1、R?VfE57E06 9-NACA-:”-”“”-.- .“ ,. .-i +-= “v”*-RESEARCH MEMORANDUMJET EFFECTS ON BASE PRESSURES OFAT MACH 1.91ANDCONICAL3.12AFTERBODIESBy L. Eugene Baughman and Fred D. KochendorferLewis Flight Propulsion LaboratoryCleveland, Ohio.-W.LSH A#-%d?.c,.cL.wsmEnDocuMmTNATIONAL ADVISORY COMMITTEEFOR AERONA
2、UTICSWASHINGTONAugust 12, 1957,=1E-Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-.bNACA RM E57E06suMMARY . . . . . . . . .INTRODUCTION . . . . . .SYM80LS . . . . . . .”MODEM. . . . . . . . .Basic Models . . . . .Rocket Model . . . . .Tail fiterfere
3、nceModelAir Supply . . . . . .Tunnel Installation . .support struts . . .?!P- TECH LIBRARY KAFB, NMIllllllllllllllull!llllllllli7=TABLE OF CONTENTSPage.Ef;:ct of struts on flowBoundary Layer . . . . .DATA REDUCTION . . . . . .INlRODUCTCEIYCONCEPTS . . .Flow Geometry . . . . . .Wake Pressure Rise Rat
4、ioTheoretical Flow Model .Role of Variables . . . .BOAEIICKIZAND WAKE ERESSURESBoattail . . . . . . . .Wake . . . . . . . . . .RESULTS MD DISCUSSION . .Effect of Jet l flow variables ticlude temperature, pres-sure, Reynolds nuniber,Mach number, and gas properties of both the exter-nal stresm and the
5、 et. Actual base-pressure calculations require a de- mtailed snalysis of the flow conditions of both the jet and the externalstream in the base region as well as the mixing process ti the wake.As a result, most of the investigationB into this problem area havebeen experimental in nature and ljmited
6、in scope. Until recently, the imost successfM. approaches to predicttig the pressure on a base surround-ing a jet have been empfrical in nature, having used experimentally deter-mined values of the governing pressure rise across the region of thetil.tig-shock fotion (e.g., refs. 1 to 4). These studi
7、es, fi genel,?srallel shilar approaches to the base-press-we problem without a jetrefs. 5 and 6. The extensive studies of the pressure rise associatedwith shock-tiducedboundary-layer separation ad reattachment have con-tributed greatly to the progress of this field. -More recently, theoretical appro
8、achesEwe been evolved for the two- _.dimensional lsmina (ref. 7) and turbulent (ref. 8) base-pressure prob-lem. The latter theory was applied to a b-e separating two differentstresms and has been modified herein to apply to the annular base.The present report provides base-pressure data for a system
9、atic set .of afterbody and nozzle geometries. The data are then used to calculatethe important wake pamuneters in an attempt to gain further insight intothe factors that govern base pressure. . The ranges of the important parameters are as foows: free-stresmMach mmibers, 1.91 and 3.12; jet Mach numb
10、er, 1.0 to 3.2; boattail single, 0 to llO; nozzle angle, O0 to 20; base-to-jet dismeter ratio, 1.11 to2.67; jet temperatures, 5400 R (air) and 4203 R (rocket);and jet total-to free-stream static-pressureratio, jet off to 30.Part of the present data has been discti.ssedpreviously h reference1. A bibl
11、iography ofeffects is ficluded.investigationsconcerning jet-stream interactionSYMBOTS()AL-lCP pressure coefficient, Po.-=c chordd diameter“”:-hw!m?3Provided by IHS Not for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA RME57E06 3L. MrTtvx.Yar.viflengthlkch numbertota
12、l or stagclation pressurestatic pressuregas constantradiustotal.temperaturethiclmessvelocityaxial distance from baseradial.distance from boattaildeflection angle at trailing shock of fluid just outside mixingregion, degsngle of boattail, degratio of specific heatsboundary-layer thicl.messangle of no
13、zzle at exit station, degPrandtl-Meyer single(angle through which a supersonic stream isturned to expand from M = 1 to M 1), degsingleof internal flow with axis, degangle of exbernal stream with axis, degSubscripts:a boattail station just upstream of base for jet-off conditionsB body maximumProvided
14、 by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-4bceiJ2two,iiw.wE9!Bbasel$ACARM E5however, since the two flows are separatedby a core of semidead air, their boundary pressures pe and pi can beassumed equal to the base pressure. (It should be noted that this
15、is asomewhat simplifiedpicture since may vary sanewhat, particularlyProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-8.amin the region just upstream of the trailing shock. Theat the base % - e depends on pj/, Ml, md T,l;theNACA RM E57E06jet deflection
16、stresm deflec-tiort - P depends on pa/ tid . - For the-three-dimensionalcasethe constant-pressureboundaries of both the jet and the stream are curvedso that both q and will very with the distance downstream of thebase x.()Since q=f #-().sud=g,%the variable /d willJplay an important role in determini
17、ng rpc and c, the flow directionsjust upstresm of the trailing shock.In the third region, downstream of the trailtig shock, the flowdirections as well as the static pressures ?nustbe equal. Therefore,the pressure of both streams must equalthe wake pressure , and fromgeometry the deflections ai d ae
18、must be such ttai + (Ze= (pC+$c.Brief consideration shows that the value of the base pressure is notdetermined uniquely by these requirements. The previous equation can besatisfied for all values of less than that for which the two flowsare parallel (qc = *C; b = 1.0) and greater then that for which
19、 the pres-%sure ratio pw/ equals the normal shock value correspondingto or, whichever is lower. Thus, the appropriateunique value of the wakepressure ratio p must be known before the base pressure isdetermined.Wake Pressure Rise RatioIt has been suggested (refs. 1, 4, and 6) that the snmunt by which
20、the wake pressure exceeds the base pressure is simply the maximum pres-sure rise which can be sustainedby the wake in the regi.m of the trail-ing shock snd must, therefore,be directly dependent on some physicalcharacteristicof the wake.Data from forward-”snd resrward-facing steps (refs. U. and 5) an
21、dfrom blunt-based bodies and airfoils (refs. 6 and 1.2)show that the pres-sure rise ratio depends on the Mach number, the fomn of the boundarylayer, =d the ratio of boundszy-layer thickness to step or base hetght.When the boundary layer is turbulent and thin relative to the base orstep, the pressure
22、 rise apparently depends cmd.yon the value of the Machnunber ahead of the shock. The variation of shock pressure rise ratiowith approach Mach nuniberis shown in figure.10 for steps and airfoilshaving thin turbulent boundery layers. The results for the airfoils fol-low the same trend as those for the
23、 reszwmd-facing steps over the Mach”.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-.NACA RM E57E06nuuiberrsmge but begti to depart frcm those forat Mach numhrs above 2.0.TheoreticalTlow ModelSome insight into the stiilarities between3the forward-fa
24、cing stepsthe wake flows for therearwsxd-fac step and the blunt-based airfoil as well as into thenature of the factors governing the wake pressure rise itself can be ob-tajned fran a flow model proposed in references 7 sad 8.k/fEdge of mixingregion Trailing shock/1 -“ /3=/ /(a)T3+J.The previous sket
25、ch shows that as the stresm passes into the wakeregion the velocity profile is altered first by the expansion sround thebase and then by the turbulent mixtig in the wake regim. Of particularimporteuce in the theory are the “separattig” streamlines (dashed lines).A separating streamline is defined as
26、 that streamline outside of whichthe mass flow is equal to that flcndmg over the bcdy just ahead of thebase. (It should be noted, however, that, because of mixing, both streamand wake fluid can cross the separating streamline. It is not intendedthat the term “separating”denote a division in the abso
27、lute sense.) Fromcentinuity all fluid outside the separatingdownstream through the trailing shock. Thestreamlinesmust centlnueinside fluid must reverseProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA RM E57E06direction and move toward the base. S
28、ince of all fluid that must passdownstream the fluid on the separating streamlinepossesses the lowestdynamic head (or total head or chnumiber), the separating streamlinemust also be the streamlinewhich limits the wake pressure rise ratioPJ a71.For splicity, the separating stresail.tiesme shown in sk
29、etch (a)to change direction abruptly at the trailing shock. Actually, the higherwake pressure will be transmitted upstresm, aud the inner streamlineswill change direction smoothlybeginning some distsnce upstresm of theshock. The compressionprocess along the separating or limiting stream- 8lines may
30、therefore be almost isentropic so that Pt.% s pw/ wherePZ is the stagnationpressure on the ltiiting streamline. The Wch num-ber Mlmust then be Z=mApplication of this method obviously requires detailed informationon.the velocity profiles in the wake region. The analysis of two-dimensional jet mtilng
31、(refs. 7 and 13) was used ti reference 8 to esti-mate base pressures. However, since the only available information wasfor fully developed turbulent profiles, the”results should apply strictlyonly to the case for which the distance to the trailing shock is large mrelative to the boundary-layer thicl
32、mess; the condition xb 20 isstated as a requirement in reference 13. If it is assumed that the ve-locity profiles sre relatively unaffected by the presence of a surface, .the results should apply to the re. srwsrd-facing step as well as to theblunt-based airfoil. The solid curve of figure I-Oshows t
33、he excellentagreement obtained between the theory snd th6 data for blunt-based air-foils orreerward-facing steps. A similar model can be applied to the problem of Jet effects on basepressure. In this case the total pressures of the jet and the streamare, in general, unequal. Figure 11 shows the case
34、 for Pd PO, and,since P / is then greater thanJ po/, Mi mt be greater than .In general, then, the stagnationpressure m.the separating stresml.tiein the jet will be greater thsm that along the sepmating streamline inthe external flow. Since the two ltiiting streamlines,which are Justable to negotiate
35、 the wake pressure rise, by deftiitionmust have eqmlstagnationpressure, the separating streamlines cannot be the lhnittigstreamlines for Pj + Po. There will exist, however, two new streamlines,one in the titernalflow and one in the external flow, which satisfy the e.following conditions:.cProvided b
36、y IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA RM E57E06 11.u.(1) The stagnation pressures (or Mach mmhers ) are equal.(2) The mass flow between the new streamline smd the separattigstreamline in the internal flow must eqya.1that between the new and sepa
37、-rating streamlines in the external flow.The second condition satisfies the requient that the total flowthat passes downstream through the trailing shock must equal that wp-stresm of the base. The new streamlines are therefore the Umit ingstresail.inesso that the Mach nuder will equal the value of M
38、2 definedpreviously.For the case illustrated in figure 11 (Pi Po), the two limitingstreamlines lie outside their correspondtig sparating streamlines. Aportion of the stresm fluid is centinually betig “trapped” in the wake,and an equal smount of wske fluid is carried downstreamby the higherenergy jet
39、. It is interesting to note that for a high-temperature jetthe jet-stream pressure ratio should play an important role h determin-ing the wake temperature; high wake temperatures should accqany lowjet presswes (PJ/Po 0.15). “This occurs because the base pressure becomes sufficientlyhighto sepa-rate
40、the boattail boundary layer. The effect on the location of thetrailing shock can.be seen in the schlieren photographs (fig. 16(a); the“effect on boattail pressure distribution is shown in figure 16(b). Varia-tion of pressure coefficientwith distance along the boattail is plottedfor several jet press
41、ure ratios. Also shown are the correspondtigbase-pressure coefficients. At low pressure ratios (P3/po the hier presses feedupstresm, and pressures near the aft end of the boattail increase. At apressure ratio of 16 l=ge pressure changes C= be observed. The flowdeflections resulting from these pressu
42、re gradients tend to increasetheeffective vd.ue of db/d,j and, as will be shown, this should decreasethe rate at which base pessure increaseswith jet pressure ratio.Reasons for certain of the base-pressure variations of figure 16are more apparent M base press,ureis factored tito component pressure *
43、Pw/Poratios as followE:pbpo = “ Values of these components calculated .Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA RME57E06 15mocomfrom the experhental data ad the correspondtig values of internal andexternal Mach nunibersre plotted h figure
44、 17. Also shown are the appro-priate theoretical wake pressure rise ratios from figure 12. It shouldbe noted that the base-to-et dismeter ratio is 2.0 rather than 1.U. aain figure 16. The change was made because more data were available nearthe minimum base-pressure point for the larger diameter rat
45、io.Jet pressure ratios greater than that corresponding to minimum basepressure (i.e., P/po 4) should be considered first. As pressure ra-tio increases (1) wake pressure increases rapidly because the angle ofapproach PC + *C increases,and (2) wake pressure rise is almost con-stmt because the Mach num
46、bers?and vary only slightly and, inaddition, in opposite directions see fig. 12). In general, agreementbetween theory ad experiment is excellent. Base pressure therefore in-creases because of the increase in wake pressure.As jet pressure ratio decreasesbelow the value correspondtig tominimm base pre
47、ssure, the jet total pressure (or ) becomes so lowthat wake pressure rise ratio must decrease rapidly. Base pressure con-sequently increases even though wake pressure continues to decrease.Values of wake pressure could not be calculated for conditions tithe base-bleed region. The Jet becomes mibsoni
48、c and, as stated previ-ously, the flow more closely reseniblesthat of the jet-off conditionEffect of Base-to-Jet Diameter Ratio.The effect of varying the base-to-et dismeter ratio is shown infigures 18 and 19 for several values of jet Mach nuniberand for free-stresm Mach numbers of 1.91 and 3.12. The boattail singleis constantat 5.63 for these curves.ticreasing the base-to-jet diameter ratio, in gen
