REG NACA-TN-3860-1956 Method for calculating effects of dissociation on flow variables in the relaxation zone behind normal shock waves.pdf

1、1.,icdcomMETHODFOR AERONAUTICSTECHNICAL NOTE 3860CALCULATING EFFECTS OF DISSOCIATION ON FLOWRELAXATION ZONENORMAL SHOCK WAVESBy OhllS. EvansLare y Aeronautical LaboratoryLangley Field, Va.WashingtonDecember 1956.Provided by IHSNot for ResaleNo reproduction or networking permitted without license fro

2、m IHS-,-,-TECHLIBRARY-, NMNATIONAL ADVISORY COMMITTEEIUUHNICJUNOTE3860METHOD FOR CALCULATING EFFECTS OF DISSOCIATION ON FLOWVARIABLES IN THE RELAXATION ZONE P3HINDNORMAL SHOCK WAVESBy John S. EvansSLMMARYGeneralized expressionsand charts which depend on the shock Machnumber, the initial state of the

3、 gas, and an enthalpy parameter (theenthalpy divided by the ratio of the pressure to the density) are presentedfor the temperature, pressure, density, and flow velocity behind a shockwave. The charts an enthalpy plot for dissociated air have been usedto find the relation in graphical form between th

4、e degree of dissociationin air and the enthalpypsrameter. Plots are presented of the resultingdependence of the flow variables on the degree of dissociation.ABecause the chemical reaction rates needed to predict the dependence+ of degree of dissociation on distance behind the shock are not known,ord

5、er-of-magnitudeestimates oftheir values have been used in a numericalexample, the purpose of which is to illustrate the use of reaction-rateequations to predict relaxation time and distance behind the shock front.One of the problemsthe determination of theproduced by strong shockINTRODUCTIONassociat

6、ed with flight at hypersonic speeds iseffects on the air of the high temperatureswaves. Among these effects, dissociation ofthe diatomic molecules 02 snd N2 is of considerable concern becausethe large amount of ener required for dissociation constitutes a heatsink which reduces the air temperature,

7、sometimes by thousands of degrees,from its undissociatedvalue. On the other hsnd, the tendency of atomsto recombine on a surface and yield the heat of dissociation may consti-tute an additional heat-transfermechanism which could cause an increaseh aerodynamic heating.Because dissociation behind a sh

8、ock wave proceeds at a finite rate,-a transition zone exists in which the gas properties gradually approachtheir equilibrium values at some distance behind the shock front. Similar*Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-2 NACA TN 3860relaxat

9、ion zones exist for other degrees of freedom (suchas vibration, delectronic excitation,and ionization)but thus, the calculationsdo not apply in the relaxationzone.The approach to equilibrium is discussed in reference 1 and approxi-mate expressionsvalid for small deviations from equilibriumare develo

10、ped.These expressions are exponential in character. The only treatment foundwhich was essentiallydifferent from that of reference 1 was that of refer-ence 4 where expressionsderived from kinetic-theoryrate equations wereintegratedto trace the course of the flow variables in the relaxationzone.This p

11、aper presents a method for calculatingthe variation in theproperties of a real gas in the relaxation zone behind a strong shockwave as a function of the degree of dissociation. When numerical resultsare desired, rate eqwtions can be introducedas a fbl step to ffnd the evariation of the properties wi

12、th distance behind the shock front. -SYMROLSalDspeed of sound in air at 300 K, 3.475 X 104 cm/secdissociation ener, 117,960 cal/mole for 02 and225,080 cal/mole for N2d distance behind shock, cmNoG = or 2.45 X 1019 m01ecsT1 cmatm-l for T1 = 300 K, .g mole fractionK equilibrimnconstantbased on partial

13、 pressures, atm(molecules)-1 -1 -% specific reaction rate for dissociation, 3 seccm PProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA TN 3860 3krENoPR- 8,0 K were cal-reference 6. Correction to latest value of dissociation ener usually, only the

14、translationalenertaken in account.386oavail-isThe values used in this report were obtained from equation (23)by,assuming that .g %.% i%? i?i% %:!? z: g;: %2 3% ;% kg 4W:LM 52L.6,2.0? M4 12J4 iwq 33.21 47.37 l.yl 84.32 11%.31 la.1.llx3.33lam !za.la 2%.k3 2*.29 334.77 377.83423.% *n.;$ .g.g :$: %$ g.

15、g:g g.w ._3 ;:$g .g :gg 2.3-26.mE.62=89 33.XH:% %: ZZ :%$?%:2 % E$ % %1 $ jjg g;2.126.0)12#59a.8733.2.U6.Q23.2,6$2a.9233.2648.4363,70 .61lc4,9H5.55.75.96.16-3.6.56.76.97.L7.37.37.T7.98.18.58.78.78.99.19.39.99.-I9.920.1* , .I1.Provided by IHSNot for ResaleNo reproduction or networking permitted witho

16、ut license from IHS-,-,-VgE E:% Z.63b34:924.e 42. 4J.809 %.934.7681.W 1.:X 2% ;:s z% k% W;.635 ,3s71.4 2.* 3.2C5 4.381 .m 7.376 9.lgl11.226u.b 15. %1 18. 21.493 .29$q.50 31.43535.UM 39.13243.309z.617 .SEg1, 9 2.1763.1.11h,2 .ti 7.139 0.* ljl.t3j6u.q6 u.h I$:g ;:%:% : ;.% :,% ;g ;g g;n .4v.% .m m. am

17、Gu26.397%:% :BJ ;.g :=.eg gg I.!; E :g ;R :;% ,.a ,.q% U, 13.6J ,. M.cq ,:% :$ :% ;:$ ?% ;:$ 2.1 . 9.452 U.l u.q54 lJ.o# lJ.a g. EM T1 = 300 K; p = 10-4 Jatmospheres J(a) 02 dissociationp, atm P/Pl iiT, OK d, cmB t, secaO.ocm x 10-6.026.oo.123.199,1409,0008,8008,6008,koo8,2008,0007,8007,6007,4007,20

18、07,0006,8006,5404.534.564.394.624.664.704.754.804.864.935.005.08;.;.0.0240.0241.0241.0241.0242.0242.0242.0243.0243.0244.0244. 024. 024.02460.0000.0016.0043.0075.0115.0166.0229.0310.04m.0574.0799a71 lu%.1820).0000a71 0120.0280.0450.0610.oa.0945.Ulo.1275.1440.1600.1750.1895.21037.90:%8.048.128.208.3o8

19、.408.528.658.798.959.109.341.7701.7651.7551.7401.725I.llo1.6881.665L6401.6181.5901.5621.5351.498.275.383(b) N2 dissociationt, sec0.00 x 10-3.08.27.681.442.996.3513.3428.69m31.4981.4701.4301.3931.3501.3031.2621.2211.1781.148P/PlT, % d, cmp, atma6,54o6,400:;0%5,8005,6005,4005,2005,4,8700.0246.0247.024

20、7.0248.0249.0250.0251.0251.0252.02530.2103.2155.2235.2320.2400.2485.2570.2650.2730.27925.285.375.525.665.826.006.186.376.586.739.349.529.8010.0810.3910.7511.1011.4711.8812.18:13.733.269.0139.1286.6583.11212Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-