REPORT. No. 783

COMPRESSIBIJJTY AND HEATING EFFECTS ON PRESSURE LOSS AND COOLING OF A BAFFLED CYLZNDER BAR;REL

By A B T H ~ W. GOLDSTIIN and HE- H. ELLIRBBOCIZ, Jr.

SUMMARY

Theoreticalinvestigations h v e shown that, became air is compresdle, the prtxsuredrop r e q u i r m for cooling an air-cookd engine wid be much greater at highaltitu&esand high speeds than at sea level and low speeds. Tests were conducted by the NACA to obtain some experimental con- firnation of h e&t of air compressibildy on cooling and peaewe loss of a bafled cylinder barrel and to eva -h ie mrbw rnethd.8 of analyh. The r& reported in i9k present paper are regarded a8 preliminary to i k t s on dngle-cylindm and multicylinder engines. Tests were conducted o w a wide range of a i r $ f ~ o w s and o h d y a&?&udes.

The results indim& that, for a given air wig&Jlaw, the r e d d pressure drop bmed on awage cooling-uir W y App.,1pr, which hm been wed to c o r r a heat-transfer cool- ing dala, & not constant f o r diferent air densities (Ap, cooling- air pressure drop across the engine; porlpt, ratw of atierage coolingair density to o h d y at sea level). Engine-cooling uariabh should therefore not be plotted against pressure drop.

dala is ehown to be the air weigh.tfEow; the reduced pressure drop b not s u h b l e for this p q o s e . An a n u l y h bused on the essumption o f u n ~ m $ m is shown to be sat.isfactory for estimating i9k egat o f compressibiliiy on data obtained in these tesls. A simpler empirim? method in which compressibility and heaing egects can be estimated Z(MB found for correlating the test data on presme loss.

From th4? present t&ts a corr&ing variable for heut-transfer

INTRODUCTION

Some investigators have heretofore correlated c o o k data for nir-cooled engines with the cooling-air pressure drop- (reforonces 1 to 4). The effect of compressibility was taken into account by using tho product of the pressure drop and the nvarnge of the air densities a t the front and the rear of the cylinder ns the correlating variable rather than the pres-

sure drop alone. With the high rate of heat exchange and the high air velocity between the fins required for effective cooling at high altitudes, however, a large airdensity change will result. This change in air density is attended by an increase in velocity, and an additional pressure loss will be incurred a t the b d e exit where this momentum will be lost. Estimates of the increase in pressure loss caused by air compressibility in engine-cooling systems with bnf3ed cylinders were made in references 5 to 9. The analyses of references 5 and 9 were based on the assumptions of one- dimensional gas dynamics, but no experimental data were available to support these analyses.

An investigation was begun by the NACA to obtain experimental confirmation of the effect of compressibility and rate of heat transfer on pressure loss and cooling of a b a e d section of a cylinder barrel and to evaluate the various methods of correlating these data. The tests covered a range of simulated density altitudes from 4000 to 33,000 feet, of velocities between the fins from a Mach number of 0.05 to near sonic values, and of h a t inputs from 0 to 500 Btu per hour per square inch of cylinder- wall surface. This investigation wns conducted a t Langley Memorial Aeronautid Laboratory, Langley Pield, Va., during 1942.

Acknowledgment is made to 1%. Frank E. Marble of the Supercharger and Airflow Research Division, Aircraft En- ,&e Research Labomtory of the NACA for his suggestion that the Prandtl-Glauert compressibility factor be used to correlate the results of the present tests.

ANALYSIS ONJC-DIh€ENSIONAL 668 DYNAMICS

The analysis of the flow around a b a e d cylinder is based on the assumptions of one-dimensional gas dynamics. The equations for the pressure and density changes through a

185

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186 REPORT NO. 783-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS

baffledcylinder system (Sg. 1) are developed by the follow- ing analysis, which is similar to that of reference 5.

1. The heat transfer between stations 1 and 2 and between stntions 2 and 4 is estimated.

2. No loss in total pressure is assumed from station 1 to station 2.

3. The pressure and the density at station 2 are then cal- ' culated from the heat-transfer estimate, the stagnation

pressure, and the maas flow.

3

RQDaE L-&& WltndfS, MeS, Mp- and rnwmfngstatfan h t f O m used in tests.

4. The analysis of the flow between'stations 2 and 3 is based on the assumption of uniform flow of a compreasible fluid with friction in a straight duct.

5. The loss at the b d e exit is computed from the mo- mentum equations for uniform flow at stations 3 and 4.

Change in gas state between station 1 and station2.-If the heat picked up by tlie air between station 1 and station 2 and the weight of air flowing through the b d e axe h o r n ,

where

Hi rate of heat transfer to air between stations 1 and 2, Btu per second (The method of obtaining El is given in appendix A,)

W weight of air floying through baffle, pounds por second

c,

T2,* Tl,i A complete list of the symbols used is presented in appendix B.

speciiic heat of air a t constant pressure, Btu por

stagnation temperature at station 2, O F absolute stagnation temperature at statibn 1, O F absolute

pound per O F

Stagnation or total temperature and pressure as usod in this report indicate gas properties that would obtain if tho kinetic energy of the moving gas were isentropically con- verted into enthalpy. The temperature may bo con- sidered equal to the static temperature at station 1 becauso the velocity at station 1 is negligible. If TI#,, W, and HI me known, the total temperature a t station 2 may bo obtained from equation (1).

The assumption is made that there is no loss in total pressure from.station 1 to station 2 and that the stagnation state of the air at station 2 is b o r n . Then, from the relations

W gA2-mv1 --

and

and by means of the relations for isentropic change, the true- stream density and pressure may be eliminated and the stagnation density and pressure inserted to give

(4)

where

g A2

b

V,

M4 y

p2

p2 ,

acceleration of gravity, feet per secondx cross-sectional mea of free-flow space at station 2,

density of air at station 2, slugs per cubic foot (based *

velocity of air in fin passage a t station 2, feet per

Mach number at station 2 ratio of s p e d c heats for air (1.3947) static pressure of air at station 2, pounds per square

stagnation air pressure at station 2, pounds per square

stagnation air density at station 2 (computed from

true air-stream temperature of cooling air at station 2,

square feet

on p2 and Td

second

foot

foot

p p , and T2, 0, slugs per cubic foot

O F absolute T2

PRESSURE LOSS AND COOLING OF A BAFFLED CYLINDER BARREL

Raws 2--BalntIon between stsgnaffon state and static state of air 83 detmmhed by mam lbW.

When b V l ) i / p l , g h , l is known, M, can be determined h m equation (4); the ratios h/h, and pllpl. I can be determined from the isentropic-change relations. A chart based on equation (4) and the isentropic relations is given in figure 2.

ahange in gas state between station 2 and station %-The pressure drop through the b d e from station 2 to station 3 is given by the following equation, which has been modified from the corresponding equation in reference 5 by inserting tho Value Of c D , f in krmS Of cD,f , f : .

where

42

UDJ

dynamic pressure at station 2, (i P P ~ z ' ) , pounds per

friction-drag coefficient between stations 2 and 3 square foot

UDJ,( frictiondrag coef€icient between station 2 and sta- tion 3 baaed on average of 'G and p3

0 3

Pa

P3

P3

v-

187

friction drtbg from station 2 to station 3, pounds

dynaJnic pressure at station 3,

square foot static pressure a t station 3, pounds per square foot density of air at station 3, slugs per cubic foot velocity of air at station 3, feet per second

If the value for the local frictiondrag coefficient c D J , ( is assumed constant for all elements of the path, Of would actually be obtained by a process of integration. The value of CDJ,( should therefore be calculated from Of by means of some integrated mean value for %pV1. The value calcu- lated from the arithmetical average of p, and ps, however, is used aa an approximation. If this approximation is good, CD. ,( thus calculated should be independent of inlet-density variations for k e d values of Reynolds number and equal to the value that would be obtained with an incompressible fluid. By means of the continuity equation, the relationship betmeen C0.f m d C D , , , r an be established BS

The density ratio required for the solution of equation (5) can be calculated from the following equation, which is modified from the corresponding equation in reference 5 by inserhg the Value for C D . 1 in brmS Of CD, f . 1 give

where

(7)

H, rate of heat transfer to air between stations 2 and 3, Btu per second (The method of determining El is given in appendix A.)

A convenient method of determining &/pa uses the vnxiables

p'=Pg/P3 (9)

(10) p'-1 M,p=

yp' [* ( 1 S p ' ) f ( p ' - 1 ) ] + ~ 1 (1-p'g)

When use is made of these dehitions, equation (7) becomes

M2= M l + T'Mbp (12)

Because Ma2 and Mbp are functions only of p' and CD. 3, (,.for each value of CD. f , g the variable a62 may be plotted a g m t M t and p' may be plotted against M2 by use of the defini-

188 BEPORT NO. 7 8 3-NATIONBL ADVISORY COMMITTEE FOR AEROXAUTICS

tions for M,Z and M:. These plots are shown in Sgure 3. The vdue M,Z must, however, be the ordinate satisfying the linear equation (12) with M; as the y intercept, M: as the abscissa, m d T' as the slope. The intersection of this line with the curve of 342 against M: for the given CD3,i. determines M:. From the curve of M: against p' for the given CDjVr the vdue of p' can be obtained.

Change in gas state between station 3 and station 8.-The momentum equation characterizing the pressure loss between station 3 and station 4 is derived for the bafEe with a tail- piece. This loss as given in references 5 and 9 was for a b d e without a tailpiece, where station 4 was in a section of very large area with very low velocity. For the present m e the momentum equation is

(13) PA sin 83--plrir+ S pdS,-Da= 9 (Vr V. sin

where e, angle between radii of cylinder to cylinder rear and to

p4 static pressure at station 4, pounds per square foot A, croswectional area at station 3, square feet A, cross%ectional area of b d e exit at station 4, square

p static preasure, pounds par square foot dS, projection of any element of cylinder-wall surfaco and

of curved part of b d e surface bacg of station 3 on

component of drag force normal to plane of & and of-

velocity of air a t station 4, feet per second

station 3, degrees (See fig. 1.)

feet

plane of A+ square feet D3

1 v, fective between-stations 3 and 4, pounds

PRESSURE LOSS AND C O O L M G OF A BAFFLED CYLINDICJR B-L 189

The integrd of p d s , is taken over the entire surfam bounding the fluid between stations 3 and 4 except at flow cross sections of stations 3 and 4. .

It can be shown that

f ds,=A,-& sin e, (14)

The preasure gradients will be proportional to the kinetic onergy a t station 3. Therefore, if

if the coefficient for friction drag in the baffle exit is

and if these symbols and the continuity equation are used, the momentum equation may be expressed as

In this equation the term 2(A3/A3 sin e, indicates that the momentum loss caused by the fact that the stream at the rear of the cylinder is not directed straight back cannot be neglected. This direction of the stream, however, tends to increme the value of 6 and the pressure recovery. The recovery coefficient G, therefore, in some measure compen-

satas for the fact that e,#90°. W h e n z is small, alI the

terms become small and consequently p3 is approximately

Aa

equal to p4.

For tho present report the losses uross the cylmder will be represented by equations (5) and (17). In the actual prac- tic0 of predicting the pressure losses, once the coefficients of equation (17) are evaluated, the density change may be evaluated from equation (17) nnd the e n e w equation.

APPLICATION OF PRANDTL-GIAUERT COMPRISSIBILITY FACTOR TO FLOW ACROSS A BAFFLED CYLINDER

Tho foregoing theory for flow of a compressible fluid is applicable only to the w e of uniform velocity or onedimen- sional flow. For two-dimensional flow, the Prmdtl-Glauert factor 4- is used to compute the effect of compressi- bility. The Prandtl-Glauert factor is strictly applicnble in flow conditions quite different fiom those ercisting around the baffled cylinder nom being considered; therefore, this name should not be used for this application of the factor

but will be used for convenience. The proper npplication of this factor is to static-pressure variations in the flow field of a body causing small perturbation velocities in an infinite uniform flow field with a frictionless, compressible fluid and with no heat transfer. In that m e the difference in static pressure at my point in the flow field from what the static pressure would be with an incompressible fluid can be com- puted by the Prandtl-Glauert factor 4- in the equn- tion (reference 10)

or rr

where Po

P O

MO P i

Po

VO

CPJl CP,i

pressure of fluid that is characteristic of flow, pounds

dynamic pressure of fluid that is characteristic of flow per square foot

(+P~V?), pounds per square foot Mach number that is characteristic of flow static pressure a t same point as p with incompressible

density of fluid that is characteristic of flow, slugs per

velocity of fluid that is characteristic of flow, feet per

pressure-loss coefficient with compressible flow p rme- los s coefficient with incompressible flow

fluid, pounds per square foot

cubic foot

second

The factor 4- was used to reduce the totnl-pressure- loss data to values that might be expected without compres- sibility effects. The application of the factor to the present data is to be regarded solely as an empirical method of cor- relation. No rational bmis for the use of this factor is presented herein.

The preasure drop used in place of p-po in equation (18) for the b d e d cylinder is pl.c-p4,c. The method of dculat- ing po and Mo was empirically dete&ed by &ding the pressure and the temperature that mould give the best correlation of the data with different densities and various rates of heat transfer. The factor CP., was then computed.

The total-preasure loss to be expected with an incompressi- ble fluid Api is then

843110--50-13

190 REPORT NO. 78 3-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS

For the same ma.w flow ( p V ) but with standard density p , , C,,, dl remain constant because it depends on only the Reynolds number. Then

where

A p i J

pa

From equations (20), (21), and (22)

loss in-total presure under standard density condi-

standard density (at 29.92 in. Hg and 60' F), slugs tions, pounds per squme foot

per cubic foot

where AP 1 =PI. 1- P, ,I

THE EFFECT OF COMPaEBBIBILlTY ON HEAT TRANSFEE

The effect of compressibility on the heat--fer co&- cients is estimated by the effect calculated for a flat plate by an equation given in reference 11. If the temperature of the plate is assumed to be 300' F (an average ik and cylinder temperature to be expected with a rear spark-plug temperature of 450' F), the Reynolds number is assumed to be 3000, and the free-stremn air temperature is assumed to be -67' F (the temperature at high altitudes where com- pressibility effects in airaoled engines may become critical), the effect of the free-stream Mach number M on the local heat-transfer coefficient h, is given by

where hZ,{ is the local h e a t - m f e r coefficient that would e t with an incompressible fluid. The effect mill be slightly less than shown in the foregoing equation for two reasons: (1) the value h,,< is proportional to the local skin-friction coefficient, which in reference 12 is shown to decrease slightly with increase of Mach number; (2) the highest possible value of AP= 1 d not &t over the entire cylinder. In practical crtsea M p mill not be unity at any point around the cylinder. Consequently, the effect of compressibility on hecbbtmnsfer coe5cients for the cylinder can be expected to be negligible.

APPARATUS AND TESTS TFST SETUP

The copper-plated steel barrel section used in the tests mas 136 inches long with a 5%inch bore. The &IS on the cylinder mere 0.50 inch wide, 0.036 inch thick, and spaced 0.105 inch. Inside the cylinder was a grate to aid the pickup of heat and to reduce the temperature variation around the inside of the cylinder. A metal bd3e with a 6-inch tailpiece was fitted around the cylinder (fig. 1). The tailpiece dowed the cross flow at the back of the

cylinder to diminish suiliciontly to permit more reliable pressure reading. The cross-sectional area of the &t of the b d e was 1.6 times the free-flow nra between the fins. The unit was placed in an asbestos-lined metal box (fig. 4) and sealed at dl edges with furnace cement to prevent air leakage.

The source of heat'was an oil burner with a capacity of 1 or 2 gallons of oil per hour, depending on the burner nozzle used. A firebrick furnace provided the space for the com- bustion to be completed before the hot gasca camo into contact with the cylinder grate. An auxiliary blower was needed with a large nozzle to supply the necessary air for combustion.

The flow of cooling air was created by two compressors used as vacuum pumps and operated in series. Each pump

I

* .

was driven by an 85-horsepower engine. In ordes to pro- vent surging and to smooth out the flow of cooling air, largo tanks mere placed upstream and downstream of the tost cylinder. Bleed valves yere placed in front of and betwoon the pumps to provide h e control of the air flow. A tank with thin-plate orifices in each end was placed upstream of the test cylinder to measure the quantity of cooling air. A throttle placed between the ori6ce tank and tho upstrom surge tank was used to control the pressure of the cooling air in front of the test cylinder. A dingram of tho apparatus is shorn in figure 5.

INSTRUMENTATION

Surface temperatures of the cylinder were obtained at W points (fig. 6) by meam of insulated 28-gago chromel-alumel thermocouples spot-welded to the steel. Tho cold junctions of the thermocouples were inserted in a sealed wooden box. The temperature in the box was obtained with an alcohol-in- glass thermometer; the thermocouple potential mas measured

PRESSURE LOSS AND COOLING OF A BAFFLED CYLINDER BARREL ' 191

with a potentiometer. Thermocouples mere also used to measure the o f i c e temperatures and the cooling-air inlet and outlet temperatures. The cooling-air outlet tempera- ture mas measured downstream of the bafae tailpiece in an expanded section; it mas therefore unnecsssq to correct tho readings for air velocity. The outlet duct mas lagged to prevent heat loss. The accuracy of the temperature mwuremonts mas within f 1' F.

Total and static pressures mere obtained in the tailpiece and at two stations on the cylinder; a total pressure mas obtained immediately in hont of the cylinder (fig. 6). The

total-pressure tubes of 0.030-inch-diameter steel tubing with a 0,006-inch-diameter hole in the side of each tube mere inserted vertically around the cylinder. The static pressures around the cylinder were measured by means of 'vertical tubos inserted through holes tapped into tho h s (Sg. 7). Station 2 mas at the baffle constriction and station 3' mas somomhat behind the bde-expansion point. Because of the location of the tube, the static-pressure readings €or station 3' were not used in the calculations. Also, in viom of the small distance between 3' and 3, the reading pst,r mas used for p3,'. Conventional-type pressure tubes mere not used betmeen the fins bemuse it mas thought they mould block too much of the channel. A d e of conventional totnl-pressure tuba mas used in surveying bhe total pressure in tho tailpiece, and a mall tap mas used to measure the

static pressure (Sg. 1). The pressures were rend on vcrticd mater or mercury manometers, depending on the range of pressures being measured.

The very small pressure drops across the thin-plate orifices were rnoasured with a micromanometer.

Boff/e

0 Tofo/-pmssure fube

0 sfafic-pressure fube

Flonas O.--Locnlion ol lhcnnocouplcs and pmsure tobm on h t aylhdcr.

Sfafic-pressure fube '

11 To fal-pressure fube

-Test cylinder

-~ - . - -

192 REPORT NO. 78 3-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS

TESTS

Tests were conducted over a range of air flow at several NACA stnndard density altitudes from 4000 to 33,000 feet simulated a t the front of the cylinder. At each altitude, data were obtained with and without heat transfer for Mach numbers ranging from low values to the highest values obtainable with the npparatus. The highest Mach numbers occurred at the b d e exit, but no accurate data mere ob- tained a t that station. In the following table are given the rsees of Mach numbers at the b d e entrance M2 and at the b d e exit Mo; the Ado values mere computed on the as- sumption of no fkiction up to that point and are therefore lower than the maximum Mach number of the flow system.

Oyllnder condition

0.06 to 0.68 -70

J7to .68 .Bto 60 .I6 to .73 .16to .67 21to .€a 2Dto 3

0.05 to 0.a .12to .70 .17to BS .18to .Bo .18to .77 .17to .I39 22 to .74 3lto .m

Pressures and temperatures were recorded only after the test cylinder had practically reached a state of thermal equilibrium. The maximum allowable rate of change of temperature mas about 3 O F in 5 minutes for the maximum temperature before readings were taken. The cooling-air outlet temperature was read before and after reading the cylinder temperatures and an average of the two air tem- perntures wns used. The two readings in no case differed by more than 2 percent of the temperature rise. Tempera- tures were rend to within 0.4O F and pressures to within 0.01 inch of mercury or water. The accuracy of the pressure readings was limited by the unsteadiness of the engines, which caused pressure fluctuations of as much aa 0.1 inch of mercury.

Summaries of the reduced test data and the derived quantities without and with heat transfer are given in tables I and II, respectively. Cylinder temperature-distribution data are available upon request to the NACA.

x COMPUTATIONS

From the tests the following quantities were determined:

where

Ab area of cylinder m d a t base of fins, square feet Ta average mall temperature, O F absolute (arithmetic

average of measured temperaturea of cylinder at base of hs)

Tf,Q, average temperature of cooling surface (fin and barrel surfaces), O F absolute

ST From these data, the fictitious exit density p m nnd tho coefficients h, U, CD.f.f, Cb,f, and 5-4 were determined ns follom :

Compuzstion of h.--The average surface heat-transfer coefficient h was calculated from the equation

total heat-transfer surface of cylinder, square foet

The average temperature Tf,,, of the fin nnd barrel surface was obtained from the measured surface temperatures by awraging the temperatures with weighting factors propor- tional to the area elements in which each thermocouplo was located.

Computation of U.-The average wall hent-trnnder coof- ficient U mas calculated from the following equation

Computation of flotitious exit density p,.-The stagnation pressure at station 3') the mass flow, the exit stagnation temperature, and the cross section at station 3 were used to compute the static pressure at station 3 by means of figuro 2. This pressure and the temperature T,,l me usod to compute the density p a by means of the general gas law.

Computation of CD,f,*.-By the method givenin appendix& TkT1*i may be computed from the cooling-surface tom- perature distribution and the over-all rate of heat transtor.

mere calculated and, from figure 2, pn, p l , nnd q2 woro found. From p3.1 and T3,$=T4,1, the vnluss of ps , q,, nnd p 3 were calculated with the aid of figure 2. A value €or c D . f . f was then computed from equation (5 ) .

Computation of exit ooef0cients.-The exit coefficionta C3 and 5 could not be separately determined nnd the valuo of 5-4 mas consequently calculated from q3, p, , and p3

(obtained in the calculation of Cb,f.f) and equation (17). From P , , ~ and T,,,, figure 2 ~ ( L S used to find the neodod values for p, and p,.

TL 1- TI, t

On the assumption that p2.1=p1.1, Pa.1 and (Pv)2/l)l.l p1.1

PRESSlXU3 LOSS AND COOLING OF A BAFFLED CXLINBm BARREL 193

aomputation of OD,,,, by estimation of a-C3.-The value of c D , / , i . was b o calculated by the method of reference 5 ; that is, by estimating the exit-loss coeflicient and assuming p3=p4 instead of using the measured value of ~ 3 . 1 . Equa- tion (17) was then used to calcult~te p,. b o from previous computations p2, p2 , pn, T’, an4 &Iss, were h o r n . The chmt (fig. 3) wns recalculated for constant values of (p2-ps)/q2 instead of for constant values of 0 D J . i . The new chart mas used to find the vdue of p’ from (p2-p8)/qs,

, MZ4, T‘; equation (5) was then used to compute CDJ,,. Computation of Reynolds number.-Reynolds numbers R

were obtained from the formula

where d p

hydraulic diameter of fb prtssclge, feet absolute viscosity of nir based on average of average

cooling-surface temperature and average cooling-air temperature, slugs per second per foot

Computation of U,,,.-The prcwure-loss coefficients CPst were calculated from the data by means of equation (20)) which was used in the equivalent form

From tho data it was found that h1 should be calculated from and Tk1 and that pql should equd p1,$ for the best cor-

relation. In the foregoing equation ~ 0 , ~ is the stagnation density. The factor - bTJ)2 was then cdculated and, from

the value of this factor, was determined from P 0 , l Po.1

Po. 1

figure 2.

RESULTS AND DISCUSSION EVALUATION OF COEFFICIENTS

Correlation of heat-transfer coeBcients 7b. and U.-The effect of altitude on the heat-transfer codicients h andU is shown in figures 8 and 9. The curve for h, the surface heatr transfer coefficient, plotted against weight flow of air at the baffle entrance shows no effect due to altitude inasmuch $8

the curves for 4000 and 14,000 feet bracket the spread of the data. The curve for U, the w d heat-transfer coefficient, shows the same characteristics as the curve for h. These figures show that the Mach number had no effect on the heat transfer for the range covered. An effect of heat load mas noted in the data but is not shown in %urea 8 or 9. The hcat-transfer coefficients h and U increase slightly with heat-tramfer load.

RQWS &-Variation of snrlam hmt-tmidm &dent with coollngdr aelght Bow.

194 REPORT NO. 7 8 3-NATIONAL ADVISORY COMMI’ITEE FOR AERONAUTICS

Correlation of pressure-loss function (App,J/X(pV)’.-The pressure-loss function (Ap~,J/j4(pV)~ is a dimensionless form of the conventional pressure-loss function App,./p,. The density par is the average of densities upstream and dom- stream of the cylinder, nnd p, is the air density under stand- ard sea-level conditions. When (AppaJ/)4(pV)2 is plotted against weight flow pVg as in Sgure 10, the conclusions drawn

pVg, lb/(sec)(sq f t )

(a) Withoot heat trander. (b) with kmt M e T .

From Io.-Varintion of prrspure-lm function with coollngatr might flow.

from the plot of the pressure-loss function may be applied to the function AppaJP,. The dimensionless form has the advantage of showing compressibility effects more clearly.

The plot of the pressure-loss function AppU&4(pV)* is shown in figure 10 for runs with and without heat transfer. These curves show disagreement for Merent altitudes and for a variation in heat transfer. Theqrise shown on the high weighbflow region of each curve indicates an additional pressure loss caused by compressibility effects at high Mach numbers. The high Mach numbers occur at lower weight flows CIS the density altitude increnses. Any correlation method must make it possible to correct for these pressuro rises and thc separation of the curves for different altitudes and rates of heat transfer.

Correlation of pressure-loss funotion (Apg~=)/%(pV)~.- Some investigators have proposed correlating the prcssuro loss by means of the function Appez, where p a is tho air clcnsity at the exit of the cylinder. This method was unsuccessfully tried with the data of the present tests. In most cases wlioro this method would be applied, the baffle exit would havo no

(a) Without heat tmnster. @) Withheattransler.

FIOW~E 11.-Variatlon of pmnm-lcm funation with cwllngelr welght flow.

tailpiece and consequently no pressure recovery at tho bamo exit. The exit density would then bo computed from tho static pressure a t the baf3e exit and the stagnation tcmpora- ture at the tailpiece. The density thus computod is lowor than any density existing in any part of the test rig uscd for the present tests. The pressure-loss function (A~)p,)/j4(pV)~ was computed by menns of the density pCl and is plottcd hi figure 11 for tests with and without heat transfer. Bccausr pa decreases as compared with par for increasing prcssuro losses, the correlation of the pressure-loss function ( A p ~ ~ ) / % ( p v > ~ is better than that of ( A ~ P ~ , ) / % ( ~ V ) ~ . AI- though the correlation of the runs with hoat transfor (fig. 11@)) is good, the runs without heat transfer (fig. ll(a)) show compressibility effects in that the data for tho difforont density altitudes form separate curvea.

PRESSDRE LOBS AND COOLING OF A BAFFLED CPLINDER BXLREL 195

Correlation of drag ooefflcients and exit-recovery coeffl- oients.-The drng coefficients CD,l,i computad from the test data by the method previously given are pIotted in figure 12 against the weight flow per unit area. The utter lack of correlation between the results for the tests without heat transfor (fig. 12(a)) and those with heat transfer (6.g. 12(b)) or between results at difEerent altitudes is evident. The s m o result is to be observed in figure 13 in which the exit- recovery coefficient G-G has been plotted against the cooling-air weight flow. In order to find the source of error in these results, the

assumptions involved in this method were examined. With

regard to the aasumption that the total pressure remains unchanged between stations 1 and 2, the d a b indicated that the prcwure drop is so small 8s to be neg ib le ; st high flows tho pressure drop amounts to about 1 percent of the total- pressure loss.

Tho mass flow ~ r a s calculated from the total and static preasurea at stations 2 and 3’.to test the validity of the assumption that the flow is uniform awom each section (one- dimensional flow). The calculation was made from the

‘ factor ( p V ) l / p t p I , which mns obtained from the pressure ratio p /p l and figure 2. The ratios of the weight flows to the weight flows calculated from measurements at the orifice m e plotted for stations 2 and 3’ in figures 14 and 15, respectively, against the weight flows obtained from the

. - -1- - . - -I ~ - ..

196 REPORT h'0. 7S3-NATIONAL ADVISORY COMMITTEE FOR URONAUTICS

orXce measurements. At station 2, figure 14 shows that the mtio is near enough unity for application of the assump- tion of uniform flow. At station 3', however, figure 15 indicates that the measurements are not =curate a t low flows. In the calculation of any coef6cient based on measure- ments at one point at station 3', correlation will probably

4 6 8 f0 I5 20 30 40 50 PVg. fblsw) (s9 fi)

FIOWE IL--Batlo d mass &w mcanvrcd at d o n 2 to mass flow at st3tlon 2 obtalnd from d w memmmeuta. Tesb made wlthont heat kader .

not be obtained. It is partly for this reason that 0 D J . i )

a splotted in figure 12, shows such lack of correlation. In order to eliminate the use of these inaccurate measure-

ments, CD3,i was recalculated by the use of an assumed exit loss instead of the measured loss. The value of as compensates to some extent for the fact that e3#900. If %+2$sine3 is assumed constant or various vduea of e,, then for O3=9O0 sepnmtion from the cylinder rear can be exFected and no pressure recovery due to pressure gradients along the wall will result. Then,

In that case ~ = 0 .

149 La, ~ + 2 - sin e3=2 A,

or

If it is Luther assumed that G=O and]'pa=p, and if qa=q4(AJA3)' is substituted in equation (17), then

This equation applies with an incompressible fluid floying through the sudden expansion of a stmight duct.

The method of calculating CD, 1, ,when this 10% is used hn.8 been previously given. The results are plotted in figure 16. Much better correlation results than ww qbtained in figure 12, especially at low flow. The data for each altitude form a smooth curve. The curves separate, however; as soon n.8 the Mach number, which increases with altitude for a fixed Reynolds number, becomes appreciable, indicating that the effect of compressibility has been overestimated by taking too high a loss at the exit; that is, a, is too lorn.

In order to determine how much these irregularities in 0 D J . i and Q-G affect the over-all total-prsssure chop, the vduea of cDJ.i and a3-G determined from the tests wore used to calculate the loss in total preasure to be expected with an incompressible fluid by assuming that the density

I. 5

LO

.8

.6

I

.2

4

Flovar 16.-Ratio d m &w measmed at station 3' to masa flow at statlon 3' obtnlnod from ortern messnrements. Testr made without heat tmaaler.

remains unchanged in all equations for pressure loss. If all losses are added and if p=Constant=fi,

The over-all prwure-loss coefficient e,,, is plotted against the weight flow per unit area in figure 17, which shows that the extreme scatter of the data points in figures 12 and 13 has been sufEciently reduced to allow fairing of curvos

PRESSURE LOSS AND COOLING OF A BAFFLED CYLINDER B-L 197

6 t,

.80

,60 50

40

.30

-20

./5

JO

.OB

.06

.02

through the data points. The effect of compressibility may be seen from the fact that the curves show systematic differences for the different altitudes although the ends of the curves do not have the sharp curvature that is evident in the plots of (Appa.)/ j4(pV)*. These differences are much smaller than the entire compressibility effect, as may be seen by comparison with figure 10, which is already some-

what corrected for compressibility effects. This result would seem to indicate that, for correction of the compressi- bility effect, the division of the pressure loss between the baffle channel and the baffle exit is unimportant because the pressure ps was no doubt in error. h order to invastigate this hypothesis, the over-all pressure-loss co&cient C,,, was computed from the estimated vdue for e - C 3 (equation (25)) and the corresponding values for CDJ,$ (fig. 16).

- L A - . . -

198 FtEPOIlT NO. 78 3-NATIONAL ARWORY COMMITTEE FOR AERONAUTICS

The results of these dculations are plotted in figure 18, which &om that the value for p , cannot be estimated in an mbitrnry fashion. If the values of c D . f , t and %-Ca from equations (5) and

(17) are inserted in equation (26) in order to determine how the pressure-loss coefficient Cp,f depends on the data, there is obtained

If the density ratios are estimated from the energy equa- tions for very low Mach numbers ( M = O ) , then

The value of 2'' (equation (8)) is always less than 0.10 and the data indicate that the term involving pa is never greater than 0.01. At low Mach numbers, tharefore, large vnria- tions in estimates of pa from ita true value d not afEect CP,+ For high hlach numbers, however, equation (27) indicntes that pa d definitely affect the result for C p , f . Figure 15 shows that the measurements of pa are inaccurate ntlowMach numbers but much better at high Machnumbers; therefore, a t high Mach numbers when the data for p , are used, fair correlation of Cp,f may be expected. At low Mach numbers, the inaccurate values for pa do not affect the result; correlation may consequently also be expected in this range. With inaccurate values for CD3.f and a,-Ca a t low Mach numbers, correlation for CPsf may be expected; whereas, in the high range, correlation may be expected only when a ~ ~ ~ t ~ t e values for C D , f . f and %-G,

Figure 12(a) shows that no correlation of C D , f . f occurs at low Mach numbers and fair correlation occurs at high Mach numbers. No accurate correlation in any range is obtained for tests with heat transfer (fig. 12(b)) but, if scatter is taken about a mean curve for the high Mach numbers, the varia- tions are small compared with the value of CPvf and thereforc do not show up so prominently. The same general features of the CD,,.fplots (fig. 12) may beobservedin the%-Ca plots

data (fig. 16) it may be presumed that the estimate of 6 was incorrect and resulted in the calculation of faulty values for

.

obtained.

(fig. 13) and the Comments apply. &Om the cD,, . f

p,. Comparison of Cp, i of figure 17 with that of figuro 18 indicates that, in the range of low iMach numbers for all altitudes, the CPmf curves are the same with the mensured and the calculated values of p,, which confirms the deduction that, for low values of Mach number, CP,* is independent of

40

pa. In fact, the lowest-altitude curve is approximatoly the same for both methods of computing Cp.f except at the very highest Mach numbers. The lack of correlation of the data of @e 18 at high Mach numbers c o n k s the deduction that the estimated values of p , are incorrect and influenco the values for CPmf and that the mensured values for high Mach numbers used in calculating C p , f (fig. 17) nre nccurato.

PREs6URE LOSS AND COOLLNQ OF A BAFFLED CYLINDER BARREL 199

The fnct that the pressure measurements in the rear of the cylinder were very inmmte at the low cooling-air weight flows indicatea a lack of uniformity in the flow, which con- tradicts the hypothesis upon which the flow analyeis wag built. A second inaccuracy-is seen in the hypothewis by which is calculated from CD;/. The method of dcula- tions is based on the assumption that q = % p V = % - increases 'linearly along the channel; j4(q3+qz), therefore, represents a good mean value for q. This assumption is

IIbY

h a U R E lO.-Rllcct of E8ynolds number on pmsurelms -dent compute3 by ernplrld method.

approrcimately true for low Mach numbers but not for high. iMach numbers where a much more rapid rate of increme is to be e.spected. Because $(qZ+q3) is higher than the mean

the coefficient that may be expected with a truly incompres- sible fluid. The nonuniformity of flow in the rear (station 3) will also modify the momentum equations for the baffle channel and the b d e exit. For these reasons values of CD,,,, and a j - 4 obtained by the assumptionof uniformflow nnd by means of equations (5) and (17) mill probably not clieck estimates from measurements of the velocity and pressure distribution dong the channel and b d e walls. Further e.speriments me required to determine conclusively the offectiveness of this method.

Correlation of the ooeffloient C, calculated by empirical method.-A plot of the pressure-loss coefficient CP,< a g h t tho Reynolds number is shpwn in figure 19. Although the correlation shown in this plot is satisfactory, some features show that improvement is still desirable. The points for

OffeCtiVe VdUe Of p hl the Channel, c D , / , i must be lOWf3l' than

the lowest density altitude without heat transfer are, in general, lower than the average of the points. The tendency for this plot to fall off at high Reynolds numbers indicates that the correction for compressibility effects is probably too large. This result might possibly be due to the fact that the correction factor applied is too large for the pressure losses occurring before station 3. This effect does not occur in the data for other density altitudes, possibly bemuse the data for the lowest densities mny be inaccurate in the high-

40

flow region os a result of the unsteadiness of the driving engines.

In order to determino the magnitude of these deviations on the actual pressures, the corrected pressure drops mere plotted in @e 20 in the customary manner. The dis- crepancies noted in figure 19 show little effect on the pressure- loss plot. The shape of the plots of figure 19 indicates that a linear curve of pressure-loss data is not to be expected.

200 REpOFiT NO. 78 3-NA'I'IONAL ADVISORY COMMITTEE FOR AERONAUTICS

GBNJ3EAL DBCUSSION

Comparison of the oorrelation methods.-For any set of pressure-loss data, the separation of the curves for different density altitudes is an effect of compressibility that has not been corrected. The effect of compressibility is accentuated at the highest weight flow for each density-altitude curve. The effectiveness of each method of pressuredrop correlation is characterized by the magnitude of the spread of the curves at the four weight flows that are the maximums for the dif- ferent altitude curvea. At the end points of the curves for 4000-, 14,000-, 24,000-, and 32,000-feet density altitudes, there are, respectively, two, four, six, and eight points on dl the curves for comparison. The average deviation from the mean of all the curvea at these points is given in the following tables in percentage of the mean value of the para- meter at that point:

I I I

These tables show that the use of the varkble ( A ~ p ~ ~ ) / g ( p V ) ~ is least effective, that the use of the variable ( A p ~ ~ ) / s ( p V ) ~ and the analytical method is better and about equally effective, and that the empirical method using the Prandtl- Glauert factor is most effective and of satisfactory accuracy.

The involved procedure needed for use of the analytical method is a definite dramback. Furthermore, certain infor- mation is needed for pressure-loss predictions that is not necessary when the empirical method is used; the relative moun t of heat picked up by the air in front of the b d e entrance must be obtained and pressures at the bde-channel expansion point are required in order to evaluate separately the coefficients C D , f , f and 6-G in the pressure-loss predic- tions. The testing technique for determining reliable values of p3 is yet to be developed. Computations made for a modern engine a t an altitude of 40,000 feet show that very high Mach numbers occur and that separate values of C D , f , f

&d 6-Cs are needed. The method is somewhat simpKed, however, when no baHe tailpiece is used, which eliminates pressure recovery at the baffle exit. In that w e p3=p4, and pressure measurements are therefore unnecxmary in the bafEe exit.

The same drawback applies to the use of tho prmure-loss function (Appbl)/g(pV)*; that is, a measurement of the pressure in the baffle exit is required to determine pa unlcss a baffle is used that gives complete loss of the kinetic onorgy at the baffle exit. This method of correcting the pressuro loss for compressibility effects haa n rationnl basis. If tho entire loss is wumed to occur at the baffle axit, if no pressure recovery exists in the baffle tailpiece, and if the nu tomper- ature in the baffle exit is assumed equd to that bohind tho cylinder, ( A ~ p ~ ) / g ( p V ) ~ should very nearly account for nll

compressibility effects by equation (17). If not. dl tho loas in energy occurs at the baffle exit and if some prmuro recovery is present there, this method should givo good results if most of the pressure loss occurs at the bafflo exit and if the rest varies in much the same manner a8 the baffleexit loss.

The empirical met.hod of computation of tho pressure loss has the advantage of being quite simplo. Thore is doubt as to the types of flow apparatus to which the empirical method can be applied because no rationnl basis for it exists at present. Test data from engin~s, engine cylindors, and radiators aro required before an estimate of tho reliability of this method can be made. -Tho same confirmation ol the reliability of the analytical metohod is needed, howover, because tbere is some doubt that it correctly represented the actual flow conditions in even this comparatively simple type of flow path.

In order to illustrate the appliation of tho empirical method, an example is computed and plotted in figuro 21.

PREGSURE LOSS AND COOLING OF A BAFFLED CYLINDER BARREL 201

For comparison, the pressure loss is also computed by means of the function (AppaJ/%(pVjz. The barrel temperature is assumed constant at 350' F; the rate of heat transfer is assumed constant and such as to require an Gr weight flow at sea level of 18.5 pounds per second per square foot of free-flow area of the b m e l - b d e channel. The atmospheric prcasures and temperatures are modXed for isentropic comprcssion corresponding to a flight speed of 200 miles per hour. The subsequent steps are:

1. Compute cooling-temperature differential Ta- 2. Compute the heat-transfer coefficient U (equation

3. Determine pVg (fig. 9) ; compute the exit temperature. 4. Compute the Reynolds number, and determine CP,<

6 . Compute the abscissa of +e 2 and read the compres- sibility-correction factor (po/po , 4-

6. Compute the pressure loss from the data of steps 3, 4, and 6. When the pressure loss is computed by means of the function (AppaJ/j4(pV)2, the first three steps are the same na those previously given. The weight flow is used to determine ( A p p , , ) / ~ ( p V ) z by means of the plot of lowest density altitude (Sg. 10 (b)). An estimate of Ap is made for dotormining pa#; the resulting value of Ap is used to r e h e tho values for pap and Ap. For less extreme cooling condi- tions, the dif€orence between the two methods is not so great.

Weot of viscosity.-For the general correlation of pressure- loss and heat-tramfer data, dimensionless parameters should bo used. The variable h, for example, should be plotted in

terms of the Stanton number - against the Reynolds

number. In turbulent flow the Stanton number varies approximately as the Viscosity to the 1/5 power. For prac- tical application of heat-transfer data to altitude-cooling prodictions, therefore, the small variation in the viscosity caused by the variations in temperature of the cooling-air surfaco film will dFect the heat transfer only slightly. Good correlation of heat-transfer data of a given engine or cyl- inder can be expected, therefore, if the weight flow is used as tho corkelation variable. The same reasoning can be applied to pressure-loss data.. Because the present pressure- loss data were obtained with and without heat transfer, considerable difference should be expected in the film viscosity. Consequently, the Reynolds number was used to correlato the pressure-loss data; the viscosity of. the surface film gave better correlation than the cooling-air viscosity in the computation of the Reynolds number. The pressure-loss coefficients were plotted against the weight flow because use of the Reynolds number effected no increase in correlation or sign5cant change in the plot.

Velocity distribntion.-Some improvement might be made in the analysis of flow in radiators, for which the assumption

(24)).

(fig. 19).

CPPV

of uniform flow at the radiator-tube exit is satisfactory, if allowance were made in the momentum equation for the nonunifomity of flow to be expected with a turbulent veloc- ity distribution in the tube. The computed kinetic-energy loss a t the exit would thus be increased.

SUMMARY OF RESULTS

Based on an analysis of pressuredrop requirements and on exporimants to determine the effect of air compressibility on coohg and pressure loss of a b a e d cylinder barrel, the following results were obtained:

1. The pressure loss from the front of the cylinder to the baffle entrance was very small, as might be expected for any b a e d engine cylinder.

2. The method of analyzing the flow processes around a bafEed cylinder baaed on the assumption of uniform flow corrected for most of the effect of compressibility.

3. The assumption of uniform flow used in the analytical method of predicting pressure losses was not veri6ed by computations from pressure measurements between the iks a t low flows.

4. Prediction of tho pressure losses m o s s a cylinder at high Mach numbers using the m a l y t i d method bnsed on uniform flow requires knowledge of the exact values of the friction codcient between the h a and the coefEcient at the exit of the cylinder. At low Mach numbers the division of the pressure coefEcients has little effect on predicted pressure loss.

5. The use of a fictitious exit density pCl in correcting pressure-loss data gives as accurate correlation n8 the anal* ical method based on the assumption of uniform flow.

6. An empirical methodhas been found which gives satis- factory correlation (mem deviation of pressure-function curves of about 3 percent) of the test data on pressure loss of bhe present cylinder and which permits estimates to be made of compressibility and heating effects more simply thm either the analytical method or the method using the bde-exit density in bafEle-flow system with a tailpiece.

CONCLUSION

If engine-cooling equations are bnsed on the cooling-air weight flow instead of on the pressure loss, good correlation of data and prediction of performance may be expected because test data and theoretical estimates showed no appre- ciable effect of air compreasibility on heat-transfer coeffi- cients in the ordinaxy range of engine operating conditions.

AIRCRAFT ENGINE R N S ~ ~ C H LABORATOBY, NATIONAL ADVISORY Cohthtr~~mn FOR ~ E O N A U T I C S ,

CLE~VDLAND, OHIO, Jdy 1,194.

APPENDIX A ESTIMATION OF AIR-TEMPERATURE DISTRIBUTION B O U N D A BAFFLED CYLINDER BARREL

In order to determine the pressure loss over the cylinder, it is necessary to know the rate of heat transfer to the cooling air between stations 1 and 2 Hl and the rate of heat transfer to the cooling air in the b d e d section H2. The following analysis presents one method of estimating HI and H2.

For an element of heat-transmittiq surface dSJ the amount of heat transferred per unit time ia

dH= h, ( T r T J d S where 22 rate of heat transfer from front of cylinder to point being

h, local surfsceheat-tmmfercoefficient,Btu/(sec) (OF) (sq ft) T f cooling-surfm tempersture average at any local flow

Tl local stagnation-air temperature, O F absolute

considered, Btu/sec

section, OF absolute

The viscous shearing stress s low down the air in the immediate vicinity of the wall and increases the temperature there until T, the temperature upon which the heat transfer depends, is more properly the stagnation temperature than the static temperature (reference 11). If WL is the local weight flow between the h s (lb/sec), the en- equation is

H=GWi.(Tt-Ti,t)

In the unbaffled section of the cylinder, WL increaaes from a value of zero at the front stagnation point to the value W at the baffle entry. The term Tt is eliminated from equa- tions (82) and (Al) cmd the quantities

and

are used to obtain b e Tf- TI,,=cooling-temperature differential, O F

where ST entire surface for heat tramfer, sq f t S surface for heat transfer from front of cylinder to point

considered, sq f t The solution of this differential equation is

BWXLUS~ S/ST=O and H=O at the front of the cylinder, the constant of integration is zero. At the b d e entrmce,

202

S/ST is equal to a, the ratio of the u n b d e d cooling surfnco of the cylinder to the total cooling surface, and H=Hl, t ho rnte of heat exchange in the u n b d e d portion of the cylinder. At the b d e exit, S/sT=1, and H=Hl+H2, the rnte of hont exchange over the entire cylinder. When these boundary conditions are inserted in equation ( 8 3 ) ,

The rest of this appendix derives expressions for ZYl and Hl+Hp, which are more convenient than equations (A4) and ( 8 5 ) for computation from the test dah. The quantity C variea little over the cylinder except at the very front. Tho

are only slightly affected by this variation. Consequontly, the qumtity Cis considered a constant in all tho intogrations. The values found for Hl and Hl+H2 from tho onorgy equations

and

(s/sT) factor r a ' 4 & ) a n d the integral of CWLte J ; ~ s r a ( S l s , )

HI= W c p ( Z , 1- TI, i)

are substituted in equations (A4) and (85) to obtnin

T2,t- T1.,= C e - c u c z lec(slsr)d (S/ST)

If an estimate is made of the weighbflow variation WL/W md measurements of f are obtained, C can be determined from the over-all tempmature rise T4,1-T1,1 and equation ( 8 7 ) and its value used in equation (A6) to h d T2.1-Tl,l.

PRESSURE LOSS AND COOLING OF A BAFFLED CYLIPU'DER BARBEL 203

In order to estimate the weight-flow vnriation in the un- b a e d portion of the cylinder, the flow in the front is com- puted by means of the equation for potential flow over a circular cylind,er. The velocity over such n cylinder is

where Vo is the velocity of the undisturbed flow, which renches a mn+mum a t S/&= 1/2. In the case of the b a e d cylinder the maximum vdue is at S/ST=a. The velocity function is therefore modified to take this factor into account

The constriction at the bafRe entrance (S/ST=a) of the flow arm to l/n its vdue for an unbaf3ed cylinder increaaes the mcLximum velocity by the factor n, but the velocity in front of the cylinder is unchanged. The velocity distribution must therefore be multiplied by an even function of S/ST, which increnses from a vdue of 1 at S/ST=O to a value of n at S/ST=a. The ossumed function is n [ 1-- cos (d/2dT)] which gives an approximate weight-flow vrtriation of

From the baffle dimensions, n=S. For the u n b d e d portion of the cylinder, a linear cooling-surfnce temperature dis- tribution is nssumed

where t1 is the value of t at S/ST=O, and t 2 is the vnlue of t at S/&=a. Equations (AS) and (AlO) are substituted in equation (A6) to obtain

where

An approximation must now be found for the integral involved in equation (AS). In the b a e d section, W,/W= 1

and t varies very littlo; nn extmme case shows 9-percent aver- age deviation from the mean. The unbafEled cylinder rear shows a much larger deviation but the decrease in the effec- tive cooling-air velocity reduces the variation of the function '(WL/W)t. The value of WJWis therefore taken to be unity and an average value used for t so th&

where f3 is the average cooling-surface temperature of the cylinder from the bafEe entrance to the rear minus the inlet- air temperature. This result is mbstituted in equation (AS) to obtain

If

equation (All) clbn be plotted in the form (T2.1-Ti.i)ha as a function of (ec(l-u)-l) and (b,-&.)/t,. This plot is shown

in figure 22. Equation (Al3), however, gives solution for the variable (T2,,-Ti,,)/t, aa a linear function of eC(l--p)-l with a y inhrcept of (T4.,-Tl.,)/ta and a slope of [~-(T4,,-Tl.,)]/t,. From data on the temperature of the cylinder, the straight line (equation (Al3)) can be located on figure 22 and the intersection point can be obtained with the curve of equation (All) for the proper value of (t,-h)/t,; thus, (T2.,-T1.3/f, can be determined.

APPENDIX B SYMBOLS

A

A, c,

cross-sectional area at a station indicated by a sub- script (axcept withesubscript b ) , sq f t

m a of cylinder wall at base of h, sq f t s p d c heat of air at constant pressure, Btu/(lb) ( O F )

coefEcient for friction drag in bafae e&, co&cient for skin-friction drag from station 2 to

station 3 baed on dynamic pressure at station 2 coefficient for drag from station 2 to station 3 based

on dynamic pressure avenged in bafae channel pressure-loss coefficient with an incompressible fluid pressure-loss coefficient with a compressible fluid acceleration of gravity, ft/sec* local surfnce heat-transfer coefficient, Btu/(sec) ( O F )

average surface heat-transfer coefficient, based on

rate of heat transfer from cylinder area between front

rate of heat transfer to air from front of cylinder to

rate of heat transfer from baffle entrance to baffle

Mnch number at a station indicated by subscript

(sq ft)

inlet-nir temperature, Btu/(sec)(OF) (sq ft)

and any point considered, Btu/sec

baf3e entrance, Btu/sec

exit (station 2 to station 4)) Btu/sec

(axcept May Mb)

P static or stngnation (indicated by subscript t) pres- sure at any point in fluid indicated by a subscript, lb/sq f t

static pressure at any point in fluid with incompres- sible flow, lb/sq f t

dynamic pressure at any point in fluid indicated by subscript, Ib/sq f t

p ,

P

R Reynolds number S

ST

surface for heat transfer from front of cylinder to

total heaGtmnsfer surface of cylinder, sq f t point considered, sq f t

204

projected mea of cylinder-wd surface and curved part of b d e surface back of station 3 on plane of 4, sq f t

T,-TT,,t % (t*+tJ average vdue oft between stations 2 and 4, O F true air-stream or stngnation (indicated by subscript t )

temperature at any point in fluid indicated by

average temperature of cylinder mall at base of fins,

cooling-surface temperature averaged at any local

average temperature of cooling surface of cylinder,

W c p WTn

subscript (except Tb, TI, and TI,,,), OF absolute

O F absolute

flow section, O F absolute

O F absolute

w d heat-transfer coefficient of cylinder, Btu/(sec)

velocity of air at my station indicated by subscript,

weight of air flowing through baWe, Ib/sec local air weight flow between h, lb/sec ratio of unbai3led cooling surface of cylinder to totnl

ratio of specsc heats for air (1.3947) angle between radii of cylinder to cylinder rear and

to station 3, deg (See fig. 1.) absolute viscosity, slugs/(sec) (ft) local true or stngnation (indicated by subscript t )

density at any point indicated by subscript (escopt

standard density of air at 29.92 in. Hg and 60' I?,

average of densities at stations 1 and 4, slugs/cu f t fictitious exit density P2/h totd-pressure drop from front to rem of cylinder,

Ib/sq f t or in. water, @ ~ , , - p , , ~ ) loss in total pressure from front to renr of cylinder with an incompressible fluid, lb/sq f t or in. mater

loss in total pressure from front to rear of cylinder with an incompressible fluid under standard den- sity conditions, lb/sq f t or in. water

(sq ft) (" F)

ft/sec

cooling surface .

PI, or, and pa), S ~ U ~ S / C U f t

slugs/cu f t

Subscripts applicable to A, p, T, V, p, M, and p: 1, 2, 3, 3', 4 stations indicated in m e 1 t stagnation condition of gas (absence of subscript t

indicates true-stream condition) 0 condition characteristic of entire flow

PRESSURE LOSS AND COOLING OF A BAFFLED CYLINDER BARREL 205

REFERENCES

1. Pfnkel, Benjamfn: Heat-Transfer Processes in Air-Cooled Engine Cylinders. NACA Rep. No. 612, 1938.

2. Pfnkel, Benjamin, and Ellerbrock, Herman H., Jr.: Correlation of Cooling Data from an Air-Cooled Cylinder and Several Multi- cylinder Engines. NACA Ilap. No. 688, 1940.

3. Schoy, Oscar W., and Pfnkel, Benjamin: Cooling of a Rsdial Engine in Flight. Jour. Aero. Sci, voL 4, no. 11, Sept. 1937, pp. 448-462.

4. Corson, Blake FV., Jr., and MoLellan, Charles H.: Cooling Charao- toristics of a Pratt & Whitney R-2800 Engine Imtalled in an NACA ShortrNose High-Inlet-Velocity Cowling. NACA ACR No. W O O , 1944.

6, Bockor, John V., and Baals, Donald D.: Analysis of Heat and Compreaibility Effects in Internal Flow Systems and High- Speed Teats of a RamJe t System. NACA Rep. No. 773, 1943.

Special Reference to Ethylene Glycol Radiators Enclosed in Ducts. R. & M. No. 1683, British A. R C., 1936.

7. Winter, H.: Contribution to the Theory of the Heated Duct Radiator.

8. Weise, A,: The Convemion of Energy in a Radiator. NACA Thl No. 869, 1938.

9. Brevoort, Maurice J., Joyner, Upshur T., and Wood, George P.: The Effect of Altitude on Cooling. NACA ARR, March 1943.

10. von TiBrmh, TL: Compmbi l i ty Effects in Aerodynamics. Jour. Aero. Sci., voL 8, no. 9, July 1941, pp. 337-366.

11. Frankl, F.: Heat T r a d e r in the Turbulent Boundary Layer of a Compressible Gas at High Speeds; Frankl, F., and Vowel, F.: Friction in the Turbulent Boundary Layer of a Compressible Gas at High Speeds.

12. Emmom, H. W., and Brained, J. G.: Temperature B e a t s in a Laminar Compressible-Fluid Boundary Layer Along a Flat Plate. Jour. AppL Mech., vol. 8, no. 3, Sept. 1941, pp. A-105-

NACA T M No. 893, 1939.

0

NACA TM No. 1032, 1942.

6. McredIth, F. FV.: Note on the Cooling of Aircraft Engines with 1 A-110.

-

i.'h ab.)

28. IO 28.12 28.19

28.34

28.11 28.14

28.24 18 16 28.16

2a.B 28.23 28. 18 28.08 28.11 28.16

19.63 20.03 19.92 20.12

-

28.28

28.m

a m

28. 1.1 a n

m. 08

m. 11 m. 10 m. ii m. 04

m. 05 m. 18 m. m m. m

m. 16 14. m

20.08 20.10

20.18 20.24

16.00 16.07 16.01 1807 14.88 14.83 14. 91 14.91 14. a 14. 91 14. ff 14. ES 14.81 1o.z 10. E 10.71

1o.x lo. a 10. 75

ia 7t

TABLE I.-SUMMARY OF DATA FOR TESTS WITHOUT HEAT TRANSFER [The pymboh nsed are deflned in appendh B]

-

Til 'F ha . )

- E428 M 2 8 643.6 644.6 644.6 645.6 €46. 6 646 6 646 6 646. 6 Mo. 7 ML 8 M 2 8 643.6 649.2 647.9 648.2 647.0 Eb5L 0 661.0 649.0 650.0 650.0 66L 0 651.0 €44.0 649.0

648.0 649.0 660.0 a 0 M7.6 M7.6 647.0 s a 6 647.6 647.6 45.520 638.6 64'2 0 645.6 Ma 0 649.0

650.0 560.0 660.0 ML 0 643.0 649.0 547.0 6520 45620 663.0 6620 663.0 a. 0 6 6 L O

€49. o

649.0

-

,:;&) @l It))

3.m 4.m 4.461 6.464 a 4 n 7.621 9. m

11.487

16.791

19.810 22 173 24.073 26.m 29.736 33.376 3a 74 40. Bo 39.76

--

18 m la ai7

a m 7.627 9.404

10.411 11. MI l h 7 9 19.40 22.22 23.74 26.31 28.81 29.08

12 34 16.25 17.72 19.84 24. Bo 6.83

12 41 16.36 17.76 8.07 9.18

10. 08 11.68 1% 88 16. 64

19.21 1L 112 5.36 639 7.39

14.46 13.23 1L 20 9. a5

ia 36

io. 80

ia 09

a08 .07 .OB .&a .14 .15 .22 .a .42 .68 .79 .91

1.12 13-3 1.73 2 2 2 2 9 9 4.61 6.14 4.97 .m .25 .36 .a .52 .91

I. 14 L Q

297 4.12 4.44 .34 .69 .a4

1.16 L40 143 .30 .@a

1.33 I. 84 .41 .47 .E5 .74 LO9 L37 1.97 227 3.31 .27 .34 .47 2 11 L n 1.16 .76

2 m

.m

28. 11 28 12

2k 31 !B. 19 28.11 28. 13 28.25

28.16 28. 16 28. 13 28.21 28. 21

28.14 28.08 28.04 28. 10

19. @ 20.05

20.08 20.14

20.01 20.08 20.16 20.01 m. 14 20.22 20.17

m. 14 14. zpd 16.05 16.08 14. BB 1hO7 14.88 14.81 14.91 14.91 14. 88 14.89 14.81 14. a 14.84 1o.z 10.75 10.75

10.87 10.67

28.20 28.28

2an

28.20

m. 08

19. m _____- ____--

m. 14 ___-_-

io. 75

in. 7c

1866 1.w L383 .a34

1.040 .a19 .796 .076 .m . n 3 .m .io8 .€a .m .n8 .m . 7 8 .lug .E34 .E37

LOB .m .sa .m . a 7 .?a .e37 .880 .a11 .840 .@I .Ma .€a5 .w .m .781 .761 .m .BBB

1.007 .m .816 .m

1.010 .m .a76 .m .m .e57 .m .m

L W

.us3 1.027 1.017 .s37

La34

.mi

.mi

* 4bv )S -- 1. es3 1.363 1.3-31 .m

1.036

.791 .ea .m

.m .no .ea

.e67

.e43 .m

.e87

.e70 . 681

.e47 .m 1. 021 .m .m .818 .818 .762 .622 .649 .718 . n 2 .74!2 .712 .ea .8a3 .747 .m .ma .76l .981 .974 . a57 .a11 . 791 .896 .534 .860 .a .rrm .797 .784 .7n . n 4 Lon .831 .818 .m .m .912 .Ea

.ma

at-Q

-0.m -. 7491 -. 1232

.m

.1w

.a82

.3582 . m6

.44w

.w

. 4 m

.m

. m 7

.6139

.6112

.6177 . a 9

.m

. 4 m

.a18 -. m

.m .1m

.3u4

. a 3 -0296 .I479 .4478 .4m1 .m . 4 w . a 1 4 .m .3%% .a .m .44€a . lW .m .m .m . a 1 7 .0188 .1m .m .4616 .am8 .m .3948 .m .4081 .076 . 3 m .as80 .a67 . w86 .m

-. mi4

. 2483

C0J.C

- a m -. 2179 .47ela

-. 1170 .3m5 .lo74 .u34 .m .1489 .2107 .1701 .1m .1m .188 . rnl .I774 .17ll . lem .1480 .lea2 .&le -. 04&3 .2167 .1m .m .m

-.%I1 -. 140s .1m .I833 .1724 .1m .1743 .17M .la .I863 . lsBs .1%1 .34a .2m3 .I416 .1m .I383 .I703 . alea .2bm .lea .la .m .1m . lm .1m .3281 .3m .9886 .1Mo

. m1 .a

. imi

- 3- nethod) - 1.7116 I. 4234

1.04M 1. m .m . 7 w .m

. .7l% .em .0ln .m .€dm . €463 .a .a . m 7 .m .6442 . ITBB

1 . o a . 9 l D .8068 .m . M40 .&sa . Q1b . 0 lW .m .8294 .e384 .a .m .7448 .w .€as3 .e517

1.0808 .m .'1869 . n 4 1 .0788

LO637 . m1 .w . a31 .m .7631 . W 6 .ma .M82

1.1627 . Mu1 -9497 .Em6 . a 1 7 .m80 .Bun

1. mi6

. e m

- 1.6888 1.3422 1. SBBQ .E331

LO23 .a141 -7865 -6648 .m .m .m .m .m .e510 .w2 .a25 .a28 .iml .6834

LO270 .9U6 .8u1 .8128

.7449 * 6737 -5838 .m - e651 .M54 . 6461 .m .81s2 .m .m .m1 .n79 .BsM .Em8 .8466 .m . 7 m .m .E#3 . E 3 4 .m .m6 . 7 w .m -7197 -6828

LoBgo .m .m1 .m .E353 . m 4 . BBl9

.mol

- leynol& lnmber x 10-1 - a m .(HE

.m1 .om

.a594 .low -1382 .I684 .1fi76

.!a77

.m

.m

.3176

.3m

.m9 -4468 - 4 7 3 .4697 .om .OB85 .I106 .m .I312 -1870 .m .2580 .m .30m .m .23m .lpe

.ISM

.21m

.23M

.2913 .m

.1%

.14@

.l8n

.2lO4 . oQ17

.lo77 . llso -1386 .la

.21m .m

.2E31 .m

.o7a .m .1m

.1m

.1m

.lo61

. a m

. i4m

. i m 3

- am .Fa

1.10 Lo8 L70

2 6 2 3.43 4.61 a 7 4 9.11

12 30 14. Bo la 19 2228 27. sa 36.08 35.89

L70 2 0 8 2 8 8 3.43 4.27 7.23 840

11.21 14.81 17.62 21.26 a37 283 4.85 Lei9

15 10 1.84 4.21 6.m

9.23 2 6 0 2 8 3 834 4.30 a 0 2 7.22 9.56

12 33 L10 L4.3 202 a 61 6.76 4.30 %OB

L m

lam

a m

8% io. 39

7. m

ia s

206 REPORT NO. 78 3-NATIONBL ADVISORY COMMFTIXE FOR AERONAUTICS

TABLE II.-SUMMARY O F DATA FOR TEXTS WITH HEAT TRANSFER me symbols used are d a e d fn eppandh Bl

T4.1 ’DP ab.)

p/ (In. Hg ab.)

l’,-Ti.r (” P)

307.00 mb8 36l.16

821.78 310.63 m m 273.38

27& 40 966.00 230.09 227. OB 117, M 211.17 107.20 186. 88 288.00 m M

227. a a b 6 317.38 am 13

24892 237.40 238M

p a w

ua 09

Ha 21

240. m

287. m Ha m

231. m - - Apia In. Et0

- 6. 4XZ 6.m 9. BEn

13.931 la 406 23.808 38.280 42074 41. 2WO 4. m 6.311

11.417 14. rn 10.421 1L Em 2787 4. Bm 6.847

12 041 3.830

9.817 2 374 3.m 4.032 h780 0.825 7.7M

am

a m a 015

-

122a 14.97 la 16 21.62 2630 a83 3all s9.m

1L 37 14. M 17.26 la 53 2-4 31 2667 2% 06

1L 40 16.41 2L 6d

E88 16.86

a66 an 1L37 1222 14.01 14. 37

4 a .s am

a m

la 8

la zs

- - 1. (“m

27.77 27. 97 a m 28 01 27.83 27.83 28l3 27.98

a 4 4 20.44

a37 20.45 23.60

16.00 14. c@ 14. w 14.86 14.82 14.81 14. s3 1 1 19 1L 16 1L 10 u 16 U 17 1L 26

a m m a

20.44

.. - _- -_ - -

.- - -__ _- -

27.27 27.21 2662 E.43 2ha x86

!i2 13 21 .8 20.07 la 78 19.39 law la38 17.82 18.83 16. 10 14.62 14.09 13.44 1226 14.13 13. 49

1266

9.75 0.49

a m

13.06

la 36 ia 11

am 8.83

27. ob 2694 26a 26.86 24. e5 2346 20.85 17. 67 16.88 20.01 20.B la 84 la 33 17.42 16. 12 14.18

14.06 13.25 936

14.16 13.34 116a 11.8 12 10 11. n 11.36

a88

ia 63

14. n

lam ia 25

27. cn x 9 8 m 49 2hKl 34. n 23.62 21.13 l a m 16. 46 1 8 @I la 5l

18.61 17. 78 16. 91 16.14 13. ob 14.24 13. M 12 78

1 3 85 1184 11 18 11.10 10. u3 a67 0. 17

7.67 7.23

10. m

a 75

am

- - CP.d

(mPh I d

rnothoc

a m - .m .7741 .m1 .717! .m .@I: .w .ea(

L W .e161 . mi . 7 m . 7 m .7342 .m .8611

L W .m .m .m .=I .w .a158 .m .Em .ffl46 .010l .w10 .m .m -

27.80 28.00 28.M a m 27.69 27. w 28.lb 288 28.01 a 4 7 20. 47 20.47

a 4 2 20.40 2a 61 20.83 14. QS 14. 97 16.03 16. 06

14.84 14.84 14.82 1L l8 1L 18 1L 19 U 18 1L 18 U24

20.43

14.67.

- - U

aM -70

L 01 L39 ala 2 76 4 . 8 6.78 7. Bo .33 .61 .86

L22 L04 2 18 a 4 4 4.01 -62 .88

L 43 4.10 .77

196 L80 2 41

.Bo

.& 1.28 LBB 2 2 2

27. €a 27.75 27.74 27. 04 27.42 27.21 27.08 2688 23.79 20.38 20.30 a14

19. @I 19.34 19.74 19.47 14.80 14.67 14.67 14.36 14. m 14.47 14.23 14.90 lL 01

mu

ia 95 la g2 la 88 ia 80 10.81

14,000

24,000

32.m.

DensSty altitude (ft) app.. WbV’

11-11

1.

a m .Em2 .8628 .Ea24 .9157 .m

L W L W L m 7 .a44 .m .7@3 .8U0 .m .m .8883

L me .m . 8616 -7474 .m . m u .m .84M -8886 .m

.m

. 7 m -7188

:E4

APP- %Y)’

1.019 .880 .a3 .846 .m .846 .w

LO77 LDBS LlS3 .fa .841 .&i7 .m .m . B31

L 018 1.180 1.011 ..go3

L 153 L 100 .9n

L 010 .E3 .Bp

Lo88 LO80 L2l3 L la La40

U-CI

- a 4b72

.41m

.4ta5

.4118

.4rm

.4m2

.4388

.Dl8 .a .nm

.m

.m1

.4H4

.4740 . 6483

.4616

.a16

.28H

. 4 m

.a03

.3836 .a .m

.w

.4217 .m .arm

.2mb

.I614

.Pu

.I% -

CDJJ

a 2a47 .10U .I834 . loio .14P .1m .m .m .ma .m .l844 .1674 .la .la33 .3178 .la16 .lo39 .m . a b 2 . la2 . on0 .sa . l7l0 .1m .11n . Ism .m .1661 .m .0747 .a968

a m . la5a . l2M -1- .1m . lrn . zsol -2620 -2389 -0763 .om .1l27 .m -1467 . lsoa .1m .la1 .m .o900 .m .1m .m .1c@5 . 11z .1m .0741 .a324 .m .m . llz! .1161 -

366.0 3886 3 4 Q O S B 6 a025 2230 26p6 254.6 226.5 am0 2 6 1 0 S O 2228 3088 p a 2 IQQ. 4 18L 8 2 B L O B 2 3 23Q0 Z L 1 m 0 3085 281.0 2750 S O a429 234.1 2a25 m. 1 226.0 -

a m a mi .Boa .‘Is0 .749 .735 .m .747 .m .m

L M I .918 .n3 * 753 .m -732 .733 .m

L 061 -885 .761 .m .em .a4 .E37 .779 .m .ob7 .M

L W . 981 L a9

am .781 -878

1020 L In LZ7l L a 1.610 LSOJ .m -726 . a 4 .on

1. om LDBS L 261 L 221 .a5 .Btu *ma

LO40 .m .788 .869 .!XI .ss1 - 610 .ea .725 .810 .E33

14,000

24,000

32,000

0