NASA NACA-TN-2399-1951 Applicability of the hypersonic similarity rule to pressure distributions which include the effects of rotation for bodies of revolution at zero angle of att.pdf

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1、cm 1.tu)cclNATIONAL ADVISORY COMMITTEEFOR AERONAUTICSIITECHNICAL NOTE 2399PPLICABILITY OF THE HYPERSONICDISTRIBUTIONS WHICH INCLUDESIMILARITY RULE TO PRESSURETHE EFFECTS OF ROTATIONFOR BODIES OF REVOLUTION AT ZERO ANGLE OF ATTACKBy Vernon J. RossowAmes AeronauticalMoffett Field,Laboratorycam.Washino

2、n ,4- ,4,“ . ,:.,.4.:.-p-.,. . . . - ,./Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-TECHLIBRARY, NMllrnlllllflulllllllluCIOL5LBE!NATIoNALADVISORYcohmlTTEEFOR AERONAUTICS0APPLICABILITYTECHNICAL NOTE .2399OF THE HYPERSONIC SIMILARITY RULE TO PRESSU

3、REDISTRIBUTIONSWHICH INCIllDETHE EFFECTSFOR BODIES OF REVOLUTION AT ZERO ANGLEBy Vernon J. RossowSUMMARYThe analysis of Technical Note 2250, 1950, isOF ROTATIONOF ATTACKextended to includethe effects of flow rotation. It is fod whereas, at K=2.0, it reaches over 11 percentof the nose tip pressure. T

4、his rapid change in magnitude of therotation effect is shown in figure 6(b) for several values of thelongitudinal coordinate. These curves demonstrate that the errorintroducedby ignoring the entropy term in the characteristicequationscan markedly affect pressure distributionsdeterminedby the method

5、ofcharacteristics.Since the ressure distribution over ogives is influencedbyrotation, the drag psrameter CDqo/po is also influenced. The pressuredistributions shown id figure 3 were integrated for drag. These dragparameters are compared in figure 7 wtth the ogive drag parameters offigure I.1of refer

6、ence 2. “Theerror in drag due to neglecting rotationis negligible at K=O.S, but amounts to a decrease in drag at K42.OOf about 30 percent of the drag obtainedwhen the effects of rotationare fncluded. This clearly shows that in certain cases the effects ofrotation can be sizable.4A third type of solu

7、tionwhich has a fictitious irrotationalflow fieldwas studSed. In this case, the flow field is made ccmq)letelyirrota-tionalby forcing the shockwave to remain straight. In the casestudied (Z/d=3 ogive at MLeft: 1- cos a 7 (M)M* sin% cos a A Right: 1 R- cos a 7 = AM* (A6)The l/cos cz is requiredbecaus

8、e the complete entrcrpyterm of equations(Al) and (A2) is applied along the characteristicdirection,whereas thevelocity increment is applied along the stream direction.The physicalof this equation.significanceof equation (A6) is shown in another formFrom reference 6, the velocity increment AM* become

9、s:AM* = tisti%l A: . 2tiSehemutic diugrum showing where rotufion begins toinfluence the Vt?/OCi?ydjstrjbufion-on cone cylinders on dogive cylinders.-. _ ._ . _ _ _ -. - _ _ ._Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-II oL ongbudnoi coordlnote,

10、 peteent nose lengthPt7gure aNK-2, /d= 3, M= 6. %w111IIProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-u.1ItI1I Longitudinal coordinate, percent nose /ength(a) K (25Figure 3. Variation of pressure coefficient along ogive cylinders for a given value o

11、fthe similarity porameter K,. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-I.PCD2.01.6v1.2.8.4 rotut/on.0-.40 go . go *O I I I100 /20 /40 160 /80 200Longitudinal coordinate, percent nose length1I.Figure 3. Con tinued.rProvided by IHSNot for Resale

12、No reproduction or networking permitted without license from IHS-,-,-NACA TN 2399 19.J,3.62.8 it1/20 i/.6t rota tion term !,)1.2.8_ Neglecting rota tion term Y.4 o 1 - A- ysy-.40 *O Go co B. ; -,;-;6(7 180 200Longitudinal coordinate, percent nose length(c) K= /.5, I/d = 4,Af;6.Figure S.Continue d.-

13、. -. . -. . . . -Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-oLongltuoinal coordinate, percent nose length -(d) K=2.oi-c!o IFigure 3.Conc/uded.,Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA

14、 TN 2399 21.6.4.20 w82(uJK= 0.5,i%f=3,M“=L5.1IQ,ffgure 4.fineness. . WK=/, l/d=2 , Mo=2.) t I I I II Io I ?*-9o 20 40 60 80 /00 /20 /40 /60 /6?2Longitudinal coordinate, percent nose length(C) K=2, Z/d=L5, 1%=3.-So/ufions to check the lower limits of Much number andratio for which Me hypersonic simil

15、arity low upplies. _ ,. - - . Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-, /. . ./0/2. ?fineness rotlo, I/dFigure 5.Range of opplicabllity of similarl ty law for ogives, itProvided by IHSNot for ResaleNo reproduction or networking permitted with

16、out license from IHS-,-,-.8M #pd633B,6.200 20 40 60 80 /00 120 /40 f60 /80 200L ongitudlno/ coordinate, percent nose /ength _(a) Variation of pressure Increment a/ong btiy.Figure 6 . Pressure Increment olong ogive cylinders due to rotation term Incharacterktics equation.Provided by IHSNot for Resale

17、No reproduction or networking permitted without license from IHS-,-,-III87.6.5.4.3.2./.6 .8 (.0 1.2 1.4 6 1.8 2,0Similarity purameter, A(b Variation of pressure increment withFigure 6.Conchded.K.w-F1IIProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-I

18、A1,II I I I Q126 I I I I x-”wt- 1 +- 10.8 .0,/ / “F“i NegrofG.4/.0.4 .6 8 Lo /.2 /.4 6 L8 2.0SYmibrhy paromete KTtion term 1111I 1.Rgure 7,-Vorlafion of drag parameter C D p. with the slmilod porometer K for ogives.Provided by IHSNot for ResaleNo reproduction or networking permitted without license

19、from IHS-,-,-26 NAC!A TN 2399.(a) Og/ve14 .6 .8 10 /.2 14 /.6 /.8 2.0Slmilarhy porumefeG K, free stream Mach numberfineness ratio of ogive(b) CyllnderFigure 8. Variation of pressufi coefficient) with K for ogive cyllndersincluding effects of rotational flow. . -.Provided by IHSNot for ResaleNo repro

20、duction or networking permitted without license from IHS-,-,-. - . . ChangO in pressure drug, percent“kProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-28 cA TN 2399.aapproximate methpdi-cburucterkties neglecting rotation termr-characteristics Includi

21、nu rotation term Asod po/ur/(o) Hodograph p/une.Y shockwave .53Ix(b) physical plane.Figure /0.Schematic diagram comparlng the convenfiona/ andapproximate method for including rotutlon.NACA-IJUey-6-21-51-1000.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-