Pressure Loss Calculation Procedures for High Speed Gas Flow

8/14/2019 Pressure Loss Calculation Procedures for High Speed Gas Flow

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Re:No-~ 26.P~SSCSS C-,CojU-Kx-;a R OCH -%IEE GAS LOW

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U. S. NAVYBureau Pcf 4Was irigto 25, D. C.

June 297, 1961

DYNATECH CORPORA.TION639 Massaichusetts Ave-.,ueCaImbridge 39, Massachusetts

SURI


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TABI O U NTNETS

LIST O- PROCEXJRES iiLIST OF ES=G 0 tAIS VPREFACE I1. 0 INTROLUCTIMM 32.0 INTRODUCTION TO PARAMTE1I7E AND GENERAL 5METHOD OF COMPRESSIBLE FLOW

2. 1 Mach Number 52.2 Total Pressure and Loss Coefficients 62.3 Total Temperature 92.4 Mass Flew Parameter and the Con, nujy 10Relation2.5 Choking in Compiessible Flow2.6 "GasProperties 17

3.0 -SOURCES AND ME i-ODS EMPLOYED IN DZVELOPMENT 18OF CALCULATION PROCEDURES FOR DUCT LOSSCALCULATION

3. 1 Straight Constant Area Ducts 183.2 Area Change 203.2. 1 Abrupt Area Increase 203.2.2 Abrupt Azea Decrease 213.2.3 Diffusers 223. 2.4 Converging Duct (Nozzle) 26

3.3 Bends 263.4 Screens and Gratings 29


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TABLE OF CONTENTS (.onr t d)

4.0 CALCULATION PROCEDURES AND EXAM-PLES 304. 1 interpretation of Procedure Diagranb 304.2 E.amples ... - ._ 314.3 Closely Coupled Comjonents 32-

P PROCEDXURES 33.D DES!GN CHAPRS 655.0 APPLICATION OF CALCULATION PROCEDURES 84TO A DUCT SYSTEM. -

5.1 Sample Duct Pressure Loss Calculation 895. 1. 1 Intake Duct 895.1.2 Exhaust Duct 94

5.2 Effect of Pressure Loss on Turbine Performance 99NOMZN CLATJ RE 103BIBLIOGRAPHY 107


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LIST OF PROCEiDRES

P- I Mach Number 33P-2 Srraight Duct

2.1 Intake Duct 35j 2.2 Exhaust Duct 37P-3 Duct Inlets, SimplifieL Pruedure

3.1 Inlet Length with Beilmouth Entrance 393.2 Inlet Length witr Shnr 2-Edged Entrance, with 41or without screeis at entranceP-4 Abrupt Area Increase

C4..1 Intake Duct 434..2 Exhaust Duc- 43F-5 Abrupt Area Decrease

5.1 Intake Duct 455.2 Exhaust Duct 45P-6 Diffusers

6.1 Intake Duct 476.2 Exhaust Duct 49P-7 Bends

7.1 Intake Duct 517.2 Exhaust Duct 53


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LIST OF PROCEDURES (cont' d)Page

P-8 Screens and GratingsS. I Intake Duct 55

*' 8.2 E ust Dat 55* P- 9 Duct Inlets, Alternate Procedure for Bellmouth Entrance

9.1 L/D > 30 579. 2 L/D < 30, rest for procedure 59x9.2.1 L/D < 61:x 9. . tr L9.2.2 < - < 30 61

P-b0 Duct Inlet, Alternate Procedure for Sharp-Edged 63Entrance

I(


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viLIST OF DESIGN CHARTS (cont' d)

PageD- 14 Loss Coefficient, C vs I - - 81D-15 Bend Algle Loss Factor 83

I7!

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The prinfry Ixzr;,ose Of tis report Isto fulinfil e-contract require-nliet for"a set of--sg at hes iilin~ form and aojkiarionk o N h~ p D i gn D Sh er I~ 8O 2 x for ca l cu l t o n6f,pres-sur losesathig ga veodIe in gas turbe ducdn~rg. M&i purpose.is'" norpJeO in ;40 design c-harts-and-design p-cdrsfudinSekxibns 4, in4 I. These have.:been prepared-in such form ftht they*may bie_ exrce fo h ohr jcinsf the-repr ti frmas-contained"set of procOdues-an data-necess-ay -~he clcaioo

4ig-ipeeo;duct;,g .-osses,- and'O contain_-thinece saryelemenvs fora inlaraShee6tAs -we iallehjnatejil -ecesarj=for the -required pFoceduialanddat serio, w~-eaizedtha Tis- epoit* w ud be of, miore; valuet6:hoe ho areu Itlnae.- ep l f& pieprartIoA and the~ pei-

-OdIO irevision;-anfd;jr _0- nb-thd e DataShetsandphas*a4Ot-t P q)ior~edols,were -b

'1,Abrifitioduct~i o td -parameters:-and genri, rneth6ds ofcompOressible Qigh-speed). flw;TIh calciulation procedures,and the govering fw p- rmes case qrtdifferent- fir those met .in cMlcUlhrind incor~pr essible*(ospeed)- du tflws.- We-hope that the short intrdco -includedasScin fTe tpr ill 4e helpful to Ehoqe -who are prirnar -ily' familiar with- the -methodss of incom~pressible flow cdlc'Uiations,in-uniderstanding the procedures recommendedin--this report, andSin appreciating SQme of the rpasbnis for thetr con p,,.4Kty Wiaacompared to Incompressible methods.


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in--te-preparatioz. ofri des-Ignh2rs Ou~d ptohr baCrsurvey of die-data-avAiblhe iiiteltrar ncnnrsii(igh speed) ef - tsdn -ductAfiows shqrwLed tOlar the-reA e-mnyare~as Where data io incomple-re or ibcondtklsive, afid-in, facE.somiezfiies confictinfg. Th.is is 0.1so true to a lesser extent ofthe afailAble damta ~incompressible &jct flowYs rwm varioussources.; Thfis situation resul ted In the necessiry, In prejgring,'the finalcharts-and procedures- which are-our.-recommzndat-ionsfor -calculation, or'aipolyffng-our Judgeinen in choosing data, scoifces;-of generalizing from incomplete dara;- and off caltulatig from dieo-

-retica- anaiysis,0 to extend existing data or methods -(e.g. .teanalysis f6 r dbrupr--aiea decirease it Section 3.2. 2).

We havE atter'tedto make -the design charts anid calculation proced-ures as complete as -po.sible. 'Ii masthat, in some cases, where

daaIs iflcomplete or inconclusive, we -have made for the designer thed_;,,.ceisio,- and judgemenis that wudconfront him, if he,were wbrkingfelt it would be-useful to iclude in our report som~e specific indica-tions of the-sources-and. methods which led to our recommendations.We hope that these no%~s will be useful if a critical -review Is made ofthese methods at some later time when, presumably, more high speedduct flow data will be available in the literature. These notes on methodsand'sources we have included as Section 3 of the report.j

James R. Turner*Project ManagerApproved by: _________

L.C. HoagXhnd


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1-0 ."ThOWalOfor low spm sl oow*, at uL of9 1:/sc and ess- For

rMhs l es, Aan, press=&: a ses =y be esumaz wirhne&g4ie by enpi ;b ~prim tl t e gas Is ;M ii'-couiressft!-izd This zsiuex L-ies tI va-kmiznsare salM aod -a be goored in caeu mrhbo 1s. Pressre lcsscllcw,~ umediods ft~ low sppwd-Gows b"s~ b 'accuV.-amible as-

umatcm haie beau coIcted and ormallzed in :esce I. -If it is desrable w deslp Wlet sis exh~aut uc ug for~highr flowvIacIn, and thus ob=ln 6iczw of smaller diameter, the lossesmay o c. -rbe esdinmare bt,, z assums of ncompressibleflow. At high subsomic gas velocities, above about Mach Number 0. 2.the magniwude of the density changes accompanying the pressurechanges &- to accelera-ons. deceleratioas, and losses should not beIgnored in calculation. Furrhermore, the loss coefficient character-

izing th pressure loss in each duc"'Mg component, usually expressedas a fixed percentage of the velocity head for a component of givenconfiguration in incompressible flow, generally depends also on theflow velocity (or Mach Number) in high speed flows. The presenta-tion of a calculation procedure for high speed duct flows thereforerequires two extensioni of low speed calculation procedares:1. Fornularion of a calculation procedure which will Lake into

account the effects of compressibility on local values of flowparameters (pressure, density, velocity, etc.)

2. Correlation of available dc.ita or. the , r~' &..;.: .o rhe prssu.re losses, or loss cefficiei::s which cha::.the pressure .oss.es, in various duct components.he pessur ' "I


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---- -- -.I: - -

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Vids :ep h describes a calculati. system -which pnrdts the c.l-c_,!arloa of dqctng losses for higb sped:flows. In thefollowingsecdons the mediods and data sources empioyed are described,and a system is devised foz application to duct presstle loss ca1:culflaxis. This system ha&- been reduced to a series of charts forcomputaticnal aid. Th e charts are-included in a separate sectdonof this riport and are arranged so thar rway may be extracted fromthe report to form a self-contained calculation system similar inform and intent to the material of Reference 1. Although the sys-tem is nor as simple in form and application as the incompressibleprocedures, they represent, -in our opinion, the simplest calculationpro&edures which can be applied to high speed flow calculations.

I


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2.0 INTRODUCTTON TO PARPAMETERS AND GENERAL AMETHODSOF COMPRESSELE FLOWAccountring for gas compressibility effects in the calculation of ductingpressure losses, necessary for high speed duct flows, introducesseveral new variables into the caiculations. Rather extensive changesto incompressible flow methods and procedures mus: be made. Thepurpose of this section is to provide a brief outline of parameters andmethods employed in this report which are peculiar to compressibleflow calculations. Those analytical relations developed which areimportant to the calculation procedure have been reduced to chartform in later sections.

2.1 Mach NumberThe Mach Number is the basic measure of the relative importanceof compressibility effects. The Mach Number is the ratio of the fluidvelocity to the local speed of sound:

M =V- cwhere

V = fluid velocityc = local speed of sound = I RT

Only subsonic duct velocities (i . e., M < 1.0) have been considered.For Mach Number M


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Shapiro (Reference 2) and others have shown diat most compressibleflow cal-,lations are most easily carried out if ha C--calation meth-ods are formulated in such a- ay that Mach Number is the ind.pendentvariable of the calculation procedure. For many of rh- pressure-losscalculations which follow, the Mach Number has herefoze been chosenas the independent vaziable. Generally, losses in ducring componentswhich do not involve area change cause the Mach Number to increase.Therefore, it is possible that in a.ong ducting system, incompressi-ble calculation methods may be appropri,:e in sections near the inlet,with compressible methods becoming necessary as the Mach NumberA'ncreases.

2.2 Total Pressure and Loss Coefficients.The total, or stagnation, pressure is defined as the pressure whicha gas stream would reach if it were decelerated to zero velocitywithout incurring any losses in the deceleration. The total pressur -is the pressure measured by a Pitot tube, or an "impact" probe. Forincompressible flow, the total pressure is the sum of the static pres-

.... sure and the velocity head.2gp + (2.1)O P + 2 go

wherep0 = total pressure (impact brobe pressure)p = static pressure (pressure at a wall pressure tap)p = fluid density

= fluid velocizy


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- ---

the,change-,In tOtal,pressure in a duct, low is a measure of the losses',ithe flow. The losses may be chdracreriz*d by, dimensiopless ,!oss-:woefficient, CPo-

op- (2. )-

Where i and 2 represent an'upstream aniddownistreTn srz~tion1 re-specivey. For incompressible-flow ina constant areg duct,

and. so,i ol - Po2 = P 2. (2.4),

duct is equal to the difference in static pressure, s6 that the flowlo~e are described-equallywell by either total pressure change orstatic pressure change. -This, however, is not true for a compres-sible (i.. i igh speed) flowv.For a compressible flow, the simple relation between total pressure,st.tic pressure, density, and stream velocity given by Equation 2. 1cannot be applied directly. This equation does nor apply -because thefluid density will change during the deceleration; that is, the density,

.... Pg n Equation 2. 1 is not a constant. The relation corresponding to"'Equation 2.1 for compressibie flow is best expressed in t'rrms-o dit-Mach Number:

-0

V

_'go,


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1~1

.?.o _-- 2 (2.5)

ewhere k ratio oi spedific. heats, a gasqpro- erty.The Iosses, can k expressed as a changein.totai pressure in,compres-'siblefl6w; this change is not equivalent to :lhbstatic pressure chaige,as in'incompe'sible.flow. The definition.of loss coefficient, Equ.tion2.2, may ,be rearranged -to more onvenient form through. the relation

V 2 2(.6

so-that, Ti'rp01-02C -. . 27

PO 1~. 211

Combined with Equation 2. 5 this becomes.

P02 ,Ck (2.8)" 1 -- k 14I2 k 1 M2 k/ K


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2.3 Total Temperature"The otal, or staiiation,, iemperatuie is similar to the total pressure

" in cefinition. That isj 'i is the tempeiatWrq whicha gas stream Wouldteach if it weredecelerated to zero vel6city. It is best expressediAre ns of the .ach Nurhber

T~ _~-12 (29)-2T'2

whereT = total.temperature (temperature of-streamdecelerated to zero velocity)

T startl- temperatureo((teriperatufe oftheflow.hg gas stlram)Unlike the tbtal pressure, however, the total temperature is un-

"afflcted by,.osses. If i a duct flow, the-total temperature can changeonly rhroughheat transfer to or from the:gas-stream. Note, :however,that the static temperature may vary considerably, as by accelerationor decelerAtion of the gas stream, according to,Equation 2. 9.If we assume that hear transfer to the surroundings is negligibly smallin a duct flow (i. e., the flow is adiabatic); the total temperature re-mains constant, irrespective of the flow losses. The assumption ofadiabatic" low has.been made in the calculation methods presented inthis report. Therefore, fo r a gas turbine intake ductflow, the totaltempera.ture is the temperature of the atmosphere (i. e., the tempera-ture of the inlet air when It was at zero veloCity), and is constantthroughout the inlet ductin..g; for a gas turbine exhaust duct flow, the


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total temperat ,ure is determined ~by thed exhaust condiffon at 'the' turbine,and is -cnstant~throughot~the e6chagsr ducting.

"K The-assumption of.Adiaba'tc flow in the-Intake ductAs qtitp accurte,since-only siall-temperature differendes exist b~tweerr the-uruct flow,and-ihe' sut roundings. For the hot,exhaust flow, 'the Adidbatic condi-ion -is~nor~so nearly achieved, thugh-insig' fi ar errior is, probably

introducea'16r insulated ducting. 'To ae.coufrt f6 thpe ffects othieaE-transfer to~thd surroundings in thi ekhaizst-duct flowW ould'precludeany simpole calcula tion,.riithod.'fo r the exhau#t duct flow lqss6s.,

-2.4 Miss Flow. Parameter and th& Contihuity Relation_For i-ncompressible flow, -the continiy. relation may be expressed as

in .p AV pAV (2.10)Sintce density i's constant barwvean any two sections, the velocity willchange-ofilyby vi'ttue of nn aroa change. in, 4.6ornpressib1e low,,however, velocity Oha.ngces (and thus -clanges in; ach--Number')- caiWoccur in a constant area dL~cr, becauise~ of changes in density resultingfrom,.pressure losses. ?'hus, the-continuity relation must be applied-along with the loss relatjins to determine Mach Number chan~ges ac-compa~nying ducting component losses. For Compressible flow, thecontinuity reldtion maybe coinveniently expressed As

01 0. 532 F(M) (2.11)

where the constant 0. 532 applies for a gas of k =1. 4 and molecularweight of 29. The function of Mach Number, F (M), is


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computational aid in determnnng-Mach Nrniber when-other flow con.-ditiojas ate~sp'cifted.

2. S Choking in Compressible Flowthe mnas- flow rate In a duct flow of 'compressible gas A liited ~the, phenomehon of "chokinig". This 'may be exp1jined iby'the following

* considerations.-~ Cosieranpl .ucin copoen ~k~ hs~a bnfus area,

dhangeq (e. g,.. a nobztle), with specified areas

A IA2'T0~AandA 9, and--flbwat total terip~rature T0 If we assudme thkathre

are-no, losses, p0 lrpo2 rPo' 'Let-us first hold the-ups5tream totalpressure, p0U1. constant and continudu~1y reduce the-downstreamn static,pressura, p -From Equation- 2. 5,

P2 2~ 2 k/k-2.14)

the Mach Number IM will increase as, static pressure,P2 is reduced.The effect on mass flow rate is-determified through Equation 2. 11,


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+- +:-- -"+--- _ _. : --- "- : _- -

532 (2. 15)

b2- MJJ

Sketch-I shows, the variation -oiF (M) with March Number. As-;IA isificiresed, F (M) creases-r#i

I -

1-1- --

/I..yt-ch, -0. 5k, forvar inas-~ lwit M4.Iachnm, r- at+ seactimuc ead A * ) Thus, as tpes sure - - 1

2 2I s -,o to N~Sketch I.a bximum., value at M =,l.01 and then decreases. Thus, for our ex-ample, as the pressure p2 is decreased, IMwill increase :qnd he mass

flow rate will increase hntilMach "hNumber2 -0 is reached, atwhic condition the flow- wi a maximrum. This occurs at a value of

-0.5"+8, for a gas-with k = 1. 4. It can- be-shown that the Mach" OK, umu . cunno; pass through MI=1.0 to supersonic values in the min-imum area A2.Thus, as the pressure p2 isS further reduced,, the

-.;" value-of M remains at unity, and the mass flow rate remains constant.- - This maximum value of flow rate is tha "lchokcdll flow rate. ThU-. *See Reference 2, Chapter 4 for a rigorous explanation of this limitation.


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-14- -1J--Variation Offlow te t With &~wnistreain sra&c presr-u~e, ac6n4tant Upstream to-aI p sure p rs shown byS ch 2.

- "S~ke~cla7 "NOte ,thuwhen the chokedflow coni M .O)-isatminei, te!ilet-Mach Number, M, -also-hag a definite-vaiue-Which is fiNdbyte .ar~a ratio A2I/A. From E-uation 2.13, at M2 =1.0, F(M =L 0)=1.,0 andpo2 -= Po .pPo2Po22

F (M - Al F (M- (2. 17)T F (M) - - (2.18)

Thus, for this duct component, there is a limiting v u c ftnlet MachNumber, M1, which cannot be exceeded due-to the "choki .$" phenome-non.If W e now assume that there is a total-pressure loss in the abovenozzle,I then Po 2 /PoI < 1.0, and the inlet Mach Number at the choked conditionis given by PIF( ' P6 1 A1" F(t) -Po' A1 2.19 .

-- - .


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- -,a- b- I, a.w-~ lach "I- -w - IE-i- ,- - V

~ wil slw ~basI~c irii Uh#W ibcz

i~~jii~i izir m~wr~nec M ch ) a~iber less-than-4Mthok an nlrN eslha ui' -with tfpe-

e-~n.c ub~ dpeIAdiigg On t-d&leng.

Thea~~-i 4iictn..:c .iutec system.*,-ige -ubeils~-taEd~ h nexa' ble. Sipo -har-uve witb -to-design6,nin~jum

size ~~snr~rLi r -rd~zfor.!gzs curbine . Thiefair j$ Eo-be ran-fonatmspe~i~LIiions ot~~ -;.d-T ate-fixed;'-

S-erh 3I


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10required~tui -bine~iIas low, in, Will be__specified., Equailo 2.1

gIe s IrItXsevl-&OlolOt -7be ppbsfizs4 cisi so hrT hal-tloe willn&

wi. fbjt:zai the ,maxitxrnrn iudecfite dvalueofF(MY, ic nin cisatMl(lo() 1)th

AA

when-ahb s~cif'Ied-values, of in and p0 aeinserted. If d ductany-smaller- than this wet e-u sed,. the specified,.mass flow would ~notbe 4ttAined, cegardless of -how,ow the gas -turbine :conpressor re- 1uced thie pressurevdt the-duct exit.if we nowala' w a- ong -inletduct in which losses are not negligible,then-p 2 < PO. Since. M' cannot exceed unity(rd (N ant

--

-n .0 0.532Po2 A

Since-_p 0 2 ig 1es than po the duct area required-to admiR the spec-Mfad flow becomes larger thin -for the short inlet duct, -because ofthe duct losses. The limiting inlet Mach Number will N;~44all- thanunity.


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'.NeAiriOking, d- - tict pfnbent losse-s '-eer~i~l become sojarge-thqt~~--4int pr aato- esign for hkdo ercoe ducting. How-ever,, it -l4 irprt~nt'to r~ali26._t1ha -regiardless of loW much pressure

* bss is all64vab1e, ihere aie- minimrum. duct areas thAt Will admit-aspeifid~mss lowatfixed'inlet Cqonditidns' (e'. g;, atMOSpheric con-1 cdit;_on!)

2.6 -O~p -Proper ies!JMAl the relations -fthealculation methods pr esentedassume thnt.thepepe6t~gas-eqiAin-of sr- re,

p =pRTis valid I&r he duct flows consider ed. In addition-, the, char ts ha vebeen prepared -for a gas, with ratio of specific:,heats of .1., and -mo-

- - 1ecifar weight,'29. thiese values will apoly!'Wirhh tiffcient -accuracyto-either atmospheric inlet ar, or gas tWrbjine exhaust gases.

. .. .. .. ..


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3.0- SOURCES .AND METHODS EMPLOYED- IN DEVELOPMENT OFCALGULATION PROCEDURES' FOR DUJCT LO ,SCAVICUL.ATIONThe data sources and correlaion mi-e-thods on which the ~clculation

* procedures bresented-in this ieport are based, ire outfinie"Ifn thissection. iln somhe casesthe available- data is incomplete, so thatapproximationis and, ektr~polarions have been necei'sariy; -in, om e

* ~cases,. data from various sourcesconflict,, so that somie judgmenthas been necessary in cho6sing data for procedures. 'Under thesecircumstances, it seerna desirable tou-supplenient the recommendedcal'ulation piocedures with this outline, of' ource's and methods.

3. 1Straight Constanr Area DuctsrThe procedures for straight ducts are based oir the calculation--methodsdeveloped by Shapiro, and othdrs. Thbese'are-developed in-detail, inRefefence 2, and'are a standard mnethod. for compiessible floy,calcu-lation -to nclude the effects of riction. The niecessary compressibleflow parameters for this calculation are plotted in Figure D-7.Duct friction factois are-,taken from Mo-ody, RAefer-ence 4, and chd.rtsare reproduced from thig reference as Figures D-3 and D-4. Keenanand Neumann, -Ref-arance 5, show that there is no significant effectof compressibility onfriction. factor for subsonic flows, so that thefriction factors of Moody may be applied hithout Mach Number correc-tion.The friction factors of Moody were determined in fully- developed ductflows and do not apply to flows in inlet lengtchs of ducting, within about30 to 50 diameters of the duct entrance. In this entrance lengtch, ye-lo'ity profiles are rot yet fully developed. Reference 7 shows that, for


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an inlet lekgE4h with a smooth .entranci; (e. g.., aI beilmouthy; the-fim~6is laina:until a lengsth- Rewr~lds-Number, Re f-0*i atie(Rex _g Vx/IL, x being the dista".ca from the .duct entrance). Thetheory of.Langhadr, Reference,6, has been shown'by Shapiro toj-pre-dict the coi rect value of, ftiktibn 1factor 1n this laminar region. Curvesprepaied from Langhaairzs theory, ;aken from-Referenqce7,. ak ro--produced asFimire D-5 At the duct length iorrespcnditg to -R e -6a, transitidr. to _t~rbulence,,occurs;, Reference 7 pr~zanted d~t4 forfriction factors in this turbulent region. thle curves of Figure.D-6represen~t, an averagre friction factor (calculated fiom. durv~s'fairedthrough this data) toahe aoplied in -this turbulent in'let iL'ength-. The,friction factor in the turbulei-r inlet region is shown-as 6 -ratio to thefriction factor for fullv-develoced~turbUlant flow at the same ductReynolds Number (Re =p V D/i.);. this- ratio is larger than unity,Therefore, loses arelarger in an inlet leghthan in a fu.lly-developedflow . If the duct 6rntrance is rnot smooth, or if there is a screen in theentrance, Shapiro has, showvn that there 'is no laminai inlet length, butthat the entire inlet flow length is tuibulant. Th~us, for such antranceconditiJons, the tur~bulert inlet friction factors -of.Figur e-D-6-should -beapplied to the entire -inle& ength.Calculation procedures have been devised *~hich take into accountthese special cases of inlet flow lengths and determine the appropriatefriction factors according to the above considerations. These arE,presented as procedures P-9 and P-10. Inspeption of these procedures

t will show that they are complex and lengthy. For this reason, a simplerapproximate proc.edure for inlet length calculations has bearn prepared,procedure P-3. This approximate procedure employs the fuilly-dav-ooedflow friction factors of Moody, a d w i ir . Ilosses. It has been recommended for use in the duct~"alcullation rnet.hod,


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however, be-cause the imrboved- accuracy of-the-more riirplex methopdsis not gikeially wairanted for duct sysiefn cdleulations, -because of 'the uncerta i-ties ir. the loss caulai'oiis 'bf'.ther duct system -'comnpon-.ents. if, however, a-,duct system' consists pfimaigy of'-straigrt runsof ducring, or if the designer jud, ,.s the iithioved accurapy desirable,the,more accurate-pr6c~dur s- P,9 -and P-1O can beuse&~Telsssb belmot etances inc r~ordted' in these procedureshave been esrima ted from the-dati of Henry, Reference, I The lossesf6r sharp- qdged inlets, ai-d-.for -inlets with screens and-gratings, ha.vebeer. computed by,-a mnethod similar to' rhzi.t de,scribed in ~the- section on1abrupt area decre6as6. irncorporating 51a!xtrapola'tion of tb~e data forc~ntr action'to~fficients, Reference 12

3.2 Area Change3.2. 1 Abrupt.Aiea Inc-reas -

A-calculation method for predidtion-of-Iosses in. subsoniic flows throughan abrupt area increase (,,sudden expansior-"1) has been develope~d byHall and:Orme, Reference 9. These authors,.hayie verified their cal-culations by experiment over a range of area ratios from 4 to 30, atentering Mach Numbers from 0. 25 to 1.0. Cole and Mills, Reference10, have confirmed the method by e-xi-eriment in the area ratio raigeculation of total pressure losses and Mach. Numbe-r change, and resultsare plotted i-. the design. charts of Figure D-9.


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* -21-

Theexperirhental'data,-of,"Hall arxl Qrme indicate tharth1~total pressureloss -andMachi N14nber dhanpg Pake place. in a. mixing length of .1 diame-rers downsream-of the-sudden-Area c1hango. In the calculation-proced-ure, tie. otal pressure ross attributed to thd-akea7 change- is- hereforew~t onld ~eoso imtr f0onte -indi n hcalculation of losses in other dutting compnents in vihich -the loss,I attributable to. a eparation and subsequent ~mixing- of the flow (e. gsudden cotrin, screens, shdr tr-ed~red entrances, etc.) the- tollpr-essure loss and Mach 'Number chan're.zttributed to that dompononthave likewise been taken to include 4 downstream duct diam~ters, on'the basis -of the experiimenta.- evidence of H1a'l .Jhd Q ine .(ind ot!-ers,e-g., Reference 13),, unlass some'data to the contrary has been aVail-able for, that component

3.2.2 .Abrupt-Area,Decrease,Apparently, the, problem of compressible flow through butae*deicreases has n6t been previo6usly considered, in the openi literature.An analysis has therefore been developed according to the model forincompressible- fl6w suggested in Reference -11.

Sketcih I /'


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*A s shown in. Sketchi1, the-flow -isaissumed -to sgepar 'e,*frm thesharp0-'cor ter,of t1, tea achange to prqduqe a frie streamiline fow,contracting-zto the streatube area, A. IturVbulent mixing then6CCUErS between sectionis-2h alnd'until the.fiow fills the area-A2,at essentially constant veloity adrossrEh6-duct dibssetidn. Theflow from .9ecton-2"1t iois-treatedas an.abiupr Area Eicrease, asdedi iiSection 3.2. 1. The area Am1rtfstbe related to the~khowhn ekeasi A1 and A2 by experimenft, since there' is -no analytical mntjifo&fpq prediction. Values-of area tatio A,"/4- 'have been,

t~knfrme dta-ortlatonsof 'Referenice. 12,-w1~cbLgiies thearea ta l A"/A ~a funltkii-of A,/A,, and -inlet Mach Nubr IThe resultsitof this analysis are presented in F-iguie D-10 whichshows exit M~ach -Number and total pressure ratio as , a function ofarea ratio-and ilet Mach Number., Total pressUre lo~,s and MachNUMbdr, changeinic ludei .4diameters of d-wnstream. ducting. Altughpressure losses are-small, note -that moderate area chlanges producelargd-increases in .Mach -Number, -so that only, small-dea decreases Ian be afforded- in high speed flows.3.2. 3 DiffusersAlthough a large amount of literature describing diffuser investiga-tions is available-, cor-relations of these data have as -yet -producedno system s for diffuser design or loss calculation that are entirelysatisfactory. Available correlations of per-formance have beenformulated on the basis of diffuser geomptry alone. Various inves-tigations have shown, however, that there can be-substantial effectsof Reynolds Number, inlet boundary layier thickness (I. e., Inletvelocity profile), compressibility, and discharge duct geometry.


31/153

'HoWever, there Is not- sufficient data yet available- to: ihtide sucheffectJn a ~generaizcorrelation, so -that W e must, Je1 o'correlations*of ,peifpirmance. with geometry alone. -Such,correlations exhibit con-

siderdble,scatter of the data, because-of the-influenice of the effect~snoted, above, and so.ate subject to some uncertainty in-,calculation.The most comnplete correlation-available in-the-opefiliterature is-that.of -Patterson, Reference 13. The design curves, of desig chart- D-11of this, report, taken from the correlAtionis.of Patterson, are recom-mtended for determination of inopesbeflow losses -Inconicaldiffusers.Various schemes-have been proposed for correlating rectangulardiffusers with conical;, the method recom~mended here is to assumie,the loss Ida -diffuser of redtang lar cros-section to be that of ani-equivalent conical-diffu'ser circumscribed about-the rectangular dif-;fuiser,, as in the following sketch.

RECTANGULAR

70nc

~. CIRCUMSCRIBEDCONICAL DIFFUSER


32/153

-~~~ -~- - -------

9ih spe lgefcso ifsrprfdrmaice-ax~e shown by Little,aihd- Wilbur, RAeference. 15i ah'd -by Young and Green; 1Aeference 14,Afor severLal coifical and rectangu@lar difhusers. 'Cbrrelations frofite'tdata of thnese investigatqrs-have-beeni Ysade, -andare shown on

design- cart D-41 for -use as correction factrs to the_ incomnpres-'Sibie loss coe6fficients. Thbesg correladlOn cuives-are based on data.from,-nygfwdfue geometries, and should -beboi~idered- tobe subjectrto revision 'if rihort data.1,ecOiies avallablei the -future.The effects of increasing Mach Ntieh nj, qriac fa.dfuaw th a fixed Inlet,boundary,:layer coiidietion has:-be~n -shon in RWO-r-ence 15 to-.be smaller thai -the effect of ic~~ni~tbxtfhickness-at a- ixed Mach, Number. Such-result as these, indicate-tbattherie will be cohsiderable-uncertLainty i-iffurser. loss-calola- - -dions. The recommendarions -in he-curves of D- 11 s-imply repre;-sent-the best cor relations ;presehdlypossible from- existing -data su e.-Refierrin-fo the Mach Number correction curvesi note thar'th'--t6Etalpressure loss for conical diffusers begins to increase markedly a~ tentering Mvach Nlumbers-of 0. 4-to 0.5; choking occurs in the range of- -0. 6 to 0. 7. Although rectangular diffusers do nor show as marked an

__increase in loss with increasing Mach Number, the incompressible-losses are much larger than for conical diffusers; thus, the total lossalways is larger than for comparable conical. diffusers.The following remarks will serve as a guide to the designer:1. An angle between diverging walls of about 60 - 100 gives be-stdiffuser performance.

* 2. For a given area chanige par unit lengith of duct, diffuwuigi ofcircular cross- section give the best effectiveness, with square dxo~s-sections next.


33/153

3. 'The -inlet-v*locift distributtion -hasbcen showm Eo-affect-diffaiserPerfbrmanc6 (ep.g.-.1Referxentt IS-. A V~ocity disbriwonwith~atihn 5oundar y lay-. At-diffuser entrance gives better (fiftiuser Performance. tan a thick-erv-budayayl with losses differing.by-as much as 200% bebween the two T ae.Atog itecnbdone-inra duct"ing systemi w control bdu.ndar y layer Eicees, this

-&ffeci 1-ndidates that-beiter- dif iier-peiformnince -can be-expected'for a diffuser relatively near the duct systemp inlet: -(less-than.30diameters5):than-would be expected after suffiin ln t iflly-developed flow tobe-establisW:d and that a diffuser-followinga bend.,or _sorh6,e sii'nflr componenjt Which ndy gereatea thick or-separated'boundary layer, -wfiiihave relaitively poorer performance.4. COmpi~ptepresgur6 recovery is nor riealized artde exirvof thediffluser;-


34/153

-26-

Thesie posslblities have noc bumn cou~dered in dsSdvnen44-fiiVe da ignr',VeS can-be &A-' db*a zr the -finpr4 design unas: ice-sddr f'roM testing wo demrminv einvirically an opdnilmzr conj&guitLe.S. Wjiei spe b1mkrariors uciuci retqile a diftv-s-er with large wanlan3 e, ivis often ir~dte cdesiraIbie to mpldoy an efficien -diffuser (Wal [

2e, of about 1 0 rfollwaad-byan abrup: area Increase wo &ade ted-area.

3.2.4 Convergizg' -act:~z'Losses in converging ducting are small compared to those in-ivergikNg

du~d~ (dffuers)-becaizse 60 e a-Celeratingflawia covergig-,duarOresenzs-a fvor-able pres-sure-gradienr for the wall h~rtdary la-yer.For small c4one an-gles: (i. e., jess tm a 300 icluded-artLe) there are

g~nr~lyitin-iaixngosss.there is~!ire infrination;avall=ble-in the lierature on Ach Nu-iber effects 1.3 converging-7sec-tions awith d=miisream uctig; m~ost availa2ble da a deals -witEh no&Ilesexhausting to a large chamber &r aunosphere. Therefore,- iE-is, recoin-men ded -thaE o=vefgiqg du c ting witin included co ue -angie-s-tnaller than360 be treated as Straight 4ucring, wizh L/D couted on the smallerdiam~eter of the converging section. iFor fncluled angles greater than300,ir is recommended that the procedurq for abrupE area decreasebe applied to coniVerging sections.

-. 33 BendsLoss data for bends are shown in design chart D:12k in the form of aIlow speed (incompressible) flow loss coefficient, and a Macn Nuinbe:


35/153

-- 27-

=.e.2dou

e-,-ev,--Lfc=

&Z- ha -aa l.aFZ. in- rn-

coS p ress.I-l sfMach &%.arv--sfrwix0.tl.. d z -sm as.~e P--., g a-cf fii Dr aenduhx vns is a as &-m. f Ffresi a 0-


36/153

ska7 !d zrgre rxaEzscLa bzetloss caafficiem-S ar=e jxossibme byare irgil~s~ ~e -wieReereoa. for sig-gi infoaiatidon),

2np ier4y rettdZ6 C=Sivr~be ssA,;L-,dmRa) in 4esigmi wdbnic-ze.v!zs dtop: er, ee-,-: 1=tra~se A less

is zpX cady'of~b sa o:-z2: as for,

- -orb~ds *!a tfi.A 0 rrs( e- , -vas v~bich are-pc f airfdlfrcDo Sneze.. Reee~e 1, b in conk=z-

cmerrecd-rarwes fix kzads wazfmm ,-a naSPT-.&,s prcare,.~~fi

i=2ds yc= gC-c-ne of;-,r w-.':e , z!eso

'Xer '900bzfbvais is Eta

cID a b azd ba siipai_2s the

-- _ Rc.- :-.. ;l


37/153

-29-

there is an isentropi cre flwihc ~Mach.Number is uhaffectedby losses in total pressure. bf ihis ex~it planeL, lOSSes%-are concentrated~:inthe_-Io,--energy flud-in a EhickenedbouiidaryIayer near the beftd Waflls.This totil pressure lossdoes nct a-ffect-tLhe-I-ach Number in die coreflxun:til a diswance of about A- iameters-dovvastr.eam, wvhen mixkinE ofz-he-coxe fivv, annd.-h& Ixwzn~ary-layer flowi has bz-.-n comaleted- fro-onrji, pears tha i on- rnusi chioose a one-dimensional Mach Number

to charactetizemiiie flov,In ffie exit-piane off the bend (as is niecessarvfor de-calculadoion procecoire) the proper thoice i ;-r assume-the-Maech~pane wl eidxit plane. Foqr di-amcezers downstream of the bend exit, after mving ;has occurreo,theffect of-the mctal pressurelosses fi theb bend YIff be felt all across theduct 2id-zhe ote-dimensffozial -V--chNOumber- ".ll ave inpreased.

34Screetns am x -gThe sul~idi compiressible fio'x zhrcuja Ecwbd-wdire screens or gratings(screems off slmrgp-e ed elenmenzs of 2de geonietry) has been.consideredjby Cornell, !Wfere-~e1.COISIgvSls cfiensorshscreens and gr2EIng-s in 6:=-R=oS, bor varigus screea Slicires (ra.Eioof cT=. area in screen to &~mdczlaw area) and upsiream &uctFMadi Xwber. ThsDmie ~zadrclyfo ee~ce 2 and re

5oscef-iet f . ra apply zq screens at theP moudr 'oia sarp-e: .sed(i.e., - no) in:-eke damt~ Carn-lls cacua-nsjfor shaip-edged screens have beea eatended for screens a. dze inlet ofa sh~rp- edged enzrar-., bssed on an enr~apoiation of the- data for con-slcmin design chart D-S.


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} 4.0 CALCULATIONPROCEDURES JAND, EXMPLES4. 1 Interoretartofl of Proceduie Diagrams* Calculation procedures for all ductipg-pomponenws are describedgraphically i1n tiezdiagramns P-I to-P-JO.. These diagrams Are to]

* be interpreted accordingEo-the followi~ng exramples, taken fromt procedure P-2. 1.I.~ ~ ~ ~maiiecruscL Nbe -.vn.as initial -dati or the calu

lation are shown in circles , e.g. -(42. Quantities wvhich ate detex-misied by the calculation are shown

in boxes, e.g.

3. Directicos-for calculation are shown on lin !sconnecting ele-mets; e.g., dle s-'~ezece

-- indicates thar the dizn&arum e -2 is tobe eatredand Re is to be read from rte diart. The sequeuice

Lcaic. ALJC4 JLI- - - - 1


39/153


40/153

r -32-_4.3 Closely-Coupled COMPOnentEs

f - ~Area canges. ben&, and screens are assumed-rto~beflo byedfam erert of straight duct 'MWhich the flow-mi~xes and srabAlizes.When two coMPOI~t-IL-1 are nrz.&sebarated-by 4 duct-diameters, the-cal-

- cW6oA-procediire is imodifiedas feollows:L. 'Thw pressureIss of the first-comnijenz is detrmined-in the

Usual mananer.-2. Thbe prtssurelc.rss of the 6ecomd compoWDen L5 determ~ined byJ

a; sumfingde same-entry Nach Numier as-employed-for thefirt ojen..Tie-pressuie loss for f-,e combined compoa-

ens Is_ thea

ipo~J - Ldn LPod 03. Te exit Mach M-1 nl-'-r for iha com.inet-com wnez s is dee-mined by calculating mue n-sass flow uirMeer at te exitc of &a

seconid compoir,-4

Exit Mach N mber is derermined; directly fom this value of mss* ~~flox parameter through char: 10-1a.Thsroereiilurae

*in Section 5for a screen follwed by abenid.


41/153

I S-33-

-PROCEDURE P-i -* " MACH NUMBER CALCOLA-!ON1"

Total pressure -kIm,

.- Static pressure inmm

- I

II" 9'

...............


42/153

af.1

- - am4

- " - -PROCEURIR -ihJAdH MMBERk CALCULATION

Total pressure kndwn DZ&

Static pressure knw

mass Flax i =12.8-1b/seeTotal Temperature T =540DUcr Diametr D = ft

STotal Pressure P = 1-4. psiStatic PI-essure p=1.2 psi I, .. _"


43/153

- ~~P.tOCIXJRE P-2.1Ia--- STRIGI IT Wc-T K-TAK17.)

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45/153

.2 V - ?JOEWRE P-2- ISTKM)Glfr w~cY (r-MCEk

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- - - --~ ____________________-~.--~-- - - -U -

at at

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00 7

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3--XXC7

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0

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61~~

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FPCERE P--. 1

PROCEDI E P-4.2ABRUPT A..EA INCREASE (EXHAUST)


60/153

-44-

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ABRUPT ?'-.EA INCr%.EASC- (EXHAUST1)


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I ... _:'T AREA DECREASE (EXI : 'AUST)


62/153

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PROCEDU/RE P-5.!2

ABRUPT AREA DECREASE (EXIIAUST)

N|


63/153

IC SI r - a

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AllY7o-


64/153

*0-EUR P-.

40 DIRSERS(MTAM

pAz.,A , -. M

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-46-

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CALII

001~35 4. 0.986y

CAL.C


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A.#.

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69/153

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70/153

- - -- - - -"43

amp..a&0804

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CALC- ________A_


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61I -

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---------

CALC-

0.334


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PROCEWRE P-7O. ISENDSJ (INTAK~E)

CALC

0,337 0.403


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(b o cf K.ASSUME J o:,

CO,2~ ~P.7 M 00 _

CHOOSC NCW' VALUE 0" M,Ao REPEAV'y


76/153

PROCEDULRE P-7.'2BENIN (EXi [AU-SI

CAL..CA-- -

-/0w _ 7,- rL


77/153

F 0

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I'K IU 1--7. 2REMM; (IUXOAJSr1)

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5W.REEM -.AD GRATIXG (IXTAIjE

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0.07I Ci

0.07.90.1-ASSUME 0.40(f) 035

CALC

0.639


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hC44LC 0.266830

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CAL.C----. -it .3oo


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PROXWEIURE P-9. 1IX=C fl4JF-**. ALTERNATEi &ROCEWREFOR 50 -L KXU1L I. P.A.NCH.

R0 -*

R*U0 5 xrRe CAC /51

R, CAA.C 30iR fJ2

7oC7

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ENE P-. oI20-. 7p w


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PROCIME P-9. IFUCT INLW I S. AL~rcRNATrL: PRocEi)LJRE,FOR RELLMOU'll IENTRANCis.

*L

5*.5.

6CAA .V

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RE.

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ri PROC:EI)(IRLiiucr INLFOR BELLNI(

Re), 0.03=4f51

C44C O 7-D Arfj

Re 0, CA Re

L Re oo ffRe ~ ~


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P-9. 2. 1cr INL '4' ALrL.-RN\ATE PROCE~DUREBELLMTI(' I L-*\ IRANCE,

f~rRP-2.i on P -Z.2AT P0/NTr

PROCED)URE P-9. 2.2VJICT INLETS. ALTERNATE PROCEDUREFOR BELLNIOLJTII ENTRANCE,

x tr L 3< D

CAL.C C+ 4f-

EN7ffiR P-2.1 qP-2.2 ,17r 1~


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FO R BELLMI

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IRRO


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P-9.2.1jIJUCr NLKI'F. ALTEMATxr PROCEWVREOR BLELLM(U1 I EN IRANCE,

I) I

PROCEIXJRE P-9.2,2DUICr INLET. , $ALTERNA^&EPROCEDUREFOR BI3LLUI ENTRANCI9.Xtr < -L < 3D-

CAL.CCALC 0.0178

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PROCKA Ul!RE P- t)FOR Si IARIl- EDIGEDl ENTRANCE~

CA CA .7

1240


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99/153

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-67-REYNOLDS NUMBER, Re -

R . FIGURE D-27 __ _ _ _ _ __ _ _ _ _ _/0 "4I. .f__ _ _ _ -- - ,-:.ii'' -- , ~ ~~.- , !.. .I I , i l _ .: :.

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I

UV

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-94-

5. 0 AMLUC TI M OF CALULATM PFROCED ES TO ADUCT SYSTEM"The azm re- syot a Flare I u cosen to Illustrate theapplicaon c de caculadc. proceuhzes an d to provide ar examplecomperlam of pres e an d po er lo-ses fm diferesm dnca diame-mrs. Tw results c de cal=Iatioas ir three different duct diame-ters of : "I a sysam are zabgalted in Table 5- L. The presv-%elosses and power looes are pkmeii in fV. re 2. Ne tbe severeIncrease in aculed loses as the duct djamer decreases.The xe los pealry asociaed izh the duca pressure losses hasbeen calculated from a linearized analysis described in Secdon 5.2.The pressurc losses are so iarge: howeverd,hat e linearzedanalysis should be regarded as giving only appromimaze esfimaesof the power pecalties.


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CA- A _W MS -AMFW

FOR VAW wEIr M3IhaEM3iTAjM VDT fw1* Uw t"W at 15 lbft)

V= ~amwm a&) 18 12 9ptreLe LW) 0a . CL.77 L165treft LAWpn5 L3 LS 1L41

UHKuSr WCT (uI& fOwum t 16 bjDo= D~mw-Tcm) 1I 12 1P-reav.r- Ls (J*f) 0.5 4.05 9-7-

42.0 233 -5-88


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TAM E 5-L Cm 4M 'WSE . -;..) E, -.. G MAC H -.WI FOR EACH S

*i 'ftKS -mrXJup= of4--.e CAD

3XTAKE Ii0m4c.102 I- U-230 i

SU~~~ 0.23,0.9a 0.0ses jo..,s +-"IO'jo9, 90e960 R.D-I.C 0.996 RDS--Ln dut -0- 62 0.996 LDz).4 _ .;2-0 L "a I@ e 90n60 102 0.999 t D-1-.33 0-.246 0.96 a c

. , , 0.246 0.9r '%a ~2eSu, t -0'- 2 -.0 L -Dz7.9TOTAL I AKE , 0.993 0.94

SYSTEM:

EXHA . TExit 0- -78 0-Straigt duct ", i,-7 0.991 L. D =23. 3 r,!33 0-935 L 1&-w, 9 .0.175 0.995 R-DO. 0.360 0.974 RE-Straigtc .uzz 0.174 0. 97 L D=12 040.067 L E

0180 0.173 0.998 R D=2,66 -- 90. ..93TOTAL EXHAUST 0,980 0..eT1

SYSM


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.i I-rER.. ,L.&O -MB l FOIE AO Srcmi NE%-T2- Ove 9p OI

)A Irnw --- w Mc Pe Se om"T

R D--0 0-.990 R. D-2-L.D-D ! 20 MM L 25a5 SMi, L0.4.67.,RD--3 C-2,,0.-9 o96 R0-,2.0 l 0.7to; 0-976 RD2-67

0,2.8 0. -,4. I 2- o. 9.3 A A;'. t 2e top 20z It *

L, ; 1; -..9- - -

.1 .e .

0.947 .700

0,4wo D 6ssL. =23.3 o-370 0.93?5 L D=V7.2.5 l0.490 0.810 L D=5!

R~)o 0.O .974 R D=0.750,7 0.965 R, D=1.0LD-3 .S47s 0.9W, LDz~2 0.42 093 iLD=28

R D=2.t .5 0.99 3 R/D4.0 0.425 0.991 R 0=5.33. ' I

.; i . iI-I II... ;.i 0 N30

@j


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mamm 15 %/iSacTmeamrae - 4gPressure ptl - 14.7 P31aDwa diamcw: D a 0 ft,

A w-.rjD/47-C. 442 ft2bMcb aMiber P- ia

II

BeIIimouth &inrance; P-3 14TL D) 1.47

P./PO* 1. 424 T l ,ADui 0. 034TL ma/Dy2 1.47 -0.03 =1.44

M2-0.465Po/.* = 1. 4i

P02/'PoIleLt. 0.993


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Bwd..%&S ge.; P-7. I .0. use of,sa emoc. Mach~ Mimbg fo loe

i5

. 75 Re .1 x

2.00M 0.460

.KI 8 P0190 2

01 -

p0 1 ~0. 9875PO benci


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-92-

-- --- = 2.67D 0.75M3 =G.7Re a2.1 x to ,CPO 0 .074; 18w1. 29 (Oeptobably rchokes) K# W1.0K1, 4 =0.0237

PoLi 040. 976[m m" 0.40, fi0=0.501.-Po 2 A P0 4 A

M4 =0.75

Diffuser ; P-6.1 ()_ _ _ _ _-_ _. . ... .. I H

4.5tan e 7)(2" 0.0972, e 55 2e.


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SA5 D5 182A4 ,2 92

2e- il.I 04 =0. 75

CP O 0. 112 D C O o 2 4KDw 2. 0 (No. no da may choke) C 0.224------ =0.061Po

o5 0.939M 4 =0. 5

m- = 0.501Po 4 A4

ro-n p04 A4 .0.0104 4 Po5 A (0-. 939) (4. 0)

M 5 -0.121

i. ill~lii i i i i i i5


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L : .,-,.1:. P rese Ritio AJ Ina, ML /tR1(0(Q. 20) (0. 6 (0 . 939) 0. 70

Exhaus Dut

m - 16 lb/sec

P5 = 14.7 psiaD = 9in.A = 0. 442 ft2

Mach Number ; P- I b

p- ) 0. 662

M. 0.6883Straight Duct ; P-2.2

L =38.25

D 0.75 Re 15. x-O=500 O


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4~~t !, L 425

K 1-63i LCPO =0-C7 46

.0- CLO;I- 99eol

MTc -"1A

M.2 0.3

PNcssare iRario c :Ez.:Zz

C.~~( ~C\( 9 1 ~ .2


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Thc~~~a2G 4eas2fti :6) 1

24- C


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S *

x %-

QLa \oi

Pn k /1Ii - ,

Assume :rt ie -* Izes choked(1) InCrease in turbine exhaus- pressure,P4

w Lwx T I k 1 ( p4 1 I;kBP4 TOm )3 P 3


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Airiply by P4awx ( k-I/k8!' a ri-r.Cp- -o3\p3P4

Lex r~= ~ -4 design pressure ratioo P4 olUinea rizing

a( \ k-I Ik-l/k&a Ik+jjj 1C -7 To3 IjA)

"I p

!!ma T Pi

(2) Decrease .in conpressor inlet pressure, p01:Assume compressor pressure ratio does not change

SP4 P4Po3 Po2 Pot; p0 3

ma)1T po3 rpJlPo

x 1 mf C k-I 4 4nT+ + rJ o3 k r r P'l 2Matil Pyo0l'

011

M


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- -01--

L1nearizing,

Al? w + l.. h \1/ p=,i+ -1 1 ,C T V 0POi x + i+ p o3I -/ )a /

Numeri"zl Example

Turbine conditions: Fuel-Air RatiG - 3. 014 lb fuel/lb airEfficiency - 0.70SHP - 1100 If Turbine Inlet Temperature - 2060RDesign Pressure Ratio - 6.5

Assume C =0.24, k= 1.4k-1

(104 28678( X01)0 . 70) (0. 21) (0. 286) (2060)(. _) 77

= 83. 1 I-P/lb/secInlet;

-) &C1f a CTm = 15 lb/secC = 83.1 'PTh soc


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P"'0"10, 3'aum 14a7t.- _P0/ . ... .eEM 14.7 =~

A ll -(IS) (83.3) (0 . 3) - 375 ItExhaust:

S=_m a C p

ma 16 lb/secCT 83. 1 IP/lb/secM4 - 0.425

P 0.883; P 4 = 23.4 psi

I P4 - Pctm 21.2 - 14.7 OPatm 14.7 0.442

A =* - (6)(83.3)(0.405) -588 If


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NOMENCLAWEREFC Po Total pressure loss coefficientA Crossametoauct, ft

DEquvalet diaeterof nion-circular cross-section duct,4 x wetted perimeter

KB Pressure coefficient compressibility factor for bendsKD Pressure coefficient compressibility factor for diffusersK Bend angle loss factorL Duct length, ftLmax Duct length to attain m =1i.0o, in a constant area duct, ftM Mach NumberR Gas constant, lb force - ft/lb mass,R.-Re Duct Reynolds Number, pV D/jjRe Inlet length Reynolds Number, pVx/.LxT Temperature, 0 R

*V Velocity, ft/sec

c Local velocit:, SC L::,, ft/secFriction factor. ACi ..veloped fno


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NOMENCLATURE, (Cont' d)f Friction factor, Ink: laminar lengthf Friction factor, inlet turbulent lengthgo ~constant = 32.2 lb imn:-ss-fr/lb force-sec 2 j

k Ratio of specific heatsm Mass flow rare, lb mass/secp Pressure, psfs Screen-olidity = open area in screen/ducE area

x Distance from duct entrance, ft

Greek,

E Duct wall roughness, ft29e Angle between diffusei walls, degrees

,V'iscosity, lb mass/sec-frp Density, lb mass/fr* Angle of duct band, degrees

Superscripts

*State at M 1,O0


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-, NOMENCLATURE (Concl, d)Subscripts

0 Stagnation or total state; condition of fluid brought torest isentropically

SfI2, State upstream of component2. Stare downstr earn of componenttr Transition point from laminar to turbulent flow21 State, four diameters downstream of state I

I


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Special Nomenclature for T1urbine PerormanceClculadon

C specific heat, Btu.Rk-ICT turine power constant +- qr CT I -To

iF net power delivered by turbine unit, horsepowerW x net shaft work, ft. lbs/lb. of airIn mass flow rate of fuel, lbs/secma mass fLow rate of air, lbs/secrp /"design pressure ratio?12 compressor efficiency71T turbine efficiency

I 0.

Ia.i


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-1I07-

0IBL 1OGRAPHY

1 Design Data Sheet, Dopartnent of the Navy, Bureau of Ships,DDS 3801-2, 22 July 195(1.

2. Shapiro, A. H. The _Dynamics' and Thermodynamics of Corn-pressible Fiuld Flow. V(-. 1, Ronald Press, New' York, 1953.

3. Keenan, J.H., and Kaye, 3. Gas Tables, John Wiley ard Sons, . iNew York, 1948Note: Compressible Flow Tables are also available in:Shapiro, A. H., Hawhoriie, W. R., and Edelman, G. M. TheMechanics and Thermodvl,:"mics of Steady One-DimensionalGas Flow with Table. r, ,merical Solutions, Meteor Rep-ortNo. 14, Massachuse :cute of Technology-Ga' dissilpsProgram, Cambric. , - , 1947; an dShapiro, A. H., H8:4, \V . R., and Edelman, G. M. TheMechanics and Ther.. , nics of Steady One-DimensionalGas Flow, in Handbook of Supersonic Aerodynamics, INAVORD.Report 1488, Vol. I.

4. Moody, L. F. Friction Factors for Pipe Flow, Transactions ofthe A. S.M. E., November 1944.

5. Keenan and Neumann, Measurements of Friction in a Pipe forSubsonic and Supersonic Flow of Air, Jour. Appl. Mech., Vol. 13No. 2(1946), pA-9i.Best Available Copy


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Mispaphy f~ad}

6. LA z, H L.- Smndy Vi, b do TrM b J h ca

7. ..iza,-IL and Sm a.IL..Im is dieWKm of Swaioh 76=d I'M". ACA T 1M115, No-

-a-r 19aS. Hmry. J.I. esp at m Pm ndoes Pressure-

Lons Cracorisucs at Icz QC.omim a N C& WR L-20S,1944.

9. Hall. W. .. andOrme, &_.. Plowmoa Cwpressible hddlthxu&g a Suddwu Enlargemem In a Pipe. Pr 2Lngo hIwze of Mechanical EM;!ns,Vol. 169, No. 49 , 1955.

10. Cole B.N. and Mills, B. Thmry of Sudden EnlargementsApplied to the Pope ExtAast-valve. with Special Referenceto Exhatc-pulse Scavreqgira Proceedings of the Institute of

4edinicha Engineers. Vol. 1IL P 364.11. Hunsaxer, J. (.. nd Rightmire, B.G. Engineering Applications

of Fluid Mechanics, McCtaw-Hill, 1947.12. Cornell, W. G. Losses in Flow Normal to Plane Screens,

Transactions of the A. S. M. E., May, 1958.13 . Patterson, G.N. Modern Diffuser Design, Aircraft Engineering,

September, 1938.


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J

t t14.I Ymo&~ DL, mdGreen G. L Tomsotft Sp10 FlowIn dfus of Recanpula: Croas-scdou, R&M No. 2201,BridA A. LC, July 1944.

15. Uzze., B H.. Jr.. and Wilbur, S.W. ftrkirma andBoudary Layer Data from 12P ad 23 C Diffusers ofArea Rado 2.0 at Mach -numbers up to Coki and ReynoldsKumbes up to 7.5 x 1 6, NACA Report 1201, 1954.

16 . Young A.D., Grew. G.L. and Owen. P.R. Tests of High-Speed Flow in Right-angled Pipe Bends of Rectangular Cross-Sectice R&M No. 2066. British A. R.C., October, 1943.

17. Higginbotham. J. T.. Wood, C. C., and Valentine, E. F. AStudy of the High-Speed Performance Characteristics of 900Bends In Circular Ducts, NACA TN'3696, June. 1956.

18. Friedman, D., and Wescphal, W. R., Experimental Investi-- . gation of a 90 0 Cascade Diffusing Bend with an Area Ratio of

1. 45: 1 and with Several Inet Boundary Layers, NACA TN 2668,i April, 1952.

19. Grey, R. E., Jr., and Wilsted, H. D., Performance of ConicalJet Nozzles in Terms of Flow and Velocity Coefficients, NACATN 1757, November. i948.

. 20. von Karman, T., Compressibility Effects in Aerodynamics,Journal of the Aeronautic .. Sciences, July, 1941.

I


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1. l-

DYN ATC HCororalA

Pressure Loss Calculation Procedures for High Speed Gas Flow

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Transcript of Pressure Loss Calculation Procedures for High Speed Gas Flow