UNCLASSIFIED

AD NUMBER

LIMITATION CHANGESTO:

FROM:

AUTHORITY

THIS PAGE IS UNCLASSIFIED

ADB805281

Approved for public release; distribution isunlimited.

Distribution authorized to DoD only;Administrative/Operational Use; JUN 1945. Otherrequests shall be referred to NationalAeronautics and Space Administration,Washington, DC. Pre-dates formal DoDdistribution statements. Treat as DoD only.

NASA TR Server website

Reproduction Quality Notice

This document is part of the Air Technical Index [ATI] collection. The ATI collection is over 50 years old and was imaged from roll film. The collection has deteriorated over time and is in poor condition. DTIC has reproduced the best available copy utilizing the most current imaging technology. ATI documents that are partially legible have been included in the DTIC collection due to their historical value.

If you are dissatisfied with this document, please feel free to contact our Directorate of User Services at [703] 767-9066/9068 or DSN 427-9066/9068.

Do Not Return This Document To DTIC

Reproduced by

AIR DOCUMENTS DIVISION

* c lllllililili''1"1-

I

HEADQUARTERS AIR MATERIEL COMMAND

WRIGHT HELD, DAYTON, OHIO

5^ ^.GOVERNMENT

IS ABSOLVED

FROM ANY LITIGATION WHICH MAY

ENSUE FROM THE CONTRACTORS IN -

HWNGING ON THE FOREIGN PATENT

RIGHTS WHICH MAY BE INVOLVED.

HEADQUARTERS AIR MATERIEL COMMAND

WRIGHT FIELD. DAYTON, OHIO

'1 • :• • H

>l ' 1

:• i :l >• iH '•

1 ' 1

K 1 1

'ii

zi En

t • A X 3 i V % » V Q O *

UNCLASSIFIED

-Ära, % 3(f/

NATIONAL ADVISORY COMMITTEE FOB AERONAUTICS COMMITTEE FOR AERONAU

ATi Mo^^y WARTIME REPORT

ORIGINALLY ISSUED

June 1945 aa Advance Restricted Report E5E04 JE04 t

J A GENERAL REPRESENTATION FOR AXIAL-FLOW FANS AND TURBINES

By W. Perl and M. Tucker

Aircraft Engine Research Laboratory Cleveland, Ohio

FH E CO I .. . = . .J

RtlURN fO ^^7 •'/#/ Spacial Documtns Branch - bRWr-6 Wright Field ewrenc« Library '.'•ection

Air uoc.rm.nts Duusion - Intelligence (T--IJ Wntiii held, Dayton, Ohio.

MAC A WASHINGTON

NACA WARTIME REPORTS are reprints of papers originally Issued tu provide rapid distribution of advance research results to an authorized group requiring them for the war effort. They were pre- viously held under a security status but are now unclassified. Some of these reports were not tech- nically edited. All have been reproduced without change In order to expedite general distribution.

E-10

•

• -

NASA Aft: He. S5BC4

KATMRAL XDTCSaBZ CWMKOTB TOR A^OÜAUTIC:

ATr.'AIICE rj-STRTCTED K&Q72

AXIAL-FLOW FATS A3D TUSBESS A GEIHtfL BTOKBTMB» JOE

B-r w. Perl and M. Tucker

SüI:IäRY

A gcafral representation at fan and tvrbino arronpojents on a single classification chart is presented which is made possible hy a particular def inition of the 3tage af an axial-flow fan or turhine. Several vnconventionel far. and turhine arrangements aro indicated and the applications of these arrangement:! are discussed.

ETCKHWCTIOH

A studj' of the idealised two-dimensional blade arrangements of axial-flow fans and turVinca, or turocsachines, indicates that, on the hasis if a certain definition of the turhomachlne stage, various fan and turbine arranea^-eaus car. he rej^osentod on a 3ingle chart. This report presents a definition of the frurbeaachir.e stage and the resulting classification chert, vhich was developed from an analysis of the general velocity diftfrcai for the fan or the turbine stage. Some unconventional fan and turbine arrangements are indicated in the chart; these urranacmeato and some foasible applications ore discussed. Turbomachines having variable exial-flow area aro shown to ho amenable to the same general representation.

SYMBOLS

Th= 8ysibal3 used in the text and on the fig.ures aro defined

aa follows:

A axial-flaw area

a parameter characterizing charge in axial-flow area A„.2

Dg total-rressure coefficient, Sy'gP

/L.,2 c pressure coeffiol«*, ap/jP«

•

-

- •

•^».

2 ".ACA AHR No. EEJ304

E t?ta?. ?re33uro

p static pressure

u design peripheral speed of rotor

v axial velocity

x ratio of rotor-entrance relative tangential-velocity component to rotcr peripheral speed

j rnti-j of rotor-exit relative tangential-velocity component to rotor peripheral speed

p r.ara density

SUBSCRIPTS

f fan or turbine stage

r rotor

od stator downstream

8« stator urafcrean

0 entrance to upstream stator

1 entrance to rotor

2 exit fror, rotor or entrance to downstream stator

7! exit fr^ia downstream stator

THE GE.TRAL KEPKESEHTATIOI! SCUMS

A single stage of an axial-flov fan or turbine may bo defined as consisting of an up3troam stator, a rotor, and a dovnstream stator, as shown in figure 1. The flov, assumed to be tvo-dinen.ilonal, incampi'esaible, and frictlonlcss, ie considered to enter the upstream stater and to leave the downstream ütitor with a velocity v in a purely axial direction. The stago velocity diagram is shown in fig- ure 1. The vulacity-dingi-aa vectors are shown relative to the corre- sponding bladir.T. Positive directions of the velocity vectors are indlcatod.

.

- •

:iACA AHP. Mo. 25EC4

The velocity-diagram parcneterc used In the stage analysis are x and y. Tiie peripheral speed of the rotor ia denoted fcy u. Die quantity x represents the ratio of the rotor-entrance relative tangential-velocity component to the rotor peripheral speed. The quantity y represents the ratio of the rotor-exit relative tangential-velocity component to the rotor peripheral speed. In figure 1, the upstream statc-r imparts a tangential- velocity component (x-l)u to the fluid. Belativo to the rotor, the incoming tangential-velocity cxiponent is xu and the out- going tangential-velocity coaponent is yu. The dovnstrean stator removes the tangential component (y-l)u fron tlie fluid.

The n-indimensional pressure coefficients across the various stage elements are, hy Bernoulli's theorom:

Upstream stator . fPsu 'Psu - r 2 ix-iv w

E ji ?r c -.Pr x2 -y2 (2)

''Pod 2 Downstream stator Cp . 3 -—— = (y-1)"

Spu (3)

The stage or over-all pressure coefficient C_ is the sun of the component pressure coefficients

Cju = 2(x-y) (•)

The rotor pressure coefficient Cy, and the over-all pressure

coefficient Cp thus are functior.3 of the velocity-diagram par-

ameters x and y. Either x or y may he eliminated from in terms of Cy, and ono of equations (C) and (4) to give C„

the parameters; that is: * \ X«- o

-Cpr + x"

°B_ + r (6)

•

MCA ASH So. SS»4

The fanilios of parabolas representing cguatiTtia (5) and (6) are ohovn in the classification chart of figure 2. The quantity x-y io, by the momentvia principle, the tans&ntial f ores or torcuo Ti-.r unit radius on each rotor 'blade por unit naae flow per unit circumf erontial speed. Positive torque corresponds to fat. action, in itfilch anergy 1B transferred to tho fluid by means of the rotor, "egatlve torque ccrrespv-nds to turbine action, in vhlch energy is transferred from the fluid b;' mcor.3 of the rotir. Positive valuea of Cp„ therefore correspond, by aquation (4), to fan action and negatives values to turbine action. Figure Z time reproaonta a gen- oral dcBl^-ation or the characteristics of axial-flow fans and

turbinee.

DISCUSGIOH

Fans ana wrcjoo ..

Conventional f".ns and turbinen. - Operating conditions for various fan or turbine arron^oiaonta can he obtained f rca the chart ir. figure 2. Fan aiTanpoiuen'wB consisting or a l'otor followed by a stator will bo deei^r-atei rotor-etator fans. F?n arrrmgomonts con- sisting of a stator followed by a rotor will be designated stator- rctor fens. All single-stage rotor-stator fans, for which evidently x • 1, are represented on the firat-qualrent parabolic ore OA. All sln.-le-Btago atator-rotor fans, for which evidently y = 1, arc represented in the first-quadrant .lrrobolic arc OB. For an over-all preasure coefficient Cp_ » 1 in tho 3lnclo-Btago rotor-Btator fan, tho rotor contributes three-fourths and tho stator one-fourth of the over-all prc3suro-rico coefficient. For an over-all proo3ure cooffi- cient Cp^ = 1 in tho single-stage Btr.tor-rotor fan, tho rotor con-

tributes five-fourths and tho stator ainus one-fourth of tho over-all prcsBure-riso coefficient. In general, tho first quadrant of fig- ure 2 contains tho design operating pointo of conventional fan arrange- ments; that in, arron^on^nta in which tho rotor pr^sauro coofficienta ar.d the over-all pressure cooffioionts arc both positivo.

Similarly, the third ruadrar.t of figure Z contains tho design operating pcinta for conventional turbino arran£Oir..'nts in which tho rotor pressure coefficients and tho over-all prossuro coefficients

are both negative. Turbinc-typ^ fans. - It is apparent frm the chart that posi-

tivo over-all pre-eauro coefficienta may also be obtained for fan arrangements in which thu rotcr vreosuro coefficients vxo nogativo. Such exr't.;igeaent3, which oro roprcaynted in tho second quadrant,

•

-

::ACA AES no. KSTCK

wl?l be ^osipnitcd t".rbine-type fang. These fans utilize the rotor to trrnsf er kinetic energy of relation to the fluid, thus accouutinG for t; e pressure iro.j across the rcior. The downstream stator con- verts the kinetic energy of rotation to prosaure energy. In thin vay the nroblen of high blade loading in the presence of an over-all adverse -aoasure gradient is transferred to the otator 'blades. The loi^wn aerod;-nanic uethods of increasing the efficiency of diffusion - in particular, tho various methods of boundcry-la; er control — nay nov be attempted without incurring the difficulties presented by application of these cethods to b?ados rotating at high speed. Such arrangements appear to offer definito advantages in developing fans of hljjh pressure rise per stage.

Hepreoantative turbine-type fan arrangements arc cresonted in figv.res 3 and 4. The fan shown in figure -1 i3 dcsi&.ed for opera- tion at point C of figure 2. The rotor velocity triangle 13 similar to that of an impulse-turbine rotor. The fan shown in figure 4.is de-signed for operation at point D of figure 2, The rotor velocity triangle is similar to that of a reaction-cv.rb'ne rotor. Although tho rotor-blade pressure distributions in tho exariplos given are similar to the favorable proosv.ro äiooributions that occur in tur- bine blading, the fan rctora transfer energy to the fluid in the i'o^a of kinetic energy of rotation.

Fan-typo turVue:;. - The fourth qualrant of flg-'re 2 contains tho deaifp o-er.iting points for tva'biues fca'ting positive rotor pres- auro coefficients. Theso turbinea, which will be designated Csn- type turbiroa, beav the oez.j ralaticji to conventional turbines that turbine-type fans bear to conventional fans.

A ^er.erai:zul'.on of the stnf-o definition. - It nay be noted that tho results enboiied in f igrre 2 hold unchanged if the sta^e definition is Generalised so that the entrance velocity to, and the exit velocity from, the stage are not necessarily axial but ar3 ocual in magnitude*. With this oxtensign, the results ore partic- ularly applicable to multistage blading.

Consider, for example, multistage far. or turbine blading in which the tangential velocities relative to a rotor art- equal raid opposite t) the taii^o.itial velocities relative to its downstroom ctator. The. Iv-.c;.i3 in figure Z of ail euch blBÜr.3 13 obtained (a) by acting tho axial and tazii/e.vtiai compr>n~nt3 cf tho stage ontronoe and exit velocities equal, respectively to v ar.d (x-l)u (aea fir*. 1), end (b) by setting jcu = -(y-l)u cr

x + ;• = 1 (7)

KACA ABB Ho. ESK04

Step (a) does away with the u^strean stator and consequently fixes the change in tangential velocity through the rotor 83 being equal to the change in tangential velocity through the dovastreaa otator; atep (b), in effect, equates the entrance velocity relative to the rotor to the entrance velocity relative to the downstream otator. Equations (7), (6), and (5) yield,

•":•

2C, (••>>

Th.'s equation would bo represented in figure 2 by a straight line through the origin and, of co'irse, expresses the fact that the rotjr and stator contribute equally to the roaultant pressure change across the 3tcgo.

Fans and Turbines with Variable Axial-Plow Area

Velocity-diagram anr.lynis. - Ths analysis may bo e::tonded to toko into account a variable"a::ial-flew ar»a through the fan or tur- bine. Tho vt-locity diac^'an to be considered is shown in figure 5. Eadial-velocity oonponaata are assumed to be nonexistent in the ulti- mate upobream and downstream conditions. The parameters character- izing the change in axial-flow area are:

. = •*? vl

_ Al

ar. = V

"•'•-'

()

where

A0 axial-flow area at entrance to upstream ctator

Aj axial-flow aroa at entrance to rotor

Ag axial-flow area at entrance to downotrocai stator

A3 axial-flow area at exit from downstream stator

- - •

NACA ARB No. E5EC4

The prospure coefficients of the stege elenents ere, by Bernoulli's equation:

U-Kitreca stator

Eotor

(10)

(ID

(12) Downstream stator Cp = (y-1)2 + f r^J 6- - 0%)

The over-all pressure corfficient le the sum of the components:

<>* - *<x-x) * ©2 C» - a°2) * GO" C1 • *i2)*(?)3 C1 - ^) (13)

The coefficient C„ is not indicative of the total energy

transferred to the fluid, hecauso of the change in axial-flow area. The lotal energy change ia given by the difference in total pren- auroa, based on abso?.uto vclociu'ea, upstrcar. and downstream of the rotor. For the frlctionlesa flov ossiuaod, no change in total pres- sure occurs across either of tho Stators, If Hj^ and Ho are the total pressures upstream and downstream of the rotor, respectively,

El = ?rn + U13 (x-l)" u" • Ti

H2 " ?ro + ?P (y-1) u + vv"

(14)

The total pressure coefficient for the stage is

-'h CB,-= §pu*

2(x-y) (15)

•

- •

- •

...»

:.-ACA A2B Ko. ESB04

A -JOEnorlcon of equations (11), (13), and (15) with equations (2) and (•',) ai.ova that the relation between the following coefficients

°B (1")

i may ho determined by the valuea given In fic'.re 2, where Cp * nay he re;;ar'lcd ao an equivalent rotor pressure coefficient. r

Applications. - In the conventional axial-flow fan the rotor transfers energy to the fluid in the form, of prcusi-re energy. In the tiirbine-typo fan the rotor transfora energy to the fluid in the fom of kiretic energy of rotation, die Schicht, or conatant- prosouro, fan deocrihad in reference 1 transfers onerjy to the fluid in the form of increased energy of axial motion. The constant- riror:3ure fan utilizes a redaction in axia3-f?ow area to increase tho axial-flow volooity Kid thereby CDnverta to rxicl-flow kinntic energy the static-preaaure riso that would otherwiee occur. Such fans aro indicated in tho first quadrant of the chart in figure 2. The coefficients On. and C-, » of equation (16) must bo used

T *r bocav.ao of tho chanfo in nxial-flow area through tho fan. Tho ques- tion as to which of the throe methods of transferring energy to a fluid is nest efficiont would depend upon the purpoeo of tho fan design under consideration. Experimental data on this problem aro limited.

The possible utility of applying variable axial-flow area to the design of constant-pressure turbines is also of interest. Such turbines are indicated in the third quadrant of figure 2. In the constant-pressure turbine the axial-flow area would bo increased in the downstream direction, ar.d the a::ial-flow velocity would thus be decreased. Tho static-pressure drop of the working fluid that would occur if the axial-flow area vore conotont nay be nullified by a change in axial-flow aroa. Tho turbine thv.3 delivers shaft work at tho cxponae of a reduced kinotic energy in an axial direction rather than at tho expense of reduced 3tatic-orossure energy.

r

:iACA ABS Ho. 25E04

Constant-pressure turbines with Increasing axial-flow area mljjit prove of use in the design of short diffuse». The diffuser lengths required to transform the kinetic energy of a flov to pres- sure energy are often excessive. In combination vlth a compressor mounted 5nmediately dovnstrean on the some shaft, the constant- pressure turbine would perform the same function as a diffuser, in a shorter length.

COIJCLUDHJG KEMÄBX

The general representation for axial-flow fans and turbines presented in this paper indicates several unconvontional arrange— cents of fans and turbinos that appear to offer definite advantages for high pros3ure-riao fara and for diffusor applications.

Aircraft Encino Roscarch Laboratory, National Advisory Conmlttoe for Aoronautics,

Cleveland, Ohio.

BEFEiETICE

1. Sorenscn, E.: Constant-Pressure Blowers. NACA TM Wo. 927, 1040,

• -

] ® NACA ARR No. E5E0* Fig. I

Posi tive peripheral veloci

eral-*—1 ty. a \

Pcsi tive axial velocity, v

Exit velocity En trance

veloci ty

Upstream stator

)))

|»(*-l)u*|

En trance veloci ty

Rotor

Exi t veloci ty

rrr Pi rection of rotation

Downstream stator

Exi t velocity-

(y-l)u

Entrance velocity

)))

NATIONAL fcOVISOHY COMMITTEE FOR AERONAUTICS

Figure I. - Velocity diagram of the single stage of an axial- flow fan with constant axial-flow area.

. •-

• •

NACA ARR No. ESEO«

CP, -4

® I Fig. 2

C NATIONAL ADVISORY uPf COMMITTEE FOR AERONAUTICS

Figure 2. - Classification chart relating pressure coef- ficients of axial-flow fans and turbines and velocity- diagram parameters.

•

-

«ACA ARR No. E5E0H

® Fig. 3

Bo tor

.Direction ^ f

rotation

» - -

- , • -

»'C* 4RR no. E5E0,

Intr»nee|\ „ »elocityl >/*it velocity

(*-lJii

Kntnncel \».(, »eloeltyl NPU »»leeity

yu

Exit '•loci ty Entr.nce »eloel ty

(y-IJu

/*>

FJ,. w

—Awrftb-saa ICS

Figure 4. - Fan design for over-all pressure coefficient C- - 2 with rotor pressure coefficient C_ - -I. Velocity vectors shown are relative to corresponding blading. De- sign values: x - 0; y - -I.

• -

- •• • «fc

* ' •

dp MCA ARR No. E5E01

Exit velocity

Fio. 5

Entrance velocity

|*(x-l)u-»|

Upstream stator

Entrance velocity

Exit velocity Di rcctianrof ro t a l i o n

Entrance velocity

Exit velocity (y-l)u

Downstream stator „J^rntt."«"^.01

Figure 5. - Velocity diagram o f the single stage of an axial- Flflow fan with variable axial-flc area.

_ . - .

ÄTT0- 8491 TITLE: A General Representation for Axial-Flo« Fans and Turbines REVISION

(None) AUTHOR(S): Perl, W.; Tucker, M ORIGINATING AGENCY: National Advisory Committee for Aeronautics, Washington, D. C.

OBIO. AOENCY NO.

PUBLISHED BY: (Same) FUOUSHINO AOENCY NO.

DATO June '45

DOC OAS1.

Unclass. courniv

U.S. IAH8UAOI

Ens. 14 LUMTBATtOfB

diatrr ABSTRACT:

A general representation of fan and turbine arrangements is presented on a single classification chart. The chart is made possible by a particular definition of the stage of an axial-flow fan or turbine. Several unconventional fan and turbine arrange- ments are indicated and the application of these arrangements is discussed. Fans and turbines having vari ble axial-flow area are shown to be amenable to the same general representation.

DISTRIBUTION: Request copies of this report only from Originating Agency DIVISION: Power Plants, Jet and Turbine (5) SECTION: Turbines (13)

ATI SHEET NO.: R-5-13

SUBJECT HEADINGS: Turbines, Axial (95520.7); Fans, Axial flow (34704)

Air Document* Division, Intolligoncs Department Air Material Command

At« TECHNICAL INDEX Wrlehl-Pottanon Air Forco I Doyton, Ohio

TITLE: A General Representation for/Äxla nd Turbines P&/? AUTHOR(S): Perl, W.; Tucker, M ORIGINATING AGENCY: National Advisory Committee for Aeronautics. Washington, D. C. PUBLISHED BY: (Same) /4«T< ajQ PI<S^> !•*<* h I wJZJ

OATQ June '45

ABSTRACT:

DOC CIA».

Unclass. COUNTIY

U.S. UNOUACd

Sag- PAGES

14

ÄTT0- 8491

/ (None) OSIO. ACEMCT HO.

ARR-KfiTMU PUBLISHING A<

luusntAnoM diagr

A general representation of fan and turbine arrangements is presented on a single classification chart. The chart is made possible by a particular definition of the stage of an axial-flow fan or turbine. Several unconventional fan and turbine arrange- ments are indicated and the application of these arrangements Is discussed. Fans and turblnesTiavtng vari ble axial-flow area'are1 shown to be amenable to the' same' general representation.

DISTRIBUTION: Request copies of this report only from Originating Agency -^ j „,—^—#B\.__. LSUBJECT HEADINGS:

)W (34704) Turbines, Axial (95520.7); Fans, Axial

IMNICAL IMDtER Wright-Pattonon Air Forco Dato Dayton, Ohio

ÜWUIASK^IJIP PEfc AUTHORITY. 3KDE7. 0? KAGA 'Efc.üNICÄL iUBLIC.".XKJMS BATED 31 19 W c