This paper will present analysis to evaluate a functional form and associated parameters to determine the radiative heating at various back-shell locations of the Mars 2020 aeroshell. The radiative heating indicators are used for preliminary vehicle design, and to determine the worst-case trajectories for peak radiative heat flux and load. Historically, the functional form for radiative heating is based on free-stream parameters of density, velocity and a length scale, typically the nose-radius (or equivalent). However, a fit of this form has been shown to not provide significant enough accuracy when compared to simulation results. Therefore, a fit based on post-shock equilibrium calculations of CO and CO2 number density, temperature and pressure has been devised. The results from the TPS 15 01 trajectory were used to develop the fit. The fit was then applied to the MSL best estimated trajectory (BET). Furthermore, the paper will quantify the uncertainty in simulations of the radiative heating for Mars 2020

Brandis, Aaron

Edquist, Karl

Johnston, Christopher

NASA Technical Reports Server

National Aeronautics and 
Space Administration
Entry Systems and Technology Division
Ames Research Center
Radiative Heating Indicators and 
Uncertainty Analysis for Mars 2020
Aaron Brandis
AMA Inc at NASA Ames Research Center, Moffett Field, California
Chris Johnston, Karl Edquist
NASA Langley Research Center, Hampton, Virginia
June 2018
https://ntrs.nasa.gov/search.jsp?R=20180007851 2019-08-31T17:21:50+00:00Z
Overview
• Background of CO2 radiation
- When and why this radiation is now considered for Mars missions
• Backshell Radiation for Mars 2020
- Mars 2020 is a re-fly of the MSL geometry. However, MSL did not 
include radiation in the design
- Update to aerothermal indicators used for estimating radiative heating 
on the backshell
• Uncertainty Analysis
- Inform design margins using a parametric study, and comparison to 
EAST
- Justification for using EAST data to validate aftbody flow
June 26, 2018 AIAA Aviation/Thermophysics
Presentation should highlight two major points: 
1) Detail a more accurate heating indicator which was a crucial piece of 
the puzzle for closing Mars 2020 TPS design.
2) A more rigorous analysis for assessing radiative heating uncertainty.  
Background of CO2 radiation
June 26, 2018 AIAA Aviation/Thermophysics
Background on CO2 radiation
• CO2 radiation was examined in the 1970s by NASA, but was deemed 
to be negligible. Two assumptions made at the time no longer 
employed:
- Simulations assumed chemical equilibrium and ignored radiation from the CO2
MWIR band.
• In 1992, a paper by Sundberg examined the emission from CO2 in 
the MWIR for Earth re-entry vehicles
• In 2001, a paper was published by Russian authors that radiative 
heat flux was important on the backshell for the Mars Sample Return 
Orbiter
• Around 2009/2010, prompted by EXOMARS, European researchers 
identified CO2 MWIR radiation as potentially a significant contributor 
to radiation.
• Mid 2010, preliminary EAST shots to probe the MWIR region for Mars 
conditions were performed.
• In 2011, Russian scientists improved the Carbon Dioxide 
Spectroscopic Databank (CDSD) to be valid up until 4000 K 
(previously it had only been valid up to 1000 K).
- Provides accurate values (+/- 20%) at chemical equilibrium conditions.
June 26, 2018 AIAA Aviation/Thermophysics
Background on CO2 radiation
• More detailed EAST measurements were made in 2011-13. 
Calibrated data for MWIR CO2 is now available for a range of 
conditions.
• In 2012 the CDSD-4000 database was incorporated into NEQAIR 
and HARA, thus allowing NASA to analyze the importance of CO2
radiation for flight.
- InSight being the first mission that actively incorporated radiation into its 
aerothermal environments.
• In 2012, it was observed that Viking backshell data not matched 
with convective heating calculations (up to 80% below the derived 
heat flux).
• In 2015, MEDLI forebody data under-predicted in some locations, 
and radiation was shown to significantly improve agreement.
• In 2018, COMARS flight data measured significant CO2 radiation 
during the Schiaparelli entry into Mars.
June 26, 2018 AIAA Aviation/Thermophysics
Significance of MWIR CO2
MWIR CO2 dominates radiation 
below ~ 6 km/s, and peaks   
around 3.5 km/s (2600 K).
June 26, 2018 AIAA Aviation/Thermophysics
NEQAIR results were compared 
with published plasma torch data 
with temperatures of ~1500 K & 
pressures of 1 atm
Equilibrium Radiation at 1 Torr
Backshell Radiation for Mars 2020
June 26, 2018 AIAA Aviation/Thermophysics
Mars 2020 Aerothermal Environment
June 26, 2018 AIAA Aviation/Thermophysics
PCC
~16 deg.
Lee-Side
Wind-Side
• MSL did not include radiation in its design.
• Due to good engineering, large uncertainties applied to convective heating, 
and flying close to a nominal (and not stressing) trajectory, the mission was 
a great success.
• Now with improved understanding of CO2 radiation, this heating 
mechanism has to be incorporated into the aerothermal environment.
• The parachute close-out cone (PCC) had the smallest margins for MSL, 
and so is the focus of this work.
AIAA Aviation/Thermophysics 8
PCC Heating Distributions
75.5 s
5.1 km/s
83.3 s
4.6 km/s
91.5 s
3.9 km/s
98.2 s
3.2 km/s
Convective Radiative Convective Radiative
Lee-Side
Wind-Side
June 26, 2018 AIAA Aviation/Thermophysics 9
For certain locations on the backshell, 
radiation is the dominant heating source
Radiation Correlation Outline
• Simple correlation needed to estimate peak radiative 
heating on the PCC of Mars 2020.
- Used to find worst case heating trajectories and as a functional 
form to fit aerothermal data to be parsed for sizing calculations.
• Needs to consider that at early trajectory times radiation 
is dominated by CO then later by CO2.
• These complications led to the use of post shock 
equilibrium values calculated by CEA for:
- Temperature, density and mass fraction of CO2 and CO.
• Functional form of fit employed:
- qrad = A(ρshMCO,sh)B (ρshMCO2,sh)CTshD
- Some intermediate results used a more complicated version
June 26, 2018 AIAA Aviation/Thermophysics
Rad Fit Compared to CFD Anchor Points
June 26, 2018 AIAA Aviation/Thermophysics
• Peak rad location on PCC
0
10
20
30
40
50
60
70
80
90
100
0
0.5
1
1.5
2
2.5
3
0 50 100 150 200
H
ea
t L
oa
d,
 J
/c
m
2
R
ad
 H
ea
t F
lu
x,
 W
/c
m
2
Entry Time, s
Fit CFD
Various Trajectories Rad. Heating
June 26, 2018 AIAA Aviation/Thermophysics
• Peak Rad Heating PCC location (fit based LAURA/HARA M2020 Design Traj)
• Independently compares very well with LAURA/HARA for MSL BET
PCC Lid: Old vs. New Curve Fits
AIAA Aviation/Thermophysics
CEA Fit
qrad = A(ρshMCO,sh)B (ρshMCO2,sh)CTshD
(Updated to be used for sizing)
Sutton-Graves Fit
qrad = Aρ∞BV∞C
(Previously used for sizing)
Sutton-Graves Fit adds significant heating 
when closi g out the heat pulse. 
This artificially adds TPS thickness.
The CEA style fit was a c ucial element for 
closing the TPS design.
June 26, 2018 13
In many cases the CEA style fit reduced heat load by ~10%.
In some cases, such as the antenna, it was reduced by ~50%.
The impact of this reduction will be discussed in a follow on 
talk in this session. 
Now with the aerothermal environments in hand, the 
uncertainty needs to be assessed.
Parametric Uncertainty 
Assessment
June 26, 2018 AIAA Aviation/Thermophysics
Parametric Uncertainty Range
• Lower bound for CO2 dissociation rate of -1/2 order-of-
magnitude assessed from literature values:
- Park value is the nominal rate.
- Ebrahim, Fujita, Annaloro have all proposed values nearly 1/2 order-of-
magnitude lower than Park rate.
• CO2 IR radiative cross section uncertainty assessed through 
comparisons with EAST measurements.
- Resulting cross sections are as follows:
 20% increase for the 4.5 µm band
 70% increase for the 2.7 µm band
- These uncertainties may be interpreted as deficiencies in the CDSD 
database or un-modeled nonequilibrium phenomena.
June 26, 2018 AIAA Aviation/Thermophysics 15
Comparison Summary: Test 54
• Test 54 (100% CO2) drove the 70% increase in the 2.7 µm 
cross section (positive values are under-predictions):
Impact of changing rate & 
cross section
June 26, 2018 AIAA Aviation/Thermophysics 16
Impact: From 70% under-prediction 
to 45% over-prediction
Sensitivity Analysis
• Impact of ½ order-of-magnitude reduction in CO2
dissociation rate:
% Increase in qrad4.86 km/s 3.25 km/s
June 26, 2018 AIAA Aviation/Thermophysics 17
Sensitivity Analysis
• Impact of 70% increase in 2.7 µm band and 20% increase 
in 4.5 µm band:
% Increase in qrad4.86 km/s 3.25 km/s
June 26, 2018 AIAA Aviation/Thermophysics 18
How can we justify use currently available 
EAST data to validate aftbody/expanding flows 
relevant to flight?
Details along Ray 1
shockwall
Tve p
Ray 1 Intensity reaches 90% of 
its wall value between 
streamlines A and B
Low pressure separated 
flow region has small 
impact on radiation.
June 26, 2018 AIAA Aviation/Thermophysics 19
Details along Streamline A
Streamline A
Tve
p
Expanding flow
June 26, 2018 AIAA Aviation/Thermophysics 20
We are now going to derive a parameter to 
characterize the state of this expanding gas
CO2 Dissociation Parameter 
• CO2 dissociation parameter defined as:
• Φ > 0: Dissociation – typically associated with compressing
forebody flow. Indicates emitting vibrational or electronic levels will 
be less than Boltzmann.
• Φ = 0: Equilibrium
• Φ < 0: Recombination – typically associated with expanding
afterbody flow. Indicates emitting vibrational or electronic levels will 
be greater than Boltzmann.
Equilibrium constant for CO2 dissociation
• Post-shock EAST measurements contain Φ > 0.
– Therefore, they are typically assumed only relevant to compressing forebody flow.
June 26, 2018 AIAA Aviation/Thermophysics 21
Details along Streamline A
Streamline A
Tve
p
Φ
Φ
cCO2
Φ > 0 along entire 
streamline
Negligible CO2
dissociation 
across weak 
oblique shock
June 26, 2018 AIAA Aviation/Thermophysics 22
As this is an expanding but not recombining 
flow, we can use EAST data for validation
Details along Streamline B
Streamline B
Tve
p
Φ
ΦcCO2
Significant CO2
dissociation
CO2 freezes 
before Φ goes 
negative
23
Sharper expansion 
than streamline A
Relationship between Phi and Emission
Regions of strong 
emission and 
positive Φ overlap
• Over 80% of the wall-directed intensity for rays 1 and 2 
originates in regions with positive Φ.
24
Due to the oblique shock dominating the radiance, there is 
reason to believe these uncertainties may be applicable to 
future Mars missions with different backshell geometries. 
Comparison with EAST: 4.9 km/s, 0.5 Torr
Tve
p
Φ
cCO2
Φ
June 26, 2018 AIAA Aviation/Thermophysics 25
Comparison with EAST: 3.6 km/s, 1.0 Torr
Tve
p
Φ
cCO2
Φ
June 26, 2018 AIAA Aviation/Thermophysics 26
Comparison with EAST: 2.1 km/s, 1.55 Torr
Tve
p
Φ
cCO2
Φ
June 26, 2018 AIAA Aviation/Thermophysics 27
Increased confidence in simulation tools and uncertainties 
due to encompassing EAST data and matching the CO2
dissociation parameter with flight. 
Aftbody Radiation Uncertainty from InSight
Analysis
• A 1.47 aftbody radiation uncertainty factor was initially used for thermal analyses 
was based on work conducted for the InSight mission
- Max. uncertainty among aftbody locations considered for InSight
• Comparisons were made between NEQAIR and HARA for Mars 2020 in order to 
update the A+B contribution (not talked about today)
June 26, 2018 AIAA Aviation/Thermophysics
~32%
Resulting Centerline Uncertainties
June 26, 2018 AIAA Aviation/Thermophysics 29
• Largest spatial margin value picked for each case  and 
applied over the trajectory. 
5.46 km/s
5.27 km/s
4.86 km/s
3.90 km/s
3.25 km/s
2.72 km/s
2.00 km/s
Uncertainty over Trajectory
• At velocities above ~2900 m/s, the velocity-dependent total 
qrad uncertainty is higher than 47%
June 26, 2018 AIAA Aviation/Thermophysics
• This uncertainty is then 
weighted by radiative heat flux 
over the trajectory, and 
resulted in an uncertainty of 
32%.
Conclusion
• Shown updated methodology for radiative heating indicators 
applied to Mars 2020
- Updated indicators significantly reduced excess heating being added 
when closing out heating pulse
- Very important element for closing the Mars 2020 backshell TPS 
design, particularly on PCC
• Overview of Mars 2020 backshell radiation shown
• Uncertainty analysis described to inform an update to 
design margins.
- Parametric uncertainty performed
- Comparisons with EAST data
- Justification for using EAST data to validate expanding flow
June 26, 2018 AIAA Aviation/Thermophysics
The impact of this environment and uncertainty work to 
the TPS sizing will be shown in a following presentation…
National Aeronautics and 
Space Administration
Ames Research Center
Entry Systems and Technology Division
Comparison Summary: Test 55
Impact of changing dissociation rate.
Impact of changing cross section
• Difference between simulations and measurements 
(positive values are under-predictions):
June 26, 2018 AIAA Aviation/Thermophysics 33


Radiative Heating Indicators and Uncertainty Analysis for Mars 2020

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