Aerothermodynamics of the Mars Global Surveyor Spacecraft

NASA/CR-1998-206941

Aerothermodynamics Surveyor Spacecraft

Russell

W. Shane

and Robert

of the Mars

Global

H. Tolson

Joint Institute for Advancement of Flight Sciences The George Washington University Langley Research Center, Hampton, Virginia

National Aeronautics and Space Administration Langley Research Center Hampton, Virginia 23681-2199

March

1998

Prepared for Langley Research Center under Cooperative Agreement NCCI-104

Available NASA

from the following:

Center

800 Elkridge Linthicum

for AeroSpace Landing

Heights,

(301) 621-0390

Information

Road MD 21090-2934

(CASI)

National

Technical

Information

5285 Port Royal Road Springfield, VA 22161-2171 (703) 487-4650

Service

(NTIS)

Abstract

The

aerothennodynamic

characteristics

and reported.

results

investigated planners

to design

Monte

Carlo

spacecraft

computer

heating.

phase

were

spacecraft

spacecraft

contingency

influence

codes

have been

the

Mars

Global

Surveyor

used by the Mars

Global

Surveyor

of the mission.

Analytical

with

three-dimensional

used

aerobraking

a detailed,

characteristics

and

for flight

spacecraft

Direct

mission Simulation

model

in free

are

of

molecular

the and

flow regimes.

The

highly

the aerobraking

to evaluate

transitional

These

of

is found

configurations.

dependent drag

to be aerodynamically

Aerodynamic

on atmospheric coefficient.

Attitude

control

forces,

density.

Transitional

moments,

Accommodation

flow

effects

thruster

plumes

are shown

the effectiveness

of the attitude

control

system

plume-freestream

interaction

effects

stable

are found

iii

and

in aerobraking and

heating

coefficient

are found

and are

is seen

to reduce

overall

to interact

with the freestream,

even

to thrust

to be highly

leading dependent

found

to be

to strongly solar

panel

diminishing

reversal.

on freestream

planned

These

density.

i |

|

Table Abstract

............................................................................................

Table

of

Contents

of

Symbols

List

of

Tables

List

of

Figures

1.

Introduction

2.

Mars Global

Surveyor

Aerobraking

Maneuver

,

,

°

Flow

..................................................................................

vi

vii

...................................................................................

viii

.............................................................................

Aerobraking Spacecraft

Mission

and Spacecraft ....................

and Configurations

' .......

.................................

Aerobraking 5.1 5.2 Sating

Configuration Results ............................................. Aerodynamics ............................................................ Aerodynamic Heating ...................................................

Configuration 6.1. Aerodynamics 6.2. Aerodynamic

Freestream

Conclusions

References

Results ...................................................... ............................................................ Heating ...................................................

Gas - Thruster

Plume

Interaction

...............................

A.

Appendix

B.

9 9 12 14 17 18 23 29 29 30

Aerobraking Configuration ............................................. Sating Configuration ....................................................

31 31 34

..............................................................................

36

........................................................................................

Appendix

5 5 7

Maneuver ..................................................... Configurations ..................................................

Regimes and Solution Methods ........................................... 4.1 Classification of Regimes and Kinetic Theory ....................... 4.2 Free Molecular Flow Solution Methods ................................. 4.3 Transitional Flow Solution Methods .....................................

7.1 7.2

8.

v

....................................................................................

3.1 3.2 ,

iii

...............................................................................

List

.

of Contents

Computational Simulation

Tools of Gas

.........................................................

Characteristics

v

.......................................

38 79 92

List of Symbols

D

drag force

L

lift force

M

moment

P

pressure shear

stress

q

rate of energy

transfer

V

freestream

velocity

P_ A

freestream

density

local area reference

area

reference

length

drag coefficient,

C D = D / (0.5p,V_

Cc

lift coefficient,

C L = L / (0.5p_V.

Cd

flat plate drag coefficient

CM

moment

c.

local

Cp

pressure

Cs

shear

m

molecular

T_

freestream

gas temperature

spacecraft

surface

coefficient,

heat transfer

2 Ar_ )

C M = M / (0.5p.V. coefficient,

coefficient,

coefficient,

2 A_f )

2 A_r Lr,r )

CH = q / (0.Sp_V_

3A )

Cp = p / (0.5p_V.'-) C s = x / (0.59_V_

2)

mass

temperature

S

speed

k

Boltzmann

O

energy

accommodation

Gn

normal

momentum

Ot

tangential

ratio

normal

constant coefficient

accorrunodation

momentum component

accommodation

coefficient coefficient

of momentum

_p

tangential

component

E_

direction

cosine

of flow with respect

to surface

element

X axis

Ey

direction

cosine

of flow with respect

to surface

element

Y axis

N

molecular

number

of momentum

density

mean free path Kn

0

Knudsen

number

freestream

incidence

angle

freestream

incidence

angle

vi

List of Tables

Table

5.1

Force

Table

5.2

Moment

Table

7.1

Drag,

coefficients

for

coefficients lift,

and

moments

aerobraking for

configuration

aerobraking for aerobraking

vii

..................................

configuration with

thruster

............................... firing ....................

48 48 74

List of Figures

Figure

2.1

Mars

Global

Surveyor

spacecraft

Figure

3.1

Original

Figure

3.2

MGS

Figure

3.3

MGS

sating

configuration

Figure

3.4

MGS

revised

safing

Figure

4.1

Flow

regimes

Figure

4.2

Flat

plate

drag

coefficient

for various

speed

Figure

4.3

Flat

plate

drag

coefficient

for various

temperatures

Figure

4.4

Flat plate

Figure

5.1

Freestream

Figure

5.2

Density

contours

for

Figure

5.3

Density

contours

for

Figure

5.4

Drag

and lift coefficients

vs. yaw angle,

Figui'e

5.5

Drag

and lift coefficients

vs. pitch

Figure

5.6

Moment

coefficients

vs. yaw

Figure

5.7

Moment

coefficients

vs. pitch

Figure

5.8

Free

Figure

5.9

Drag

coefficient

Figure

5.10

Drag

coefficient

normalized

by baseline

Figure

5.11

Drag

coefficient

normalized

by respective

Figure

5.12

Moment

coefficients

for various

Figure

5.13

Moment

coefficients

for various

Figure

5.14

Pressure,

Figure

5.15

Heat

Figure

5.16

Heat

transfer

coefficient

Figure

5.17

Heat

transfer

coefficient

contours,

o_ = +15 °, 0 = 90 ° ..........................

57

Figure

5.18

Heat

transfer

coefficient

contours,

ot = -30 °, 0 = 90 ° ...........................

58

Figure

5.19

Heat

transfer

coefficient

contours

Figure

5.20

Heat

transfer

coefficient

contour

aerobraking aerobraking

angle

molecular

transfer

configuration Figure

5.21

Mean

Figure

5.22

Velocity

Figure

5.23

Mean

free

for various

free

ratios

system,

molecular

flow flow

angle,

..............................

43

coefficients

44

aerobraking

panel

configuration.

configuration

path

above

revised

for various

above

areas

models

for free

above

sensor

viii

49

..........

49

............... .....

.....................

51 51

......

52

...........

53

detail...

53

flow ...........

54

o_ = +15 ° .............

55

deflections

coefficients, molecular

aerobraking

configuration

56

.....

59

aerobraking

..................................................

sensor

50

52

coefficients

flow;

50

o_ = +30 ° .....................................

lines for revised

power

...........

..........

for various

for transitional

47

deflections

accommodation

contours

sun

46

aerobraking

area for various

for revised

sun

45

...............

configuration

accommodation

contours,

............

configuration

vs. yaw angle,

contours

43

configuration

aerobraking

panel

42

field ....................................

aerobraking

of density

42

...............................

aerobraking

aerobraking

angle,

transfer

41

......................................................................... path

41

field ......................................

angle,

coefficients

coefficient

.........................

........................................

accommodation

reference

transitional

and heat

revised

.................................................

maneuvers

as function

magnitude free

aerobraking

moment

and

40

..........................................................

of incidence

shear,

original

configuration

coefficient

39

......................................................

configurations,

for

drag

scenario

..................................................

.............................................

shunt ................................................

6O 60 61 61

Figure

5.24

Velocity

Figure

5.25

Heat

Figure

5.26

Location

Figure

5.27

Heat

transfer

coefficient

along

panel

Figure

5.28

Heat

transfer

coefficient

along

panel

Figure

5.29

Heat

transfer

Figure

5.30

Heat

transfer

coefficient

contours,

Figure

5.31

Heat

transfer

coefficient

along

-Y inboard

Figure

5.32

Heat

transfer

coefficient

along

-Y outboard

Figure

5.33

Heat

transfer

coefficient

along

+Y inboard

Figure

5.34

Heat

transfer

coefficient

along

+Y outboard

Figure

6.1

Freestream

Figure

6.2

Moment

Figure

6.3

Heat

Figure

6.4

Heat transfer

transfer

6.5

coefficient

Density

7.3

Pressure, with Yaw

moment

diagonals

densities

...........

63

diagonals,

9 = 120 kg/km 3..............

63

diagonals,

9 -- 60 kg/km 3...............

64

diagonals; 0 ° and

-Y panel

30 ° panel

sweeps

diagonal

diagonal

for sating

...................

65 66 66

.............................

67

...........................

67

configurations

configuration sating

64

............................

diagonal

sating

-Y axis .......

.............................

diagonal

system

revised

along

.......

......................

configuration

................

........................................................

along

plume;

and heat transfer

aerobraking

configuration

configuration contours

with thruster

of aerobraking

..............

71

firing ........

72

configuration

with density,

aerobraking

73

with thruster

firing

at o_ = 0 ° ............................................................................. Figure

7.5

Yaw

Figure

7.6

Location

Figure

7.7

Pressure

Figure

7.8

Heat

Figure

7.9

Pitching

Figure

A. 1

Inner

Figure

A.2a

Normalized

number

of simulated

Figure

A.2b

Normalized

number

of simulated

Figure

A.3a

Drag

coefficient

before

Figure

A.3b

Drag

coefficient

at

Figure

A.4a

Lift

coefficient

before

Figure

A.4b

Lift

coefficient

at

coefficient,

of simulated

and

69

70

...................................................................

variation

transfer

68

70

........................................................

plot of aerobraking

coefficient

68

outer panel diagonal,

thruster

firing

moment

62

..............................

angle;

configuration

thruster

for various

62

along inner panel diagonal,

coefficient

shear,

panel

configuration

contour

panel

contours;

coefficient

of simulated

Figure

outboard

for pitch

sating

7.2

diagonal

angle reference

revised

Figure

shunt ............................................

panel

along

coefficient

Heat transfer

Location

and

incidence

power

along

of inboard

safing

7.1

7.4

coefficient

transfer

Figure

Figure

above

coefficients

revised Figure

magnitude

aerobraking thruster

contours

contours

plumes, of sating

for sating

moment

coefficient;

outer

computational

sating

configuration

with

molecules

steady

molecules

firing ......................

configuration

...................

with thruster

with thruster

configuration

domains

steady

thruster

configuration

sating

before

steady

at steady

76

firing .......

78

model ................

86

state ..............

87

state ....................

state ...............................................

state .................................................

state .......................................................

_[x

75

77

with thruster

spacecraft

tiring ....

75

firing ...........

state .....................................................

steady

steady

with

74

87 88 88 89 89

Figure

A.5a

Lift

to drag

ratio

before

Figure

A.5b

Lift

to

ratio

at

Figure

A.6a

Surface

collision

sampling

Figure

A.6b

Surface

collision

sampling

drag

steady

steady

state ...............................................

state ..................................................... before

steady

at steady

X

state ...................................

state .........................................

90 90 91 91

1 INTRODUCTION

The

Mars

characterizing two years, orbiter

Global

the planet

Mars'

launched

"'Aerobraking" spacecraft

orbital

measurements.

energy

aerothermodynamic

research

discussed. be rugged

enough

aerobraking

and

description

Control

of the mission

The spacecraft

of the various

System

this

was

on September

of

Every of an

successfully

11, 1997,

and was

propulsion. being to

report

is

used

the

to reduce

onset

intended

aerobraking

of

to and

the

scientific

ascertain to

the

study

the

(ACS). designed

to perform

an aerobraking

spacecraft

properties.

(MGS),

prior

during

with the goal

Each pair is to consist

Surveyor

orbit

and the spacecraft

in the mission

surface

is presently

MGS

was designed

to perform its role

of

and

chemical

the in

by NASA

Mars.

at Mars

atmosphere

characteristics

goals

arrived

presented

field,

Global

circularize

initiated

towards

Mars

MGS

upper

and

of the Attitude

The

gravity

orbit using conventional in the

The

effectiveness

orbiter,

7, 1996.

into an elliptical

has been

will be launched

The first

on November

Program

atmosphere,

a pair of spacecraft

and a lander.

captured

Surveyor

to carry

a number

maneuver.

will follow.

configurations

them

of scientific

A discussion This

out will first

discussion

employed

experiments

yet

of the history

of

will also

for flight

be

through

include

a

the Martian

atmosphere. Aerobraking molecule

and

Navier-Stokes used.

in the atmosphere

transition

regimes.

equations

cannot

The characteristics

used to obtain Results spacecraft

configurations

60

3.

kg/km

The

Since

at altitudes

conventional

be applied

of these flow

aerodynamic using

is performed

to these

regimes

where

numerical flow

the flow is in the free

methods

regimes,

will be presented,

based

on

the

must

be

other

methods

along

with the methods

coefficients.

analytical

and

for freestream

aerodynamic

forces,

statistical densities moments,

methods above and

will and

be below

heating

of

presented

for

the nominal the

various value

aerobraking

of and

contingencyconfigurationsarediscussed.Finally, the effectivenessof the attitudecontrol systemfor flight through the transitionalregimeis investigated.The interactionbetween the gasplumeof an attitudecontrolthrusterandthe freestreamflow is analyzedfor both configurations.

2

MARS GLOBAL SPA CECRAFT

SURVEYOR

MISSION

AND

Mission The basic goals

of the Mars Global

1) Characterize

the surface

2) Determine

the global

character

Establish

the global

evaluate polar

These

goals

instruments.

The

reflectometer,

This

mapping

weather

uses atmospheric

fields,

radio

smacture

scientific

through

of the atmosphere

and thermal

of

payload

a

structure

to on the

system,

orbit

thermal

the use to create

over

consisting

magnetometer

Data will be taken

mapping

friction

a

consists

relay

field,

and clouds.

with

for radio science.

sun-synchronous

and gravitational

of the weather

dust,

payload

altimeter,

resolution,

and mineralogical

and thermal

impact

achieved

orbit will be acquired

type of maneuver desired

laser

oscillator

near-polar,

to be

at high spatial

material,

atmospheric

instrument

camera,

and ultra stable altitude,

are

are to:

thermophysical,

of the magnetic

the seasonal

caps,

morphology

topographical

the nature

5) Monitor

Mission

elemental,

of the surface

3) Def'me the global 4)

Surveyor

and

emission

of two

of an aerobraking drag and reduce

electron

in a low-

Martian

maneuver

orbital

six

spectrometer,

with the spacecraft

a period

of

energy

years. _.

This

until the

orbit is achieved.

Spacecraft The Mars and

consists

arrays,

Global

of four

Surveyor

subassemblies:

and communication

antennas.

Spacecraft the The

was

equipment spacecraft

built

by Lockheed

module, is shown

Martin

propulsion in Figure

Astronautics module,

2.1.

solar

The equipment

module

houses

the avionics

1.22 x 1.22 x 0.76

meters.

All of the

the nadir equipment

deck

on the +Z side.

The thrusters,

propulsion

module

and propellant

tanks.

on the

the thermal

-Z direction),

and one for roll control

in a mono-propellant, The two solar

length

blankets.

and

1.85

comprised

which

m in width.

Each

of gallium

are mounted decrease

arrays,

arsenide

The structure

which

provide array

propulsion

modules

via electrically

orientation

of the solar

array

power

the main

attitude

engine,

shaped

box

1.06

per comer;

to the others).

to

control

m on a side,

two aft facing Each

of an inner

cells, respectively.

and

measure

0.81

during

the solar powered

assembly

for the spacecraft,

consists

coefficient

supports

are attached

thrusters

normal

and measures

thruster

(in

burns

mode.

and silicon

ballistic

are three

(oriented

on the ends of both arrays

the spacecraft's

contains

instruments

the magnetometer

of a rectangular

There

pulse

except

-Z side

It consists

not including

hydrazine

instruments

and science

gimbals

can

and

outer

"Drag

flaps"

m in length.

aerobraking

array

is herein

panel

3.53 which

made

The

m in are

of kapton

flaps

serve

to

1.

and connects

be adjusted

measure

it to the equipment

referred

to as the yoke.

by activating

the inner

and The

and outer

i

gimbals.

In an uncoupled

coupled,

they

respect

protective

the panel

these

gimbals

assembly

provide

to achieve

rotation a large

about number

the X or Y axes. of orientations

If with

to the main body. The

During

allow

mode,

primary

aerobraking, cover

communication the

remains

HGA attached.

antenna remains

is the

stowed

1.5 meter

against

the

high

gain

equipment

antenna module

(HGA). and

its

3.

AEROBRAKING

3.1

Aerobraking refers

or planetary

the latter usually trajectory

involves

however,

drag

usually

over a very

ranging

from

structure

pass

been

applied

was performed multiple

passes

through

of a spacecraft

upper

Aerobraking,

mission

gradually

Venus'

to circularize

upper

provided

mission the

atmosphere

orbit. in

at altitudes to study

also allowed

atmosphere

once;

Experiments,

an opportunity They

upper

only

the primary

and Termination

atmosphere.

in a planetary

and most of the

is achieved

After

aerobraked

the Windmill

of the Venusian

planetary

to Venus.

was

experiments

flyby

atmosphere.

during

These

in that

a hyperbolic

is quick

and the total drag

mission

spacecraft

from

the atmosphere.

a previous

the Magellan

the Magellan

made

in

atmosphere

from aerocapture

Aerocapture

through

the upper

the

the study

of

mainly

of

consisting

dioxide 2'3'4'5'6. The

that such maneuver

use of aerobraking

a maneuver must

will gradually circular

a single

the upper

140 - 170 kin.

the aerodynamics carbon

during

landing.

through

has

and behavior

an object

of passes

achieved,

the spacecraft

to capture

period

goals

which

differs

a longer

it was used during

aerobraking

Aerobraking

over

specifically,

Further

to create drag.

orbit or immediate

place

number

Aerobraking

were

CONFIGURATIONS

the size of an orbit by using

using the atmosphere

is obtained takes

large

to changing

satellite

into an elliptical

total desired

AND

Maneuver

Aerobraking of a planet

MANEUVER

has been

be successful

considered

Aerobraking velocity

for scientific occurs

Global

Surveyor

in a critical

for the primary

alter the spacecraft

orbit needed

the spacecraft

in the Mars

orbit from

mission

part goals

the highly

mission

marks

of a planetary

the first mission.

to be realized.

elliptical

capture

time The

Aerobraking

orbit

to a nearly

measurements.

near the orbit periapsis.

and thus energy.

The reduction

Drag

induced

of energy

by aerobraking at periapsis

reduces

decreases

the

apoapsisaltitude. After severalmonths,theapoapsisis decreased to the requiredaltitude andtheperiapsisis thenincreasedto terminatethe aerobrakingmaneuver. In the case of MGS, the aerobrakingmaneuverwill progressively lower the spacecraftfrom its captureorbit (56,600 km altitudeapoapsis,353km altitudeperiapsis) downto a nearlycircular orbit (450km altitudeapoapsis,350 km periapsis). The original planwasfor this maneuverto be accomplished in thethreephasesshownin Figure3.1 The first phase,which lastedelevenorbits, loweredthe periapsisto 110km using propulsiveimpulsesat apoapsiswith theattitudecontrol thrusters. This gradual"walk-in" wasnecessitated by thelargeuncertaintyin theatmosphericdensitymodel andallowedtime to studythealtitudinalandtemporalvariabilityof the atmosphere. The secondor mainphasewasto follow andlast aboutthreemonths. MGS was to make300-400successive passesthroughtheatmosphereat 110 km, bringing the apoapsis down to 2000km. The last phase,or endgame,was to takeaboutthreeweeks. During this time, the apoapsisaltitudewould be loweredto its final value of 450 km, and periapsisgradually raisedto 143km. Aerobrakingwould endwith a terminationburn to raisethe periapsisto its final altitudeof 350km. Theplanwasalteredshortlyinto the mainphasewhen the flight dynamicpressure, coupledwith the structuralconditionof the panel(discussedin next section),causedpanel deflectionsand vibrations that greatly reducedthe panel's structuralintegrity. Mission engineersdecidedthatthe dynamicpressureattheplannedaltitudeof 110km would not be safeandthat the mainaerobraldngphasewould haveto takeplaceat an altitudeof about 120 "kin altitude about

or greater, rneans

eight

mapping equivalent

depending

less drag

months

orbit.

for each pass

of additional

The aerodynamic

AV decrease

on the altitudinal through

time forces

to the during

of 1300 m/s

6

variation

of dynamic

the atmosphere. aerobraking aerobraking

pressure.

Thus, maneuver

are expected

A higher

the new

plan

adds

to reach

the

final

to account

for an

3.2

Spacecraft

Configurations

The solar panels their

orientation

spacecraft

are the main

is the most

and its stability

The originally The solar panels the panels

significant

planned

are swept

launch

factor

aerobraking

out,

30 ° relative

to the Y axis,

exposed

and insertion

remained

suspected

that

thereby

causing

yoke.

Recent

structural

with

by mission

that the hinge the

aerobraking

configuration.

The

configuration,

is shown

To obtain

full

new

in Figure

damper

the secured -Y panel

position,

solar

cells

sweep

would

In configuration.

the

event

are now

This

of

on the

from

the inner

yoke.

It was

shortly

between

that

after

the inner

that a second

launch,

panel

and

incidence

of

interface.

engineers

referred

the aerodynamic revised

to as the

the

revised

torques

aerobraking aerobraking

3.2.

ensuring

exposed

the -Y panel

assembly

51 o from

the -Y axis

that any deflection

damper

arm

doubling

to the freestream;

are addressed

is first instead

of the array as a mechanical

aerodynamic

and

rotated of 30*. would

180 ° This be into

"stop". heating

The issues

in this report.

contingencies,

configuration

joint

discovered

of the

broke

determined

MGS

hereafter

3.2.

lie on the side of

it was

to the plane

not be able to withstand

maneuver,

ceils

in Figure

The array,

mechanism

has

configuration,

while

the solar

into place.

at the yoke-gimbal

with the wedged

to this configuration

of drag

is shown

trajectory,

into the hinge

engineers

configuration,

the revised

the 30 ° panel

As such,

flow.

extension

the -Y axis, and the yoke is then oriented

retains

related

and locked

to wedge

may have occurred

Concerned

about

arm

and

into an interplanetary

in the deployment

analysis

the amount

for MGS

to the freeslxeam

20.5 ° from

the damper

failure

associated

about

a shaft

of the spacecraft.

in determining

configuration

the -Y solar array had not fully deployed panel

structures

characteristics.

that are not directly

After

drag producing

will cause

the

MGS

spacecraft

the spacecraft

can

to roll over

adopt

a

"sating"

until the solar

arrays

arealignedin the directionof the sun. This allows the navigationteamto be fairly certain of the MGS attitudeatthe endof a dragpass. To achievethis orientationfrom the aerobrakingconfiguration,the spacecraftinner gimbalsarerotated650abouttheY axistowardthe HGA. This configurationcanbe seen in Figure 3.3. aerobraking shown

There is a

configuration;

in Figure

revised

sating

configuration

in this case, the panels

3.4.

8

are rotated

associated 65 ° away

with from

the

revised

the HGA,

as

4

FLOW

REGIMES

Aerobraking atmosphere transition

of

where flow

AND

the

spacecraft

the gas is highly

regimes.

SOLUTION

will

be

rarefied.

A discussion

METHODS

conducted

This region

of these

flow

throughout contains

regimes

a region

the free

of

molecule

and the methods

the and

of analysis

for each follow.

4.1

Classification

of Regimes

Two gas molecules the centers path

will collide

of the molecule

is defined

molecules.

It is inversely

gas in equilibrium be determined

to the molecular

distance

traveled

proportional

with molecules

Kinetic

if their trajectories

decreases

as the average

and

Theory are such that the distance

diameter

d. The

by a molecule

to molecular

that are treated

number as hard

between density

spheres,

molecular

mean free

collisions

with other

(molecules/m3). the mean

d is the molecular

Classification The regime.

of mean

diameter

and N is the local number

density

of the mixture

free

The parameter

path often

is an important

parameter

used to classify

in determining

the regimes

L is some characteristic

reference

length.

Free molecular

of their energy

The differences collisions

between

regimes

arise

is analyzed.

9

when

type

of flow

number,

(2)

the molecules

will give up a fraction

the

is the Knudsen

flow for Kn in the range

surface

7.

Regimes

to exist for Kn > 10, and transitional

surface.

flee path X, can

(1)

Kn = -L where

For a

from, 1 = _--2 v27rd N

where

between

flow is usually 0.1 - 10.0.

and momentum molecular

upon

behavior

considered

In both regimes, collision before

with a and

after

In free moleculeflow, the moleculesare not consideredto significantly interact with the freestreamafterreflectionwith a surface. Or, conversely,a freestreammolecule can be expectedto travel the distancefrom upstreamof the spacecraftto the spacecraft surfacewithout encounteringanothermolecule. Likewise, the moleculewill only impact the spacecraftonce. Transitionalflow occurswhen intermolecularcollisions becomesignificant and cannotbe ignored. As thesecollisions increasein number and significance,the flow approaches thecontinuumregime. A moreaccuratedeterminationof Kn is obtainedby using the local evaluated

in the

flow

field

significant

collisions

molecules

and freestream

Figure

4.1

between

over

spacecraft regime

the atmospheric

around

periapsis,

regime.

In

Knudsen

numbers,

spacecraft

molecules

plot. density

where

properties

at Mars

in the

freestream,

since

between

the reflected

(or

and MGS

spacecraft

will take place

In the course

regime

any local)

at high altitudes

to deep

Kn is about in the

0.2, which

Magellan regime

that is being

10

20-30

pass,

was

the

into the transition

regime.

It can be seen

is well into the transition

mission

performed

flow

at higher

dominates.

encountered

in the regime

in a Mach-

in the Mach

of an aerobraking

out into the free molecular

the free molecular

the type of regime

aerodynamic

of the Magellan

spectrum.

density,

aerobraking

of

take place

Aerobraking

and then back

periapsis

contrast,

would

instead

free path,

7

from the free molecular

that at the nominal

Once

spacecraft

the trajectories

number

passes

the

molecules.

shows

Reynolds-Knudsen range

near

mean

is determined,

must be performed.

the evaluation

of

Kinetic

Theory The velocity

molecular

level.

distribution moment

diso'ibution

Macroscopic

function. provides

A gas

in form.

each species

in the gas.

equation,

which

the velocity

of the Boltzmann

method

provides

these

be applied The particular

situation.

significant

obtained

method

set of problems

the equilibrium

for viscous

stress

the monatomic

assuming

1st

which

is for

is the Boltzmann

terms and

by simplifying method

Maxwellian

and heat flux

perturbation Thus,

would

yield

or solving

provides

a solution

the distribution form.

function

Derivation

that can

the

of this

be substituted

of the Navier-Stokes from equilibrium,

the Navier-Stokes

into

equations. which

would

equations

cannot

depends

on

8

a solution

For free molecular

situation

the

is needed

in principle

in which

gas form

a small

gas problems

of obtaining

the

function function

solution

must be obtained

on the size of flow gradients.

and thus collision simplifies

from

to obtain

to most rarefied

density,

flow regime

S. The Chapman-Enskog

for a restricted

amount

are obtained

a restriction

analysis

manner

expressions

equations

However,

greatly

equation

by a small

conservation

imply

in some

of the

7.

distribution

whose

at the

moments

gas

distribution

in the rarefied

equation

give

temperature

velocity

of a gas

by obtaining

would

a separate

equation

description

for each gas constituent.

gas dynamics

equation

is perturbed

gas,

is an integro-differential function

yields

a Maxwellian

The pertinent

distribution

can be computed

and the 2nd moment has

a statistical

the Oth moment

For a polyatomic

Any rarefied Boltzmann

example,

in equilibrium

exponential

provides

gas properties

For

velocity,

function

flow,

to the

Boltzmann

intermolecular

may be eliminated enables

an

8.

11

from

analytical,

equation

collisions

by definition

the Boltzmann closed

form

equation. solution

the

are not This to

be

4.2

Free

Molecular

Analytical and assuming the velocity material

for free

an equilibrium

velocity

temperature

properties

parameter

of

modeled

energy

characterize

Solution

equations

and

The

Flow

molecular

is defined

as accommodation

of energy

q_ and

cL. represent

qw is the energy

Diffuse

reflection is given

the

incident

to a perfectly

momentum

accommodation

_

is

are functions

of the

spacecraft,

an

important to a surface

parameter upon

of and

used

collision.

and tangential

qi - q, q, - qw

to This

elastic

energy

to reflection thermal

In this case, collision,

coefficient

(3)

and reflected

fluxes,

with surface accommodation

q_ = q,_ and

where

is also

cL.= q_ and

defined,

and

respectively (wall)

7.

The

temperature

T_.

where

o = 1.

all molecular

Specular

thus _ = 0. is usually

reflection

An analogous

decomposed

components. momentum

accommodation

a.

where

collisions

coefficients.

to complete

up to the surface.

The normal

equations

temperature

up by a molecule

flux that pertains

corresponds

corresponds

normal

by disregarding

by,

variable

energy

the

coefficient given

are derived The resulting

the freestream,

a -

where

flow

distribution.

accommodation

the amount

Methods

1"1is the normal

component

coefficient

is defined

as,

= r/, - r/_____ r/i - rL

of momentum.

The tangential

(4)

coefficient

is determined

from,

at

:

_Oi

--

_0r

_Pi

--

_Pw

12

(5)

into

with tangentialmomentumcomponentq0. For diffuse reflection, all momentum is transferredto the surface. However, for specularreflection, the normal componentof momentumis reversedwhile thetangentialpartremainsunchanged. Anothervariablein the free molecularequationsis the speedratio, which replaces theMach numberin rarefiedflow regimes. This parameteris defined as the ratio of the ffeestream,or spacecraft,velocityto themeanmolecularvelocity. Foraerobrakingat Mars or Venus, the free molecularequationsshow a greaterdependenceon accommodation coefficientthanon speedratio or spacecraftsurfacetemperature. Figure4.2 containsa plot of flat platedragcoefficientvs. incidenceanglefor free molecularflow attwo differentspeedratios. Dragcoefficienthasbeennormalizedby the flat plateprojectedareawhich varieswith incidenceangle. For MGS, the speedratio at walk-in wasabout20 andis 14for the original endgame.Note thatthe valuein Cd at 900 incidenceincreasesby only 3% for a 30%decreasein speedratio from 20 to 14. Thus, changesin spacecraftvelocitywill not havea largeeffectondragcoefficient. Figure 4.3 shows the variation of drag coefficient with wall and freestream temperatures TwandT, respectively.At most, Cd only changes1.4% for a 50% increase in

Tw.

This

accuracy line

allows

in predicting

drag

on drag

coefficient.

effect

also not essential The

because greater

of

coefficients

the normal

coefficient

a lower

cy, means

the momentum

accommodation

uncertainty

coefficient.

drag

a precise

coefficient

is shown

knowledge

less diffuse

lead

with

in Figure

is decreased

can

temperature

without

a loss

T w, variation

of freestream

of

in T

has

temperature

is

C d.

that is imparted

coefficient

in spacecraft

Also note that for a given

Thus,

in determining

variation

accommodation when

considerable

from

4.4.

to a surface.

amount.

13

and

tangential

C_ decreases

1.0 to 0.9.

reflection;

to drag

normal

the

This

closer

predictions

that

by as much

significant to specular

Consequently, are

momentum

a 10% in error

as 10%

change

arises

reflection, uncertainty by

the

the in same

Thus, the assumptionof an accommodationcoefficient is very important in evaluatingtheaerodynamics of a spacecraftin free molecularand transitionalflow. In the Magellan Windmill Experiment, accommodationcoefficient was found to vary with freestreamincidenceangle3"4.In the TerminationExperiment,it was difficult to ascertain the accommodation coefficientof the spacecraftbecauseof exhaustplumes,dependence on incidenceangle, andotherfactors. The value

lay somewhere

between

With this in mind, and momentum conservative

value,

since

amount

are

Boltzmarm tracking

more

equation

collide

Direct

is set,

and

computed

for

the and

equation

the

readily

to receive

that the

assumed

be considered

energy

to be a very

the greatest

amount

transitional

flow

s.

sample

of

are handled.

collisions intermolecular

Carlo

analytical

solution

available itself,

simulation

physics

of

molecules

of heating

the

gas

prevent

yet

flow. a time

the

This leaves

the

necessitates

the

to solve

solutions

throughout

the integro-

direct do

simulation

not

This

solve

the

involves

the

period

in which

with a surface.

differs

from

In other

methods,

are deterministic.

That

collisions

terms.

function

Direct

the

of collision

methods

distribution

model

Monte

form,

are numerical

obtained

in

by elimination

velocity

but rather

Simulation

that collisions

in this report

This would

collisions

with each other and perhaps

manner

was

Methods

intermolecular

There

of a representative

molecules

the spacecraft

The lack of a closed

methods.

equation

solutions

of

to be solved.

use of numerical

performed

of 1.0.

Solution

of the Boltzmann

full equation

differential

coefficients

Flow

significance

simplification

be made

1.0 2.3

of the analyses

it allows

that could

of drag.

Transitional

The

most

accommodation

and the lowest

4.3

0.8 and

only conclusion

occur

14

earlier

simulation

methods

an initial configuration is,

when

the

trajectories

two

trajectories

in the

of molecules

of molecules converge

are to the

moleculardiameter. For eachtrajectory,all other moleculesare examinedas possible collision partners. In DSMC, however, the collision computationsare DSMC

has been found

be applied

to a larger

collisions

number

take place,

quantities

that the change that should

significant

requirements

variations

are

several

at least

times

shock

twenty

the speed

the case of a boundary accurately

match

The binary For

collisions a discrete

equation two

motion those

in every

probabilistic

in increments

step

are

size,

Yet, strict do not create

time step,

studies

for

a

so long

to time step

gradients

and

example,

not critical size

grid resolution flow

them

For

such

showed

and these

as

is not that in

solutions

solution 9. is related

the

to the

molecular

This allows

but distinct

as cell

sample

dimensions

time per molecule. from

to define

and

is advanced

ratio of cell

do not restrict

cell and the treatment

step,

particles

the

grids

of all the particles of

per cell

In addition,

have

application.

and time

and

Time

such

the cell size

layer,

coarse

parameters

in which

are needed partners,

must

and deviations

the particular

6.

are decoupled.

pairs

on

of the shock

approach

time

consecutive

wave,

molecules

a fine-grid

DSMC

are not necessary Simulation

Cells

The cells

collision

and can

the method

collision

each cell is small.

with the mean

are dependent

of a strong

molecular

methods

8.

region.

into cells.

a solution.

across

in results.

of molecules

simulation there

in flow properties

to these

identify

to discuss

the simulation

is sub-divided

to generate

than the earlier

In order

to discuss

in question,

used

intensive

situations.

in DSMC

be small in comparison

adherence

number

region

of the body

macroscopic

of flow

it is first necessary

The simulated the geometry

to be less computationally

probabilistic

events

Boltzmann of these

motion

the simulated in one

and

is deterministic)

which

have

been

means).

15

collisions collision

gas particle

time step.

(which

equation

identified

as

the

restriction

as instantaneous terms

of

the

to be considered

Specifically, followed

by

there

events. Boltzmann in terms

of

is a collisionless

by a motionless collision

to

partners

collision (through

of

In essence,

a single

time step consists

1) Collisionless

motion

2) Enforcement

of boundary

3) Pairing

of collision

4) Collision

sampling

sampling There popular

are many

model

diameter

uniform,

isotropic

proportional

Collision collision

partner

Using assigned

the probability less,

acceptance-rejection

(VHS)

permitted.

depending

cross

The collision

on

velocities

is proportional

section.

A molecule

generated probability

will not collide s.

A

model,

the

In addition,

section,

which

is

velocities. The

probability

to the product

of their

is then determined

of a relative

to be a collision

method. numbers,

every

is then compared

the collision

A method

by randomly

collision

used

of molecules selecting

pair

in

to this random

pair is accepted.

that is often

is to limit the number

This is done

cross

function.

in a gas

In this

of the molecules.

collision

a probability

characteristics.

model.

of the molecular

using

than the number,

method

actual collision

molecular

The

of the acceptance-rejection

for collisions.

flow quantities,

to simulate

of the relative

are paired

molecules

is greater

the molecules

considered

is

a set of randomly

a number.

partners.

for macroscopic

of d, is a function

and total collision by application

collision

hard sphere

scattering

two

partners.

that attempt

d is a function

partners

between

velocities

models

to the square

conditions.

frequency.

is the variable

molecular

of particles.

of selected

5) Possible

of:

a cell

number.

If

If the probability

in conjunction that

are

a number

is

is

with the

allowed

to be

of molecules

in

each cell. The

VHS

acceptance-rejection

model, method

decoupling

of

are implemented

molecular

motion

in the LaRC

16

and

3D DSMC

collisions, algorithm

and 1°.

the

5. AEROBRAKING The design

aerodynamics

phase

a simpler

be

kg/km 3 to twice Unless

accommodation

results

were

investigated

in this report

spacecraft.

model,

presented

to freestream

Appendix.

Surveyor

RESULTS

Even though

the overall

reflect

during

the

the aerothermodynamic

the earlier

aerodynamic

earlier

results

were

obtained

have

been

validated

trends

herein. will

corresponding

the

for

free

densities nominal

otherwise

molecular

ranging

value.

noted,

a value

flow,

from

1/20

and of

for

the

Freestream

characteristics

of 1.0 was

used

transitional

nominal

flow

density

are

given

for momentum

and

of

in the energy

coefficients.

The reference freestream

flight

computational

Results

Global

L_. The

of the actual

and are discussed

60

of Mars

of the mission

characteristics using

CONFIGURATION

velocity

system vector

for freestream

relative

angle

to body-fixed

of incidence

is shown

axes is related

in Figure

5.1.

The

by:

V x = -V sincz sin0

V v = V sincz cos0

V z = V cos(X

Flow

Field The aerodynamics

the spacecraft. transitional change

As discussed

flow regimes.

as the spacecraft

in Figures

of the spacecraft earlier,

These

5.2 and 5.3 using

aerobraking

regimes

penetrates

are directly

results

takes

will cause

deeper

influenced place

the flow

with DSMC

in the free

field around

into the atmosphere.

obtained

by the flow

molecular

and

the spacecraft

This variation

for freestream

field around

flow

to

is exhibited along

the Z

axis. Figure the free

5.2

molecular

shows

a normalized

regime.

The flow

number field

around

17

density

contour

plot of carbon

dioxide

in

the spacecraft

can be seen

to take

the

form of a relatively large and diffuse gas layer. This flow structure was achievedby runningtheDSMCcodein collisiordessmode. This modedoesnot allow inter-molecular collisions but differs from free molecularanalyticalcode in that the moleculeshave a thermal

velocit3'

velocity

of a molecule

random

component

velocity.

no sharp

flow

relative

The field

associated

with

their

motion.

to the freestream

contribution

boundaries

velocity

of this velocity in regions

The and

can

component

behind

thermal

velocity

be viewed

is the reason

spacecraft

gaps

or edges,

is the

as being

a

why

there

are

such

as at the

end of the drag flap. As the flow Figure now

regime

5.3 is a density taken

moments,

5.1.

layer.

at a density This

layer

the

gas

layer

becomes

of 60 kg/km 3. The influences

the

flow

smaller. field has

aerodynamic

forces,

on the spacecraft.

Aerodynamics

by

Drag,

normal

as

much

aerobraking, as

20 ° .

for a range

Lift,

and

Values flow

Reference

area

surface

the spacecraft

This

situation

angles and area

5.5, respectively.

and

may deviate

necessitated

the

from

evaluation

zero angle of

of

spacecraft

of angles.

and moment

coefficients

at a density

length

are also

of

120

given.

of the computational

from the tip of one solar panel Drag

attitude

Moments

of force

freestream

distance

to transitional,

plot for flight

of a thin shock

and heating

aerodynamics

frontal

contour

the form

During attack

progresses

kg/km 3 can Reference

model;

area

reference

configuration

be found

in Tables

corresponds length

for various

to the

is usually

I and

2.

projected

taken

as the

to the other.

lift coefficients

are plotted

Yaw

here to refer

is defined

for the original

vs. yaw

18

and pitch

to flow confined

angles

in Figures

to the Y-Z

plane

5.4 and (0 = 0°),

andpitch

refers

expected,

drag

change

to flow restricted is greatest

C D values

of Figure

at ct = 0 ° and

not be discounted

of equipment

drag; this is inherent

shock

layer

incoming

that

flow develops

freestream

The decrease

effects

reduce

upstream

molecules.

in drag

when

over the time of the whole

drag

Yaw and pitching

selected

angles

C._,y and C_

spacecraft

due to transitional

an individual

for free molecular

of the

This results

considering added

by about

pass.

moments

The

effects

However,

moment;

can be ascribed flow reduces Figure configuration

however,

there

to asymmetries the slope 5.8

contains

to demonstrate

a free

shields

in attitude reduction

figures,

and

between

free

flow

to

because

it by

the

scattering

on the spacecraft. is not large

is indeed

when

significant

implies

molecular

that the stability

the curves

19

validate

notably

plot

up to 30 °

are included

for

slope

earlier

and transitional

a slight decrease

characteristics

are maintained.

results

in pitching

most

moment

of incidence

at 0 ° and negative

molecule

difference

the Y-Z plane,

which

of angle

(null moment

is a significant

of the curve

10-11%

is reduced

and shear

Transitional

of MGS

in these

about

partially

as functions

5.6 and 5.7.

It can be seen that there is little difference yaw

the

in comparison

attitudes. Drag

pressure

in the event

maneuver.

stability

vs. c0 is exhibited

11%.

and variation

are plotted

flow in Figures as well.

in lower

flight

up for

by the HGA

are to be considered

and planned

drag

makes

to drag

of lift coefficient

as

less difference

gain antenna

The contribution

that,

10% out to a 30 °

with even

the high

configurations

design

5.4 shows

by about

variation

Also note the insignificance

to the spacecraft

Transitional

a similar

incidence.

flight

Figure

changes

15 °. This is because

if ahemate

malfunction.

(0 = 90°).

and only

5.5 reveals

most of the drag that is lost with non-zero should

plane

at zero incidence,

in c_. Inspection

between

to the X-Z

moment the HGA.

revised

of the original

for

results values

values

_. for

which

Transitional

in stability. the

for

aerobraldng configuration

Variation

with The

revised

Freestream

variation

of drag

aerobraking

12, and

rrgs and angles These

not contain

values

the two

in Figure

the increase

Knudsen

5.9.

velocity

Results

in this figure.

models.

is inversely

lead to a smaller

density

was

investigated

were obtained

3 kg/km 3. The freestream

are plotted

namely, number

freestream

for the

for density

magnitude

was

cases

of

kept timed at

o_ = 0 = 0 °.

between

differences,

with

Drag coefficients

drag flaps are included

agreement

Knudsen

coefficient

configuration.

p = 150, 120.60, 4811

Density

The trends

Differences

in reference

proportional number,

an earlier

can

length,

increasing

which

be attributed

with the addition

to reference

model

did

of C D vs. p are in very

in values

length

thereby

from

of drag

an increase

transitional

effects

good

to model

flaps.

Since

in length

would

and

decreasing

C D• A functional corresponding

curve

form

for

is shown

C D vs.

p was

in the figure.

C D=I:860-0.1733*X-2.866*10 This curve

lies within

limit of 2.13

as density

approaches

in that it clearly

densities.

It also demonstrates Careful

zero.

predicts

appears

examination

that

two

model whether actual

shows

the

this trend

same

is:

with

2,

the

This

is useful

curve

coefficient

variation

a curve

different

[Wilmoth,

further

R.,

artifact

to expect

of transitional

effects

aLl the points

could

be

the

molecular

planners

for a wide

fit through

and

range

drawn;

to understand

The

in each model. one

with results

communication].

of

with density.

for both models.

to the characteristics

study may be warranted

2O

to mission

trend

private due

the free

an unusual

slopes

and

(6)

and approaches

drag

results

X=log_0[p/1.2E-7]

one for la > 12 kg/km 3. Comparison trend

current

in the plot,

5.9 reveals

below

is a computational

flow phenomenon;

what

of Figure

curves

p < 12 kg/km 3 and another

This function

the non-linear

value at 12 kg/km 3 lies significantly It

for

2*X

3% of all the points

engineers

obtained

curve from

for

a third

It is uncertain of the cells this situation.

or an

Flexible

Solar The

ability

Panel

partial

deployment

to treat it as rigid and lead

flexible

panel.

determined constant

During

spring

gave a prediction

cruise,

constant

early

in the

vibration the

tests

panel.

at the maximum

such a deflection

mission

of the aerodynamics

for

of 10 ° of deflection

of the effect

array

to the examination

interplanetary

an approximate

The determination was

of the -Y solar

would

eliminated

associated

were

the with a

performed

which

Analysis

using

spring

expected

dynamic

have on spacecraft

this

pressure.

drag

coefficient

investigated. Three

were

analyzed.

5.10

compares

deflection drag

density

cases

This deflection the drag

gives

limits

coefficient

by

the

or, the effect

is essentially

throughout

projected

due to the 6% reduction

the higher

densities.

At

much

area.

of the panel.

both

drag

cases.

is reduced

area.

panel

In this figure, normalization

when

the panel

in flee molecular

This difference

p = 120 kg/km 3, there

is a 9%

line

Figure

This

This

The 6% difference

in projected

"hinge"

of 40.5 °.

or a 6% difference.

area for

of how

- yoke

sweep

deflection

to 0.944,

reference

the panel

an effective

with and without

estimation

of reduced

l0 ° about

the -Y panel

nominal

a non-dimensional

deflected,

gives

an area ratio A_f_o / Arof0 equal

is normalized

provides

with the panel deflected

is CD

is maintained

difference

in drag

coefficient. It shouId

be noted

the actual projected area

and

is obtained

consistency

from

for each factor

occurs

the value for area tends

is due

to the discretization

same

model

the

this area must

5.11 is a plot comparing

areas

as a possible difference

which

with the results,

Figure reference

area,

that although

configuration.

in differences

at the highest

density

as the

to be an overestimation

method,

aerodynamic

it is indeed results.

of

a relevant

To

maintain

be used.

values

that have

This normalization in drag

coefficient.

of 120.

density.

21

The

been

normalized removes

The

coefficients

only differ

by the respective

projected relatively by about

area

effects

significant 3% at this

For a given referencelength,an increasein densitywill decreasethe meanfree path and decreaseKnudsen number. A lower Knudsen number meansan increasein transitionaleffects. Thus,this distinction in dragcoefficientvaluesmight be explainedby transitionaleffects and would accountfor the remaining 3% CD difference not due to reducedarea. This analysisshowsthatthe changein dragwith paneldeflectionis mostly dueto reductionof projectedareaandtransitionaleffectsare not significant. In addition to the curvesjust discussed,a databasecontainingforcesand momentsasfunctions of density, attitude,andpaneldeflectionis very usefulto missionengineersfor it providesa methodto estimatetheactualpaneldeflectionfrom measuredquantities. It is importantto notethatfor both 0° and 10° deflectioncases,the freestreamwas alignedalong the spacecraft+Z axis, which is not an equilibrium orientationfor the 10° deflection. The corresponding

Variation

equilibrium

to an equilibrium

of

Equilibrium

In addition coefficient,

and -Y panels.

raised

5.12

The

original

with

values

of

coefficients around

the equilibrium

with

0.8,

accommodation

at 1.0).

coefficient

of the -Y panel accommodation

moment

Figure

the 5.13

angle.

22

-Y

strongly

cell side

coefficients

between

the +Y

was analyzed. vs.

coefficients

shows

(yoke

a detailed

drag

the solar

coefficient

panel

influences

to expose

or trim, angle

accommodation

for

the two curves,

Coefficient

with AC = 1.0 is compared 0.6

between

Accommodation

a plot of yaw

and

halfway

5 °.

of this on equilibrium,

configuration

kept constant

of about

of unequal

and momentum

1.0,

lie approximately

The "flipping"

the issue

contains

configurations

flow.

deflection,

earlier.

The effect

Figure

angle

Angle

to panel

as discussed

to the freestream

various

C D would

incidence

(AC) for free

to the revised and

flap

angle

for

molecular

configuration accommodation

view in the range

of values

Notethatthetrim angleshifts almosttwo degreesfrom the original configuration to the revisedwhile acco_runodation coefficientis kept fixed at 1.0. This is due to the increasedsweepof the +Y panel;equilibriumshifts in the direction of reducedprojected area. The trim angle then shifts almost three degreesfrom the new position when accommodation coefficientis decreased to 0.8. The changeis almostsix degreesfor the extremecaseof AC = 0.6. The value of 0.8 is not unrealisticsince results from the Windmill Experiment showed normal and tangential momentum accommodation coefficientsto benearly0.8for a 300panelsweep4. This in itself may not appearto be significant. But, it cannotbe discountedwhen othervariablesthataffecttrim angle,suchas atmosphericwinds andpaneldeflection, also produce2° - 5° of changein trim angle. Contributionsfrom wind andpaneldeflection wereseenin datafrom earlyaerobrakingpasses.

5.2

Aerodynamic

Heating

rate calculations

the spacecraft protective design

design

phase,

molecular

is different collisionless

in the middle, because

The thickness

investigate flow gives

to the greater

mode.

designers

calculations

as seen in Figure due

at a freestream

to help

Recent

and further

on the panel,

occurs

phase

paints _.

Free

lower

Heating

confirm

panel

yoke

pressure,

angle).

These

shock

decreases

that were

shear,

thermal

insulation

discovered

and heat

configuration contours

during

layer

transfer

in and the

on the yoke

obtained near

with DSMC

the panel

displayed

in Figure

5.15.

that scatters

incoming

freestream

as the panel

23

edge,

distribution

(distribution

were

the heat load is higher

as seen in the orientations

of this layer

trends

panel

performed

heating.

a uniform

flow,

of 120 kg/km 3 were

lay out solar

5.14 with the revised

For transitional

of the upstream

density

or undisturbed

This

flow

edges

in and

difference molecules.

boundary,

is

approached. The fewer the moleculesthatreachthe middle of the panel, the lower the amountof energy,or heat,thatis transferredto thesurface. Figure5.15 comparesthe nominalcase(a = 0°, cases

where

the flow

0 = +_ 15°). Figure

is at an incidence

The panels

5.16 compares

similar

trends.

incidence,

that are inclined the nominal

Figures

5.17

respectively,

heating

along

less exposed for the determine

when

to the flow; The

if and where

contain

the flow is confined The -30 ° incidence

however,

variation

into the flow

5.18

the shear

of C H with flow

any excessive

receive

cases

greater

for

flow

z axis)

case receives

angle

may occur

(c_ = + 15 °,

heating

as expected.

cases

which

( 0 = 90°).

slightly

show

allows

during

-30 °

Notice

less heating

for this case would

incidence

with

at o_ =_+ 15 ° and

to the XZ plane

coefficient

heating

along

15 ° in the YZ plane

case to the + 30 ° (0 = 0 °) incidence

and

the panel edges.

15 °.

of approximately

e = 0 °, flow

as it is

be greater

mission

the

than

engineers

the mission,

to

and to plan

accordingly.

Aerodynamic

Heating

Heating on one panel Figure

trends are now

5.19 shows

for

for the revised exposed

angle

relative

are shown evidenced

in Figure by lower

5.20.

contours

incidence

configuration

to the incident

Aerobraking configuration

to the freestream

heat transfer

of 120 kg/km 3 and 0 ° flow from the original

Revised

Configuration were

and must

over the whole to the spacecraft.

is that the -Y yoke receives flow is greater. The

heat transfer

scattering

Contour

24

not exceed

since

the solar cells

temperature

limits.

spacecraft

for a freestream

density

The

significant

only

less heating

lines over

of molecules

coefficients.

investigated

from

difference

than the +Y since its

the -Y panel the center

and drag of the panel

flap is

Local

there

Heating

for

The

field characteristics

flow

would

instruments

be any

the diode

comers,

with

velocity

shunt,

and sensor

the sensor

7" long,

3" wide,

vicinity

the solar

on

diode

is nearest

near

the instruments

of the sensor.

The

The magnitude

on

to determine

the

panels.

if

These

The power

shunt

is located

of the inboard

panel

on opposing

panel.

The

local

mean

free

path

on

and

were determined. from

indicated.

2" high.

evaluated

mounted

an edge

outboard

free path vs. distance

and

were

and sun sensor.

the

of the sensor

panel

instruments

are located

of the flow just above

with the location

Configuration

about

heating

a power

The local mean 5.21

Aerobraking

excessive

included

the yoke;

Revised

the panel

centerline

The dimensions

mean

free

path

of velocity,

is shown

of the sun

is about

as shown

sensor

2 cm,

in Figure

in Figure

or 0.8 5.22,

are about in.,

in the

is about

150

m/s.

The mean free path above 100 m/s,

as seen

in Figures

measures

approximately A comparison

values

and

associated

freestream the heating

since

of heat

transfer

does

regime

Variation were

particularly

characteristics

m/s).

the flow

engineers

density,

free

236

Heating

Mission

and

shunt

5.24,

path

and

Therefore, not exhibit

Each

in), and the velocity section

of the

shunt

1" in height. width

size and

and

height

flow velocities

there

are

that

are subsonic

no shocks

continuum

shows

directly

characteristics,

the

(speed

above

heat

the

transfer

is not an issue.

with

Freestream in the

for the revised

coefficent

3 cm (1.2

respectively.

to insmament

interested

of the solar

is about

2" in width,

of the instrument

with the continuum

Aerodynamic

variation

of mean

is approximately

instruments,

5.23

12" in length,

of k are on the order

of sound

the power

variation

of solar

configuration.

arrays across

Density

over

25

This allowed

a wide range

the inner

and

panel

outer

of flight panels

heating them

to know

conditions. for

with

a number

The of

freestreamdensitieswascalculatedto assisttheengineersin developing

solar

panel

thermal

models. In Figure panel

diagonal

diagonal

strong

for

starts

and outer

5.25,

either

diagonal

for

respectively. shown panel

in Figures inboard

The

outboard

in Figure

5.26.

of lower

outboard

panel

outboard

curves

heating

panel

molecular

layer

diagonal

off more

as seen

there,

Figure

Thus, 5.30

angle,

or sweep,

sweep

to non-zero

presents

is compared sweep

effects

this u'end to the

comparison

120

nearest

the

There

lower

using

assembly

C.

of each panel

26

is a to 3

contours. none

member

the inboard. along

and

kg/km _,

60

inboard

a

panel,

as

for the outboard and

thus a larger values

between

for the

inboard

and

is approached.

the

evenly

with

There

overall

being

at some

incidence

molecules

outboard

is little

are fairly

inner

distance

distance

of the panel.

for a case where

to the panel.

transitional

of

incidence,

the

the shielding

both panels

gives

regime

towards

Each

than

than the inner

For a non-zero

panel

thus increasing

that is, the flow is at 0 ° incidence panels.

the

The

decreases

of C H vs.

is due to the freestream

assembly.

5.26.

panel

12 kg/km 3, the differences

panels

along

along

heating This

inner

3 kg/km 3.

in length.

with diagonal

5.19.

By

of C. between

pushed

the comer

rapidly

and

the

free molecular.

are plots

as the free molecular

to the panel

get

from

along

As density

at densities

less edge

in Figure

are insignificant

plot of C H vs. distance

between

has

inches

for the outboard

panels

starts

12,

densities.

which

outboard

than for the inboard.

with respect

inboard

and

by 60

distance

in Figure

approaches

are greater 5.28,

60,

as shown

for the higher

and

the outboard

This variation angle

5.27

C Hdrops

than the inboard;

region

effects

against

120,

in width

as the flow regime

transitional

both

150,

the yoke,

73 inches

the panel

is little variation

This is exhibited

nearest

about

is plotted

densities:

comer

in C H across

In addition,

coefficient

freestream

measures

variation

kg/km 3, there

five

from

panel

heat transfer

and Figure

-Y panel

create

the

a thicker

5.29

is along

difference

above

contains

a

the -Y axis;

in center

region

CH

distributed. A panel (panel reveals

along

assembly

at some

Y axis).

that this angular

A zero effect

canbeappliedto a singleflat plate,not just a collectionof them. For example,inspection of the inboardpanelwith sweepshowsthatthe centerregionof onehalf of the panelhas greaterheatingthantheotherhalf. Comparingthis to the no-sweepinboardpanelmember revealsno differencein centerregionheatingthroughoutthemember.

Aerodynamic

Heating

A similar spacecraft

for

analysis

was

in the case where

objective

Alternate

a configuration

altitude

in the event

of excessive

density,

and presumably

panel

analysis,

to create

aerobraking

was modified

kept

referred

sweep

heating.

the aerodynamic

is reduced

is to give the ability

heating.

In order

a larger

from

to raise

A raise in altitude

area.

heating

the nominal

mean

the same

the

aerobraking

lower

amount

This is achieved

on

30 ° . The

the spacecraft

would

to maintain

projected

The

baseline

configuration 5.31

panels,

sweeps

atmospheric of drag,

by reducing

the the

configuration.

panel.

All results difference

area

oriented

to the Y axis.

to as the baseline

along This

The trim angle

of 18.4 ° for the

for

the

reduced

at 0 ° incidence and 5.32 contain

Figures were obtained

occurs

referred

-Y panel,

the -Y axis,

new

and

and the +Y

configuration

for such

in this

will

be

a configuration

is

15.4 ° for the +Y panel

at its trim angle.

respectively,

baseline

was

configuration.

to be 18.15 m 2. Comparing

Figures outboard

is oriented

henceforth

that the -Y panel

sweep

effective

projected

configuration,

of 33.8 ° relative

to as the reduced

if the spacecraft

estimated

such

at a sweep

-18.4 °. This gives

heating

to investigate

sweep. The revised

panel

lower

must be oriented

performed

the solar panel

for such

panels

Configuration

sweep

this to the projected gives a 4% increase plots

and

5.34

at a density

at the comers.

27

distance

are compared the

of 120 kg/km

The largest

an

attitude

of 17.44

is

m 2 for the

in area for the new orientation.

Values contain

at such

area value

of C a vs. diagonal

for the -Y panel. 5.33

configuration

same 3. For

along

inboard

to those

information the -Y panel,

AC n for the inboard

is 20%,

and

for

the

for the

+Y

the largest while

for

the outboardit is 10%. For the +Y panel,the largestinboardAC H is outboard

it is approximately The reduced is obtained

heating

are both directly

altitude

must be raised

the same time. of heating

However, velocity same

is reduced,

altitude

is proportional increase which

configuration

at a "cost"

proportional to where

when

the 20% AC_ flight

reducing

drag

nothing

at a higher

analysis where

as the altitude

before

17%.

of heating.

is gained.

is eliminated, altitude

assumes

Thus,

Since

To reduce

eliminating

an increase drag

and

heating,

the

the gain

in drag

would

maintain

the same

a constant

periapsis

velocity.

the increase

the gain in drag is removed.

will be nullified

for the

at

amount

sweep.

then the altitude

to V 3. Thus,

by about

the same percentage

to density,

the preceeding

at which

increases

of roughly

In other words,

and drag

11%;

17%.

sweep

in drag

about

the drag

a gain in drag can be achieved

without

is raised increase.

Drag

is removed

is proportional

with a velocity Therefore,

any penalty

28

in heating

in aerodynamic

is not the

to V 2, but heating

reduction,

there

If the

is some heating.

the heating altitude

at

6.

SAFING

6.1

CONFIGURATION

Aerodynamics

In the event

of contingencies,

safing

configuration.

mode

and so the fuel usage

will have

During

to restrain.

orientation of MGS

RESULTS

relative

flight

this maneuver, will depend

The

nature

was therefore

the attitude

an event

control

over

a wide

MGS

system

moments

precludes

at the beginning

investigated

will command

on the maximum

of such

to the freestream

software

the

is in a rate limiting

that the control

knowledge

system

of the spacecraft

of its occurrence.

range

to adopt

The aerodynamics

of orientations,

but confined

within

the X-Z plane. The

reference

configurations

system

is shown

approximately

for

in Figure

with the equilibrium

of stability

are

more

determined

from,

angle 6.1.

angle.

obvious.

The

of

incidence

This

for

reference

both

system

That is, zero incidence

components

of

the

original

and

is chosen is chosen

freestream

revised

to coincide

so that regions

velocity

vector

are

configuration

is

are presented

at

V x = V cos_

V z = V sinot Pitching

plotted

Moments

and

Stability

The moment

coefficient

as a function

of pitch

15 ° intervals presented

results

the Y axis CMy for the original

in Figure

6.2.

coefficients

Free

(AC)

density

suggest

coefficient

of 120 kg/km that

of 1.0 would

using

the

provide

29

molecular

of 1.0 and 0.8;

0 °, 30 °, 60 °, 120 °, 180 °, and

to a freestream

These accommodation

angle

for accommodation

for the angles

correspond

about

-135 °.

sating results

transitional

All n'ansitional

results

are

flow

results

values

with

3.

free

molecular

a conservative

moment

estimate

of fuel usage

since

theseare the greatestvalues. Note thattransitionaleffectsserveto decreasethe moments andaremostsignificantat -135° and60°. Inspectionof the curve at c_= 0° suggeststhat the stabletrim angle is a few degreesbelow the X-Y plane, noting that it is sensitive to assumptions about accommodation coefficient. This uncertaintyin trim angle is a considerationfor attitude controlaftersating. Also, thereis anunstableequilibriumat 180°, while -60° and 120° are near-equilibrium. MomentsaboutX andZ are not shown becausetheir magnitudesare no greater than0.01over thecompleterangeof incidenceangles_.

6.2

Aerodynamic

A thermal the

regions

Heating

analysis

of the revised

of greatest

heating

spacecraft

at the approximate

120 kg/km

3.

on

the

6.3 shows

C H over

around

the upper

portion

of the panel,

arises

at the lower,

diagonal

2 for the

Diagonal

2 begins

C a gradient

exists

in gradients

the revised

sating

configurations. panel

thermal

the inboard

Heat

coefficients

heat edge,

is plotted

in Figures as shown

to determine

for a freestream

Greater

coefficient

panels

performed

transfer

the leading

6.4

in Figure

the

density

of

transfer while

against and

for

is visible

less

distance

6.5, 6.3.

heating along

respectively. A stronger

than the outboard.

for the aerobraking

encounters

to supplement

was

spacecraft.

near the yoke,

but not in maximum

This information

panel.

is now

transfer

panel

with C a trends

configuration

model

which

outboard

comer

configuration

of o_ = 7 ° were obtained

the whole

Heat

and

in the upper

A comparison difference

edge.

inboard

along

solar

trim angle

Figure

trailing

sating

configuration

heat transfer. less overall

heating

was used by the mission that existing

3O

An important

show

distinction

than the revised

engineers

for the aerobraking

a significant

aerobraking

to help develop configuration.

is that

a solar

7. FREESTREAM INTERACTION Thruster attitude

firings

excursions,

plume

torques

freestream forces

from reaching

on the spacecraft

Surveyor

7.1

and

z3'_.

significant

interaction has

predicted

by considering

data

prevent

large

the thruster

gas

Experiment

in

for aerodynamic

the effects

may

of a spacecraft.

between

the Termination

and

plume

operations,

of the interaction

some

of the incident

This interaction

will redistribute

moments.

found

the freestream

to planned

effects

during

flight

A thruster

portions

and induce

_2. The

between

best explained

certain

studies

spacecraft

interaction

between

been

revisited

effects

the Mars and

for

Global

investigated

the

Surveyor for both

Mars

Global

ACS

thruster

aerobraking

and

configurations.

Aerobraking A DSMC

0 ° incidence the original the -Y panel

simulation

aerobraking yoke

the thruster

from the freestream;

for the interaction

+Z axis)

was performed

configuration.

one thruster

at a freestream

The jet that is fired as indicated

and the freestream

density

is located in Figure

at

of 120 kg/km 3 for at the comer

7.1.

nearest

Thruster

plume

in the Appendix. fires,

the solar

in effect,

the plume

can be visualized

in Figure

density

between

and the high gain antenna

are given

When

this shadow

Configuration

(flow along

characteristics

number

were

due

Interaction

first discovered

Discrepancies

PLUME

aerobraking

rate control.

and freestream

Additional

during

flow were

mission.

plume

- THRUSTER

occur

or attitude

on the spacecraft

between

sating

may

and the freestream

the Magellan

plumes

GAS

of CO 2, the dominant

panel creates 7.2,

species

closest

to the thruster

a "shadow" a contour

on the panel.

gas mixture.

shielded

The formation

plot of the normalized

in the freestream

31

is partially

of

molecular

In Figure

7.3,

the effect of the shadow is evident in contoursof pressure,shear, and heattransfer coefficient. The plume effect on drag and pitching momentis significant. The plume interactionwill inducea 7 N, or 15%,decrease yaw

moment.

Given

opposite

in direction

moment

of 3.2

termed

"thrust

direction,

a thruster to the 2.6

N-m

were

freestream

is a torque

dimensional yokes

the small

stowing

angle.

Table

along

portion

cases

contains

For

of the inner

panel

result

the net has

a moment

been in one

on freestream

of 60 and moment

analysis,

that is left after

density.

40 kgJkm 3 at the zero values

lift, and moment

this plume

thus,

is

direction.

yaw

with the net drag,

respectively.

to induce

for dependence

density

7.1

is fired

This

in total

moment

fh-ing;

intended.

non-desired

investigated

in aerodynamic

by the thruster

to the one

change

and

their

contributions

the yoke cutting

non-

from

is defined

the comers

the

here to to permit

for launch. The

table

appreciable main

were

and a 5.8 N-m

increase

induced

in the opposite,

the additional

coefficients,

the

if a thruster

for

and inner panels,

include

torque

in direction

effects

obtained

incidence

of 3 N,

In essence,

Plume-freestream Results

N-m

is opposite

reversal".

the result

force

in total drag

also

difference

body

includes between

(equipment

The table values As expected, squares

yaw

fit was

spacecraft

to extrapolate

the values

and propulsion

values

for

being

are plotted

can

be seen

to decrease

to draw

a curve

through

the results

the

for the panels

modules)

for yaw moment

moment used

moment

solar

array

shadowed

as a function with

to zero density,

There

and the total spacecraft partially

the

only.

three

where

data

in Figure

in density.

points

it is known

due to the

by the plume.

of density

a decrease

is an

for

7.4.

A least

the complete

that the moment

must

be zero. Since the effect the density

the yaw moment

of the plume is increased,

is positive,

at low densities there

is more

and the torque

is to diminish

the effectiveness

plume-freestream

32

produced

interaction

by the jet is negative, of the thruster. and

therefore

As more

shadowing. At torque.

P --

Beyond

28 kg/km 3, the

this

density,

total spacecraft

the

aerodynamic

pitching

moment

moment

is greater

is equal and

to the jet

thrust

reversal

Occurs.

It should is an order

be noted

of magnitude

that the pitching smaller

than

will

be used

moment

the

yaw

CMy is included moment

and

in the table

its variation

but its value

with

density

is

insignificant. Since attitude

the thrusters

deviations

ffeestream

interaction Figure

cases

from equilibrium

7.5 shows

with and without

is the same

at angles

for three

different First,

mission

previous

discussion,

avoiding

this would

have

must

incidence.

thrust

scenario

be made

in Figure

is at

reversal

angles

for the Attitude

to create

is beyond

the

and the natural

add negative

System

15 ° from

of angle

Transitional These

and a non-zero the

will occur

plume-

of incidence

flow

results

attitude

necessary

if such

desired

that employs

for

system

results

were

can be analyzed

an action

attitude before

restoring chosen torque

for simulation to the negative causes

effectiveness

during

the freestream

direction.

33

place.

is not

given

spacecraft

of

entry.

sufficient

aerodynamic

no significant

Extrapolating

the

encounters

to a non-zero to return

will fire for positive

commands

the

A method

is if a correction

is not affected.

aerobraking

the

atmospheric

is desired,

However,

takes

before

moment

angle

torque.

the use of thrusters

interaction

and thus the ACS Control

to investigate

is 120 kg/km 3. The reference

+ 15 ° and 0 = 0 °.

30 kg/km 3, or even

7.5, the plume-fi-eestream

at positive

as a function

density

o_ = 0 °

angle of 0 °. The thruster This would

necessary

to correcting

situations.

be to acquire above

it was

in addition

of incidence.

coefficient

freestream

rates

15 as is the jet that is fired.

to be fired

densities

The second

equilibrium

The

if the spacecraft

would

attitude

a jet.

angles

moment

of c_ = 0 °, + 7 °, and

thrusters

atmospheric

yaw

angular

or other angles,

for non-zero

as that in Figure

obtained

attitude

effects

to control

moment. change

The the

current

thrusters the results

to the

angles

of

As seen

to the moment control

logic

to f'Lre if the (using

slope

of a curve fit through datapoints) to beyond 15° is difficult becausethe reduction of projectedareastarts to play a role and soon dominates. Interaction effects are not necessarilylinearwith angleoutsideof this range. However, an assumptionof linearity wouldrevealthatplume-frees_xeam interactionwill enhancetherestoringmoment. The third situationis the dampingof angularrates,such as angular velocity or acceleration.In this case, the thrusterwould be fired for negativeanglesof incidence. Negativeangleswouldcreatea positiverestoringaerodynamicmoment;the thrusterwould pulseto createa negativeyawmomentto damptherateof positiveangularmotion. The net aerodynamiceffect,asseenin the figure,is a significantlylargerrestoringmoment. This increasein yaw momentwould most likely induceangularmotion. This motion would decreasesomeof the dampinggainedby firing thethruster. The result is that althoughthe spacecraftremainsstable,the effectivenessof the ACS is diminished,possibly increasing theamountof propellantused. The plume simulation assumesa steady-statecondition and does not exactly reproduceflight conditionssuch as the number of thrustersthat are fired and specific impulse,which is a functionof propellanttank pressure. However, the simulationdoes providestrongevidence,alongwith Magellanmissionresults,that the situationcanoccur andshouldbe seriouslyconsideredby missionoperations.

7.2

Sating

Configuration

A DSMC plumes

simulation

and the freestream

120 kg/km 3. Referring opposite

was

done

to examine

for the original to Figure

7.6,

sating

the

interaction

configuration

the positions

between

two

at a freestream

of the two

thrusters

thruster

density

are on the

of side

the high gain antenna. Since

flow at positive

the only significant incidence,

interaction

between

a case was run for flow

34

the plumes

and freestream

at an c_ = 60 °.

This

angle

occurs was

for

chosen

to compareto the no-jet casepreviouslyinvestigated,and also since transitionaleffects appearto begreatestnearthis angle. The effectof theplumecanbeseenin Figures7.7 and7.8, which display contours of Cpand CH over the spacecraftin comparisonto the no-jetcase. The plume createsa shadowover the yoke andhalf the inboardpanel,creatingregionsof lower pressureand heattransfercoefficients. Pitchingmomentcoefficient,or momentaboutY axis, is plottedagainstincidence anglein Figure7.9; thejet andno-jet casesaredenotedat 600. It can be seenthat the momentis increasedby about 15% with the thrustersfired; that is, the magnitudeis decreased,makingit lessnegative. An angular rate damping analysis demonstratesthat the plume will help the effectivenessof the ACS. Foran angleof 60°, the naturalrestoringmomentis negative,as seenin the figure. The thrustersin questionwill fire to createa positive torqueaboutY in order to damp out the negativerate of angularmotion. With thrusters,the resulting aerodynamicmomentis lowerin magnitudethanthe originalmoment.Therefore,the trend is in thedirectionof reducingthe angularrate. It should be noted that the centerof mass location for the analysis of this configurationwasnot alteredfrom theaerobrakingconfigurationandremainedalongthe Z axis. A realisticcenterof masswould follow the panelsand lie off the Z axis in the directionof the +X axis. This movementwould affect the magnitudesof the preceding analysisbut not thetrends.

35

8.

CONCLUSIONS The aerodynamics

have been those

investigated

obtained

design

and aerodynamic for a wide

by other

the mission

for flight 2.13

was calculated

was

found

transitional In

and sating

transitional

drag

drag

coefficient

was

the

determined

was

found

flow

spacecraft

together

were

used

to help

to be aerodynamically drag

conditions

stable

coefficient

and a value density.

In

dependent

on

of

of 1.87 general,

11% from its free molecular

highly

with

operations.

periapsis

by about to be

results,

A maximum

nominal

coefficient

Surveyor

of this study,

configurations.

at twice

These

to assist mission

at free molecular

flow

reduce

conditions.

utilized

spacecraft

for aerobraking

flow effects

addition,

being

Surveyor

aerobraking

of flight

of the Mars Global

near the conclusion

and are currently

in both

for

range

researchers

The Mars Global

heating

value.

accommodation

coefficient. The trim angles

for both aerobraking

on the accommodation three degrees

coefficient.

for a 20% variation

Heat

transfer

dependent

produce

high gradients

near the panel

greater

heating

than

regions.

panel

flow effects

the trim angle

will shift

almost

Transitional

flow

coefficient. atmospheric

edges,

These

are also dependent

creating

gradients

at the outboard

density. edges

decrease

panels

and corners with

that receive

freestream

due to the angular

density.

sweep

of the

assembly. Thruster

drag

are stronger

on

configurations

mode,

in accommodation

effects

Transitional

sating

In aerobraking

is strongly

the inner

and

by

15%

moment

plume and

opposite

dependent

- freestream

creates

thrust

in direction

on freestream

effects

will not significantly

reduce

the effectiveness

interaction reversal.

The

to the one

density impact

and

intended.

begins

changes

of the Attitude

in the aerobraking tiring Such

to occur in attitude

Control

36

of one

System

configuration

thruster

a reversal at about

to restore when

may

is found

28 kg/km 3. equilibrium, damping

reduces

create

a net

to be highly Interaction but they will

of angular

rates

is

desired. Plume-freestream interactioneffectsin the satingconfigurationwill increasethe effectivenessof theACS.

37

REFERENCES

Dallas, S.S., "Mars Global Surveyor Aerospace Conference, Vol.4, Feb.

.

Mission", 1-8, 1997,

Cestero, F.J.,"An Exploratory Analysis Characteristics during the Termination Washington University, August 1997.

,

Proceedings pp. 173-189.

of the Magellan Aerodynamic Experiment," M.S. Thesis, George

Tolson, R.H., Patterson, M.T., and Lyons, D.T., "Magellan Termination Experiments," International Symposium Space CNES, Toulouse, France, June 1995.

.

Espiritu, R.C., Characteristics

.

February

and Tolson, R.H., "Determining Using Magellan Attitude Control

Windmill and Flight Dynamics,

Venusian Upper Atmosphere Data," AAS Paper 95-152,

1995.

Rault. D.F.,"Aerodynamic Characteristics of the Magellan Upper Atmosphere," Journal of Spacecraft and Rockets, 1994. pp. 537-542.

,

of 1997 IEEE

Spacecraft in the Venus Vol. 31, No. 4, July

Lyons, D.T., "Aerobraking Magellan: Plan versus Reality," Astronautic Sciences, 87, part II, 1994, pp. 663-680.

.

Bird, G.A.,

,

Molecular

Gas Dynamics,

Bird, G.A., Molecular Gas Dynamics Clarendon Press, Oxford, 1994.

8.

.

Haas, B., "Flow Body flows,"

Resolution

AIAA

Paper

Clarendon

and the Direct

and Domain 93-2806,

Press,

Influence

Advances

Oxford,

Simulation

in Rarefied

in the

1976. of Gas Flows,

Hypersonic

Blunt-

July 1993.

10.

Rault, D.F., "Aerodynamic Characteristics of the Shuttle Orbiter at High Altitudes," Journal of Spacecraft and Rockets, Vol. 31, No. 6, Nov. 1994, pp. 944 - 952.

11.

Rault, D.F., Aerobraking 1996.

12.

Rault, D.F., "RCS Plume Effect on Spacecraft Aerodynamics During Aerobraking Maneuver," 20th International Symposium on Rarefied Gas Dynamics, Institute of Mechanics, CAS, Beijing, China, August 1996.

13.

Woronowicz, M.S. and Rault, D.F.,"Direct Simulation Monte Carlo Prediction of On-Orbit Contaminant Deposit Levels for HALOE," NASA TM 109069, August 1994.

14.

Beguelin, A., Dongarra, J., Geist, A., Manchek, User's Guide to PVM Parallel Virtual Machine," ORNL/TM-

Cestero, F.J., and Shane, R.W.,"Spaceraft Aerodynamics During Maneuver in Planetary Atmospheres," AIAA Paper 96-1890, June

11826,

July 1991.

38

R., and Sunderam, Oak Ridge National

V., "A Lab.,

High-Gain Antenna Main Propulsion Module

Engine

AACS Thruster S

Drag Flap

1 of 4

Solar Array Solar Array

+y

Nadir

Deck

Figure 2.1. Mars Global Surveyor

39

Equipment Module

spacecraft.

Drag Flap

Initial Orbit Pedapsls _

- 352.8 lan

Period - 48 hours

Pedapsis altitude - 100 I_ Apoapsls altitude = 56608 to 450 Ion Period = 48 to 1.88 houm

End-Gam

Final O_It Periapsis aJtJtude= 350.8 km Apoapsis altitude ,- 450 km Period = 1.97 hours

Figure

3.1.

Original

aerobraldng

4O

scenario.

3°° ___J

30° +Y

Original

Aerobraklng

Configuration

(pre-launch] Solar Cells

+zT 3°.___,_7

....J .t"

33.s°

•

Revised

Figure

3.2.

Aerobraking

MGS

+y

Configuration

aerobraking

(post-launch)

configurations,

original

and revised.

n*

+×

+Z

P

+Y

Figure

3.3

MGS

sating

41

configuration.

Figure3.4. MGS revisedsatingconfiguration.

KNUDSEN

=

10.0

1.0

0.1

/

/

0.01

4O

Magellan

30

_

p__,o.,..,=/0.04 0_2 1.014.0 / II--B-_BB-II-IIIIIB

/ O l/OT /

_o

== =o

/ Free

0 10 .2

i

Mars/;Iobal

/

10 "1

10 °

/

Surveyor

//___..._o,,,m'

/._/

/

101

102

103

10 +

Reynolds number Figure

4.1.

Flow regimes

for aerobraking

42

maneuvers.

105

2,20 I

.....................................

....................

2.12

j

..........

...............

' ................

: .........

CJsin_ 2.08' '":

'E

........ :'"':":''. 2.00

;

i 10

;

....... I 20

;

J 30

:'": ,

"i ..........

! 40

i

_ ":'":

_ 50

:,

I 60

,

:

_':

I 70

i

......... t 80

;

t 90

O_

Figure

4.2.

Flat plate drag

coefficient

for various

speed ratios.

2.16

i

2.12

.....

Tw:4SO

K,T

: 150K

Tw = 300 Tw= 300

K'T-= K.T

150 = 100

Ca/sin(_ 2.08

2.04

.

. :.....

;

.

.

+

...... ;

2.00 0

: I

10

;

I

20

;

I

30

,

.:

+

.!

:

.

:

.

i

I

,

t

,

40

50

. :

:

I

,

60

-

. _

_

:

:

.

I

,

70

t

80

.

,

I

90

(X

Figure 4.3. Flat plate drag coefficient

43

for various temperatures.

K K

2.4

..................

2.3

2.2

Cd/sino_ 2.1

2.0 .

: .o

. . =13,

: Gi=O

.....

9- _ ................... _. i

•

"

!

_

;

......

.....

1.9 T./T

=2,

S_edRatm=20

,l_l,l,l_t_l,l,!

1.8 0

10

J 20

30

40

Figure 4.4. Flat plate drag coefficient

_

60

70

80

90

for various accommodation

44

coefficients.

+×

v

÷¥

Figure

5.1.

Freestream

angle

of incidence

reference

45

system,

aerobraking

configuration.

Ioglo [ N / N_ _

0.87 0.68 0.50 0.31 0.12 -0.06 -0.25 -0.44. -0.63 -0.81 - t.O0

Figure

5.2.

Density

contours

for free molecular

46

flow field.

IOglo [ Nco 2 i N_ ]

0.50 0.31 0.12 "0.06 -0.25 -0.44 -0.63 -0.81 -1.00

Figure

5.3.

Density

contours

47

for transitional

flow field.

CFX DSMC

CFX FreeMol

CFY DSMC

CFZ Free Mol

0 -10

0 0

-0.007 -0.008

-0.006 -0.001

-0.003 -0.30

0.000 -0.36

1.98 1.90

2.15 2.12

-15

15 15

0.065 0.066 -0.009 -0.008

0.13 0.13 -0.001

-0.51 .... 0.51 -0.95 0.95

1.82 1.82 1.50

-0.001

-0.43 0.42 -0.78 0.78

1.50

2.06 2.06 1.66 1.66

0.285 -0.309 0.586

0.514 -0.53 0.950

-0.002 -0.004 -0.002

1.9 1.9 1.66

1.98 2.06 1.66

15 -30 30 -15

9O

15 -30

90 90

Reference

Area

Table

Angle

An_le 0

1. Force

CMX DSMC

0 -10 -15 15 -30 30

0.003 0.092

15 15 0 0

0.13 -0.12 0.246 -0.238

-15 15 -30

90 9O 9O

0.003 0.003 0.003

coefficients

CMY DSMC

[

I configuration.

CMY

CMZ

Free Mol

DSMC

CMZ Free Mol

-0.001 -0.007 0.006 0.006 -0.007 -0.006

0.000 -0.001 0.003 0,002 -0.002 0.001

0.000 -0.001

-0.13 01238 -0.238

-0.001 -0.001 -0.005 0.005 -0.00i -0.001

-0.001 -0.001 -0.001

0.023 :0.025 0.046

0.044

0.000

-0.053 0.077

0.000 o0.001

0.000 0.000 0.000

-0.007 0.092 0.13

Area = 17.5 m" Length = 9 m

p = 120 2. Moment

3

for aerobraking

CMX Free Mol

Reference Reference

Table

0.000 0.000 0.000

= 17.5 m _

p = 120 kg/km

--

CFZ DSMC

CFY FreeMol

coefficients

kg/km

3

for aerobraking

48

configuration.

-0.007 0.007 -0.004 0.003

2.5

.........

.

Co

...........

•

.......................

2

•

i

...................

2.0

© 1.5(_

C D,

C L 1.0 Transitional,

0

I 0.5

Free

:

I

AC = 1.0

I

. Reference

CL

]

-0.5 -30

l

J

i

(_

Drag and lift coefficients

= 17.5

m t

............... o..............0

I 0

i

-15

5.4.

Area

o

!

0.0

Figure

AC = 1.0

Molecular,

,

,

[ 15

,

J

I 30

[(:leg]

vs. yaw angle,

aerobraking

configuration.

2.5

C D

2,0

CD_

CL

I

.....

0 ............................. 0 ............

0

10

I --

O

= 1.0= 1.0 i TrsnsitionaI, Free Molecular,AC AC - Roferln¢4

0.5

Area

= 17.S

I

mz

0

o

C L

o,o

0 ( ,,.

-o.5 -3o

a

t -15

_

_

t 0

_

,

I 15

or, [deg] Figure

5.5

Drag and lift coefficients

vs, pitch

49

angle,

aerobraking

configuration.

0.3

............

•

0.2

......

0.1

...........................

OrO

...........................

.........

................

CMx

-0.1

.........................................

-0.2

I t

-0.3 -30

_----_---

Free

i....

Molecular,

AC--1.0 _

Reference

Aree

Reference

Length

,

,

= 17.5

I ...... • .........

"........

_ _,.._.

m

= 9 m

I -15

,

,

I 0

,

J

I 15

,

,

I 30

O_

Figure

5.6.

0.10

Moment

coefficients

vs. yaw angle,

aerobraking

....................................

configuration.

- .........

0.05

CMy

i

i

i

i

o

!

!

i

o.oo

i

_ o

I

-o.o5 Reference

-0.10 -40

,

I -30

,

Length

I -20

= 9 m

,

I -10

,

I 0

T

I 10

,

1 20

O_

Figure

5.7.

Moment

coefficients

vs. pitch

5O

angle,

aerobraking

configuration.

0.4

.......

0.1 \ CMX

-o1°° ii i ii i ii _i i ii !i/i _i .o__i i il _,,i,=_7._'14mi _i ilil i_iii

-0,4 i i _ _ I i t -90-80-70-60-50-40-30-20-10

i

l 0

i i i i I i i i i 10 20 30 40 50 60 70 80 go

degrees

Figure

5.8.

Free

molecular

moment

coefficients

vs. yaw

angle,

revised

Coefficient

= 1

aerobraking.

with

Freestream V

Accommodation

Incidence

=4811

Angle

1

All Values

"0

2.3 = 0 °

m/e

2.2 Free

Molecule

Limit

i

2.1

: .........• ,_................ i.............................. i...........

C D .

2.0

. _.................

_',,:

:

? 1.9

.....

.........................

:

II b

!

--

.......

Early

Model,

Ct, = 1.860-

1.8

i

,

1.7 10-1o

,

,

No

Flaps,

0.1733"X

X = Iog,o

,,i

[p

=

DSMC,

A m = 13.31)3

- 2.866'10"'

1 1.2E-7

i

* X =. .!

]

z

i

-

•

_ •

: ............

.

•

rn z ....

-

•

i

]

10 g

i

AtJ

i

104

i

t

L

i

L = =i

i

10"7

p, kg/m 3 Figure

5.9.

Drag

coefficient

as function

51

of density

for various

models.

220

Free

Molecule

Limit,

0 ° Deflection

---n 2.10 Free

200

Molecule

limit,

10 ° deflection

----1

"

"...

:

........

:,.,

..............................

C D 190

1 80 [ -

-B-

[

-A--

-

-

0° Deflection,

Sweep

,0oOe|ioction,

= 30"6°'

Effective

A"_=

Sweep

17"44

m=

= 40.5°,A,,,= 44m':

I 17.

""

]

_',dk

1.70

1.60 10"1°

,

,

, .....

i 10"

,

,

,,

,,,,I

_

T _ = ....

10"i

I 10"z

9, kg/m 3 Figure 5.10. Drag coefficient

230

....................

normalized

by baseline area for various deflections.

: ......................

: .........................

, ..................

2.20 Free

2.10

Molecule

Limit

i

............. ...... n_ .............................

2.00 C D

.

I.go

-

D.............

1.80 I --J-I-.-_-

-

0°Deflection, 10 ° Deflection,

Sweep Effective =30.5°,A,-,=lT"44m= Sweep = 40.5

°, A,,_ = 16.47

m z ]:

1.70

1.60

L

I i

tJ=_l

=

I

_

10"

,,,,,I

i

I

,

10 "_

,,,,,t

t

,

=

10"_

p, kg/m 3 Figure 5. l 1. Drag coefficient

normalized

by respective

52

areas for various deflections.

05

0.4 .//-'"

........

"',..

0.3

.

_....

I ...=dCon.go.ot.o°..c =,o I

.........

..,,..d co,w_,.,_,, AC=0.8]

"_o

,.: y---...

OrtglnmlCordlgumtlon,

,,

,,7

\,

.

AC

= 1.0

0.2

0.1

:""

"_'k_:?.,.

I._, = 9

CMx 0.0

-0.1

-0,2

-75

-90

-60

-45

-30

- 15

0

15

30

45

60

75

I

I

I

_

[

I

I

I

I

I

I

I

I

I

[

_

1

1

I

I

l

_

[

[

I

I

I

I

I

1

I

'

[

I

I

-0.4

I

-0.3

90

0_ Figure

5.12.

Moment

coefficients

for various

panel

accommodation

coefficients.

0.2

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

_'",,..,. _,_ '- ,

- .... --

RevisedConfl_JraOon,AC= 1.0 Orlglml Corflgumtlon,AC= 1.0 I

........ .........

Revised Rev_ld

Configuration, ConllgurltJon,

AC AC

I

= 0,8 = 0.6

"',.,%

0.1 ..............

"""-...

A,,,,,= 17

CMx

F-

0.0

"'_"_...

I

I

I

l

I

I

I

I

I

-9

-8

-7

-6

-5

-4

-3

-2

-1

"'-.,,

I'"

-0.1 -10

0

1

2

3

4

5

6

7

8

_ 9

I 10

O_ Figure

5.13.

Moment

coefficients

for various

53

panel accommodation

coefficients,

detail.

C H H ,.

1.00 0.69 0.7_

i

0.67

i i

0.11 0.00

i i i i

Figure

5.14.

Pressure,

shear,

and heat

transfer

54

contours

for free molecular

flow.

o56 o. 0.33 0.22

C H

I

....

.78 0.69 0.60 0.43 0.35 0.26

I

0.17 0.52 0.09 0.00

o: = 15 ° e=-15 °

_ - 0°

_ - -15 ° e- 15 °

Figure 5.15.

Heat transfer coefficient

55

contours for transitional

flow.

C H

0.78 0.69 0.60

0.43 0.35 0.26 i

0.17 0.52 0.09 0.00

•, 30 ° 0 = 0°

_ ,, 0 o e - 0°

Figure 5.16.

_ - .30 ° 8 ,, 0 °

Heat transfer coefficient

56

contours.

I.

0.78 0.69 0.60 0.4.3 0.35 0.26

i

0.17 0.52 o.og 0.00

o_.. 15° 8.90 o

o_- 0 ° e-O °

Figure 5.17.

o_- -15 ° 9..90 °

Heat transfer coefficient

57

contours.

L

C H

0.60 0.43 0.35 0.26 I

0.17 0.52 0.09 0.00

_7

(X=0

o_= -30 ° 0=90 °

°

0 = 0°

Figure 5.18.

Heat transfer coefficient

58

contours.

+X

In

+¥

C H 0.20

0.28

Figure 5.19. Heat transfer coefficient

0.37

0.45

0.53

contours for revised aerobraking

59

0.61

0.70

configuration.

• 7-_

_\ p = 120 kg/km 3 V =4811 c__-O_

Figure

5.20.

Heat

transfer

0.14

coefficient

contour

lines for revised

m/s

aerobraking

....................................

0.12

0,10

_,,

m 0.08

0.06

0.04

0.02 ] SENSOR

]

"

"

0.5

1.0

0.00 -1.0

-05 Distance

Figure

5.21.

0.0 from

Mean

panel

centedine,

m

free path above

60

sensor.

configuration.

7001 .............. f

600

500 tl

:

.....

: .......

_-

-

-

.....................

/_

,oort ...... _................ /_ vm"=or / ......... .... _....i _ 100 r

........

:.............

.............

.0.5

0.0

Distance

Figure

5.22.

i ...........

from panel

Velocity

i

0.5 centedine,

magnitude

1.0

m

above

sensor.

0.10 i

:

:

7

:

7

0.08

0.06 _,,m

0.04

0.02

: : ; ............

: ! 7 ! ...... 7..............

L I0.00

7 ! . : .....

: !......

: : !

Powe_7 Shunt Asxembly

I 1 -0.6-0.5-0.4-0.3-0.2-0.1

1

Distance

Figure

7 : _.

5.23.

Mean

1

I 0.0

from panel

I 0.1

"l i 0.2

centedine,

free path above

61

i :

I 0.3

0.4

0.5

0.6

m

power

shunt.

400

300

V,

/

m/s 2OO

.

. " ........

i ......

J

/

½

/

Ioo

_i

0 -0.6

["

.

:

Powei_

t

I

I

i

i

i

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

Distance

Figure

1.00

.......

5.24.

=...............

.......

: .......

Sh.nt

from

Velocity

_ 0.1

panel

:

magnitude

.....

i

t

I

I

0.2

0.3

0.4

0.5

centedine,

_..................

: .....

I

Assembly

• ........

_........

I 0.6

m

above

power

".........

:.........

:

. .............................

.........

shunt.

'............

.-!. i! :!/i:!i!:! i!!!!ii _i!!!!!!!!i!!!ii!!:!!!!!!!!! i!i _iii!

0.90

0.80

C H

f_ : 0.40 k 0

'_"Z','T',' :":':'T,'I 10

20

,", T,'/,

7'["."/.

30 Distance

Figure

5.25.

Heat transfer

coefficient

7'i':':",'","i':"i","Ui"7/,";"i"7',"',";'

40

50 along

60

diagonal,

along

62

panel

70

i ;, 80

90

inches

diagonal

for various

densities.

Iiiiiiiii !iiiiiii !1 ::::::::::::::::::::: ii::'

,::::::::::::::::::::::::::::::::: ::::

. Y::,_i_.:!:!i 15:_.? ! !!i i?ii i i_ _ii

::::::::::::::::::::::::::: ::::::::::::::::::::::::::::::::::::::::::_;: _:!:!:]:i:]:!:i:_:i:_:i:i:!:!:_:!:!:!_:::i:_; ,:. :!:33:_:!: :::::::::::::::::::::::::::::::::::::::::::::::::::::::::_,.._ ::5:::::::;:

============================================

::::::::::::::::::::: ::::: :::: ::: : ::: ::5: ::.-:: -::

Figure

5.26.

Location

of inboard

and outboard

panel

diagonals.

1.0

0.9

0.8 C H

\

!: ! i::i ! ! i i :i !!!:"=:_2° ._:_,!i::i!:i!:i!::: !:i::!: !! i):i

',

.

0.7

• :

:'",: :.... 0.6

'",..

i : _

. •_

:- .:

:-.::.:

::/:::: :: ::i: .:. ::::::::::::: :::::::::: -:

.:/

: :. ::. ::_::: :.:::: :::::::::::::::::::::::::::::::::::::: ,!"

"

.

:

....

.: ........ .

....

,..........

:......

: ....

: ........

..

/ /

: ,' .......

0.5

• : 0.4

i

.... _:,

;, i.,

10

20

0

Figure

.

5.27.

.....

Heat transfer

" ...... -7:':-.-

., i', ...i 30

...,

;,: ,:.

...... i ...:

7.- ..... :.... i,,,

40 50 60 70 Distance along diagonal, inches

coefficient

along

63

panel

diagonals,

,i ,; ,, i,, 80

90

p = 120 kg/km

3.

0.90

...........

080

........

[

.............

I,

.

,

:

......

:

\ vl_-H

• '

0.70

:

_

",tX

....

i.

,

'

]

Panel

- '

.....

J .....

'

" '

/J

.......

"

-

: .....

.

; / "

...... .....

.

:_'-'_'.

t/

/

..............

...................... "

....

,o

:

: ..............

:

Panel

Outlx)ard

_=6okg)km' " ......

:

X

0.60

I.

"

:.......

"

Inboard - - L-

: .................. ; . .

_/ ; ......

;..

......

I

-- :..................................... --_

j

" .................

.......i .... :........ ! ...... !......::_:----_--.--.-_.-'..........

...i

0.50

.... 10

.........

i .....

: .....

: ...................

......

t ....

i ....

,....

i ....

, ....

20

30

40

50

Distance

Figure

5.28.

Heat

0.8 •

transfer

....... :

i ....

along

coefficient

60

70

diagonal,

along

i..

80

90

inches

panel

: ........................ ............. ; .....

L

i ....

diagonals,

:.......

: ............. " .............

p = 60 kg/km 3.

: "_" r

..... .. - I__i::::i::::i::i:::::!i:: ll.Lh,_ml,_ll_l=nw,l. :i::::i:i::: I.... ; ...... :ii::: : i0.9I'i ...... :........ :i.......... i......... " T ..... " . . ....... i i

: :...........

0.7

.,:! !

:::::/:

: ::::,':

: :::: :_:: : _o=120k_ _:::::::::::::::::::::::/

C H

0.5 0.6

0.4

...............

0.3 F, ;','/i 0

:............

, ;', ;i 10

_ .....

5.29.

Heat transfer

:..........................................

:',"; ",'i ",, ; , i',"; ",'; "i'; ,'L3"i ;',';, 20

30 Distance

Figure

i .........

coefficient

40

50

along

along

64

diagonal,

60

:....

i', .,', i', ;',, i , , 70

80

90

inches

panel diagonals;

-Y panel

along

-Y axis.

÷xI

-Y Panel along Y Axis

-Y Panel at 30 ° Sweep C H 0.00

Figure

0.10

5.30.

Heat

0.20

0.30

0.40

transfer

coefficient

contours,

65

0.50

0 ° and 30 ° panel

0.60

sweeps.

01 1 .....:i

0.9

....

C H

:

"

"

.....

"_';'-;"

08 _:\: :: !,,.

::

. ::.::

"Ba_ rmCordli.Jra:tiori"

I:

:

:

.. :

+ :

"'