AIAA 98–2445 Prediction and Validation of Mars Pathfinder

AIAA 98–2445 Prediction and Validation of Mars Pathﬁnder Hypersonic Aerodynamic Data Base

Peter A. Gnoffo, Robert D. Braun, K. James Weilmuenster, Robert A. Mitcheltree, Walter C. Engelund, Richard W. Powell NASA Langley Research Center Hampton, VA 23681-0001

7th AIAA/ASME Joint Thermophysics and Heat Transfer Conference June 15–18, 1998 / Albuquerque, NM

For permission to copy or republish, contact the American Institute of Aeronautics and Astronautics 1801 Alexander Bell Drive, Suite 500, Reston, VA 20191

Prediction and Validation of Mars Path nder Hyp ersonic

Aero dynamic Data Base

Peter A. Gno o, Rob ert D. Braun,

K. James Weilmuenster, Rob ert A. Mitcheltree,

Walter C. Engelund, Richard W. Powell

NASA Langley Research Center

Hampton, VA 23681-0001

Post ight analysis of the Mars Path nder hyp ersonic, continuum aero dynamic data

base is presented. Measured data include accelerations along the body axis and axis

normal directions. Comparisons of pre ight simulation and measurements show good

agreement. The prediction of two static instabilities asso ciated with movementof the

sonic line from the shoulder to the nose and back was con rmed by measured normal

accelerations. Reconstruction of atmospheric density during entry has an uncertainty

directly prop ortional to the uncertainty in the predicted axial co ecient. The sensitivity

of the moment co ecient to freestream density, kinetic mo dels and center-of-gravity

lo cation are examined to provide additional consistency checks of the simulation with

ight data. The atmospheric density as derived from axial co ecient and measured

axial accelerations falls within the range required for sonic line shift and static stability

transition as indep endently determined from normal accelerations.

Intro duction Nomenclature

A axial acceleration, earth g

A normal acceleration, earth g

HE hyp ersonic aero dynamic data base used in

C axial force co ef.

Tthe Mars Path nder entry, descent, and landing

C drag co ef.

EDL was predominantly generated using computa-

C pitching moment co ef.

tional uid dynamics. While ground-based and ight

C pitching moment co ef.

data from the Viking pro ject were used to check p or-

derivative, p er radian

tions of the aero dynamic data for Path nder, di er-

C normal force co ef.

ences in entry velo city and angle-of-attack between

D prob e diameter, m

Path nder and Viking required a more critical eval-

h altitude, km

uation of high temp erature e ects on hyp ersonic aero-

M Machnumber

dynamics. A systematic evaluation of Path nder aero-

m entry mass, kg

dynamics as a function of velo city, altitude, and angle-

p pressure, N/m

of-attack in a continuum regime revealed twointervals

T freestream temp erature, K

during a nominal entry in which static aero dynamic in-

S reference area, m

stabilities would induce vehicle \wobble". The static

V freestream velo city, m/s

aero dynamic instabilitywas asso ciated with changing

x; y ; z Cartesian co ordinates, m

sonic line lo cation and asso ciated pressure distribu-

angle-of-attack, degrees

tions as a function of chemical kinetics and ow energy.

total angle-of-attack

2 2 1=2

These predictions and explanations were published in

+ , degrees

1, 2

journal articles in 1996 and the \wobble" was con-

angle of yaw, degrees

rmed by Path nder ight data accelerometers on

e ective ratio of sp eci c heats

July 4, 1997. The physical phenomena leading to

freestream density, kg/m

the static aero dynamic instability are reviewed, the

measured accelerations con rming the instability are

discussed, and additional p ost- ight analyses are pre-

sented. The delity of comparison b etween pre- ight

prediction and ight data signi cantly reduces uncer-

and Astronautics, Inc. No copyright is asserted in the United taintyin the atmospheric reconstruction pro cess and

States under Title 17, U.S. Co de. The U.S. Government has

provides enhanced con dence in the application of

aroyalty-free license to exercise all rights under the copyright

CFD to future planetary missions with reduced design

claimed herein for governmental purp oses. All other rights are

margin.

reserved by the copyrightowner.

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American Institute of Aeronautics and Astronautics Paper 98{2445 corner .06625 m bubble leeside 70o x

2.65 m .6638 m .59 m nose

V∞ α windside 43.4o V∞

1.506 m α = 2o

Fig. 1 Diagram of the Mars Path nder prob e.

Pre ight Analysis

Fig. 2 Sonic line lo cation over the Mars Path nder

The Mars Path nder con guration is shown in Fig.

at 2 deg. angle-of-attack and Machnumb ers equal

1. The foreb o dy is a 70 half angle cone with base

to 22.3 left, 16.0 center, and 9.4 right showing

diameter 2.65 m, nose radius 0.6638m and shoulder

the e ect of gas chemistry.

radius 0.06625 m. The on-axis reference p oint for aero-

dynamic moment co ecients is lo cated 0.662 m b ehind

the nose. The actual center-of-gravity CG lo cation

1.0

is x ;y ;z = 0.000107, -0.000435, 0.71541

CG CG CG

where z is distance b ehind the outer mold line of the

nose and x and y are orthogonal to the b o dy axis.

Predictions of a static aero dynamic instability for

ath nder vehicle asso ciated with shifting of

the Mars P 0.9

the sonic line from the shoulder to the nose and back

2 ∞

1, 2

have b een describ ed in the literature. Sp eci c con- V ∞ ρ

/ clusions of the rst citation relating to the o ccurrence

p y on the 70 degree, of the static aero dynamic instabilit M

0.8 ∞

Path nder con guration are sum- spherically capp ed 22.3

marized here. 16.0 ath nder prob e descends through

1 As the Mars P 9.4

the Mars atmosphere the minimum value of the p ost-

k e ective rst decreases from frozen gas chem- sho c 0.7

-1.0 -0.5 0.0 0.5 1.0

alues to equilibrium values 1.094 corresp ond-

istry v x, m

ing to a velo city of 4.86 km/s. As the prob e continues

to decelerate through a near equilibrium p ost-sho ck

Fig. 3 Pressure distributions in the plane of sym-

gas chemistry regime, the value of increases, until

metry over the Mars Path nder at 2 deg. angle-of-

reaching its p erfect gas value at parachute deployment

attack and Machnumb ers equal to 22.3, 16.0, and

0.42 km/s.

9.4 showing the e ect of gas chemistry.

2 For the spherically blunted, 70 degree half-angle

immediately b ehind the b ow sho ck just downstream of

cone at small angles of attack the sonic line lo cation

an in ection p oint in the bow sho ck. The sonic line

shifts from the shoulder to the nose cap and back again

from the nose skirts ab ove the edge of the b oundary

on the leeside symmetry plane b ecause of the change

layer. Still later, at Mach 9.4, the bubble expands to

in . This transition in sonic line lo cation is shown in

merge with the subsonic region at the b oundary layer

Fig. 2 for a 2 degree angle-of-attack. The subsonic ow

edge. The in ection p oint on the bow sho ck disap-

region, as de ned by the frozen sound sp eed, app ears

p ears.

as the light gray region. The darker region represents

3 Pressure distributions on the cone fustrum ap- zones of sup ersonic ow b ehind the b ow sho ck. Ata

proaching the shoulder tend to b e very at when the Machnumb er 22.3 on the pre ightPath nder simula-

sonic line sits forward over the spherical nose, as shown tion, the sonic line on the leeside dips deep into the

in Fig. 3 for Mach 22.3. E ects of the expansion b oundary layer over the spherical nose cap. Later in

over the shoulder can only b e communicated upstream the tra jectory, at Mach 16.0, a subsonic bubble forms

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American Institute of Aeronautics and Astronautics Paper 98{2445

through the subsonic p ortion of the b oundary layer. In

trast, pressure distributions on the cone fustrum

con 1.80

approaching the shoulder tend to be more rounded

when the sonic line sits on the shoulder, exhibiting a more pronounced in uence of the expansion on the

1.75

upstream owasshown in Fig. 3 for Mach 9.4.

In general, windside pressures exceed leeside 4 0deg.

pressures on the cone fustrum, pro ducing a stabi-

C 2deg.

moment that pitches the prob e back to zero

lizing 1.70

angle-of-attack. However, the b ehavior of the pres-

sure distribution in the vicinity of the shoulder sig-

5deg.

tly in uences the pitching moment co ecient

ni can 1.65

b ecause of the larger moment arms and surface area

at the edge of the prob e as compared to the inb oard

nose and fustrum regions. For the Mars Path nder

angle-of-attack, the at, leeside pres- prob e at 2 deg. 2000400060008000

V∞,m/s

sures approaching the shoulder when the sonic line

sits over the nose can exceed the rounded windside

a Axial co ecient

pressures approaching the shoulder when the sonic

line sits over the shoulder. The net e ect of this

crossover distribution near the shoulder tends to pitch

k static instability.

the prob e to higher angles of attac 0.005

The overall balance crossover-p oint lo cation is sen-

sitive to freestream conditions and corresp onding gas

hemistry within the sho cklayer. The combination of

c 2 deg.

small angle-of-attack, large cone angle, windside sonic

line over the shoulder, and leeside sonic line over the

nose with a secondary, subsonic zone ab ove the leeside

fustrum yield conditions whichfavor but do not nec-

tee a destabilizing pitching moment.

essarily guaran 5 deg.

Representative parts of the aero dynamic data

5 -0.005

base as a function of velo city during the hyp ersonic,

continuum p ortion of the tra jectory are shown in Fig.

4. Conditions for a p ositive, destabilizing moment

co ecient derivative C o ccur twice in the Mars

Path nder mission. C is zero when equals zero; T m 2000 4000 6000 8000

V∞, m/s

C is p ositive where the C curve for = 2 deg.

m; m

crosses the C = 0 axis in Fig. 4 b. The rst o ccur-

b Pitching moment co ecient

rence 7:5 >V >6:5 km/s, 51 >h > 37 km, vicinity

Fig. 4 Predicted aero dynamic co ecients as

of p eak heating for this tra jectory results from the

function of velo city and angle-of-attack for early

transition in the sonic line lo cation as a function of

Mars Path nder tra jectory with ballistic co ecient

gas chemistry changing from nonequilibrium to equi-

equal to 45.

librium. The second o ccurrence 4:0 > V > 3:1

km/s, 25 >h>22 km results from the transition in

dynamic pressure, the magnitude of the o -axis accel-

the sonic line lo cation as a function of decreasing ow

erations abruptly decrease, corresp onding to a brief

enthalpy in a near equilibrium gas chemistry regime.

p erio d where CFD simulations show the sonic line

xed to the spherical nose at small .

Measured Accelerations

The trend is more clearly observed in Fig. 6 in which

2 2 1=2

Measured accelerations during Path nder's entry, a total normal acceleration A = A + A is

x y

descent, and landing EDL validate these earlier con- plotted as a function of time. In this gure, a rather

clusions. The raw, three-axis accelerometer data for abrupt increase in normal acceleration is observed on

the hyp ersonic p ortion of EDL are presented in Fig. either side of the relative low level A 0:014g

5. In this gure, the z-axis is in the axial direction. near p eak dynamic pressure to a relatively high level

The x- and y- axes are xed on the body as it spins A 0:04g. This change closely corresp onds to the

approximately 2 rpm, pitches and precesses during predicted times when the sonic line shifts from the

descent. Peak dynamic pressure o ccurs approximately shoulder to the nose 71s and then back again to

78 seconds after entry interface. In the vicinityofpeak the shoulder 82s.

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American Institute of Aeronautics and Astronautics Paper 98{2445

freedom 6-DOF Program to Optimize Simulated

ra jectories POST co de and aero dynamic co e-

16 0.04 T

cient tables derived from CFD simulations are pre-

sented in Fig. 7a. The corresp onding measured values

of normal to axial accelerations are presented in Fig.

12 0.02

The predicted and measured results show very

Ax 7b.

go o d qualitative and quantitative agreement. For ex- g ,

y ample, the e ects of the predicted and measured static A g ,

aero dynamic instabilitybetween 82 and 90 seconds are

A 8 0 n A

evident in b oth the magnitude and duration of the x

pulse. The time averaged aero dynamic co ecient ratio

ty of p eak dynamic pressure b etween 71 and

4 -0.02 in the vicin

82 seconds is also in go o d agreement with magnitude

duration of the measured ratio of accelerations

Ay and

when the sonic line sits over the spherical nose. The

show a much larger oscillation ab out the 0 25 50 75 100 125 150 predictions

t, s

mean in this domain than was measured. An overly

conservative sp eci cation for C in this region in the

m;q

Fig. 5 Science accelerometer measurements

simulation is the susp ected cause. The magnitude and

recorded on Mars Path nder during 2.5 minutes

frequency of oscillations b eyond 90 seconds are in fair

following entry interface with the Mars atmo-

agreement but the mean value of measured accelera-

sphere.

tion ratio .0016 remains at a constant level while the

mean value of the simulated acceleration ratio starts

lower .0008 and gradually rises to .0024. Reasons for

20 0.05

these discrepancies are not yet understo o d.

The total angle-of-attack predicted in the 6-DOF T

analysis is presented in Fig. 8a. The corre-

16 0.04 POST

sp onding values in ight Fig. 8b are derived from

aero dynamic tables of C =C as a function of

N A T

12 0.03

using the measured ratio of normal to axial acceler- g g ,

ations. Here again, b oth qualitative and quantitative A N A

t are generally go o d and servetovalidate the

8 0.02 agreemen

simulation metho dology for aero dynamics.

4 N 0.01

Atmospheric Reconstruction

of the Mars atmosphere based on 0 0 Reconstruction

25 50 75 100 125

accelerations on Mars Path nder has b een

t, s measured

describ ed by Sp encer et. al. Velo cities are derived

from measured accelerations. Densities are derived

Fig. 6 Total o -axis acceleration recorded dur-

from measured axial accelerations, the derived velo c-

ing 100 second interval surrounding p eak dynamic

ities, and the predicted aero dynamic data base for

pressure.

C as a function of velo city, Machnumb er, and total

In general, the corresp ondence of measured accelera-

angle-of-attack. The p oint-by-p oint transformation is

tions and predicted aero dynamic co ecients is compli-

given by

cated by the unknown freestream density. Velo city can

b e derived from integrated accelerations but densityis

= 2

V C

not directly measured. This complicating factor can

b e removed by examining the ratio of normal to axial

forces and normal to axial aero dynamic co ecients. Errors in the predicted aero dynamic data base are lin-

early related to errors in the derived densities. The

reconstructed density is plotted as a function of velo c-

C mA A

1=2 V S

N N N

= = = 1

ity in Fig. 9. The o -axis accelerations are plotted in

C mA A

A A A

S 1=2 V

this same gure to show the corresp ondence of simula-

tion co ordinates velo city, density with the onset and The predicted values of normal to axial force co ef-

decay of the aero dynamic instabilities at small angles cient using the initial state vector determined four

of attack. hours prior to entry interface in the six-degree-of-

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American Institute of Aeronautics and Astronautics Paper 98{2445 0.005 5

0.004 4

0.003 3 g A e C d / N , T C α 0.002 2

0.001 1

0 25 50 75 100 125 25 50 75 100 125

t, s t, s

a Predicted ratio of normal to axial force co ecients from a Predicted from 6-DOF POST

T 6-DOF POST

5 0.005

4 0.004

0.003 g e A d A , / T N α A 2 0.002

1 0.001

25 50 75 100 125 25 50 75 100 125

t, s t, s

b Derived from recorded accelerations

b Measured normal to axial acceleration ratio

Fig. 8 Comparison of total angle-of-attack pre-

Fig. 7 Ratio of normal acceleration to axial accel-

dicted by 6-DOF POST using initial state vector

eration recorded during 100 second interval sur-

determined 4 hours prior to entry interface with

rounding p eak dynamic pressure. The ratio is

values derived from measured accelerations.

equivalent to the value of C =C for Path nder at

N A

its total angle-of-attack .

change in the reference lo cation.

All of the solutions generated for the next section

Uncertainty Analysis

and most of the solutions used to generate the aero dy-

The uncertainty in center-of-gravity CG lo cation namic data base were obtained on a surface grid of 30

is 5mm in the axial and 1 mm in the radial direc- by 60 cells half b o dy to symmetry plane with 64 cell

tions. Given C 1:7over the hyp ersonic, continuum normal to the b o dy. A grid re nement to40by 80 cells

p ortion of the tra jectory, the uncertaintyinC asso- for a case with V = 3515 m/s at = 2 deg yielded

m 1

ciated with the uncertainty of the CG lo cation in the achange in C =C of less than 0.00015, so that the

N A

pitch plane is C = C r=D = 0:00064. The un- predicted ratio of normal to axial acceleration has an

m A

certaintyin C asso ciated with an axial translation of uncertaintyof at least 0:00015. The change in C

m m

the CG is two orders of magnitude smaller for small for this re nementwas less than 0.0004. In a related

angles of attack. Note that there is no uncertaintyin grid coarsening test the solution at the 6000 m/s and

the aero dynamic reference p oint; we simply treat CG = 2 deg. was computed on a grid with every other

lo cation uncertainty as equivalent to a corresp onding mesh p oint removed in all three computational direc-

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American Institute of Aeronautics and Astronautics Paper 98{2445

certaintyin should b e less than 0.6 degrees. The

uncertaintyinC due to the uncertaintyin is less T

0.0020 0.0050 A

than 0.7. E ects of base pressure on the hyp ersonic

ρ∞ 1

aero dynamic drag are less than 0.5. Consequently,

AN/AA

the total RMS value for uncertaintyin C in the hy-

0.0016 0.0040 A

p ersonic, continuum domain at low angles of attack

is less than 3. The corresp onding total RMS value

0.0012 0.0030

for uncertaintyin in this domain is less than 4. ρ 1

∞, 1

of computed drag co ecient to exp eri- A /A Comparison 3 N A

kg/m 6

mental data for the Viking con guration in ballistic

0.0008 0.0020

range tests in CO fall within this 3 estimate.

As a nal note, all of the simulations assume lami-

w. The assumption should b e valid for most of

0.0004 0.0010 nar o

the hyp ersonic, continuum tra jectory presented here.

At the V = 3996 m/s tra jectory p oint M = 18,

1 1

Re = 1:2 million, the value of Re =M is less

1 e 2000 4000 6000 8000 D;

V∞, m/s

than 500 over most of the cone and drops b elow zero as

ow expands over the shoulder. In recent comparisons

Fig. 9 Reconstructed density and ratio of mea-

to engineering co de assessments of Re =M the CFD

sured accelerations as function of velo city for Mars

valuation of this quantity is roughly twice the engi-

Path nder during ight through the continuum,

neering co de valuation. Assuming a transition criteria

hyp ersonic ow regime.

of Re =M = 250 for blunt b o dies from engineering

co de assessments turbulent ow may o ccur near this

tions. This test yielded a change in C =C of less

N A

condition. The contribution of laminar skin friction

than 0.00012 and a change in C less than 0.0003.

to C is less than 0.2 as noted in blo ck2of Table

4 M = 16, V = 3515 m/s, = 2 deg. in the

Measured axial accelerations in the hyp ersonic, con-

1 1

pre ight analysis. If we assume: 1 no relaminariza-

tinuum domain are accurate to within 1. Uncertain-

tion at the shoulder where the strongest contribution

ties in measured normal accelerations are more dicult

of shear to C will o ccur; 2 negligible displacement

to characterize; they are exp ected to b e less than 1

thickness e ects of a turbulent b oundary layer on pres-

of full scale A <:008g in this domain. Velo cities

sure for this very blunt con guration; and 3 a factor

are derived byintegrating the measured accelerations

5 increase in shear over laminar values, then an ad-

in time from the initial state vector. Uncertainties in

ditional uncertainty of 1 in C is intro duced. The

the derived velo cities should b e less than 1 b ecause

contribution from turbulent shear at the shoulder to

random errors in measured accelerations smo oth out

C at small angles of attack is more dicult to esti-

and calibration checks remove bias errors in measured

mate b ecause of the greater imp ortance of di erences

accelerations. Furthermore, an indep endent check of

between windside shoulder and leeside shoulder con-

derived velo city with altimeter data prior to parachute

tributions. The laminar shear contribution to C for

deployment showed di erences less than 1.

the M = 16 simulation noted ab ove is a destabilizing

Uncertainties in the derived density are linearly re-

increment equal to 0.00012. Again assuming a factor

lated to the total uncertainty in the simulated values

5 increase in the turbulent contribution leads to an

C which include uncertainties asso ciated with and

A T

additional uncertaintyinC equal to 0.0006.

gas chemistry mo del. Recall Eq. 2. Uncertainties in

the derived density are quadratically related to the

Sensitivity Analysis

total uncertainty in freestream velo city. Comparison

of LAURA simulations to ground based exp erimental The aero dynamic data base used in the POST co de

data for an axisymmetric blunt b o dy METEOR at was originally generated on the basis of a simulated

Mach 6 in which uncertainties in gas chemistry p erfect tra jectory for a 418 kg vehicle with a ballistic co ef-

gas and sting mounted are near zero relativeto cient of 45 kg/m in the Mars-GRAM atmospheric

the ight case show di erences less than 2 in C , mo del. The vehicle grew as the design matured and

and less than 5 in C and C . UncertaintyinC the actual entry mass was 585.3 kg with a ballistic co-

N m A

asso ciated with the gas mo del is dicult to de ne, ecient of 62 kg/m . In the nal design phase, cruise

but thought to be approximately 1 for low angles and entry op erations, and p ost- ight analysis, the

8, 9

of attack based on computational analysis in the next Clancy atmospheric mo del was used. The POST

section. Uncertainty in the derived is implicitly co de used velo city as a curve t parameter for aero-

related to the uncertaintyin C and measured accel- dynamic co ecients ab ove Mach 12 in the continuum

erations; and, given the values discussed ab ove and the regime b ecause of the imp ortant role of e ective on

tables and gures from the pre ight analysis, the un- aero dynamics and its dep endence on total enthalpy.

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American Institute of Aeronautics and Astronautics Paper 98{2445

Below Mach 8, Machnumber was used as a correlat- y e ects on

ing parameter to emphasize compressibilit 0.0050 0.001

aero dynamics. Between Mach 8 and 12, a bridging

function is used. As a result of di erences in mass, try angle, and atmospheric mo del, a comparison of

en 0.0040 0

the early pre ight and p ost- ight tra jectories will yield

di erent densities for the same velo city. As a p ointof

0.0030 -0.001

reference, the data base used aero dynamic co ecients

3 A

simulated at V = 3996 m/s and = 1:55 10

1 1 N A /A C

3 N A A

kg/m ; the density at that same velo city in the recon-

0.0020 -0.002

3 3

structed atmosphere was =1:13 10 kg/m .

In the continuum, hyp ersonic ight regime, the

hange in densitywould b e exp ected to in uence aero-

c 0.0010 -0.003

dynamic co ecients through Reynolds number and

gas kinetics. As discussed in the previous section, the

umb er is exp ected to b e small, in uence of Reynolds n 2000 4000 6000 8000

V∞, m/s

but the in uence of gas kinetics on the e ective is

unknown. The primary purp ose of this section is to

Fig. 10 Ratio of normal to axial accelerations and

quantify the sensitivity of the aero dynamic data base

moment co ecient at =2 deg. for the pre ight

to p erturbations in density and the gas kinetic mo del.

simulated tra jectory as a function of velo city. The

A secondary purp ose of this section is to critically eval-

transition b etween regions of static instability and

uate the transition regions between statically stable

static stability are b ounded with the rectangular

and unstable regions and check that the simulation is

boxes.

consistent with measured normal accelerations.

The moment co ecient at = 2 deg. for the

and allows us to check the assumption that critical

p ost ight, simulated tra jectory is plotted over the sim-

values for C and C can b e de ned. Values for

m;U m;L

ulated Path nder measurements of normal to axial

C and C based on this sub jective selection crite-

m;U m;L

acceleration as a function of velo city in Fig. 10. The

rion are resp ectively -0.0003 and -0.0013 see b ounding

value of C at = 2 deg., designated C 2, is

m m

boxes in Fig. 10. When the ma jor contributor to un-

prop ortional to C at = 0 assuming a forward dif-

certaintyin C , CG lo cation, is included the transition

ference approximation C 0 = C 2 0 90= .

m; m

range expands to +0.00034 to -0.00194.

The purp ose of this plot is to identify values of C 2

that are asso ciated with the transition b etween regions

of static instability and static stability. The transition

Results and Discussion

region is delineated with the rectangles.

Weintro duce an assumption that critical values in

Four test p oints are chosen along the reconstructed

C 2 may b e de ned that serve to delineate the var-

tra jectory and are identi ed in Table 1 and in Fig.

ious stability regions as determined from measured

11. The simulated data in Fig. 11 is based on ight

accelerations. In each transition region an upp er limit

through the reconstructed atmosphere, in contrast to

on C 2, C , is identi ed such that any simulation

the data in Fig. 7 a based on ight through the

m m;U

with C 2 >C would b e exp ected to b e in a re-

pre ight atmospheric mo del. Except for the lack of

m m;U

gion of static instability. In like manner, a lower limit

high frequency oscillations in the measured data be-

on C 2, C , is identi ed such that any simulation

tween 3400 m/s and 6000 m/s there is fairly good

m m;L

with C 2

qualitative agreementbetween the measured and simu-

m m;L

gion of static stability. If C >C 2 >C one

lated data. Temp oral resolution of the accelerometers

m;U m m;L

would exp ect measured accelerations to b e within the

should have picked up such oscillations if they were

transition b etween the two stability regions.

present. The magnitude of measured accelerations is

Values of C and C are obtained from analysis slightly larger 15-30 than the temp orally averaged

m;U m;L

of four di erent simulations of the Path nder tra jec- level of simulations in the statically stable region b e-

tory through the reconstructed atmosphere. The ve- tween 4500 and 6000 m/s and in the statically unstable

hicle was numerically own using the 6-DOF POST region b etween 3400 and 4000 m/s. The measured du-

co de with the baseline aero dynamic data base and ration of the statically stable region in velo city space

three p erturbations in which the curve ts of aero- is shorter than the simulated duration. These obser-

dynamic co ecients as a function of velo city were vations are consistent with trends shown in Fig. 9of

shifted by +1, -5, and -10 in velo city space i.e. Braun et. al. in which the CG moves o the axis.

C = C V 0:1V . This shift causes the instabili- The current simulation assumes a 0.448 mm o set CG

x x 1 1

ties to arise earlier or later in the simulated tra jectory lo cation.

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American Institute of Aeronautics and Astronautics Paper 98{2445 0.005 0.0005 1.72 flight data POST simulation 0.004 0 1.71

D m C A C

0.003 A C C A A / -0.0005 1.7 N B A 0.002 A

coarse grid results -0.001 1.69 0.001 Cm

2000 4000 6000 8000 4.0E-04 4.5E-04 5.0E-04 V∞, m/s ρ 3

∞, kg/m

Fig. 11 Comparison of A =A as measured in Fig. 12 The computed sensitivity of Path nder

N A

ight and as simulated with the POST co de in the aero dynamic co ecients on freestream density for

reconstructed atmosphere using the CFD derived avelo city of 6000. km/s.

data base for aero dynamic co ecients.

able1-Test Points and Baseline Aero dynamics

T 0.0005 1.72

Pt. V , C 2 C 2 C 2

1 1 3 A N m

s m

A 6000 4.53 10 1.707 0.004399 -0.001292

4270 1.00 10 1.714 0.004394 -0.001929

B 0 1.71

C 3996 1.13 10 1.712 0.003250 -0.000812

3 m

D 3648 1.26 10 1.698 0.001883 +0.000331 C CA C

-0.0005 1.7

The aero dynamic co ecients for the baseline eight

sp ecies CO , CO, N , O , NO, C, N, O kinetic

2 2 2

mo del are included in the Table 1. Point A is in the

-0.001 1.69 middle of the transition region, near p eak heating and

prior to p eak dynamic pressure where the sonic line

is completing its movement to the nose with decreas-

ing . Point B is in the middle of the next transition,

0.5 1 1.5 2

p eak dynamic pressure in which the sonic line

after rate factor

is b eginning to move back to the shoulder from the

nose with increasing asso ciated with decreasing ow

Fig. 13 The computed sensitivity of Path nder

enthalpy. At this p oint in Fig. 11 the POST simula-

aero dynamic co ecients on disso ciation rate co ef-

tion indicates a region of static stability, in apparent

cient for CO at a freestream density 0.0004532

disagreement with the ight data. Point C is at the

kg/m and velo city of 6000. km/s.

end of this transition region containing Point B; the

for C that de nes the transition region.

velo city here corresp onds to one used in establishing

m;L

the aero dynamic data base. Point D is at the lo cal

The sensitivityof C 2 and C 2 with resp ect to

A m

maximum for A =A .

and kinetic mo del at p oint A are shown resp ec-

N A

Given the assumptions stated previously, values of tively in Figs. 12 and 13. Op en symb ols represent

C 2 for Points A-C would be exp ected to be be- the baseline grid results 60 x 30 x 64 and the lled

tween C and C . The value of C 2 for Point symb ols show a result with a factor two coarsening

m;U m;L m

Dwould b e exp ected to b e greater than C . As is in all co ordinate directions. Aero dynamic co ecients

m;U

evident in Table 1, the baseline kinetic mo del yields are insensitive to p erturbations as large as 10 ab out

4 3

values of C 2 which are consistent with the critical the nominal density of 4.53 10 kg/m . The value

values of C and C for p oints A, C, and D, even for C 2 at Point A is at the lower edge of the

m;U m;L m

without adding the uncertainty bar asso ciated with exp ected transition range. Aero dynamic co ecients

CG lo cation. The uncertainty bar around p oint B as- are also insensitivetochanges in the disso ciation rate

so ciated with CG lo cation just overlaps the lower limit constant for CO by factors varying from 0.5 to 2.0.

8of10

American Institute of Aeronautics and Astronautics Paper 98{2445 0.0005 1.72 0.0005 1.72

CA CA

0 1.71 0 1.71 m m A A C C C C

-0.0005 1.7 -0.0005 1.70

Cm Cm

-0.001 1.69 -0.001 1.69

1.0E-03 1.2E-03 1.4E-03 1.6E-03 0.1 0.5 1.0 1.5 2.0 ρ , kg/m3

∞ rate factor

Fig. 14 The computed sensitivity of Path nder Fig. 15 The computed sensitivity of Path nder

aero dynamic co ecients on freestream density for aero dynamic co ecients on disso ciation rate co ef-

avelo city of 3996. km/s. cient for CO at a freestream density 0.001127

kg/m and velo city of 3996. km/s.

Insp ection of CO mass fraction in all three solutions

shows that CO is substantially depleted, other sp ecies

play a more dominant role in establishing . Chang-

ing the e ective temp erature for disso ciation in all

such reactions at Point A from the baseline mo del

0:5 0:5 0:7 0:3

T = T T , op en symb ols to T = T T

ef f ef f

V V

lled symb ols has almost no e ect. While thermal

nonequilibrium is present in the sho ck layer there is

not enough thermal nonequilibrium over substantial

p ortions of the sho cklayer to make a signi cant e ect

on aero dynamics through e ective kinetic rates.

The sensitivity of C 2 and C 2 with resp ect

A m

to and kinetic mo del at p oint C are shown resp ec-

tively in Figs. 14 and 15. Aero dynamic co ecients are

still insensitive to p erturbations as large as 40 ab out

3 3

the nominal density of 1.13 10 kg/m . In contrast,

(a) 0.1 (b) 0.5 (c) 1.0 (d) 2.0

the e ect on C 2 of a 7 p erturbation in velo city

at the same density is large, as observed by comparing

p oint B in Table 1 with the result for equal to .001

Fig. 16 The computed sensitivity of Path nder

kg/m in Fig. 14. The e ects of disso ciation rate con-

sonic line lo cation on disso ciation rate co ecient

stant for CO on aero dynamics is stronger at p ointC

for CO at a freestream density 0.001127 kg/m

than at Point A. Previous characterization of the ow

and velo city of 3996. km/s.

at this p oint as \near equilibrium" over-simpli ed the

role of gas kinetics during this p ortion of the tra jec-

the moment co ecient to move into the domain of

tory. Doubling the rate factor moves C 2 closer to

static stability. Decreasing rate factor causes the sonic

a predicted domain of static stability. Reducing the

bubble to grow and approach a condition of static in-

rate by a factor of 10 moves C 2 closer to a pre-

stability. The sonic bubble emanates from an in ection

dicted domain of static instability. Nevertheless, the

p oint in the bow sho ck which eventually disapp ears

change in C 2 over this entire range of kinetic mo del

with the merging of the bubble with the sonic line on

adjustments is less than 0.6.

the edge of the b oundary layer.

The movement of the sonic line asso ciated with The sensitivity tests at Points A and C show that

changes in the CO disso ciation rate at Point C are aero dynamic database is insensitive to p erturbations

shown in Fig. 16. The baseline kinetic mo del results in density as large as 10. It is b elieved this lackof

are in Fig. 16 c, with rate factor equal to 1. Increas- sensitivitywould p ersist across the entire hyp ersonic,

ing rate factor causes the sonic bubble to shrink and continuum domain for the Path nder vehicle shap e.

9of10

American Institute of Aeronautics and Astronautics Paper 98{2445

tions are consistent with measured data within the The sensitivity will manifest itself during the transi-

de ned ranges, including the uncertainty band. tional ow regime prior to continuum; in fact, Moss

et. al. predicted static instabilities in the transitional

Acknowledgements regime for Path nder as a function of Knudsen number

variation.

The authors thank Rob ert Blanchard of the

The baseline thermo chemical mo del yields values for

Aerothermo dynamics Branch, Langley Research Cen-

C 2 which are consistent, within estimated uncer-

ter for supplying data for the reconstructed atmo-

tainty bands, of the measured normal accelerations.

sphere, tra jectories, and accelerometers.

Point B shows the greatest disagreement between

measurement and simulation of normal accelerations.

References

Agreement would likely be improved using a simula-

Gno o, P. A., Weilmuenster, K. J., Braun, R. D., and Cruz,

C. I., \In uence of Sonic-Line Lo cation on Mars Path nder

tion with a larger o set CG and/or slower CO disso-

Prob e Aerothermo dynamics," Journal of Spacecraft and Rock-

ciation rates to de ne C .

ets ,Vol. 33, No. 2, March-April 1996, pp. 169{177.

The normal acceleration data is useful as a con-

Braun, R. D., Powell, R. W., Cruz, C. I., Gno o, P. A.,

sistency check for the simulation mo dels, much like

and Weilmuenster, K. J., \Six Degree-of-Freedom Atmospheric

Entry Analysis for the Mars Path nder Mission," AIAA 95-

measurements of sho ck stando distance in ground

0456, January 1995.

based exp eriments are used. While one could not use

Brauer, G. L., Cornick, D. E., and Stevenson, R., \Capa-

the data by itself to prop ose changes to any elements

bilities and Applications of the Program to Optimize Simulated

of the chemical kinetic mo del, one should question

Tra jectories POST," NASA CR 2770, February 1977.

any mo del changes that cause inconsistent values of

Sp encer, D. A., Thurman, S. W., Peng, C.-Y., Blanchard,

R. C., and Braun, R. D., \Mars Path nder Atmospheric Entry

C 2 with measured normal accelerations along any

Reconstruction," AAS 98-146, AAS/AIAA, February 1998.

p oint on the Path nder tra jectory. In the tests con-

Gno o, P. A., Weilmuenster, K. J., H. Harris Hamil-

ducted herein, rather large p erturbations in the kinetic

ton, I., Olynick, D. R., and Venkatapathy, E., \Computational

mo del are required b efore computed values for C 2

Aerothermo dynamic Design Issues for Hyp ersonic Vehicles,"

AIAA 97-2473, AIAA, June 1997.

are pushed outside of the exp ected limits based on

Intrieri, P. F., Rose, C. E. D., and Kirk, D. B., \Flight

measured normal accelerations.

Characteristics of Prob es in the Atmospheres of Mars, Venus

and the Outer Planets," Acta Astronautica , Vol. 4, 1977,

Conclusions

pp. 789{799.

Justus, C. G., James, B. F., and Johnson, D. L., \Mars

1 Predictions of two regions of static instability

Global Reference Atmospheric Mo del Mars-GRAM 3.3.4: Pro-

during the hyp ersonic, continuum p ortion of the Mars

grammers Guide," TM 108509, NASA, May 1996.

Path nder tra jectory are veri ed by ight measure-

Clancy, R., Lee, S., Gladstone, G., McMillan, W., and

Rousch, T., \A New Mo del of Mars Atmospheric Dust Based

ments of normal accelerations. The relation of these

on Analysis of Ultraviolet Through Infrared Observations from

instabilities to sonic line movementbetween the nose

Mariner-9, Viking, and Phob os," Journal of Geophysical Re-

and the shoulder as a function of tra jectory p oint and

search ,Vol. 100, 1995, pp. 5251{5263.

kinetic mo del is demonstrated.

Sp encer, D. and Braun, R., \Mars Path nder Atmospheric

2 Perturbations to density as large as 10 ab out Entry: Tra jectory Design and Disp ersion Analysis," Journal of

Spacecraft and Rockets ,Vol. 33, No. 5, Sept.-Oct 1996, pp. 670{

nominal values for the reconstructed tra jectory dur-

676.

ing the hyp ersonic, continuum regime cause negligible

Mitcheltree, R. A., \Aerothermo dynamic Metho ds for a

change less than 1 in C . Large changes in the

Mars Environmental Survey Mars Entry," Journal of Spacecraft

kinetic mo del in this regime cause changes in C of

and Rockets ,Vol. 31, No. 3, May-June 1994, pp. 516{523.

Moss, J. N., Wilmoth, R. G., and Price, J. M., \DSMC

approximately 1. Given other sources of uncertainty

Simulations of Blunt Bo dy Flows For Mars Entries: Mars

unrelated to the simulation mo del, the reconstructed

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density, with uncertainty linearly related to uncer-

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tainty in C , is exp ected to have approximately 4

uncertainty in the hyp ersonic, continuum regime.

3 The o ccurrence of static instabilities as recorded

by normal accelerations during the Mars Path nder

entry, descent, and landing EDL provide an opp ortu-

nity for computational uid dynamic CFD co de val-

idation. Computed moment co ecients are consistent

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from 6 degree-of-freedom tra jectory simulations us-

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through the Mars atmosphere. The present simula-

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American Institute of Aeronautics and Astronautics Paper 98{2445