n66 36859 - nasa o nasa contractor report no. 66109 gasl technical report no. 605 numerical flow...

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NASA Contractor Report No. 66109

GASL Technical Report No. 605

NUMERICAL FLOW FIELD PREDICTION

FOR PROJECT RAM-C "

By G. Widhopf, B. Kaplan and J. Jannone

Prepared for

National Aeronautics and Space Administration

Langley Research Center

Hampton, Virginia

NASI-5519

Prepared by

General Applied Science Laboratories,

Merrick and Stewart Avenues

Westbury, L. I., New York

Inc. I

June 30, 1966

N66 36859!

(ACCESSION ]NU ER)

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Ik _A GR ORrTMX OR AD NUMBER)

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|CATEGORY)

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GASL TR- 605

Total No. of Pages - xii & 145

NASA CONTRACTOR REPORT NO. 66109

copy (81) of Ii0

By


FOR PROJECT RAM-C

G. Widhopf, B. Kaplan and J. Jannone

Distribution of this report is provided

in the interest of information exchange.

Responsibility for the contents resides

in the author or organization that pre-

pared it.

Prepared for

National Aeronautics and Space Administration

Langley Research Center

Hampton, Virginia

NASI-5519

Prepared by

General Applied Science Laboratories, Inc.

Merrick and Stewart Avenues

Westbury, L oI., New York

June 30, 1966 Approved by:

Anto_q FerriPresident

TABLE OF CONTENTS

TITLE

SUMMARY

INTRODUCTION

LIST OF SYMBOLS

ANALYSIS

Inviscid Field

One-Dimensional Inviscid Flow

Boundary Layer

METHOD OF CALCULATION

RESULTS

APPENDIX - Summary of Chemical Reactions

and Their Rate Constants

REFERENCES

TABLE I - RAM-C Flight Conditions

FIGURES

PAGE

1

2

4

7

8

9

l0

16

17

20

28

30

",31

ii

LIST OF TABLES

SUMMARY OF CHEMICAL REACTIONS AND RATE CONSTANTS

TABLE I - RAM-C FLIGHT CONDITIONS

21-27

30

iii

F IGURE

1

2

4-8

(4)

(5)

(6)

(7)

(S)

9-13

(9)

(i0)

(ii)

(12)

(13)

LIST OF FIGURES

RAM-C Vehicle Geometry

Schematic of Subsonic and Supersonic Flow

Field Regions

FlowField Schematic

NOMENCLATURE - Altitude = 36,800 Meters

Velocity Profiles at Surface Coordinate

Locations:

X=.09137, X=.I048, X=.1225 Meters

X=.1457, X=.1723, X=.1979 Meters

X=.3174, X=.4144, Meters

X=.6060, X=.8361, Meters

X=i.036, X=I.143, X=1.309 Meters

Temperature Profiles at Surface Coordinate

Locations:

X=.09137, X=.I048, X=.1225 Meters

X=.1457, X=.1723, X=.1979 Meters

X=.3174, X=.4144, X=.6060 Meters

X=.8361, X=I.036 Meters

X=I.143, X=Io309 Meters

PAGE

31

32

33

34

35

36

37

38

39

40

41

42

43

44

FIGURE

14-17

(14)

(15)

(16)

(17)

18-21

(18)

(19)

(20)

(21)

22-26

(22)

(23)

(24)

(25)

(26)

27-31

(27)

(28)

Electron Density Profiles at Surface Coordinate

Locations :

X=.09137, X=.I048, X=.1225 Meters

X=.1457, X=.1723, X=o1979 Meters

X=.3174, X=.4144, X=.6060, X=.8361 Meters

X=I.036, X=I.143, X=1.309 Meters

Specie Profiles (N) at Surface Coordinate

Locations:

X=.09137, X=.I048, X=.1225 Meters

X=.1457, X=.1723, X=.1979 Meters

X=.3174, X=.4144, X=.6060, X=.8361 Meters

X=I.036, X=I.143, X=1.309 Meters

Specie Profiles (0) at Surface Coordinate

Locations:

X=.09137, X=°I048, X=.1225 Meters

X=.1457, X=.1723, X=.1979 Meters

X=.3174, X_144, X=.6060 Meters

X=.8361, X=I.036 Meters

X=I.143, X=1.309 Meters


Locations:

X=.09137, X=.I048, X=.1225 Meters

X=.1457, X=.1723, X=.1979 Meters

PAGE

45

46

47

48

49

5O

51

52

53

54

55

56

57

58

59

v

F I GURE

(29)

(30)

(31)

32-35

(32)

(33)

(34)

(35)

36-39

(36)

(37)

(38)

(39)

40-43

(40)

(41)

(42)

(43)

X=.3174, X=.4144 Meters

X=.6060, X=.8361 Meters

X=I.036, X=I.143, X=1.309 Meters


Locations:

X=.09137, X=.I048, X=.1225 Meters

X=.1457, X=.1723, X=.1979 Meters

X=.3174, X=.4144, X=.6060, X=.8361 Meters

X=I.036, X=I.143, X=1.309 Meters

Specie Profiles (NO) at Surface Coordinate

Locations:

X=.09137, X=.I048, X=.1225 Meters

X=.1457, X=.1723, X=.1979 Meters

X=.3174, X=.4144, X=.6060, X=.8361 Meters

X=I.036, X=I.143, X=1.309 Meters

Specie Profiles (NO + ) and (e-) at Surface

Coordinate Locations:

X=.09137, X=.I048, X=.1225 Meters

X=.1457, X=.1723, X=.1979 Meters

X=.3174, X=.4144, X=.6060 Meters

X=.8361, X=I.036, X=I.143, X=1.309 Meters

PAGE

60

61

62

63

64

65

66

67

68

69

70

71

72

73

74

4

vi

FIGURE

44-46

(44)

(45)

(46)

47-48

(47)

(48)

49-52

(49)

(50)

(51)

(52)

53-55

(53)

(54)

Contour Maps - Altitude = 36,800 Meters

Pressure

Temperature

Electron Density

Pressure Profiles at Surface Coordinate

Locations:

X=.09137, X=.I048, X=.1225, X=.1457, X=.1723,

X=.1979 Meters

X=.3174, X=.4144, X=.6060, X=.8361, X=I.036,

X=I.143, X=1.309 Meters



Locations:

X=.01623, X=.03677 Meters

X=.I099 Meters

X=.1725, X=.2817, X=.4799 Meters

X=.6564, X=.8807, X=1.309 Meters


Locations:

X=.01623, X=.03677, X=.I099 Meters

X=.1725, X=.2817, X=.4799 Meters

PAGE

75

76

77

78

79

8O

81

82

83

84

85

86

vii

F IGURE

(55)

56-58

(56)

(57)

(58)

59-61

(59)

(60)

(61)

62-64

(62)

(63)

(64)

65-67

(65)

(66)

(67)

X=.6564, X=.8807, X=1.309 Meters


Locations:

X=.01623, X=.03677, X=.I099 Meters

X=.1725, X=.2817, X=.4799 Meters

X=.6564, X=.8807, X=1.309 Meters

Specie Profiles (Ns) at Surface Coordinate

Locations:

X=.01623, X=.03677, X=.I099 Meters

X=.1725, X=.2817, X=.4799 Meters

X=.6564, X=.8807, X=1.309 Meters

Specie Profiles (0s) at Surface Coordinate

Locations:

X=.01623, X=.03677, X=.I099 Meters

X=.1725, X=.2817, X=.4799, X=.6564 Meters

X=.8807, X=1.309 Meters


Locations:

X=.01623, X=.03677, X=.I099 Meters

X=.1725, X=.2817, X=.4799 Meters

X=.6564, X=.8807, X=1.309 Meters

PAGE

87

88

89

90

91

92

93

94

95

96

97

98

99

viii

FIGURE

68-70

(68)

(69)

(7o)

71-73

(71)

(72)

(73)

74-76

(74)

(75)

(76)

77-79

(77)

(78)

(79)

80-81

(8O)


Locations:

X=.01623, X=.03677, X=.I099 Meters

X=.1725, X=.2817, X=.4799 Meters

X =.6564, X=.8807, X=1.309 Meters


Locations:

X=.01623, X=.03677, X=.I099 Meters

X=.1725, X=.2817, X=.4799 Meters

X=.6564, X=.8807, X=1.309 Meters



X=.01623, X=.03677, X=.I099 Meters

X=.1725, X=.2817, X=.4799 Meters

X=.6564, X=.8807, X=1.309

Contour Maps - Altitude = 53,500 Meters

Pressure

Temperature

Electron Density


Locations:

X=.01623, X=.03677, X=.1099 Meters

PAGE

i00

i01

102

103

104

105

106

107

108

109

ii0

iii

112

ix

F I GURE

(81)

82 -84

(82)

(83)

(84)

85 -87

(85)

(86)

(87)

88-90

(88)

(89)

(90)

91-93

(91)

(92)

(93)

x

X=.1725, X=.2817, X=.4799, X=.6564, X=.8807,

X=1.309 Meters



Locations:

X=.01623, X=.06126 Meters

X=.I1338, X=.1621 Meters

X=.5119, X=I.0077, X=1.309 Meters


Locations:

X=.01683, X=.06126 Meters

X=.I1338, X=.1621 Meters

X=.5119, X=I.0077, X=1.309 Meters


Locations:

X=.01683, X=.06126 Meters

X=.I1338, X=.1621 Meters

X=.5119, X=I.0077, X=Io309 Meters

Specie Profiles (Ns) at Surface Coordinate

Locations:

X=.01683, X=.06126 Meters

X=.I1338, X=.1621 Meters

X=.5119, X=I.0077, X=1.309 Meters

PAG____EE

113

114

115

116

117

118

119

120

121

122

123

124

125

126

FIGURE

94-96

(94)

(95)

(96)

Specie Profiles (Os) at Surface Coordinate

Locations:

X=.01683, X=.06126 Meters

X=.I1338, X=.1621 Meters

X=.5119, X=I.0077, X=1.309 Meters

PAGE

127

128

129

97-99

(97)

(98)

(99)


Locations:

X=.01683, X=.06126 Meters

X=.I1338, X=.1621 Meters

X=.5119, X=I.0077, X=1.309 Meters

130

131

132

100-102

(!00)

(101)

(102)


Locations:

_= n1_ X= 06126 Meters

X=.I1338, X=.1621 Meters

X=.5119, X=I.0077, X=1.309 Meters

133

134

135

103-105

(103)

(104)

(105)


Locations:

X=.01683, X=.06126, X=.I1338 Meters

X=.1621, X=.5119 Meters

X=I.0077, X=1.309 Meters

136

137

138

xi

F IGURE

106-108

(106)

(107)

(10S)



X=.01683, X=.06126 Meters

X=.I1338, X=.1621 Meters

X=.5119, X=I.0077, X=1.309 Meters

PAGE

139

140

141

109-iii

(109)

(11o)

(IIi)

Contour Maps- Altitude = 71,000 Meters

Pressure

Temperature

Electron Density

142

143

144

(112)


Locations:

X=.01683, X=.06126, X=.11338, X=.1621, X=.5119,

X=I.0077, X=1.309 Meters 145

xii


FOR PROJECT RAM-C

By G. Widhopf, B. Kaplan, and J. Jannone

General Applied Science Laboratories, Inc.

SUMMARY

Detailed flow field calculations have been performed in

order to investigate the state of the gas in the shock layer

surrounding the RAM-C vehicle. Calculations were performed at

altitudes of 36.8, 53.5, and 71 km. For numerical purposes the

shock layer flow field was separated into an inviscid and

viscous layer wherein the viscous-inviscid interaction was

taken into account by a displacement thickness iteration pro-

cedure. A nonsimilar boundary layer approach was assumed to

be applicable in the viscous region where edge conditions were

computed by tracing non-equilibrium inviscid streamlines as

they were entrained by the boundary layer. Finite rate chem-

istry was computed throughout the entire shock layer. Detailed

plots of profiles of velocity, temperature, electron density,

pressure, and species mole fractions are presented at various

surface locations. The results indicate that this type of

computational procedure is not valid for this configuration

at the two higher altitudes.

INTRODUCTION

A series of flight experiments has been designed by theLangley Research Center in order to investigate the interfer-ence of the ionized flow field immediately surrounding areentry vehicle with radio transmission, communications andtracking. The official designation of these flight experimentsis Project Ram (Radio Attenuation Measurements). Utilizingthese experiments, coupled with detailed computations, methodswill be sought to eliminate the "blackout" phenomena. Also,assessments of theoretical analyses used in the prediction offlow field ionization and the associated RF signal loss will bepossible, since in-flight experiments have been included tomeasure specific reentry observables.

Project RAMhas been divided into specific flight experi-ments (RAM-A,B,C) where a spectrum of reentry flight conditionshas been investigated. RAM-A,B have been concerned with avelocity regime of 18,000 ft/sec and below, where various meas-urements and experiments have been made.

The RAM-C series consists of flight experiments at ahigher velocity regime (_ 25 kfps). Data from onboard sensorswill be transmitted in real time and recorded onboard for play-back after reentry. Tracking and telemetry data will beobtained throughout the flight. Experiments included in theRAM-C series are: onboard reflectometers, Langmuir probes,material addition schemes, thermocouples, multiple-frequency RFtransmission systems and antenna measurements. The RAM-Cvehicle has a payload of 200 pounds (see Fig. 1 for geometry)boosted to orbital reentry conditions by a four-stage Scoutvehicle launched from Wallops Island, Virginia, in the directionof Bermuda. The reentry data period starts after the fourthstage separation at an attitude of about 350 kft and continues

through the telemetry playback period which extends to below

50 kft. A beryllium heat sink nose cap will be used down to

about 160 kft, then expelled, and ablation heat protection used

for the remainder of reentry. A second payload using only

ablation heat protection will also be tested. It is likely that

Teflon will be the primary ablation material, with mass loss

expected to initiate at 200 kft or below. The payload will be

spin stabilized during reentry in an attempt to maintain a zero

angle of attack attitude.

2

The purpose of the study reported herein is to provide anumerical evaluation of the state of the gas in the shock layerbetween the vehicle surface and the shock wave envelope extend-ing from the nose region to the aft portion of the vehicle.This numerical investigation was carried out at the conditionsspecified in Table I.

Computation of the flow field about a blunted reentryvehicle of this type is a complex problem wherein the inviscidand viscous portions of the fluid field can interact to a highdegree. Certain restricting assumptions must therefore be madeto obtain a feasible line of approach toward a numerical solution.

Consideration must be given to the nature of the objectivesto be realized. The primary objective of the RAM-C program isto determine electromagnetic-fluid dynamic interaction. There-fore the most important feature will be to determine the magni-tude and spatial distribution of free-electron concentration inthe flow field.

A few conditions have been outlined to define the minimumrequirements needed and the general scope of the requirednumerical investigation. The gas in the complete shock layerflow is considered to be a multicomponent mixture of reacting

air species in the continuum flow regime. Radiation is to be

neglected as well as any angle of attack considerations. The

surface of the vehicle is to be considered as nonablative and

nonreactive, but is catalytic with respect to a non-equilibrium

reacting boundary layer. The surface temperature is constant

at a value of 1000°K while the flow near the surface is viscous

as well as reacting. The boundary layer is to be considered a

laminar region, where finite rate air chemistry, diffusion,

viscosity and heat conduction effects are taken into account.

Corrections should be made to account for momentum flux effects

(displacement thickness) and for inviscid flow vorticity.

3

LIST OF SYMBOLS

CP

Do •

_3

6c

_H

F

h

H

k

L

m

M

n

Ne-

P

Pr

r

R

eL_

specific heat at constant pressure, GM-CAL/G_K

specie diffusion term in energy equation

specie diffusion coefficient, C_/sec

species diffusion term in energy equation

enthalpy diffusion term in energy equation

characteristic function in finite difference notation

static enthalpy, GM-CAL/GM

total enthalpy, GM-CAL/GM

surface recombination coefficient, cm/sec

thermal conductivity, GM-CAL/CM sec ° K; Boltzmann constant

= 1.38032x10-s3 joule °K-z

body length, meters

finite difference mesh indicator

Mach number

finite difference mesh indicator

electron density, particles/meter s

pressure, Newtons/meter s

Prandtl number

local body radius, meters

free stream Reynolds number based on body length

4

Sc

T

U

V

V.1

1

X

Y

8

(

1,2

X

P

T

nose radius, meters

Schmidt number

temperature, 0K

velocity component in x direction, meters/sec

velocity component in y direction, meters/sec

diffusion velocity at wall, meters/sec

.thnet rate of production of the i specie, moles/cm s sec

surface coordinate, meters

coordinate normal to surface, meters

mass fraction, _ = D ./Dl

local bow shock angle, degrees

ratio of specific heats = Cp/C v

nondimensional ratio = (7 - 1)/(7 + i), boundary layer thickness

_0 - two-dimensional flowan index 1 axisymmetric flow

coordinates along and normal to body centerline

Mach angle, degrees

viscosity coefficient, _/CM-sec

kinematic viscosity; _ = _/D, cmS/sec

density, GM/C_

stability parameter for finite difference scheme

shear stress, GM/CM sec2; transformed coordinate = 2_/_

5

interaction parameter

stream function, GM/sec

Subscripts

b base

e boundary layer edge

i ith specie

sh shock

w wall

free stream conditions

6

ANALYS IS

In the situation where the Reynolds number is high, vis-

cous phenomena which occur in the flow field about a reentry

vehicle could be assumed, for computational purposes, to be

restricted to the boundary layer, enabling the inviscid and

viscous portions of the flow field to be calculated independ-

ently. If in addition, the Prandtl* and Schmidt** numbers are

on the order of one, a finite rate chemically reacting flow

field can also be separated in this fashion.

Separation of a flow field into inviscid and viscous

fields is dependent upon the condition that inviscid-viscous

interactions can either be neglected or accounted for in a

reasonable fashion. For conditions where neither of the above

is true a shock layer approach is necessary, wherein the entire

field is solved as a viscous region.

Viscous interaction effects can generally be accounted for

by an iteration procedure (when the Reynolds number is high)

whereby an apparent body is introduced to calculate the alter-

ation of the inviscid flow due to the presence of the viscous

layer. The apparent body utilized is the original body contour

plus the local displacement thickness as calculated from the

boundary layer flow. The entrainment of outer inviscid stream-

lines can be taken into account by the actual finite-rate-chem-

istry computation along these streamlines as they are "swallowed,"

and by the utilization of these computations to provide the vari-

able boundary layer edge conditions needed to compute the viscous

layer structure.

Due to the severe discontinuities in flow variables across

the curved bow shock and the resulting associated high tempera-

tures, ionization and dissociation phenomena are generally

important in the entire shock layer flow. Chemical considera-

tions are important in varying degrees in the inviscid region

where streamlines have associated with them a relatively higher

velocity and lower temperature (due to the decrease in curva-

ture of the bow shock) than those swallowed in the viscous flow.

*Prandtl No. _ Pr _ Cp_/k = viscous/thermal transports.

**Schmidt No. _ Sc _ _/PD = viscous/diffusive transports.18

7

Inviscid Field

The shock shape and the subsonic portion of the flow field

is computed by solving the elliptic Euler equations utilizing

the inverse method (Refs. 1-3). Here the body geometry in the

nose region is specified, and an initial estimate of the bow

shock shape is made by satisfying continuity conditions.

Characteristic lines are then constructed in the transonic

region (see Fig. 2) immediately downstream of the sonic line.

The characteristic line which extends from the shock and

terminates at the supersonic body point which is nearest to

the soni_c point, and subject to the condition that k < 1.0,

(k = sin i), is chosen as a reference line. The subsonic

portion of the flow field is then solved using the "inverse

approach" where the governing equations in the transformed

T,y plane are (Ref. 3)

Continuity

_¢ =_ p vx _¢ =p ubX p= u_ bY p= u

----y (i)

Momentum

u r +_-_ V - U 2 bY _ u

= 0

= 0

(2)

Energy

+ + (i + 8) 2u_

2_where Y = 7 ' and 8 = (y - l)/(y + i).

- 1 + [ (i - 6)/6M_ 2 ] (3)p8

8

Streamline entropy conservation

P p6

p_ '_Uco

= f(Ty s ) (4)

where f(TY s) is an arbitrary function determined by the shape

of the shock which maps into the line T = i.

The calculated profile of the nose between the axis of

symmetry and the point on the body common to the reference line

is compared with the given body profile. If deviations are

found the basic shock shape is automatically perturbed and the

calculation procedure described above is repeated until satis-

factory agreement is obtained. The gas is considered in chem-

ical equilibrium and includes the effects of gas dissociation

and vibrational excitation.

Conditions previously computed along the reference line

are utilized as initial conditions for computation of the

supersonic portion of the flow field. The familiar axisym-

metric rotational characteristic method is used assuming a real

gas in either chemical equilibrium or frozen flow. The program

has the capability of detecting discontinuities ±**_-the _-_--_u_

contour and therefore flow fields about body shapes containing

reentrant or expansion corners can be computed.

One-Dimensional Inviscid Flow

Assuming that non-equilibrium effects are small perturba-

tions on the basic equilibrium or frozen inviscid pressure

distribution as obtained from the inviscid solution described

previously, finite-rate chemistry can now be computed along

suitable streamlines.

A one-dimensional finite rate chemistry program (Ref. 5)

is used to compute the pointwise state of the fluid along

streamlines wherein all initial conditions and a streamwise

pressure distribution are prescribed. The analysis includes

the effects of vibrational relaxation in the chemical kinetics.

9

_0

The post shock conditions are solved utilizing real gas

thermodynamics whereas the species are considered frozen across

the shock. The governing equations are then integrated numeri-

cally along the specified streamline path utilizing these initial

conditions. Up to thirteen air species can be analyzed utilizing

up to thirty-nine air reactions. These reactions and their

associated reaction rates are specified in Appendix I. A com-

plete description of the analysis and the governing equations

can be found in _(Ref. 5).

Boundary Layer

The governing partial differential equations for the

viscous flow of a multicomponent chemically reacting gas mix-

ture are derived from the pertinent conservation laws with the

classical boundary layer assumptions (Ref. 4). The transfor-

mation of the boundary layer equations to von Mises coordinates,

X, _, is carried out to obtain a form more appropriate for

numerical solution. The stream function _ satisfies the con-

tinuity equation and eliminates the need for numerical inte-

gration of that equation. The transformation variable is

defined by

c (5)pur ( = 5-_ ; Pvr = - 5-_

where ¢ = 0 for two-dimensional flow and ( = 1 for axisymmetric

flow. The body coordinate X is retained in the equations to

simplify specification of distributions of body pressure and

wall conditions as well as to facilitate the tracing of inviscid

flow streamlines from shock to body stations.

The conservation equations take the following form in the

transformed plane:

i0

.e

Momentum

5u 1 dp + r --5X pu dX _

(e)

Energy

c 6c5X- r _--_ (6H + ) (v)

Species continuity (i = 1,2,3,...N)

_. -_.

- + r5x Pu 5@

(8)

"where T is the shear stress, 6H is the total enthalpy diffusion

term. 6c is the energy diffusion term due to species gradients,

is the species diffusion term and wi is the net rate of pro-

duction of the i th specie (Ref. 4). The diffusion velocity

resulting from gradients in the species distributions is assumed

to be specified by Fick:s law for a binary mixture and the lam-

inar viscosity is assumed to be given by the Sutherland law.

The reactions and their associated reaction rates are listed in

Appendix I where the reactions included in the analysis are the

first seven.

The equations are solved in the d,-__ a,_-F-_ _y inner

boundary conditions at the wall, outer edge conditions in the

inviscid flow which are unknown a priori, and the initial con-

ditions for property distributions through the layer at an

initial body station. The inner conditions at the wall and

distributions of initial conditions are specified as input to

the problem. The species distributions at the wall are assumed

known as a function of the effectiveness of the wall partici-

pating as a catalyst or a reactant in surface chemical reactions,

or are selected to be in local equilibrium.

ii

The catalytic wall assumption is as follows:

- P(_iVi ) = _P_i(9)

where KR = surface recombination coefficient and V. = diffusion

velocity at wall. i

For binary mixture

D 5O_.

i 1

• " BY K_ iR

(i0)

For fully catalytic wall, K R _ = for recombination of atoms and

"intermediate" molecular species. Therefore, for these species

m 0 at wall. For air there results

_02 = (_0_)"

= (XNz_N_ ( )_

at wall (ii)

all other _'s = 0.

The varying streamwise outer edge conditions are obtained

from one-dimensional non-equilibrium chemistry calculations

carried out along approximate inviscid streamlines from the

shock to the body station of interest• The air ingested in the

boundary layer by the swallowing of the inviscid flow is used

to determine the streamtube area at the boundary layer edge

(Fig. 3). Since the shock shape is specified data for this

portion of the problem,* the coordinates of the shock intersec-

tion point with the free streamtube are readily determined• At

that point all local post shock conditions are obtained from

*From the inviscid calculations, described above•

12

solutions of the shock equations with the assumption of frozen

species composition across the shock. The properties along the

streamlines, and thus, at the boundary layer edge, are then

determined for the chemically reacting air; where it is assumed

that the streamline pressure variation is of the same form as

the body pressure variation. The pressure level along each

streamline is uniquely defined by the post shock pressure and

terminating body pressure of each streamline.

Thus the conditions for solution of the problem (in the

absence of ablation) are:

X = X(0,_) ; u = u(Y) , H = H(Y) , _. = _. (Y)1 1

= @ (x,0) ;u = 0, v = 0, H = H (X), _. = _. (X) (12)W 1 lW

$ = $ (X,$e)', u = Ue (X) , H = H_ ' _'i = _'le (X)

• The deviations from zero slope condition at the outer edge of

the profiles (velocity, total enthalpy and species mass frac'

tions) beyond specified numerical tolerances are subsequently

used in the computer program to establish a call for new edge

conditions, via the forenoted streamline procedure.

The set of partial differential equations is reduced to a

system of algebraic equations for numerical solution utilizing

an explicit finite difference technique. The finite difference

form is developed by expressing the explicit difference rela-

tions for each of the dependent variables of the conservation

equations (the variable here denoted by a characteristic func-

tion, F) as follows:

_x - A x

(13)

13

_t _ = [a(X,_+ _-A _)

l A_)- a(X,_ --

2

{F(X,_ + A _) - F(X,_)] -

{ F(x,_) - F(X,_ - A _}3(14)

where

1

a(X,_ ± _ A _) _i [a(x,_) + a(x,_ • 4_)]2

The resulting difference equations are of the form

F(X+LiX,_) = A + B F(X,_) + C F(X,_ + A _) + D F(X,_- A @)n n n n

(15)

in which A, B, C, and D depend upon the equation (n index), the

coordinate, and the various air species.

The X,_ plane is divided into a finite mesh with grid

spacing of _ X and _ _, with nodal points denoted by intersec-

tions of lines m - i, m, m + i, and n - i, n, n + i, shown insketch.

n+ 1

n

n - 1

--A X--

m- 1 m m + 1

X

14

Solutions are obtained for the variables along line m + i,

corresponding to X + _ X, on each line n by stepping off from

line m subject to the known conditions at nodal points (m, n)

and (m, n ± I) corresponding to (X,_) and (X,_ ± _ _).

The system of algebraic equations which results from the

explicit finite difference method is subject to stability con-

ditions that impose restrictions on the permissible relative

grid dimensions. A general analytical method for determination

of stability requirements of a nonlinear system of equations

considered here is not known. However stability estimates can

be formulated analytically for a linear system which can be

applied to the present problem by linearizing the equations to

develop locally constant coefficients. The analytical estimate

of the stability condition for the present problem is given by

iX (16)

where the parameter _ must be determined for each equation at

every grid point. The _ expressions for the momentum, energy

and the i species equations, respectively, are as follows:

2E

_H = r Pu -- (17)Pr

2E= r

c.1

@u S_c (i = 1,2,...)

(where the Schmidt number is the ratio of Prandtl to Lewis

numbers, or Sc = PD/_).

Transformation of the boundary layer momentum equation by

the von Mises stream function coordinate, _, results in singu-

larities at the wall where the velocity vanishes. It has been

shown that a series solution _ _n/2 satisfies the incompressible

flow boundary layer equations; the extension to compressible

flow with the species conservation equations coupled with the

coefficients of the series for u from the momentum equation has

been shown (Ref. 4).

15

METHODOF CALCULATION

Described herein is the computational technique utilizedto investigate conditions at the three altitudes of interest.The methods used in order of application are:

(a) The inviscid flow field is computed for the basic

RAM-C configuration assuming equilibrium flow at the two lower

altitudes and frozen flow at the higher altitude. The analysis,

and the IBM 7094 program utilized, is described in Refs. 1 and 2

and in the ANALYSIS SECTION of this report. Results of this

program include the shock shape, and the tracing of inviscid

streamlines.

(b) The resulting shock shape and pressure distribution

serve as input to the non-equilibrium, reacting boundary layer

program detailed in Ref. 4 and in the ANALYSIS SECTION of this

report. Here the viscous region is computed utilizing non-

equilibrium chemistry and accounts for "swallowing" of vortical

inviscid streamlines. Among the parameters computed, the dis-

placement thickness is of immediate importance.

(c) Utilizing the resulting displacement thickness com-

puted from (b) a "corrected" body inviscid flow field is com-

puted (where the "corrected" body is the original shape plus

the displacement thickness). The resulting body pressure dis-

tribution is then compared to that pressure distribution which

was used in the previous boundary layer calculation. If there

is serious disagreement, step (b) is repeated. Steps (b) and

(c) are repeated until agreement in the pressure distribution

is reached. We then proceed to step (d).

(d) Non-equilibrium chemistry along streamlines in the

inviscid flow field is computed using the analysis described

in Ref. 5. Here the chemistry package utilizes ii species

and 22 reactions accounting for vibrational relaxation where

the species are considered to be frozen across the bow shock.

16

RESULTS

Detailed plots of the results obtained are shown in

Figs. 4-112. Profiles of velocity, temperature, pressure,

electron density and specie mole fraction have been plotted

at various stations along the body surface. Contour plots

of electron density, temperature and pressure are also in-

cluded for each altitude of interest. The results have

been divided into sections, according to altitude, with a

separate cover sheet describing in detail the nomenclature

utilized on the enclosed figures.

The complete profiles in the shock layer are depicted by

solid or dashed lines while the points illustrated by symbols

pertain only to the inviscid field calculations. The curves

represent computed values where no interpretation has been

impressed on the graphical presentation.

It is noted that the various chemical species are shown

approaching their respective free stream values which is con-

sistent with the concept of a thin shock (i.e., frozen species

across the shock). Thermodynamic and fluid mechanical quan-

tities approach values which are very near perfect-gas shock

_ .... m_ _ ...... _ _m1_n_ chemistry_ program

accounts for finite vibrational relaxation times, and immed-

iately behind the shock the vibrational mode has not been fully

excited, hence the near perfect-gas results.

Examination of the results poses some interesting questions

as to the feasibility of the approach utilized and interpreta-

tion of the results. It is therefore necessary to investigate

the assumptions and procedure used.

In order to obtain a feasible approach to a numerical

solution of the state of the shock layer flow certain initial

assumptions were necessary. A boundary layer approach was

taken to be feasible if modifications were made to compute

variable edge conditions and account for viscous interaction.

An iteration procedure was utilized whereby the viscous and

inviscid flows were perturbed until agreement was reached on

the body pressure distribution. The validity of this assump-

tion is contingent upon the degree of these interactions. The

17

interaction parameter X (Ref. 6) is indicative of pressure andviscous interaction, where

S_

(18)

For altitudes of 71, 53,5, and 36.8 km, X has the values 2.17,m

0.53, and 0.19 respectively. Values of X _ 0(i) represent condi-

tions where strong interaction effects should be taken into

account.

It would be expected, then, that the results of the lower

altitude calculations would be acceptable whereas the results

of the two higher altitude cases would be open to doubt. This

situation was, in fact, borne out by the results. The results

of the 53.5 km case were marginal and those of the highest

altitude case (71 km) were completely unrealistic.

Results of the 36.8 km case are presented in Figs. 4-48.

The match between the two solutions is reasonable. The curves

shown for this case represent the type of results attainable

from this type of computational procedure.

The mismatches between the viscous and the inviscid

results at the boundary layer edge (for any streamwise station)

are due largely to the arbitrariness associated with picking

an edge streamline. At any given station an edge streamline -

and thereby the complete state at the edge of that station - is

chosen by matching the mass flow in the boundary layer with an

inviscid streamtube in the free stream; i.e. the radius of the

inviscid streamtube, _ _, is chosen so that the mass flow_ _ sn

matches that in the moundary layer.

[ s° ]= 2 Pur (X) dY

@_u _ o

½

(19)

The arbitrariness comes, of course, in the choice of 6, wherein

the resultant streamline (defined by _ sh may be relatively hotor cool depending at what portion of t_e curved bow shock it

originated. Therefore computation of the edge conditions is

18

dependent upon this edge definition as well as the approximate

technique used to trace the swallowed streamlines. The dis-

placement thickness is also dependent upon this edge definition.

The iteration procedure used to perturb the inviscid flow

becomes questionable when the displacement thickness is large,

since a fundamental assumption involved in the utilization of

this technique is that the boundary layer is only a small

perturbation on the inviscid field. For the two higher alti-

tude cases the displacement thicknesses are large and thus the

mismatching between the inviscid and viscous solutions becomes

worse with increasing altitude.

Results of the 53°5 km case are presented in Figs. 49-81

where the streamline locations for the initial and final iter-

ations have been indicated° Successive iterations for the

71 km case resulted in boundary layer thicknesses larger than

the shock layer thickness and these results have been included

for the sake of completeness only, in Figs. 82-112.

At the higher altitudes the concept of a boundary layer is

no longer a realistic representation of the viscous layer about

the RAM-C vehicle. The classic assumption of a "thin" viscous

layer, fundamental in the derivation of the boundary layer

equations, is not valid and therefore the structure of the

viscous region as a boundary layer t_e flow is subject to

question. An approach whereby the entire shock layer is con-

sidered to be viscous must therefore be utilized to adequately

investigate the flow field properties at these reentry condi-

tions. This type of shock layer formulation, where non-equili-

brium chemistry is considered, is an interesting problem and

should be given future consideration.

19

APPENDIX

SUMMARYOF CHEMICAL REACTIONS

AND THEIR RATE CONSTANTS

This appendix summarizes a large number of chemical reac-

tions which are significant at the high temperatures of reentry

into the earth's atmosphere at hypersonic speeds.

The presentation here includes two classes of units,

namely cm, sec, particle (used in Ref. 12) and meter, sec, kg

mole (required for the present analysis). The tables are self-

explanatory, though a word of caution is in order for the ioni-

zation reactions i0 through 15. The rate constants for these

reactions are tabulated as the forward (i.e. to the right)

values, which is contrary to the remainder of the appendix.

20

E_

ZOL)

V}

IM

U<

IM

O

O

{/)

C/) I.-I ,.-,

O _

t ....... L ,

C

U I-4 I I I I

I I I IQ) (3 O O O O

0 co X X X X

C

O

O

E i i i l

01 o 0 o 0

0 _ t_ 0 c,] 0

I

Io,-.4X

I

Io,-.4X

tD

p...

I

¢'1

IO

XO

I I

C0

IO IPl O

_D u_

I

m

IO_MX

e

I'N

C

[-t

H

O

O O

O

It>

Pl

+N+

,-_

0

I I I I I I

0 0 _' .t_

0 0 0 v,--I ,--I ,-I ,--I ,--I ,--I

CO ,-_ I"- 0 0

Z

Izl

II>

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<

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II>

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+

O

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p.

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4-0

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ZOH

O

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t_Ol

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++

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II

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0 ++ c_ +0 _ 0

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o +_+O +

25

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¢1

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O_tOC_

In.r-I

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0.,--I.pD

r_

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,, , ,,,, ,

,, ,, ,,, ,,, ,,, , , , ,, ........... , , ,i , ,, ,," , ....

0

o ¢+a/ + +

o + _ +_ +_II_> II II. II

_0• r-I I.D C_l Cnl

+ 4 _ 4 4+ + + + +

O Z +11 O +Z + O + O+ + + + +

O O 0_0 Z I_ l_i Z

(_ 0+ 0 0 0 Z +

Z + _ ++ + +0_ + +_/ +0 + Z + _ 0_Z 0 II Z II 0II II I> II l> II

I__* 4 J# + _4 + j+ + + + +

+ O + O OO Z O l_i +Z + I_ + ++ O ÷ 111 OO I_ Z I_ Z

_.D r_ GO O_ O ,.-4 o,_ _'_ _1'

,.. H

26

0

r.d

r_

ZoIM

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=_.=.w=...--.-=-

c_ -_

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29

REFERENCES

lo

o

o

o

.

o

.

•

•

i0.

Lieberman, E., Computer Programs and Analysis for Flow

Fields About Bodies in Hypersonic Flight - Air in Chemical

Equilibrium and Frozen Flow Chemistry, GASL TR-460,

September 1964o

Lieberman, E., Input Formats and Operating Instructions for

IBM 709/90/94 Computer Programs to Calculate Inviscid Flow

Fields, GASL TR-460A, September 1964.

Vaglio-Laurin, R. and Ferri, A., Theoretical Investigation

of the Flow Field About Blunt Nosed Bodies in Supersonic

Flight, JAS, Vol. 25, pp. 761-770, December 1958.

Galowin, Lo So and Gould, H_, A Finite Difference Method

Solution of Non-similar Equilibrium and Non-equilibrium

Air, Boundary Layer Equations with Laminar and Turbulent

Viscosity Models, Part I - Analysis, Part II - Computer

Program and Supplement, Part III- Input Manual, GASL

TR-501, February 1965.

Gavril, B. D., Generalized One-Dimensional Chemically

Reacting Flows with Molecular Vibrational Relaxation, GASL

TR-426, January 1964o

Lees, L., Recent Developments in Hypersonic Flow, Jet

Propulsion, Vol. 27, ppo 1162-1178, November 1957.

Lin, S. C. and Teare, Jo D., Rate of Ionization Behind Shock

Waves in Air, II - Theoretical Interpretations, The Physics

of Fluids, Vol. 6, No. 3, March 1963.

Whitten, R. C. and Poppoff, I. G., Ion Kinetics in the

Lower Ionosphere, J. Atmos. Sci., Vol. 21, No. 2.

Eschenroeder, A. Q., Daiber, J° W., Golian, T. C., and

Hertzberg, A., Shock Tunnel Studies of High-Enthalpy Ionized

Airflows, Cornell Aeronautical Laboratory Report No.

AF-1500-A-I, July 1962.

Zeiberg, S. L., Oxygen-Electron Attachment in Hypersonic

Wakes, AIAA Journal, VOlo 2, No. 6, ppo 1151-1152, June

1964.

28

ii.

12.

Lees, L., Hypersonic Wakes and Trails, Presented at 17th

Annual Meeting of the American Rocket Society, ARS

Reprint No. 2662-62, November 1962.

Steiger, M.H., On the Chemistry of Air at High Temperatures,

GASL TR-357, June 1963.

29

TABLE I

RAM-C FLIGHT CONDITIONS

Conditions

Geometric Altitude

m

ft

Relative Velocity

m/sec

ft/sec

Ambient Conditions

Pressure

N/m _

ibs/ft _

Temperature

0K

0R

Density

kg/m a

ibs/ft s

Velocity of Sound

m/sec

ft/sec

71,000

232,900

7913

25,960

Case Number

II III

53,500

175,500

7864

25,800

36,800

120,700

7425

24,360

4.735

.0989

215.8

388.4

--57. 644x10

51.63

1.078

268°5

483.3

--46.697x10

4.772xi0 4. 181xl0

294.5

966.2

328.5

1000.8

445.5

9.305

241.5

434.7

311.5

1022.0

The ambient conditions used for these cases are those found in

the following document: Anon.: U.So Standard Atmosphere, 1962.

NASA, U.So Air Force0 and UoSo Weather Bureau, December 1962.

SI Units are shown, followed by the corresponding English Units.

30

%

t_

rjH

!

H

31

...J

oo_

oF

0H

H

UH

0

U

0

0

OI-I

r.)

H

32

/

I-4

33

NOMENCLATURE

ALTITUDE = 36,800 METERS

The shock locations for each profile are indicated by

the short solid lines drawn along the normal coordinate.

Since the shock layer thickness increases with increasing

surface coordinate location, their identification is there-

fore self-explanatory.

The data points indicate the results of streamline calcu-

lations where the code utilized for each station is indicated

on each figure. The symbol _ indicates the post bow shock

entry angle of the streamline considered.

34

.014

.012

.010

O)4o

.008

4J

-,-I'u

0o .006

oZ

.004

.002

!

0 X =-09137

• x=.1o48

• X=.1225|

X = 1225 _h

X = .1048sh_--_ s_r

/

0

0 i000 2000 3000 4000 5000 6000

Velocity, Meters/Sec

FIG. 4. VELOCITY AT SURFACE COORDINATE LOCATIONS X=.09137,

X=.I048, AND X=.1225 METERS, ALTITUDE = 36,800 METERS

35

.035

.030

.025

.0204_

d.015

oou

.010

oZ

.005

O X =- 1457

• X =. 1723

O X=" 197c"

sh

/ X=.l£

sh

x=.=53°A

53 ° - X =. iz

65 °

I'C

.___,-0 i000 2000 3000 4000 5000 6000

Velocity, Meters/sec

FIG. 5. VELOCITY AT SURFACE COORDINATE LOCATIONS X=.1457, X=.1723

AND X=.1979 METERS, ALTITUDE = 36,800 METERS

36

.14

ooU

o

..12

.i0

.O8

.06

.04

.O2

,,

--X = .4144

_ sh

3i 250

g[35°

/

--X =. 31746so: 6s°

i

Ji

0 2000 40On 6000 8000


0X=.4144

_X=.3174

T

i0,000 12,000

FIG. 6, VELOCITY AT SURFACE COORDINATE LOCATIONS X=.4144


37

m

.4"O

00

,-I

0z

• 16

• 14

.12

•i0

•08

.06

.04

.O2

0

X=.8361

0 2000 4000

sh

{so

#=s3 t

[ 65 °

6000 8000


X=.6060

OX=.8361

_X=.6060

10,000 12,0(

FIG. 7. VELOCITY AT SURFACE COORDINATE LOCATIONS X=.8361


38

6

@-_

_D _q O__q_ O0 ,--t _'_

AAA

O00

m

I I

s_aW

O

AI!

O

i

! w

O

.AII

OOO

_D

O,O

I

AIIX

O_O

AI!

X

,--4

,-'4

U

O

IIx

U_

iu_

o4_ _n

ioo°H

-_. _oo0

,,,-i

o I>00

OOOc4

OOO

O C0 _O _ c_O O O O

'X 'a_uTp_ooD T_uz_o_

O

O

O_DO

r_U II

H

.<

0,_

H

39

-r4

ooo

_4

_4o

.016

.014

.012 ......

.010

.OO8

.006

(7i°|

71 °

.004

.002,

0 X=. 09137

Q x=. lO4S

• x=. 1225

lO00 3000

FIG. 9.

5000 7000

Temperature,

9000 ii,000 13,0(

O

K

TEMPERATURE AT SURFACE COORDINATE LOCATIONS X=.0913

X=.i048, AND X=.1225 METERS, ALTITUDE = 36,800 METE

4O

4-I

4-I

-,4_D

00

r-Inl

0

.O4O

.035

.030

.025 -

.020

.015

.010

.005 ,,

I I • I

Ox =. 1457

0x=.1723

0x=.1979

=. 1723

0

i000

FIG. i0.

2000 3000 4000 5000 6000 7000O

Temperature, K

TEMPERATURE AT SURFACE COORDINATE LOCATIONS X=.1457,

X=.1723, AND x=.1979 METERS, ALTITUDE = 36,800 METERS

41

I0

o

000

42

L

to tqr_ 0

Q0 ,_II I!X NO •

ooo

0

t'qII

QO.,

X

_0Z

0 00 H

U

O

O4.J H

_ .• OO4OoN _O

o ud

r_i u

m_

i-t

oo

,-4

0 H00

0

0"_

II IIX X0 •

I,-t

0

l--

---1%

6

,-t

II

L o _

II V

0

IIX

i

_-I _-I _-I 0 0 0 0

s_e_W '_ '_%EuTp_OOD T_m_ON

000

0 IIo Xu_

0

0

0 II

r_Z0H

0 Uu_ 0

ql H _0 _ _ _1o _ _0 ._ 0

_ 0 0

(D gO

0

0

r-"

GH

000,-_

0

44

n_ 00 Ln

o_ o oio _1 ,-4

," ," ,"N N N

OOQ

.J _i

or-ix

,-4 _g

I1"X

0,-t

X

_0

_ % oo

0

I I I _fio 0

s_N 'A '_euTp_ooD Ie_ON 45

46 q

II' II" II'

X X X

0,.00

o

o

o

-J _

vJ

p..

×r-4

o% .

-,.-I

o

0

,---t

i

r..)_

X,-.4

_.j >:

_o_ _D_O

><><

cq,-4 ,-4

sla_W 'A

• o.'a_uzpaooD I _UXON

b

o

O

H

_7

48

0o ,,_ oo,--I(','1

II II IIM N N

0@_

ICO _0

II,-I

%

/_'_ o

s_a_N 'A

__J >:

o0

o

/

IIX

o o o

'a_uTpxooD I_mXON

0_

oe

,-4

×,-H

e

C_Z<

_g,-4

IIM

frl

_g

X

o/¢'}

-t

X

II

aJ Z0

u H.,-i E-_

8

_ OO

_ UO

4-1 Uu <

o

<-o

_m

O _

al<

m

t-

,-t

,-4

o

_z,-I

H

.014

.012

.010

4_

>; .oo8

d

-,-.I

X=-1225---_

0 .006

71°

,004

i__ 650

X =. 1048

7

sh

O

sh

-------------0

sh

____---------_

ASL, _ tl_smu_'. N.Y.

0 X =- 0913"

_X=.I048

_X=.1225

0

.25

FIG. 18,

.35 .45 .55 .65 .75

Mole Fraction (N2)

SPECIE PROFILES (N_) AT SURFACE COORDINATE

LOCATIONS X=.09137, X=.I048, AND X=.1225 METERS,


.85

49

.040

.035

.030 .....

.1723

•005 i

sh

sh

, ,,

sh

OX=. 1979

Ox=.1723

OX=. 1457

50 ¸

FIG. 19.

.4 .5 .6 .7 .8

Mole Fraction (N_)

SPECIE PROFILES (Ns) AT SURFACE COORDINATE

LOCATIONS X=.1979, X=.1723, AND X=.1457 METERS,

ALTITUDE = 36,800 METTERS

L _ _

E

-r4

00rO

,--4

E

0Z

.16

.14

.12

.i0

.08

•06

.O4

.O2

O X =- 3174

• X =. 4144

OX=.6060

"_,X=. 8361

_ G ASL) '_smum', ItY. ,1

_ sh

sh

X='8361 _ 25o

_ x:oo+o/_

x

IX_x=.3174

0

FIG. 20.

.4 .5 .6 .7 .8

Mole Fraction (N2)


LOCATIONS X=.3174, X=.4144, X=-6060, AND

X=.8361 METERS, ALTITUDE = 36,800 METERS

.9

51

.24

.22

.2O

• 18

• 16

14_) -

g .nm

.i0OOU

.4

08•

O

.O6

.04

.O2

m

m

m

O x:l.036Q x=1.143O X=l" 309

I

q_ sh

lJsh

250

,

65 °

X=l. 036

0.3

FIG.

.4

21.

GASL

.5 .6 .7 .8

Mole Fraction (N_)

SPECIE PROFILES (N2) AT SURFACE COORDINATE

LOCATIONS X=I.036, X=I.143, AND X=1.309 METERS,


.9

52

I

t'-

,-4G_

O

ii°

M

O

,-4

O

1

(D u_

O e4,,-4 ,-4

,,. _"I_ 1,4

O0

X

CO I_

0 ,-I,-I O_

.1:: 0

I1" I_ II_

, ,, , ,,,,

Ji

nf.._

,-I

II

I It_ 0 013 _O _ c_-,-4 ,-I 0 0 0 0

0 0 0 0 0 0

sx_W 'A '_u_paooD I_UL_ON

O

O

,-4

,-4

O_

O

II'

°o x

Z

<

_a

O

_ _ -

,4

I

,-.t

0

53

t_

o.

54

Q

0 0

D

x

i_. c_

_-I',-I ,-I

," ,,","

000

(33,-I

Q

p..

,--t

ii°x

u_oq

I ,Iq R R'_ '_euTp_ooO T_oN

X

o

(_ JI'

_gp..,-I

u i,--4

,'-'t

II'

x

M

_0O_

-,.-I

U_

O0

r..)

X,-t

113

b

'o,--IX

,-4o

ul

v O:

O:

I--t _

_ ii I

al

UH

i-i

,-,It

oal

I|

I,

o,,D0_)

I"

0,-4X

%

55

O

II' II

O0

Q0

e

I I,-4 r-i

_0tOO

IIX

L

O

to

O

u'lto

i̧ i_ ,i_Ooh00

II'

CO

• I

r.i ,-t o o o o

OO,-I _OX to

,-4 O

II

oX _O

r-I t_CO

IIX

I H

oN O

O

_ H

o _• f'l .

_ 4.) 0I 0 0

0 rd U

0 _

m 00

0,-I (_o IIX "-"

I--t I-I

o_

N _ E.I

m _

_o,-4 H

O

56 sx_al4 'A 'aW_uTpxooD TEU_oN

II IIx

OO

I l

%

sxe_eN 'A 'o_uTpxooD T_mXoN

57

•016

.014

iii . .......i I

OX=.09137

QX:.lO48

_X=.1225

X=.1225

I I i I J

.002

0

0 .10

FIG. 27.

.20 .30 .40 .50

Mole Fraction (N)

SPECIE PROFILES (N) AT SURFACE COORDINATE

LOCATIONS ](--.09137, X=.I048, AND X=.1225

METERS, ALTITUDE = 36,800 METERS

.6O

58

o

D

.035

m

{_35 o

.03O '

.025

O X=. 1457

• X=. 1723

O X=. 1979

,,u

i i

_ /__x:1979

, i I015

• Ix=1723

OlO ,' i/

• _ x='1457 "_ i_GASL1'"" "".005

0

0 .i0 .20 .30 .40 .50 _60

Mole Fraction (N)


LOCATIONS X=.1457, X=.1723, AND X=.1979


FIG. 28.

59

4j TM

Z

00 04-

0Z

.O9

q_%o

.08

m

•07 (L_35o

• X=. 4144

.05

X=. 3174 ---J _

.O3

.O2

.01

0

6O

0

bIf

.i0

FIG. 29.

, n

.20 .30 .40 .50

Mole Fraction (N)


LOCATIONS X=.3174 AND X=.4144 METERS,


.60

e

•18

.16

.14

.12

.i0

4-*

.08

-H"O1.400C)

.o6

0

. O4

.O2

OX=. 6060

IK--.8361

i,

b25 °

I-- X=. 8361

0 ,.

0 .i .2

GASLW. ll._

.3

Mole Fraction (N)

FIG. 30. SPECIE PROFILES (N) AT SURFACE COORDINATE

LOCATIONS X=. 6060 AND X=. 8361 METERS,


.6

61

_ o'_

o_1 _

II II IINN N

OOOi

I II,--t

m_

_ 0

S_ W '_

O

II m II

x Q.jx

II

/OO ',D0 0

'a_uTp_ooD I_tu_ ON

o o

o

u_

o

u_

A

Zv

0

oc,_ o•

0

Lr_

o

u%o

o

o

<

00O

0<

<

Z

H

Hr..)

m

H

O

IJN

,--40

Xm

- II

m _

o_

H_

O

62

.016

.014

.012

.002

O X=. 09137

X=.1225

GASLWen'_. N.Y.

0

.26 .27

FIG. 32.

.28 .29 .30 .31

Mole Fraction (0)

SPECIE PROFILES (0) AT SURFACE COORDINATE

LOCATIONS X=.09137, X=.I048, AND X=.1225


.32 .33 _

63

.036

.032

O X=. 1457

_X=.1723

Q X=. 1979

.028

.024

,.020

d

-,'-I'_ 016

00U

0 012Z"

.OO8

-X=.1979

-X=.1723

53 o

.004

o&64

.27 .28 .29 .30 .31

Mole Fraction (O)

FIG. 33. SPECIE PROFILES (O) AT SURFACE COORDINATE



GASLi,..,,.,.,,..o,,o_, .

.32 .33.

.16

.14

.12

.i04J

.o .08

00

•-4 .

0

.O4

.02

m

7

I0 X=. 3174

• x=.4144

i0 X=. 6060

_a x:.8361

_ X=. 6060

_X=. 3174

.24 .26

FIG. 34.

GASL

.28 .30 .32 .34

Mole Fraction (0)

SPECIES PROFILES (0) AT SURFACE COORDINATE

LOCATIONS X=.3174, X=.4144, X=.6060, AND

X=.8361 METERS, ALTITUDE = 36,800 METERS65

.4,-_

ooo

,--I

oZ

66

.24

.22

.20

•18

•16

•14

.12

.i0

•08

.06

•04

.02

O X=I. 036

Q X=I. 143

X=I. 309

X=l. 036

_ _"- X=I. 143

i- X=1.309

'__ 53o

g0.24 .26

FIG. 35.

.28 .30

Mole Fraction (O)

GASLWESTBURY,N.Y.

.32 .34 .36

SPECIE PROFILES (O) AT SURFACE COORDINATE

LOCATIONS X=i.036, X=i.143 AND X=1.309


0

o.,..40

i

m

o

×

m

o o

sxa%eW 'A "a%euTpxooD leU_ON

cq

8

o

H

o

67

u%

68 q

u_ (-4

,-_ ,-4 ,_

ooe

\

r

z

oo

X,-t

o

,-t

o

o_ _ _ 0

q q o o qsleweW 'A 'e_uTpaOOD I_mXoN

--r-4

I

u0

I0

,-_X

o ,-4

ce)

i_--r-I

l.r)

II"

X

to

0I-I

t.)0

g

---o_0

0 o-,_ _ _0

_Ho__,

'H (J_ir..) ,-'1

m

6I--t

It

o

o_D

Ii° II

o o

69

P_

7O

_O

J

IIX

0_o

liX

O o

liN

o

U3II

O _ __ O O O

• I

s_a_W 'A '_EuTp_ooD IE_ON

o

of-4X

O_o

IIX

o

x,-.-II[N

,do

IIX

r/lz

oH

N U,--I _ O

O _Z

E-I

O-,-t H

u __ o_ o

IIJ r.r.1 _

X,-.-t r._ o

o

_ r¢)o

H H

O _,-4x _ad

m_

Io

M,--t

o

H

.016

.014

.012

010-

Z

G

.oo8-H

"0

00L)

006

oZ

• 004

.002

-X=. 1225

X=. 09137

OX=.0913_

OX=.I048

OX=.1225

650

o

71

53 °

q

7 c __

GASLII_s'rmu_, N.Y.

0

0 .0001

FIG. 40.

.0002 .0003 .0004 .0005 .0006

Mole Fraction (NO + ) and (e-)

SPECIE PROFILES (NO + ) AND (e-) AT SURFACE

COORDINATE LOCATIONS X=.09137, X=.I048,

AND X=.1225 METERS, ALTITUDE = 36,800 METERS 71

.040

.035

5oF-X=.I979

0

0 .0001 .0002 .0003 .0004



COORDINATE LOCATIONS X=.1979, X=.1723, AND


OK=. 1979

_(=. 1723

Ox=.1457

72

ASL_.smU_o N.Y.

.0005 .0006

FIG. 41.

] r

r.

X

.16

.14

.12

.I0

25

Ox=. 3174

E_X=.4144

QK:.6060

m

-,-4

.08

g _35 °

53a -x='3174

.02 _

J

0

0 .00002

FIG. 42.

.00004 .00006 .00008

Mole Fraction (NO + and e-)

SPECIE PROFILES (NO + AND e-)AT SURFACE

COORDINATE LOCATIONS X=. 3174, X=.4144,

AND X=.6060 METERS, ALTITUDE = 36,800

METERS

.00010 .00012

73

4J

oo

0z

• 24

.22

.20

•18

•16

•14

25 °.12

,25 °

OX=.8361

OX=l. 036

OX=I. 143

_X=I. 309

I

X=I. 036

X=.8361

X=i.143

74

_--65°.02

o0 .00002 .00004 .00006

FIG. 43.

•00008


.00010 .00012


COORDINATE LOCATIONS X=.8361, X=I.036,

X=I.143, AND X=1.309 METERS,


6,

a)

m

o6,

U

4

8

a_

- u,3

r_

,.D

C0

O

r:

r_

tJ

_4 z

.q o

f,l

_,_. _

_. _ .-, .-,,.,,-I

• ° ...... ° °

N_//e_ _ N&_NI(I_OOD _ON _I_OISN_IO-NON

d

o

o

75

oq

o

° ooo o

o oo

\o

ou_

o

6

r.. e_0

I

_._

U

o

o

Z

,.d

q

o

r_

8

o

r_

0

o

M

,.D

,4

o

un o o

gor'-

'.0 _ e.I 0 CO _O _' C',l 0 _lO _0 _ ¢',1 0 O0 '.O _1'

76 N_/_ 2 _ S._.VNI(]_OOD q%"_F_ON qVNOISN_4I(]-NON

o

co

_0

d

, oo

m

.032

.028

.024

ul

o

020-

= .016

o0U --"

,-4

E 012 "-.

o

•008

.004

FIGo 47.

78

OASL]K = . 1979

I I ,L

/

i

X=. 1723

X =. 1457

X=./225

. / / X =. i0/48

X =. 09137

/ ////', ///

4 8 12 16 20 24

Pressure, Newtons/Meter e x 10 -4

PRESSURE PROFILES AT SURFACE COORDINATE LOCATIONS

X=-09137, X=.I048, X=.1225, X=.1457, X=.1723, AND


.16

.14

= .12

4J

- . 10Iii

-,.4

_ .oa,,-.t

0

.06

.O4

.O2

0

X=1.309r•X=I. 143

i X=I. 036X=.8361f

/.X=.6060

, ,| ,

X =. 4144

X=.3174

i

,i

G ASLi, ,,_,,,,,..,

0

FIG. 48.

1 2 3 4 5 6

Pressure, Newtons/Metez e x 10 -4


X=.3174, X=.4144, X=.6060, X=.8361, X=I.036, X=I.143

AND X=1.309 METERS, ALTITUDE = 36,800 METERS

79

NOMENCLATD-RE


The shock locations for each profile are indicated bythe short solid lines drawn along the normal coordinate.Since the shock layer thickness increases with increasingsurface coordinate locations their identification is there-fore self-explanatory.

The data points indicate the results of streamline calcu-lations where the code utilized for each station is indicatedon each figure. The symbol _ indicates the post bow shockentry angle of the streamline considered.

The initial and final iterated streamline locations areindicated on the figures; where the squares indicate the initiallocations.

80

• 0O8

.007

OO6

005(D "

.004r

00

.003

0

.002

.001

0

0

FIG. 49.

|

O X =- 01623

• X =. 03677

I

ASL

sh

X=.03677----_

A

4---X=.01623

400 800 1200


1600 2000 2400

VELOCITY AT SURFACE COORDINATE LOCATIONS X=.01623


81

.016

.014

.012

,010

d .oo8

00

.006m

O

.004

.002

82

I i I i

00

FIG. 5 0.

J

65 °

O

77 °

nl

i000 2000 3000 4000


VELOCITY AT SURFACE COORDINATE LOCATION


s_=.i099

GAS.L_ Wl_r_mt. N.Y.

5000 6000

X = . 1099

ii"

I

,--IaO

000

E-,

ooo 0_cO 0_

ITM I_D ITM

,."4 _I _I'

OOO

, , -- q_ , g

o II- , " o X

C.'_

. • nn _'

o

r_

I11

o

III H

O -,.4O _ _,_ 0

..-,4.

1"4

ooo

0:0o

0o0

c,,l O CD _O,-'-4 ,--4 O O

I:o 0

sao_oN 'A 'a_uTpxooD T_m.xoN

oo

83

r.J9O_O_

t9<o_o

tel e,_

O_

H

oOr-4

84

0 I"

01oM

X

r_ _ o

OD u_ L_

It* I1'x

%%%_• I,

_.000,_ OOo')

o

II It II

Ir_

,Ic_,-4

s;[e_eW

0 0 0• , 0

a_ ,a_.TeuTp.,_ooD TEm.-co N

=.J >_

c/)

,.(.9

1

o

ooo00

ooop_

0oo

ooou_

ooo

ooom-)

0oo

ooo

o

o

O_0

II

0E)QO

II"

x

ii°

ul o

4-1

u'3

I'-t

00

o

o

i II o _o H.... _

o _ _ _ _ o_ 0 o o o

0 0 0 o o o

8.5

p, r-,

II' 11' II°

II'X

00

II' ii°X

• 00o

<

o

o

II"X

o0

IIX

Zo o

I,-4 0 0 0

0

0 _ II'

0C_

u_

Io

000

0

H

sxeg, eW 'A 'eBeu_pxooD IeUL_ON

86

.18

.16

.14

.12

m.i0

40

O840 -m

.,4

oo{)

.06

oZ

. O4

.O2

i

!

0 X=. 6564

OX=.8807

"_X=I. 309

3_

35°I iI

-- X=I. 309

m X=.8807

X=. 6564

5_._ 5_ '

. 3 °

'__ G ASL

0

i000

FIG. 55.

2000 3000 4000 5000 6000 7000O

Temperature, K

TEMPERATURE AT SURFACE COORDINATE LOCATIONS X=.6564,

X=.8807, AND X=1.309 METERS, ALTITUDE = 53,500 METERS

87

O88 '

or--I

II"x

0

o

1 .-I

C/)

l

o,

o,

x

/ ilJ II :

o o 8. 0 0 0

s_e_eN 'A 'a%eu?p_boD TeUmON'

02

%

(D

.4

o

o

&

O4

,-4O

IIX

(3Z<

coo

II

8,

o_ ,.-4

O•,-4 H

_ O

_ H

OC O00

4..1O<r_ ul

o_o_tn

Zun

II

(.) H

,du'3

H

,-4

0 •

i °" X

If"

OD

o ,_ _

U

_4/ X._-_

0

/ _

m

co _o _ o_ o

_. _ o. o'A 'e:_uTp_ooD i_m_ON 89

r-I

9O

_o o 0u_ 00 oh

II' II II

o

,-.I

4_

44_m

-,4'0

00t5

,-4

0z

.016

•014

.012

•010

.OOB

.006

•004

.002

m

!

Ox=.01623

0X=.03677

OX=. i099

/

B=53 °

-X =. 1099

sh

"s_:-03677

. shX =. 01623

00

FIG. 59.

GASL_'mu_Y. N.Y.

.2 .4 .6 .8 .i0

Mole Fraction (Ne)


LOCATIONS X=.01623, X=.03677, AND X=.I099 METERS,


.12

91

.16

.14

.12

.I0

d.o 08

i.looo

,-..t.06

O

.04

.02 --

0 _-

0

FIG. 60.

92

O X=.4799

QX=.2817

Qx=.1725

sh

--X=.4799

' 35 _35 °

_=53O sh

53°D i_

_-X=.2817

4_ . X=.1725

i

GASLWESmURY, N.Y.

.2 .4 .6 .8

Mole Fraction (N2)

SPECIE PROFILES (N2) AT SURFACE COORDINATE

LOCATIONS X=.4799, X=.2817, AND X=.1725 METERS,


.12

m

4J

c

_o_4oorj

,--im

.24

.22

.2O

•18

.16

.14

.12

.i0

.08

•O6

.O4

.O2

0.3

FIG.

OX=.6564

O X=.8807

_X=1.309

53°_,

I X= I. 309 -

shJ,

:Il

X=.8807_._ p shsh

_=35° _ /

53°_ / /530_55°_

GASL

61.

.4 .5 .6 .7 .8 .9

Mole Fraction (N_)

SPECIE PROFILES (N2) AT SURFACE COORDINATE LOCATIONS

X=.6564, X=.8807, AND X=1.309 METERS,

ALTITUDE = 53,500 METERS93

o

Ooo

0 E) O

o

o _ _ _o o o o

o o o o 0

s_e_a_ "A '_euIpaooD Te_oN

94

O_

o

,-4>¢

o eaO

X_

O

4au

_4

o

?o

To

>¢r-4

o,-4

Z<oH,-4

N _r,.) N

r_

m_Doe,._o

ii ¢,__Mm

o _. ii

t.r.1 ,-t _

H

o_Hd

NU_

m_

tD

o om

mAlJ* JlX X• 000

96

,--I ,-..4

h

O 0

ofel

O

O

-J_ o,-4 O

_ X

o.

0co

I. o o

N O

o

uh

OI ou3

01

otXl 0 CO _D _1',--I ,--I 0 0 0

I0 ¸,-I

_O

Io

' Xm

I

i

m I0,-_N

,-.I

E.t O

4

6H

.016

.014

.012

4_

:Z .010

4_

"_ 008-

oou

|w

o .006

.004

.002

O X=. I099

- X=. 1099

- X=. 03677

.

0 .i

FIG. 65.

.2 .3 .4 .5 .6

Mole Fraction (N)


LOCATIONS X=.I099, X=.0367_, AND X=.01623 METERS,

ALTITUDE = 53,500 METERS 97

0 X=.4799

• x=.2817

• x=.1725

-X=. 4799

-X=. 2817

X=. 1725

98

0

0 .i

FIG. 66.

.2 .3 .4 .5

Mole Fraction (N)




.6

X,-4

o

o0,-4X,-4

70,-4

x,-4

!0

Z

0

1.4P.4

0,-4o

,c0cO(D

II"

X

II"

x_

H O

8,;Om

_.1 I|

m [-4

_,1 ||_Nr_

Hr_

99

.016

.014

.012

4_

_ .010

.oo8

o

i .006

.004

i00

.002

i

O X =- I09S

X=.i099

ii i

- x=.01623 ___

0 _ __

.24 .25 .26 .27 .28 .29

Mole Fraction (0)

FIG. 68. SPECIE PROFILES (O) AT SURFACE COORDINATE

LOCATIONS X=.I099, X=.03677, AND X=.01623


.30

i

b

•-4 O O• • • •

(2) z "

-,4

o_ _

I/3

p-

JlX

iio o

o

o

oo

0 . ii

r_

H

_Z

o d_H

_uEt

_ O_

6H

sxew_H 'A 'a_EuTpxooD I_XoN i01

•18

.16

•14

.12

0 35°

n

O X:. 656_

X.i0

D 35°• _ 35°

;_ .08

o --X=.8807

___=35°0 -X=.6564 . _53°C_53°

.06 __" ,,_a_ _53o

• O4

.O2

102

0 .05 .10 .15 .20 .25 .30 .35

Mole Fraction (O)

70. SPECIE PROFILES (O) AT SURFACE COORDINATE

LOCATIONS X=.6564, X=.8807, AND X=1.309


FIG.

,-IO

m

w

O

L

Cr_0r-I

if °

",4

c_

II

0,-I0

0

I1"

X

0

O O OO O O

s_a_N "A '_u3p_ooD I_UL_ON

('W

OO

IO;-IX

,....Ix

;-.tX

AOZ

c:0

-,-I

U

,"4

'o,-4

IO,-IX

_ ,--4

!O,--I

X

O

',O

O

It"

X

<

,.2I".-

O

if"

X

O_O

ii °

X

ZOH

<uO

<ZH

L_

Dmo

o

._u3

0Z II

N_H H

_dH_U _

mN

H

103

u%eqr,-,-4

O

,-40

104

F--,-4co(',,i

I

O

0_o_r--

Q

o_o_r--

U__

,_ ,-4

o

,-.4

s_e_a_

¢N0 0 0

'A 'a_euTpa6oD lemaoN"

o

m

o

o,-4

,_' r,,- o'_

II" I! IIXX_

DEll000

r-4 r_

omoD a)=i

N

F"-o

IIO

_ O O

0 _ £1_omo

• II0 iO

t/_ t.nII

,--4

I,-'1 f-I 0 0 0

• £ ip " "8.Z_N a aO_.eu. _[OOO "[RUL.'[ON

¢N0

.%,--IX

'= ,--I

m

tI

0

X,-j

c_

I0r-4

0

0.r4

Um

(1)

r-JI O

N• ,-.-t

o,,..4N

,-t

?O

X,,-t

O

o0el

IIX

1:1Z

o

_0

_D

t/3

M

O

[-4

H

O_m

O

H H

H_

Hr_

105

.016

.014

.012

0104J •

008-

0

,, •

--X=. 1099

o

006 _

--X='03677

.002

I _ --X = .01623

_oo_ / )

106

0

0 .0002 .0004 .0006 .0008 .0010 .0012

Mole Fraction (NO + & e-)

FIG. 74. SPECIE PROFILES (NO + ) AT SURFACE COORDINATE

LOCATIONS X=.I099, X=.03677, AND X=.01623 METERS,


_DH_r..) H

o'_ o'1

sxe_eN 'A 'eWRuTpxOOD TenON

O

[-,.

_4

H

107

_oo

II° II II

xxx

,-I ,-I ,-,4• 0 •

108

o

AII

0 0

o

o _0

0

o_D

0

o

• • o • o

...., ° • .... • ° .

.,4

oorJ

,-I

•016

•014

.012

•010

•008

•006

m

i

X=. 1099

X='03677 I I X='01623

• 004

112

.002 ,

0

0 lO, 000

FIG. 80.

J20,000 30,000 40,000

Pressure, Newtons/Meter e

50,000 60,000


X=-01623, X=.03677, AND X=.I099 METERS,


o

AJ

4J

--4

oo

.16

.12 --

.10

.O8

• O6

.O4

n

X=l. 309

X=. 8807

X=.6564

X .4799

fX =. 2817

//f

.O2

0

0 4000

FIG. 81.

X=.1725

GASLIn_mJ_o N.Y.

8000 12000 16000 20000

Pressure, Newtons/Meter _


X=.1725, X=.2817, X=.4799, X=.6564, X=.8807, AND

X=!.309 METERS, ALTITUDE = 53,50G METERS113

24000,

NOMENCLATURE


These results have been included for completeness only.

The shock locations for each profile are indicated bytheshort

solid lines drawn along the normal coordinate• Since the shock

layer thickness increases with increasing surface coordinate

location, their identification is therefore self-explanatory.

The data pOints indicate the results of streamline calcu-

lations where the code utilized for each station is indicated

on each figure. The symbol _ indicates the post bow shock entry

angle of the streamline considered.

The solid lines on the enclosed curves represent the final

iterated boundary layer results. These profiles have been cut

off at the shock. The dashed lines represent profiles drawn

through the results of the inviscid calculations.

114

L

4J

4J

-r4

oo

rj

oIz-

.016

.014

.012

i

.010 !

I

.008

.006

.004

.002

OX=. 0168

OX=. 06126

] I

X=.01683--b

0 500 i000 1500

X=.06126--

FIG. 82.

2000


VELOCITY AT SURFACE COORDINATE LOCATIONS

X=.01683 AND X=.06126 METERS,


2500 3000

115

.032

.028

.024

.008

I0X=.I1338

_X=. 1621

• 004

116

0

0 i000 2000 3000 4000 5000

Velocity, Meterl/Sec

FI@. 83. VELOCITY AT SURFACE COORDINATE LOCATIONS

X-.I1338 AND X_.1621 METERS,

ALTITUDE . 71,000 METERS

6000

.32

.28

.24

.20

X

• d .164.1

00

_ .12

.O8

. O4

0

i

Ox=. 5119

Ox=i.0077

Ox=l. 309

X=l. 309 -

\m

xp,,5o°

'L'

12,0000 2000 4000 6000 8000 i0,000


FIG. 84. VELOCITY AT SURFACE COORDINATE LOCATIONS

X=.5119, X=I.0077, AND X=1.309 METERS,

ALTITUDE = 71,000 METERS117

_D ,-I,-4 _D0 0

0 0

N

0

118

I0

0

I0 0 0O o o

s_e_eM 'X 'e_euTpxoo_ leu_oN

00

o0

4'

.032

.028

•024

m

X

. .020

-,.4

.016OOU

m

o_ .012

•008

.0O4

0

O X=. 1621

Ox=. i1338

i _ i

_ ! J_oo._____,,3,8

i .)/ ,

x_-._._,__ _,_ ._.__/

0 2000 4000 6000 8000 I0,000 12,000

Temperature (OK)

FIG. 86. TEMPERATURE AT SURFACE COORDINATE

LOCATIONS X=.1621 AND X=.I1338


119

00

i i

I

0

0--

ooOD

000

6H

!

120.

. Io

'_Eu_. p:_ooD I_m-ZON

,¢o

o

o

-00

t

,-4O

(D%0,-4O

O

%Oc_

%0O

,-4%Oo

e

@

IO,-4o

sae_aN

I0o0o

o o oo o o

(D

o ,-4

'A 'e_eu_paooD IE_ON

121

0

i 0

0

X

122

mmmmmmmm

0 0 0 0

a__0

r,-

,-i o o,-4 o

OO0

•Q u'_

'i', v l,, oII I _ _ OoOiI I

<.-7o_-r _ _,,

,I I o_.- _ _

I - _ _II I I _ _ _II I -, _ _

,,,II I _o ..

,I I -"_ii i -- _,

I I C_i _

"1 o1, - " _o°_I _ _ _

II T o

I I . '-

I! s0 _ 0 I.n 0,-'1t",i _iI ,-4 0

s_e_W 'A 'a_uTp_ooD I E[ua°N 123

0

L

m

016

.014

.012

.010

.IJ

°_

oo

X_ • 06126-

IOX=. 01683

I

_X=.06121

0 B=85

i _/--X=.01683

.006 %

.004 _ ,, .

, \085°_

.oo= .... , G ASL

00 .2 .4 6 .8 1.0

Mole Fraction (N2)

FIG. 91. SPECIE PROFILES (N_) AT SURFACE

COORDINATE LOCATIONS X=.01683 AND

X=.06126 METERS, ALTITUDE = 71,000

METERS _124

1.2

00U

,-.I

.032

•028

.024

.020

IOX=.I1338

0X=.16211

/.016 /

__ W

Z/ o°_ p.o12

.008 _/85°

.004

/"/"

N H •

jJ

X=.1621

.3 .4 .5 .6 .7

Mole Fraction (N_)

FIG. 92. SPECIES PROFILES (N2) AT SURFACE

COORDINATE LOCATIONS X=.I1338 AND


.8

125

,-4 0 0_I 0I.CI °

,__O0 0

o

H

0

0

126

e,io

I

i

II

\

O

O

X_4

7o

Io

,-4M

o

u%04O

\\

I_1 _-I _ 00 0 0 0

/

o

c_

o_

,.q

I1"

_D

II"

H

O

ZH

OO

UI

mO

_O

O t"_

H £'4U H'_1 [-4

m<

t/3

H

s_a_ 'A 'a_Ru_pxooD IEU_ON128

0_.-4.,-4u',

IIX

0

o,-4

o,4

o_ ,-4

J

a

o

o

,-4IIX

Z0I-4E*

<ZI-4

"-" CJ

,-4

v

in

i-4

O

0.,

H

[.,.]a_

_n

oOO

r'-

tl

o_,-4

Oo

,.--4

_,Oo_

H

129

.01_

.o14

.012

.010

.OO2

00

130

• " m

O X=. 06126

0 X=. 0168

.06126

• 85 °

.1

11G. g7.

GASL

.2 .3 .4 .5

Mole Fraction (N)


X_.06126 AND X-.01683 METERS,


.6

i I ,

t

.032

.028

024

4_

=_ .020

4.1

" -r,I

.016

oou

,-4m

_ .012o

0 x=.162]

• x=.1133s

m

k , .

\\

"_"_ .x:.16_1

',,#:7o° _,!

.004 -- r

_ _'-t_ _x:.11338, -- G A SL0 _ wmmm¢. I1.%'.

0 .i .2 .3 .4 .5

Mole Fraction (N)

FIG. 98. SPECIE PROFILES (N) AT SURFACE COORDINATE

LOCATION X=. 1621 AND X=. 11338 METERS,


.6

131

i._0'_ I_ 0_

0 0,-.I 0u_

0 00

132

o

o

s _'e_,es "A

oo u%u% 00GO

r,-

oG

,-4II

X

//

u% o

o

I!°II

'&_uTp=ooD _=o_

o o

0_

,-4i£'1

Co,-.4X

,--4

70,-4

0tIo

,-4

+o,.-4

,r

o

o,-IX

0

o •o

,.-.4

o+,-4ut_

IIX

Z0H

r_

i-4o

_o o

0.4 It,]II.o 0

mH

,-.4

_d

m_

H

O0

_ •

H

1'I

•018

•016

.014

.012

m

_.010

._ • 008

oou

_.006o

.004

.002

IO X=. 06126

IQ X=. 01683

I

X=.01683

X=.06126-

i

ii

0.18 .2O

FIG. i00.

.22 .24 .26 .28

Mole Fraction (O)

SPECIE PROFILE (0) AT SURFACE COORDINATE

LOCATION X=.06126 AND X=.01683 METERS,


.30

133

.036

.032

.02E

OX=. 162]

OX=.I1338

l,

ii• ,m

w

.02G

d

c 016_J

0 __0

U

,--4

•012O

008,

•004

134

0_

.18 .20

FIG. 101.

X=. 1621 -- D

\

%

70 °

\\

, /85 °

-X=.I1338

I,

.22 .24 .26 .28

Mole Fraction (O)

SPECIE PROFILES (O) AT SURFACE COORDINATE

LOCATION X=.1621 AND X=. 11338 METERS,


.30

.36

.32

.28

.24

®4J

(_=I. 007";

OK:. 5119

_:1.3o9

, ,,i

I

,I

.20

X=l. 0077-

_.16 .....

o== =,=,==. _=_

.12 i

.04 , =

_-X=. 5 i//_19

0

0 .05 .i0 .15 .20 .25 .30

Mole Fraction (O)

FIG. 102. SPECIE PROFILES (0) AT SURFACE

COORDINATE LOCATION X=I.0077, X=. 5119,

AND X=1.309 METERS, ALTITUDE = 71,000METERS 13-5

.018

.016

.014

012

.010

X

4.1

_ 008c °

8

,--4

, m . 006

o

.004

.002

136

_X=. 0168. _

_X=. 0612_

_X=. 11336

K=.I1338

- /.

/\

X=.06126

\\

\\

'Ii

//

/_" _ 85 °

70 °

J

--X=. 01682

0 .02 .04 .06 .08 .i0 .12

Mole Fraction (NO)

SPECIE PROFILES (NO) AT SURFACE COORDINATE

LOCATION X=.01683, X=.06126, AND X=.I1338


FIG. I03.

.18

O x=.511s

• x=.1621

.16

.14

i

-- x=. 5119

.12 ,w

35 °

_.10 .

_ 08 '

' _ 06

o_ _

0 _ wa_u_,, N.y.

0 .02 .04 .06 .08 .i0 .12 .

Mole Fraction (NO)

FIG. 104. SPECIE PROFILES (NO) AT SURFACE COORDINATE

LOCATIONS X=.5119 AND X=.1621 METERS,


137

.36

.32

.28

.24

.20

16

oou

_ .120

.08

• O4

0

138

5°

35 °

IO X=I. 0077

-X=I. 0077

i

!

• i _ X=I. 309

ill

)

[ ,!

0 .02

FIG. 105.

.04 .06• .08 .i0

Mole Fraction (NO)

SPECIE PROFILES (NO) AT SURFACE

COORDINATE LOCATION X=I.0077 AND

X=1.309 METERS, ALTITUDE = 71,000

METERS

•.12

,-Io

kD('_ a)

_D ,.-I0 0

IIx _0 Q

o

_0

.,.._

0

IIi

qr

I

0

u_{:9N

r_

GO_D

0

Yd

Io o 0o o o

sxe_eM 'A '_uTp_ooo I_U_ON

Io

1 _ ooo

_o_i

doo

139

"_'0

mc

%

.03_

.02E

r_

Z.020

4rd

._. 016

I.l00

,.-.4

_.012o

.O08

.004

140

O X=. 1621

OX=. i1338

t

B'=s

\.\

70 °

85 °

X=. 1621 _

X=. i1338

/ /

0 .0002

FIG. 107.

.0004 .0006 .0008 .0010



COORDINATE LOCATION >[--.1621 AND >[--.11338


.0012 .0014

un

+

Oh _ O_r4 0 0

• _ _

OO0

I

141

, ° ° , ° ° ° • ° ° • . ° 0° °

0o

r_

_D

0m

%

B

o

0

0U

o.-.-I

M

_o

\

ooo

ou_

g• 0 0

'- o

_D

Go

,.4

o

,_ _ o co _ ,_. _ o _ _ _ _ o co _ ',_• • ° • • (_ 0• • • •

e_ _ r_ rn c_ c_ c_ c_ c_ _4 _ _ _ _ 0 0 0

142 NH/_ _ _ _q._.VNI(_HOOD q_WHON q_NOISN_41G-NON

Z

om

OO[J

o

O

o

c_

o

(13

,4

r,l

,-.i

o

o

d

c;

o

o

0

G

i'oo

II

rj

o

ooo

oooo

oooo

%oo

oooo

o

d

• , • • • ° o• °

N_/_ _ _I_M000 T4W_ON T4NOIS"N_I_-f_ON143

• , l • l , . _ _ : . , .

co

00

_o

Nun

o

_D

,.D

I-

X

oN

oU

0U

,-4,-4,...I

_ 0

N

Nt_

o

%

,-.4 _,

%

L_

• • . . • . o • •

N_/_ _.T._I(I_OOD '_P_O_ _OIS_3?_I(I-_O_

144

_o

o

co

_D

,So

co[.-i

00

4 _

4 _

r.,

_ o

o0

t_

_4

d

d

c,l

o

(13

,-4

tip

,-4

e-t

,-.-i

o

,.-4

0g

o

o

o

o

o

J

oo

0z

1.6

1.4

1.2

1.0

.8

.6

.4

00

X=I.0077, X=1.309

X=.5119

/

X=.1621 [

GASL

f" _i 338

X =.06126

I Ix='°_i000 2000 3000 4000 5000

Pressure, Newtons/Meter e

FIG. 112_ PRESSURE PROFILES AT SURFACE COORDINATE

LOCATIONS X=.01683, X=.06126, X=.11338,

X=.1621, X=.5119, X=I.0077, AND X=1.309

METERS, ALTITUDE = 71,000 METERS145

n66 36859 - nasa o nasa contractor report no. 66109 gasl technical report no. 605 numerical flow...

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