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CLEARINGHOUSE

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Re:No-~ 26.P~SSC SS C-,CojU-K

x-;a R OC H -%IEE GAS LOW

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U. S. NAVYBureau Pcf 4

Was irigto 25, D. C.

June 297, 1961

DYNATECH CORPORA.TION639 Massaichusetts Ave-.,ue

CaImbridge 39, Massachusetts

SURI

T A B I E O U NTNE Y T S

LIST O- PROCEXJRES ii

LIST OF ES=G 0 t AIS V

PREFACE I

1. 0 INTROLUCTIMM 3

2.0 INTRODUCTION TO PARAMTE1I7E AND GENERAL 5METHOD OF COMPRESSIBLE FLOW

2. 1 Mach Number 5

2.2 Total Pressure and Loss Coefficients 6

2.3 Total Temperature 9

2.4 Mass Flew Parameter and the Con, nujy 10Relation

2.5 Choking in Compiessible Flow

2.6 "Gas Properties 17

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

3. 1 Straight Constant Area Ducts 18

3.2 Area Change 20

3.2. 1 Abrupt Area Increase 20

3.2.2 Abrupt Azea Decrease 21

3.2.3 Diffusers 22

3. 2.4 Converging Duct (Nozzle) 26

3.3 Bends 26

3.4 Screens and Gratings 29

TABLE OF CONTENTS (.onr t d)

4.0 CALCULATION PROCEDURES AND EXAM-PLES 30

4. 1 interpretation of Procedure Diagranb 30

4.2 E.amples ... - ._ 314.3 Closely Coupled Comjonents 32-

P PROCEDXURES 33.

D DES!GN CHAPRS 65

5.0 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 99

NOMZN CLATJ RE 103

BIBLIOGRAPHY 107

LIST OF PROCEiDRES

P- I Mach Number 33

P-2 Srraight Duct

2.1 Intake Duct 35j 2.2 Exhaust Duct 37

P-3 Duct Inlets, SimplifieL Pruedure

3.1 Inlet Length with Beilmouth Entrance 393.2 Inlet Length witr Shnr 2-Edged Entrance, with 41

or without screeis at entrance

P-4 Abrupt Area Increase

C4..1 Intake Duct 434..2 Exhaust Duc- 43

F-5 Abrupt Area Decrease

5.1 Intake Duct 455.2 Exhaust Duct 45

P-6 Diffusers

6.1 Intake Duct 476.2 Exhaust Duct 49

P-7 Bends

7.1 Intake Duct 517.2 Exhaust Duct 53

LIST OF PROCEDURES (cont' d)

Page

P-8 Screens and Gratings

S. I Intake Duct 55

*' 8.2 E ust Dat 55

* P- 9 Duct Inlets, Alternate Procedure for Bellmouth Entrance

9.1 L/D > 30 57

9. 2 L/D < 30, rest for procedure 59x

9.2.1 L/D < 61:x 9. . tr L

9.2.2 < - < 30 61

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

I(

V

LLST OF DISTGN CHARTS

D-I Mass Flow Parameter

(a) Compu:ed from total pressure 65

Ca) Computed'from static pressure 66

D-2 Reynolds Nurrber, Re 67

D-3 Relative Roughness, "D 68

D-4 Friction Factor, 4 T (fully developed) 69

D-5 Laminar Inlet Length Loss Coefficient, 4 - 70

D-6 Turbulent Inlet Length Friction Facto~r, 2 71T

D-7 4T Lmax and 0 72

D-8 Sharp-edged ilets 7.3

D-9 Abrupt area increase 74

D-10 Abrupt area decrease 75

D-11 Diffuser Loss Coefficients 76

D-12 (a), (b) Circular Cross-section Bends, Loss Coefficients 77

(c), (d) Square Cross-section Bends, Loss Coefficients 78 j-13 (a) Round Wire Screens 79

(b) Sharp-edged Gratings 00

I °vi

LIST OF DESIGN CHARTS (cont' d)

Page

D- 14 Loss Coefficient, C vs I - - 81

D-15 Bend Algle Loss Factor 83

I

7!

I

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 e i g n D a t S h e r I ~ : 8 O l 2 , x ~ r f o r c a l c u l t o n -6 f , p r e s -sur losesathig ga veodIe in gas turbe ducdn~rg. M&i purpose.

is'" n corpJeO 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 t oi frmas-contained"set of procOdues-an data-necess-ay -~he clcaioo

4ig-ipeeo;duct;,g .-losses§,- and'O contain_ -thi nece saryelemenvs fora inlaraShee6t

As -we ialle thjnatejil -ecesarj=for the -required pFoceduialanddat serio s, w~-eaizedtha Tis- repoit* w ud be of, miore; value

t6:hoe ho areu Itlnae.- ep l f& pieprartIoA and the~ pei--OdIO irevision;-anfd;jr _0- nb-thd e DataShetsandphas

*a4Ot-t P i q)ior~edols, were -b

'1,A brifitioduct~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 t flws.- We-hope that the short intrdco -included

asScin 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, and

Sin appreciating SQme of the rpasbnis for thetr con p,,.4Kty Wiaacompared to Incompressible methods.

- Z-

in--te-preparatioz. ofri des-Ignh2rs Ou~d ptohr baCr

survey of die-data- avAiblhe iiiteltrar ncnnrsii(igh speed) ef - tsdn -ductAfiows shqrwLed tOlar the-reA ae-mny

are~as Where data io incomple-re or ibcondtklsive, afid-in, facE.somiezfiies confictinfg. Th.is is 0.1so true to a lesser extent of

the afailAble damta ~incompressible &jct flowYs rwm various

sources.; 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. .te

analysis f6r 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_;,,.c deisio,- -and judgemenis that wudconfront him, if he, were wbrking

felt 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 speed

duct flow data will be available in the literature. These notes on methods

and'sources we have included as Section 3 of the report.j

James R. Turner*Project Manager

Approved by: _________

L.C. HoagXhnd

1-0 ."ThOWalO

for low spm sl o now*, at uL of9 1:/sc and ess- ForrMhs l es, Aan, press=&: a ses =y be esumaz wirh

ne&g4ie by 1 enpi ;b ~prim tl t e gas Is ;M ii'-couiressft!-izd This zsiuex L-ies tI va-kmizns

are salM aod -a be goored in caeu mrhbo 1s. Pressre lcss

cllcw,~ umediods ft~ low sppwd-Gows b"s~ b 'accuV.-amible as-umatcm haie beau coIcted and ormallzed in l :esce I. -

If it is desrable w deslp Wlet sis exh~aut uc ug for~ highr flow

vIacIn, and thus ob=ln 6iczw of smaller diameter, the lossesmay o lc. -r be esdinmare bt,, z assums of ncompressible

flow. 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 given

configuration 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 therefore

requires two extensioni of low speed calculation procedares:

1. Fornularion of a calculation procedure which will Lake intoaccount the effects of compressibility on local values of flow

parameters (pressure, density, velocity, etc.)

2. Correlation of available dc.ita or. the , r~' &..;.: .

o r the prssu.re losses, or loss cefficiei::s which cha::.

the pressure .oss.es, in various duct components.he pessur ' "I

---- -- -.

I: - -

hU

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 for

computaticnal aid. Th e charts are-included in a separate sectdonof this riport and are arranged so thar rway may be extracted fro mthe report to form a self-contained calculation system similar in

form 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 calculation

pro&edures which can be applied to high speed flow calculations.

I

-5-

2.0 INTRODUCTTON TO PARPAMETERS AND GENERAL AMETHODSOF COMPRESSELE FLOW

Accountring for gas compressibility effects in the calculation of ducting

pressure losses, necessary for high speed duct flows, introduces

several new variables into the caiculations. Rather extensive changes

to incompressible flow methods and procedures mus: be made. The

purpose of this section is to provide a brief outline of parameters and

methods employed in this report which are peculiar to compressible

flow calculations. Those analytical relations developed which are

important to the calculation procedure have been reduced to chart

form in later sections.

2.1 Mach Number

The Mach Number is the basic measure of the relative importance

of compressibility effects. The Mach Number is the ratio of the fluidvelocity to the local speed of sound:

M =V- c

where

V = fluid velocity

c = local speed of sound = I RT

Only subsonic duct velocities (i. e., M < 1. 0) have been considered.

For Mach Number M <0. 2, compressibility effects are small, and

incompressible calculation methods can be applied with sufficientaccuracy.

9 -6-

Shapiro (Reference 2) and others have shown diat most compressible

flow cal-,lations are most easily carried out if rha C--calation meth-

ods are formulated in such a- way that Mach Number is the ind.pendent

variable of the calculation procedure. For many of rh- pressure-loss

calculations which follow, the Mach Number has herefoze been chosen

as the independent vaziable. Generally, losses in ducring components

which do not involve area change cause the Mach Number to increase.

Therefore, it is possible that in a. long 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 which

a gas stream would reach if it were decelerated to zero velocity

without incurring any losses in the deceleration. The total pressur -

is the pressure measured by a Pitot tube, or an "impact" probe. For

incompressible flow, the total pressure is the sum of the static pres-.... sure and the velocity head.

2gp + (2.1)PO P + 2 go

where

p0 = total pressure (impact brobe pressure)

p = static pressure (pressure at a wall pressure tap)

p = fluid density

= fluid velocizy

- ---

the, change-,In tOtal, pressure in a duct, flow is a measure of the losses',

ithe flow. The losses may be chdracreriz*d by, a dimensiopless ,!oss-:

woefficient, CPo-

op- (2 = ¢. 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. e. i high 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 in 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,

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 V 2 2(.6

so-that, Ti'rp01 -02C -. . 2 7 )

PO 1~. 21 11

Combined with Equation 2. 5 this becomes.

P02 ,

Ck (2.8)P" 1 C° -- k 14I2 k - 1 M2 k/ I K<'. 2

Thus, if the loss coefficient, CPo, and the inlet conditions, M and Po

.are known for a given ducting component, the exit total pressure for

that component can be determined from equation 2. 8; the exit Machnumber, M 2, is determined from continuity relations, as Will be shown

in Section 2.4. These exit conditions will, of course, .,6,, . l'..L

conditions for the following ducting component,

-9-

2.3 Total Temperature

"The total, or staiiation,, iemperatuie is similar to the total pressure" in cefinition. That isj 'i is the tempeiatWrq whicha gas stream Would

teach if it weredecelerated to zero vel6city. It is best expressediAre ns of the .ach Nurhber •

T~ _~ k-12 (29)-2

T'2

where

T = 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. Ifi a duct flow, the-total temperature can change

only rhroughheat transfer to or from the:gas-stream. Note, :however,

that the static temperature may vary considerably, as by acceleration

or decelerAtion of the gas stream, according to, Equation 2. 9.

If we assume that hear transfer to the surroundings is negligibly small

in a duct flow (i. e., the flow is adiabatic); the total temperature re-

mains constant, irrespective of the flow losses. The assumption ofadiabatic" flow has. been made in the calculation methods presented in

this report. Therefore, for a gas turbine intake ductflow, the total

tempera.ture is the temperature of the atmosphere (i. e., the tempera-

ture of the inlet air when It was at zero veloCity), and is constant

throughout the inlet ductin..g; for a gas turbine exhaust duct flow, the

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 duct As 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'preclude

any 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 will

change-ofilyby vi'ttue of nn aroa change. in, 4.6ornpressib1 e low,,

however, velocity Oha.ngces (and thus -clanges 'in; ;ach--Number')- .caiW

occur in a constant area dL~cr, becauise~ of changes in density resulting

from,.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, the

continuity 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

---- ------

-F(M ) Y ' ~ .2

Ths untonis~terei coal of- the, fu~cn~AA ~uae Table30-ofRefeience 3.

-For an,,adiabatic 'duct-flowy (T__ : onstant), th& c6htinutlfy-qution be-comhes, with ra

ThtUs,* for-'a given duct Component, With-fixedlarea, ratio, the exitMaC NU'ber, M, mfay be~foun'd if -inlex condition-s p 1 and are

kn'on; and hc.~ato 2-/po n iskon from loQsS~coffidient~data

(see Section. 2.2).

Equatioit2. '11 gives a. convenieift WYtd deter r-ie, the Mach Numnberfor a duct fl'ow when nmass flow, areda, total presadre, And- total tem-perature are known.

pA

is, denoted the 'mass flow paramneter!, for a given gas' this pa rqmeterdepends on the Mach Number only. A simila& parameter employingstatic pressUre,

pAcan also be determined as a function Qf Mach Number. These parail-

eters areplotted vs. Mach Number in a later sectiofi, to give a simple

computational aid in determnnng- Mach Nrniber when-other flow con.-

ditiojas ate~sp'cifted.

2. S Choking in Compressible Flow

the mnas- flow rate In a duct flow of 'compressible gas A liited ~

the, phenomehon of "chokinig". This 'may be exp1jined iby'the following

* considerations.

-~ Cosiera inpl .ucin copoen ~k~ hs~a bnfus area,

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

A IA2'T

0~A1andA 9, and--flbwat total t ,erip~rature T0 If we assudme thkathre

are-no, losses, p0 olrpo2 rPo' 'Let-us first hold the-ups5t ream total

pressure, 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 2 will increase as, static pressure, P2 is reduced.

The effect on mass flow rate is-determified through Equation 2. 11,

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

532 ( 2. 15)

b2- M

JJ

Sketch- I shows, the variation -oiF (M) with March Number. As-;IA is

ificiresed, F (M) icreases-r #i

I -

1-1- --

/I..yt-ch U, -0. 5k, for var ginas-~ lwit h M4.I cachnm, or- tat+ se Mac

timuc ead A * ) Thus, as tpes sure - - 12 2I s -,o to N~

Sketch I.

a nbximum., value at M =,l.01 and then decreases. Thus, for our ex-ample, as the pressure p2 is decreased, IM2 will increase :qnd he mass

flow rate will increase hntil a Mach "hNumber M2 -0 is reached, atwhic condition the flow- wi 4 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 MI2 =1. 0 to supersonic values in the min-

imum area A2.Thus, as the pressure p2 isS further reduced,, the

-.;" value-of M 2 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.

-14- -1J

--IVariation Offlow tet With &~wnistreain sra&c presr-u~e, a

c6n4tant Upstream to-aI p sure p r is shown byS ch 2.

- "S~ke~cl a7 "

NOte ,thu when the chokedflow coni M .O)-isatminei, te

!ilet-Mach Number, M, -also-hag a definite-vaiue-Which is fiNdby

te .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 Mach

Number, M1, which cannot be exceeded due-to the "choki .$" phenome-

non.

If We now assume that there is a total-pressure loss in the abovenozzle,I then Po 2 /PoI1 < 1.0, and the inlet Mach Number at the choked condition

is given by P

IF( ' P6 1 A1 F" F(t) -Po' A1 2.19 .

-- - .

- -,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~ l nec M ch) a~iber less-than-

4Mthok an nlr mN Ueslha ui' -with tfpe-

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

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

size ~~snr~rLi r -rd~zfor. a !gzs curbine . Thiefair j$ Eo-

be ran-fonatmspe~i~LIiions ot~~ -;.d- T ate-fixed;'-

S-erh 3I

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

gIe s IrItXsevl-

&OlolOt -7be ppbsfizs .4 cisi so hrT hal-tloe will an&

wi. fbjt:zai the ,maxitxrnrn iud pecfite 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 ~not

be 4ttAined, cegardless of -how, low the gas -turbine :conpressor re- 1duced thie pressurevdt the-duct exit.

if we nowala' w a- long -inlet duct in which losses are not negligible,then-p2 < 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.

'.NeAir ciOking, d-- tict pfnbent losse-s '-eer~i~l become sojarge-thqt~~--4int pr aato- design 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-a

speifid~mss lowatfixed'inlet Cqonditidns' (e'. g;, atMOSpheric con-1 cdit;_o n!)

2.6 -O~p -Proper ies!

JMAl the relations -fthe calculation methods pr es entedassume thnt.thepepe6t~gas-eqiAin-of sr- re,

p =pRT

is valid I&r the duct flows consider ed. In addition-, the, char ts ha ve

been prepared -for a gas, with ratio of specific:, heats of .1. 4, and -mo-

- - 1ecifar weight,'29. thiese values will apoly!'Wirhh tiffcient -accuracy

to-either atmospheric inlet ar, or gas tWrbjine exhaust gases.

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

-18-

3.0- SOURCES .AND METHODS EMPLOYED- 'IN DEVELOPMENT OFCALGULATION PROCEDURES' FOR DUJCT LO ,SCAVICUL.ATION

The data s§ources and correlaion mi-e-thods on which the ~clculation

* procedures bresented-in this ieport are based, ire outfinie"Ifn this

section. iln somhe casesthe available- data is incomplete, so that

approximationis and, ektr~polarions have been necei'sariy; -in, some

* ~cases,. data from various sourcesconflict,, so that somie judgment

has been necessary in cho6sing data for procedures. 'Under these

circumstances, it seerna desirable tou-supplenient the recommended

cal'ulation piocedures with this outline, of' ource's and methods.

3. 1Straight Constanr Area Ductsr

The procedures for straight ducts are based oir the calculation--methodsdeveloped by Shapiro, and othdrs. Thbese'are-developed in-detail, in

Refefence 2, and'are a standard mnethod. for compiessible floy, calcu-

lation -to include the effects of friction. The niecessary compressible

flow parameters for this calculation are plotted in Figure D-7.

Duct friction factois are-,taken from Mo-ody, RAefer-ence 4, and chd.rts

are reproduced from thig reference as Figures D-3 and D-4. Keenan

and Neumann, -Ref-arance 5, show that there is no significant effect

of compressibility onfriction. factor for subsonic flows, so that the

friction 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

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). The

theory of. Langhadr, Reference,6, has been shown'by Shapiro toj-pre-

dict the coi rect value of, ftiktibn 1factor 1n this laminar region. Curves

prepaied from Langhaairzs theory, ;aken from- Referenqce7,. ak ro-

-produced asFimire D-5 At the duct length iorrespcnditg to -Re -6

a, transitidr. to _t~rbulence,,occurs;, Reference 7 pr~zanted d~t4 for

friction factors in this turbulent region. thle curves of Figure.D-6

represen~t, an averagre friction factor (calculated fiom. durv~s'faired

through 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 the

friction factor for fullv-develoced~turbUlant flow at the same duct

Reynolds Number (Re =p V D/i.);. this- ratio is larger than unity,

Therefore, loses arelarger in an inlet leghthan in a fu.lly-developed

flow . If the duct 6rntrance is rnot smooth, or if there is a screen in the

entrance, Shapiro has, showvn that there 'is no laminai inlet length, but

that the entire inlet flow length is tuibulant. Th~us, for such antrance

conditiJons, the tur~bulert inlet friction factors -of. Figur e-D-6- should -be

applied to the entire -inle& length.

Calculation procedures have been devised *~hich take into account

these special cases of inlet flow lengths and determine the appropriate

friction 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 simpler

approximate 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 nd w i ir . Ilosses. It has been recommended for use in the duct~" ealcullation rnet.hod,

-20-

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.ve

beer. computed by,-a mnethod similar to' .rhzi.t de,scribed in ~the- section on1abrupt area decre6as6. irncorporating 51a! extrapola'tion of tb~e data forc~ntr action'to~fficients, Reference 12

3.2 Area Change

3. 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 raige

culation of total pressure losses and Mach. Numbe-r c hange, and resultsare plotted i-. the design. charts of Figure D-9.

* -21-

Theexperirhental'data,-of,"Hall arxl Qrme indicate tharth1~total pressure

loss -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. total pressure ross attributed to thd-akea7 change- is- thereforew~t onld ~eoso imtr f 0onte -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- toll

pr-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 tine .(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 for 1incompressible- fl6w suggested in Reference -11.

Sketcih I /'

*As shown in. Sketchi1, the-flow -is aissumed -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 then

6CCUErS between sectionis-2h alnd'until the.fiow fills the area-A2,

at essentially constant veloity adrossrEh6-duct dibssetidn. Theflow from .9ecton- 2"1t io 2is-treatedas an.abiupr Area Eicrease, as

dedi iiSection 3.2. 1. The area Am1rtfstbe related to the~khowhn ekeasi A1 and A2 by experimenft, since there' is -no analy

tical mntjifo&fpq prediction. Values-of area tatio A,"/4- 'have been,

t~knfrm te dta-ortlatonsof 'Referenice. 12,-w1~cbLgiies the

area tal A"/A ~a funltkii- of A,/A,, and -inlet Mach NubrI

The resultsitof this analysis are presented in F-iguie D-10 which

shows exit M~ach -Number and total pressure ratio as, a function of

area ratio- and ilet Mach Number., Total pressUre lo~,s and Mach

NUMbdr, changeinic ludei .4diameters of d-wnstream. ducting. Altugh

pressure losses are-small, note -that moderate area chlanges produce

largd-increases in .Mach -Number, -so that only, small -dea decreases Ican be afforded- in high speed flows.

3.2. 3 Diffusers

Although a large amount of literature describing diffuser investiga-

tions is available-, cor-relations of these data have as -yet -produced

no system 's for diffuser design or loss calculation that are entirelysatisfactory. Available correlations of per-formance have been

formulated on the basis of diffuser geomptry alone. Various inves-

tigations have shown, however, that there can be-substantial effe cts

of Reynolds Number, inlet boundary layier thickness (I. e., Inlet

velocity profile), compressibility, and discharge duct geometry.

'HoWever, there Is not- sufficient data yet available- to: ihtide sucheffect§Jn a ~generaizcorrelation, so -that We must, Je1 o'correlations

*of ,peifpirmance. with geometry alone. -Such, correlations exhibit con-

siderdbl e, 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 -In conicaldiffusers.

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

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

9ih spe lgefcso ifsrprfdrmaice-ax~e shown by Little

,aihd- Wilbur, RAeference. 15i ah'd -by Young and Green; 1Aeference 14,A

for se§verLal coifical and rectangu@lar difhusers. 'Cbrrelations frofi

te'tdata of thnese investigatqrs-have-beeni Ysade, -and are 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 -be boi~idered- to

be subjectrto revision 'if rihort data.1,ecOiies avallablei the -future.

The effects of increasing Mach Ntieh nj, ~ qriac fa.dfuaw ith a fixed Inlet, boundary,:layer coiidietion has:-be~n -shon in RWO-r-

ence 15 to-.be smaller thai -the effect of ic~~ni~tbx

tfhickness-at a- fixed Mach, Number. Such- result as these, indicate

-tbattherie will be cohsiderable-uncertLainty i-iffurser. loss -calola- - -

dions. The recommendarions -in the-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'--t6Etal

pressure 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 loss

always 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-st

diffuser 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.

3. 'The -inlet-v* elocift distributtion -has bcen showm Eo-affect-diffaiser

Perfbrmanc6 (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 itecnb

done-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.30

diameters5):than- would be expected after suffiin ln t i rflly-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 art de exirvof the

diffluser;-<abour 4w to 6exit duct dianiereridoWnistiram of rhe exit ard?

requaired for-complere recovery. usedarea riosabou 6:1 an bruVpro most Commi'i~ sdae raris (Up toaou6)anarp

araincreas z sm i les.S -total -pressure loss than a diffujser wirth

wall angle, gr gr~aier 'rzn40 0 50.

6; Tot a-1 presuire loss inc-eases -with increasing 'ndot M~ach Number;

!-he 6ftect-is m6re severe with large wall angles an4 also with ri± Ientry bondary lay~r~s.I

7., Variousheie-s such-as.-boundAry laver control by suction,

in~ection, anfd Vortex traps, ajid dOlay of fi w ieparaion by curvedwall, hve een ev~ed-o impirove diffuser performance. Vanes

have been used to Lrabilize the-flowi and thus Improve performan:ce.

-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 wanl

an3 e, ivis often ir~dte cdesiraIbie to mpldoy an efficien -diffuser (Wal [2e, of about 1 0 rfollwaad-by an abrup: area Increase wo &a

de ted-area.

3.2.4 Convergizg' -act:~z'

Losses in converging ducting are small compared to those in-ivergikNgdu~d~ (dffuers)-becaizse 60e a-Celeratingflawia covergig-,duar

Oresenzs-a fvor-able pres-sure-gradienr for the wall h~rtdary la-yer.For small c4one an-gles: (i. e., jess tma 300 icluded-artLe) there are

g~nr~ly o itin-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-m en ded -tha E co=vefgiqg duc ting witin in clu ded co ue -angie -s-tnalle r tha n360 be treated as Straight 4ucring, wizh L/D couted on the smaller

diam~eter of the converging section. iFor fncluled angles greater than30 0 ,ir is recommended that the procedurq for abrupE area decrease

be applied to coniVerging sections.

-. 33 Bends

Loss data for bends are shown in design chart D:12k in the form of aI

low speed (incompressible) flow loss coefficient, and a Macn Nuinbe:

-- 27-

=.e.2d -ou

e- L,-ev,--Lfc=

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

coS p ress.I-l s

fMach &%.arv--s 2frwix0.tl.. d z -sm as. t~e P--., g a-c

f fii Dr ~ 2 aen tduhx vns is a as &-m. f Ffres ii a 0-

ska7 !d zrgre rxaEzscLa bz !etloss caafficiem-S ar=e jxossibme by

are irgil e~s~ ~e -wie Reereoa. for sig-gi infoaiatidon),2n p a ier4y rettdZ6 C=Sivr~be ssA,;L-,dmRa) in 4esigmi wdbnic-ze.

v!zs dto Xp: er, ee-,-: 1=tra~se A less

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

- -or b~ds *!a tfi.A 0 rrs( e-, -vas v~bich are-pc f airfdl

frcDo Sneze.. R eee~e 1, b in conk=z-cm ~ errecd-rarwes fix kzads wazfmm ,

-a naSPT-.&,s prcar e,.~~fi

i=2ds yc= g

C-c- ine of;-,r w-.' o:e, z!eso

'Xe r ' a 900bzfbva

is is Eta

cID a b azd ba siipa 4 i_2s the

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

-29-

there is an isentropi cre flwihc ~Mach. Number is uhaffected

by 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- ciameters-dovvastr.eam, wvhen mixkinE of

z-he-coxe fivv, annd.-h& Ixwzn~ary-layer flowi has bz-.-n comaleted- fro-on

rji, 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,th

effect of -the mctal pressurelosses fi theb bend YIff be felt all across the

duct 2id-zhe ote-dimensffozial -V--ch NOumber- ".ll have inpreased.

34Screetns am x -g

The sul~idi compiressible fio'x zhrcuja Ecwbd-wdire screens or gratings

(screems off slmrgp-e ed elenmenzs of 2de geonietry) has been. consideredj

by Cornell, !Wfere-~e1.COISIgvSls cfiensorsh

screens and gr2EIng-s in 6:=- R=oS, bor varigus screea Slicires (ra.Eio

of cT=. area in screen to &~mdcz flaw area) and upsiream &uctF

Madi Xwber. ThsDmie ~zadrclyfo ee~ce 2 and re

5e loscef-iet f . ra apply zq screens at theP moudr 'oia sarp-e: .sed (i.e., - no) in:-eke damt~ Carn-lls cacua-nsj

for 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.

} 4.0 CALCULATIONPROCEDURES JAND, EXMPLES

4. 1 Interoretartofl of Proceduie Diagrams

* Calculation procedures for all ductipg-pomponenws are described

graphically 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.~ ~ ~ ~m Qaiie hcruscL Nbe -.ivn.as initial -dati for 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 !s connecting ele-mets; e.g., dle s-'~ezece

-- indicates thar the dizn&arum e -2 is tobe eatred

and Re is to be read from rte diart. The sequeuice

Lcaic. AL

JC4 JLI- - - - 1

-33-

inadicates that 4 f, which is a result fpeiosccuatio, ind

L/D, which is knowrvas iial data, are to be coinbined'by cad-

j -culation to give 4f(L/D). Here, the equatlin required~for cal--

-culationis obvious; i.e.;- 4fU.L/D) 4 -I x L/.Iq cases whee

ibe ecpariba isno ob-4ous, it-ts incluciedin the box contaifing

the result, osin the-SO~ec

-caic 0 2 Pa'o

The result of the indicated calculation (L. e-, the loutour-, of the

box) is always showa on zhe rignr-hand side off the equzation.

4- In somtne cases, alterzate caicaio~w prodmu~res are iniikazed,

aS in the seience (:aken from procedure P-16).

D- 2

This diagram frinicaL. -;;.e upper path is followed if LID <30

and Che lower pa-h" if ' f.~ O

-2 Examziples

E E amples ilustrating the x.;e ,~f each procedu re diagram follow the

diagraff. Each box contains die numnerical result of using the design

cbari; or of calculation as prescribed by th.- procedure diagram.

r -32-_

4.3 Closely-Coupled COMPOnentEs

f - ~Area canges. ben&, and screens are ass§umed-rto~beflo byedfam erert of straight duct 'M Which 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 pressure Iss of the first-comnijenz is detrmined-in the

Usual mananer.-

2. Thbe prtssurelc.rss of the 6ecomd compoWDen L5 determ~ined byJa; sumfing de same-entry Nach Numier as-employed-for the

firt ojen..Tie-pressuie loss for f-,e combined compoa-

ens Is_ thea

ipo~J - Ldn LPod 0

3. Te exit Ma ch M-1 nl-'-r for iha com.ine ft-com wnez s is dee-

mined by calculating mue n-sass flow uirMeer at te exitc of &aseconid 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.

I S-33-

-PROCEDURE P-i -

* " MACH NUMBER CALCOLA-!ON1"

Total pressure -kIm,

.- Static pressure inmm

- I

II" 9'

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

af.1

- - am4

- " - -PROCEURIR -ihJAdH MMBERk CALCULATION

Total pressure kndwn

D Z&

Static pressure knw

mass Flax i =12.8-1b/see

Total Temperature T =540

DUcr Diametr D = ft

STotal Pressure P = 1-4. 7 psi

Static PI-essure p=1.2 psi

I

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- ~~P.tOCIXJRE P-2.1Ia

--- STRIGI IT Wc-T K-TAK17.)

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(CA L.C

______ 7~1

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0.68 AEft Ci -C

.0 94

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A4 *F___ I

As |

0U

FPCERE P--. 1

PROCEDI E P-4.2

ABRUPT A..EA INCREASE (EXHAUST)

-44-

- -S

606( Lip

PROCEDURE P-4.2~

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

__ .7L

U

....

hfh

.1,0

.j'sOCERE P-3-'-A

! -0 !po02

i . i-XJ/tE P-5. 2

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

4D

I -IN!

~I"

S- E

PROCEDU/RE P-5.!2

ABRUPT AREA DECREASE (EXIIAUST)

N|

IC S

I r - aze KvC

AllY7o-

*0-EUR P-.

40 DIRSERS(MTAM

pAz.,A , -. M

- b-14 c .. A

-- -.

V -

1-I jIIiIiiI.ClI S d- a

S

1 <0~:I.

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Id,i1.1 Dm14

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I.1

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200

CALII

001~35 4. 0.986y

CAL.C

A.#.

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~~~~oi I__ _ I__ _ _ _ _ I

aPa

CAI.

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UU

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C4&C ~4I 0.@8o4

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05(1)

DmI&. O-44

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C..ePARE £ pwr 0.167

- - -- - - -"43

amp..a&0804

f O-CO CAA-U

0AW35oo:Aawf J~ws

CALC

- ________A_

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---------

CALC-

0.334

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PROCEWRE P-7O. I

SENDSJ (INTAK~E)

CALC

0,337 0.403

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D-2

(b o cf K.

ASSUME J o:,

CO,2~ ~P.7 M 00 _

CHOOSC NCW' VALUE 0" M,Ao REPEAV'y<LCLA1rfoN

PROCEDULRE P-7.'2

BENIN (EXi [AU-SI

CAL..CA-- -

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L..

I'K C IU 1- I-7. 2

REMM; (IUXOAJSr1)

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D-4. .0t CALC 0 91

0.0160. 84

CA-

I I'PROCE"WRE P-8l.1SCRIES AND) GRAMMNG (INTUE~)

0-/ c O/*oa CALC Pe

Eail

MIME. FXJRE& P- 8. 2

Li SCREEiNS AND) GRATINGS (EXI IAUSI1)

IbO _CALC

CALY77

cc#-.4PAJ~dPLorMa -/. pA

CHOOSE NEW VAWCJOr Al, AND REPEATiCALCUL A-r/O

(I -i-----:---:--g .

A-55-

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pea AC*

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5. 0 AMLUC TI M OF CALULATM PFROCED ES TO ADUCT SYSTEM"

The az m re- syot m a Flare I u cosen to Illustrate the

applicaon c de caculadc. proceuhzes and to provide ar example

comperlam of pres e and 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-%e

losses and power looes are pkmeii in fV. re 2. Ne tbe severe

Increase in aculed loses as the duct djamer decreases.

The xe los pealry asociaed izh w the duca pressure losses has

been calculated from a linearized analysis described in Secdon 5.2.

The pressurc losses are so iarge: howeverd, that e linearzed

analysis should be regarded as giving only appromimaze esfimaes

of the power pecalties.

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FOR VAW wEIr M3IhaEM

3iTAjM VDT fw1* Uw t"W at 15 lbft)

V= ~amwm a&) 18 12 9ptreLe LW) 0a . CL.77 L165treft LAWp on5 L3 LS 1L41

UHKuSr WCT (uI& fOwum at 16 bj

Do= D~mw-Tcm) 1I 12 1P-reav.r- Ls (J*f) 0.5 4.05 9-7-

4 2.0 233 -5-88

TAM E 5- L (Cm 4

M 'WSE 3 . -;..) E, -.. IG MAC H -.WI FOR EACH S

*i 'ftK TS -mrXJ

up= of - 4--.e CAD

3XTAKEIi

0m4c. -102 I- U-230 i "SU~~~ 0.23, S 0.9a O 0.0

ses jo..,s +-"IO'j

o9, 90 e960 R.D-I.C 0.996 RD

S--Ln dut -0- 162 0.996 LDz).4 - _ 0 .;2-0 L "a I I

@e 90n 960 102 0.999 t D-1-.33 0- o.246 0.96 a c

. , , 0.246 0.9r '%2a ~2e

Su, t -0'- W2 -.00 L -Dz7.9

TOTAL I AKE , 0.993 0.94SYSTEM:

EXHA -. T

Exit 0- -78 0- 4

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. 997 L D=12 040.067 L E0180 0.173 0.998 R D=2,66 -- 90. ..993

TOTAL EXHAUST 0,980 0 0..eT1SYSM

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2- Ove 9p OI

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R D--0 0-.990 R. D-2-

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0,2.8 0. -, .4. AI -2- o. 7 9.3 A A

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0.947 .700

0, o4wo D .6ss

L. D =23.3 o- 0370 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=1.0

LD-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

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mam am 15 %/iSac

Tmeamrae - 4g

Pressure ptl - 14.7 P31aDwa diamcw: D a 0 ft,

A w-.rjD/47-C. 442 ft2

bMcb aMiber P- ia

II

BeIIimouth &inrance; P-3 11

4 TL D) 1.47

P./PO* 1. 42

4 T l , ADui 0. 03

4TL ma/Dy2 1.47 -0.03 =1.44

M2-0.465

Po/.* = 1. 4i

P02/'PoIleLt. 0.993

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

i5

. 75 Re .1 x

2.00

M 0.460

.KI 8 P =019

0 2

01 -

p0 1 ~0. 9875PO benci

-91 -

Mach ).wjmber (abr- CIGRe-c-pe comt)P-1 a

-o cu 9,5 .. 0gs .o94% a o.93) - 0- 931- -o

mrx 0. 373 a.401

p A Po2 p A 0.931p

M2 -- 0.507

Staight Duct ; 0-2. 1

D = Iin. =0. 75ft

L = 33.5ft L/D=44.706

Re = 2. 1 x 10 .0181

z /D = 0. X5/.75 = 0.00067

4! T 9.D -0. 09

Y 2 =0. 507; 4T ) = .5= 1.33

max) (4fLI) amax)4- V3 .05-0.8909

i PO

M 3 0. 7 -- .09Lo /2

P- 0. 820Po2

-92-

-- --- = 2.67D 0.75

M3 =G.7

Re a2.1 x to,

CPO 0 .074; 18w1. 29 (Oeptobably rchokes) K# W1.0

K1, 4 =0.0237

Po

Li040. 976

[m m" • 0.40, fi -0=0.501.-

Po 2 A P0 4 A

M4 =0.75

Diffuser ; P-6.1 ()

_ _ _ _ _-_ _. . ... .._ I H

4.5

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

S 2A 5 D5 182

A4 ,2 92

2e- il.I 0

4 =0. 75

CP O 0. 112 D C O o 2 4

KDw 2. 0 (No. no da may choke) C 0.224

------ =0.061Po4

o5 0.939

M 4 = 0. 75

m- = 0.501

Po 4 A4

ro-n p04 A4 .0. 501

04 4 Po5 A (0-. 939) (4. 0)

M 5 -0.121

i. i i ll~l ii ii i i i i ii5

L : .,-,.1:. P res e Ritio A J Ina, ML / ct

R1(0 3 (Q. 820) (0. 6 (0 . 939) 0. 70

Exhaus Dut

m - 16 lb/sec

P5 = 14.7 psia

D = 9in.

A = 0. 442 ft2

Mach Number ; P- I b

p- ) 0. 662

M. 0.6883

Straight Duct ; P-2.2

L =38.25

D 0.75Re 15. x-O=500 O

L51

D001l82

m5 G. 688 ; (41[ m ) 0. 225; Po =.0D5

4T D0.225 .- 0.928 =1. 153D 14

M4 =0.49 , p =1.36

0.810p04

Bend, 180° ; P-7.2

R1.0

M4 =0.490

Re =1.1 x ,L0

Cp0 = 0.177

Assume M3 = 0. 470

KB i. 0 8 6 K B Cp 0 0.192

p,= 0.,025 0 9703 0. 975I

-21.1

Da

f - -0006;

D

4-. s2 0. t

4 0- 7518D

L 2i Z

467 Ta

= o- G-51r

D

4 -n -'a~

I =. 4.

J2 . 5 ~ 5 = 1.86

~) p-Po293 O.

12 0.92

4~~t !, L 425

K 4 1-63

i LCPO =0-C7 46

.0- CLO;

I- 99eol

MTc -

"1A

M.2 - 0.3

PNcssare iRario c :Ez.:Zz

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

Thc~~~a2G 4eas2 £fti :

6) 1

24- C

S *

x %-

QLa \oi o

Pn k /1Ii - ,

Assume :rt ie -* Izes choked

(1) InCrease in turbine exhaus- pressure,P4

w Lwx T I k 1 ( p41 I;k

BP4 TO \m )3 P 3

Airiply by P4

awx ( k-I/k

8!' a - ri-r ,.Cp- -o3\p3

P4

Lex r~ = ~ -4 6 design pressure ratioPo P4 ol

Uinea rizing

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

"I p

!!ma T Pi

(2) Decrease .in conpressor inlet pressure, p 01:

Assume compressor pressure ratio does not change

SP4 P4

Po3 Po2 Pot; p0 3

ma)1T po3 rpJl Po

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

Matil Py Po0l'

011

M

- -01-- r

L1nearizing,

Al? w + fl.. h \1/ p w =,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 air

Efficiency - 0.70SHP - 1100 If Turbine Inlet Temperature - 2060R

Design Pressure Ratio - 6.5

Assume C =0.24, k= 1.4

k-1

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

= 83. 1 I-P/lb/sec

Inlet;

-) & nCA 1f a CT

m = 15 lb/sec

C = 83.1 'PTh soc

P "'0"10, 3

'aum 14a7 t.- _P0 -/ . .. . .PeEM 14.7 =~

A ll -(IS) (83.3) (0. 3) - 375 It

Exhaust:

S=_m a C p

ma 16 lb/sec

CT 83. 1 IP/lb/sec

M4 - 0.425

P 0.883; P 4 = 23.4 psi

I P4 - Pctm 21.2 - 14.7 O

Patm 14.7 0.442

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

NOMENCLAWEREFC CPo Total pressure loss coefficientA Crossametoa duct, ft

D Equvalet diaeterof nion-circular cross-section duct,

4 x wetted perimeter

KB Pressure coefficient compressibility factor for bends

K D Pressure coefficient compressibility factor for diffusers

K 0 Bend angle loss factor

L Duct length, ft

Lmax Duct length to attain m =1i.0o, in a constant area duct, ft

M Mach Number

R Gas constant, lb force - ft/lb mass,R.-

Re Duct Reynolds Number, p V D/jj

Re Inlet length Reynolds Number, p V x/.LxT Temperature, 0 R

*V Velocity, ft/sec

c Local velocit:, SC L::,, ft/sec

Friction factor. ACi ..veloped fno

NOMENCLATURE, (Cont' d)

f Friction factor, Ink: laminar length

f Friction factor, inlet turbulent length

go ~constant = 32.2 lb imn:-ss -fr/lb force-sec 2 j

k Ratio of specific heats

m Mass flow rare, lb mass/sec

p Pressure, psf

s Screen-olidity = open area in screen/ducE area

x Distance from duct entrance, ft

Greek,

E Duct wall rou±ghness, ft

29e Angle between diffusei walls, degrees,V'iscosity, lb mass/sec-fr

p Density, lb mass/fr

* Angle of duct band, degrees

Superscripts

*State at M 1,O0

-, NOMENCLATURE (Concl, d)

Subscripts

0 Stagnation or total state; condition of fluid brought to

rest isentropicallySfI

2, State upstream of componentI2. Stare downstr earn of component

tr Transition point from laminar to turbulent flow21 State, four diameters downstream of state I

I

Special Nomenclature for T1urbine Perormance

Clculadon

C specific heat, Btu.°Rk-I

CT turine power constant +- qr CT I-To

iF net power delivered by turbine unit, horsepower

W x net shaft work, ft. lbs/lb. of air

In mass flow rate of fuel, lbs/sec

ma mass fLow rate of air, lbs/sec

rp /"design pressure ratio

?12 compressor efficiency

71T turbine efficiency

I 0.

I

a.i

-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, . i

New York, 1948

Note: Compressible Flow Tables are also available in:

Shapiro, A. H., Hawhoriie, W. R., and Edelman, G. M. The

Mechanics and Thermodvl,:"mics of Steady One-Dimensional

Gas Flow with Table. r, ,merical Solutions, Meteor Rep-ort

No. 14, Massachuse : cute of Technology-Ga' dissilps

Program, Cambric. , - , 1947; and

Shapiro, A. H., H8:4, \V. R., and Edelman, G. M. The

Mechanics and Ther.. , nics of Steady One-Dimensional

Gas Flow, in Handbook of Supersonic Aerodynamics, INAVORD

.Report 1488, Vol. I.

4. Moody, L. F. Friction Factors for Pipe Flow, Transactions of

the A. S. M. E., November 1944.

5. Keenan and Neumann, Measurements of Friction in a Pipe for

Subsonic and Supersonic Flow of Air, Jour. Appl. Mech., Vol. 13

No. 2(1946), pA-9i.Best Available Copy

Mispaphy f~ad}

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

7. ..5iza, A-IL and Sm a.IL. 5.Im is die

WKm of Swaioh 76=d I'M". ACA T 1M115, No--a-r 19a L

S. Hmry. J.I. esp at P m Pm ndoes Pressure-

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

1944.

9. Hall. W. .. andOrme, &_.. Plowmoa Cwpressible hdd

lthxu&g a Suddwu Enlargemem In a Pipe. Pr 2Lngo h

Iwze of Mechanical EM;!ns, Vol. 169, No. 49, 1955.

10. Cole B. N. and Mills, B. Thmry of Sudden Enlargements

Applied to the Pope ExtAast-valve. with Special Reference

to Exhatc-pulse Scavreqgira Proceedings of the Institute of

4edinicha Engineers. Vol. 1IL P 364.

11. Hunsaxer, J. (.. and 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.

J

t

t14.I Ymo&~ ADL, mdGreen G. L Tomsotft Sp10 d Flow

In dfus of Recanpula: Croas-scdou, R &M No. 2201,BridA A. LC, July 1944.

15. Uzze., B H.. Jr.. and Wilbur, S.W. ftrkirma and

Boudary Layer Data from 12P ad 23° C Diffusers of

Area Rado 2.0 at Mach -numbers up to Coki and Reynolds

Kumbes 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. A

Study of the High-Speed Performance Characteristics of 900

Bends In Circular Ducts, NACA TN'3696, June. 1956.

18. Friedman, D., and Wescphal, W. R., Experimental Investi-

- . gation of a 900 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 Conical

Jet Nozzles in Terms of Flow and Velocity Coefficients, NACA

TN 1757, November. i948.

. 20. von Karman, T., Compressibility Effects in Aerodynamics,

Journal of the Aeronautic .. Sciences, July, 1941.

I

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