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DESIC,_ OF POWER-PLANT INSTALLATIONS

PR_URE-LOSS CHARAOTERISTIOS 0_' DUCT COMPONENTS

B_" John R. Henr 3

Len_Ioy Memorial Aeronautical Laboratory

Langley Field, Va.

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https://ntrs.nasa.gov/search.jsp?R=19930090921 2020-07-23T10:44:27+00:00Z

SACA No. a

NATIOI_L ADVISORY C0W_ITTEE POR AERONAUTICS

//

ADVANCE"RESTR ICTED "REPORT ....

m

DF_ION OF POWeR-PLANT INSTALLATION8

PRESSURE-L03S CHARACTERISTICS OF DUCT COMPONENTS

By John R, Henry

SUMMARY

_

4I:

i.i. -_A

l,i:Ii.

!.

"_._.

!J

. L

A correlation of what a_e believed to be the most

reliable data available on _uot components of aircraftpower-plant installations i._ presented herein. The in-formation is _Iven in a convenient form and is offered

as an aid in designing duct systems and, subject tocertain qualifications, as a 8uide in estimating theirperfoz'mrcnoe.

The design and performance data include those for

straight ducts; simple bends of square, circular, andelliptical cross section; compound bends; dlvergi_ and

convergin_ bends; vaned bends; diffusers; branch ducts;internal inlets; and angular placement of heat exchangers.

_:amples are included to illustrate methods of applyinRthese data in an_l_zin_ duct systems.

INTRO_ICTION

The objectives in the design of an aircraft duct

system ere to fit the components of the system withinthe available space and to meet an air-flow demand with

minimum of ener_ lo_s. Analyses e£ duct systems are,

in general, made for one or more of the followlng

pttrpoees_

(I) Estimation of pressure lossIn a duet

(2) Determination of rate at which air will £1owthrough a given duct system

I .....

(3) Calculation of exit area required to obtain adesired rate of air flow through a given

duct system

(4) E_aluation of airplane drag chargeable to flowtl_oueh a duct system

Aircraft duct systems occur in an infinite diversityof forms but, for the purposes of design and analysis,must at present be treated as a series of component parts -such as bends, nozzles, and diffusers - for which designand performance daSa are available. Analyses of ductsystems are Generally step-by-step procedures in which

changes in the energy and the physical state of the

• _cted air are followed progressively from the free stream

ahead of the alrplanethrough the successive duct com-ponents to the point of disc_har_e from the airplane.

Simplified procedures for making such analyses are givenin references I and 2, and a precise, rigorous method is

given in ref_renc_ 3. _ese references are primarily con-oerned _th analytical procedure aud do not deal with loss

characteristics of duct components.

A lar6e amo_uut of experlmental data and some theo-

retical treatments of the flow in duct components exist,

but the data often appear to _ inconsistent and some of

the theoretlcel treatments _.e contradictory. This lackof s_reement is princi_aily due to inadequate cousidera-

tlon of all variables affecting fi_e flow characteristics -

a natural consequence of the Undeveloped state of the

theory.

The purpose of this paper is to present, An simple

and concise form, information useful for the analysis anddesign of duct systems for aircraft power-plant instal-lations. Data are presented on deslgn criterions and

pressure-loss characteristics of strai@ht ducts, duct

bends of varlous cross-sectional shapes, vaned bends,

branch ducts, and several types of diffuser. Severalexamples are presented to show mehhods used in analyzing

duct systems.

In the present report the most reliable data avail-

able have been used but some of these data are recognlzed

as questionable. In cases in which data from differentsources are inccnsJstent, the material presented is,

as far as possible, a mean weighted by consideration of

the conditions under "_nich the results were obtained.

_ACA APE No. rJJ_26

In oases in which data for'a partioula_ type of duct oc_-.... ponent have been obtainable frcm_n_y..O...ne source and were

therefore without adequate cor_oboration, these data havebeen presented for lack of better,"

The flow characteristics og any duct ccnrponent areconsiderably arrested b 7 variations in the nature of theup.o'ir-ee.l.1 flow; for the data presented the type of flowis _._aa,_ genernted by a long stralght pipe. Because ofth, _ c "" ...... ._.*_.._,,_ _.vo.d the limitations or, available date. thepre.oent d:s_.L_.s_ion of flow coe_A_ole_ta for d.ue.t com.po-ne::L_ le sub.:_*ct to extension and revision when more com-

pr:_n_n_ivo d:_a become available, If the prensu_9 andve3.:,c:;.Lyd.:c.r:._b-_._J._:zsof tLe flow at the irle'-_ of a

du':'_ _::.,r,?¢.._._';,c ape n,-,t uniform, t"_ze t._Is.l-pre.osure losstlu'5'.'::hthe ,:_,.wT,c:_,-rmwill be _r_ate...• th_n "could be _x,e-dlc.,." ' "_ t:s,'..-f t-:e present data, -_ilbJect to thesequ,:.'.".fi:'A_._.o_-.,,t.b._".qaterlal pre._ented 13 o_'fero_ as a

_u:.'_."":'_d_'iijn'.n 6 duct systems and e,-._Imat_g _z._irpe-':.'.',:r,:.$::ce;L,._._ve.._, for the attninmert oD bes_ perform-

anc_, co,npiet-_ _:-s_em,- should be refined by tests ofai._p!ane models in wind tunnels or tests of duc._ _ys_ems_in w'nioh the air flow is ir,_uced by-blo_e_8.

A duet cros_-sectlonal area, squaz, e feet _,|.

a velocity of sound, feet per second

," t_ -_1., ; .,#

i

CL llft coefflelent (L/qo_

o length of vane chord, feet

D hyd_aullc diameter, feet

\ of -/

f

diameter, fe_t

i

rrictiou factor for straight "ducts |_,,-_--

%

s

H

h

K

k I

k2

L

ra

n

P

P

Q

q

R

r

T

V

NAOA ARR No. L4F26

gap or vane spaQir_, perpendlculor distance between

vane chords, feet

total pressure, pounds per square foot

hei@ht of duct (An oa_e of bend, dimension in planeperpendicular to plm_ of bend), feet

al_bltrary constant

bend-loss coefflcien_ (_ of bend dlvided by q_

of equivalent oonstant-area 0_nd wii_. Identical

inlc t)

total-pressure-loss coefficient of diffuser expressed

as fl,sctir-n _f loss due be suddr_n expansion

l-- % i_ .r f ,*

lift, poLmd_ _er foob of spaz_

axial ler_gth of c_ct, feet

Math him'bet (V/a)

mass rate of fiov:, slugs per second

nu_:ber of vaues in _uct b_nd

perimeter of duct cross section, feet

static pressure, pound_ per square foot

volume rate of flow, cubic feet per second

dy_mlc prassm-e, pound._ pe_ square foot (_V_

R_olds number (pVD/_)

_adius, fee_

Cra + rb5mean radius of be ud, feet \_j

temperature, oF absolute

velocity in duct, feet ptr second

w.

_ACA ARR go. LI_'26 5

_/w radius ratio

h/_ aspect ratio

Subscripts :

a inside wall of bend

b outside wall of bend

6NACA ARR No. L_;26

d

e

f

fl

i

r

x

0

diffuser

exit

face

flared inlet

inlet

resistance unit

arbitrary suation

in free stream

1,2,3,... stations in duct system

max m_ xls_m

min minimum

GENERAL PRINCIPI._.S 0F DUCT DESIGN

Skin friction and flow sepaL-ation are t_.o fundamental

causes of pressure loss in fully turbulent flow t_rcu_1

any duct component. The lose in a given duct c_.Iponent

from each of these cadses is roughly proportional to the

dynamic pr_szurs of air flow. Since the dynamic "_ressureof the air flow is proportional to the square of the flow

velocity, the first basic principle in the design ofefficient ducts is th_ mai.utenance cf a lovl flow velocity

by the use of .ducts of adequate size. T_e importance ofthis principle may be illustrated by notin_ that, for a

given rate of air flow, halving the diameter of a circular

duct multiplies the velocities Dy 4 and the losses by 16.

Although skin fraction is the dominant cause cf

pressure loss in flow through strai_it ducts of constantcross section, this pressure los3 is small compared with

the losses that occur when the main £Io_ s_parates fromthe duct walls and thus creates areas of reverse flow r_d

violent turbulence between the main flow and the duct wall

These areas require velocities in the main strean higher

than are otherwise necessary. The second basic principle

in the design of efficient ducts, therefore, is the maxi-mum reduction of flow separation.

[

!II

II!I!

!

NAOA ARR No. L_26 7

...... One t_pe of flow.-separation,-oeoura..when forces arisein the air stream in a direction opposite to the direc-tion of flow. Such a fores ls the pressure rise (or"adverse pressure Eradient e) produo'ed by a decelerationof the air flow - for example, the .deceleration of theair flow in a diffuser, "_ne rate of pressure rise thatmay occur without producing flow separation depends onthe velocity of flow near the duct wLll, because the

presence of thick boundary letters of slow-movlng air is

conducive to separation. Conversely, a deoreaslnE pres-sure in the direction of Slow (or a "favorable pressure_radlent"), such as occurs in a nozzle, tends to prevent

separation.

Changes of flow direction, as in bends, also Eive

rise to forces that tend to cause separation of flowfrom the inner surface of the bend. Surface ro_essor protuberances that cause local disturbancea or re-

tardation or the air near the duct wall ag_avate condi-tions of inclpient separation. Screens or resistances

across the entire duet, on the other hand, tend to

stabilize _e flow and oppose separation by resistinEflow increases in the center of the duct at the expenseof the flow near the walls of the duct.

PROPERTI_S AND DESIGN OF DUCT COMPOI_NTS

i|.

Pressure-lose charaeterlstics and design criterlons

of several typical duct components are Eiven In fiE_ures 1 to 16. The total-pressure-loss coefficient AH/q,a ratio of loss in total pressure to dynamic pressure atthe entrance to the du=t component, has been given di-rectly wherever possible; in all other eases, coefficientsare glven from which the pressure-loss coefficient can

be computed.

straight ducts of uniform.cross see clan.- Thepressure-loss coerflc_en_ r_r s_ralght duets of uniformcross section Is given by the relation

The friction factor f varies with the character of the

duetsurface and the Reynolds number based on mean air

velocity and the hydraulic diameter of the duct. Valuesof f obtained from figure 51 of reference _ are plotted

against Reynolds number in flgurel. Data i_ fi6_re I_

of reference 5 kgree closely with values In figure I.

Determination of the Reynolds number is facilitated by

supplementary curves obtained by plotting the ratio ofmass rate of flew to duct perimeter against Reynoldsnumber for a number of air temperatures. The kinetic

viscosity of the air used in constructing the supple-

mentary curves of figure i was determined by Sutherland'sequation as presented in reference 6.

A typical value of &H/q for straight aircraft

ducts is 0.02 _, which is usually inconsequential com-

pared with other parts of the system, and the loss insections of straight ducts is generally neglected. Long

winding ducts of small dlameters, such as cabln-heaterducts, ere sometimes treated as attaint ducts of higher

than average pressure loss due to friction. The us_ of

a.-gE: o.o4 q

is recon_nended in reference 7.

_0 ° bends cf constant-area rectar_ular cross sec-tion. Pressure-less coef£iclents 6f gO b bends of

c-o--_tant-area and rectangular cross section given in

figure 2 for three values of Reynolds number based on

hydraulic diameter are derived from data appearing inreferences _ and 8 to 12. The beneficial effect of

large radius ratio appears throughout the range of Rbut the optimum aspect ratio shows a marked change with

Reynolds number.

9Q ° bends of constant-area elli_tical cross sec-

tion.- Pressure-loss _aracteristics of 90o bends of

c-'_tent-area elliptical cross section are given in fig-

ure _ for three values of Reynolds number. The datainclude circular ducts as a special case and were derived

from data in reference 5. The benefits of large radiusratio and the existence o£ an optimum aspect ratio arenoted for the bends of constant-area elliptical cross

section as well as for rectangular bends. The effects of

Reynolds number are much Sess for bends of ellipticalcross section than for bends of rectangular cross section

and appear mainly for the bends of high radius ratio.

|

• .<

NACAAPa No. L4 26 9

_0 ° bends of chansinK area.- Significant data (de-rived .from reference 113 concerned with the relation of

_ a_ea' 5h_/ige' _o"'tl_S'" l'oss- in _0 ° .bends of- a.-particulargeometry are shown in figure _. In .this figure the ratio

of loss in a bend with changing area to that in a bend.with identical inlet form but constant area is plotted

against the ratio of entrance width to exit width of thenonuniform bend. Important reduction of los_ in con-

verglnE bends and serious _ncreases in lose in divergingbends are noted; the loss increases are particularlyserious for bends of small radius.

Simple bends other than 90°.- No satisfactory" corre-

lation r_s been made o2 sara" £6# variation of pressure-loss coefficient with angle of bend. Pressure Io-".s of

_5 ° bends can apparently vary from one-third to two-

thirds the loss of a similar 90 ° bend, according to thetest conditions.

Co_ound bends.- Pressure-loss coefficients for threetypes of compc_----_end (fi_. 5) derived from reference 5are shown in fl_'.,re 6. Inasmuch a_ differences in thelosses between the U-, 7.-, and _O°-offset bends a_pear

from reference _ to be small and inconsistent, the curves

p_esented are aver'ages of results for the three types ofband. There appears to be l._.ttle vari--tion of loss with

Reynolds n_unber. Introduction of a 5-foot spacer bet.'_eenthe two parts of the compound bend has relatively llttle

effect on the over-all loss bnt tends to give highervalues for optimum aspect ratio. A comparison of the180°-bend (U-bend) data of figure 6 wl_h _he 90°-bend

data of figure 2 shows that the reletlve loss varies _oa marked degree _vith the radius ratio and aspect ratioof the bend.

Effects of surface rou_ness on bend losses.- Theeffee_ orsurr_ce rougj%ness on t_e'loases i_aight

pipes has already been given by the c_rves of fi_ame I.A study of pressure-loss data for bends of'an_les from_0 ° to 90 ° and radius ra_ios from i _o6 (r_fcrence ii)indicates that the influence of surface roughness on the

loss in bends, and _re_umably of other duct componentsin which major flow disturbances arise, is vary much

greater than can be attributed to the increase in skin

friction at the mean velocity cf flow. Analysis of thedata in reference ii suggests that the ratio of losses

throu6h two bend_ identical except for surface roughness,

I0 NACA ARR No. L_26

ts equal to the 1.75 power of the ratio of frictionfactors; that is,

(2)

(The subscripts 1 and 2 in this equation are usad to de-

note the two bends of di1'ferent surface rough-hess. ) Theexponen_ greater than u_ulty oar, be explained by the fact

that any devlaticn from a uniform velocity distributionbecause of extensive boundary-layer separation or the

e_istence of secondary _lows would require t_hat some of

the fl._w be at velooltles greater than the uniformvelocity. Equation (2) would not, therefore, be expected

to apply for a duct compo:_ent not involving extensive

seconda._y flows ow sepa_atlon.

Equation (2) can be used to correct the bend-loss

data of _,is report to values correspcndlng approximatelyto flow through duct bends wiDh rough sur1"aces. The

total-pressure-loss coefficient for smooth-surface bendscan be determined f_om the data curves of fi._Ares 2 to 4

and _. T_.e curves label_d "_mooth st_rface" _n figure 1

are used to detez_in8 the friction factor for smooth-

surface .bends. A reFresuntatlve value of frlctlon factor

for rough surfaces ccrr_sponding to ducts in prcdu_=ion

airpSane_ _Ith tb_ usual _nufacturing irregularitlesis b.Ol.

Vaned bends.- Vanes may often be advantageously use_

in duc-E-_en_s, espmclally when an unfavorable radius ratioor aspect ratio must be tolerated because of some llmi-

tation peculiar to the particular design. A correctly

desiened vane installation will improve the velocitydist_-_butlon at the exit of the bend and _ill generally

re_ce the pressure losses through the ben_. l_.e reduc-

tion in Dressure loss arises from the fac_ thac the flowin a good vaned-turn installation approaches that flow

which _ou_d occur Sf the pasaaEe were divided Iz_o

sm_i!er pcnsag3s of the same depth out shorter w_dth and,coneecuently, of more favorable aspect and radius r_tioe._hen more than tLree vanes are used, practical consldera-

tions usually require a bend with evenly spaced vanes andequal i_er and outer radii. The value that these radii

!

NACA ARR No. .. 11

may attain Is usually, limited b 7 .the. space .requirements:.Figure 7 shows an installation of thln olreular-are vs_sSand defines the variables concerned in the design of sucha vane installation. The vanes are equal in radius andchord to the curved portion of the duet surface. From

figure _ it can be seen that the chord o is equal to

2r sln2.E

From material given In referenae Ii, the following

expression for the number of vanes required Qan be dorlved#

2 _Vw i

The quantity AV is the vector difference of the veloc-ities upstream and downstream of the bond, as illustratedin figure 7. For a given bend configuratlon, therefore,the number o_ vanes depends on the llft coefficient at

which the vanes are to operate. If too high a lift coef-ficient is assumed in determining the number of vanes

requi_ed, high losses and a poor velocity distrlbutiondownstream of the bend will result. A_ assumed lift coef-

ficient that is too low will result in too marly vanes and

the total-pressure loss through the bend will aEain beexcessive. Reference 9 Indicates that, for thin vanes

i installed in a 900 bend, use of a lift coefficient of 0.8

glvos approximately minimum losses and a satisfactory

velocity distribution. It is not.known whether CL=0.8is _e optimum for th_n circular arc vanes for bend

anglos other than 90 ° , but a study of reference 17 indl-

i cares that use of this value in designing bends other

Othan _0 bends should give satisfactory results. Resultsgiven in reference 9 show that for a 90 ° bend the angloof attack of the vanes = should be _8 °, or 3? more than

half the angle of bend. For other anglos of bend, t_o

! " amount by which the ansle of attack exceeds half the

anglo of bond might be adjusted propor-tiona#ely to theanglo of bend as a first app_oximation; that is, for a

,. _5 ° bond, an ar_le of attack of 2_ ° would be indicated.

.For a 90 ° bend with inlet and outlet the stone inarea and shape, equation (1} reduces to

2 w

12 ARR No.

ulng the valueof OL = 0,8 for thin vanes, equa-

tion (3) becomes

n=2_'-_.. Ir/w

Results for vanes which have two different thickness

distributions applied to mean lines approaching a circulararc ape given in reference 9 and show that, for the opti-

mum vane installation, the loss coefficient AH/q. is

about 0.25, a value relatively insensitive to vane thick-

ness. For vane installations other than the optimum,

the losses are higher and vary cons&demably with the pro-file of the vane. The angle of attack fop thick vanesis approximately the same as for the thin circular-arc

vanes and small variations from the optimum angle ofattack do not appreciably affect the pmessume loss. Values

of CL from 0.9 to 1.0 ma@ be used in determining theoptimum nmnber of these vanes to be used.

Thin vanes of noncircular profil_ which are suitabl_for installation in bends of equal inlet and exit cross- •

sectional areas, have been developed theoretically byKrbber (references _, I_ i_, and 14). Profiles for these

vanes are given in table I and figure 8(a). Tests (ref-

erence L_) indicated that installations using a vane of

the type developed by Er_ber are very efficient, as shownby the low losses glven in figure 8(b). The required

number of vanes for a given installation can be deter-

mined directly from the chord length and the _ap-chordcurve of Ii8ure 8(b;. The break in this curve betweenangles of bend f_om 4_ O to 60 ° is apparently a result of

the methods used in developing the profiles. References 9,i_ and I_ give specific data only for angles of bend of_0 &, 45 °, 60 ° , and 90 ° .

Diffusers.- Losses of straight-wall diffusers of

circular cross section may be computed from the curve of

figure 9, which was derived from figure i0 o£ reference i_and figure 1 of reference 16. The loss coefficient is

given by the relation

" Ads/

NACA ARR No. IL_F26

where, k 2 is the quantity plotted in figure 9 againstthe' equivalent, oonioal. ;- angle of expansi.on,... The loss dueto an abrupt expansion is obtained from equati'on (_)-bytakir_, k2 equal to unity. To a limited extent, the

losses of diffusers of _oncirmula_ cross section; particu-larly those of square cross Section_ are approximated by '"the loss of an "equivalent oonloal diffuser" .which has acIPcula_ cross section and of which the leith, the inlet

apes, and the outlet area ape equal to those of the non-olroular diffuser.

The most efficient straight-wall diffusers are shown

in figure 9 to be those of equivalent conical angles ofexpansion between 2 ° .and'lO °. Prequen_ly, however,because of restrictions on the length of diffuser, it Isnecessary to diffuse at angles higher than i0 °. Ou_ved-

wall diffusers (references 14 and 15) , such as the designshown in figure lO, have been.found to have appreciablyhigher efficieno!es than straight-wall diffusers, espe-

cially at hig_: angles of expansion. The performance for

this type of diffuser is also shorn in figure i0. At thehigher angles of expansion, the lower pressure losses are

obtained by diffusing gradually in the first part of thediffuser and more abruptly in the last _art in order to

delay the separation point in the flow. Tests reported

in reference 15 show no gain when the angle 2_ is madegreater than 40 °. 0tner sources (unpublished) indicate

that, if the angle 2@ is greater than 60 ° , large losseswill occur.

Diffusers followed by resistance units, such asintereoolers_ are subject to lower pressure losses at

high angles of expansion than are indicated in figure 9-

An experimental investigation to determine the shapes ofcircular diffusers for highest diffuser efficienoles i_

diffuser-resistance combinations is reported in ref-erence 17. _'iEure ii is a sketch of _he optimum shapeand a plot o_ the included angle between the straight

walls of the diffuser 2_ a6ainst the equivalent conicalangle of expansion 28. The val_es of 25 are those

values that gave the highest diffuser efficiency. The

solid and long-dash curves of figure 12 show the pres-sure'losses _n terms o_ the loss due to sudden expansionfor dlffuseDs designed acoordlng to figure ii. Theshort-dash curve of figure 12, which is an extension of

the cu_e given in figure 9, applies to stralsht-wall

circular diffusers not followed by resistance and isshown for comparison.

I Illi il El I 1 a '

NACA A RR No. L_:;-'6

_E____.- The problem of taking branches fromamain air duct resolves _to division o£ the main air

stream and diversion of one or more of the consequentsubdivisions of the main stream. Division should be

made as nearly as possible on a basis of rel_tive air

flows and is best accomplished with dividers or splitters

of rather blunt-nose airfoil shape, such as the NACA 0021

airfoil section. (See fig. 13.) Enlargement of crosssections immediately downstream of the _oint of divi-sion and in bends is to be avoided. Entrances to branch

ducts should be normal to the air flow. Figure 13 illus-t_ates th3 application of these j)rincAples and shows the

division of the L_aln stream, the diversion of one stream,and the subsequent subdivision of ths diverted stream.

The internal-duct Inlet is a special problem associ-

ated wit/-, branch ducts. The inlet of a duct that taps

air from a chamber in which the air is essentiallystagnant is known as an internal inlet. Figure i_ shows

several examples of such inlets with accompanying repre-sentative values of pressure-loss coefficient taken from

reference ii. The designs subject to the least pressure

losses are the flared entrances, particularly the designusing a lemniscate. The equation of the carve in polarcoordinates is

r 2 = 2K '?- cos 2B

The.part of the lemnlscate uzed In. the inlet design ex-

tends over a range of B from 16 ° to _5 ° (fAg. i_).

Flow-resistance units set at angle to upstre_ duct.-The m_etlng at an angle Of the incoming air with t_e face

of a resistance unit causes a _otal-pressure loss that

depends on the muount of angle, t_he efficiency of the

resistance-unlt core in its action as a turning vane, and

the air-stream velocity. Data on these losses, from whlchthe curves of figure 15 were derived, wore obtained from

reference 18 and from the Wright Aeronautical Corporation

and the Naval Aircraft FactorT. The data apply to inter-

coolers, circular oil coolers, and a vlscou_-implngementtype of air filter. The geometry of the ducts and

resistances is also shown in figure 15 . Thu curves

indicate that the pressure loss is similar to the pres-sure lo_s of a duct bend in that. the aspect ratio of ti_e

resistance-unit air passages is a controlling factor.

laSS No. L4 -6

im_me

J,]

ILLUSTRATIVE PYU_PLES OF DUCT ANALYSIS

Several examples illus%rating the calculation of¢

pressure loss, ai_ flow, exit area, and internal drag

for duct systems I and IV of f_'_pu_e 16 are glve_ in. tables II to IV. Each. of the hypothetical duct system_

shown in figure 16 adheres to the same _eneral space 1

msquImements and haa a_4,ovsr-all Increase in the cross-sectional area from _ square foot at station 1 to h ¢ ._ _T_

).Q square feet at station 6. _he selection of the m,pressure-loss coef£1cients is illustrated, for s_stem I

in table II. Step-by-step computations for sys_ems.I

land Iv at@ 81yen in tables III and IV, and the pressure-loss dlstributlona of the four systetns are compared infigure 17.

Duct system I (fl_. 16) was desIzned accordin_ tothe two basic principles o£ dL_t desl_n set forth in the

section entitled "General P_ncip_es of Duct Design."The hiEh-_el6clty air at station _ is expanded in a

diffuser havin_ an e_tivalent c3ntcal angle'of expansionof 7 °, whici_ is shown in f!_e _ to be subject to mini-

num. pressure losses. _e d%ffuser is followed by a well-rounded 90 ° bend cf constant cross-sect_onal area. The

_est of ths dlffu_ion is accompllshed at a higher re_ein a d!ffu_e_..Lavln_ a_ e_ivalent conical angle of i_.80.

Altho_F_1 th_ rate of expanslon is high in the seconddiffuser, the loss is not excessive because of the low

dynamic pressure at the entrance. The second _0 ° turnis qu_te sharp but does not cause a large pressure lossb_cause of the low-veloclty air. Duct systen II_.16)

was designed so that oart of the._ren expansion is accom-plished in the first 90 ° bend. Duct system III is anexample of a compromise whlch emphasizos more than

system I the principle of havlr_ Io_ flow velocities."-The low flow velocity is obtained by diffus!nE at a

hlg_er rate of ex_ansior,. Duct systems III and IV repre-

sent opposite extr@mee in rolation to the Initikl expan-slon of the &It. In system III the expansion is accom-

plished rapidly in a diffuser having an equivalentconical angle of 16 ° located upstream of the first bend;.

in _ystem IV all the _xpa_slon is accompl_shed betweenthe two 9'0° turns, with thearea constant-from:stations 1

to "

The d_ct systems were assumed to be installations

in an airplane flying at Sea level in Army s_uamer air at

16 NACA ARR No. L_F26

a true airspeed of _00 miles per hour. For slmpllclt_the total-pressure losses from the free stream to station 1

were assumed to eqlml the pressure rise given the air bythe propeller; therefo._e, the total pressure at station 1

is e_al to the free-s_ream total pressure. The a_ia-

batic temperature rise from tSe flVee stream to s_ation 1was calculated by use of the followi_ equation from ref-erence 2 :

- - (5}

The total-pressure loss threugh each duct unit was calcu-lated from the curves of this re@oft as illustrated in

table II for e_stem I. Thm compressibility correction

to the dynamic pressure was **eglocted except at st_.tlons 0

and i because of tLe low velocities. The following equa-tion (from reference _9) was used to calculate the com-

pressibility factor Fc a_ stations 0 and i:

Fc=l+ +_

The temperature from stations 1 to 5 was assumed constant

because the systems contained no heat exchangers and the

static-pressure changes were insufflci_nt to cause sig-

nificant changes in temperature. With the foregoing con-ditions and assumptions, the properties of the air steach station were calculated as shown in tables IIi

and IV.

The total-preosure losses for each system are plotted

against the duct stations in figure 17, in which system IIs shown to be the most efficient.. The h_gh losses asso-

ciated with bends of increas£ng cross-sectional areas are

verified by the curve for system II. _,e curve for sys-

tem III emp.hasises the importance of efficiently d_-fusing the hlgh-velocity air even at the expense of

greater bend losses, provldin_ She ben_ design is rea-

sonably good. The data for system IV Indlcate the

importance of efficiently reducing the air velocity assoon as possible even in those cases in which the effi-

ciency of some of the £ollowing units must b_ reduced.

The calculations for system I ha_e been extendedto illustrate the method of obtaining air flow, exit

°.

ACA No. l?

area, and internal drag. _oause the ealculatlon of pres-_"_ops'ac_oss he_t exchangers is.a-pr_o.blom.outaide

the scope of this repo_t, tl_ heat-exchanser pressure d_.'opis not ccnsidered in the subsequent discussion. Thenature of t,he calculation Is in no way affected by this

simplification, b,_ the resultant drag, internal-dragpower, and exit ares will consequently be much too omallto be representative. A well-desi_ned exit duct wasassumed to extend from station 6 to statlon 7, the exib,

and the total-pressure losses fn this eontractln S section

were assumed to be negligible. Several mass. air flowsthrough the system were assumed and the estimated total-

pressure losses, exit veloclty, exit area, and internal-drag horsepower were evaluated for each sir flow. Thestatic pressure at the exlt was ass_ed to equal t_e

static pressure of the free stream; the temperature dropassociated with the drop in static preosure from station 6to t_e exlt at station 7 was _seumod to be adiabatic.

The fol!owin_ equation e_r_sses this adiabatic relation:

T 6 - T7 = AT e

The exit velocit_ V_ was calculated b I substitu_in_

AT c end _V6 in ecuAtloz, (5). "_o cslcul=.ti__ns ;'or"a

mass air flow of 0.109 s_ug DP.i" s._cond.are s,_u_a_ized

in tab£e III. T._ ".ntsrnel-drag hol,_o_ower caused bythe momentum deficiency of the dlschs_od a_- and th_exit areas required to obta;n cert_._n ma_s flows throug_

the sy4tem arc plotted against mass sir flew in figure l_Fro_, these curves the exit area required re._ a given _.assflow or, conversely, the _.ase flow ccr_espondlng to a

given exit area, may be deter_r_zed. If a heat exchanger

had been included in the fore_oin_ arrangement, thepressure drop ecro=s it, the rise _n coolins-alr tem-per,.ture through it, and the resultant dc_sity chan_eswould have had to be taken into account.

'CONCLUDING R'A']_P_. S

The pressure loss throu_h a duct component is.af-

fected by the natare of th$'enteriz_g flow and, when

uns_m3trical velocity distributions omcur, tl_

18 NACA No. L4_ 26

preesume-loss ooefficlents are higher than those givenherein for condlt_.ons of uniform flow. This cons!dera-tion raises the question o_ the aoouraoy with which theover-all losses for a duct sustain can be pP-)dloted by

summation of component losses obtained Smom _he mstemlal

in thZs report. As _et. no sstis,_'aotoz7 answer to this

question exists, but _hls lack of data _.n no _ey .tmpairethe usefulness of the material contained heroin for de-

s._.gnlnG duct e_stems fop a mlnimmu of loss.

Alt_hough the pressure losses in a well-desi_led duct

system should be small _ompared with %dle unavoidableheat-exchangur pressure 4_op, t_e marEin of pressure

available over pressure requlred is v3ry small, partlcu-

larly foP fuil-power climb; and e!Im.in_ion of unnecessaryduct losses often makes the d_fferenoe between s_n accept-

able and an unacceptable installation.

Langley Memorial Aeronautical Laborsto..vyNational Advisory Committee for Aerenau_Icz

Langley _Isld, Va.-, Kay 13, 19_

I

NACAa_ No. Ll_26 Z9

REFER_OES

• . .... ° .... r.-

i. Rogallo, F. M.: Internal-Flow S_stems for Aircraft.

NACA Rap. NO. 713, 19_i.

2. Rubert, Kennedy F._ and Enopf, George S. : A Method

for the Deslgn of Cooll,_ Systems for AircraftPower-Plant Installations. NACA AILR, March 1942.

3. Boelter, L. M. K., Morrln, E. H., Martinelll, R. O.,and Poppendlek, H. I_.= An Investigation of Air-cralt Heaters. XIV - An Air and Heat Flow Analysis

of a Ram-0perated Heater and Duct System. NACAA_R _,,o. hcoz, 19;dA.

4- McAdams, _illlam N. : Heat Transmission. Second ed.,NcGraw-Hlll Book Co., Inc., l_l_, p. 118.

5- Weeks, John R. : Pressure Imss in Ducts with CompoundElbows. _ACA A._R, Feb. 19_3.

6. Chap_,an, Syc!ney, anS Cowling, T. G.: The Mathnr2sti._alThecry of Non-Uniform Gases. Csmbrl_ge Univ. P_'ees,

1939.

7. Smihh, F., and Stott, J. R.: Losses In Cabin HcatingE_cts. Pe_. No. B.A.16_3, R.A.E., June in);1, andAddend:ml, Rap. No. B.A.1683a, Aug. 19_l.

8. Wirt, Lorlng: New Data for the _.esi_n of Elbows inDuct Systems. Gen. Else. R._v., vo!. _0, no. 6,June 1927, pp. 286-296.

9. Patterson, O. N.:Duct Systems.

1937.

Note on the Design of Corners in

R. & M. No. 1773, British A.R.C.,

i0. Patterson, G. N.: Corner Dosses in Ducts. Alrcra_tEngineering, vol. IX, no. 102, Aug. 1937, PP- 205-208.

ii. Abramovioh, G.: Fluid Motion in Curved Channels.

From Collections of Reports on Industrial Aerody-namlcs and Fen-Constructlon, Rep. No. 211 (text

in Russian), Trans. Central Aero-Hydrod_n. Inst.

(Mosco-), 19_5, p_. 97-15z.

D

°ram-

20 NAOA AR. Lip'26

12. McLellan, Charles H., and Bartlett, Walter A., J_. :

Invest4.gstloi_ of AID Flow in Risht-Angle Elbo_s

in a Rectangular IX:ct. NAGA ARR, Oct. 1941.

i_. }.ir_ber, G.: Guide _nnes for Deflectir_ Fh'.i4 Currents

_,Ith Small Loss of Ene;,gy. _NACA ']%1N._. 722, 1939.

14. Patterson, @. !I.: _e D_s.4.gn of Aeroplane Duct_,

Aircra:_t E_Ir, ee.q.ng, vol. ;_!, no. 125, Y_iy !9_),

15. Pstberson, @. N.: ACode_n Diffuscr Dezlgn. A_,crnfb

E_:inee1,_ng, vol_ X, no. llj, Sspt. i_58,2o7- 7 .

16. Gib_o_, A. H.: On _he Flow of ,ste_ theouCh Pipcs nnd

Pa'_sa_es Eav:r_ Conv_r'_!r_ or I_i,,erF,£,_ Boun_urie_

P_'oc. Roy. :_,,c. (I,or.do;';),_,,,, ..,'_'_r"A, rol. C_, t%o. 56__l._Pch 2, 1910, pp. >Co-p,c.

17 • I.'.cLeilan, ,_hsrles P_•, and ._ichoP.', Mark R. : An Inv_s -

ti._ation of Diffa_r-R_ _ b._ce Co_biuatlon_ inDuct Syste;ns. I_A_A AR._, _eb. 197_.

18. N£C,nol-_, ._:.:arkR. : L_vestAc.ation of Flow _hrouI>_ az,

In_crc.)oler Set at _arious Angles to the Sup@J.:.D.,ct. NACA ._ER, Aimll i_'_2.

19, GlauePt, H, :" The El._mcnts o_" Ae_ofoll _,nd Airscrev#

Thoory. OambrZdE._ Univ, Pr_.ss# 193.,, 9- I_.

!:

,J

t.

NACA ARR No. L)4226

TABLE I.- ORDINATES FOR KROBER VANE PROFILES

0.0_.05•i0

.15

.20

.50

.95

.60

.65

.70

.85

.951.00

....... )/,_...........i

90 ° bend 60 ° bend

0.000

.o87-

.].54•200

23

.2_

.219

.lOL

.oTz,037•000

45 ° bend

0.000

.04x

.o74

.i00

.x.24

•161

•166.148.x64•zS?

.129

.IIi

.096

.oTa

.o_8•026•000

0.000

lltll

.io5

•xo3

.o94

.o78

.o58

.o3o

.000

20 ° bend

0.000

.o)I

.o51

.o67

.o71

.o7_

.055

.oh3

.0;'4

.oO0

NATICNAL ADVISORYCOMEIT_ FOR AERONAUTICS

21

TAM n.- _TI_A_Z0,OF_O_AL-P_SV_-LOSSO0_IC_E,_SFORDUC_SYS_ I[Uassno_ = 0.I09sl_/,e_;_por_t_ = 584.4o ; abs.J

Inltlai|Zlnalstatlon_station

Controlling paraueters Calculated values

Duct component, rectangular diffusers

Diffuser

equivalentconical

angle ofexpansion,

26

(cegi

Initial- [Final-station station

cross- cross-sectLonal ucctlonal

arelz;

Diffuser I

coefficient,

k2

(fig. 8)aP@a#

I 0.250.5z5

Duct component, 90 _ rectangular bends

Bend '_'-_d

aspect ira_liusratio, ratlo,

1.0

1.0

N._ss flow

Perimeter'

ml_

\ ft -)o,o3.3o.0158

Diffuser

total-

pre s sure-loss

coefficient,

A_/q(',)

o.o}_.is}

.00

.78

Reynoldsi r.t_lb ___ ,

(fig. llb)}

570, OOO

155,000

Bend total-pressure-los_coefficient,

_H/q

(fAg. 2]I

0,069.5oo

IDiffuser total-pre.s-me-loss coefficient -_-- k2 - Ade_

NATIONAL ADVISORY.

COMMITTEE FOR AEHONAUTICS

M,

o

"=;_-'7-'-"-"_---_J_'_ I_L____ ____ILl J J[!! I I ........ - .......... I I I _ I_ ..... _ ....

i :: _)-. : ; f

,>. _ .<_..f I _,:,,,r,r_,".i,v ://F P

. , .g\ .006__ z d_ct/_th I _ _.004_- D h_,_,'o,,,t__,,,,,,,,,-,.,_ .):_-_;--'-__, ,d-.003_ P per�meter [_,","A/'4,_: E,'i

I°°e 3 p_,_o,u, r:j._.. "_ ,, ,Z\"_-../ J > /• I ,>--..I---J ,2l

.0010: " .... " _ _ _ _ I _,,i. C(_'_msreiQ! 'D,

i'_.O_ 6 " } ' _ ? I _ .-.-L----..¢..LJ_i _ i_;r.O06, _%' I -_ I I I 7"=" ooth',,,,,,-,',_.,._".q_k,_

/ 04 .u

, , _1! Ill oz' _"" III"°"

/ I , j. '00

Re(/holds number, R

(o) Re_Inold_number, I_OOO fo IO0_O00.Fiqure 1,-f-fiction-factor and Re_nolds number deterrnlmtion for.rtr_lgM duets.

>)

),

))

Zo

t-"

o)

F,.

#.,

. IOQ

(._ ' ,

3-,900

,,(

010:Z

pplou ha_l {q)

_ .OOO

• .//

", "//6/ Ill1

/All_ _///

//I _ __

20/

/0"_

_'0' -%

_0'__' '

?

__

_,-,_

07

7i.

NACA ARR No. L4F26 Fig.

lw

4

il,

Z

I l,. I _, • ' _1

Ill,;'" ,'ii _1 ! 1''_l_ i! "

i i '

....J I:

_3

Z

o

t._

_0O_

i

NACA ARR No, L4F26 Fig. 3a

Jo

G

oU

t ,09

t

!

I

\L

\ Rodb_ rotJ_

/r

//.0 i

/Jr

/

/._/ r__.__..r /

\\\ /" ,4

\

NA'II!l@l'l-rl

' . • '_A_t_et ratio j h/w

/

4. ,5 678910

_) Re_/nold._ nurnbew" :, 150._000.

Figure3_ To fcd'prea._vre -Io_, eoefficienf._ _orelliptical ,.0_ ° herod.

/

NACA ARR No. L4F'26 _i_. 3b

t'

['i

.ga

.8o

.7o

.5O

"q .,.50

o

I

L.

%%.

h.04I

0F.

.01

l?adiu# ratio_

'_//w

\ /r

\ / i

/'h\\

\'_ k \ ...... / / ,I

_ ' _ _ !I:__51/ / //\k - / /,

p

\k _ / II\\ _ _" _!

/j'

NA1]O__COlMITTEE:ORA

(b) t_eynolda number, _TO0,O00.

Figure ._ - Continued.

4 5 d .zdB[o

_A

NACA ARR No. L4F26 Fig. 3c

I:

.kr

!,i :

I

.6O

\"\ Rad,u; ratio. _ i

\,,-"\."\\--.L_4/II,,

L ADtCO_ JlT'i'EE f OR AE10101file

i I t i I I I I

.0/ 2 .3 4 .,,_ .6 .7 B 9 / 2 3

A_f ratio, h//w

(c) Reynold._ number, 600,000,Figura 3.- Conclude d.

4 S 6 7 89/0

NACA ARR No. L4F26 Fig, 4

/_

IZ i I 1 _ t IPodlu= r=tto, _/w/

-- 2.5 1,5 .5 !

rb ra+We

-S

%.o

_ [..

k NAI_ A_ ncs

O0 .4 B /2 • !.6 . Z_9 2.4

Wrdth of entrance/ wtdfh of" exlt,_Tg_re 4.- TotoI-pre_ure-lo_ coefficient £octor k I

for _)o bend of changing orea.

I.

iL

NACA ARR No. L4F26_ig. 5

NACA ARR No. L4F26 FiB. 6a

......... . ,. . . ,...

O2

(q/Bends wifhouf apaeers; Re_tnold_ nut,r, JTO_O00.Figure 6.-Tofal-precaurQ-Iosa coeff /'c/enta for compound

rec_ungular U_ Z-, and go e_ oFFaef benda.

i i i i i . , . ..1

NACA ARR No. L4F26 _ig. 6b

iL-,

.0#.£

NACA ARE No. L4P26 Fig. 6c

Q

a|

&.

I

_. -,.v./'._ ..,_--

" 1.00

f/

./'// /.

/ f

. /2,"'-..__Iz S_ I / /__

"_"_ "/.SO t / /1_ _"_,_l _ "_ _

4

._ _.f9 )_.. = _ = _-

_'110Nl,l _ lSOHf

COl _ FOR A liON_;[IS

.OJ

Atpeet ratlo_ I_/w,l s _ 7O_lO

(¢) Bend$ with 3"foot Jpaoer _ _e_Inoldt number s 600_000.

Fi 9 ure G, - Concluded.

/I

1 /

Fig_re 7.- Dend

I

NA_i. N3VlWIrfCOUN_ FORdB_ON/UJIIW

with thin circular-arc vanes.

=¢

('3

_0

==o

4=,z3¢oo_

i_.oq

.4O

0 .I0 o,_0

Ancjle of bendj/3(d 9)

1__05, _ 901.

--..2

•_ 0 .40 .50 .60 .70 .80 _ ,90 1.00

x,_ '

(aTVone profiles (x and _/_coordinata_ of poin_a on vone profile).

Figure 8.- Design d_t_ for Kr_ber thin w_e_.CDat_ for ['3= 30;4-_60_¢znd qO ° _:_ken from eeFerence 9 .)

C33.

Zo

O_

F-OQ

CO

K.%_iI

III

m_

_0

U

0 Zo 30 40 5o O0 7O 80

Angle Of ber_l_/_, de 9(b) Vane characteristics at a Re_tnolcls number of 40,000.

Figure 8 .- Concluded.

Z3.£3>

>

0

_oO_

k_oQ

COc_

D

.ta

F

//

II

0o 4 8 12 16 zo z4 z8

E_uly_zlent comcoJ ezngle of

ff

r

i Adi! z

Qll ITEE )R_ ONAUlCS

3Z 36 40 44

expo.nalon t _ , dog

FLgure_7 Tot(_l-pre$_ure-loa$ coefflceent factor k_straight-wall conical 41ffuaer_.

Z

(-j

o

t_

NACA ARR No. L4F26 Fig. i0

T

I

Z_rnax" 40 ° _9;rnin " 15°Equation ofcurved-_ecr/onprofile•

_._._ IiTI I i_bdf II_. 1.i/. !. Je"Fl i i.._1.:...!.....L._-! <_1i. I..1..t.;-I t I 1 _;@%_.

0 _ 8 IZ. I_ gO Z4 28Equivalent con#col angle of expansion, Z 8,de 9

Figure lO.- Total-pres_ure-loss coefficient f_ctor kzfor curved-wull con/co/ diffusers.

t jf // /

z+ , A. =z-_ /Adi l ]

oq

/ //_ " 'Ado

/

° i / "/_8

+ // <_+ //

//'I t I

O0 I0 ZO 30 40 50 _0 70 80

_FcLuivczlen_ conical angle of expo./_,_,on, Ze, d=_

Figure I/.-Design of conical dlffuaer_ {of/owed bg re_ietance unit_,

| I

• l_esist_ce unit"7

' _r.. _ /a . /'-

90 ,_j

Z

o+

t-'

too_

"L_r

Z

CJ

_J

oo

_-_

/0 ZO 30 40 50 70

E_u#valen# comc<zl oJ_Rle of exl_n_lon, _.t9, deg

F#_ure 12..-To_'oJ" pressure-loss coefficient l_¢for k¢ for"

conical dlffUSeF_ illustr<zfed in fl_ure II.

80 90.

\,

"Rp,

NACA ARR No. L4F£6 Fig. 13

._tat/on UppeP: Lower, + - _ement_:sureoce s_rPo_

" o .g,,2._ _,_1

• I _.ooI _.z,z l-O.zzI 7'.SOl 7.,_I-7._I lo,ool a,+oI.+,zot +,8,ooi o_l o,_._

+ -+o ..--,,-- ! zo.oo i +o.o4ti-+o._! U, 001 00,40 I-/0,_0I/ ,_0.00 I IO.._OI -,O

-|00 Io tO ......_ + rim.c_,_ ¢mmmum_

NACA ARR No. L4F2_Fig. 14

o

Ea.u_t,on ot: lemn,sc_t_

o Po/_r coord,ne2tes

r.,OmlITIEEFOR_i_I_TIOI

F_gure ;4.- Tntern_l-duct-inlet design,s a.ndtotal-pressure loss coefficients.

iG

NACA ARR No. L4P26 Plg. 15

Cooliny._, l L55 C/_'C_Y i' oil coolurlntercooler ,

tu

_s-______-_:7 _ _iE--[ntercooler , _w.a 644 V'_c°u= - /mP/ngeme_t

type o/r filter

NAC_ ARR No. L4F26 Fig. 16

Illi

:D

NACA ARIRNo'. L4FP6 F£g. 17

/I

/LL ' /

I

I

/

!

/

.0

I / L,

CI_MITTEEF,)RAEROHAUTICS

/ Z jr 4 5

F_g_re 17.-" Compo.f'i$on oY tol:o.J-pressur'eIo3ses _:hrough s_mple duct s.ys_em.s.

I .............

NACA ARR No. L4F26 Fig. 18

6=al_ - lOWW_7 w I

\

E R R A T A No.. 1

_ACA _a L4F26

DESIGNOr Po_m-Pum_ I_ST_U_IONSPRESSURE-LOSS CHARACTERISTIOS OF DUCT COMPONEBTS

By John R. Henry

June 1944

r-

' L_ -.-s --¸ I I

Pages 8 and 9 and figures 2, 3, and 6 have been corrected to include a

calculated friction loss in the over-all loss coefficient for the

bend. The corrected pages are attached to replace the corresponding

pages and figures in the original version of this paper.

NACA-1LamzI_¥ - 1|o24-52 - 350

78

B ¸a dB

E R R A T A No. 1

B

NACA ABR _F26

velocity and the hydraulic diameter of the duct. Values of f obtained

from figure 51 of reference h are plotted .against Reynolds number in

figure 1. Data in figure 13 of reference _ agree closely with values in

figure 1. Determination Of the Reynolds number is facilitated by supple-

mentary curves obtained by plotting the ratio of mass rate of flow to

duct perimeter against Reynolds number for a number of air temperatures.

The kenetlc viscosity of the air used in constructing the supplementary

curves of figure 1 was determined by Sutherland's equation as presentedin reference 6.

A typical value of AW/q for straight aircraft ducts is 0.02 _,

which is usually inconsequential compared with other parts of the system,

and the loss in sections of straight ducts is generally neglected. Long

winding ducts of small diameters, such as cabin-heater ducts, are some-

times treated as straight ducts of higher than average pressure loss due

to friction. The use of

_---= o.o_, !q D

is recommended in reference 7,

90 ° bends of constant-area r_ctangular cross section.- Pressure-loss

coefficients of 90 ° bends of constant-area an_ rectangular cross section

given in figure 2 for three values of Reynolds number based on hydraulicdiameter are derived from data appearing in references 5 and 8 to 12.

The data of reference 5 are presented as a loss coefficient chargeable to

turning which was obtained by subtracting from the measured over-all loss

of the combine_ approach duct, bend, and tail pipe a calculated friction

loss for the approach duct, bend, and tail pipe. All the bend data pre-

sented herein have been reduced to an over-all loss coefficient for the

bend proper, or the data of reference 9 restored to an over-all loss by

adding in the calculated friction loss of the bend. Figure 2 indicates

that increasing the radius ratio beyond a value of about 2.00 yields no

further reduction in loss, and that the optimum aspect ratio varies

markedly with Reynolds number.

•90 ° bends of cons%ant-area elliptical cross section.- Pressure-loss

characteristics of 90_ bends of constant-area elliptical cross section

are given in figure 3 for three values of Reynolds number. The data

include circular ducts as a special case. The same general effects of

radius ratio and the existence'of an optimum aspect ratio are noted for

the bends of constant-area elliptical cross section as well as for

rectangular bends. The effects of Reynolds number are much less forbends of elliptical cross section than for bends of rectangular cross

section.

NACA=Langlry - II-24-5_ - 350

/

r

NACA ARR L4F26 E R R A T A No. i 9

90 ° bends of changing area.- Significant data (derived from

reference ll) concerned with the relation of _rea change to the loss

in 90 ° bends ofa particular geometry are shown in figure _. In thisfigure the ratlo of loss in_ bend with-ch_aging area to that in a

bend with identical inlet form but constant area is plotted againstthe ratio of entrance width to exit width of the nonuniform bend•

Important reduction of loss in converging bends and serious increases

in loss in diverging bends are noted; the loss increases are par-

ticularly serious for bends of small radius•

Simple bends other than 90_.- No satisfactory correlation has

been made of data for variation of pressure-loss coefficient with

angle of bend. Pressure loss of 4_o bends can apparently vary from

one-third to two-thlrds the loss of a similar 90° bend, according tothe test conditions.

Compound bends•- Pressure-loss coefficients for three types of

compound bend [fig. 5) derived from reference 5 are shown in fig-

ure 6. Inasmuch as differences in the losses between the U-bends,

Z-bends, and 90° offset bends appears from reference 9 to be small

and inconsistent, the curves presented are averages of results for

the three types of bend. There appears to be little variation of

loss with Reynolds number. Introduction of a 5-foot spacer between

the two parts of the compound bend increases the over-all loss appre-

ciably due to the added friction loss. A comparison of the 180 ° bend

(U-bend) data of figure 6 with the 90 ° bend data of figure 2 shows that

the relative loss varies to a marked degree with the radius ratio and

aspect ratio of the bend.

Effects of surface roughness on bend losses.- The effect of sur-face roughness on the losses in straight pipes has already been given

by the curves of figure 1. A study of pressure-loss data for bends

of angles from 30 ° to 90 ° and radius ratios from 1 to 6 (refer-

ence ii) indicates that the influence of surface roughness on the

loss in bends, and presumably of other duct components in which major

flow disturbances arise, is very much greater than can be attributed

to the increase in skin friction at the mean velocity of flow.

Analysis of the data in reference II suggests that the ratio of

losses through two bends, identical except for surface roughness,

NACA-I_,n@Iey - 11-9.4-52 o 350

NACA ARR L_F.26

g

E _R'AT A" No. I

m

Fig. 2a

#0

U

o

ulv]

u_

_.04I

-_.03

.0Z

.0/

. .... i . ,.

• ! . |

js

.2, i_ .-i-._ .6.7.agx z ,3A:rpec_ rQtio, h/w

(a) Reynolds number, lO0_O00,Figure 2.- Total-pressure-loss coefficients

rectangular 90° bend5.

Radlus_/_

2.502.001.751.50/.25

.76

ratio,_.__

I f I ;

I I 14 5 6 7 89t0

for

,L'

NACA-I_ngley l 11-_,1-_2 - _,_{]

x_CA ARR L_Y26 ER RATA No. 1 Fig. 2b

Io

2. ,3 .4 ,5 .6.7_.9 I 2

Aspect ratio, h/w

(b) Reynolds number_ 300,000.

Fiqure Z.- Continued.

3 4 5 6 78910

NACA-l.,anlley - 11-24-52 - 350

'.._ .. - ........

NACA ARR L4Fe6 E R]_ ATA No. 1 Fig. 2c

\

\\

\\\

U

"7".o7

rl.I

.O2

.01

_N.% ,,

h\

\

"_ / .>

2- .3

,, ,,J%.

_J

"_._.__..%

.5 .G .7.8.9 I

Aspect ratio, h/w

: --: --- ..... : : F

// /

/ /r.1/

Jf

#

,/ // /

/ /

/ ,,/ j

-=

2

/

J

(c)Reynold_ number, G_.F,#ure Z.- Con¢laded.

Radi_wra_o,4003,002.5#2.001.75

1.50t.25

_l Z)O

3 4 5 6 7,$910

NACA-]..angley - 11-2A1-I'_' - 350

N_CA ARB L4F26 E RKAT A No. 1 Fig. 3a

°

.4O

U

_A

.o_

L

I

I

_! _ _ , J , L

\

\F\

_ =

I

_ _l._|O__. I''

i-'_°_0 ' , .I

/_ad _u$ Fatio t

"4,00.... 3.00

-2.00.l,gO -- --1,00,75

rI:I.o_ I I II

.2. .3 .4 .5 .G.7.8.,91 Z 3 ,_ .5 _, 78.910A_pecf ratio,, h/w

(o) Re-_/no/da nurn_:_e," j lgO, O00.F/'_ureS_ 7"of_l-pre,_r'e-/o,_e ¢oefYicie_._ _or

o / i /ptie_l .¢_0 ° be_d.

NACA-11.anfflly - 11-2.11-52 - 350

......... .,,_. ,

w

NACA ARR L_F26 ERRATA No. 1 Flg. 3b

.70

.60

_.30

o 20_=.,

o ,15U

InOl0I

_.o_,.os

?.04

N.03

.O2

.0/

.. L * * |

,%

\

,%,"

T',¢)%,

.,JJ,. /

/ /• I

/

/' ,_/

I

/_adius Tatio_r/w

4.0&........ 3.00

-2.0D.... 1.50

...... ! .0075

.2, .3 4 .5 .& .7.8.91 Z 3

A_pecJ" rdf/o; h//'w

['bJRe_/nold# numL:_r, JO0)O00,

Figure .5 - Centinued.

I)I

4- 5 678910

NgC,',-/.angle/ - II-24-52 = 3_0

_ACA APa LaF26 ERR ATA No. 1Fig. 3c

.80.7O.60

.50

4O

_.._o

,®.20

OU

_..!

_ .o6_ .os_.0_¢5

_- .o3

.O2

.o/

• " _ _ . _

_ _ _ = = ....

\

\",

%

%\

. \

f

__, 4 t

/"

/f

/

/' /

?

.2_.. .,3 ,4 .5 .G .7.8.9 I 2_

A_pect ratio, h//w

('c) Reynolds number, 600,000.Figure 3.-Concluded.

Redius ratio,

4.003.002_.001,50t.00 --.75

,_-3 4- 5 G 78910

NACA-[,4t_tI_IOy - 11-24-52 - ,._5_0

I

• - _,.,t-.__. L_" . -

_' .4,a,

,ll

NACA AER L4F26 ERR'A T A No. 1

.i

Fig. 6a

.70 ......./o0

50 ......__ _ i L i ....

.-40

¢:OJ5,:c."t-,

,J

(

.07.Ohgl

tn ,05k,

.04

P-

I..,.,j..-- I

:Y ,v ........

_...._ I ,: _.V __....-

.20 ..... _ .... -_

.03

.02

. L

Radius rutio_

3.002.502.DO1.751.50

..... 1.25....... /.00

-- .75

.0/.Z_.. .3 # .5 .G .7.8.9 I 2.

A=pect ratio, _/'w

I ! I

3 4 5 4, ? 8g/o

(¢/ gends without ,_pacer#; Regnold_ number, 300,000.

F/gure 6.-To_a/-pre,c¢ure-los3 coeFF,'c/'ent3 For compound

recP<_ngutor U3 Z', ctnd 90 e- oFF._et bend,_.

• ,.=...: •

@

NACA ARR LAF26

@ •

ERB ATA No. i Flg. 61o

.6e

.4#

e%

tn

04

.O3

.O2

(b) Bend,_

!FJw "_".7_" /

/I"

_i"f

P

/f

.. "" /

i.w..1

.. .... .--..- j j,-

.3 .4- .5 .& .7.8..9 1

Aspec%

t_odius rc1_ioj

4.O03.002.502.00_1.75/.501.25i.oo

.Tg

!!,l I ]

_ 3 4 5

r a t ,o, h/,,,& 78_io

without apaeera ; Re(/nold_ .umber; 600_000.

Fiqure 6. - Continued.

NACA-LaaKIo? - II-N-6i - 3BO

I ......

_f

!°s,

w_t d

4b =

NACA ARR L4F26- E i_ 'R A _r A

I J .

No. 1 Fig. 6c

"Ik4

0

's-.,

O]OO

caE)[

,a

Radius TatiO,

"4.003.002.50-_.001.75

.... /.5OLt5i.00

75.... o____

.02

,Ol .2

(¢) L_e n d,s

.3 4151r,, I/t_pecf ra fio_

wifh 5 "foot ._pecerFi 9ure 6. -

2 d 4L 5 (o 78910

Pfe_tnold_ numberj dOd_O00oConc/uded.

NACA-LanBley - 11-_4-52 - 350