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NATIONAL ADVISORY COMMITTEE FOR AERONAtiTICS.....—— —.

_..— ... .-. ______,-

TECHNICAL NOTE NO. 831 .—— _. :.-

A METHOD 03?DETERMINING THE EQUILIBRIUM PERFORMANCE

AND THE STABILITY OF AN E?:GIHEEQUIPPED WITH

AN XXHAUST TURBOSUPFIRCHARGER*

By James Buchanan Rea ,--..-.:

SUMMARY . .-—- ..._=-...

The performance of an exhaust kur%ine drivimg a super-charger is investigated by means of a sanple calculationbased on reasonable assumptions for the purpose-of dekertiin=””-,--’”ing whether the assumed installation is stable with respec~ “-—to changes in the mass of gas handled, %oost pressure, etc. - ‘T-The arrangement was found to be stable throughout tli-e~ ““ ““”r’”=tire range of operation. The method.developed can be gene-$-”‘-””--ally applied. ..=-.._- ..-

INTROI)UCTIO]T ----.-..

This paper presents a method of determining tlw equi- __li.hriumperformance and the stability of a-iiongiri~equipped ‘. 1.with an exhaust-turbine supercharger. . . .—.— ‘1... -.——“.,X-

Tho exhaust-turbine superdarging mechanism is osson-ti.allycomposed of five parts: the engine, tke noz-~lobh”xwith nozzles, the turbine, the blower, and the infior~”-o~~riThe sequonco of events is shown schematically in figuro 1.—..—.

The author wishes to express his appreciation toProfessors C. Fayette T~.ylornnd Edward S. Taylor for t-hc-%rguidance and su~orvision; ant to Professor Josoph Keonati”for his helpful suggestions,

....-—F-

*Thesis submi.t%od,in martial fulftllmont of the reqtiire-ruentsfor the dogr~es”.Gf Bach&lar of Scienco and Mastbr-of’Science, Massachusetts In:t:.tutoof Technology.

..—. .

—.=

.

--- —----

.- —-

—

____

.

---- .— . . --- . . - --- .2

CHAR.ACT3RISTICSOF COMPONENTS

Symbols

The following list of symbols has bocn used in theanalysis and charts of tho presenti-study.

w weight .—

r/fi fuel-air ratio by weight..—

A

P

E

H

v

v

s

T

3s

R

u

g

hp

J

D

B

N

n

zwoa

pressure

energy

total enthalpy

volume

specific volume

total entropy

absolute temperature (460 + *F)

internal energy

universal gas constant

velocity (speed)

acceleration of gravity

horsepower

mechanical equivalent of heat.

diameter

pressure ,coefficiont

revolution speed, revolutions per

revolution speed, revolutions por

rnirluto

-second

.—

.

-.

~:.

?

~—

..=

—=

—*

*.——

..:=--

~.;

-.

.—

-.—

-_,=

x .. ‘P .:spocifi’cMat at constant pressuro.,’~ ..,;. ,.% specific heat at dtinstantvolume

Y ratio of specific heats. .

I moment of inertia..T ‘“ Efficiency ‘

w angular velocity of rotating parts

h rate of change of angular velocity

T torquo

8 Pi()o.ae7z

Ya=~ -1a

. r radius of blowor to blade ttp, feet

● P clensity ..

Subscripts: .

0 exhaust gas (nozzlo box)

i intako (boforc throttle)

N through nozzlo.

th throat

b blower

a air

w.g. waste gato -

t turbine

ad adiabatic ..

av availakle

roq required

.,

..—

. .

(du/dt)

—

.

. ..— ... :

Boforo the equilibrium porformanc~ Qf the comp~oto su.-pcrcharging oporation can be dctornfnod$ it Is nocossary

t

to know tho performance.of each of tho component parts ofthe suporc%ar~ing rnochanism.

Tho nothod of analysis will bo illustrated by givingthe analysis of a specific installation using tho UnitedStiatesstandard atmosphoro as a basis for variations in at-mospheric conditions with changes in altitude.

Engine Data

Assuno the following test conditions:

(a) Wright G-302-A engine

(b) Engino speed hold constant at 1900 rpn by pro-pollor .govercor

(c) The temporaturo of the air .entbringth~ onginois that of the standard atnosphoro corre-sponding to tho ontoring prossuro

(d) Tho engino will bc run at?full throttlo

(c) Air cofisunption: 0.11 poud per brake-horsopowor por minute

(f) Fuel/air ratio of 0.0782

In figuro 2, tho full-throttle brake horsepower isplottod against sta.ndard-densityaltituclofor various on-gino speeds.

Fron figuro 2 and roforonco 1, n curvo of–full-throttlo brako horseyowcr against prossurg bofor~ throttlowas constructed anclis given in fi.guro3. A curvo of f3x-ha.ustgas weight por socoud against brako horsopowor isalso plottod in fi~gro 3.

Based upon tha st.and.ardand nccoptod methods of noz-zle design, the following fundanontal nozzle data wore used(critical conditions at nozzl.othroat}:

.—

.

.— ..

—

.

.

(fl)

(b}

(c)

(d)

ThO

lTACA.TechnicalHOtO 2TO0831 5

Simple cor.vo.rgingnozzlos of squaro cross section

Total nun%cr of nozzles, 9 —.

Total nozzlo throat area, ‘7.37square incho.s

HO2Z1O angle, 20°

calculation of the DOZZ1O perfornaacc curves willbo treated in three parts:

,.

(a) Tho offoctivo ideal..

jot voloc.ity.-It is assunodthat the velocity of the gas as it hits tho turbine whcolis the fully expanded velocity even ,thou~hthe velocity attho nozzle throat ‘.is.not greater thag,t.hovelocity ofsound. This o,s-mption, although not,.strictlycorroct for

.—

largo changes in pro,ssureacross the .nq.z+e,should bo goodin this ‘wlysis boc~ausc+of tho “coupnrativelylargo dis-tance botwoon tho no”z~lothroat and the closost turbinoblate, Abovo 30,000 feet this assumption should bc usedwitk caution hecauso the higher the altitu.dotha noro thoa.ssuuptionis in error.

..?2h0velocity of tho exilaust gas at tho turbi~o blades

can bo calculmtod by the following for.nula: —

where

U

A Pe

r ... ,.A He

u=..il+x\’2~J=

21505 ~~e -

\ A,

.

(1)

velocity of exhaust gas hitting turbine blades,feet per second

change in e,ntkalpyfor (1 + F/A) pounds of theexhaust gas as found from figure 4 by expand- .-ing adiabatically”fron the nozzle-box pressureand temperature to the atmosphere pressure out-.side.the:nozzle box

(Sufficiently accurate”~alues of AHe may be calculatedfrom the perfect gas law provided that consistent valuesof y, CD, and R are used and that the mrrect value of”--R “-is also ~sed+ The data for fi~re 5 were calculated fro-m

.

equation (1) and from figure 4.)

(b) We.i,~ht,rp.toof flow of oxhavst”,?as~hrou,~hnoz-Z1OS.- Tho woi~ht rato of flow-throuzh tho nozzles nay bocalculatocl%y the following fornula: ,“

(2)

whore

~f~? wei~ht rate of flow through nozzles,pounds per second

Uth velocity a.tnozzle throat, feet per second,“calculated by using equation (1). In thiscase AH8 is the change in enthalpy ob-tained by nerely expanding adiabatically tothe throat pressure and not the atmosphericpressure

Ath throat area, total, square feet

‘th spf3clficVolurm, found in fi~ure 4 of 1 + ~pounds of ox!aaustflasat the throat con-ditions

Results of calculations for WIT aro plotted in fi~ro 6.

(c) Nozzlo horsepowego- The UOZZ1O horsopowor nay bocalculated %y the following formula, where J is taken as778 foot-pounds per Btu,

AHe 778 .

hnl= ‘N (1 + :) 550 = 1*312AEe “N

(3)

In this case, AHe is the change in enthalpy for completeexpansion of the exhaust gas to the pressure I?a because itis the horsepower of the “exhaustgas as it contacts the tur-bine blades, which is the value desired. Tho results ofthe calculations are plotted in figuro 7.

Turbino Data.

A single-stago igpv.lsoturbino of,..llol“imchos.indiam-,,

r

iTA.CAqechnical Hots No. 831 7

eter was chosen. This turbine was assumed to havo afieffi-ciency curve asoshown in figure 8,

—.corresponding to a noz-

zle angle of 20 . This cfficioncy curvo was taken frofidata in roferonoe 3 (fig. 218, p. 234). —-

—

Blower Data

A single-stage, str~ight radial-blade, centrifugalblower 11.1 inches in diameter was used. T!ho-tur~ine aiitlblower wore directly connectod. Tho dotnils of the desigmof this blower have ,beenomitted in this paper, but c.xpori-mental cur~es for a blowor of tho samo dinonsions and de-sign are given in fig.uro9.

Intorcool~r Data

It will be a.ssuncdthat an intorcoolcr is providodand regulated so thr.ttho tonporaturc of t~e gir entoriugthe onginc is the st’nnd~ardUnited Str,tosntaosphoric totiper- ‘-ature (roforencc 1), corrospondirigto tho pressure of the

..——

entering air. Tho pressure drop of the chargo air has boonneglected but, in general, as pointed out in roferenco 4,it should be taken into account. “

DETERMII?ATIC?NOF XQUIL13RIUH

Now that the performance curves

PER7C)RMAHCE

for oacn conponentpart of the supercharging nechanisn ha~e leen det~r-r.ined,the over-all pcrforuanc6 will be obtained for”th~ g“~ui.lib-riun conditions.

First, curves of roquircd prossuro coefficior+tagainstrevolution speed at v?.riousa.ltitti~~~.ndffirvarious fidl-

throttle hrako horkopowcrs m.rodcter~in~d h~;‘the”uso of thefollowing oque,tion,which invo”lvesthe definition of 3“;the pressure coefficiortt.

L?~23T = J Cp ha Ya -

a(4)

where the si~nificance of the subscripts and the unitsused-in tho calculations arc+as follows:

8 NAGA Technical lTotoNo. 831

u~ tip spood of.tho %lowcr, fqot For spcond

!l?noutsido-air tonporaturo, ‘F absoluto,“Y.-l.~Ya

Ta =Pf

()~-1 ●

pi intako manifold prossuro, pounds por squaro inch

Pa standard”atmospheric prossuro, pounds por squaro inch

Ya ratio of specific heats cpa/ov ; 2or air

(Ya -a.

l)/Ya = 0.2872

Db blowor diameter, foot #

Nb ro~olution spocd of blowor, revolutions por minuto r

Thus

[( )

Pi 0.2872J Cm Ta

z -1 g-~wB= 2 .—

(m Db ~~b

. --———%o—)

But

Pa g (’7’78)(0.2397) (32,2) (3600) = 25 ~ ~ 105—— =

;’ )mD3a (3.142)260 (*)2 “ ●

so

3 6 ‘n YQ= 25.6 X 10 —-lT#

or

Z!~ Ya

= 2*56 ,.

/)‘illa1000

(5) .

,

A curve of Ya for various values of ~i/pais given infigure 10. Tho zwgauiredprossuro cogfficlents havo booncomputod and the results are plotted as soli.cl-linecurvesin figure 11.

I

KACA Z?echnicalNote No. 831 9 .- ..4

*

.

Second, curves of available pressure coefficientagainst blower speed, at various altitudes and for variousfull~throttle tra~e horsepowers are determiri%d”fro-mthe—formula

vreq = Va,c $ bhp (6)

where ‘a is specific volume and c is specific fuelconsumption. At a given altitude and brako horsopo~e”r,

vroq —V.aluosof

Nb Db3can be calculated from equation (6) for””

various values of N~. From figuro 9 values of avmilable

pressure”coefftcionts corresponding to values of +l?~D~

s.rod.eterminod.,The calculated availablo pressure coeffi-cients are,plotted as dotted-line curves in figure 11*

The intersection of corresponding curves of qvatlatleand required prossuro cocfficionts’gives data for curv~sof hlowar speed roqu5.redagainst altitudo for various brakohorsopovors. Sinco the 310wor and.the turbine are directly “-connected, it is ~ossible to calculatc3curves of turlinctip spooiirequired against al.titu~ofor.various brakehorsepowers. Those e-ccrvosare shown in figure 12; the ~til-lowing formula was

Turbo* tip-spac& =

Zhir&, blower

used a.stk~ basisOf“calculation:

(7)

shaft horsemowcr reauirod akainst alti-tude was dcterminot fo~...vriou~u~brake fiorscpow~rsas fol-lows: Sinco values of .~oquirodblower s~ec&s against a,lti-tu~c at various brake horsepowers aro known and since val-UCS Of Vre

%against altitude at various brake horsapowors

can bo foun from equation (6), it follows ttiatvo,’lue6”ofvreq can bo calculated for different altitud.osand “tit

lfre~Db3 .—

various brake horsepowers. Thus, from figuro 9, valucscfa~-iab~ticofficicncy mad c~.nbe doterninod for corrospond-

J,ro

ing values of ., -’ ?lhovalue of Ilad-used was tdccn“roq Db3

from figure 9(a) or 9(b) i!opotidingon which rpn rango moroclosely corresponded to tho rpm used in t-hooxanplo. It

1,

iS assume?.hero that ~ad is a function only of ‘roq

~~rc1q,D#nnd is indopondont of :Jroq, which is Tory nearly true rtscan bo scon from figuro 9. Values of roquirod ndiahatickorsopowor for various altitudes and engine brake horso-‘poworsare easily calculatq,d,bythe formula bqlow:

whoro Wi is tho air consumption, pounclspor minntc.

Finally, corros~onding VNIUCS of adiabatic officicncyand adiabatic horsepower rcqu.irodboi.ng-known, curves of.blowbr-shaft horsepower required.against a.ltitud~,for var-ious brake horsepowers, nay be Tlo{tod as shown

13$ USing the”following relation:

Blowor-shaft hproq =-.adiabatichpro

.T”~d

in fi.gura

(9)

b

.4

Fourth’,curves,of nozzlo-hox prossur~ roqwirod againstc.ltitutonro dtitcrminodfor vnrious brake hors-cpowors“bythe use of figures 5, 7, 8, 12, and 13, ~S follows: Eecideupon a constant brake.horsepower...An..altitudeshould thenbe chosen and the turbine t-ipspeed re~~ired obtained.fromfigure 12. A value of the required nozzle-box pressure —should be cho,senand the’nozzle gas veloci’ty’nnd the nozzlohorsepower at the assumed-altitude should bo obtained from~hgures 5 and 7, res-poctivolye With the nozzlo,velocityand the required turbino tip gpood, the turbine ~di~b~ticefficiency mny 10 obtainod from figure 8. Then tho blowor-shaft horsopowor is o%tainbd,by multiplying tho cfficioncyby tho no.zzlohorsepower. “#iththis .hlowor-slmft l~orse-power, nn a.ltitudois obtainod from figure 13 at tho con-stant brako horsoyo.worfirst decided upon. If this alti-tude does not agree with the a“ztitiudachoson at tho begin-ning, then a differ.ontvaltioof the roquirod riozzlo-boxpressure is taken and s.uccossivoofforts,are made until thosoq,uoncois in consistent equilibrium.

This process may socm very long nnd tedious, but oxpo-rionco has shown that tho equilibrium valuo of tho turbino

c

NA.CAT6chnica-1Note No. 831 11

efficiency tiariesby only a slight amount with changes Inaltitude at constant’brake horsepower. ?hus-,~hi number oftrials ne’cess’~ry-isseldom more than two if”a tur~ine 6ffi-ciency is first estimated and lqter substantiated by ustngthe foregoing curves. -.

Figure 14 sho~s the results of the foregoing ncthod.

From figures 14and 6, curves of required “nozzleweightrate o.fflow against .altituriefor various brake horse-powersmay be .det.ermined;,they are shown in figure 15. -

.Fi:fth, ‘ ~curv”esof required l~nozzle-equivalent‘twaste-gate area against.altitude are determined for various

..

brako horsepowers, as follows: At any given altitude, theweight ra”terequired through.the.nozil.es-in order to main-tain a given Irake .horseyower.is found from’“figure15.The exhaust-g’asweight .rat.e,availableis determined fromfigure.3,:and the difference,be’cwe”enthebe two rates $epre- -sents the-Weight rate.‘:thatmust pas’s“throughthe wastegate. -ROW, since. th,e”pres.s.l.me.required and thoassumedconetaht temperature of the gas In-:.tfieno.zElebox ~re known,figure 4 may,be.,us.e~to:fand the ~chang.~.inie:n$halpy’af thegas leaving the nozzle box. Also,,figur:8..j4.may..he..usd.dtofind v, the chart volume of the gas as it leaves the wastogate. ~hese values being known, the required ‘~nozzlo-equivalenti~was.te-”gat,ear”e.a”may’be”fQutidby ‘tho conditionof continuity, as ropresontod ly the following equation:

- (lo)

A much simpler met’hodof calculating tho “nnozzlo”oquivalentllwaste-gate area is shown in tho following equation”:

,,.-

(11)

?2iguro.16 shows.thb curves resultiag from equation(12) fol’required ‘*nozzle-oquivalcnt!’waste-gate area “--”against altitude, at various brake horsepowers”.“- . .

Discussion

Tho curves of required pressure shown in figuro 14 in-dicato a dofinito minimum. This fact is substantiated byexperimental curves of 3erger and Chonowoth (rcfcronce 4),rcproducod in figure .17.

A.

12 NACA Technical Noto No. 831

It should be remembered that the analysis thus far isonly valid for determining the eauillbrium conditions ofthe supercharging cycle. But once theseconditions havebeen determined, the static and the dynamic stability ofthe system may be easily found by assuming a small changein one of the variables and following this effect complete-ly through the cycle. Equilibrium conditions cannot occurat .altitudosabove that at which tho curvo of weight ratorequired is Infiersectcdby tho curve of wofght rate”&v.ail.-nblo, for constant brako horsepower. (Seo fig. 15.) Inthis particular Oxarnple,theso curves do not i.ntersoctwithin tho ranges investigated, but they night intorsoctif experimental data rather than thoorot$cally cal.culcboddata, wore used throughoutthe analysis.

It ‘ispossible for the systox to bo in oquilibriunCVOn though it iS statically unstable. In othor words, aslight c.hangoin ono of tho variables from its oquilibriunvaluo might not be followed.by a tendency for the systezlto return to its original state. lt ~layalSO b@ possiblofor tho system to be statically stablo but dynar~icallyun-stable, that iS, a slight chango in one oflthe varfablesfrom its equilibrium value might result in an undamped andcumulating oscillation. .

DETZRXINATION 03’STATIC STABILITY

Development of Formulas Used inStatic-Stability Calculations

.

The fundamental expression”used in determining thestability of the exhaust-turbine supercharging cycle isbased upon Newtonrs second law of notion, and is as follows:

d (Tt-- ‘b) < 0(12)

du)-,-

where.-

UI angular velocity of rotating parts,radians/second’

T; turbine torque, foot-pounds .

Tb blower torque, foot-pounds

k

,

.

*

NAC!ATechnical Eote No. ’831.

An’expression for the turbine torque Ttfrom the basic equation fourhorsepower:

!-3.1s0

Turbine hp = hyN Tt

where

13

is derived

,-- _____

(13)

(14)”

hylt horsepower of exhaust gas froa nozzles asit cones in contact with turbine hl~des

‘f)t tur%ine efficiency (See fig. 8.)

If equations (13) and (14) are conbined, there is obtainedfor turbine torque

Tt = hpl; Vt 550 (15)w

An expression for tho blowor torque nay also be foundby using tho basic equation for horsopowor: -.

1?ywBlower-shaft bp = —

550(16)

/31s0,

Adiabatic hpnb = (17)

310wer-shaft hp —.

where ‘nilis tho adiabatic efficiency of tho %lowcr andis defined by equation.(17). Tho adiabatic horsepower canbo ottain~d from equation (8).

z c

Adiabatic hp =Pa ‘[i‘a ‘a33000

By the introduction of equation (4) and tho equalityUb = u)r, an expression nay Wo dovoloped as follows:

g J Cpa ‘a ‘aBU2 = ar

(18).-

—

14 NACM Technical lToto No. ~31 4

E~uat.ions(16), (17),a final oxprossion for the

and (18) nay be combined to give ,M.owortorque,

Additional equations, such a<

wi = (bhp) (0.11)

are needed for the stability calculations-

Since Nb = .% and since Wi = V pa, an

for the.dimensionless blower coefficient v

developed: NbDbs

and

thus,~vexhaust= “N(*)

w~~=(

weAW.g.)1-1-.

Procedure jor Determining Static Stability

(19)

(20)

expressionis easily

(21)

(22)

(23)

(24).

Select an altitude at which the stabil~ty is to be in-vestigated. This altitude will.determine the pressure,the temperature, and the density of the air as consistentwith the standard atrJosphere. Colunns 22, 23, 24, and 25 oftable I nay be filled in innediately. Then, decide upon anequilibrium value of the brake horsepower (colurm 1) a’cthis.altitude and fron the equilibrium-perfornanco calculations,deternine the corresponding value of tho waste-gate area(nozrlo oquivalcnt) for colunn 13. The value of W’e (col-unn 2) nay ho.found fro~ figure 3; Pi (colurm 3 ) nay befound ?Jyusing figure 3; and Wi (column 4) may be found

.

.

NACA.Technical lToteNo. 831 .15

obtained by using coluan 5 and.figure 10. Colunn 7 nay bofound using equation (18)0

.-

N(3X’C, ostinate a value of w and use equation (21) togot .-v Then,

Nh Db3 ,“got the corresponding.value of E

fron figure 9 nnd calculate Bwa.” When this value agrbeswith thovaluc in colunn ‘i’,the W is “corro–cut,and the ?lbnay then be doternined’fron figuro 9 corresponding.to tho

vcorrect valuo of

—Thus,

Hh Db3*COIUZlnS8,”9, 10, and”ll ,-—.

P.P.Yhe filled in once this equilibrium,value of. $0 hasbeen obtainsd.. Colunn”12 nay be calculated using equation(19). C“olunn13 is determined fron the equili3riun-perfornance calctilations,and coluan 14 nay therefore b&

● obtained fron;equation (24). With the value in colunn 14enter figure 6 at th~e‘properaltitude“and get Pe faa-col- ,

. unn 15* Then, with tb.isvalue of Pe, get h~N (colunn16) fron figure 7 at the correct alti.tu@e. Also get,(colunn 17) froc figllre5,

‘gusing the.foregging walue of Fe

colunn 8 rand the sanealtitude. co~unn 18 = and thiscoluzm 17 ‘value Day be used to obtain ~t (colunn”19) frou fi,~re 8.ITOW, Tt (colu.nn20) nay be calculated using equation (15).Colunn 21 is found by subtracting colunn 12 fron coluzm 20.

Pinally, a plot of IL against w nay be na?!.easshown in figure 18. Each line in this figura representsthe stability at a constant altitude, for a fixed waste- .gate position and for the equilibriutihorsepower corre-s~onding to this fixed,waste-gate positior;. ‘~ho sjs-~e~-~~stable for any altitude and waste-gate position on~y when ‘“the slope of the corresponding line is nogativo, that is, “- -a &Qcroase ia u .fronits oquilihriun v~.lue‘CauSf3S an:fn-crease in T~ - Tb, , thus causing tho systen ;o-return toits equilibrium conditions. On the other hand, an increasein w would cause a ?ocr~ase in -t - ~~ti for a stablesysteas —

~ib~re 18 soens to indicato thatl for a constaht Vnluoof the cquilibriua korsepowor, the sfia3ilitydecrdasos wi-th

-.

increase in altitudo as shown by tho 600-horsopow6r-”&!?Vesat 20,000 and 25,000 feot- An incroaso iu horsepower at thosarlcaltitude seens to ,affecttho stability very little.

.

16 NAGA Technicrl Note No. 831

DISCUSSION

It should be remembered that the shape of the actuafcurves as obtminod by the equilibrium performance and thostability calculations made in this analysis depend upontho .orifiinalcharacteristics of each component part of thQsupercharging cycl,o. l?hoanalysis of a. particular theo-retically calculated cycle was made in this case moroly tooutline a genord procedure that could be used in dotormin-ing tho over-all characteristics and stability of any ex-haust turb.inoeuporchargor installation.

Turbosupercharger installations are apparently static-ally unstable in tihoregion of low V/nDs whoro the supor-chargor”stalls and the curve of” B (or q) plottod againstV/nD3 is discontinuous. Dynamic instability is frequent ,

but is caused principally by control difficulties, and con--sideration of it has therefore teen avoidod in this pmpor. ;-

It is generally known that in the p~st many actualexhaust-turbine installations have been unstablo under cer-tain critical conditions. Boco,usoof the socrocy at thopresent timo in connection with the general subject of ex-haust turbines, the author has found it impossible to ob-tain data necessary for an analysis of any actual installa-ticm.

It is suggested that, if an analysis of this type weremade prior to the installi.n~of any exhaust-turbine sys-tem, information might be discovered which would help toeliminate causes for instability and thus enable the de-signer to obtain a reasonable estimate of the performanceof the entire supercharging cycle.

Massachusetts Institute of Technology,Cambridge, Ih.ss.,Ma.Y15, 1941.

.

11

.

NACA Technical Note No. 832

REFERENCES

1. Brombacher, W, G.: Altitude-Pressure Tables Based onthe United States Standard Atmosphere. Rep. No.538, NACA, 1935. “

2. Hershey, R. L., Eberhardt, J. E., and Eottel, H. c.:Thermodynamic Properties of the Working Fluid inInternal-Combustion Engines. SAE Jour., vol. 39,no. 4, Oct. 1936, ppm 409-424.

3. .stodola,A.: Steam and Gas Turbines, pt. I. McGraw-Hill 3ook Co,, Inc., 19270

A-* Berger, A. L., and Chenoweth, Opie: Supercharger In-stallation Problems. SAE Jour., VO1* 43, no. 5,ltova1938, pp. 472-4a4.

.

T*.-+; A=. 0.Ct512aq ft; ?/h . 0.0872; ~= m 0.792ou ft; & _ B2.2ft/meo/aeo;J m 778;o = O.Q~ ;P=

r = 0.462s1-1

I I b=. z 4’42) i -m) I (14)I[15)1(

-.

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.:Sw.676

*:664.669

, .u.666.650

NW&4!T!echnicalNote No.831

.

.

.—

II standard

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Figurel.-Schematicsketchof theexhaust-twbinesuperchargingmechanism.

IU,,CA Tochniod Noto No. 831 Fig.2

.

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Altitude$t

Figure2.-Altitudeperformance.Horsepower(withoutram)forWrightG102-A

(Frombookof instructionsonWrightOyclone

andmanifoldpressureaircraftenginesEngine,GR-1820-G300.)

. . . .

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Wei&t ofexhauetgasfromengine,We,lblsec.}

low”.2 .4 .6 .8 Lo 102 1.4 1.61 I 1 , & I 1

1,8 1 @/ ~

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Pressure~

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10 15 a 25 30 35 40Pressurebeforethrottle,Pi,in.Hg

Variationofexhaust-~sweightandpressurebeforethrottlewithbrakehorse-power,Wri@ G-1234 engine;engine speed,1%X) rpn; fullthrottle;fuel-air ~ratio,0.0782. n.

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12 16 xl 24 28Nozzle-boxpressure,Petlb/sqin.

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Figure8.-Tqriationof efficiencywithvelocityratiofor single-stageimpulseturbinewithnozzle

angleof 20° (fromreference3).

??ACATechnicalNoteNo.831 Fig.9&

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N*3Figure9a.- Characteristicsof Cyclonesuperchargerat 15,000rpm;

tipspeed,720fps.

NA.OA.9

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TechnicalNoteNo.831 Fig.9%I t I P2

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NACATechnicalNoteNo. 631 Fig.10.

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Figure10.-VariationofYa withPi/Pa.

NAOATeohnicalNoteHo. 831 Tig1.6

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FigureU(f) .

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Figure 14,- Wwiatlonofnozzle-boxpressmwwithaltitude.Er@no speed-,1933rim;fullthrottle. P

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Figure 15.- Variationofrntosofflowthroughnozzlewithaltitude.Enginespooa,1900I’PKO:fullthrottlo.

wG.‘P(n

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. I?ACATechnicalNoteNo. 831

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Figure16.-Variationofwaste-gateareawithaltitude:enginespeedy1900rw ;ml thrott~e=

N.&4.CATechnicalNoteNo. 831Ii I

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Figure17.-Flighttestof e-ust turbine-drivensuporohargershowingeffectof properlydesigneddisposalsystem(raforence4).

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