1、O,3DO-4L.HIiRESEARCH MEMORANDUMDRAG OF CONICAL AND CIRCULAR-ARC BOATTAIL AFTERBODIESI AT MACH NUMBERS FROM 0.6 TO 1.3!t,) 0u O “_| I _ _II ,_ _By Frank V. Silhan and James M. Cubbage, Jr.Langley Ae ronautical Labo ratoryLangley Field, Va.TECHNICAL118,_RyAIRESEAREH I_A,_UF_,_T_#_IN_ CO.LOS ANGELES45,
2、 CALIF,CALIFORNIACLASSIFri_ DOCUMENTThis material contaLns information affecting the Na_o_s/Defense o_ the United States within th_ meaningof the espionage laws, Title 18, U.S.C., Sees. 793 and 794, the trar_mlsslon or revelafdoct of whlch in anymamner to a_ u_u_r_e_ person is pzo_bZte_ by biw.ATION
3、AL ADVISORY COMMITTEEFOR AERONAUTICSWASHI NGTONJanuary 22, 1957(c=Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-,k-_i=fi i=i .aProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-R NACA RM L56K22NATIONA
4、L ADVISORY COMMITTEE FOR AERONAUTICSRESEARCH MEMORANDUMDRAG OF CONICAL _D CIRCUIAR-ARC BOATTAIL AFTERBODIESAT MACH NUMBERS FROM 0.6 TO 1.3By Frank V. Silhan and James M. Cubbage, Jr.SUMMARYDrag characteristics of a series of related conical and circular-arc afterbodies are presented for Mach numbers
5、 from 0.6 to 1.3. Dragwas obtained from pressure measurements on the boattail and solid base.The boattail angles tested ranged from 0 to 45 for ratios of base diam-eter to maximum body diameter ranging from 0 to 1.0.The results of the investigation indicate that increasing the ratioof base diameter
6、to maximum diameter beyond 0.95 is, in general, detri-mental from a drag standpoint. The minimum-drag boattail angle forconical afterbodies at a Mach number of 0.9 and all diameter ratios testedwas approximately 7 and for circular-arc afterbodies approximately 16;at a Mach number of 1.2, the data in
7、dicate optima of approximately 4for the cones and 7 for the circular arcs. On the basis of equivalentfineness ratio and ratio of base diameter to maximum diameter thecircular-arc afterbodies gave lower boattail drag than conical afterbodiesfor conical boattail angles greater than approximately 8 (16
8、 circular-arc boattail angle), but for angles less than 8 the boattail drag for thecones was slightly lower. For total drag, similar results were obtainedexcept for a reduction of the difference between the two types of boat-tailing for cone angles less than 8.INTRODUCTIONAt transonic and supersonic
9、 speeds a significant part of the totaldrag of aircraft or missiles is associated with reduced pressures alongthe afterbody of the fuselage or nacelles. The problem of designing anafterbody to fair from a fixed diameter of a fuselage or nacelle to afixed diameter of the base so that minimum d_ag wou
10、ld be obtained forboth supersonic and subsonic flight has received considerable attention.Calculation of afterbody drag can be readily accomplished at supersonicspeeds and the literature containsnumerous experimental investigationsUNCLASSIFIEDProvided by IHSNot for ResaleNo reproduction or networkin
11、g permitted without license from IHS-,-,-2 NACA RM L56K22at these speeds. At the higher subsonic speeds of current interest forcruise operation, theoretical determination of the drag is not readilyaccomplished, and at low supersonic speeds the theory is restricted tothin bodies. Experimental data at
12、 transonic speeds are reported in ref-erences i to 6 and elsewhere, but for the most part consist of resultsfrom specific configurations or from afterbodies with stabilizing fins.The investigation reported herein is part of a general program inprogress in the Internal Aerodynamics Branch of the Lang
13、ley Compressi-bility Research Division to study the drag of afterbodies through thetransonic range. The present work concerns the drag of a series of con-ical and circular-arc afterbodies without an issuing Jet. The boattailangle of the conical and circular-arc afterbodies tested ranged from 0to 45
14、and the ratio of base diameter to maximum diameter varied from 0to 1.0. These 1-inch-diameter afterbodies were attached to a cylindri-cal sting which extended upstream into the tunnel entrance bell. Thetunnel test section was slotted and data were obtained over a Mach num-ber range from 0.6 to 1.3.
15、The corresponding Reynolds number range was3.3 106 to 4.4 106 per foot.SYMBOLSAdCDCD,_CD,bCpHlMPareadiametertotal-drag coefficient, boattail plus base,boattail-drag coefficient, F (rb/rm) 2base-drag coefficient,pressure coefficient,total pressurelength of boattailstream Mach numberstatic pressure.h-
16、Cp,b AmPx - P_%CD,_ + CD, bCp 2rm/IProvided by IHS Not for ResaleNo reproduction or networking permitted without license from IHS -,-,-NACA RM L561_2 _CLAssIFI_._ 3q dynamic pressure, pV2/2r radiusV velocityx distance downstream from point of initial decrease from diameterof i inch (for cylindrical
17、afterbody only, x is measured froma point 2 maximum body diameters upstream of base)y radial distance from surface6 boattail angle between center line of model and tangent line atbase of modelp mass densitySubscripts:boattailb basex localm maximumstream conditionsAPPARATUS AND METHODSA photograph sh
18、owing the general arrangement of the experimentalsetup used in this investigation is presented in figure i. The top andbottom walls of the 4_2- inch-square slotted test section contained fourslots each; the width of the slots was such that the ratio of open areato total area of each slotted wall was
19、 1/8. The afterbody models wereattached to a 1-inch-diameter sting supported along the tunnel centerline by the system of struts shown in figure I. Air at a maximum stag-nation pressure of 2 atmospheres was supplied by a centrifugal compressor;auxiliary suction was applied to the plenum chamber surr
20、ounding the testsection to obtain supersonic Mach numbers. The test-section-empty Machnumber distributions and construction details of this tunnel are presentedin reference 7. For the range of Mach numbers near i, tunnel-wall effectscause some uncertainty in the data. At the higher Mach numbers of t
21、heinvestigation, however, reflected disturbances which originate on theONCLASSIFIEUProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-boattail fall well downstream of the base for all but a few of the longestmodels. For the longest of these the reflecte
22、d disturbances are just rear-ward of the body at the highest Mach number. Although the magnitude of anywall effect present is unknown, it is felt, from previous experience andchecks with other data where possible, that these effects are relativelysmall and that the data trends established are valid
23、throughout the speedrange of these tests.Two types of afterbody contours were tested in this investigation:conical and circular-arc contours. Photographs of several models arepresented in figure 2; sketches are also shown in figure 3 together withtables summarizing pertinent dimensions and the numbe
24、r of pressure ori-fices of each model tested. Boattail angles of 0, 3, 5.6 , 8, 16,and 45 were tested; ratios of base diameter to maximum body diameterwere 0, 0.55, 0.70, 0.85, and 1.0. Radii for the profiles of theclrcular-arc afterbodies were chosen so that the tangent to the arc atthe base formed
25、 the desired boattail angle. Afterbody models with lowboattail angles and small-diameter ratios were not tested due to theirextreme length. Pressure measurements were obtained from a number oforifices installed in a helical path around the afterbody and on themodel base. The number of orifices in a
26、particular model varied accordingto the length of the model. For models containing more than one base-pressure orifice, an average of the base pressures was used in determiningbase drag. The free-stream static-pressure orifice was located on thesting approximately I body diameter upstream of the cyl
27、inder-afterbodyJuncture.A boundary-layer survey was made to estimate the depth and profileof the boundary layer approaching the afterbody. The survey model hadsix total-pressure probes, 0.030 inch in diameter, equally spaced aboutthe circumference at varying heights from the surface and in the plane
28、corresponding to the sting-boattail juncture. The ends of the probeswere flattened to give an opening approximately 0.006 inch in height.Velocity profiles obtained at three stream Mach numbers are presented infigure 4 together with a i/7-power profile. The profiles show a thickturbulent boundary lay
29、er approaching the afterbody. The effect ofboundary-layer thickness was not investigated although it may change thelevel of the curves. However, it is felt that the relative drag of thedifferent models would not changewith boundary-layer thickness. This isborne out in the investigations of reference
30、s 5 and 8 which include theeffect of varying boundary-layer thickness for afterbodies with jetflow. Both show only a small effect due to increases in boundary-layerthickness from 0.095 to 0.184 of the maximum body diameter at transonicspeeds and at M = 1.5 (ref. 5) and from 0.05 to 0.18 at M = 1.9(r
31、ef. 8). Extrapolation to the no-Jet-flow condition of the data ofreference 8 (Cp,b as a function of jet pressure ratio) indicates achange in Cp,b of approximately 4 percent.11Provided by IHS Not for ResaleNo reproduction or networking permitted without license from IHS -,-,-Afterbody pressures were
32、recorded at Math numbers from 0.6 to about1.3. At each test point, all pressures were photographically recordedfrom a mercury-filled, multltube manometer. The measured pressure dis-tributions were mechanically integrated to obtain the pressure drag.Schlleren photographs of the flow were also taken a
33、t a majority of thetest conditions. The Reynolds number range of these tests was 3.3 106to 4.4 lO6 per foot.RESULTS AND DISCUSSIONS/Afterbody Pressure DistributionsPressures measured along several _f the conical and circular-arcafterbodies studied in this investigation are presented in coefficientfo
34、rm as a function of the distance along the afterbody in figures 5and 6. Schlieren photographs of the flow field about the afterbody forseveral of the afterbody models are also shown in figures 5 and 6.Figure 5 shows the changes that occur in the pressure distributionsover conical and circular-arc af
35、terbodies with boattail angles of 5.6 and 16 as the stream Mach number varies from 0.6 to 1.3. The pressuredistributions over the 5.6 conical afterbody (fig. 5(a) are typical ofthose over other low-angle cones. The abrupt expansion of the flow atthe cone-cylinder Juncture at M _ 1.0 is in good agree
36、ment with thatcalculated for a Prandtl-Meyer turn equal to the boattail angle _.(The latter value is indicated by the arrow on the ordinate at x/d m = 0.)Compression of the flow over the afterbody at subsonic Mach numbers ismore rapid than the supersonic compression. For the shortest afterbody,db/d
37、m = 0.85, the pressure coefficient decreased abruptly ahead of thebase due to the influence of the base pressure. The initial expansionand pressures upstream of the base were nearly independent of the ratioof base diameter to maximum diameter. The continued compression of theflow over a longer after
38、body (db/d m = 0.55) was sufficient to producepositive values of Cp,_ at M = 0.9 and 1.O. The influence of thebase pressure extended somewhat farther forward as the afterbody lengthincreased. Although the extent of the initial expansion and subsequentcompression was greater at _ = 16 (fig. 5(b) the
39、effects of Machnumber and ratio of base diameter to maximum diameter were essentiallythe same as at the lower boattail angles. The values of Cp, B calcu-lated for a Prandtl-Meyer expansion of 16 is not in as good agreementwith the measured pressure as it was for the _ = _.6 model.The schlieren photo
40、graphs of figures 5(a) and (b) show the differ-ence in the flow over a 5.6 and 16 boattailed afterbody. The absenceProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-s6 _ NACA RM L56K22of a trailing shock on the 5.6 afterbody will be noted in figure 5(a
41、)at all speeds due to the gradual recompression of the flow along theafterbody following the initial expansion to 5.6 . Along the 16 model(fig. 5(b), however, the recompression occurs in a much shorter distance,and the flow, unable to negotiate this higher gradient, separates from thebody to produce
42、 the trailing shock observed in the photographs. As theMach number increases, this trailing shock moves rearward on the modeluntil at M = 1.3 it is located close to the base.For the circular-arc-profile afterbodies (figs. 5(c) and (d) thepressure just downstream of the point of tangency was well bel
43、ow thefreestream static pressure in some instances (fig. 5(d). This must beattributed largely to the thinning of the boundary layer ahead of thetangency point and subsequent acceleration of the flow. For a long, low-angle afterbody db/d m = 0.70 (fig. 5(c) the pressure coefficient alongthe afterbody
44、 was nearly constant at all Mach numbers. Along the shortestafterbody_ db/d m = 0.85, the pressure tended to decrease to a minimumat x/dm_ I and then remains essentially constant. For B = 16(fig. 5(d) the decrease to minimum pressure was quite rapid as was thesubsequent increase in pressure. The poi
45、nt of minimum pressure movedrearward on the afterbody as M increased and as the afterbody becamelonger (decreasing db/dm). Positive pressures occurred on the rearpart of the afterbody for the B = 16, db/dm = 0.55 model from M = 0.6to 1.O. The schlieren photographs indicate no separation of the flowo
46、ver the low-angle body (fig. 5(c), and limited separation affected onlya small portion of the 16 afterbody (fig. 5(d).Figure 6 shows the variation in the pressure-coefficient distribu-tions over the afterbody for different values of boattail angle at aconstant value of db/d m. The distributions show
47、n for 6 = 0 (cylln-drical afterbody) were obtained from reference 5. Since the pressuredrag of a cylindrical afterbody is represented entirely by the base drag,the area under the curve for B = O in figure 6 does not represent apressure drag force. The schlieren photographs and pressure distribu-tion
48、s for the conical afterbody with B _ 45 show the flow to be sep-arated over the entire length of the afterbody. Unpublished data obtainedby the Internal Aerodynamics Branch for a 30 afterbody show that the flowcompletely separates at this value of B also. The distributions forB = 8o and 16 at M = 1.
49、1 are not consistent with the trend of thedistributions for other Mach numbers perhaps as a result of an error inthe static-pressure measurement. As indicated in figure 3(b), these modelshad only three static orifices available to determine the pressuredistributions.For the circular-arc models (fig. 6(b) the boattail angle
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