvelocitycomponentstothemotive ?uid at different radii from the axis of the bucket wheel so that the tangential Mach number of said velocity component varies substantially inversely with the radius from the axis of rotation, and a plurality of radially extending, rotatable blades dis~ posed beyond said nozzle partitions and attached to said rotary-bucket wheel, the leading edges of said blades being warped from root to tip toward the plane of rotation so that the entry angles of said blades vary with radius to conform to the ?uid leav ingsaidnozzlepartitionswhenthebladesarerotating. 2. In an axial ?ow turbine, means de?ning a ?ow passage of arcuate cross-sectionPDF Image | FLOW TURBINE WITH RADIAL TEMPERATURE GRADIENT
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