1、J RESEARCH MEMORANDUM EXPEFC“TAL INVESTIGATION OF SUPERSONIC FLOW WITH DETACHEI SHOCK WAVES FOR MACH NUMBERS BETWEEN 1.8 AND 2.9 By W. E. Moeckel Lewis Flight Propulsion Laboratory Cleveland, Ohio SS “ yt“-II“ NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS WASHINGTON July 5, 1950 .- . Provided by IHSNo
2、t for ResaleNo reproduction or networking permitted without license from IHS-,-,-I Resulte of an eper.lmAa+nl Meetigtian of the flaw near the nose of plane and ads3ly syrmaetric bodies i the preaenoe of detached shock wave8 qe campared with predictions of theory. The location of the detached shock w
3、ave was determheii frcrm schlieren photogmphs for a variety of nose ahapse mer a range of free- stream Bch nmbers from 1.8 to 2.9. At a Mmh nuniber of 1.9, the form of the detached YBVB asd the pressure dietrikution mer the body were iwestigated for each no68 shape. In addition, the rela- . tion bet
4、ween shock location and flow spillage IAE determined for . - “ several axlally symmetric nose Wets. In the range of Iation, the contours shown in ffgure 2 were used, but the me.ximm thickneesea and diameters were reduced to 0.5 inch. The A-group in thie aeries was 1.5 inches in span, so that b/T for
5、 these models was 3.0. No pressure inst;rUmantation was attempted for these models . All models in both tunnels were sting- supported from the rear. RESULTS HID DISCUSSIOH Schlieren photographs. - Typical schlieren photographs of the models tested in the 18- by 18-hch tunnel are shown in figure 30 F
6、igures s(a) to 3(f) are representative of the configurations obtafned for the plane bodies at zero angle of attack and at the nraxinum angle of attack for which the portiween the model and the wall. me Bnalogo configurations for the axially synane-tric bodies are shown Fn figures 3(g) to 3(1) . The
7、A and B configurations are seen to produce similar flow patterns, except that the detached wve is considerably clcser to the nose 3n the B-poup. The thichess of the shock appears to be greater for the A-bodies than for the B-bodies. “hie effect is believed to result from a slight Provided by IHSNot
8、for ResaleNo reproduction or networking permitted without license from IHS-,-,-6 mAcA RM SOD05 misalinement of the A-bodies with respect analyzing the data, the upstream boundary ygmme*ic Plow. For b/T - 6.16, the Provided by IHSNot for ResaleNo reproduction or networking permitted without license f
9、rom IHS-,-,-8 V- experimental and assumed shock form almost coincide; w=hereas, for the-test Kith end plates, the experimental WBVB lief3 slightly upstream of the predicted form beyond the shock sonic point. The anrall difference between the shock forms .for b/T of 6.16 and for the end-plate test in
10、dicates that the spiUage arouad the ends of the model for b/T of 6.16 had little effect m the ahock form. The shock locatian, however,. which is indicated by the translations of the model contour In figure 5, changes quite noticeably in the range blT26.16. (See also fig. 4(b).) The transition toward
11、 the axially symmetric shock form and location as b/T decreases is to be expected from the consideration that the cross-sectional area of the A-bodies approaches the wose-sectional area of axially symmetric bodies. In particular, for b/T of 1.0, the configuration for the A-bodies would be expected t
12、o be vay close to that obtained with the B-bodies, although some difference ehould persist because of the difference between the areas of a quare and its inscribed circle. Effect of bcdy form on shock form. - The form of the detached wave8 obtained for each of the plane bodies with b/T of 6-16 is co
13、mpared with the assumed hyperbolic form in figure 6. Similar plots for the axially symmetric bodies are ahown is figure 7 . In fig- urea 6(a) and 7(a), the bodies are placed at their observed location relative to the deta.ched wave; but in figures 6(b) and 7(b), only the average locaticm is shown be
14、cause the differencee in L/ysB were Bmall for the bodies in these figures (table II). The theo- retical sonfc line is shown a8 a solid line between the shock and the body, and its end point on y/ys of 1.0 ie the theoretical locatian of the bcdy sonic point relative to the shock wave. Rrom figures 6f
15、a) and 7(a), the f for more gradually curved bodies, the detached wave beyond it6 sonic Point may dew lese rapidly than indicated by equation (7 ); (appendix A) In either ase, however, uae of the hyperbolic form to compute tote3 -8 by the methods of references 7 or 8 is unwarranted, inasmuch as Chan
16、gaS In shock contour can introduce considerable changes in compu%d drag- . and B-6 can be obtained by comparison of figures 3(g) to 3(i). Whether the hyperbola is a good approximtion to the form of the detached wBve at hbch numbers much higher than 1.9 remains .to be established. For that Is, the de
17、tached wave at angle of attack for each body wae almoet identical in form to the detached wave at zero angle of attack. When the two dock vBv68,wBre superimposed, the relative positim of the bodies w whereae, for the axially symmetric bodies (S-4 an8 B-5) the pressures approach closer to the corresp
18、onding cone preeeures. These figures than pointed bodies,of the 8- thickness ratio or Len-to-diameter ratio. If the regi-on of underpressure (relative to the correeponding polnted body) is sufficiently Large to more than counteract the effect of the region of overpressure near the vertex, lower drag
19、 can be attained with a blunt Body. As will be pointed out subsequently, of the bodies tested, only B-5 attained a total drag lower than that of the correspaadhg cane. . ahw haw blunt bodies, if correctly designed, may have lower drags The effect of finite span on the pressure distzibution along the
20、 center line for the A-bodiee waa ilegligible for the portion of the contour upstream of the shoulder (fig. 9(b). This result is somevhat surprising in view of the large effect of b/T on shock location. The difference is probably due to the fact that shock location Bepends an conditions along the en
21、tire span; whereas the effect of the edges an pressure distribution is greatest near the ends and decreases ae the center line is approached. Downstream of the shoulder, the pressure coefficient for body A-2 approached zero slightly more rapidly when end plates me attached (fig. 9(b). This result in
22、dicates that the preseure coefficients far the other .plane bodiee may also have approached their asynqtotic value6 more rapidly if they were truly two-dimensional. Drag coefficiente. - From figures 9 and 10, the drsg coefficients for each model me obtahed by numerical integration of the preseure co
23、efficients plotted agaet y/t and y/R . These drag coefficients are permeated in table III The“ coefflolent ( CD)to*l 16 baaed cm the mxtnnrm woes-rsectiaarsl area of each madel and is defined a6 E Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-13 or
24、 1 Theoretica3J.y predicted mlues of ( CD)sB are also shown In table III for coruparison. For the A-bodies, the erperimenkl values of range from 1.U to 1.28; for the B-group, the values vary from 1.07 to 1.13. !Fhe assumption that the farm of the nose has lfttle effect an the drag upstream of the so
25、nic point is thus seen to be me valid for axially symmetric than for plane bodies. If the bluntest of the plane bodies, A-1, is ignored, however, the values of (%)Em for the remaining noae f arme are found to lie witbin 5 percent of the mean value. Hence, except for ertremely blunt bodies, the afore
26、- mntioned assumption can probably be cansidered vetlid as azl approx- imation for plane as well a8 axially sgnrmatric bodies at a Wch num- ber of 1.9. (CD)sB comparison of the mean eqerimental dues (1.20 for plane bodies and 1.11 for axially symmetric bodies) with predicted values shms that the pre
27、dicted values are almost the reverse of the erper- imsntal values; that is, the predicted value for axially symnetric bodies is close to the mean experimental value for plane bodies, and vice versa. Most of this discrepancy can probably be attributed to the aversimplificaticm of conditions near the
28、eonic line used in reference 1. Small changes in the the value obtained from shock location may therefore be more comect than the value obtained fram the ncrminal outlet arear eUppO6edly Comglehu ClOeed, 8- lmkgS -0 believed t0 have In table IV, the value of 7 of 0.N for the inlet of fig- ure U(c) w
29、ae obtained from an examin8tian of the negative of the schlieren photograph shown in figure 3(0), in which the slip stream- line origlnating at the intereecticm of the oblique shock with the detached wave could be clearly seen. Because this elip stzeamllne paesed close to the lip of the Inlet, an ea
30、tinate of y, was eaeily obtained. In figure 12(d), the outlet of the diffuser was completely closed, and the value of 7 was estimated from the nmber of per- foratiane in the inlet. The flow coefficient for these perforations was aesmd tc. be 0.50, which has been found to agree reasonably well with e
31、lperimental reeulte (reference 6). Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-I NACA RM E50DU5 The agreement between predicted values and actual values of 7 appears to be good. The experimental and assumed shock forms also agree fairly well exce
32、pt in figure 12(c), where Interaction w%th the oblique ahock from the nose OCCUTB. Although none of the detached waves is precisely ROFKTB at p = ym, the assumption that the detached wave is an hsperbolawith origin at y = rm leads to fairly accurate values of 7. A procedure for improving the accurac
33、y is discussed in appendix B. An investigation of shock form, ahock location, and drag for a variety of plane and axially symmekric bodies that produce detached shock waves was conducted. The shock locatim was obtained for a range of kch nmbere from 1.8 to 2.9, and the shock form and drag were obtai
34、ned at a Mach nlLmber of 1.9. The reeults of this inves- tietian may be summarized as foUows: 1. The form of the detached wave between its sanic points at a Mach number of 1.9 was represented to good approximation for all bodies by an hyperbola asymptotic to the free-stream l23 1.25 5 -00 2.07 1-25
35、A -7 A-2 b/T Experimental PredrLcted 6.16 1.97 4.62 1.33 6-16 2.04 6.16 2-08 6.16 2.01 4000 1.98 .4.m 2.04 4.00 2.04 mm 2.23 2.31 B-1 B-2 B -3 3-4 B-5 B-6 0.90 . 97 1.00 1.00 . 97 1.00 0 -925 23 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-24 - E?
36、ree-etrerun Mach number, 1.94 CD,SB Boar Predicted Experimental Wtotal A-1 loll 1.07 A-4 1.21 loll A-3 1.20 loll A-2 1.12 1.28 1.24 A-6 .82 “( 051) 1.15 A-7 077 1.21 A4 1.17 .72 . I I . Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-(a) Body A-1; an
37、gle of attack, 0. (b) Boas A-3; angle of attack, Oo. (a) Body A-f; angle of attack, 5.7O. “ (e) Body A-3; angle of attack, 5.7O. 27 (f) Body A-7; angle of attack, 5 .So. C- 25505 3- 30- 50 Figure 3. - Tspioal detaohed-shook ccqfigurations at free-stream Bch number of 1.9. Provided by IHSNot for Resa
38、leNo reproduction or networking permitted without license from IHS-,-,- Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA RM SOD05 (g) B angle of attack, 0. (i) E-6; of attack, Oo. (1) Body B-6; angle of attack, 8O. C- 25506 3-30- 50 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-
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