NASA SP-3085

(NASA-SP-3085) TABLES AND CHARTS OF N74-34701 FQUILIBRIUM NORMAL SHOCK AND SHOCK-TUBE

SOLUTIONS FOR HELIUM-HYDROGEN MIXTURES

WITH VELOCITIZs T0 7C xm/seC (NASA) Unclas 812 p HC $17.50 CSCL 20D H1/12 5164)

_TABLES AND CHA SONVOF EQU LH it

= “ ett RR te Sm re eee

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SSS

“NORMAL sHock AND’ 3 FOCK- TUBE

SOLUTIONS -X0R HELIUM-HYDROGEN

‘ a ’ ma Mae) ees ’ SS SS AS | |

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_ MIXTURES OURO 70 km/sec

VMILLER and WILDER

NASA SP-3085

‘TABLES AND CHARTS OF EQUILIBRIUM

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NORMAL SHOCK AND SHOCK-TUBE

SOLUTIONS FOR HELIUM-HYDRODGEN-

“MIXTURES WITH VELOCITIES TO 70 km /sec

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By Charles G. Miller HI and Sue E. Wilder

NASA Langley Research Center

Prepared at Langley Research Center

Scientific and Technical Information O fice 1974 NATIONAL AERONAUTICS AND SPACE ADMINISTRATION Washington, D.C.

PREFACE

Equilibrium thermodynamic and flow properties are presented in tabulated and graphical form for moving, standing, and reflected normal shock waves into helium- hydrogen mixtures representative of proposed outer planet atmospheres. The volumetric compositions of these mixtures are 0.35He-0.65H9, 0.20He-0.80H9, and 0.05He-0.95Hp5. Properties include pressure, temperature, density, enthalpy, speed of sound, entropy, molecular-weight ratio, isentropic exponent, velocity, and species mole fractions. Inci- dent (moving) shock velocities are varied from 4 to 70 km/sec for a range of initial pres- sure of 5 N/m2 to 100 kN/m2, The present results are applicable to shock-tube flows and to free-flight conditions for a blunt body at high velocities. A working chart illus- trating idealized shock-tube performance with a 0.20He-0.80H9 test gas and heated helium driver gas is also presented.

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CONTENTS

Page

PRE PAC Bg teu Se SOS Rie Sheen’ caer dee an as wie ee me ee ee Os iii SUMMARY 6.0 0 a ES Sek es, Ss RA SEO ee US PS Sad ES 1 INTRODUCTIONS as ts, eee oh te eo tec we pee ae. cee te eae he Wee sc er ee Se te ee 1 SY MBO Sis. wie te Eee ee a we ee a SE i Siege ea a ce, SR ea BR ia a, erie 2 CONVERSION FACTORS AND CONSTANTS .......2. 008 se eevee eves 3 COMPUTATION PROCEDURE AND ANALYSIS ..........00-+08 +28 ee eae 3 Shock=Tilbe Flow Regions: <a oo aie ek Oa ee RS ES i ee mS 3 CONnSErVation RElANONS: 5. x.35 ese ale Wat a a ee es ates ae wt SS ee 4 ENEFMOGYNaMIC: PrOPeETUies © <5: $626) 4. oo GO oe. Wee He Se, Bee ES ea es Bea SS ) M6thOG OF SOLUMION: | <-c% <¢ inc 55, fm eine. oe ee ie SR: ER ed. ee: Bess 6 PCCULACY: 55: eli see hy ce ie es Poca we Sew ee a Ge Se Ee er Se ee 7 DISCUSSION OF TABLES AND CHARTS ........ ae ee ee Bs andes Risiele det 8: Ae te 8 MOOS 6, ars Besa eo Ge Wea eM een aaa het GR, a RO Rectal che Re Wee we, Be Ve 9 Char Sik os A Beslan dbeayeis Yar sbi aat seh wiee, oh ee Sg ere Rie es te “Se wtroteh: ees Bs ne Ae a Re tg: hin Jei- iss 13 THEORETICAL SHOCK-TUBE PERFORMANCE.......... lg: ION Je ee 13 CONCLUDING REMARKS «....8) 6 se48 2 ON HSS eS AR SR SASS ee er ee 14 REFERENCES 6.405064 4-6 Sebo wi Sn a8 ibe vig estar a GR ce Oe Wide eee ia te 15 TAGES shu os Snes Ge an A Meee ee ee ee wt ere Ge a ee a Ba 17 PIGURES: gaxceSex vote cy Ay Sy. Soe ev ee eae WR. Rte. awe Re apes See er aw wwe 8 . 691

SUMMARY

Equilibrium thermodynamic and flow properties are presented in tabulated and graphical form for moving, standing, and reflected normal shock waves into helium- hydrogen mixtures representative of proposed outer planet atmospheres, The volumetric compositions of these mixtures are 0.35He-0.65H9, 0.20He-0.80H9, and 0.05He-0.95Hpo. Properties include pressure, temperature, density, enthalpy, speed of sound, entropy, molecular-weight ratio, isentropic exponent, velocity, and species mole fractions. Inci- dent (moving) shock velocities are varied from 4 to 70 km/sec for a range of initial pres- sure of 5 N/m2 to 100 kN/m2. The present results are applicable to shock-tube flows and to free-flight conditions for a blunt body at high velocities. A working chart illus- trating idealized shock-tube performance with a 0.20He-0.80H» test gas and heated helium driver gas is also presented.

INTRODUCTION

Interest in entry probes to Jupiter, Saturn, Uranus, and Neptune ushered in a num- ber of proposed atmospheric models for these planets. These models consisted primarily of helium and hydrogen. (For example, see refs. 1 and 2.) Exploratory studies with helium-hydrogen mixtures have been undertaken in the arc-driven Langley 6-inch shock tube (ref. 3), where incident shock velocities from approximately 12 to 30 km/sec were generated in a 0.20He-6.80H» mixture. Such studies require a means for determining thermodynamic properties and flow velocity for incident, standing, and reflected shock waves in helium-hydrogen mixtures and a means for estimating shock-tube performance pricr to a test with these mixtures, The wide range of flow conditions and very short test times impose stringent requirements on shock-tube instrumentation. In order to prepare facility instrumentation properly for a test, the investigator must have reason- able estimates of the magnitude of flow quantities to be measured.

The purposes of this report are threefold: (1) to present charts and tables for use in the determination of thermodynamic properties, flow velocity, and species mole frac- tions for incident (moving), standing, and reflected normal shocks in helium-hydrogen mixtures; (2) to provide a convenient means of determining post-normal-shock flow con- ditions for a vehicle at high velocities in a helium-hydrogen mixture; and (3) to provide reasonable estimates of shock-tube performance in a 0.20He-0.80H» mixture for an arc- heated helium driver gas.

Three mixtures, representing the maximum, approximate mean, and minimum atmospheric models proposed for Jupiter (ref. 1) and Saturn (ref. 2), were used for the present calculations. The volumetric compositions for these mixtures were 0. 35He-0.65H9, 0.20He-0.80H9, and 0.05He-0.95H2. Normal-shock conservation rela- t.ons for an incident, standing, and reflected shock and the method of solution of these relations, as well as the procedure for determining shceck-tube performance, are dis- cussed briefly herein and in detail in reference 4.

sW,/R

U

Uy

7*

YE

SYMBOLS speed of sound, m/sec specific enthalpy, m@/sec2 (J/kg) pressure, N/m2 universal gas constant, 8.31434 kJ/kmol-K specific entropy, kJ/kg-K nondimensional specific entropy temperature, K velocity, m/sec velocity of reflected shock, m/sec velocity of incident shock, m/sec molecular weight, kg/kmol molecular weight of undissociated gas mixture, kg/kmol

number of kmoles of dissociated gas mixture per number of kmoles of undissociated gas mixture, W,/W

a log 4 es 5 sW,/R

isentropic exponent, (

density, kg/m3

Subscripts:

1 state of quiescent test gas ahead of incident normal shock

2 state of test gas behind incident normal shock (see fig. 1)

or state of test gas behind reflected normal shock into region @ (see fig. 1) 2s state of test gas behind standing normal shock in region @) (see fig. 1)

3 state of expanded driver gas (see fig. 1)

4 driver-gas conditions at time of diaphragm rupture

CONVERSION FACTORS AND CONSTANTS

Conversion factors between the International System of Units (SI) and U.S. Customary Units (ref. 5) for the quantities presented in tables I to III and figures 2 to 10 are

1 N/m? = 9.8692 x 1078 atm = 1.4504 x 1074 psi = 2.0885 x 10-2 Ibf /ft2 3_ -2 3. ~3 3

1 kg/m” = 6.2428 x 107° lbm/ft” = 1.9403 x 10° slug/ft

1 J/kg = 1 m2/sec2 = 10.764 ft2/sec? = 4.3021 x 1074 Btu/lbm

1 m/sec = 3.2808 ft/sec = 2.2369 mph

Physical constants appearing herein are W h a T Mixture Oo 1; 1 1,

0.35He-0.65H» 9.711 2.842 1,160 1.463 | 300 | 1.0 2.413 3.334 1.217 1,433 | 2.115 3.964 1.288 1.406

0.20He-0.80H5 COMPUTATION PROCEDURE AND ANALYSIS

0.05He-0.95H»

Shock-Tube Flow Regions

The regions of interest for a shock tube are illustrated in figure 1. The quiescent driver gas at the time of diaphragm rupture is designated as region @, and the quiescent

3

test gas is designated as region @ (fig. 1(a)). Upon rupture of the diaphragm, an incident shock wave propagates into region 1) with velocity Us. The flow conditions immediately behind this shock are denoted as region @) (fig. 1(b)). An expansion wave propagates into

the driver gas; the region between the contact surface and the expansicn wave is desig- nated as region @). For a blunt model positioned in the driven section of the shock tube, a standing shock wave is formed at the model, provided the flow in region @ is super- sonic (fig. 1(c)). The flow conditions immediately behind this standing shcck are desig- nated as region Qs ‘

When the incident shock wave reaches the end wall of the shock tube, it is reflected back into region @ (fig. 1(d)). The gas behind the reflected shock wave is brought to rest, relative to the shock tube. Flow conditions behind this reflected shock wave, which is propagating upstream with a velocity U,, are designated as region Qr

, ®

Conservation Relations

For an incident normal shock wave moving through region 1), in a laboratory -fixed coordinate system, the conservation relations for mass, momentum, and energy are

p1Us = p(Us : Up) (1a) Pp, + p Us. = Po + Po(Us - Up) (1b) h, +4 UE: Shine 4(Us - Up) (1¢)

The conservation relations for a standing normal shock wave, where the conditions down- stream of the incident shock wave (region ®D) are the upstream conditions for this stand- ing shock wave, are

Pao = PogUog (2a)

p + p,U,” =p +p5_U : (2b) 7 ae a 2s ‘2s 2s 2. 2

hig + 4 Uo = ho, + 4 Uo, (2c)

The conservation relations fcr a reflected normal shock wave, where the conditions in region @) are che upstream cenditions for this reflected shock wave, are

Po(Up + U,) = P9,U, (3a)

2 2 Bg + Po(Up + UL)” = Poy + P2,U, (3b)

hg + dive + Ag = ho, +4 u. (3c)

Thermodynamic Properties

The equation of state (that is, source of thermodynamic properties for real-gas mixtures) takes the form of the thermochemical equilibrium procedure of references 6 and 7. (The equation of state cannot be expressed in closed analytical form when chemical processes occur.) This procedure, which is based upon the Gibbs free-energy minimiza- tion method of reference 8, includes dissociation and first and second ionization. Basic assumptions are:

(1) The mixture is composed of ideal gases (intermolecular force effects are neglected).

(2) For diatomic species the rigid-rotor harmonic-oscillator model is used with vibrational-rotational corrections.

(3) Only electronic levels with principal quantum number less than or equal to five are included.

For a given pressure and temperature, the free energies for individual species are computed from partition functions of statistical mechanics. The equilibrium composition is then obtained by minimization of the free energy. In the present study, iterations on species concentration (number of kmoles of species i per mass of mixture) were con- tinued until the absolute value of each concentration changed by less than 10-8 between successive iterations. This iterative criterion is referred to in reference 6 as the abso- lute criterion. A relative criterion was also employed to prevent termination of the iter- ations while a minor species was still changing by as much as 0.1 of its previous value. Once the equilibrium set of species concentrations are known, the mixture properties (p, h, s, a, Z*, and YE) can be calculated.

In order to examine what effect the absolute criterion might have on the present results, a number of sample cases were run in which the absolute criterion was relaxed to 1074. These cases were for a 0.20He-0,80H» mixture, with initial pressure Py of 10 N/m2 and 100 KN/m2 and an incident shock velocity Us ranging from 4 to 64 km ‘sec in increments of 1.2 km/sec. Comparison of these results with those obtained with an absolute criterion of 10-8 showed that the largest variations occurred in the second-order properties (a and YR): In no instance did these variations exceed 0.07 percent. The

maximum variation in mole fractions was 0.4 percent. Fence, tie absolute criterion of 1078 employed in the present computations provides a high level of precision,

In reference 7, it is shown that calculations of thermodynamic properties of air, as obtained with the program of references 6 and 7, generally agreed with the more rigorous imperfect air results of references 9 and 10. For the temperature range 1500 K to 15 000 K and pressure range 0.7 N/m2 to 0.7 MN/m42, first-order properties (p, h, 5, and Z*) agreed to within 1 percent and second-order properties agreed to within 5 per- cent (ref. 7). Since the same sort of difference between computational schemes could be expected for other atmospheres, the method of references 6 and 7 should give, for the present study, first-order properties to within 1 percent and second-order properties to within 5 percent over the range in which results were extensively checked (T = 15 000 K, 0.7 N/m2 Sp 20.7 MN/m2)}, Thermodynamic properties are expected, in general, to be in better agreement than species concentrations (mole fractions).

Required inputs to the procedure of references 6 and 7 and an iterative-interpolation scheme enabling determination of thermodynamic properties from combination of h, p, SWo /R, and p are discussed in reference 4. The species used in the present calcula- tions for helium-hydrogen mixtures are

e- d He H* Het Ho He*t

Thermodynamic data for the helium-hydrogen species were obtained from reference 11, and a listing of the thermodynamic data is presented in reference 4.

Method of Soluticna

As mentioned previously, the upstream conditions for the standing and reflected shock waves are conditions in region 2. Fence, it is necessary to solve first for condi- tions behind the incident shock wave. The thermodynamic properties and gas composition (mole fractions) in region D are assumed to be known, as is the incident shock veloc- ity U,s. Hence, quantities aprearing on the left-hand side of the conservation relations for an incident normal shock (eqs. (Ja) to (1c)) are known. The method of successive approximations ‘iteration on po, ref. 4) is used to solve equations (1a) to (1c) for Pos Po, ho, and Us, in conjunction with the equation of state Po = Po(Poshy | ( Thermody- namic properties corresponding to Po and ho are obtained from the equation of state. With the conditions determined in region 2), the corresponding conditions in regions and ar are obtained in a similar manner, that is, by an iterative procedure on density Pos and Por respectively.

In predicting shock-tube performance, the helium driver-gas pressure P4 and temperature T, are assumed to be known, in conjunction with p, and T,. Thermo- dynamic properties in region 4) are determined from imperfect-gas relations based on the virial form of the equation of state (ref. 4). The unsteady expansion, which occurs upon rupture of the diaphragm, is assumed to be isentropic. An array of thermodynamic properties, including Py, is generated in the expansion ‘region 3) andts ~ . >sponding velocity Ug is obtained numerically from the differential equation for .cne-di. sional unsteady expansion. By varying U, over a range, an array of Ug and po is «'s0 generated. The solution is found by requiring that Pg equal po and U, equal Uo; that is, the solution is the intersection of the Uo,P9 rand Us,pg curves (ref. 4),

Accuracy

The iterative procedure for solving the conservation relations (eqs. (1)) was con- tinued until successive values of density (Po Pag and Por! were within 0.5 percent. To examine the effect of this iterative tolerance, the tolerance on density was decreased to 0.25, 0.1, and 0.05 percent and increased to 1 percent. This variation was perrormed for a 0.20He-0.80H2 mixture at two values of p, (10 N/m2 and 100 kN/m2) and Ug, fron 4 to 64 km/sec. Increasing the tolerance from 0.5 percent to 1 percent had essentially no effect (less than 0.07 percent) on thermodynamic conditions in region 2) and resulted in a variation of less than 0.6 percent for thermodynamic conditions and less than 0.9 per- cent for velocity in regions and @r . Variations in thermodynamic conditions and velocities in regions @), @s) , and Qn) , resulting from a decrease in iterative tolerance from 0.5 to 0.05 percent, were less than 0.4 percent. This relatively small increase in accuracy with decrease in tolerance from 0.5 percent was not warranted, in view of the corresponding large increase in computer time required fo. the smaller tolerance.

Comparison of results from the present computational -rocedure and those of sim- ilar studies was performed. Since results for helium-hydrogen mixtures for the present range of conditions were not found in the open literature, the program (ref. 4) used to generate the results herein was also exercised with a 16-species CO model (e-, O, OF, O*+, O-, Oo, O9*, O29, C, Ct, C*t, C~, Cg, CO, CO*, and COp). Incident, standing, and reflected shock solutions were compared to the graphical results of reference 12 (which are based on a 10-species COg model including second ionization) for an incident shock velocity range of 1 to 16 km/sec and initial pressure of 100 N/m2. With the exception of a few points (3 out of 105), the thermodynamic properties of reference 12 for regions %, Qs), and @r) (as read from charts) were within 2 percent of the results obtained with the program of reference 4. in no case did disagreement exceed 4 percent. For this range in Ug, the maximum values of Tg and Tg, were approximately 17 OCU K and 25 000 K, respectively.

A similar comparison was performed by exercising the program of reference 4 with a 26-species air model and comparing these data with the tabulated results of ref- erence 13. The volumetric composition of air was the same for both studies (0.7808 No, 0.2095 Og. a'd 0.0097 Ar), as was the initial pressure (6.67 N/m2), The incident shock velocity was varied from 17.1 to 34 km/sec. This range of Us corresponds to a range in Tg of 15 000 K to 42 000 K (ref. 13). Agreement between the studies, for quantities Po. To, Pg, hy, and Uo, was within 1 percent for Ug, to 30 km/sec, corresponding toa Ty of 34000 K. Above this Us, the agreement in these quantities diminishes rapidly, being within 5 percent ata Us of 32 km/sec and within 20 percent ata WU, of 34 km/sec ‘maximum Us examined’. This rapid diminishing of agreement is attr:buted to the fact that first and second ionization were included in th: present air calculations, whereas third ionization was included in the more rigorous calculations of reference 13.

The present computational procedure yields thermodynamic properties and veloc- ities, for COpg and air, within 2 percent of results of similar studies (refs. 12 and 13) for temperatures less than 25 000 K to 30 000 K. For the more simple helium-hydrogen mixture model, the uncertainty in thermodynamic properties and velocities is not expected to exceed that observed for the CO» and air comparisons, As stated previously, the ther- modynamic properties are more accurate than the mole fractions. For example, the comparison of CO9 results stowed that thermodynamic properties agreed to within 2 per- cent, whereas the agreement for individual species mole fractions was within 10 to 12 per- cent inthe U, range (Ty. range] where the mole fraction was near its maximum value. The accuracy in mole fractions is expected to be at least within the limits of : ‘ference 13, these being less than 1, 5, and 20 percent at temperatures less than 10 0° 9 000 K, and 25 000 K, respectivel ;.

DISCUSSION OF TABLES AND CHARTS

Before discussing the present tables and charts, it should be noted that flow prop- erties behind the normal portion of the bow shock wave of a hypervelocity entry body are equivalent to the properties behind a moving shock in a shock tube. In free-flight, the free-stream conditions and flight velocity correspond to the initial conditions in region and the shock-wave velocity, respectively, whereas the condition. behind the bow shock correspond to conditions in region @). In the present study, an initial temperature T, of 300 K was used for all calculations. A method permitting use of a range of ambient temperatures is discussed in reference 12, and should prove useful in determining free- flight conditions using the present tables and charts for an incident normal shock wave.

Tables

The solutions for incident (moving), standing, and reflected normal shocks are pre- sented in tables Ito II. The volumetric composition (mole fraction) of the helium- hydrogen mixture is 35 percent helium and 65 percent hydrogen (0.35He-0.65Ho) in table i, 20 percent helium and 80 percent hydrogen (0.20He-~0.80Hg) in table II, and 5 percent helium and 95 percent hydrogen (9,05He -0.95H9) in table III, ‘hese tabulated computer results are arranged in groups of constant pressure in region @) (P1) and the incident shock velocity (US1) is varied within the group. In tables J to II, Py is varied from 5 N/m2 to 100 kN/m2 and U, is varied from 4 to 30 km/sec in increments of 1 km/sec and from 30 to 70 km/sec in increments of 2 km/sec.

For each Py, a comtlete list ot calculated thermodynamic properties (p, T, ?, h, a, sWo/ R, Z*, aud Ye) flow velocity (U), and species volumetric composition is given for the three shock-tube regions under consideration. The rows in the upper por- tion of each tabulation, for a given Py and Ug, are identified by letters (FORTRAN symbols), the designations of which, in terms of the symbols de.ined, are given in the following table:

Pane | Po/Py Pas/Py Pop! Py

H ho/hy | heg!hy hor! hy

A ag/ay 498 /4i agr/ ay

5 | $95/51 Sor/ $1

z 1 295/21 Zoy/ 2]

GAME YE 28/7E,1 YE, 2r/ YE, 1

Uas/ay

The lower portion of each tabulation illustrates the species composition for moving, Standing, and reflected shock regions. Rows are identified by the species symbol.

The conditions in region T) are used to nondimensionalize calculate: pronerties in regions @), Qs), and @r) . The temperature in region @ T, is 300 K for all cases in tables Ito I. Corresponding thermodynamic properties for the three helium-hydrogen mixtures in region (D, in SI Units (see section on Symbols), are given in the following tables.

~~

eee

INITIAL CONDITIONS AHEAD OF INCIDENT SHOCK IN 0.35He-0.65Hy

T, = 300K

hy = 2.642 x 108 J/kg

a, = 1.160 x 10° m/sec

hein ner ee ST a i rr

Z; = 1.0

Vp 1 = 1.463 | 5 5.435 x 1076 26.09 | 10 1,087 x 1075 25.40 20 2.174 x 107° 24.71 50 5.435 x 107-9 23.79 100 1.087 x 1074 23.10 200 2.174 x 1074 22.40 500 5.435 x 1074 21.49 1 000 1,087 x 1073 20.79 2 000 2.174 x 1073 20.10 5 000 5.435 x 1073 19,18 10 000 1,087 x 1072 18.49 20 000 2.174 x 1072 17.80 50 000 5.435 x 1072 16.88

100 000

10

1.087 x 1972

INITIAL CONDITIONS AHEAD OF INCIDENT SHOCK IN 0.20He-0.80H»5

=)

10

20

00

100 200 900

1 000 2 000 > 000 10 000 20 000 90 000 100 000

YR, 1

T, = 30U K hy = 3.334 x 108 J/g

a, = 1.217 x 10° m/sec

“ee Z*= 1.0 = 1.433

py, kg/m?

4.834 x 1078 9.675 x 1076 1.935 x 1079 4.838 x 1079 9.675 x 1079 1.935 x 1074 4.838 x 1074 9.675 x 1074 1.935 x 1073 4.838 x 10-3 9.675 x 1073 1.935 x 1072 4.838 x 1072 9.675 x 1072

S,W

26.03 29.34 24.64 23.73 23.03 22.34 21,42 20.73 20.04 19.12 18,43 17,73 16,82 16.13

11

INITIAL CONDITIONS AHEAD OF INCIDENT SHOCK IN 0.05He-0.95H»

: T, = 300K

hy = 3.964 x 108 J/kg

4,240 x 10-6

8.480 x 1076

1,696 x 10-9

4,240 x 10-9

100 8.480 x 1079 200 1.696 x 1074 500 4,240 x 1074

1 000 8,480 x 1074 2 000 1.696 x 1073 5 000 4,240 x 1073 10 000 8.480 x 1073 20 000 1.696 x 1072 50 000 4.240 x 10-2 100 000 8.480 x 1072

12

It is recommended in reference 7 that pressures should be restricted to less than 10 MN/m2 and temperatures restricted to less than 15 000 K in order to insure accurate calculations of equilibrium compositions. This recommended upper limit on pressure is to minimize imperfect-gas (intermolecular force) effects. Temperatures considered must be such that only negligible contributions are realized from coulomb interactions and from electronic energy levels past the fifth electron shell. These considerations are not accounted for in the equilibrium program of references 6 and 7. For temperatures below 15 000 K or so, the latter consideration should be negligible. Comparisons made in a previous section entitled "Accuracy" showed that equilibrium COs and air thermody - namic properties, as generated by using the method of references 6 and 7, are in good agreement (within 2 percent) with COs and air calculations (refs. 12 and 13) for tempera- tures to 25 000 K. Now, in the present results of tables I to I, no upper limitations on pressure and temperature are imposed; hence, values of pressure exceeding 10 MN/m2 and of temperature exceeding 25 000 K are presented for the three shock-tube regions of interest. The user of these tables is cautioned to exercise discretion in employing the present results at pressures exceeding 10 MN /m2 and temperatures exceeding 25 000 K,

Charts

Working charts for the helium-hydrogen mixtures (corresponding to the results of tables I to I) are shown in figures 2 to 10. In these figures, the nondimeusionalized thermodynamic properties and flow velocity for regions @), Qs), and Qr) are plotted as a function of incident shock velocity U, for various quiescent test gas pressures. For each property in each region, the incident-shock-velocity scale is 0 to 32 km/sec and 30 to 62 km/sec, and is 0 to 40 km/sec for the standing (except in fig. 9) and reflected shocks. This division of the Us scale is to enhance the readability of these charts. The figures were generated by machine and linear line segments were used to connect adjacent data points.

Unlike tables I to IJ, maximum pressure and temperature limitations were imposed on the results of figures 2 to 10, these being p10 MN/m2 and T § 25 000 K; calculated quantities above these limitations are not plotted. Again, the properties in region @ pre- sented previously must be used to obtain the desired value of the thermodynamic property or flow velocity from the ratio presented.

THEORETICAL SHOCK-TUBE PERFORMANCE

Before a study is performed in a shock tube, it is essential that the theoretical per- formance be ascertained for the gas being tested. The wide range of flow conditions and very short test times (generally, a few microseconds to several milliseconds) impose stringent requirements on shock-tube instrumentation. ‘hus, in preparing shock-tube

13

instrumentation for a test, it is necessary that the physical quantities to be measured be known to within reasonable limits.

Results from the procedure for determining shock-tube performance for a 0,.20He-0.80Hg mixture test gas are shown in figure 11 for heated helium driver gas. In figure 11, the ratio of driver pressure in region @ to quiescent test-gas pressure in region @ is shown as a function of incident shock velocity for various driver-gas tem- peratures Tg. With p,, Tg, and p, known, a theoretical value of Ug may be obtained from figure 11. (Some discrepancy between real physical conditions and condi- tions calculated by using a simple shock-tube theory is expected, with this discrepancy increasing with decreasing Pp, due principally to the "leaky-piston" effect (ref. 14).) Corresponding thermodynamic properties and flow velocity in regions @, @s , and éx may be obtained from figures 5 to 7, or from table Il. Variation in Py / Py is obtained by varying P)- The range of T4 is 4000 K to 16 000 K and Py is equal to 68.95 MN/m2, At the maximum Ty, of 16 000 K and P4 of 68.95 MN /m2, ionization of the helium driver gas is essentially negligible (ref. 15), and the results of reference 4 are applicable.

CONCLUDING REMARKS

Equilibrium thermodynamic and flow properties are presented in tabulated and graphical form for moving, standing, and reflected normal shock waves into heliu:n- hydrogen mixtures representative of proposed outer planet atmospheres. The vclumetric compositions of these mixtures are 0.35He-0.65H», 0.20He-0.80H9, and 0.05He-0.95H». Properties include pressure, temperature, density, enthalpy, speed of sound, entropy, molecular-weight ratio, isentropic exponent, velocity, and species mole fractions. Inci- dent (moving) shock velocities are varied from 4 to 70 km/sec for a range of initial pres- sure of 5 N/m2 to 100 KN/m2, The present results are applicable to shock-tube flows and to free-flight conditions for a blunt body at high velocities. A working chart illus- trating idealized shock-tube performance with a 0.20He-0.80H» test gas and heated helium driver gas is also presented.

14

1. 2. 3.

4.

10.

11,

12.

13.

14.

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Anon.: The Planet Jupiter (1970), NASA SP-8069, 1971. Anon,: The Planet Saturn (1970). NASA SP-8091, 1972.

Nealy, Jolin E.: Performance and Operating Characteristics of Arc-Driven Langley 6-Inch Shock Tube. NASA TN D-6922, 1972,

Miller, Charles G., II: A Program for Calculating Expansion-Tube Flow Quantities for Real-Gas Mixtures and Comparison With Experimental Results. NASA TN D-6830, 1972.

. Mechtly, E. A.: The International System of Units — Physical Constants and Conver-

sion Factors (Second Revision). NASA SP-7012, 1973.

. Allison, Dennis O.: Calculation of Thermodynamic Properties of Arbitrary Gas Mix-

tures With Modified Vibrational-Rotational Corrections. NASA TN D-3538, 1966.

.» Newman, Perry A.; and Allison, Dennis O.: Direct Calculation of Specific Heats and

Related Thermodynamic Properties of Arbitrary Gas Mixtures With Tabulated Results. NASA TN D-3540, 1966.

. White, W. B.; Johnson, S. M.; and Dantzig, G. B.: Chemical Equilibrium in Complex

Mixtures. J. Chem. Phys., vol. 28, no. 5, May 1958, pp. 751-755.

. Hilsenrath, Joseph; and Klein, Max: Tables of Thermodynamic Properties of Air

in Chemical Equilibrium Including Second Virial Corrections From 1500° K to 15,000° K. AEDC-TDR-63-161, U.S. Air Force, Aug. 1963.

Hilsenrath, Joseph; and Klein, Max: Tables of Thermodynamic Properties of Air in Chemical Equilibrium Including Second Virial Corrections From 1500° K to 15,000° K, AEDC-TR-65-58, U.S. Air Force, Mar. 1965.

Moore, Charlotte E.; Atomic Energy Levels. Vol. I. 1y.23y, NBS Circ. 467, U.S. Dep. Com., June 15, 1949.

Simcox, Craig D.; and Peterson, Victor L.: Charts for Equilibrium and Frozen Flows Across Plane Shock Waves in Carbon Dioxide. NASA SP-3018, 1965.

Menard, W. A.; and Horton, T. E.: Shock-Tube Thermochemistry Tables for High- Temperature Gases. Vol. I — Air. Tech. Rep. 32-1408 (Contract NAS 7-100), Jet Propulsion Lab., California Inst. Technol., Nov. 1, 1969.

Mirels, Harold: Test Time in Low-Pressure Shock Tubes. Phys. Fluids, vol. 6, no. 9, Sept. 1963, pp. 1201-1214.

15

15. Olstad, Walter B.; Kemper, Jane T.; and Bengtson, Roger D.: Equilibrium Normal- Shock and Stagnation-Point Properties of Helium for Incident-Shock Mach Numbers From 1 to 30. NASA TN D-4754, 1968.

16

The user is cautioned about using these tables at pressures exceeding 10 MN /m2 and temperatures exceeding 25 000 K.

Table I.- Nondimensional Thermodynamic Properties and Flow Velocity for Incident (moving), Standing, and Reflected Normal Shocks in a 0.35He-0.65H»y Mixture ......... ee ee ee ee -. 18

Table 0.- Nondimensional Thermodynamic Properties and Flow Velocity for Incident (moving), Standing, and Reflected Norm:zl Shocks in a 0.20He-0.80H» Mixture ........ ae se ibe Be eB itt erate, eee

Table II.- Nondimensional Thermodynamic Properties and Flow Velocity for Incident (moving), Standing, and Reflected Normal Shocks in a 0.05He-0.95H» Mixture ......... Si ceases Ue ney acti ved. uaandes ah ers . 466

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