NASA NACA-TR-933-1949 Performance of conical jet nozzles in terms of flow and velocity coefficients《圆锥喷嘴对于流量和速度系数的性能》.pdf

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1、.-, . . NATIONAL ADVISORY “_ :i: COMMITTEE iIFORAERONAUTICS:_ERFORMANCE OF CONICAL JET I_OZZLES IN TERYIS_oF_ow _-v VEL0crryCO_FIC_TS_. “, “ “f _,. . - I_ODUCED BYNATIONAL TECHNICALINFORMATION SERVICEU S OEPARIM(N! Of COMMERCESPRINGFIELO. Vk. 22.lGlProvided by IHSNot for ResaleNo reproduction or net

2、working permitted without license from IHS-,-,-oY/r U / )_:*“;- _W_. ( - _,I-eii -/7 - _QlJagth=k Tinm lAKRONAUTIC SYMBOLSxL FUNDAMXNTALAND DERIVED UNITS“ MetrioUnit _._. .mmomd- =.; weight of 1 kilogram .8t_ad_l _mLtiou of gravitym01S0(_ m/s )or 3_.17(0 ft/_fM-_-8._“ ._._awla_, .,.Olp . . ., .OL/ i

3、 i iJet“ dlornel“er4 D=f/a)3 I m.z5._-_o i“OxlO,=e a /5,/3LO 1.2 /.4._LI Jl!iiii?_foGel _ozzt_s _ f1.6 1.8 _0 _2 2.4 2.6 _.8Pressure rat/o,Pjp,Floultg 2.-Range and oompariaon ot Reynolds number for model and fuli-sc_le nozzles overrange ot pcemtm ratios.nozzles is approximately between 3)iRot_o iSX:

4、_ctf_c- 1.40I; _ i i i1.6 1.8 2.0 2.2 2, 2.e z.eFl6glt_ 3.-Comparison o| Math number for two values of ratio of specific heats over ranwof i)_tlre ratio. (r for model nozzlt_, approxinmtcly 1.4t); ._ for fal-scale nl)_.zv$. L3,to 1.40.)mately t.40 and the value of _, for typical full-scale jet-engim

5、nozzles is between 1.30 and 1.40. For test conditions of equaMach number, the difference in pressure ratio is small. Thi:small difference in pressure ratios will be shown in the following section to have very little effect on the nozzle (oefficient_From the foregoing analysis, flow similarity betwee

6、n th,model and full-scale nozzles al)pears to have been s.t:=.fi_.,Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-PERFORMANCE OF CONICAL JET NOZZLES IN TERMS OF FLOW AND VELOCITY COEFFICIENTS 5with reasonable accuracy and the results of the model te

7、stsare considered directly applicable to full-scale-nozzle designand performance.FLOW COEFI_CIENTThe.reflects on nozzle performance of changes in diameterratio, cone angle, and pressure ratio are presented. Figure 4shows the measured effects of change in pressure ratio on theperformance of all nozzl

8、es investigated. For all nozzles, theflow coefficient increased with an increase in pressure ratio.Also a rapid decrease in flow coefficient with increasing nozzlecone angle can be seen.Values of flow coefficient for nozzles with cone angles of5 , 15 , 30 , 45 , and 90 were obtained from cross-plott

9、ingvalues of flow coefficient obtained from figure 4 against thenozzle cone angle for each diameter ratio. These data wereProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-6 REPORT 933-NATIONAL .ADVISORY COMMITTEE FOR AERONAUTICSCone boll-angle, t.9442

10、._ .86_ .82_.7490 j _#wi. Io“ _Or_41ure.“ rotioZO/.4.o. tl.5 .6 .7 .8 .9 /_Oufle f - in el diome ?er retio, JPs/DIFIOUBIt 5.-Varit_oD O con_al-llogg_ flow c(_t wi th out_t-ialet diameter ratio fornoZZles with various corm half-angles at two _ ratio.again cross-plotted (fig. 5) to show variations in

11、flow coeffi-cient with changes in diameter ratio for pressure ratios of2.0 and 1.4. The nozzles with small cone angles reach anoptimum diameter ratio of about 0.75. At a pressure ratioof 2.0, a maximum flow coefficient of 0.972 is indicated forthe 5 nozzle. In general, the flow coefficient for nozzl

12、eswith large cone half-angles increases with increasing diameterratio. The curves for all nozzles approach a particular valueof flow coe_cient at a diameter ratio of 1.0 because thisvalue represents a straight length of pipe. The flow coeffi-cient for a straight length of pipe is shown in figure 6.T

13、he variations in flow coefficients for nozzles of variouscone angles with changes in area ratio ri=/riL over a range of.9_: i.36,“_,i . ._.9_ + o o/.e /.+ /,+ /.+ z.o z.e z., z+ e.+Pressure re?/o, P_PoFLGURI8.-V,riation in flow coefficient with pre.,_ure ratio for dischar_ from stroil_ht pipes./. O0

14、.I 2. .3 .4 .5 ._ .7 .8 .9 LOOutlet-inlet areo rot,o, ARIA,(a) Corm half-angle, 5“. (d) Cone hair-angle. 30.(b) Cone half-angle, 10_. - (e) Cone half-angle. 45.(e) Cone hall.angle. 15.FIOURI 7.-Variation of conical-nozzle flow coeCfleient with outlet-inlet area ratio for variou_pce,_mro raticel.Prov

15、ided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-PERFORMANCEOFCONICALJETNOZZLESIN TERMSOF FLOW AND VELOCITY COEFFICIENTS 7.6O.I .2 .3 .4 .5 .6 .7 .8 .9 /.0Outlet-inlet area ratiop Am/Ai(f) Cone hslf-angle, 80 . (g) Cone half-sntle, _0.FIGUR 7.-Concluded.

16、Variation o/ eoniesl-nozz_ flow ecefllc|ent with outlet-in_t aresratio for vsriot_ presure ratios.pressure ratios are presented in figure 7. The maximumvalues of the flow coefficients mentioned in the discussion offigure 5 are better seen ill figures 7(a), 7(b), and 7(c) forcone half-angles of 5, 10

17、, and 15, respectively. Figure 7presents the data in the most convenient form for use inuesign of conical nozzles. The use of area ratio instead ofdiameter ratio for these charts simplifies the selection of anozzle to give a desired flow rate.vELOCITY COEFFICIENTThe velocity coefficients C, are give

18、n for all nozzles infigure 8. One value of w,loeity coefficient, 0.945, representsthe ,lata obtained with all rmzzles within +0.03, betweenp,cs.:ure ratios of 1.3 and dw eritical vahie (approximately1.9). The scatter of the data due to inaccuracies in themeasurements of flow and thrust at pressure r

19、atios below1.3 was great enough to obscure any trend of the nozzleperformance at the very low pressure ratios. At super-critical pressure ratios, the velocity coefficient decreased to avalue of 0.893 at a pressure ratio of approximately 2.8. Themean curve represents the supercritical data within 4-0

20、.03.The velocity coefficient was essentially independent of coneangle and diameter ratio and dependent only on pressureratio.The effective velocity coefficients (7,., (fig. 9) are used onlyfor the simplified thrust calculations for all the nozzlesinvestigated. One value of effective velocity coeffic

21、ient.0.945, represents the data obtained with all nozzles within4-0.03 between pressure ratios of 1.3 and the critical vah|e.This value is the same as that obtained for the velocity coeffi-cient of figure 8, because the velocity coefficient and theeffective velocity coefficient are identical in the

22、subcriticalopressure-ratio operating range. At supercritical pressureratios, the average value of effective velocity coefficientdecreases slightly to 0.934 at a pressure ratio of approxi-mately 2.8.COMPAI_8ON O/F THIUST PER/VOS_MANCEThe variation in thrust with change in pressure ratio is afunction

23、of only the flow coefficients and exit areas, as canbe demonstrated:From equation (16)F,. (22)The velocities are functions of only pressure ratio andinitial temperature (equation (9) and at any particularoperating condition are therefore equal. The velocity co-.Otl0O._,7Lc,3_AIlD1.0 1.2Cor_ Cone bol

24、l-30 50-_ ,_40 .5090 .50-,_ /5 _- 9/16 .67 !, 29 _ 9148 - .67 _ 90 ,.919o q7%.1 I: i I:b _ ,: I I i I i : ,i i il!i /.4 /.6 /.8 2.0 2.2 2.d 2._ 2.8Pressure ro t_b, _.lpoFc,I,a 8.-Variation of onie_al-nozzle velocity coefiicient with prc_uure ratio for variou_ (onehalf-angles and outlct-in|e_ diamete

25、r ratios.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-8PREPORT 933-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICSefficients are also equal because they are a function of onlypressure ratio (fig. 9). The air-flow ratio W,.z/W,.u isequal to the ratio o

26、f outlet areas for any particular operatingcondition. (See equation (12).) The thrust ratio may bewrittenasF,., C,=A,.,F ,.,ffi (23)Inasmuch as the exitareasare fixed,theratioofperform-ance (airflow and thrust)of nozzlesof differentdesignselectedforthe same thrustata particularconditionispro-portion

27、altothe ratioofflowcoefficients.Thrust with the90and 5nozzlesiscompared infigure10over a range of pressureratiosbetween approximately 1.0and 2.8. These two nozzleswere designed togivethe samethrust(effectiveflowareaand airflow)atapressureratioof2.0 and were chosen to show the maximum variationinthru

28、st. The variationin thrustbetween the two nozzleswith increasingpressureratioresultsfrom the largeroutletarea of the 90 nozzle and a more rapid increase in flow co-efficient than for the 5 nozzle. The thrust ratio increasesfor the 90 nozzle with an increase in pressure ratio above thedesign pressure

29、 ratio because of the greater effective flowarea, and decreases with a decrease in pressure ratio becauseof the smaller effective flow area.SUMMARY OF RESULTSFrom an investigation of conical jet nozzles with inletdiameters of 5 inches, outlet-inlet diameter ratios from 0.50to 0.91, and cone half-ang

30、les from 5 to 90 at pressure ratiosfrom 1.0 to 2.8, the following performance characteristicswere determined:1.16“SOLO 12 W /6 /8 20 22 24 26 28Pressure rot,o, Pt/PoFIGURE 9.-Variation of conical-nozzle effective velocity coefficient with presmlre ratio forvarious cone halt-angles _tntl outlet-inlet

31、 4iametcr ratios (used only for simpllflcotio, ofthrust calculationsl.1. The flow coefficient for all nozzles increased with in-creasing pressure ratio.2. The flow coefficient for all nozzles increased withdecreasing cone half-angle.3. The flow coefficient of nozzles with small cone half-angles reac

32、hed an optimum at a diameter ratio of about0.75. The flow coefficient of nozzles with large cone half-angles in general increased with increasing diameter ratio.4. The velocity coefficient could be reasonably wellrepresented by a value of 0.945 in the range of pressureratios from 1.3 to the critical

33、 pressure ratio. At pressureratios above the critical value, the velocity coefficientdecreased to a value of 0.893 at a pressure ratio of 2.8.5. The velocity coefficient was essentially independent ofcone half-angle and of outlet-inlet diameter ratio./,i.I?/LO L2 t4 1.8 1.8 2.0 _8 _“ 2.8 2.8I%-essur

34、e rat/o, P,/p,FLOURS lO.-Comparison of thrust of 90 _or._le with that of 5 nozzle at various pressur_r_l_. (Design Points, PdPt, 2.0“, AtlAt of 90 nozzle. O.f_,; At/At of 5“ nozzle, 0.490.)6. The effective velocity coefficient was based on tlvassumption of complete isentropic expansion to ambienpres

35、sure when the nozzle is operated above the criticapressure ratio, and was identical with the velocity coefficien:below the critical pressure ratio. Above the critical pressureratio, the effective velocity coefficient (lecrea_ed from 0.94:to 0.934 at a pressure ratio of 2.8.7. The comparative perform

36、ances (thrust and air flow) o:nozzles selected for the same performance at a particulaidesign condition were proportional to the ratio of their flox_coefficients because the velocity coefficient is essentiallyindependent of nozzle design.LEWIS FLIGHT PROPULSION LABORATORY,NATIONAL ADVISORY COMMITTEE

37、 FOR ._kERONAUTICS,CLEVELAND, OHIO, September 7, 19._8.REFERENCEL Anon.: Flo_ Measurement 1940. A.S.M.E. Power Test Code(Instruments and Apparatus Sec.), pub. by Am. Soc. -Mech. Enu(New York), 1940.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-PERF

38、ORMANCE OF CONICAL JET NOZZLES IN TERMS OF FLOW AND VELOCITY COEFFICIENTS 9TABLE I-NOZZLE CONFIGURATIONS AND MEASUREMENTSCone half-angle a measured at 90“ intervals around periphery; outlet diameter D_ measured st 60* interval., around periphery; inlet diameter D, ofall nozzles, 5 in.Cone half-angle

39、 Outlet diam- Diameter ratioConfl_wation Measurement a, (deg) eter Dz, in.) D_/D_ArBtC/D, /| uE, .8F G. /t ,pH|IJJ/t wK ,nit _.MINfto1234AV1234Av1234.t.v1234AvI234AvI234AvI234AvI234AvI234Av1234Av1234Av1234Av1234Av134Av12:|4Xv5.84.05._4.5OVERNMEIIITf_RINtIN.OFFICIO:i|$oProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-. , /“ / )=“ . /- *r_- %_.4111_1Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-