US1917029A - Multistage rotary compressor - Google Patents

Description

July 4, 1933. P. 5 D

MULTI STAGE ROTARY COMPRES SOR Filed March 14, 1931 5 Sheets-Sheet 1 HI-H'II IH In July 4, 1933. P. E. GOOD MULTISTAGE ROTARY COMPRESSOR Filed March 14, 1931 5 Sheets-Sheet 2 July 4, 1933.

- P. E, coop MULTISTAGE ROTARY COMPRESSOR Filed March 14, 1951 5 Sheets-Sheet 3 Q 1 1 INjEiO R 9W4 July 4, 1933;

P. E GOOD MULTISTAGE ROTARY COMPRESSOR Filed March 14, 1931 5 Sheets-Sheet 4 Jul 4,1933. j

' P. E; GOOD MULTISTAGE ROT RY COMPRESSOR 5 Sheets-Sheet 5 of a fiuid, s'uch"for e am le {as all; by theuse Qfo'If' anOthQi' condition of operatio They; i f

' 3 inisuc'hmannex that'flui'd hwifng itspressurje 'a' substantiallyconstant p ed. a y

' 4, f g I awnwajzrnnsny; lassrenonjTo Q LnIo T'IwoMuANi;Ion

anAnnn'mn, pnnnsynynma 4 soon cannonon? imn irsyLvAum 1 H i ,-MI1LTISTAitq agyijeeurmssba "Theffpresent invention relates broadly toarithmidspirali The-angularprogressionof the art'of fluid pressure changingdeviees, such a; spiral'iin-thebend along-ithe axis of f and more particularly to so-oal'led' multi 'the-compressorvariesjin aceolfdance With'the; 1 stage devices of the-rotating or turbo 30111 oonditionsunder-which the eompressoli isb e j '5 pressor type, 1 f 'ing opefatedficliangingifor differentspeeds; 5

In manycases, eithenbyffeasonof high," lead andjthe fike, 'ltis,lthereforefapparent l speed driving devices Whiohfare' .readily. thatanyyanes orguide devioes ofj th'e chaf V available, or eonservat1on.ofspaee-,; it isjde aoten're'ferredjtopifeonrect for'j one1oondi' sir ableto effect an inerease infthepressure?tionfof'oper'ationape not atthe properfanglei s of. a turbo compressor; -,NVhe1 e extremely ynlust"' thenefofebe eonsider-ed as a: compro'- desired, theseturbooorn-fl" miss bELSECl-gOIljthG assumptionfthat a given" a "the foiln'j'of a-se fies-ofapparatuswill-joperate alnajorityjofthe time under a substantiallyconstant load and at hi h" reassures-are b I l s pressors usually take stages operatiyely connected one toith e"other-j inor'easedina preceding; stage is deliyeredto'; ij To those 'skil'led'finthe'art t w ll known-"1- v the inlet of thesueceeding stage.'}-Normal1y1 that suohconditmns are subj eot to wide yam 1 the Conyeying means between the sta ges'is in" aucs'n, and that theiy a'nes are thereforeiealledk theform of an annuluslwhich, du'ezto the ,{llp o'n'ilto e'fieo't --'atf"difie1:ent times. varying-1 a gradually increasing areaavailable by'reasonoh'anges' in the-pathWhichthefluidparticles of gradually increasing diameten' is"efie'otive wouldnaturally follow, and ito diyert such; for decelerating the veloc ityrofthe fluid 'rep'ai't icles-into -an arbitrary path determined oeived and therefore increasing'ft]ae* staticj' by-ztheva'n'esl I 1.: j pressure. 'This is desirable,gin-asmuohflas The-fluid streamdoesnot perfectly ffilllthe 1 I v V with amulti stage oompress'orof *thefcem annular difiuserand there a'rethus losses due 7 trifu'ga'l type'itiside'siredto effect pressure; to" eddyfjmotion at the boundaries of they an'd'n'ot elocity, conditions. 1 j 1% :ff fi'uidj'stiea'mgln addition tosuoh eddyxlosses 1tfis also customafy in' niu'lti -istage c'om-; there'are surface frictionlosses whiohnlay be I pressors ofthe-charaeter refer lied 'to'to prqconsideijedas arising fromfa tendencyof the diatecontact'vvith the I3 yide rthe annular passages} intermediate the fluid particles in nnme If stages Withflllid dines/ting Vanesihaving for eo'nfining surfaceofthe" annulus to beatrestv their primary purpose to efiectaguiding as; relative to that-surface, while the fluid: par

the;"'fl'uid and prevent the sformation. of a5tielesr1remote froin'fs'uchsur faee are travel-z high velocity vortexattheinlet ofasu'oceed lingatanappreeiableyelocity; Therezis thusj I 3 1 ing stage. oiwSuch a-yortexwouldgive l iseto relatiyemotion of thecmolecules'inthe di z i I -j y a centrifugal aotionopPosed tothe ;preced-, lr'eetion o'f flow'whichintroduces ea-resistance;

1 ing stage and" to lagreater 01 -'1esser;extent fto*fiow"or a drag on the moving streamasanul lifyythe pressureincrement-Which'oould: wholeilt has-been determined that under be realized in the apparatus. Suchxgu'ide' substantially}normal conditions of 'operation 0 vanes therefore have necessarilybeen present w'ith'st'an'dardtyp'es of apparatus the percent 90 injon e formoranotherin knownn ulti stage'. age loss-due 'to'su'rfacefr'iotion,lnayiarnount to compressors of the type embodyingja:seriesf 5.75%, which"represents an app'reciable re''- of co-aXial impellers in'a single housing." duc'tion'in effioien'oydue tosuchsurfacefrjg given stageof a centrifugal'conipressoiis-ro 5 In additionto lossesduetO eddy "ourrent 5 tating at an extremely high velocity, such -and*surface friction, t ere areshookxlosses fluid; has a tendencyto travel inthe path of which-, under Certain oond'1tions, tun )ulotedl-y 'a sp'i r'a-l'in the annular return'bend between arepfesent fairly highpropor tion of the successive sta'gesfl The natural -i -path-ofa total, losses in the apparatus.

W N on only .do esfa multi-stage compressonof1' the usual type represent a more or less inefliciently operating structure due to losses of the character referred to and due to a large extent by the guiding vanes necessarily supplied, but it requires accurate machining in order to make proper provision for such vanes and the proper cooperation of the impellers therewith.

It is one of the objects of the present invention to provide for multi-stage pressure increase in a single housing in which such guide vanes are not required and in which the stream of fluid in passing from one stage to the next progresses in a predetermined and controlled angular direction which does not vary for variation in load or speed. By predetermining the direction and controlling the same, asdistinguished from the attempt to modify the tendency of a fluid particle to follow a logarithmic spiral, uniform conditions of operation are obtained and maintained.

It is a further object of the present invention to replace the annular diffuser with its ""metal core across which the fluid particles must pass, with a coreless channel in which there is a solid or undivided stream of fluid. Instead therefore of having a stationary core adjacent which the fluid particles are substantially at rest,.there is provided a moving core in which the fluid particles have a maximum velocity. There is thus completely eliminated the surface friction due to such an inner core as necessarily exists in a multistage turbo compressor of the conventional type.

It is a further object of the present invention to provide a multistage apparatus which avoids entirely sharp bends in the direction of "'travel of the fluid flow. To attain this object I preferably discharge the fluid from the impeller of any stage into a diffuser which discharges into a volute or snail shell increasing or progressing in cross sectional area in direction cireumferentially of the impeller. Since the volume of fluid is continuously increasing around the periphery of the impeller, starting from any assumed point, the farther one goes from such point in a direction circ'umferentially of the impeller, the greater is the volume in the direction of motion. The

increase in cross sectional area of the discharge volute preferably increases in accord ance with a substantially uniform law and in accordance with the increase in the volume of the fluid which it must handle, each portion of the volute handling a proportionate part of the charge as received from the impeller. This discharge volute in turn delivers its fluid volume through definite transfer means 69 into an inlet volute of successively decreasing cross sectional area, which commences to converge after the point of discharge into the inlet of the next succeeding impeller is attained. As the volute progresses circumferentially, the need for additional area disappears because of fluid admission into the impeller, and the volute therefore converges preferably in exactly the proportion that the fluid is delivered into the inlet of the succeeding stage, thereby being effective for proportionately dividing the fluid in accordance with its circumferential progression.

Such a discharge volute and inlet volute are provided for each stage of the machine.

W' here it is desirable to have such volutes lie in substantially the parallel planes in which the respective impellers rotate, and since the impellers themselves are necessarily axially offset, it is necessary to make provision for transferring the collected fluid from the region of maximum cross sectional area of the discharge. volute into the region of maximumcross sectional area of the inlet volute. This transfer in accordance with the present invention, and as before pointed out, is preferably of such characteristics as to afford a solid or undivided stream which is attained by progressively moving all of the fluid toward a common point in the discharge volute, collecting the fluid at such point, and then transferring the collected fluid from such point to the inlet of a succeeding stage by causing it to travel .through a passage having only a fluid core and defining a path progressing simultaneously in a predetermined and controlled axial and circumferential direction. In thisrespect there is a radical distinction from the annular distributed condition of discharge and delivery in a plurality of divided streams such as occurs in the usual type of apparatus. In accordance with the present invention the transfer zone may extend over any desired number of degrees either more or less than a complete circle, but is preferably only of such length as required to effect the desired axial advancement without abrupt changes in the direction of fluid flow, and may be complete in a comparatively few degrees.

In the following detail description the form of the volute disclosed is one in which the polar vector increases, i. e., one in which the increase in area takes place in the direction of the raeius of the impeller. It willbe understood, however, that it might be one in'which the result is accomplished by widen ing. the volute in a direction substantially parallel to the impeller shaft. It will be understood therefore that the term volute as hereinafter used in the specification and claims is used in a generic sense in accordance with its functional characteristics, and not in the limited sense as defining any particular type or conflguratioin In the accompanying drawings there is illustrated a sin 'le housin for a multista e;

turbo compressor embodying the features of the present, invention. In the drawings:

Figure 1 is a perspective view of a housing "Figure 4,

I IFigure,8 is aneX lO d d I showing two halves. of a-single housing is a iI'vertical 'seoti'onal;,-"v1evv,

' A through ahou sing at right angles to theplane I v y -"firststage impeller 5.. I

this time that-the construction of, impellers, per se constitutes'nopart seam present inven- I I I i are thereforeonlyrdiagraniniati" the line I i Figure 7' is a transver'seisee .,.:Figure '2 is a vievv similar, t Figure l shoyv-z ing :in greater detail the location and rangenient of the transfer zones;

of division of the seet1onsinFigure 3; II I Figure 5 is a transverse sectionalvieyv on the line TiL-Vof Eigur e;

sectional: view, on

vFigure 61s a transverse VIVI ofFigure 4;";

' j he 1m vir-vi qr Figures"; and I I -vvhere the housln'gisofflsuch strueture jasi, to g ve the I advantageous features] of opera,- tio'n here nflset forth.

"Figure 8 is a diagrammatic v1 W ndicate} ing the ter In ,the drawings have illustrated a [coii pressor having three stages IfiWlll'bQUIlClQif" stood, however, that the drawingsareg for purposes ofillu'strationl v utility of the invention'is not limited to the number of stages provided in a single housshowing is entlrely diagramniatic In this of the air, it 1 machine hereinafter} more particularly 'de-i figure the arrows A represent axis ofrotation being understood; that in the scribedfthere is a single axis of'rotation l o'r The arrows Brepresent What has been 'he'f re'referred'to age con- S all of the impellers.

". trolled aX'ial a-nd circumferential progression such as characterizesthe flow through 'tthe a The arrows C represent .clr-

- established, the diagrammatic sh'owingitloes; not represent relative relationship offpartsin a'ooinmercial stru'cturerhut merely the se-.

quence, vof struetural features'insofar asthey arefsuccessiv'elyf effective. for I producing results desired, I Thus,v

While in aeam1: 1-acg tice an inlet volute. by means oflivhiohlairjis delivered to i'apeller necessarily extends around the" axis of rotation of theirnpeller for progresslvely delivering theretoyt-h'ef I relationship lndicated inthe d agram as, :straightflin'e sequence.

I Thesame true With respect to the discharge volutes' hich-,1 1n

aetual practice; extend "around the impeller Y axis but are diagrammatically illustrated-tor urposes of a clearer'understanding a'sI a' c tupressure of fluids which comprises at plural ity offpressure producingstages 'in' a single,

ally following an impeller; This explanation ure. I

r opened view} tional on relationship andifoharaoteri'stie con-.1 figuration of the various 'volutes} and;trans-, Zones as embodied n the -preceding fiig ures:

' and*"de1iv ers the '-.previously' collect lQ- fluid: into t-lieinl'etof an inletvolutelOcominuni-f catingfvvith' the eye 'Ilfof the-second st ge ".1"

12. Thisin pellensi nilarly tothe first; stage impeller I, 5," discharges I its} j fluid only I and [that the" v impeller fluid discharged, exists; lute 22 co1nmun1cates' with an'outlet COHDGG.

Having reference first to: Figure 8 era-ai geia hith uiia ame -is sa as I I a rnaticallyillustrated,thereI-is shown an inlet a "connectionfl Which Communicates-With an I ',in1e t-* .-vo1ute 3- effectivefor proportionately dividinglth'e fluid flovv'inaecordance With its circumferential} progression in such volut/e This linlet' volute isf'shovvn jas extending) v I I I I H {360? jjfor' d'elivering" through substantially lt' is to be observed at drawings. a

delivers I 4 I its fluid I at an increased .;'pressure and high velocity. through a diffuser 6 into a; discharge volute 7 llhisidiseharge volute effective for progressively"collecting-and moving all: 4

in e q'poi t 8'rp ifisenting the cQinmencek i of the. fluid Ifroin -the impeller '5 toward}, a"

througha diiluser- 14 into a dischargevohilte 15,similar.31nall respects to thefdischarge; I i a volute 7pm the firststage;and efiectivewfor v aware-a ,c'ommon point-"16. 1; 'Ihis cornmon,

having, the ksan e ei'rcuniferentialfand axial Inentof"aftransfer 'zonefll-whioh 'hasgawcone 2 [trolledcircumferentialandaxial prog BI gand progressivelynioving the fluidprogression as the "transfer zone 9; anddelivlikewise similar 1n all; respectsto th i l t! volut'e -lO forithe 'seeond stage;

sectional area cireurn'lerentially ofthe casing] I desoribed, f and in oreaSBS'in; Cross sectional areas. as the need "for additional area, due to increasing volume of 7' i -This inletvolut'e dueto' fts decreasing cross The. discharge vo-: I

' ering all of the oolljected J fluid the first andflsecond stages ime an. inlet"volut ls li proportionately divides theffluid Iinfiacoord .F' ancevvith its-circumferential progression anal-110 tion aabym 'ans of which-the fluidlat itsthen. I

' pressureand velocity'niayfbe deliveredto any desired p jointof use.

"The inver -men in its im lest for'minay be defined asj an apparatus for increasing the housing-vv'th an inletvolute 'toreach' stage one stage and inlet volute for a succeeding stage connected by a transfer zone. This transfer zone may obviously be of constant cross sectional. area throughout its length. for maintaining substantially the same velocity as that at which the fluid is received by it, or may be of either decreasing or increasing crosssectional area in the direction of how for increasin or decreasing the velocity of the fluic it revels therethrough. Since its mechanical function, however,is purely one of effectin transfer within the confines of a single housing and therefore in the smallest space possible, it may conveniently be of constant cross sectional. area as herein illustrated. I

As will be apparent more particularly from Figure 2 of the drawings, each such transfer zone extends through a circumferential distance of approximately 45, the axial progression being as required to con nect the outlet of the discharge volute of one stage to the inlet of the inlet volute of the succeeding stage. T have found that a transfor zone of this length may effect the. desired transfer of fluid without any abrupt changes in the direction of fluid flow and without completely reversing the direction of flow is characteristic of the transfer annuli of multi-stage turbo compressors of the usual type in which the flow passage is outwardly from one stage and then at right angles in the direction axially of the housing and then inwardly to the inlet of the succeeding stage. Each transfer zone in accordance with the presentinvention therefore, may be'considered as a continuation of both a discharge volute and an inlet volute which provides a controlled flow path of fixed circumferential and axial progression for a solid or undivided fluid stream, and located within the physical confines of the outside dimensions of the housing itself.

Since the fluid in passing through such a transfer zone is in a solid stream, it is not subjected to the surface friction losses characteri ie of a divided stream of the character provided by a series of eddy current producing direction changing and vortex preventing veins. Also, since the solid. stream has a moving core as distinguished from a stationary metallic core of the type usually provided in a multi-stage turbo compressor,

the surface friction losses are only those ccasioned by the outside confining surfaces or envelope. These surfaces are of materiall v less extent, as will be readily apparent to those skilled in the art, than the corresponding outer surfaces of an annulus as heretofore provided and extending completely around the housing at substantially its point of maximum diameter. I

It will also be apparent that the flow through the transfer zones is always in a path predetermined by the zones themselves and not influenced or changed byvariations in the load on the apparatus. The transfer zones always receive fluid from a discharge volute travelling in a circumferential direction and deliver it to an inlet volute in a circumferential direction. Since they always receive fluid travelling in the same direction,

directly from an outlet volute into an inlet volute, it will be apparent that if desired, the housing may be provided with suitable con nections to the'transfer zones whereby the fluid may be conducted to an extraneous piece of apparatus effective thereon intermediate the stages. In some cases such an operation desirable, and I wish it to be understood that the present invention lends itself theretd F or purposes of simplicity, the invention is shown as comprising a housing of noncooled type. The problems of cooling-compressors, however, are well recognized, and to those skilled in the art it will be obvious that the present casing may be provide-d with cooling means at the will of the designer, such cooling means, however, not constitutmg any part of the present invention.

I have also defined the construction as mg one which may be completely devoid of vanes of any nature whatsoever. It is to be understood, however, that many designers arbitrarily provide short vanes as indicated at 24, Figure 4, for inlet purposes adjacent the eye of an impeller. The present invention, while not requiring such vanes, may be utilized in connection therewith, tie vanes always receiving fluid at a predetermined and constant angle so that they may be designed with this thought in mind. Where the vanes are. eliminated, the inlet volute wall may be continued inwardly toward the shaft until the surface thus provided by it would stop any vortex action.

The structure described is one in which the respective discharge volutes and inlet volutes are substantially parallel to the plane of the impellers. It has been pointed out. however. that each transfer Zone, which effects th i axial and circumferential progressionof the fluid stream is a continuation of both a di charge volute and an inlet volute. This will make it readily apparent to those skilled in the art that the parallel relationship is not a lim encean axial progression offlui d. The seine 4 istrue of the inlet volutes, thus making it possible for the 'Volutes i I :lutes, transiercan; be consideredas a transfer-zone eventhough its exact po nt of 3,,(OII11T1QT1C111I113-' and termlnatlon 1s not sus- V Which are effective for'handlingithe fluid as f received from an impeller as delivered (to an impeller respectively. In the'ordinairy rotary" impeller operation, energy is commuof.v In other wordsythe" airlin" passing through the impeller is caused tate therein;v This-rotation communicates 1 {energy in the form-oi velocity, 1 ilocity is subsequently destroyed, inasubstan tially frictionless process,

, this end maybe structurally of aWide Variety of different types andl arrangernents; Thus,

v but alsotrans'fer mean J 'ment canv be afforded by "having thefvolutes "themselves" extend spirally of th'e 'housin'g fWherebythe point of termination 'ofa charge ,volute Would"correspondj'tothe point ofinletof an inlet voluteythus obviatingthe .I1ocity'du i g 't av l Q th fluid' r m n e progression different froIntheaXial cumferential progression ofthevolutes thern- I I n selves. In such case, however,fthere would With the-drawingsforming afpart' hereofe W I bean effective transfer intermediate the V05 While I have illustrated,and-describeda, ,j i j -preferredembodiment,ityvillbejunderstoodl" that the utility of the, inventionis not limited r configuration or design disa;

pthe fact thatin the: centrifugal type it is desired to efi'ect' pressure, and not velocity, conditions; v Will also be apparentfromthejforegoing de-"- scription that I haveprovided astructurein- 50 energy Willre-appear as static, pressure, 1, sure and vice versa. I multistage apparatus of :the character here-'1' Z in providedis designed for the purp'oseof ob= taining a greater totalpressure at the outlet pellet therein ,{atleast one stagehaving a, 1 than the pressure hichc'ouldbe producediby discharge: volute and the succeeding s g any individual 'imp ellerl" This-incfease in {be transformed i' terniediate the impeller stages into pressure'en'ergy,

tion being obtainable by not onlycons'tructing: the discharge volutes,. for example, so

that they are. effective 6: ,flatldiffuSers-Ghli and 21j fiuid as'delivered itation ivithir spe'ot to "the present,invention but- ,irnerely one form' which {Inayassl'lniex To those skilled inthe arfiit willxbe apparent that the volutcsfneed onlyflb'e effective for carrying "out their respectivefunctions and to qavai lablef at C111? In this manner instead Of having the discharge volutes in the plane of the impellers, they may, be construct?" ed to provide throughout their cireuinferg 'alnct'ersL I It has been pointed'jout 'butes, or that they may,

mselves toconstitute' str buti'ng jlneans, U Such: an arrangetuallyj Imaintaining 'Ve derstood, however, that" as 'practice,-s 1n'ce;- pressure not only collecting an disz'im'peller to the'next. 1,;-

The vadvantages ofithe'invention will vbe apparent from {the foregoing,specification necessity of distinctively different transfer zones'having an axial andmcircumferentlal and Cir- "to the particular ceptible of accurate definition. I closed Yand described, sincetheiinvention con- Reference has her"'inbefore'beenf inade'to templates character stic'difierences ofopera-i s i a multistage-compressor"o I v structural limitations; It j. I claim;

fluids comprising initial,

eluding discharge "volutes and inlet volutes volute and fan' inlet volute' nicated to the air bythe acceleration there-"1' to actually r05 v y I substantially t and if this 've f thereof changing only slightly from one secf i e;t e t changln'glits direction only gradually; v j energy is convertible into pres-j other Words,

{It is apparent that" a pressure is a function of the design 'ofthe v0 lut es which is suchthatvelocity energy may this transformafor collecting-fromlthe,

path" characterized A by thatfth'e volutes" "and the transfer zones rnay have such sari-:

be constructedfor a c-f locity'. It Will be una niatter' of-iactual andflnot velocity is "theconditionrequired,.l, the{"constructional" characteristics-Willbe such asto insure aninl 1 crease in 'staticpressure atthe expense of ye? f and statenient of objects taken n connection v r a v I 90 2. device for increas ng" the'pressureoi ifiuids'coinprisingj a [plurality of stages. in-" eluding atleast an inltialand a final'stag'e, eachhaving animpellerchaniberwith an iInstanti'ally the, same shape, the! dimensions;

such additional 'crfossfis ecti'onal area as; to en-- able'any desirediener'gytransformationto oc' -z there is built up-in the f] fluid-?passing' through the '-a] )paratu s a grad ually incre'asin'g' static pressure which; l

the outlet; TkIn any cas'e,'-'s1 1ch1a" a transformation? from velocity into; statica pressure'is'necessarily efiectedby thefiatdifg 'fusers 6, 14 and 21"due totheirincreasing di g f' tion which are not dependent onspe'cifie ljA deviceifor-increasingythe pressure 01 9. a I interrnedia teand l finalstages, each includinganilnpeller-charni' f ber havingan iinpel-ler therein, a discharge f f'f for each of 5 intermediate stages, anda'connectionbetween 9 Tv Ethe dischargevolute-ofone'of said'interrnedi-- ate stages and ftheinletvolute of thesucc'eedj ing stage, successive cross sections taken along said volutesv and connections having .e same shape, theidimensions tion to th6111821t=,fi11d the center line of the path defined by the volutes and th'econnection havingan inletfvolute, anda connection be-" 1 jtweenjsaid volutes fadjacenttheir portions of maximum radius, successive cross sections 7 ofsafid *volute's. and connection haying subthereof changing only slightlybetvveeni se v --L.ti0ns and "thecenter line thereof changing its-direction only gradually, defining a fluid v substantially siinilar contourthroughout,'and by the absence of let volute of the succeeding stage, successive cross-sectionsot said vclutes and connections taken along the line of fluid flow having similar shapes, and difiering only slightly in dimensions, the center lines of the volutes and connection changing direction only gradually, defining a fluid path characterized by low losses.

4. A device. for increasing the pressure of fluids comprising a plurality. of impeller chambers each having an impeller therein, a discharge volute communicating withone of said chambers, an inlet volute communicating with the chamber of the succeeding stage,

anda connection between said volutes, said volutes andconnection being characterized throughout their length by a similar crosssectional contour and dimensions ,which change only gradually between successive transverse sections. through the fluid path, the center line of the fluid path changing its direction only gradually.

In testimony whereof I have hereunto set my hand. i

- PAUL E. GOQD.

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