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CONFjDENIiALLARAP DOCUMENT CQINTrPNo. BIC53, 61op7 (ii?

HYPERVELOCITY KILL MECHANISMS PROGRAM (U)

Aerothermal Phase

EXPERIMENTS ON FREE AND IMPINGING

UNDEREXPANDED JETS FROMA CONVERGENT NOZZLE

by

Richard S. Snedeker

and

Coleman duP. Donaldson

The preface (pp. iv-vii) of this report isclassified "CONFIDENTIAL" and the remainder(PP. 1-59 and appendices) is "UNCLASSIFIED".

Sponsored by

Advanced Research Projects AgencyBallistic Missile Defense Systems Branch

ARPA Order No. 149-60

This research was supported *,y the .',dvj'ni'-et siesearchProjects Agency, Ballistic Misslle Defense SystemsBranch, and was monitored by the U.S. Naval ResearchLaboratory (Code 6240) under Contract No. ton;: -3903(oo)(x).

Aerorautical Research Associite. of Princeton, Inc.50 Washington Rjad, Princeton, New Jerr-y

September 1964

L

CONFIDENTIAL

I

ABSTRACT IExperiments wera performed in which tne velocity pro-

files and decay and spreading properties of free underexp...ndedJets of cold air were measurea. Stagnation point heat trans-fer parameters for Impingement of these Jets on various

surface shapes were evaluated and correlations made with the

free Jet data. Pressure distriltuton and photographicstudies of the free and impinging Jets revealed that anunusual siparated flow phenomenon can exist under certain

Impingement conditions. Problems associated with hanges inJet atabilc~y Rnd the effects of interfere•nce due to geometricarrangement of the apparatus were considered in a qualitative

way.

INI,-;

+i

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

--------------- - - TIC

SS- - - - - - - - - - --- --rJE

ZM YL4ýAL

M . , K X , R... . . .. . . .. . .S.E+ 1.+

A Tjo- --- -- -- -- -- --

I am~aý 22c ms -------- - rL- 1. T

AM•" NM•t , LWIu• ---- -- - -- -- - wi" _ M. z

~I

CONTENTS

Preface

1. Introduction. ....... . . . . . .. .. .0 * 0 * * a a a * a * a 0 a *.1

2, Free jet studies .. .. ...................... ..*

2.1. Structure of the turbulent, axially symmtricfree J t .. . . . . . . . . . ...

2.1.2. Moderately underexpanded jet..,..,....62.1.3. Highly underexpanded Jet .......... ,.. .7

2.2. Experimental program.. .... .......... .. .82.2.1. Apparatus and instrunentation...........iO2.2.2. Results of velocity prof.!e andphctý,vphic stui4Jes ............ 1

2.2.3. Special uchl2eren LtudY i•f

underexpanded jet .................. **.* . 20

2.2.4. Factors affecting profilemeasurements ..................... ..... .22

2.3. Discussion of results and comparisonwith theory ........................

3. Impingement studies .............. ................. 293.1. Basic flow characteristics ...................... 293.2. Experimental program.. ................. ...... 32

3.2.1. Apparatus and instrumentation.......... .33

3.2.2. Results of pressure distributionmeasurements and photographic

3.2.3. Evaluation of heat transterparameter (due/dr)r-O . .... ............. 40

3.2.4. Visu-11.zatir., studi'" ofstagnation region flow..................43

3.2.5. Momentum balances and interferencee ffectr.... ........... .......... c.... cc ..... 6

3.3. Pisoussion ............ . .................... 84. Conclusionr .. ...... ..................... . ........... .

5. Cited References ...................... ............. 5

Appendices

CONFIDENTIALPRUEACE

The key aerothermal process in the hypervelocity killmechanism is the transfer of heat to a solid surface from an

impinging Jet of hot gas. In order to understand and evaluate Ithis process, a thorough knowledge of Jet impingement flowphenomena is necessary. Because of the relatively littleuseful information already available on the details of impingtngJet flows, a broad program of experiments designed to providebasic understanding of the process has been carried out. Before

presenting the results of these experiments, however, a briefreview will be given of those aspects of the hypervelocity killmechanism which involve Jet impingement.

In considering a reentry vehicle whoca wall has betupunctured by the hypervelocity impact of a pellet, two ilowconditions have been shown to be possible, each depending onthe value of certain geometric parameters, and each involving

the formation and subsequent impingement on interior surfacesof a high energy Jet. It has been convenient to classify eachof these conditions in terms of the nondimensional geometry-dependent ratio A/V2 /3 where A is the area of the puncturedhold and V is the volume of the interior cavity. Althc.igh

no exact criterion for separating the two regimes has beendeveloped on this basis, it is generally conceded that forA,•2/3 < .01 the interior flow is "uncoupled" from theexterior flow and that the primary energy transfer tco Lheinterior is effected by weans of mass transfer due to a discreteJet ahose strength depends on the pressu- ratio through thehole. On the other hand, it is quite well established that forA/%/3 > .05, the interior flow is "coupled" to thvý exteriorflow. and that large energy transfer' to the ir--erior can occurin the absence of mass flux. This proceer has been discussed indetr.il els-.where*, but may be descib, briefly as follows:

*Hypervelocity K1!! Mechanisms Program, Ss-'•innualTechnical Progress Report, April 1964.

iv

CONFIDENTIAL

. . ..

CONFIDENTIALAs the external flow leaves the upstream edge of the hole,

a free shear layer or mixing zone forms which entrains gas

from the interior, thus transferring both momentum and energy

to the interior gas. If this mixing zone izz locally super-

sonic as it impinges on the downstream .i e of the hole, a

shock wave is formed which statilas off from this edge at a

distance which depends on the relative bluntness of the edi;,g

and the local mixing zone Mach number. Because the static

pressure behind such a shock is conniderably higher than theinterior pressure, the entrained interior gases form a jet

carrying high enthalpy from the high pre3sure region behind

the shock into the cavity. Under such conditions, the rateof energy addItton can be considerably higher than that foruncoupled flowi.e. transfer by mass flux.

Because of the difficulty of making reliable and -nean-

ingful direct measurements of jet impingement heat transfer

under real or simulated aerothermal kill conditions, amethod has been sought that would make possible the extrapo-lation to such conditions of data taken under less stringentcircusmtances. Such a method consists in the application ofexiiting etagnation point heat transfer theory to the I'vinge-ment of jet flows whose characteristics have been establishedexperimentally under a variety of conditions. Since this

theory relates the stagnation point heating and the radial

velocit. Zradient (computed from the pressure distribution)

at that point, the value of the method depends mainly on howwell this gradient can be predicted at a given point in termsoý' the characteristics of an impingement flow.

The over-all problem of jet heating has been separated

into three basic flow regimes in order to facilitate the

understanding of each. These regimes vnd their 'mportance

to the impingement prob!;... are:

1. -ree jet regimes axial velocity decay and radial

spread of axial velocity vrofile

CONFIDENTIAL v

CONFIND,. N'I 1AL

2. Impingement regime: stagnation region pressure

distribution and location of stagnation point for

oblique imopingement angles

3. Wall Jet regime: radlal vel0ocity decay, velocity

spread normal to surfe!ce, and azimuthal distribu-

tion of radial momentum for oblique impingement

angles.

Each of these regimes has veen studied experimentallyfor a variety of impingement surface shapes, ImpingemAnt

distances, Jet strengths, and impingemenz angles. Because

of the impossibility of specifying the exact contour oi a

hypeiveloci'y !ioact hole and because, In general, the jets

which form within an impacted vehicle are underexpanded, a

circular convergent nozzle was chosen as the experimer.;al

Jet source. The present report is devoted to the results of

studies of free Jets issuing from this nozzle and the normal

impingement of these jets. The results of oblique impinge-

ment and wall Jet experiments are reported separately.

It should be pointed out that in order to interpret

these results properly in the context of real or sImula&.x

aerothermal kill configurations, the influence of surrounding

structures must be taken into account. It is known, for

example, that seemingly remote obstructions can cause measur-

able ch'.,-,es not only in the structural and stability charac-teristics of a free Jet, buD also In its impingement pressure

distribution through, among other things, an alt'iration of

the momentum flux pattern of the entrained flon. Thus, theimpingement pressure distribution of a small diametor Jet

issling into a large open room would be expected to differ

somewhat from that of the same Jet surrounded by a much

smaller cavity. In a similar manr-.r, 'he structure of a free

Jet isanInx from a hole in a large i•.t plate differs slightly

from that of a jet issurig from the end of a l',:: pipe.

CONFIDENTIAL Vi

CON F1)EN IlAL A

Although a full invsatigation of such secondary or inuew-ference effects is beyond the scope of the present experi-ments, some measurements have been made which serve to

illustrate the nature of the problem., These matters are Idiscussed further in 2.3 and 3.2.5.

I ,

CONFIDEiNTIAL v

6

1. INTROXICTION

The problem of estimating the stagnation point heattransfer from a Jet of hot gas to a cold surface upon whi•chit impinges can be treated by aplying the usual techniquesof stagnation point heat transfer computation. These solu-tions are generally expressed with the stagnation pointvelocity gradient (du/dr)r.0 as a parameter (see, e.g.[1]). For the case of the Impinging Jet, this parametercan be readily determined from the pressure distributionmeasured on the Impingement surface. In order to providesuitable data for such determinations, a broad expeiimentalstudy was made of a number of different .Jot impingemer.1cases. This study included the impingement of an unheated,turbulent, axially symmetric jet of air on several differentsurface shapes. The Jet, which issued from a convergentnozzle, was run at several pressure ratios, both subsonicand sonic (underexpanded), and the impingement distance wasvaried through a wide range. The surface shapes used werea convex hemisphere, a flat plate, a concave hemisphere, anda shallow cylindrical cup.

In addition to the stagnation point radial velocitygradient itself, the correlation of this gradient withmeasured free Jet properties was evaluated. One correla-tion wad based on properties of the free Jet at the nozzleexit, and another was oased on local properties of the freelet at the same location as the impingr..(ent our.-.ace. ThesepaWameters are discussed in 3.2.3.

Although the primary characteristics of turT-,'lent freeJets (axial decay, radial spread, -'tc.) are :ell 1nown,several interrelated secondary factors .hich Influence theirdetailed itructure should be coneidered if one is to corre-late dat, resulting from tests mada with different nozzlesand supporting structures. In the present c:ct, in whichIt is assumed that solid boundaries may exist within a few

2

nozzle diameters of the Jet source, the most important of

these factors are thought to be (a) a dynamic instability

effect and (b) a blockage or interference effect. The

dy•flne instability rer'erred to is chrracterized by aprimarily leteral oscillation or "flapping" of the entire

Jet flow field, and is to be distinguished from the shear

induced instabilities of the turbulent mixing flow fieldwhich are, in general, of higher frequency and lower ampli-

tude. The blockage effect is distinguished by changes in

core length tnd spreading rate due to the presence of

obstructions in the entrained flow field. Since the jxter-nal configuration of the nozzle itself can thus be a fantor,

it is important to consider this effect in determining jaz

flow field momentum balances. A Set with a coaxial fruestream velocity superimposed about it is, in a sense, equiva-

lent to a free Jet with a prescribed entrairment flow.

Studies which reveal the changes in core length and spread-

ing for different ratios of Jet to free stream velocity arethus indicative of some of the effects to be expected due to

blockage. In addition to the two secondary effects Just

described, there is an interdependence uf the nature of the

instability upon structural interference through, for example,the reflection and/or excitation of acoustic disturbances.

The afor.aAentioned effects and their qualitative infiýnceon the measurements are liscussed more fully in 2 . 2 .4.

In recognition of the importa-noe of 'he abovs factors,

a thorough experimental survey was made o" the &ame free

Jets that were used in the Impingement studies ustng ti.eidentical test setup. In this way, it was ho~d that more

meaningful correlations of impingement bat transfer param-

eto-s could be obtained.

Also of interest, in the ove:c.-ai program, wae the

evaluation of effects duo to the shook structure- rresent in

the core of underexpanded lets. Decay and spreading paramet••a

_______.

3

were determlned for a number of combination. of Jet pressureratio (subsonic and underexpanded) and axial location. The

results of this free Jet study as well as a general discus-

sion of free Jet structure are presented in Section 2. Th

lpingaement studies and the correlations based on the free

Jet data are treated in Section 3.

I

I

4

2. F:RM M! STUDIES

2,1. Structure of the turbulent axially symmetric free Joz.

Although an extensive literature on the structure ofturbulent tree jets exists (see, e.g•. (2)), relativelylittlo quantitative information Is available on decay andspreading behavior for underexpanded cases (3,,4.5,17, 23].Analytical and semi-empirical methods for detei.iining thesecharacteristics have usually been restricted to either sub-sonic or properly expanded supersonic jets. In the presentstudy, however, It is of interest to determine ot only thelocal details of the flow within the jet core$, but Oheeffects of underexpansion on decay and apreadinr rate" inthe downstream portions of the jet, Only recently hasinterest In the characteristics of rocket exhaust plumes athigh altitudes and In space spurred efforts to understandsuch structural details. Some specific problem which havebeen studied involve pressure, thermal, and shock inter-ference effects on adjacent structure, as well as vehiclestability effects, and the blocking of CoMuMni, Ation signalsdue to ionization radiation in the plume. The emphasiz,however., has been on the determination of initial spreadingboundaries of the plume and the strength and location ofthe initial shock structure (6-17, 21, 22, 24,2. ratherthan &dcay processes. Other recent studies h n.. con-cerned with jet applii4tions in the fluid ampl or field(114] and the interrelation betr-. en un 4 ,'expandi 1 jet stabill-t•, and associated sound generation phenomena [191.

The general structural features of turbuler.." free jet)we k # well kni If we cor 'der .ne f), iesuiag from

a simple, circular, convergent noz•leoos three major variations

*Beause of the specifi'c I:e.'dt in underezaded ,jits,1 Ohe con trgent nozzle was conraiderv to be well suited to astudy of basic effects -,nce there is no dependence of thedegree of underexpaersion on area ratio or nozzl. divergenceangle. The following discussion is thus limited to convergen.tnozzle lowns, and the description of certain aspects ou"k asshook formation is not to be considered general. I

.'[•

I

of the flow pattern are possible, depending upon the pres-sure ratio Whrough the nozzle. (Although a properly expEadedMach 1 Jet can exist in principle, it is not treated in the

presei,. discussion.) The idealized structural f4atures ofeach of these variations as wrYl as the nomenclature andsymbols used to describe these jets throughout the remaianOr

of this report are shown in Figure 1. The pressure ratio

values given are for air. A typical schlieren picture of

each Jet type is shown in Figure 2.

2.1.1. Subsonic jet. A region of turbulent mixing between I.Jet and amblent fluid begins to form a short distance awayfrom the nozzle lip. Radial diffusion or spreading of th13region continues both inward and outward as the distancedownstream Increases until finally the inward diffusionreaches the Jet axis. At this point, the "potential" coreends, but the outward diffusion and entrainment of ambient

air continue. After a so-called "'ransition" region, at apoint somewhat farther downstream, the decay of axial veloc-ity on the center line and the radial spread of the velocityprofile behave in a manner consistant with the self-similarittof velocity profiles from that point on. The Jet is now saidto be fully developed. For air, the Jet will be subsonic for

isentropic pressure ratios 1 > P/P 5 0 > .528. Throughoutthis range it can be assumed that p./14 - 1.

It should be noted that an ideally expanded supersonic.et, which contains no shock w , ha.ý eosewtially the seam

structure as the subsonic Jet. Effects due to compressibility,h-wever, become much more important in det.ermin.16a the corele7gth and decay.

*"ldeally expanded" refers t, a properly exoanded jetissuing from a nozzls with zero exit divergence angle, i.e.with parallel flow at the exit.

St~a. I

CoeXS,.Tanaition - Fully" -

f eveloped

VO

Pee Mixing region *

Subsonic JetV

1 .- P.:> .528

-1-

Mixing region

~'Oblique shocksModerately undsrex21nded Jet

1.1 < p1/p.4 4 2

Z Intercepting Reflected oblique shock

Po Normal shock~ds

Fi u e P. S S i~ l n Obliq~ue shook

Hiphly underexpanded Jet

Figre . Treemajr vriations of jet flow from" sonic nozzle.

Subsonic jet: p./pvc m .552

Moderately uriderexpanded Jet: pL'. 1.4

Hltnly underexpandeci jet: 'P2/p. 3,57

Figure 2. Schlieren photographs of typical jet types ai~own in Figure 1.1

6

2.1.2. Moderately underexpanded Jet. When the sonic, or

critical, pressure ratio is reached, a very weak normal

shock f'orws at the exit. This shock dimininhes in size

rapidly with increasing preasuite ratio, however, and at

pl /pw =_ 1.1 the tamlLiar pa%-Ottn of' "shock diamonds" or"cells" composed of intersecting oblique shocks is estab-

lished in the core. Except for a lengthenitn and broadening

of the first few cells as Jet pressure ratio is increased,

this structure persists until p 1/p • 2.* The term "moder-ately underexpanded" is used herein to tenote jets within

this pressure ratio interval (1.1 < pl/p. < 2). Because of

the additicn:-.l expansion required in the iunonfined Jet fluow

beyond the nozzle, the boundaries of what oas once the

potential core, In the subsonic case, are now determined by

the requirement of pressure equilibrium between the outer-

most portion of the flow within the shock structure anid the

surrounding ambient air. The initial underexpanded condi-tion and the accompanying shook pattern result in a flow

which soon becomes vgerexpanded at a point In the central

portion of each cell. In this region, the local Pach numbeA

exceeds that which would obtain in a properly expended jet

with the same pressure ratio p 1/p 6 . The inward diffusion

of the mixing region,, however, does continue, although to a

relatit,-"y lesser degree at first, and ultimately results

In the complete dissipation of the shook dominated core.(Tn the-absence of viscous and shock effects, the

.. ow would continue a sequence cfexpanLor tQ overexpsnon

anl recompression to underexpension.) Because of the gradi-

er,•s of pressure, density, and Mae;h number that vxist In

the core, the impingement of this portion ol such a Jet

*Although the value of P/.. •- 2, at which the ncrralshock dW hr reappears for a sonsr. exl•, has been predictednalytically and verifl.J experimentally by several authors(Bee, e.g. L11]), any dependence nn interference and stabilityeffects does not appear to have been investigated specifice.)v.

&, '

?I

might be expected to result in surface pressure distributions

that are quite sensitive to impingement distance. Downstream

of the core, of course, after the Jet ,ls v.oome subsonic,

the Impingement behavior should be simn. ar to that of a

totally subsonic Jet.

Within the moderately underexpanded range, effects dua

to instabilities In the otter-all Jet flow £lsld are usually

found to have an increased influence in determining its decay

and spreading characteristics, both actual and measured.

This problem is discussed in detail in 2.,2,4.

2.1.3. Higitly 1,1nderexpanded Jet. At a pr6isure ratio /pO

of approximately 2, the form of the shook stzuctur-e it-, the

initial cell begins to change. Along the centerline, where

the expansion is a maximum, the pressure becomes so low (or

the Mach number so high) relative to ambient pressure that

the recompression possible in the remainder cf the cell

through the existing oblique shocks is insufficient to raise

the pressure (or lower the Mach number) to the required

Initial level at the end of the cell. In order to provide

the required compression, a normal shock disk forms on the

centerline. As the pressure ratio plip. is further increased,

this normal shock increases both In 3trength and diameter,.

At the .ne time, the original oblique shock structile is

maintained In the pernferai region, although altered some-

what in strength and shape due to the ad4itional expansion

ivquired and the presence of the normal Phock. FoPr vezr

hijh pressure ratios, the normal shoc3c dominates the struc-

tur-e of the first cell. For example, with p,,1 /pu = Pot It

comprises about 40 per cent of the total cross-eectLrnal

area within the Jet bouidtres ([1]L. It has alro beon

found [13• that the pressure ratio -;. which the normal shock

disk reappears is not ir..ariant with exit Mach number and

nozzle angle. The value p1/p, . 2 applies only to a sonit

nozzle.

8

Immediately downstream of the normal shock, the flcw

is subsonic. Since the surrounding flow in the oblique

shock region remains supersonic, a slip line exists at the

boundary between the two concentric reglons. For a fairlyhigh degree of underexpansion, Pay pl/pw 4. , the central

subsonic region is quickly accelerated so that approximately

sonic conditions prevail near the beginning of the second

cell. In this case, the second cell may resemble the first

and even require its own normal shock. For very high pres-

sure ratios, the structure just downstream of the first

cell is not well defined (for a recent investigation, see

(17]). However, it is probable that the jet will be

dominated fo' some distance downstream by tne very str•ng

normal shock in the first cell. Ultimately, it decays

through a structure with only oblique shool-. The mixing

region surrounds the core as usual, but its radial diffusion

rate is small at first with the result that the effectivecore of the highly underexpanded jet can be extremely long.

It should be noted that while a strict definition of core

length for any underexpanded jet may be given as the pointat which the shock structure disappears, effects due to the

instabilities present make this point difficult to definefor a real jet. The downstream behavior in such cases,

therefore, is best given in terms of the point at which the

core's influence ceases. As in the case of other jetstrengths, this may be uaken as the point beyond which

vel.city profiles are self simil.ir,

2•. Experimental program.

Since each of the three major jet variaiions dercribed

above was expected to exh4 bit an Imopingement behavior some-

W.at different from the othera, a tv-11cal case representutive

of each kegime was chosen for detailed study. Values of

radial spread and axial decay for 3ach of these jets were

91used later to correlate the results of impingement measure-wiants wade using jets with these same strengths. The jetsused to provide these correlation data are listed below.

The ~rsoure ratio for each is given In two ways,, viz.p./greand p1/p., where PO to the ambient pesoure intv

which the jet exhausts,, p 0 Is the stagnation pregssure inthe settling chamber, and p1 is the static pressure (assumnedto be constant) In the Jet exit plane.

Subsonic jet:

Pu/pec - .834&

M, W .52

Moderately underexpanded Jet:

-. 372

-1.42

Highly underexpmnded jet s

p/O- .148

PjpP- 3.57

Velocity profiles of each of the. above listi"4 jits were

measured at several axial locations. 7bese locations werevlhosen tn represent each of the -agions of basi~ally diffa..-*nt str eoture within a typical .,01-e;. jet of highi subsonicMich snhmber. They or, Listed in terms of nos!'4 diameters

4-~

10

dN downstream from the exit as follows:

X/dR Region of typica, s.ubsonic let

1.96 Core7.32 End of core (transition region)

23.50 Fully developed39.10 Fully developed

In addition to the cases Jisbed above, a number of

others were studied in less detail. The entire pr ram is

ýabulated in Ap;endix 1.

2.2.1. Apparatus and instrumentation. A convergent aozzle

with an exit diameter dN - .511 inches and exhaustlng to

atmospheric pressure was used. This nozzle was mounted on

a 4.75-inch i.d. settling chamber which was supplied with

air from a storAge tank through an automatic regulator

valve. The maximum storage pressure was 220 psig and the

maximuma settling chamber stagnation pressure was 125 l; Ag.

The settling chamber and nozzle are shown in Figure 3, which

also shows the flat plate model used in a portion of the

impingement studies described in Section 3.

Lý,:al velocities were computed from measured Pltot and

static pressure profiVs. The Pitot and static pressure

prar s used were mounted on a co~wnon be which could traverse

tne Jet in a vertical plane at any axial location up to about

6G nozzle diameters downstream from the exit, Bmth probe

tIrA were made of .032-inch co.d. 8tainless steel tub!.ng; thePiMot tip was cut off square, and rhe static tip was awslender ogive with two .C435-Inci- I-oles on oppocAte sides.V16 Inch from the tip. A skete1 •-,.- this probo and itsmounting is shown in Figare 4. Pressures were -"sasured on

liquid mwiooeters or with Bourdon-type test gauges accordirn-

to the pressure level encountered. Readings for ea',h run we'etv I, r ',•. • , .

I II

mI

Figure 3. Nozzle and impingement model setup.

ISet Screw

I .~032"o..

S ýU.tic t ip .O \\

Jack screw -.

Supporting track (total. length 20"1).

Fir Combination probe. used ,2 fr, jet surveys.

~ - .4?,

recorded photographically. The stagnation temperature was

measuretd with a bare copper-constantan thermocoup *N in thesettling chamber.

Photographic studies of the Jet wtre made using sevei. 1

techniques. Schlieren pictures and shadowgraphs were talzen

with both continuous and instantaneous light sources. Acoaxial type spark source with a duration of less than1 vsec was used. The basic optical system was of the usualsingle pass, off-axis, parallel-light type employing twospherical mirrors of 6-inch diameter and 60-inch focallength. In addition, a limited number of pictures 0eie

taken using a nore sensitive double pash unincident systemwith a single mirror. While the resolution of these la4ter

pictures is inherently less than that achieved with tiesingle pass system, the extra sensitivity provides a usefulqualitative picture of certain structural features (seeSubsection 2.2.3.).

2.2.2. Results of velocity profile and photograDhic studies.Results of the free Jet measurements for each of the e:*: 01-fled cases chosen for detailed study are presented in the

following paragraphs, Basic data for these and the remain-ing cases tabulated in Appendix 1 are to be found inAppend& .. 2.

For each typical let, lhe ,-easured total and staticpressure profiles are presented with a Park schlierenpýtograph to the same scale showing thal jet for the Atirst

10 nozzle diameters downstream (Figures 5, 7, and 10). ]&onh total and static pressures ae pletted in th' form of apressure coefficient expressing the local value as a percent-

age of settling chamber &uge preý,au're. The local total!.p~ressur[e in p J and the local satit"_. pressure is pj.

Velocity profiles, and z;reading and decay characeteristics

calculated from the pressure meaburements are given in

Figures 6, 8, and 11. In Figure 12, the spreading chs'aoteur-

.,•'•.• •. I

12

istics of all three •tets are replotted together in order toemphasize certain basic differences.

Local velocities were computed on the basis of the

measured local pressure ratio and the meazued stagnation

temperature with the aid of compressIbl. flow tables. One

pressure ratio at each point wu6 evaluated from curves*falred through the data for each pressure. * Because of the

uncertainty in locating the true mean axis of symmetry

before running the Jet, the probes were traversed through a

range well to either side of the assumed axia. The true

jet axis was then taken to be the axis o0' symmetry or the

measured profile. The data were then replotted with refer-

ence to thi. 'rue axis and the curves draw-.. In some cases,

the radial traverse extended outward only far enough G$ive

a proper determination of the spreading parameter r. 5 , the

radius at which the velocity is one-half the maximum value.

In Figures 5, 7, and 10, a number of data points have beenomitted to avoid crowding. The velocities shown In the

profiles of Figures 6, 8, and 11 are nondliensionalized on

the maximum velocity, even if It does not occur on thecenterline. The radial coordinate is nondimensionalizee

on r 5 . In the plot of decay and spreading behavior, the

velocity on the centerline V i ts given as a percentage of

Its value Vol at the nozzle exit. The 14nterline value ofthe totas pressure coefficient is also plotted. Spe,'efic

structural features revealed by the pictures and data for

each of the three jets will now be discus'ed.

Subconia jet (Ml .5.2). The pressure and velocity profiles

of 'Igurem 5 and 6 clearly reveal the expecte'd oit,'•tursl

featares. The core with its profile of unifoz'. veloci•;y near

'the centerline (x/d. - .1.96 and 3.929) anct the fully developedr wit!,on .L self-smilar prct1les(z=./ - d..7, 23.5,39.1, and 58.7) .e-

*Por the subsonic ca:.e, the static pressure. vas measuredonly for the three stations farthest downstream. At otherpclnts, It was assumed that p4 t p•.

-------

15 20

11 .. 7

x/dN 0 1.96 5 7.32 10

10-

r8N 6-

1" 4-

k0

-! -•-_ _ _ _ __,[

.2 .4 .6 .8 1.08-4 I LI 1 L Jl

0 0 .2 ,4 .1 ,8 1.0

10- p 0- po - 0 .2 .6

p -p PO

Pac - P"

Figure 5. Measured total and static

eresaure distributions.

0,/r:,Oc = .834pl/p,, • .00

20 25 30 35 40

1 .04

2 .2 .4

. .

, ' .a

2A P/p. - 1.000,/pO -. 83

2.0 M, - .52 x/dN

r 0 - 17.9uwa o 1.96r.5 x 3.92

1.6 v 7.320 11.7c 23.5

1.2- A 39.1tý 58.7

.4-

0 .2 .4 .6 .8 V/Vmx 0.

r-I I

V,.

.2 . PC "P .....

L I L i I I . L •I0 5 10 15 20 25 30 35 l_ 4 0Figure 6. Normalized jet velocity profiles and axiAl deey arfd

spreading characteristics.

13

the usjaY ,.pearance.* Although the decay curve (V,/Vcl)sho- , x/dN - 7.32 station to be In what is probablythe traw ition region, the velocity profil- does not exhibitany noticeable core effect. DowTntreu! of x/dN - 11, t•decay is seen to follow a characteristic Incompressiblel/x-dependence quite closely. If this curve is extended 'acxupstream to a value of unity, thus negleelring the transitionregion, an apparent core length x./d, of about 7.5 isfound. While this Is in approximate numes. cal agreementwith the results of other studies for similar subsonic Machnumbers, the meaning of such absolute comparisons ',s limited,even for suso-tc jets, by the secondax.y effects alreadymentioned. The experiments of Warren (.Oj, for et4,

with X1 - .69, give a core length x/dN -7.2 wl'h avalue of x/dN -u 10 for the start of the fully developedregion. Since this shorter core length with a higher Machnumber Is in contradiction with the usually observed corelength-Ibch number dependence, it is possible that differ-ences in the secondary factors affecting the two experimentsmay be important enough to account for this apparent 7 omaly.This is not to Imply, however, that experimental errorscould not account for a difference of this -ngitude.

The spreading behavior is best observed on a plot ofr. 5 /r es a function of x/dN (Figure 12). It le neenthat the initial spres.e'I :eate decreases slightly for theTfr--st four or five nozzle diameters dowvstre=. .!-e ratewnen ir 'ýreases until, at x/d. Z 11, It becomes fairlye.natant. A otransition" region defined In zhe interval in41hlch the spreading rate Is ehea-gin most rapid*y '-t seen to

'StrIctly speaking, *fully .zte'oped" self-similarvelocity profiles imply a flied 1 " 7,ionship between spread-Ing nd & ecay rates. Hwever, because it Is difficult todetect and confirm sw*.!. deviations from self-, -ý.llarlty inthe present data, "fully developed" is used only in arelative sense in these discuasions.

match very closely a region similarly defined on the basis

of the decay curve, i.e. 5 < x/d. < 11. (Note that adifferent transition region is shown schematically inFigure 2, In that case it wac defined as beginning at theend of the core as a convenience in designating the ideal-

ized core length.) In the "fully developed" region(x/dN > 11), the data indicate continued slight deviationsfrom a truly linear spread. While it is felt that thesedeviations exceed experimental error, it is not postble toconclude how much the spreading rate actually varie3 because

of the unknown magnitude of Jet stability and turbu-.enceeffects. It is shown that spreading ratce based on ae23uredstatic pressure, are slightly higher than those based on aconstant ambient static pressure. If a constant spreadingrate is determined by a straight line fitted among the threepoints farthest downstream (x/dN - 23.5, 39.1, and 58.7),a spreading angle of 5.50 is found. Using the ambientstatic pressure data, the angle is 5.20. In either case,

these values exceed Warren's result of 4.10 by an amountthat is probably more than should be expected on the L"isAof the Nach number difference alone. Warren's data howeverare based on surveys downstream only to x/dN - 25. Usingthe present data for a similar axial interval, with thestatic iiressure assumed equal to ambient as in Warr.-,' scase, an angle of 4o° results. Only if one can assume

tnat differences due to seconda-y effe.,s as we'.1 as Nachnruber are small for the interval of axial distance andPf'ch number being considered, can it be cono.ludc,• that theag-9eement is quite good.

The schlieren picture shows the characteristic subsonictvrbulent Jet mixing region, lnc'.iu'c.g the initial stages ofthe min•. -5 process Just outside t.t nozzle exit. The core,

however, is not readil! discernable because co *ie three-dimensional visual block'ng effect of the mixing disturb-ances (cf. the continuous light schlieren picture shown in

151

Figure 2 for the same case, but made with the double passsystem, in which the core is more easily recognized),

Moderately underexpanded Jet (pl/pI-n1. 1.2). Effects due tn

underexpansion are at once apparents especially in the axial

decay curve (Vc/Vol) of Figure 8. The centerline velocity

Is observed to be supersonic in the core region at the three

points chosen for the measurements. However, because of

the local velocity variations to be expected within thelength of each shock cell, these three points alone areInaufficient to show the detailed core structure, and thecurve throtu•, them is thus drawn dashed. Although additional

measurements of velocity were not made in rhla r the

highly detailed survey of Pitot pressure shown in Firire 39is indicative of the kind of axial variations to be expected.

The velocity profiles show clearly the local effects

of expansion in the core. At x/dN - 1.96, for example, thecentral portion of the profile ie seen to be supersonic. In

addition, there is a marked radial gradient of velocity with

the peak occurring some distance from the centerline. Super-sonic central portions are also observed for x/dN - 3.92and 7.32, although the position of the peak velocity isdifferent in each case. For x/dN - 11.7, the profile issubson.', th"oughcut, but still shows a slight flatteningnear the centerline. ADpa&.ently fully developed subsonic

prnfiles are observed for x/dN - 23.5, 39.1, and 58.7.The behavior of the measured spreading parameter

r.5/rW is different from that observed, for the subsonic

Jet (see Figure 12). Beginning t an exial ditstance ofabout 20 nozzle diameters downstream, and continuin& to at

Icast 40 diameters, the m-preadIMr rate in each axial portionis substantially higher. Fainthet 7.stream, the rate

decreases. As a means %" comparing apparent changes inspreading rate in different regiois of the jet, several

spreadirg angles have been computed. In the Interval

I

mI

15

11 .7

,4 i • 0 1.96 57.32 10

10-

rN

4-

S.2 .4 .6 .8 1.0

L - IIJL i •J _ _ _

0I- ib .2 . 6• . ." 1.0

1N0-- •-

8P - -, . 0 .2 .4 .6

S - p_ 0.2 .4.6

i . . . . .. .,. - .

P... . ... ,-,;, ,, ,

Figure 7. Measured Jet. Lotal and static

pi'enzur. distributions.

Pa Dec . .372pl/p. - 1.42

25 30 25 x/aN 40

23.5 39.1

,0

.6 G • .

0 .22*

I

2.0 p./p. 0 - .3T2Ml . 1.00 x/dN

rpO- 39.7 gala 0 1. 96x 3.92

1.6 V 7T32011.7023.5

1.2 •mt.. 9•. 1

C 58.7

Supersonic to.8 - 1. "iht ofthese marks

. -

Ot.-o0 • .4 .6 .8 " :o

.- V/Vmax

1 0

See ?i.a3for details qVe.6 - o ýhis -

region - Cv

,4 - '

0 •

x P50 r,.

o [ ..... '.---------•o - IL!0 5 10 15 20 25 30 x/dN 35 Ito

Figure 8. Normalised jet velocity profiles and axial decay awti.spreading eharacteristios.

" , ~- -. . / ,v,• . , f ,,.'/ .,-

16

4 1x/dN .20 the angle Is only 3.00 but for 20 < x/dkj.eit is 7.40. Using the two points :arthest downstream

(x/dw - 39.1 and 58.7), an angle of 44*.8 results for thedata based on measured statin preesw.,:, with an angle of4.50 for the data based on ambient static pressure. It

Is believed that the increased spreading observed nearestthe nozule exit (x/dN < 4) is due to the widening of the Jet

as It expands on leaving the nozzle. Throughout the remain-

Ing region of high spreading rate (out'to, say, x/dN - 40)there Is reason to believe that the observed rates are at

least partly the result of Jot instability. PhotL~raphic

evidence in s'pport of this belief Is discussed inr 2.2.3.The possible consequences of Instability effects inaolar

as the measurements are concerned can only be sugge.bed

qualitatively (see 2.2.4) on the basis of the present data.

Far downstream, the return to a lower spreading rate moretypical of an Incompressible flow appears to be consistentwith expected trends.

Of particular Interest In the pressure distributions,

shown in Figure 7, is the behavior of the static prezure Inthe core region (also see Figures AI1-9 and 10). Atx/dN - 1.96, a strong radial sradlent is observed, with a

muxlam pressure on the centerline which is considerably

h:44hbe.- than ambient, and a minimum pressure near t.%z edgesof the Jot which is ".wc ihan ambient. At points farther

d•wnstream, the central peak rmalrns, 'jut the over-all

pressure level in the core drops below ambient pressure,Iinally, at a point beyond the end of the core, t'he certral-isak disappears and the over-all level grac~al¥y Inareases

Stowmrd the ambient value, ihile thi& behavior Is qualita-tively, both axially ana radlal: 7, the same as that found to

exist In subsonic and propeA-lr exi.-inded supersonic jets 4

(see, for example, [2 ),p a comparison with #",r present casecan be misleading without further clarification. An axiala

survey of centerline static pressure was made, therstore, t",

~~~~~~~~~.... ........ '• • • ';• ' ... • ,• •!

17

help in understanding this situation. Figure 9 presents

the results of this survey for a subsonic Jet (P/Psc =

,552) as well as the underexpanded jet (p 1 / ., 1.42) in

question. The core shock structure for 'the latter case is

sketched to scale so that the piessurea may be referred to

their approximate locations in the Jet. The dashed curve

interpolated among the data is, of course, orly a qualita-

tive suggestion of the actual behav4 or. As such it is based

not only on the measured points, but also on the assumption

that minimum and maximum pressures occur near the canter and

end points, respectively, of each cell. In any case, the

extreme Srad ent% within the core are clearly evident, and

It is seen that the values found during profile measur.menrt

(solid symbols) cannot be Interpreted as indicating a

smooth variation in the axial direction. Also of interest

is the fact that the measured pressure at the center of

the Jet exit plane ((p, - p.)/(p'o - PO) = .291 at x/dNM 0)

is higher than that indicated by the nominal pressure ratio

pj/P.- 1.42 (or (p1 - p.)/(P,8 " p-) - .247). Xn addi-

tion, the axial variation near the end of the core and

farther downstream closely resembles the typical subsonic

behavior. It is therefore suggested that the extreme pres-

sure gradlents due to shocks are modified by a superimposed

rr Lal -1 axial distribution which Is similar to that

existing in a subsonic or 1,roperly expanded supersonic

ctwbulent Jet. Velocity profiles determined from the pres-sa.re ratios at an axial station in the zhock itructurevtuuld thus reflect a combination of two effects (resulting,

e.%. in a peak velocity off the cinterlirse)., &•e, would, ofcourse, be expected to vary in shu.pe from point to point

along the axis. The p'iles aown in Figure 8 for the

core Oatstions, therefore, are xo --acessarily representat've

of a smooth transition -,f profile shape from one axial loca-

tion to aaiother,

, ++' II

• • .;+:I_ _ _, •

CQ 0

r4)

~. .- 4-4

4) 'V4)

-~ 00 'Vla

00

0 4)o1 o fA

00 1.0 .00) .

0*

0 s~

18

The spark photograph of this Jet, shown in Figure 7,reveals some distortion of the stable core structure asearly as the second cell. Farther downstrweam, the core

becomes highlv unstable, and the shock cells appear tobreak up and diffuse into the :rrounding mitxing region.

In the continuous light picture of Figure 2, which portrays

the time-average appearance, the downstream cells are more

easily recognized. Weak sound waves emanating from the

mixing region can be detected in the spark picture.

Highly underexpanded Jet (Pu/p. = 3.57). It is clear fromthe velocity profile and decay data (Figure 10 and 11),

that the distinguishing structural feature of this Jet Inthe upstream region is the normal shock disk in the firstcell. The picture shows that this shock occurs at x:/dN -

1.58. Just downstream of this point, at x/dN - 1.96, thevelocity profile exhibits the expected subsonic central

region. Within this region, the minimum velocity appears

to occur Just inside the slip boundary, while the peaksubsonic velocity lies on the axis. In the surrounding

region of supersonic flow, a peak Mach number of 1.9 isreached, which, coincidentally, happens to correspond to theMach number for proper isentropic expansion to pl/pO -

It it fPLt, however, that at a point somewhat upstream ofthis, an even highse lach number associated with an over-

expanded condition should exist. The photographs of Figure10 and Figure 2 both reveal an uparen. noemal ahock In the

second cell at X/dN - 3.3. Slightly downstream of thisp-int, at A/d, - 3.92, the velo-.-ty profile e-a.'& shows asUI'sonic central region, although ,he radial extent is muchless than it is for the x/!N - 1.)6 case. At x:/d - 7.32,tna ent!SV central region is zup/ýr&rtjiic, but the maximun

velocitl still does not occur on the centerline. In this

respect, the profile is similar to aome of thost, found in

the core of tCo; -. de.amtely underexpanded jet. A substantial

• :,, -.

15I

.-.

11.7 1

X/d N 1.96 5 7.32 10Me - Center line Maoh number

r 6- .5rN

2--

T 4 K-O... . . -_ _ _

41 ct:

- I0 .2 .4- .6 .8 1.O

o 0 .6 2 8 1.0

i - - 0o o2 i. .4 .6

pSc- P -

"" " P,,

Figure 10. Measured jot tot.al and t",aiticprersure distributions.

8 8pl/p, 3.57

0, j 25 30 35 X/dN 40

3.5 39.1

-ter lno Kach nl-"m' I C

L

.. ... .. .o

.6 .1

p/p,= 3.57 x/dN

r NZM1 - 1.00 X 3-92

r ~ ps 7.32I0 11.7

23. 39.1

r)• 8.7

Supersonic to righto, these marks

o . .4 .6 .8' 1.01.4- V/Vmax

1.2 1 /Vc1

1.0l.2

t

I

L-,4Ii .2 r- p.-.-

_I_ _I t L . I I •aJ

0 5 10 '15 20 25 3 35

Figure 11. Normalized Jet velocity profiles ,nr axial decayand sprei ling characteristics.

19

supersonic core remains at x/dN - 11.7, although, at leastat this specific point, the peak velocity lies on the axis.

haile the oblique shook structure in the region between the

laUt normal shook and the end of the co•'4 tay not consist Iof well-defined cells such as th.ose round in the moderatelyunderexpanded case, it Is likely that whatever shocks are

present will produce local periodic changes in the velocity Iprofile as long as they are of sufficient strength. Thus,no smooth variation from profile to profile uhould be inferred

fromthe adata presented for this region. Farther dow.nstream,it Is observed that the centerline velocity is Just subsonicat x/d m 2 --5. Reference to the spreadinr parameterfr.5/)~ behavior and the velocity profiles fcr the X/dli

23.5, 39.1, and 58.7 stations reveals that a fully developedJet flow may not occur short of at least 30 or 40 nozzle

diameters downstream.The results of a highly detailed Pitot pressure survey

on the centerline of this Jet are given in Figure 39. Thissurvey Is Indicative of the local effects due to the normalshocks present and the subsequent oblique shook structure inthe core. Of particular interest is the substantial recovery-of Mitot pressure relatively far downstream.

In order to verify the presence of a normal shock disk

in the s"'ond cell, some additional Pitot-static pressuremeasurements were made on tbe centerline at selected pointsin the region of interest. The Mach number distributionrv.•ting from these measurements is shoi. In Figure 10.

The subsonic region Just downstream of each normal shook Isa M--rent. It is Interesting to notiý the slarpv 'J'.ic.rease In

Mact, number from .45 to at least L.2 Just upstrew ofthe second shock,

The vloclty spread data for je,- Jet (Figure 12)reveal a amewhat erratic behavior. In the region immediate-ly downstream of the nozzle exit, the bulge observed is

S. . . . . . . . .. . . . . . .. .. . . .. .. ..

I ~pl./p.c - 1.00

o20 30 50 /'d7tl -7

rI

4 -

12.~~ ~~ mesrdrda pe~ad sured c J8 ~4

an ievepno 148e

21''

S:l. 35

0.1 1

--

20

consistent with the boundary shape assumed by the expanding

flow in the first few shock cells. Except for slight devia-

tions, the spreading rate is then essentially constant fora considerable distance downs'tream (u/ds = 40). In the

Interval 4 1 x/dN 1 12, the 7preadIng aznle is 2.50,

and for 12 < x/dN 440, an angle of 3.90 is found usinrathe data for measured static pressure. The very low spread-Ing angle for 4 1" x/dN 1 12 :is in sagrowent with the sl•

apparent spread observed in the schlleren •ioture for this

case in Figure 2. Downstream of x/dN = 40, thk measured

spread Increases. Although an increase in this region seemsto be consistent with the appearance of essentially fullydeveloped vtuiocity profiles at x/dN - 39.1 and 53.7, the i

angle of 6.00, based on the two data points, Is somewhat

higher than might be expected for such a region of subsonic

decay.

The continuous light soblieren picture of this jet in

Figure 2 reveals a structure downstream of the second cell

that seem to differ somewhat from the relatively well-defined

oblique shock cells observed at lower pressure ratio&.

Although oblique shocks appear to be present, the structure

Is more like that of a properly expanded supersonic Jet with

fteh waves in its core.

2.2.3. Snecial sohlieren study of underwx ded Jiv. A

series of continuous iaght schlieren pictures was taken

uding the high sensitivity doub:'e-pase joinciitit optical

saytew. In this series, the jet preasure ratio p 1/pW wasvft'ied in small incrments througb a range from 1.00 to

more than 4. In Figure 13, a sels-tion of t',ese pleturesIt shown in order of increasing prosstur ratio. (A subsonic

ce is In hown for reference.) Tt '&- observed that an IntVais-

tied w-•!- of the mixig region Is obtained. Because of the

relatively long ezpopswd tim (1/50 sec.), tIl image isrepresentative of the tive aver•age appearance. It Is at ornce

u i• |I

-r4

rq r-I80i

apparent that there is considerable variation of the observed

aWread of the Jet as the pressure ratio is changed. This

variation is interpreted as being due to chai4ee In the

stability characteristics of the entire at flow field.

Although the Instantaneous detalis of the structural degrada-

tion of the Jet due to Instabilities are readilr observed in

spark pictures, the intensity or amplitude of th. motion is

difficult to interpret from single p-lctures because of Itsthree-dimensional nature, The pictures of Figure 13, there-fore, are useful in making qualitative couparisons of over-

all stability effects for jets of different strength& It

has been dewucitrated (19] that the stabilAiv of a given Jet

can depend not only upon the pressure ratio, but also uioai

&e*metric or interference effects as well as the cross-

coupling of acoustic disturbancos generated within the jet.

Because of this dependence, It Is probable that the changesin stability observed in Figure 13 are unique for this

particular test apparatus. As an example of this uniqueness,

It has been found that the proximity of the mirror (about40) to the jet in this optical setup produces a shift i!,

what Is believed to be a region of high instability in the

pl/pw w 1.42 Jet. A curve of spreading parameter measured

with the mirror In place Is given in Pi"Lre AI-ll4 in order

to Inust ._rte this effect. The corresponding change ±" the

decay curve (Figure An-16).. hz.wever, Is relatively small.

This Is consistent with the assumptions aout stability

efiits oan profile seasureonts discussed i.n 2.2.4.As the pressure ratio is inoreased, two distinct rangos

sam vaoted In whiab the lnmtabitity avpcarz to lbe v,,,r I ntense.An lrnrease of pressure ratio from 1.15 to 1.42 and then q

furthcr to 1.59, pans tý,o firet xue.h rang, with theL/pa - 1.59 case appearing to be W:,tively stable. A

second range of even great-r Instability seems to center

about the oace for p./p4 = 1.84. At a pressure ratio of2.00, the normal shock disk is first observed, Withln %dOie

. •. • , .... ..... .. .. ... . . . ..r .' .. ..i : • • • • ,

22

region covered by the pictures, the degree of instability Iappears to lessen with further Increases in pressure ratio

above 2. It should be noted that although the Jer chosen

(j/p,, - 1,42) for detailed sttdy ifn the moderately under-

expanded case appears to tall .' 0hin one of the ranges of

high Instability, the behavior showv In the picture is not

In itself conclusive because of the aforementioned mirror

proximity effect.

The time-average appearance of the core shook utruoture

Is also of interoet. As -.4ht be expected, the more unstablejets show rover well-defined cells, One contr-ast is particou-

larly great "tween the cases for p,/p. . 1.59 and 1.84.

One* the normil shock occurs In the first o311, there t.s a

gradual change In the appearance of cells farther downstream. tAt first, these cells seem to follow the charecteristios-type

of pattern used as a model for the moderately underexpanded

Jet. Bwever, between the pressure ratios 2.59 and 3.57,the regular cellular division seems to give way to a more

continuous pattern of Intersecting oblique shocks.

2.2.4. Ftctors affecting m-•tile measurements. The velocity

profiles upon which the jet spreading and decay results are

based were, of course, determined from measurements made with

Mirot and static pressure probs, Inherent In such measure-

menta are certain limitations introduced by the properties

of the flow itself. In the case of turbulent jets# the most

t'i'~..rtant limiting factors ae tAought o ba the turbulence

in the alying region and the over-all jet Instability. (It

It felt that alipment errors due to neglea ol, '4ie radial

cwponent of the mean velocity and Probe "ar.e -of-et tack"

errors due to the shear flow mean p.ofile are of minor

ixrportance..) Although no quartltl.ti ja evaluation of theue

factors ý.a possible on the basis of the existing data, some

general conclusions about the relative validity cof the

measurements should be pozsible.

23

The pressure sensed by a static prefaure orifice ia

affected by transverse velocity components arising from

turbulence as well as any other phenomenon having a cross-'

wise component. The magnitude and sign of the resulting

errGr, however, depend on a complex re.ationship among

probe size, turbulence scale, and the magnitude and space

correlation of local velocity fluctuations. In general$

therefore, the validity of the static pressure measurements

car, be assumed to be the greatest In regions of the jet

where turbulence and Liatability are the least relative to .

the magnitude of the mean motion, namely, In the upstream

regions.

In many c"es, Jet velocity profil!s are determined

from the measurement of Mitot pressures alone, with tie

static pressure considered to be constant and equal ;o

ambient pressure. In the present experiments, In which

static pressures were measured in most cases, it Is possible

to compare profile parameters determined in both ways. In

Pigure 12, values of the spreading parameter based on ambient

static pressure are shown for several oases. It Is seen

that a. somewhat larger spreading rate results when measured

static pressures are used. It is not possible, however, to

determine the degree to which these measured pressures

actually contribute to the determination of a true profile

becaus.. the measurements are most in doubt where tT"; can

have the greatest inflnce, i.e. in the outer portion of

thd downstrom region where the, appros .h the nignitude of

the total pressure level.

While total or Pitot pressure measurements are alsoaxtected by turbulent velocity components, 1- iL fel; that

over-ali jet Instability effects may bf of greaLer Impor-

tence in some of the present aas• s. In such cajes, the

-esponsr of the Pitot tube at e•cn paint in the profile canbe considered to be thai, resulting from a flu,%'.'ating veloc-

Ity at thrt point. If it is assumed that this response

I

24

represents the time-average value of the fluctuation, atyplial jet mixing profile measured in this way will differfrom its Instantaneous shapet Assuming a lateral disturb-ance motion %hoe* mean amplitud- is dist.ributed axisymiet-r!cally, the measured profile wmý,Id appear to be somewhat

flattened at the center and spread out at the edges.Spreading and decay rates based on such time-average profileAwould, of course, be larger than those based on Instantane-ous profiles.

Because of the foregoing factors, It is clear that the

measurment, for example, of a high spreading rate for agiven jet MX only be indicative of the fact that the jet ishigh•ly mstable. The Instability would hcr. have to beeither eliminated or eveluated by other means before the

true viscous spreading rate could be determined.

2.3. Discussion of results and eomparison with theor.

The main objective of the foregoing study of free jetproperties has been the determination of apreading and decaycharacteristics to be used to correlate the results ofmpi-nement experiments using the same jet apparatus, By

using such data in this way, the Influence on the correla-tion of secondary effects such as jet stability might beexpecte,. ;o be minimized. Also of interest In this studyhas been the general behavlor and structure of free jetstht-selves, especially cases In which the jet is under-

expanded. 'The results of the three typical cames presented in

detall In 2.2.2 confirm a nvumbur ol expected stallaritles asweli aA important differences among the basic flow types.Inx the care region of eaQ. jet, tbe differences are most inevidence. The core of the eubsonl -at is, of course,determined by the inward 4iffusion of the turbulent mixing

region, Whereas the moderately underexpended jet has an

S I

25

additional determining influence in the system of oblique

shocks present. For the highly underexpanded case, thenormal shock disk is a dominant factor• in te local struc-ture of the core. Because of Ohe very ;-.esence of shocks

in the undererpanded cases, howver, it is difficult tospecify a consistent criterion for core length that can be

applied with equal pertinence to all the Jct&. It is felt.therefore, that the most meaningful basis of comparison is

the downstream behavior in terms of the point at which afully developed turbulent mixing profile is observed. The

present data are sufficiently detailed to be used In thisway.

Using the measured velocity profiles bj them3,s.c1 . 1,is found that the subsonic Jet can be considered fully

developed somewhere between A/dN - 7.32 and 11.7. Theconstant relationship between centerline velocity decay and

Jet width or spread, which Is thus implicit and which musthold if axial momentum is to be conserved, is fairly well

confirmed in separate plots of these two parameters. Themoderately underexpanded Jet (p 1 /ps - 1.42), however,

exhibits a profile at x/dN u 11.7 that still does not

match those far downstream. It has been pointed out that

this particular Jet appears to be quite unstable and that

measure. -elocity profiles may represent a distortion of

the actual instantaneous pr-:f4 le. Because of this, the

definition of a fully developed region is difficult. ItI.n: ceen, for example, that the velocity proftoiles are ve'y

clo';e to being similar for x/dN - 23-.5, 39.1, and 58.7,vh±l2e at the same time there is a marked decrease in thespri.adIng rate in the same zrange. .Phis situation couldresult if Jet instabilitf.-.3 were atronger in the upstreamregion and thus resulted in broad&- -.-.asured profiles there.In fact, .f it is assumed that the measurements far down-stream at x/dN - 58.7 are relatively unaffected by Instabi-lity, it is found that the over-all spreading rate requircd

.. .... .o .-.....

26

to reach the measured width at that point is very nearly

the same as that required for the subsonic Jet at the same

point. The highly underexpanded Jet is apparently dominated

by a very long supersonic core, as shown by the low initial

spreading rate and the centerline Mach amber survey. It *-.

doubtful, in fact, that a fully developed region occurs ait

all within the range of the measurements. Velocity profile,:i

for x/d% - 39.1 and 58.7 are essentially similar, but the

spreading rate between these points is higher (6.00) than

that usually associated with a fully develop4d subsonic

mixing region.

A comparison has been made between the results •f this

study and the semi-empirical integral arnAlyis of Warren (201based on Prandtl's constant exchange coefficient conj1z.

This theory differs from the usual mixing length hypotiesis

in that it defines the effective eddy viscosity or exchange

coefficient a directly in terms of the mean flow proper-

ties. For a typical ful~y developed Jet mixing region, it

Is assumed that

eV

where K is a proportionality constant to be determined

experimentally. Warren found that K could be correlated

with K1 within his experimental range. This correi."Uon,

which was based on Wart-a's data for both subsonic and

iduaily expanded supersonic Jets. '¶s giv.non by

K - .o43o - .Oo69 M1

The principal objective of the present ':-mparison is to see

how well the decay behavior of an L-Oezexpanded Jet may be

carrelatel with that for a jet that a properly expanded at

the same pressure ratio. Although it il probst,"..- that the

27

relationship of K and M1 is unique for a given test

condition, the determination of such a relationehip is notwithin the scope of the present experiments.* Therefore thecomparison with Warren's method is carried jut on the basisof his correlation of K and MI.

In order to compare the measured decay of a given under-expanded jet and that computed for a properly expanded jet ,1

0the same pressure ratio p./p. , it is firt assumed that thejet exit locations coincide. The nondimensional axialcoordinate x/dN of the computed jet is thex based on adiameter given by the area ratio for proLer isentropic

expansion to the given pressure ratio with the throý 'areaequal to thai. of the actual nozzle. Sinl.acly, the ratio ofthe exit velocity of the equivalent properly expan•ed• Jet tothat measured at the sonic exit of the underexpanded !)t is

used to scale the entire computed decay curve. The resultsof this type of comparison for several cases are given in

Figure i4. It is seen that the degree of correlation is verygood for the subsonic jet, but somewhat varied for the othercases. In Figure 15, the ratio of measured to computed decayparamet'r (V, 4 /c th) is plotted as a function of ,4et

pressure rat.c in the underexpanded regime for several axiallocationsa. Within a range of pressure ratios centeredabout that for the formation of the normal shock, the agreementis no b-,ter than 60-70 per cent.. For pressure ratlcsPi/Pa > 3, however, thu. agreement is much better. It is also

*I faw:-. , it Is possible that a better correlation can be-ound if K is assumed to be a function of some local Mach

nu.ber which is characteristic of ihe flow0 at t'•± axial station.Thrae such Mach numbers which have been su g,ýteu are those onthe centarline, on the dividing striamfilne, and on the stream-li•ne at r 5 .

•The pressure ratio for appear tice of the normal oh,-ckshoten in .4;ure 15 was determined from a plot of shook diaetoreas a funotion of pressu-re ratio by extrapolat! :o the shockdiameter to zero.

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

-4-(~J C (0 .4

CM 0

0 0O

CI 0 0CjC)A

00

q 4.)

0 o to4in

064 44

IA L 0

0V *I.(WId 9-4-)

z~ 4 4

tu]C

zI-~~~ ~ :A cý n '0 W'u~~.

r~i co0 4.) Ci4

.4.

14u0 130

a . ~ "

CdU

cli

ODI-

28

observed that while the per cent agreement falls off withaxial distance, the difference in agreement due to the pressure

ratio effect is also less far downstream. Since the theory

does not account for secondary effects, these results lead to

conclusions that are quite consistent with those based on.

photographic evidence and measured spreading rates alone,

namely, that Jet instability effects may be large in the

moderately underexpanded range, and that such effects are

diminished at points far downstream. It io also evident that,

except in the moderately underexpanded range; the sei:i-

empirical method used for a properly expanded Jet regiults ina reasonably good approximation to the underexpandaA Jetwithin the r=r&e of pressure ratios invcrtigated. While thecore shock structure can, under certain oonditions, have adefinite influence on the stability of the Jet, It is apparentthat its over-all effect on decay rates is minor.

It should be pointed out th.t the known applications ofWarren's method to properly expanded Jets have usually beenrestricted to axial distances of less than x/dx - 25. Forthis reason, it is not possible to verify that the method is

any better for properly expanded Jets far downstream Wian it

Is 4*or the present underexpanded ones. The single point for

N1 - .515 at x/dN - 39.1 shown in Figure 14 is, of course,

by Itself inconclusive.

,I. .4

29

3. IMPiNGEMENT STUDIES

3.1. Basic flow characteristics.

IlRecent interest in ground effe'tz .4achines, V/STOL• air-craft, and the vertical lauiAhirg and landing of rockets

has led to a number of studies of various aspects of the j-aImpingement problem. In addition. there -s been increasedstudy of certain industrial proceases involving heating byimpinging hot jets and flames* In the ground effects andV/smOL field, the need to understand Impingement processeshas arisen not only with regard to increasing the ,,hidel's

S~lifting ef'Ztt~venese while in ground p.-olalmt¥ [2T-34],9 but

also in connection with dowsah erosion effects on theground below (35). 3tvA:' of the ground erosion effert hasalso been extended to tie problem of lending rockets onhypothetical lunar and planetary surfaces (36-401. Problemsassociated with the Impingement and deflection of rocketexhausts and the resulting loading of adjacent surfaces havebeen treated both theoretically and experlmentallv [41-W45.The basic problem of determining heat transfer betweensurfaces and impinging jet flows has also been InvestigatedIn a variety of wW ([46-59]. Other investigators haveempba :Led the basic aspects of flow procese~s involved In1

uplng -ant [60-08] as well as certain special problems suchas noise generation (691.

The flow field produced when a axially symmstric airjia I•inge3 on a solid surface held ncvmal to It conolts ofW-Lee general regimes. Pirst, there is the Jet itself, up- 1bt*ream of the .oInt where any I 1 tnfluenoeb due to thestrong interaction of the ImpingeLent are felt. Ttoughoutthis regime, of course,, zecondau effects (such as thosedescribed In Section 2) produced t7, the impingeewnt surtmueWill umcioubtedly play e past In determining the exact jetcharacteristics. The second regime of Interest is the

. ..

30

impingement regime, wherein the flow properties are primarilydetermined by the direct interaction of the Jet and the solidsurface. It is here that the large gradients of pressure,density, and velocity associated with the rapidly changingflow direction occur. Once the flow hat been completelyturned In a direction parallel to the impingement surface andis no longer influenced locally by impingement processes, ±Lenters the third basic regime, that of the wall Jet. Herethe primarIly radial flow develops Lrto a fully developedwall Jet characterized by an Inner layer of b%undary layer-like flow and an outer layer of free shear turbulent mixing.It Is probable, of course, that the character of at 1,-aat thefirst two of . regimes will be highly s,,sitive to localchanges In " structure of the Impinging Jet, espeolai3- Zov'cases In which an underexpanded Jet Impinges at close -ange.Each of the basic regimes and the symbols used to designatecertain quantities are shown in F•gure 16.

In order to estimate the heat transfer at the stagnationpoint of an impinging flow such as that just described, thelocal radial velocity gradient (due/dr)rO which appears asa parameter In the usual stagnation point heat transferequation nust be evaluated. This can be done experimentallyby relating the parameter to the static pressure distributionon the surface in the imediate vicility of the stagnationpoint. ...suming the flow ontside the boundary laycr to belocally Incompressible, the 1ýcal pxressur In the laminar Ib*1disry layer may be written

0 (1)

ord ~ 1 2 dPe

where iO s the total pressure s we stagnation point(i.e. where ue - 0), ue Is the velocity at 4..: edge of

tlt,. . , - , ,• , ..,". ... • ' ,.•.( I I.____ I!

Wall jet regime

Impingemuent regime/

No::Impinging jet regime C1

a______ Fla plate42

in place.

r8 r

I 6"

Convex hemlerh.ere Concave hemisphere

I 6n

Cy' ..ndrical cup

Figure IT.. ;*,s ic impi ;eiuert model shape$.

7i -

31

the boundary layer, and peis the local density. Neglectingthe second term on the right, since dp,/dr -0,

dre e

At r 0, ue =0, so that

(4%2 -. (du'\)

Thus the parameter in question Is proportional tG ti-hecia~~root of the curvature of the pressurre distribution at bhestagnation point. For the purpose of evaluating (due/dr)r.directly from measured pressure data, however, an alternateform. of this relation Is derived directly from Equation 1making use of the equation of state 0o PR .Ths xadins Ue in a power series about the stagnation point r -0,

I2. Pe2PP

26-- (5)

.1 ~ (r.2 du-, k 2

",her rw Is the wetted radius of the Jipingement surface,1Pis tLe stagnation temperatur~e .,," tie flow, and Rt Is the

apvaifie ,vas constant. Solving fo.- k'due/dr r.

' IEl

32

we have

SII

The evaluations or this partaeter for a nimber o0" Impinge-

ment conditions are given in 3.2.3. The experimental program

is described In detail in the next subsection.

3.2. Exj2.r.r•ntal Dro .am

The bulk of the experimental program was devoted toC astudy of the normal impingement (a - 900) or the three basic WJet types described in Section 2. Each of these jets wasimpinged upon four different model shapes and the stagnationregion pressure distributions determined. Stagnation pointradial velocity Zradients were then computed, In addition,

two methods of nondimensionalizing the measured gradients interm of known Jet properties were evaluated. One suchmethod was based on conditions at the jet nozzle exit, andthe other on local conditions at the impingement station inthe free jet. These nondlmensional forms are discussed In3.2.3.

The three Jets used for the Impingement studies were asUlited In the discussion of the free Jet program in 2.2,

""aept for the subsonic Jet which had a rnegliLibly difterentf prtaslure ratio# I.e. Pa/eac - ,800 rather than .834. The

0okrately underexpended Jet had 0/O - .37', and the

hi lyl underexpanded jet had P/p " .14. ge iingement±tstances chosen were ali: the asme as those for the freej Jet experiments, i.e. z/dN i.3t; .32., 23.5, and 39.1.In additt•on, several otbor locations were used in order tofill in data in regions of special irnterest. The entire

' -

hI

33

program of normal impingement cases, which included measure-

ments of over-all surface pressure distributions and certain

additional studies with the flat plate modnf, aa well as the

detailed stagnation region meadurementm is tabulated in

Appendix III. An additional x,.gram devoted primarily to

the study of impingement on the flat plate at oblique angles

(a < 900) in to be reported separately.

3.2.1. Apparatus and instrumentation. Except for the Impinge-

:m:ent models thselves, the test setup was exactly the same

as that used ror the free jet studies (2.2.1). In F rige 3,

the no70le 30i,, shown with the flat plate model mounted inposition. The mounting was designed so t|hat fire eenternL?:

adjustment could be made either horizontally or vertically.

The •angle was adjusted by means of a Jack screw

which rotated each model about a horizontal line passing

through Its stagnation point. Axial changes in Impingement

distance were made by shifting the entire model supporting

structure to the desired location along two steel angle

rails at the bottom. The mounting as a whole was made to

be rigid enough to -Animize deflection under jot dynamic

loading, while at the same time having the main members as

far removed as feasible from the impingement region so as

to maiu" -:ze the possibility of interference with the flow.

All of the Impingemert models were made with the same

wetted diameter, i.e, the distance along the impingement

oueface from edge to edge thxouge the eentar. This distance,

"..s-ed on a hemisphere model diameter of 6 inches was 9.42

inahes. hbe individual nodel oha.acteritt•Os •%ýi• as

fcoLlowe (see Figure 17)s

PlA Dlate: Aluminum disak. !/ inch thick and 9.42

in las in diameter, 27 pz.rsaurs tapi along vertical

diameter and 15 along horizontal diamet-:.

i I! 1

1

34

Convex mnd concave hemipheres8: Fiber glass-epoxyresin molded shells8 about 3/8 inch thick and 6 Inches

in diameter. Concave model made first on male moldj

concave model then used as mold fcr convex model.27 pressure taps along vertical diameter and 5 alork

horlzontal diameter.

Cylindrical cuD: Brass flat plate 1/2 inoh thick and

6 Inches In diameter with braba cylindrical rim

I/8 inch thick and 1.71 Inches high. 28 pressure tapo

along vertical diameter including i•im and 11 alonghorizontal diameter.

All the pressure tap holes were drilled wi'h a nuwib*i 75

drill except for four closely spaced (1/16 inch spaocing)

holes including the stagnation point hole which were number

80 (.0135 Inch). The latter holes were along the vertical

diameter,Pressure readings for each run were made on multiple

manometera or test gauges and were recorded photographically.fte stagnation temperature was measured as before.

3.2.2. Results of pressure distribution meassurements and

yhotogato, studies.

rM ., distri•utionso. Por each of the basic ^or=b&.ttons

of Jet strength and wmtnge=nt distanoe, both detailedct~nation region and over-all pressure 1lstribtionos were-.ta uroe for each model. Of particular Importance inobdaining these results was the initial aligTownt of thewdels relA~tve to the jet flow. A mi•ol waas Me•t altlmedpaallel to the jet exit plane by weana of direct measure-

Mimt between Its outer rcies and ' etraightedge .bald acrossthe nazzle exit. Vertical and hotri-ontal centering were then

accomplished with the Jc,' running by nulling thp pressure

differential between pressure taps equidistant from the

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

35

center tap. Although the initial parallel alignment cannot

take into account the fact that the Jet may not issue fromthe nozzle exactly coaxial with it or that interference or

S. buoyant effects may change the Jet'se direction slightly, it

was found that stagnation regz diatributions were quite

Insensitive to small changes in impingement angle. Thus itwas felt that these factors could be neglected as long as

the model was centered.In order to obtain high resolution diebributions in the

vicinity of the stagnation point, a technique was used of

translating the model slightly between each of several Jetruns. In tts ease, the model was exactly centered onlyhorizontally. The vertical centering adjuetment was thtif

used to shift the model slightly up or down in its ownsurface plane so as to bring the central pressure taps to a

S~different point In the flow. Because of the usually oonsist-

ent data obtained, it was assumed that the max.tam over-all

translation of about 1/ inch had little or no effect an theabsolute position of the Jet. A typical pressure distribu-tion resulting from the use of this technique is shown in

SFigure 18.The results of these detailed stagnation point measure-

ments are shown for all the basic combinations in Figures 19through 30. On these plots the pressure t.s given as a ratio

of local to stagnation point absolute value, while Lae radial

distance is given in nozzle radii from the stagnation point.Tri order to show clearly the slight d~l'.eerkvueý, betwoon thed~stributions for different shapes on each plot, the data!ints have been omtted. Fot reference, tee Pl.d.e,;t b pestwre

prtfile of the free Jet at each -ýial locat 4 an is aleosS~plotted.Ss=•,,opt f'or, the cue V,./Aw 3.,• :..r x/N w 1,96, It is

observe.' that the pressure distributions follow the ganersli local character of the free jet (cf. igures o ., 7, and 10),

although there is a tendency for the impingement distribution

i *' '4

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36

to be relatively spread out. The excepted case exhibits a

flattened distribution with no distinct peaks. Other cases

involving the highly underexpanded jet show apparent stagna-

tion points to either side of the center with a relatively

flat distribution or a third pemk at the center. This beh..-.lor has been investigated further and Is discussed in 3 . 2 .4.

A consistent trend is that due to surface shape. Thee convex

hemisphere distributions always drop off more rapidly thanthose of the flat plates while those for the concave shapes

drop off lees rapidly. The relative behavior of thecylindrical cup and concave hemisphere shapes appears todepend on the impingement distance.

"Over-all pressure distributions, mi.iaured from edge to

edge across the vertical wetted diameter of each model, are

shown In Figures 31 through 38 for each Jet strength and

model shape. These data are plotted with the local pressure

as a percentage of its value 0 at the stagnation point.

Thus it is possible to note the relative change In shape ofthe distributions for different impingement distances. Plots

of these same data given in terms of the jet settling chamber

stagnation pressure are included In Appendix IV.In general, the effect of distance as shown in Figures

31 through 38, is as might be expected, with the pressure

distribution following the basic spreading trends of thefree Jed. Certain details, however, aro apparent which arenot observed in the ftrna# jet data. In particular, there iso'tin a distinct reversal of the radia3 pressuri. radlent

its a short interval between 2 and 3 nozzle radii from the

seagnation point when x/dN - 1.96 and 7.3P. r..2. reversaldepends to some extent on the surf-"oe shape, being srron$est

*W 1.e reversal Is to be dlstr.ý,iished from that foundnear the center for the P3/P.- 3.57 jet which does occurin the free jet and *hi,.h is apparently asuoc5:• •-.-1-w-th thejet normal shook disk.

f7i

1.0

p- P 1. Flat plate

PPo, PC*

.8.P- = .800

1.96 .

7.32 --

04 23.5

39.1

00 .2 .4 .6 .8 1.0rN/rw /r.

1.0

.8 \.6/p-/,. 1.42

.6

.2 \

0 2/ .r - " 8 10

r I"8w r/rw

Figure 31. Measured over-.all pressure distributions.

Y, Q

1.0{ 1'l at plateS .8 pl/Pl0 3.57

.6-

•~' ,

0 0 -V.2 .4 .6 .8 1.0I. rNFigure 32. Measured over-all pressure distributions.

I *i jI!

I. ~i~

• aH•••' • hb• ,

1.0

"P Pp. Convex hemisphere

Pp 0 POOp .8 t 0PM Ps O= .8oo

.6 x/dN

1.96

7.)2 -

.4 23.5

39.1

. . \ .6 .8 i.00 I I

rN/rW -

1.0

P p.

.8

p/. 1.42

.4

.2

o .2 .4 .6 .8 0 o.rN lrr /r w.

Figure 33. Measured. over-all pressure distriluticns.

I'v

1.0

P PO Convex hemisphere

pP , .8

Pl/P0 -3.57

.6

L.2

F 0iu 3 4.2 Meue .osur .i orN/rw r/7Figure 34. Measured over-all pressure distributions.

P .4 CorncaVe heMisphere

Pp P6,P",/po0 =.800

1. ~1.96 -

.8 ~7.32 -

39.1

.6-

.4

.2-

1.0 1 1.0

07 .2 .4 .r~,/rwI

Figure 35. Measured ovea. -all pi-suy-- distribution's.

1.0P P_ pConcave hemisphere

P0 Pp.8 \ 'N P/P - 1.42

.6 .

.2 \\

O0 .2 w-. ,r.8 W/r"

1.0P P-

.8 pl/P. 3.57

.6

.4N

2 "

00 \ .\ •. r/_ .8

rN/rw

Figure 36. Measured over-all pressure distributions.

I1.0 Cylindrical cup

Pp,7 P.~

//d/ \\ \.6 I 7.32

1.01

S23.5.4 39.1

Pp .2.8* /\ 7\.2

or/rw r/rw

1.0 M-P P pl/poo 1 .42

PP P.8

6

4

0 1.0i •

"rN/rw r/r. W /Figure 37. Measured over-all pressure distr•ihutioiis.

Cylindrical cupp.- p 00p - P, P 1/P,, 3 .57

.8

062 .6 1.0

Figure 38. Measured over-all pressure distributions.

I

37

for the convex hemisphere. Since it occurs for this shapeeven for subsonic impingement, it appears not to be associt-ted specifically with Jet underexpansion phenomena. Whetheror not the reversed gradient Ia sufficimnt tc cause localasparation is impossible to deatermine from these data alone.Mother region of reversed gradient occurs near the outeredges for all the surfaces but the flat plate, although,again, separation cannot be confirmed.

The behavior of the concave shapes (hemisphere and cup)for Impingement far downstream is of particular interest.In these cases, it is seen that a large portion of the surface

¶ iS subaecti• to a pressure nearly as hIgb as that at thestagnation point. In effect, the entire f'low inside these

, shapes approaches a stagnation condition when the jet Iasspread to a size comparable to that of the model. En thecylindrical cup, the, stagnation region& in the sharp cornerare quite clear. The over-all tag•ratlng effect is apploachedthe closest for this model, especially in the case of impinge-ment by the moderately underexpanded jet (pl/p, - 1.42). Itis seen that the corner stagnation pressures ame as high asf 80 per cent of those at the central stagnation points.

The results or a highly detailed axial survey of thepressure at the center of the flat plate model are given inFigur% 39. Also plotted Is a similar survey of the Pitotpressure at the center of each free jet. Pitot pressure iprlotted because the total pressure loss due to the stand-offiitormal shook cannot be determined for tho .pingamenet case.'Zae data points for the free jet have been oWLtted forj clarity, a measurement having betn made at Ir'ti'vals of0.2 no-xle diameters through moo,. of the ru,4e 0 e x/dN < 10.

The values of xo/dN r-..m repreaent core lernthe for anequivalent properly expandod J%; or the same prcssure re.iocomputed using Warren's method (see 2.3). For the subsonic

Scase, as might be expected, the curves are vexri close. Infact, ts plotted on the present scale, they cannot be

1'

40c~latplate

(PO/oc~reejet (PC Pitot pressure)

.9 Free jetFlnt -late

ýo 0

.14

.70

.6

.4 Fre jetxc/dN

3 po/poc = .372

* .2

'First nor'mal ohock

* 0 5 10 15 2

Figure 39. Comparison of pressures

at center of flat plate model

with pitot pressures on

free Jet center line.

P./Ps " .800Free jet

p s/pC .8 1.O

Flat plate u - I

.800

" - • - ' ' -.----- -----" --- - - - ----

-

-- 0-

20 2r, 3 35

2535/

• .- 'ir

38

separated. Both of the underexpanded oases reveal the Idegree to which small local changes due to shock structureare duplicated in the two kinds of measuremezt.. The mostimportant difference observed between th- free Jet andimpingement data, is an axial sika.t such that the plate Inseen to experience a pressure which actually occurs In thefree Jet at a point upstream of the plate location. This

* ii•shifting effect is thought to be at least partly the result Iof the different stand-off distances of the impingesentnormal shocks. Since for a given Maoh Jr the stand-offdistance of a normal shock increases with the effectivebluntness of t.,s body, it is clear that the r•obe stani-off fdistance must be considerably lees than that for the plate.Other factors contributing to the shift may involve possiblechanges in the stability of the Jet itself due to thesecondary interference effect of the plate on the Jet flowfield. In this regard, it Is Interesting to note that inthe case for pl/p. - 1.42 the shift continues in the samedirection to points well downstream of the supersonic portionof the jet. Some evidence has been given that seem to showthis free Jet to be highly unstable at a conuiderable distancedownstream. Characteristics associated with this Instabilityare increased decay and spreading rates. If it were assumedthat the 77-esence of the flat plate and its supportingstructure had a net stabilizr-3 Influsnce on the jet In thisaxial range, the higher impingement prtssures observed inth.- downstream region could be at Ioast 1ýartAlly aoountoedfor,. Ther is, however, no other evidence to suppvrt sucha, assumption. For the highly unde•e•aided Jet 9 1/p., -3.57, the shift is seen to disappear near ths end of thesupersonic portion x/dý - 20. In tne range 10 < z/dN < 18,how.ever, the apparent reversal of thL shift may oslyt be thw,result of limited data takin in a region %tiore values are

still quite sensitive to axial locastien because ok theoblique shock structure. ioth curves in thlUe region are

M'. , '- .

,i. , ,, , L

1' 39based on only three data points. An interesting feature of

this Jet is the large recovery of Pitot pressure in the

core downstream of the normal shook disks.

Photorayhic studies. Photogp&phs were made of the impinge-

ment floe on the flat plate model by means of schlieren and

shadow techniques. A selection of the schlieren photographs,

taken with a spark light source, is reproduced here in

Figures 40 and 41 for the moderately and highly underex-

panded jets, respectively. For these pictures, the knife

edge Is vertical so that density gradients in the .

direction 1,-dcmiinate. Figure 42 showe es. sries of continu-

ous light schlieren pictures taken undeo: similar conditions

for the highly underexpanded jet. In the Impingement region,

it is apparent that the character of the local structure asI" revealed by the density gradients varies considerably with

Impingement distance. No distinct normal shock is observed

in this region, although this may be because It Is masked

by disturbances in the surrounding flow which are of compara-ble strength. As the .Apingement distance is decreased,there is a definite distortion of the jet structure upstream.

For the P 1/P, - 3.57 case the axial location of the Jet

normal shock disk is seen to start moving upstream for an

lmpingr--nt distance between x/d, - 6..n4 and 5.32. The

continuous light pictures nbr-:w the listortion as a sort of

"telescoping" effect in the core. Possible changes in theI •&bility characteristics of theme J*et due tca impingemnt

o'.*.iOt be deduced from these pictures.

The radiation of strong souw.6 weves frcm 'Oe Impinge-

mecait region is quite clear for boti Jet strengths. At

J1 aapll Impingement distar!'s, there tis considerable Inter-Saction between these waves and tl,• 4ot itself.

Another series of s.hlieren pictures was taken In hopes

off revealing a visible correlation with the measured changes

in sign of the radial pressure gradient for sowe of the

0

Of' I-q f"or saci9

Free jet

x/dN =7.32 x/d, 6.2

x/dN =5.32 x/dN 3.91 X/d 2.60 xdA19

Figure 41.

I.

Spark schlieren photosof air jet from sonicnozzle impinging onflat plate.

"Pl/Po = 3,,57

Free Jet

XICI- 7.32 x/d. = 6.24

- 5.32 - 3.91 x/dN 2.6o x/x Id ... G

nl+•, -- • m, •.+I'- -' . .. I., ,. +, ,, + , ., ... ...

#4 ontimixous light schlier'enphotos of air jet!-m

1ý k W, sonic nozzle imnpinging onflat plate.

~ plp00 3.57

4 Free jet

O/N 7.32 x/dN -6,24

X/dN 5.32 x/aN 3.91 x/d. 2.60 x/4,.=.9Cg

............... ~ N

40o

oases cited earlier. In order to distinguish gradients in

the radial direction, the knife edge was held horizontal.With the flat plate at an axial distance x/1• - 1.96, Ithe jet pressure ratio was varied In -m.17l increments in therange 1.00 < pl/pa < 5. This zeries of pictures is shownin Figure 43 . It is seen that definite gradients of densityrappear in a concentric pattern about the stagnation region.These gradients are visible in every picture although theyare relatively weak for the pressure ratios used In thebulk of this study. Nevertheless, they Ao occur at radialpositions corresponding to those of the measured changes inpressure graE:Lent. These pictures also On" the stand-off

Sshook in the impingement region very clea•-,ij for tbs' In-wer

pressure ratios. The decrease in stand-off distance withIncreasing pressure ratio is evident. Also of interest Isthe change observed when the pressure ratio Is increasedfrom 1.88 to 1.95. It is in this range that the normalshock lisk appears in the free jet. In the impingementcase shown, the shock apparently forms at about the samepressure ratio even though its position is shifted due tothe shor• impingement distance.

3.2.3. Evaluation of heat transfer parameter (due/dr)r.O.The sta•_.Ation point radial velocity gradient (d /dr)r' wasevaluated from the detailed Ptagtir, re!fion pressure distri-buttons given in 3.2.2. The calculations were made by fit-ttl•ig the data to Equation 6 at the uta&tetIon point. Inorf-er to assure the best possible fit exactly at r = 0, thep-ressure data were first plotted aiv a function Qi (r/x- )2.

wThe! slope of the resulting curve w6 s dntezulimd grap.±callyaat r - 0, and the va3-= of (dui,)r, was then computed.'In most oases the data fell c-oce- tn : straight line for areaaonab.,e distance from r - 0, Po that the slope evalua-

tion was not difficult. The values computed in chis mannerI are shown plotted as a function of impingement distance forV

?I

U U5

NC1.

'4-3

>4)Q.4

44 AH

H0

cm

14t HL.i4

I; jji

IA Qe

41

each jet strength and model shape in Figures 44, 145, 46, and47. Referring to the flat plate results, which are more

*detailed, there is .- '.cndene-i for& I to Increaseat first until a maxiisum Is reached at mt point near the endof the free jet core, * arthei downstream, a characteristicI decay is observed. This behavior appears to be a logicalconsequence of the ailchanges injtttlpesr and

velocity profiles,, since the radial gradients of these Iquantities are smaller near the centerline in both the coreand fully developed regions. In the co-e of the mo4eratelyunderexpanded jet,, It Is seen that the values fluctuAateIsharply in !L manner similar to that observ-!d for the Pitot

pressure (Figure 39). In the case of tiAe. hlsftly -unerfexp~a'idedjet,, the negative value is a result of the reversed raidialpressure gradient found to exist for some distance downstreamof the normal shock diskc. The existence of such a gradientstrongly suggests that there is a separated region of re-versed flow In the Immediate vicinity of the usual stagna-tion point.* A flow visualization study that seems to confirmj this condition is discussed in 3.2.4.

Figures 45, 46,~ and 47 show that uhi?.e the general axialvariation of (due/dr)r=O is not highly dependent on surfaceshape, the imagnitude Isn, This dependence Is made clear In

Figure- 48, 49,, and 50,, which show the values for aln fourov ~shapes plotted together fce7, eaich jrt pressure ratio, A

ourve In drawn only for the more 06tailed flat plate data._t, ie seen that the values for rhe coniex hi-u=aphare are

almgas higher and those for the concave uhapes always lower

tk-"%n those for the flat plate. ?izis is, of ccasthe saimeas the effect noted in the discuadilon of the preassw~ diatri-

but-onsthemselves.Lw ehd fpeetn vaiie auso dabout'

in temA.ofmeasured. et.be.avio.a.e.give.............

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makes the stagnation point velocity gradient nondimensional

through the use of dN and V1 , i.e.

V1 a-7 /r-O

The second method, which is more fundamental but whichrequires a knowledge of the decay and spreaa of the freejet, makes the stagnation point velooity gradient r-o.•;dlreLn;-

sional through the use of measured local free jet conditions

in the plane of Impingement, i.e.

Vc 7dr /r-O

The results of the first of these methods are shown inFigures 51-54, and those of the second method are shown in

Figures 55-58.Referring again to the flat plate data, the behavior of

the nondimenstonal velocity gradient based on nozzle exit

values is similar for the two weakest Jets (cf. Figure 44).This similarity is indicative of the rou~hly equivalent corelengtho and rates of decay a.0 well as rather mild er-a11effects due to shock ijfttesia. For the highly underexpanded

ca"s, however, the behavior is pite dl,'ferent, with the

eifects of the much longer core region and strong shookEtructure clearly shown. Similar results are o'C!.!ined for

tha other shapes, but the magnituies are ditfferent, ao

expected.The nondimensional gradient LaA-.d on local frei jet

propert -;3 appears to achieve a eough correlation cf, themeasured results, although the core effects '. •he strongest

"Jet are still in evidence. In general, the two weakest Jet3

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are well correlated about a value (r./Vc)(due/dr)r O 1.1

for a considerable distance. Par downstream, the strongest

jet also approaches this value. Aside from factors limiting

experimental accuracy, certain deviatio". roay very likelvstem from changes in the stability characteristics of tht Jet

due to the presence of the plate. This in particularly truo

of the p 1/p, - 1.42 jet. Of the other shapes, the best

correlation Is shown for the concave hemisphere. In Seneral,

however, the shape effect on magnitude is the same as that

already noted, I.e.# higher values for the convex shape andlower values for the concave shapes,

3.2.4. Visn.±uilation studies or stagnat.on region -fow. hshpressure distributions measured for Impingement distances

downstream of the normal shock disk In the highly underex-

panded jet, show peaks of maximum pressure to either side ofthe usual centerline stagnation point. A typical example of

such a distribution along with the Pitot and static pressure

profiles In the free jet at the same axial distance Is shown

In Figure 59. The pressures are all shown as a fraction ofthe free jet centerline Pitet pressure so that relative

changes In pressure level due to impingement may be observed.The shape of the free jet profile at this point Is, of course,a result ,f the total pressure drop through the no"al shock

disks upstream. Even thougl there has been a substantialrecovery on the centerline (see FisuA'e 39), the outer region*-' the core retains its higher level f-ci the beginmiu,

becr'.se of its structure of relatively wLk oblictze shocks,The corresponding Impingement distr.1bution ahow,: ý,ne outer 4peaL to be displaced outward, whIhl the central region is

relatively flat. At the mae time, the magnitude of the

ov.ir peak is seen to be even les. ti'-n that at tht, center.

line of t,,e free jet. Thfs condition suggests the exIatenoe J

of a separatted region caused by the reversed pressure gradient

to the inside of the outer- peak. The flow pattern based ,nr.

. • •!•,• •I~i:,

4 U-N

r-4 , Cu 0

000

Ca.j

4)

Q4)40 1 4.

4)-

145 46

7,

I

44

this idea is shown in Figure 60. The usual central stagna-tion point is transformed into a ring surrounding theseparated region. A pattern similar to thim is known toexist under certain ground effects mxachines [27]. A conse-quence of such a flow in termc .'f heat tranefer, of course,would be the existence of a cool central spot surrounded bya ring at stagnation point heating levels.

Although confirmation of the phenomenon by means ofdirect measurement of velocity or pressure gradients off thesurface was felt to be impossible, a method was devised forobserving surface streamlines. This method consisted ofImpinging the Jet for a short time on a laver of hignlyviscous water pump grease applied to the surface c.T the fretplate. In order to achieve maximum visual contrast in theresulting pattern, the grease was mixed with lampblack, andthe plate was given a smooth finish of white lacquor. Sinceit was found that the initial distribution or thickness of thegrease did not affect the resulting pattern, the applicationmethod did not present a problam. With the grease appliedin a small blob, the plate was covered with a baffle boardIn order to shield the grease fzrm transient phenomena duringthe starting of the Jet. Vhnen the Jet reached the desiredrimning condition, the baffle was withdrawn for a short timeinterval 'f about 3 to 5 seconds. After replacing the baffle,the Jet was shut down.* Inerreasing the time of exzprure tothe Jet was found on3. to remove more grease from the impinge-r-nt region and not to change thu yatte'..n. I*Thn, it wasdet;-rmined not only that the phenomenon #ias ba3ically astitdy one, but that it was also qvite rerpatat1. z. A photo-gri•ls.h of this pattern for the high:.i underexjaided jet

*Becituse of the hubstantla-.l ,et • Aressure force, trhebaff le we, made with two raised -cdgea that rested on lheplate surface away from +-:10 center. Exposure of the greasewas accomplished by quickly sliding the baffle out of the mylaterally.

_ -I•o.,•,.: .•... • . ..• !• I.,

Figure 60. Flow pattern of separated region (distance normalto sur-face exaggerated).

4 ~"Node"

.... -'kSadOlc point"

Figure 6'.. Typical sur.face st.CfM e pattern based on

grease streak pictures.

• I- - .-''•,,..-,

S,•....• ! • , • '.'i•

45

(pI/pa 3.57) at A/dN - 5,32 Is shown in Figure 62. The

behavior of surface strea*lines suggested by the observedpatterns is shown schematically Inra Pigure61. lk is seenthat a dividing ring exists which app.",,ntly separatesregions of Inward and outward Lalow. To the inside, there isa central region of thick grease, while to the outside analternating concentric pattern of more and les grease Isobserved. Of particular Interest I.s the manner In which thestreaks curve near the dividing ring resulting in segmenta-tion of the central pattern. Along the dividing ring, eachsegment carn be identified by two types of points hqving thetopological .•hnracter of nodes 7- and saddlepoints *N .~ The number o~~I~ns in~ th'e patternapparentlry decreases with Increasing impingement dist'nce.For this Jet, the inirmm number of three segments Isobserved for all distances beyond about xNd3 - i.• (seeFigure 63). Another factor which was found to affect notonly the number of seguents at a given distance but alsothe orientation of the pattern, me the jet nozzle. Rota-tion of the nozzle about Its axis between runs resulted inan Identical rotation of the observed grease pattern. Itwa found that tiny nicks in the nozzle lip could be eorm-lated with at least some of the pattern segments. Removalof the -rger nicks resulted,, for a fixed Iapingeant dis-tance, In fewer segments. #:,!, patterns shown In tne present-ae, however, are those resultirg from tests after the&Wcks had been rmoved from the nozzle. Obndar lO-power I;w=nification, no nicks were observed thet could be corre-Iated with the resulting three equal pattern amionts.

A co-marlson of seblieren phc•ographa grease ypttern,amd suraees preasure ditributlon for a typical case is

shown in Figure 64. It can be 54t- that local pr-issure Wiaksae deolfnitely related * the observed patterns, with less

mase remaining where the pressure is higher. These localpressure w/maiz also correspond to the dark regions of

.. ,

, ," - • "" "•'"

... ,; • T.•"L'.

F61ur •. Typical grease streak phc4*ograipD• of flow pattern d.ue to

II " ,

Impingement on flat plate. p l/pM 3.-57; X/dv 5 .32•. ,il

I L

I.�II'-I,

x M 81N'-4

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I. *u1 I*0

*

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- I

I Iiii

HIAHII

- A I

cu Cu

q-I

co in

P4

VV06 c"P4

ix)-

increasing density near the surface as shown in the echlierenpicture. In addition, the position of the streansline divid-Ing rings which can be thought of as a ilne of zero radialshear, is found not to correso, pnd to tht local pressureMaximum.

3.2.5. Momentum balances and interference effects. In orderto help clarify certain aspects of jet impingement flows,especially those which way involve interference in thp en-trained flow field, it is useful to consider qualitauivelythe balance of jet momentum fluxes with the pressure Zorceeon the implrkr.ement surface. In Figure 6K. four basic condi-tions are illustrated. Case I shows a free aet flow 1Jiulngfrom a nozzle of the type used in the present experimf.,ts,while Case 2 shows this Jet impinging on a circular flatplate. Cases 3 and 4 represent corresponding flows but witha flat baffle plate inserted at the exit plane (AB). Forconvenience, a cylindrical control volume is defined by the"impLngement plate (surface CD), the baffle plate (eurface AB),and the cylindrical surface S. The pressure is assumed tobe unchanged across the free boundaries except within theconfines of the nozzle. It is clear that the total axialmomentum flux leaving the volume across surface CD in

Case 1 .,- made up not only, of that entering across .2through the nozzle (inc¢udiiS the effeit of any pressuredi ffrence across the nozzle exit, plane) but a81-i the sum of.L! the axial components of entralraunent flow entering across

tae entire plane AB as well az the surface S. Moreover,Sa c.Aplets force balance for thia avsa"tu would also hi~ve to

include the proper components of viscoue forces at all the

boundaries. For Case 2, negleotlr,.; viscous forces, th.m

beilance 1i primarily between the e-xi momentum fl1r ',f the

Jet (across AB and S) and the pressure forer n the plate.P It should be noted, howQver, that part of the axial flux

across S is contained in the wall Jet, which becaus o1' o tr i

- -....... . *-. . V ' ..... • '

Cu I

C ,,) *1*,

Fl-IU I"!

IIq

C,)

• {,,,l i jIIL'

1

47

spread makes a contribution in the niegative axial direction.

The possible consequences of blockage due to a baffle plat3

are clear in Cases 3 and 4. It is seen thel; a large portion

of the axial momentum flux is lost bec'ise of the solid

boundary at AB. The entrainuwaint flow Is thus primarily

radial. Because this flow must turn as It approachev the

Jet, however, a pressure gradient will be established on

the surtace AB which can result in an additional axial pres-

sure force contribution. Basically, Case 4 represents a

combination of Cases 2 and 3. Using the measurements of

free jet velocity profiles and over-all flat plate pressure

dilstributtin•, a comparison between Jet enial momentum flux

and plate pressure force has been made .Coz the p-In - 1 JtPJet. Each of these quantities is plotted as a function of

axial distance in Figure 66. In addition, the free Jet mass

flux, the radial boundary of the nozzle mass flux rk/rN

(i.e., the dividing streamline between nozzle and entrained

flow), and the over-all Jet spreading parameter r.5/rN are

given in Figure 67. The behavior of the Jet momentum flux

and plate force can be explained In terus of that portion ofthe over-all axial flux actually measured at each station.

Near the nozzle, of course, the plate force represents

practically all of the axial flux due to the nozzle as well

as ent A±nment. It is seen that the jet alone accounts for

only about ,e-half of thii total force. The initial decrease

of each parameter with axial distance is believed to be

rximarly due to pressure gradients whiob are known to exist

&-.;rose the boundary AD near the nozzle, but wrAch werenot evaluated. Farther downs"tro-, the portio-. of' the total.ccrntrol volume cross-section inciided in the free J•t measure-

isents Increases because i~f jet arreading so that a Uargerportion of the total axial fiux !P :.ecounted for. At thi,saMe tVIae, since the JP4, diameter has grown to be nearly :1

that of the plate, some of the Jet I'low is deflected aroundthe plate without contributing to the force. This dror-'Mf

S:1 1 . . . ...... .. . .. ... .. ,c .•, "

S.. .. ' •: . .•' ';

on f'lat. plate 1

4- ý Free jet womernt1. f lux based on

measurec. jet velocity profile

0 0 15 20 25 .Wrigue 6. cmpaiso offree jet uomentuaa flux arnd force '-*i flat plate.

P/. 1.142

I ~Jet spreading paramzeter

C1tOIA.< jet massflux 2

(slugs/aeo)x10 2

-1Z:7'pread of nozzleflux rAN,/rN

FIgare Or. Measurea cotal mass flux in free and sra

of nozzle and total mass flux.

ýjs

448

is slight within the r~ange or these measurements.?he measured jet mass riuxs as shown In Figure 67. is

possible existence of Instabilities itn this region has al.ready

ofe toe Increasedfu Isr ractualy du te to Inoatsd entrtion-

seen to be approximately i24 times that or the jet alone, I:norder to illuatrate the Interference effect of 4L baffle plateat surface AD, several upingement conditions were rerun

both with anid without such a baffle plate. A cowparison of

in shown In Figure 68. The change In distribution In thisparticualar ease Is characterized by a decreased pressurenear the center and an Increase in the outer porticns.While sacme of the few cases tested exhibited similar changes,others did not. On the whole$ the relationship between jetand Impingement behavior and Interference effects In extremeo-ly complex and the present simple tests are intended toprovide kxay some idea of the changes that cau result fromjCh c ane In geometry.

3.3. L)~u-ain

The experimental &atev-:,at1on of stagnation pointho~-a transfer parameters for normal jet Impingement h.U been12~cribed In detail. It has been round t~hat by masking *aseOf iowil free jet characteristics at reastnable correlation0o% tzhe stagnation point velocity *raeioent (dus/6r)r,. Isachileved for a number of cases of 4et .,trswgh Sm, iki1ping-

wetdistnce*. For Imp~i~ement on a t'Ut plate ft w~s tun4thtat (r SA/i)(due/dr)r.,. foll vwt'!- 20 per cent of avalue of 1.1 at axial !istanees between 10 and 40 nozzlediameter* downstream for a subsonic AM~4 .0) jet anid

AýI

x/d ~ ~ ~ ~ ~ ~ p - 235Wtotbflplt

w 1.42

.04 -With baffle platt

-03-1

.021

.01

.8 .6 Ak .2 0 .2 .4 .6 rw.8

Fi.gure 63. Example of changes in impingement pressure distributiondue to baffle plate.

p/2 23.5 39.1 2.4172 0 or

..... .( .

49

. derately underexpanded Jet (p1 /p - 1.42). For a highly

,Adexrxpanded Jet (Pl /P - 3.57) a value of 1.1 wasapproached within 20 per cent downstream or 30 nozzlediameters. For a convex he'i•.here, g;enerally higher corr..-

lation values were found. These values showed an upward trendwith Increased axial distance. Such a trend might be expectednince far downstream the axial drop-otf o:C the gradient(dUe/dr)r.0 itself is less rapid "Ian it 1z for the flatplate. While the concave shapes exhibit lower values thanfor the flat plate, data do not clearly indicatE the downwardtrend which rmight be expected on si=43 ,v-orda. .he

correlation %,alues can be r-elated to th: gfometrie c onritionaIn term of the free jet half-velocity radius r.5 and themodel surface radius of curvature r.. With -r, desitnednegatively for the concave hemisphere, the values for thefully developed region of each Jet are shown In Figure 69.In the range -0.6 < r. 5 /r < 0.6 , the surface curvatureeffect can be approxuimted by the linear relation

r t dUeýSk 1.13 + 1.08 !A,

In addition to these basic measurements of (dud/dr)r.Oseveral other measurements and photogaIc studies havebeen made which help to illustrate certoin features of

impingement flows, particularly of highly underwpanded Jets.Yt 'as been foted that under conaitionL .-f i•.grnheamnt outto about 8 nozzle diameters for a let with pl/pem 3.57, astp.arated region my exist in the violnity of -11o* stagnation

polnt with the result that max•i, hset tran~fez, may occur In

*i a ring surrounding the eantral region. Some unusual festuresof this tlow have been investiga!',A. ,y oomparing IMPInge•a..tpressure uistributions, .,urfaoe streamline patterns, andschlieren photographs. Of special lnterest has ascn the

mamner in which the separated flow region becomes segmnte6

along the ring dividing the inwaft from the outward rlcq on

V I

50

the surface. It has also been found that the maximum

ipingement pressure occurs outside of thiu ring.

The problem of interference dutp to ob-tructions in

the flow field surrounding the jet •?p• er has been discuez4dS~br~ofly in a qualitative %Wa. In particular, it has been

stressed that the presence of auch obtruotions can resul'

In substantial changes in the impingement pressure distri-

button. An example of this effect has been given in which

Interference was introluced by placing a bfle plate inthe plane of the nozzle exit.

|I

1J

i, ' i1 .

5144 CONCLUSIONS

This study was perfoined In order to obtain a generalknowledue of the behavior of free Jets uhern they impingenormally on a flat surface. In narticlarla, the general

e1taracter of thae st tion point beat transfer parameter

(due/dlr),m_ and its dependence on shook structure ad other

.features o the tfre Jet wee r tudied In detall.The purpoce of this Investigation was to provide a

soneral guide to the study of such matters at high enthalpy

where the effects of density variations awe of Importance.It me8 felt th.at by knowing; the enzaral fe-atures of &aes jat

Impingsawwt ror low temperature constant denslty flows, agreat deal of labor and expensive hig temperature testingcould be eliminated and a limited but essentially definitive

test program for the high enthalpy problem evolved.The results of the low temperature studies presented

herein are thought to be sufficient to permit the order ofMnWltude of the stagnation point heat transfer parauster(due/dr)r.0 to be estimated for thn case of high enthalpyjets In a imier of important practical applications.

Ibe results of these low temper-ature studies of

(due/ydr ) were presented in two nandimenslonal form., Inthe first form (Ue/d*.O was made diamnsionless using the

I jet exit diameter and Jet exit velocity, i.e.

S~~dN ( du,, •

I "Mots form Is useful for quick estlistates of (duel4W)r. whenlnaomstlon Is not awailable concetimtk the uocay of the freeJelt under consideration, Thie other method of presentinS the

data. In rioadiamasionaI form settcxptý' toa corlate the stWj~a-tion point heat transfer parametetr with local conditions Inthe free jet at the plane of impingemnt, I.e.

52

r /dueý

The data show that such a correlation 1' useful in the region

of fully developed free Jet fl.. In pex'ticular, for the

case of normal impngement on a •fct plat-r i' d a

11)ro

The effect of curvatux of the impingement ourtace on

the stagnation point heat transfer parameter was al& Inverst!-

gated. Typicully, for fully developed J3.a when the rtLo of

the haat width of the free jet r at the plane of

lmplngeaent to the radius of curvature rs of the impingement

surface falls in the range -0.6 •'/r8< 0.6 (the plus sign

refers to a convex surface and the minus sign to a concave

surface), the effect of surface curvature on (ro) (duo/dr)r.OI& given approximately by the expression

r 4 (du)m -- 1.1:3 + 1.08 r

In order to use this second method of nondimensionallz-ngthe sta-.,itlon point heat transfer parameter, it U3 'essar

to compute the proper•.- -sa a given jet downstreaa of itspciu,• of issuance. This problem was ala' investigated.

"",..ar.sons were made between meavured and oamputed w'ae'ov

of 1.5 and V at various poul:ona aloug th*e jet. Cc4Wutedva•ss were found by avplying a*-ren'b moment-f-a Integral method

to all the cases studied including r•ho&e for which the jetwars undeL'ezpded. It was found at the predicted decay

rates bsr-ad on this wethod agreed. w.L.A the measured v.lue.

quite well in the subsooh.c range. For moderately underexpandedjets, however, the agreement was no better than about 60 per

cent. This is believed to be due prixtrLly to the uffbcLis of

S.. . . .... - ,• •,:,•, I..

. . . . . . . . .,. . •

53

a large seale instability or "flapping" observed for theseJets. The agrement was much better In the highly under-

expanded range, although a steady drop-off In agreement with

inreas Jet strength and &xl&i locatiun was noted. Sinoe

the analytical method was based on a turbulent exchange

coefficient that was assumed to be a function only of initial

Jet Mach number, it is felt that such a drop-off might be

expected as the Jet decays to subsonic velocities. These

data would seem to Lndicate, therefor*, that In the ab3enoe of

Jet "flapping", the core shock structure does not have a

fIrst-order effect in determining the decay rate of L.%ee Jets.

lt appeara that &he disagreement is due 'i-ma!riy to th;

limitation imposed by assuming a constant exchange coseticient

independent of position along the Jet. Only In cases wnere

shocks contribute to Jet instability does it appear that they

may influence over-ell decay processes.

711A

4,

~ ~ ~

5. C=TD FWEREIES 5

1. Pashotko, Z.# and Cohen, C.B. Beat transfer at therorward stagnation point of blunt bodies. N ACA T-N-3513.1955.

2. frTwoblockip X.Z. Jets-]*.tview of literature, jilPrD.Vol- 9§p No. 9, pY6. 760-779, Sept. 1956.

3. Anderson, AR., and Johns, P.R. Charecteristics offree supersonic Jets exhausting Into quiescent air,1*tp.3-5ad 5 7n 95

4.* Seddon, J., and 11hverty, L, Some tests on the spreador velocity in a cold jet dischaxgirg with gocens prea-sure from a sonic exit Into still air. AeRC. Wch.&S~t. C.Z. No. 2*46 19.56.

5. Bashenovs, T.V., Leont'eva, ZuS.# auri Pihkir, V4.1Rperimiental investigation or the density distrirbU;A.O)nIn a three-dimensional supersonic jet, Uas 0

30 -ýpracow IYYS -1 8619,translation by the.Israel Program for scientific Yrsnslationas, 1962.

6. Moe, M.M., and Proesob B A jet flows with shocks.A

7. Eastman, D.V., and Plsdtke, L.P. Location of the normalShook wave in the exhaust plumi of a jet.* ADA Journ. 1.4o PP- 918-919a (1963).

8. Charvat, A.P. Boundary of =1drexpanded axcisyninetrlcJes asip Itostill air. AIMA Journ. 2, .p.11

10 Nsde, .. Masurement of the flow field of an under-*qmadedJet n ahypersonic etra ten.( .)PW. irratIstab * Tech, No AD.i: _a Dece.

1.1 lvvv .S.,Grigsby, U.S., LtI., DP., nNverimen anda theoz'eti~asio xssmtifree jet&. ftcii Bi R-6.. 1959.

IN

5512. Adanson,, T.C.s Jr,, and Nicholls, JA. On the structure

or jets trm highly underexpanded nozzles into stillair. Joirn. of the Atro. Sciences a-6. 1 16-24, (1959),

13. Lewis, C.H,0 anid Carlbon,, D.J. Normwal elioak locationin urderexentn4es anid gas~ par'ticle~ Jeta. AIA Journ.

14, 1WkM 0.7.,, and Peterson,, JEB. Spreading of supersonicjets from a.xially sywmeetric nozzles. Jet PaoD.2pp. 321-328, (195 2.

15. Lord, W.T. On rocket lot flow fields at high altitudes.U~ch, New. No. Aero. 62, .A.E. , Farnbo.roushp - .959.

16. Lord, V.T. On axisymretrical gas jetes with applicationto rocket jet nlow fields at high altitudes, trt.. No.

Aero e62' R..A.E., Vaznborough, 1959.1.7. D'Attoxra, L., arad Harshbaz'gr, F, Rpai~isntal and Pthao-

ratIcal studies of underexn %e jets near the Nach disc.Gen. RMWAstro.. ODI-=- -008.

18. Olson, R.I., and Niller., DP. Aerodynanic studies atfree and attached Jets. Rles. Labs., United AircraftCorp.j, A-l1-7=e prepared for Hsrr~j Diamond Labs.$

1.9. ftaiitt. A.G. 2be oscillation and noise of ani over-nraBf sonic jet, JoUr. Aerosip. Sol. &8 9, pp.

63-68Os (1961).

20. Warrena, V.Re An analytical and experimental study ofcoinpreaaible free jets. flmtn 62,1 w.or Aeronautical ftineerIE FM. U1 79.

21. 7.4tvala, I.K., ard Anderson, T.P. Experimiental deter-umnat in of Jet spreading sr uper.sonic nm-.S2.es athig alt itudes. Am"J§9. Jan. 1959.I22, Jatwala* RA,. Spreading of rocket exhaust, jetsi at highl

23. Owens P.L., and Thornhills C.I. the flow In an axially-symmtric supersonic jet ftk*w R noarly-eonic orificeInto al vacuum. Ini 1952.

2~4. vick,, A.R., anid Andr:-.as, .E. An experimental Inveatiga-

paralel fasurf ace upo aXL:

9,56

25. Vicks A.R., Andrews, E.I.,o Jr., Dennard, J.S., andf%-. 4 d 11,B. Comparisons of experimentoal free jetboundaries with theoretical results obtained with themethod of characteristics. NAS T ,L164.I

26. Vick, A.R.,, Cubbage, J.M., and Andre.B.r, E.H., Jr.Rockeat exhaust plume proble~w and some racent relatedresearch. Presentetd at Sneialists Meet. on "The FluidiDynamic Aspects of Space lilght" under the sponsorship .,the Fluid Dynamics Panel of AGARDO Marstille, France, 1964.

2-7. Wernicke,, [.0. (Bell Helicopter Co.) Performance testirngof a five-foot air cushion model. SmD o~n ground effeutrmachineS. P. 363.& Princeton Univ., c..oKI4

expriens.- 9 . n rondeffect mahies P. 341A,

29. Shen,, Y.C. Theoretical a..lis of jet-ground planeInteraction. IMB DlAB.6-34 National -q'MzerMeeting.. JuneM2

30. Vidal. R.. Aerodynamic processes In the dounwashimpingement problem. 10 lABPar No. 6g-316, XAS 30th Ann,Meeting, Jan. 3962.

* 31. Curtis, 1.3.1 and Ptisterer, VJt, (W~dronautics, !no,,)Experimental Investigation of the viscous effeets onbalanced jets in ground proximity (Final Reporti.TICCK-"f-63-61; AD-1126131; Tech. Rept.. 41-3* (1963).

.4

32. Veslgot, J.P.,, anid Gire,, B. Ter~rain de decollage ouatterriasag pour, avion v/sTor,. SMp. on VSTOL Aircraft,Part 2, 46, June 1960.

33. O'Melley, J.A.2 Jr. FPvw phenomena experienced wit~hVTOL aircraft in &rv,'md proximity. Symp. on VSTOLAircraft,, Part 2, AGBqjr 4 JU'a* 1960.

.. Grotz, C.A. Simulated VTOL exhaust tinpinig~nt on groundsurface. SM on VSTOtL Aircraft, P&rt 2 ~ a

3,53 Kuhn, R.J. An Investigation to determine conriitionsunder which dcunwash Orom VTOL~ aircraft will start Isurfa-a erosion from various ty>'of terrafii. AgM-D1§6 (1959).

36. sibuikIn,, K.,, anid OGliaher, V,.L Some as;-.0- of the ~Inter-Action of a jet with a dust covered surface in aj

acimeviomet. Lab. * yn./AstronautIca, ftice

SoIejb ap- o g...a------- .- 94 (-6-3

57

37. Spady, A.A., Jr. An~ exploratory inveatigation of' jet-blast effects on & dust-covered surifaoe at low ambientpres sur. NAAZ!D1 (1962).

38. Stitts L.E. Interaction of highly uridae-xpanded jetswith elaulated limrar surfaces. KA-1 THJ D-1095, (1967L).

39. Situlkin, N,. Jqt Imapingement. on a diu~t -ooered surface.Phys of Ilulds T. 5, pp. 696-6990 (196i4).

40O. Roberts, L. The action of a hyperscaiic jet on a dustlayer. lAS PaDjer No., §3-50 I~3S n.Meeting,Jell. 1903. ,1Q38An

411. Stitt, L.E., and Latto, W.T,s Jr. Ir~teractICon of highlyumdez'ezpanded exhaust jet~s with a~djacent surfaces. lAS

42. Yoehihara, H. Rocket exhaust ImpingPe-*at on & a oi3urface. Oen. Dfn.Astronautles Rent, ZRRfl..A-1j7i1962.

413. Eastman. D.W.,, and RadtP,9, L.P. Flow field of an exhaustplume lapingirtg on a simulated lunar surface, ~AU

W14 Anderson, A.R., Johns, P.R., and Hawkeas, WA, Nondimen-siomal characteristics of free and deflected supersonicjets exhausting Into quiescen air U.S, Naval AirDevelopment Center,, NAMC-ED 541. 3.954&).

415. Her,'erson,, L.P. The Impingement of a supersonic, jet ona flat plate. Australian Defense Scientific Service,DePt. of Supply,, Koch. Scri=. -Note ?38.

416. Tac, , :,ewa, P., and Naito, x. Heat transfer between aflat Plate und a fluid 4et * Prprst;J a~ese 500 of

4~.Perr~v, 11.1P Rest tr~wifer bv- ncVa,.Cn. '1 ,11~o~ a hot gasjet to a Plane sorface . ! T2,nstltatsen of Moch.

418. Nevins, E.G. mie cooling powe-. w7 an mtgi J.P'h.D. Thesat', Univ. of Illinois, 195r3.

4~9. *evine~. E.G., and Ball, H.D. R transfer b~ttieen. aflat piate and a puloating i~.~~.gjet.

50. VWOlfteln, K., and Stotter, A. H[eat transfer betweenan Impiin Jet and aflat surface, * u!a1_4uraofTechq 2.-131-134o, (1%64).

.- A

do

58'

51. Baxter, AJI. The influence of jet properties on thedeeirm of uncooled deflecting surfaces. ORSPaperNo_._62:5-8___ Semi-Ann. Meeting June 1987.

52. Metzger, D.E. Spot cooling and heating of aurfwaces withplane surfaces. S tanroti. 2nv lg.ýo (1962).

53. Ge.rdon, R., and Cobonpue, J. Beat transfer between aflat plate and jets of air Impinging on it. ' 0enlDevel2Mente in Heat Transfer, Part 11. pp. ~45I4--,40

54. Vickers, J.N.P. Heat transfer coefficient's between

Chemistr 51. 8, pp. 967-W720 11i9).

55.n FrieR.R, .. and Made.lr W.L Ju. Hat raser. to. o.,7pp. uio 52-55 (1ea9. ige Lno, 13

59. smgirn. V.A., Sublmato from disk, tnd airdc st.em.fowInat rnoreat btween srajet. anda el pateR Anormaltonflow. Yo'k, Paper. Neat M56Ass rasfr, pp. 1-bo a-7, (961)

67. Jakob, , an DezIaton d'n Heat transfe pr in~ the flownofair agaisot pane surfa t1cs oc af lihui 6eth bya p'lat

Ceffit for8 axis)ec . Lobne arEois, Blanche, pp.9816-

58. Johny, H.C., ane Backeffe. ofa al na. JourraAeRoSc .2 -pp.52-52I5, (1959).

62. k'adr3ha, V.., and Loveki, LX.E ane crml impigeen P.fHat cii'culr bi etween a jeat and a held pate noma to

63.0. L-x, A.~4 Dvandtionlg 0.u jeoriietipal mnd experienanormle smonging wel-ormino aIqi jets by a 63-2t.

perpendicular ~ ~ ~ ~ ~ ~ ~ "A to1tiai) L oil lncep,86

64. Nakbikeu,, J. Contribution a l'etude aerothermique d'un 5

jet plan evoluant en presewie d'urae Lroi, France,M~irdbtere de 1'Air. PST 374, Jan. 1961, SDIT, 2 Av.For'te-MaIsy, PERi 15.

65. mhthieu, j., and Tailland, A. Stu~dy if 9, plane jetdirected tangentially to a %w&I. C..Aa,$!Prgg~. PP. 3736-3738, June 1961.

66. Kadosch, K, The mechanism of jet deflectio~n. Pubi.Soient. Tech. Min, Air, Prance, mo. 12 (1959)-.

67. Poret4 x., mid cewmsay, j.E. Plow charactertatics or aolrwular submrgd J84% Impinging normally on a 13uaothsurface.* Proc * of the. 6th Midwestertk Conf. oai '.Lu. !4eohe,Univ. of Temms, Austin, Texas,, pp. IW1-a2s2 kI!, LqI5

68. PiraJero, A.A, David iayor 1odepli Asr.Lb

69. Il.xsh& A.H. Noise measurements around a subsonic c...rjet Impinging on a plane,, rigid surface. ~2iLwo. 21MAcoustical Soc., of Amer. 33. 8, pp. 1065-1066,A16)

1144

APPENDIX I

Suua7y of free Jet oases for which

velocity profilee were deterf4ined.

0 0 1.96 3.92 5.87 17.32 116.4 ••5 39. I8-T

08341 V V' V V t V

0552 V V V V/ 4

U ~~: 1.14)- - -

1.4)V V V V(p1/p* --1.112) -.-. -

0 1 48 i t V VVl,(p p as 3.5)

In addition to frk-z above listed oases, axial decay

=rasurements, almoe were made a* reveoW of the sae locationsrr the following Jet pressure ratios:

-- p~ps~o - .2• pul/p, - 2.1L6.183 2.16

212 4.36

".10 5. Of-mI

| )

APPENDIX II

Poresrmesrmn data and ocarAVte.G velouity profilesfor ll f te fee et casess Ilsted It. Appendix I are

included In the following psgeis.Suwm7 potsof the radiali spread and axial decay

characteristics of these Jets are also included.

Noe.Por ease In making oomap oari jE, ;.112 moaaiuwedIpressure data have been converted to the same"ra~its--inwles of achl(s.g., .820) gauge*

VI ,

suoaonic Jet

TOC/ .. 1.00 3.92

1A 5.87c 7.32

0 V 11.74

1*10I 0 1 ,, I

0 .5 1.0 1.5 r, in 2.0

250,

100 '1 '5o

00 .5 1.21

Figure All-I

1.4 -Subsonic Jet

1.2- pi/p, - 1.0o l'

1.0 so./ 4 - .969 D 23 .5

JT0 /T. ..1.00 to 39.4~

.2 -

0 C5 1.0 1.5 In 2.0

0

-.01

o .02I: ~-.03 b1

.05

-*0

10

0 .5 1.0 1.5 r, ina 2.0

Figure AII-2

ig" lo

Subsonic Jet

100. 1.00) X/dN

P.ps .834 0

TOOAi! . 1 .00 0 1.9iS

75-43 3.92A 5.8T

low 7.32v 11.74

oo~50-

25-

0 .5 1.0 1.5 r, In 2.0

600

500

300-4

r, in 2.0

Figure AII-3 .

Subsonic Jet

plp 1.00 I\dP/9,- .83'4 0 23.5

T/T - 1.00 058.?

4 I0 .51.0 1 -.5 ta 2.0

0 .5 1.0 1.5 in 2.0

.41

-1.2j

0.5 1.0 '.52.

Figure AII-J&

Subson~ic JetI

500p 1.00 x/d,,

0 '*.pe - 552 a 1.96

ao/ *Tq 11.74

~300

1 00

0101

4 .5 1.0 1.5 rIn 2.0

g600

VeV

0 51.0 1' In 2.0

~Figure A11-5I

Subsoni.c Jet

00.5 23.5

20~

IC

InI1.2.0n 2.

o0. 1.0 1.5 2.0~~&

, V4

Moderately Underexpanded Jet

600P6/Pa - 1.152 x/dN

500 - .458 0 7.32

400T/T, 1.00 1 lJ.71!

c 300-7

0~

5 1.0 1.5 r, in 2.0

-2

-41

1 1

12

0 .5 1.0 1.5 r, in 2.0

S~Flwe All-7

.I...

V.:•• "/ '' ••'-• •- - ;

Nbomeitely Under.oLpanded Jot

PjP 1.152 XldN50 -. 5 2

30

2.40

ca10

r, In

0 .5 1.0 PI

0

-1

-2

'-6

-5w

'orL

0 *5 1.0 1.5 r, In 2.

FigUre AII-8

I ;I

1000 ModeratelJy Undereipanded Jet

8o0 PllP. - 1.42 x/dN

PJýý- .372 o 1.96Vo-I.T . 4 3.9Z

S0 .51015 r, i~n 2.0150o

0.

-2 . . r, in 2". 0

1400-

1200

-;001

b,0 .5 ..0 1.5 r, In 2.0

S~F.K',ui-e A11-9

|IIll <,'

I * .,svoo, ....... ,... •]7

140dei'ately Undei'expanded Jet

p i.42 /d N

~o/T~sc .372 VL.

053-7

50

0 .0i 2.0

0 51.0 1.5 " 2.0

-12

-18

4. . Q

CIO

'Iy 200 __

SH~ihly Underexpanded Jet

200 P/pA., 3,57 x/dN

p 1..c 0 1.5 o 1.96

S31,92

o*~~00OV 11.7h4

0 .5 1.0 15 rin 2.0

r, I

-1001-.

1500

0 V.

: 5 00S0 .51.0 . r, In 2.0

F~g e All." .1 -

1w', -•.h

Highly Underexpanded Jet

P1/Pom - 3.57 x/dN

. .148 0 23.5T 0 /T = 1.00 3.

~ 200~513.7

D.00

0 .5 1.0 1.5 r, in 2.0

o .5i

10

20r

6D.

300

0

C .5 1.G 1.5 r, In

Figure All-12

-is

t, t' 4:1.

!• i I Ji I . I ,; _

0 4

•,',i • •: .• i, ,: n 0" a'q•''.:•'

'I,

':4

r4 P

0 A ,

i~ o C-5a I ( Y0

*ý1j

''045

V

V

U 4�r

'-4'4 C" K.

U0 U � .* CU

S

o�o I

00

u.� y-4 III4-4o �..

v�

0 I0'4 I0

4,

-� U''-4

*4�

1-

I I I � 2.�..0 t-. '0 ir� (V� CU �4 o

I I I I I-4

.�

t ; (1� �

0. 000

ii 44)t

I 4)

4-4

0

.5.4

-HH

f4 p

1~ 4)

APPENDIX III

1. Saruy of impingement oases for which radial velocitygradient was determined from detailed istagnation pointpressure distribution. rals. matrb., was repeated foreach of the fou.' Impingement models.

1/d 1.96 7.32 23.51

VV _/

.372 %V V V V

.1418 VV V V

Additional cases were as followesaFor the flat plate model.,

0C w.961# V/% - 7.32

./P- .1462, X/dN - 7.32

pJ9- 800 8 J .O 3.51 5.3. 11.0, 16.0

pp0 -32, /% 0l 'ý.57, 2.,94, 3.49,

5.70* 64,25, 6.62ý,, 7.17,.i3.C0, 16.0

C .144.9 x/dN, w 3,91, 11.0, 15.0, 18.0

2. Neat *Irewer.'Ze of over-all suu±fa~e pressure distributionswere made fo.r all four models for the cac..ia listed inthe main matz- Lx above~.

3. Stagnation region pressure distribttIoans were also

measured under the following conditions with the flat

plate model (these data are not all tx-xted specifically

in this report):

0varied In small incresents, 1/d. - 1.96, 7.32,23,5, 39.1

O" .372& x/d, varied In ma, iricreammts

0 .- O8, # K/d varied in smaI inerieentpI.~s

APPINDXX IV

Pr*ssure distribution data for vach banjo teaft condi-I ,tion. Over-all surface pressures are plotted as a percentageof jet settling chamber stagnrat~on pro6sur'e.

..... i

tooC'C

00

0

'-4-

44

0.

P4

(\X)

No

Cu -•,. - -

oc

Figure AIV-1. Impingement pr,',.We

distributions fo•' seve".J0impf.ngement ds•o'•

O~

~. , , . . ,

CtiI

coA

I.l

06

94

C\i M'

Figure AIV-2. ImpIrnaener)t Dlw',SU C

02H HIr-

a) q:1 0r-H

~.4.Q 0 02 a

H 4-) 0 .1)

fH4co XQ4 cl

4)vIV~ co a) 0

P4 u) - 0 2 0 2 . 3

02 Cd .H 0 o"~. 11 g 0 %

Oa) ;.~J4'-

aa

a. 0

I-I

-t

0 M

*0 x-i

,C)

>5 0 44

4) 0-4-1

cm'

CLi

Figure *I-3 Impingement v 'Ceý uredistribution.a !or aev+1e1.l

ipinigemenit dlzt% cýýs

r4

COI

0~0

, 6f..I

0c

H

cu-

Cu

00

Figure Aiv-4'. impin~emeflt y.rcbourE

distributios fo~r e .Iupneetdlýwz:3'AV;V* A''

CD\

00

4u (Y)

cnu

ko

distrj~butions for veeaI.%nenet distarneea.

11 0

0- 0

(UV0. 0 o

4.jc ) 0~

(I.) V

0) W

00

00

PLn

C/,

H4

OH

p. 4 C4

$44

LLI

r4 0.

co-

" -

0

0

.94

0

H'9 0

09-

c'J�0 0�i rV�H H

'LoI I

4.0% 3'

0 * pH

0�l

Iix .

e-t4

0 UN

00 4

f-I

0 U ip�I

ai HC)

'.9

0�a 1h'- �J70

000.

OR 4

00

co

c\Figure I7.lp._eetpvw e

distributions for t~fvral

0 im~pingemnent distancee.,

'.0j

8 H4

P4-

S4.

ol

* 'I r

0o

Hl

Ln (Y) 4

FiueAV8 Ip$ie!en e4vr

dit'iutoa o

4)ipneetd~acs

0 M 4( D

coc0 - 10 1)

T4r

4J 1ý 0(D V G;0 04 ~~

00ý

8 00

~~Ous

H

wW

-4

C 0,~ 0 14 ~4-4 V4

j4) 14u C

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Figure AIV-9. XMIPlfjernent. pres redibtributions for .ieveral

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f Dacwd-147CMioNtOL DATA -R&D(~.4*ftJap ,e.10-MA o of @1 18M.O b 0 o &M0=1M "d ,nd.*h, I04*W u st 606 -Iae W* ,.. " w .3vet 6 M91 pa'f & ktasoose

1, aqt(.h4Ar~f Y';I a Y A C e. vy (Cpefouthot Is. M4196RY a49044ý?V 6 6AIAf"

U.S. Naval Research LaboratoryV~ashington, I)X. 20390 a__ __. I11"..... .Z11. fSOGNT ?ITLE

Progress Report NO. 17, *Hypervelocity KWil Machaniisrrn Program.' Sezmiawlua4-Technical Progress Report. for period ending 30 Septemnber 1964

4. 0CRIPTIVI NOT" -(I) .;;- af 56Maw ib.dewIs)

Semiannual technical progress roport for period ."nding 30 Septemrber 1964F nIMMSo A;-teronatvIc Reeac Asoit.MfWrneon n.-This NRL Report contains a paper by Richard S. Sot-Joker and Colemnan duP3.

D*cembez 196( W 165 7& 4__

ARPA Order No. 149-60) NRL XI~op.;zt. U6Z - 1.t

NRI, Problem Wr04- 11 ___________

06 AVAILABILIMNTATumAva a l ~~All distribution of this report is controlled. 044aliel. DOC Wsrxqs Ue re~~,:throfagh Director., U.S. Na'vAl Research Laboratory. WashiAglon, D.C. 20390

41. s5IiPP.98"?AN NOT"S This report contain. it. 4;=*Sý;YiViAAC.Y-JLIV %4a siia Jnnuml progress repaort fromnAeronauial Research Associates of P$Iaeton. Inc. titld

oFreAnd I ngain orde10

Experimnents were peixformt~d in wkch the V*1oefty profiles an d ka a.preading properties of free undeliexpoaded jieh of cold &Atr~~aeae

agaimpoint heat transfer pai~aa~etstsd for iropingemnwt of these )eto ou v~axl.assurtface shapes were evaluated and correlations mad. with thei -ree jet -dta.Pro. .,%,re distribution and photographaic Studies Of the itio Ai4 iA a jt*i* jaeo that an untgsual CA&swA~1~ osd.~sca 4a u~rdor Cotain

:iivalafeMnot conditions. r~,i~iems associated with CMW*gesia jt samltthe effects of interfiarence due to g*6metric ax agret4 heaprt.wr

C%~2lt~r~din a qualitative wbl*.

0, 4M, 14,73

Naval Research LaboratoryTechnical Library

Research Reports Section

DATE: December 20, 2002

FROM: Mary Templeman, Code 5227

TO: Code 6300 Dr Gubser

CC: Tina Smallwood, Code 1221.1,2 /0 A

SUBJ: Review of NRL Reports

Dear Sir/Madam:

Please review NRL Report 6214, 6077, 6011, 6265-VI and 6265-V2 for:

zV ossible Distribution Statement

Possible Change in Classification

Mary Templem#(202)767-3425mary,.libary.nrl.navy.mJI

The subject report can be:

" Changed to Distribution A (Unlimitey)

•- Changed to Classification /I"! Other: ,

Sij•tiarure''..- J D ate

Key WORDS~

Five Underexpeaided JettImpinging Uadar. pazjdf.J0t horn a convergeiut 'i;-.1oStagnatlou Point kHeat Tranvlar T Fr-afloý: I

246 REPORT IS~CUIST CLASIUWATIMh Bomi the evop #pat11i.So.ii at ltp . imahllomi of the ta"mt. Teiatiog bob.~e (2 n lo m st 001ad "lai i.tt

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2b. OROCIP: Autmomtic Agome.g is oited jig DvD s. thsueu bettbe 3. C'Nee 010169" ed

eostlye 520010 and A~m. Vo lodwapt a hamot r ater 08"alk~iMii

the protp maimor. Also, whent am licable. shea that opti nlom *- _ _ _ _ - - .0

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6.t REORT DATI~ Water th do of tuthe p b o i I pi 00doah voin a r ma" os If am gthem the dalsu app.tearst ~ d~ hiteebbw te~eW4aasw~es udI the tta rupod*oflmiabo. 13. loraecc-al. nowh pm ovit. etma 6 dads laoi7&. Tm'.ACTA .aPGRANT Te Witt pea~tono It ma *I" t'1app e ar . ig eate o*O -- *A."lsO' hmalk.theU (O** .*, Z PM%140401 9046of0 i a the potetep twae hc eejo~t. I t t &"&M .~t t, .4vuAemtit as (00 004, #IV. ( 0). 01:m ashe of 0 ectg... 08he,.~ is~ali &I Uwtflutvtwwog *fte ihe76k ~ .Nuis EC or a ittiuips Sit. the tm eppepht. or it iesuidkg sL' hick tel"* 6 ~" o, =0wde

0oeencOatiNtod in CTIUI~ e the rcM' b tigitan t .Setib shmp a. th wead ob hereid6 .;XNA...agh 0 ,ic tRA a wicuast If0 410w4W hepmte sece at. the do .aawrsup eta -ItA "tMe a 4iwed ftdstioth mad oiw'Ie byheclasla mq o b rmot-t. vhu i mi t olt.melon Ia qatim aw it ..edelnemtid as it' ito).*a, oo~vt'I:. dqu sti WUe~a Theme ois ea* Uns. O y a n Ow*Ma k y4 of o baf Ma,10 1. CiWPROJUVT MUIUMEM No the apeopriut he. hdti sorE maoot 14101ti amII dIos@ W Av-114itti -.#p~t@ e iteQout aittos m, t soc sa veef I h i1 a i d A

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to AMN2M5RPR .A~bMkrtb M C k *A.iýwoSa o

Naval Research LaboratoryTechnical Library

Research Reports Section

DATE: December 20, 2002

FROM: Mary Templeman, Code 5227

TO: Code 6300 Dr GubserCC: Tina Smallwood, Code 1221.1/• /0 A5

SUBJ: Review of NRL Reports

Dear Sir/Madam:

Please review NRL Report 6214, 6077, 6011, 6265-Vl and 6265-V2 for:

r o ssible Distribution Statement

Possible Change in Classification

Th U,yu

Mary Termnplern9(202)767 -3425/mgWy(&librarv.nrl.navy.mil

The subject report can be:

•" Changed to Distribution A (Unlimite9), Changed to Classification /M.0_i

"1 Other:,

SiYaJlxe""-" -- / Date