AIAA 2006-2946
Numerical Assessment of Data in Catalytic and Transitional
Flows for Martian Entry
Matthew MacLean
*
and Michael Holden
†
CUBRC, Aerothermal/Aero-optics Evaluation Center, Buffalo, NY, 14225
The conditions for a typical run from the MSL phase two study of transition that was
performed in the LENS facility have been analyzed to understand the sensitivity to the
freestream conditions of the facility. A simplified analysis technique has been used based on
energy accounting to freeze specified portions of the chemical or vibrational energy during
the expansion process in the nozzle. The effect of freezing this energy results in increased
shock standoff distance that better matches the measured shock shape. Based on several
cases, it was found that freezing approximately 42% of the total enthalpy of the flow in the
vibration mode results in the best agreement with the measured shock shape. This modified
condition also results in significantly better agreement with the measured surface heat
transfer at the stagnation point and with the measured pressure at the shoulders of the
model. Based on this adjusted freestream condition, the surface heat transfer data shows
behavior generally consistent with fully-catalytic recombination on the cold wall. This
behavior is consistent with previous results obtained in shock tunnel facilities in carbon
dioxide, air, and nitrogen. Although the mechanism causing this frozen energy in the flow
has not been identified, the sensitivity of the transition onset point of the flowfield to this
phenomenon has been estimated to be less than 10% based on a simple transition criterion.
I. Introduction
eliable payload delivery systems are necessary to deliver lander and rover payloads to other planets in the solar
system in order to fulfill NASA’s current planetary exploration directive, a primary focus of which is Mars.
Although the costs and limited launch opportunities of such exploratory programs require that the re-entry vehicle
have a high factor of safety to insure good odds of success, an overly conservative design will result in reduced
payload capacity and, hence, reduced scientific opportunity for the mission. Because the opportunities for flight
tests in the Martian atmosphere are rare and the ability to collect data from such an experiment is typically limited or
impossible, the optimization of heat shield design to insure robustness while minimizing unnecessary conservatism
must be carried out in ground test facilities here on Earth.
R
The Mars Science Laboratory (MSL) mission is the next scheduled NASA rover vehicle targeting the
exploration of the Martian surface that will depart from Earth. As part of the aerothermal environment specification,
a two phase program has been completed at CUBRC to measure the effects of flow transition on the forebody design
of the entry, descent, and landing (EDL) shape. Although the 70
O
sphere-cone aeroshell geometry is quite similar to
previous missions to Mars such as Viking, Pathfinder, and the Mars Exploration Rovers (MER), the MSL design
will be considerably larger than any previous EDL configuration. The increased size results in trajectories which
will be more significantly dominated by turbulent heating than in any previous mission. This augmented heating
environment requires additional understanding of the physics involved to accurately design the vehicle.
In phase one of this program, CUBRC tested a 61 cm (24”) diameter sphere-cone model in the LENS-I
facility over a wide range of Reynolds numbers at effective flow enthalpies of 5 and 10 MJ/kg. The model was
constructed of stainless steel and coated with magnesium-fluoride. The instrumentation package consisted of a ray
of thin-film heat transfer gages on the centerline of the model running from the windward corner to the leeward
corner. Additional angular rays of gages were located on the leeward side of the model at three constant radius
locations. This primary instrumentation was supplemented with several forebody pressure gages, several forebody
*
Senior Research Scientist, AIAA Member.
†
AAEC Program Manager, AIAA Fellow.
Copyright ©2006 by Matthew MacLean. Published by the American Institute of Aeronautics and Astronautics, Inc.
(AIAA) with permission.
1
AIAA 2006-2946
coaxial thermocouple heat transfer gages, and a few thin-film gages on the backside of the model to assess wake
establishment. Laminar, transitional, and turbulent heating data was acquired at angles of attack of 16
O
, 11
O
(the
nominal flight angle), and 0
O
. The details of the phase one study and the post-test data analysis are given by
MacLean, et al
1
. and Hollis, et al
2
.
The results of the phase one study showed that we did not acquire data for a fully laminar baseline case at
angle of attack because of the large size of the model. Also, surface catalysis was found to be a central problem in
the ground test studies. In studies in both LENS and the Caltech T5 facility
3
, measured surface heating for laminar
flows always showed a level that was consistent with predictions for fully-catalytic recombination to pure carbon
dioxide at the cold wall. The phase two study tested a 31cm (12”) sphere-cone model, or half the size of the original
model. The smaller size was designed to better target laminar flow conditions at angle of attack to compliment and
verify the phase one results. To investigate the catalytic heating effect, the phase two model employed three distinct
types of instrumentation. First, coaxial type thermocouple gages were installed on the windward and leeward
centerline of the model, forming a continuous metallic surface exposed to the flow. Second, thin-film gages were
employed on a continuous strip of pyrex, eliminating the discontinuity of alternating metallic/non-metallic surfaces
that the flow was exposed to in phase one. Third, silver calorimeter gages were installed in the model, as silver is
known to be a catalytic material to many reactions.
In our efforts to measure transitional and turbulent heating on these bodies in a high enthalpy carbon dioxide
flow, we have found that the understanding of this data is a highly coupled process. In order to understand the
transitional heating on the surface, one must understand the surface catalysis of the steel ground test models. In
order to understand the catalytic response of the model, one must understand the thermodynamic and chemical state
of the gas on the freestream and the shock layer of the flowfield. Thus, these effects must be considered in this
order to make a correct estimate of the data.
In the phase two results, our measurements of shock shape deviates from the shape predicted by CFD when
computed with a nominal set of freestream conditions. These freestream conditions are found for each run by
computing the nozzle flowfield from reservoir to test section with a single degree of freedom simple harmonic
oscillator using rates from Camac and appropriate chemistry reaction rates evaluated using a T-Tv dissociation
coupling model. This model predicts that the vibrational degree of freedom is approximately in equilibrium with the
translation-rotation temperature for the range of densities that we studied. In each case, the bow shock that was
measured from Schlieren photography shows a larger stand-off distance than the prediction. Further study of these
conditions suggests that there is a larger frozen energy component in the freestream of the facility than the current
modeling methodology predicts.
II. Experimental Facility Background
Currently, CUBRC operates the 48” reflected shock tunnel, the LENS-I and LENS-II reflected shock tunnels
4
,
and the LENS-X expansion tunnel
5
. The reflected shock tunnel uses a shock to heat and pressurize a stagnant test
gas to high enthalpy levels. This test gas may then be expanded through a converging-diverging nozzle in a manner
similar to a blowdown facility
to produce a hypervelocity test
flow. Expansion tunnels like
LENS-X also operate as short
duration facilities, but an
expansion tunnel produces a
high enthalpy flow without the
need to first stagnate the test
gas. In an expansion tunnel, the
high enthalpy gas is generated
in two stages. In the first stage,
the test gas in the driven tube is
compressed and heated by a
shock, but the moving flow
behind the incident shock is not
immediately brought to a halt
by a reflected shock as in a
reflected shock tunnel.
Secondly, additional energy is
(a) LENS-I Facility
(b) LENS-II Facility
(c) LENS-X Facility
Figure 1. Drawin
g
s of CUBRC LENS H
y
pervelocit
y
Shock Tunnel
Facilities with Nominal Dimensions [all values shown in inches].
2
AIAA 2006-2946
added to this moving gas by an unsteady expansion in the acceleration segment of the tunnel to produce a low static
temperature, high velocity test gas which is then isentropically expanded in a diverging nozzle to achieve a high
enthalpy test flow at a thermodynamic state like that of a flight condition. The result is a freestream flow that is free
of frozen, dissociated chemical contamination that can plague reflected shock facilities at enthalpies exceeding 10
MJ/kg. While the useable test times from an expansion tunnel are generally shorter than those from a reflected
shock tunnel, the clean, very high enthalpy flows that an expansion tunnel can generate provides a unique testing
capability. A schematic of all of the LENS facilities with basic length scales is given in Fig. 1.
The LENS reflected shock-tunnel facilities were developed primarily to study the full-scale, hypervelocity
flow physics of interceptors and air-breathing engine configurations. The scale and flow duplication capabilities of
LENS are such that these vehicles can be studied at their full scale, inclusive of effects such as transition to
turbulence, turbulent mixing from cross-flow jets and thrusters, duplicated flow chemistry and other effects that are
difficult or impossible to simulate at cold-flow or sub-scale conditions. Besides aerothermal measurements,
extensive studies in this facility have been made using non-intrusive diagnostics such as aero-optic and aero-acoustic
measurements, including recent work with tunable laser-diode diagnostics
6
. The capabilities of LENS-I duplicate
the flight conditions of interceptors and scramjet engines from Mach 7 to 15 (with Reynolds number matching to
Mach 22), while the LENS-II facility complements it in such a way that this capability is seamlessly extended down
to Mach 3.5 at sea level density.
Although any of the three LENS facilities or the 48” tunnel can use carbon dioxide test gas with no special
effort to set up, LENS-I was used for all tests to date because it is most compatible with the primary goal of
obtaining transition data on a 70
O
sphere-cone model for the MSL program. The capability to use heated hydrogen
for a driver gas in LENS-I provided transition data at the most relevant enthalpy for the Martian entry trajectory.
The contoured D nozzle using some of the existing throats in LENS-I was found to produce reasonably uniform exit
profiles in carbon dioxide without any modification, despite the fact that the expansion of carbon dioxide into the
test section produces a lower Mach number than the same nozzle does for air at the same enthalpy. Sample results
demonstrating the uniformity of the test core in carbon dioxide have already been shown
1,7
and will not be repeated
here. A typical capability map of density versus velocity is shown in Fig. 2 for carbon dioxide showing the three
LENS facilities. The potential
range of conditions, particularly
for LENS-II and LENS-X, has
been assessed analytically because
the range of calibrated conditions
are currently limited. A velocity-
altitude graph for the Martian
atmosphere was initially
considered but was found to be
uninteresting as the Martian
atmosphere is so thin that all three
facilities are capable of producing
significantly higher than surface
level densities. A typical entry
trajectory is also shown from the
Pathfinder mission
8
. The density
of the trajectory has been
increased to maintain a (
ρ
L)
simulation on a model scale that
can fit conveniently in all three
facilities, and the resulting
trajectory has been found to fit
well in the LENS capability range.
Figure 2. Density-Velocit
y
Map of the CUBRC Facilities usin
g
Carbon Dioxide Test Gas
III. Supporting Numerical
Tools
A. DPLR Code
All ground test studies in the LENS facilities are extensively calibrated and validated with numerical tools.
The primary CFD tool used in these efforts is the DPLR code provided by NASA Ames Research Center. DPLR is
3
AIAA 2006-2946
a multi-block, structured, finite-volume code that solves the reacting Navier-Stokes equations including finite rate
chemistry and finite rate vibrational non-equilibrium effects. This code is based on the data-parallel line relaxation
method
9
and implements a modified (low dissipation) Steger-Warming flux splitting approach
10
for the convection
terms and central differencing for the diffusion terms. Finite rate vibrational relaxation is modeled via one simple
harmonic oscillator vibrational degree of freedom
11
using the Landau-Teller model
12
. Vibrational energy relaxation
rates are computed by default from the semi-empirical expression due to Millikan and White
13
, but rates from the
work of Camac
14
are substituted for the CO
2
-CO
2
collisions and those collected by Park, et al
15
. for the other
collisions in the cases studied here. Vibration-dissociation coupling is currently modeled using the T-Tv approach of
Park
16
with an exponent on both temperatures of 0.50. Transport properties are appropriately modeled in DPLR for
this type of flow
17,18
using the binary collision-integral based mixing rules from Gupta, et al
19
. Diffusion
coefficients are modeled using the self-consistent effective binary diffusion (SCEBD) method
20
. Turbulence models
available in the DPLR code currently include the Baldwin-Lomax 0-equation model
21
, the Spalart-Allmaras model
1-equation model
22
, and the Shear Stress Transport (SST) 2-equation model
23
each with corrections for
compressibility effects
24,25
.
The issue of the chemical wall boundary condition deserves some specific consideration and DPLR is
programmed with several options. The non-catalytic wall boundary condition provides the lowest level of surface
heating. The super-catalytic boundary condition provides the highest possible level of heating because the mixture
is returned to its lowest possible chemical energy state at the wall, meaning that the maximum amount of chemical
energy has been distributed to the other energy modes. In this case, that state corresponds to 100% CO
2
. The super-
catalytic boundary is non-physical in that it does not identify a specific mechanism by which the recombination
occurs, but assumes that it has occurred by some unidentified process without consideration of rate mechanisms. In
the case of short-duration facilities like LENS, the surface temperature of the model never rises appreciably above
room temperature, so the super-catalytic CO
2
condition corresponds to a fully-accommodated chemical state.
B. CREST Code
The LENS facilities are typically operated using a tailored interface, meaning that the interface between the
driver and the test gas is brought exactly to a halt by the reflected shock off the endwall. This results in the
maximum of test time for the facility as the test period ends when expansion waves from the driver arrive at the
endwall. For a large scale facility operating using a tailored interface, the state of the reservoir gas may be
computed assuming a single incident shock into the test gas followed by a single reflected shock. The state of the
gas behind these two shocks is that of the reservoir.
The reservoir conditions for each run are computed from measured values of shock speed and the initial
temperature and pressure in the driven tube. The CUBRC Reservoir Equilibrium Shock Tunnel (CREST) code has
been developed to compute the properties behind each moving shock
26
. Downstream of both the incident and the
reflected shock, equilibrium chemistry and thermodynamics are assumed. Equilibrium contributions of vibrational
and/or electronic energy excitation are included in the state calculation, and the equilibrium concentrations of all
included species are also solved for. Further, because the LENS-I facility can generate dense reservoir states in
excess of 100 times sea level density, the excluded volume equation of state as discussed by Lordi and Mates
27
is
employed. In the excluded volume approach, the ideal-gas law is modified to include a term that accounts for the
effective volume taken up by the gas molecules. Thus, at low densities, this term becomes insignificant, and results
consistent with the ideal-gas law are returned. Because of the equilibrium calculation, the downstream properties of
each shock must be found with a non-linear, iterative solver. The measured reservoir pressure during the run is used
to correct the computed reservoir state of the gas, which accounts for effective area change in the endwall region of
the facility resulting from our centerbody valve system that protects the test articles and instrumentation from
excessive particulate damage after each run.
In the case of carbon dioxide tests, a four species model that includes CO
2
, CO, O
2
, and O is used. Initially, C
was also included but was found to be negligible at the conditions for the LENS facilities. The results from CREST
have been found to agree with the results from both the ESTC
28
and CEA
29
codes for low density cases where the
non-ideal gas effects are not important. CEA, which includes contributions from several dozen species, shows that
only the four included species are present for our range of conditions in any significant concentration.
C. Nozzle Code
A specialized code has been developed by Candler
30
to compute the nozzle flowfield for a high-pressure,
high-enthalpy ground test facility. This code shares much of its heritage with the NASA Ames DPLR code
(described in A above) as it employs the same flux splitting and time integration treatments. The nozzle code has
been streamlined by hardwiring parts of the code to solve for a single-block, axisymmetric nozzle with fixed
4
AIAA 2006-2946
boundary conditions. These modifications lead to a substantial decrease in required solution time and allow us to
compute the nozzle flowfield in the same length of time that it requires to set-up and make a run in the LENS
facilities (about 2 hours).
The nozzle code employs the Spalart-Allmaras
22
one-equation turbulence model with the Catris and Aupoix
compressibility correction
25
. This turbulence formulation has been shown to adequately predict the displacement of
the turbulent boundary layer in the throat region of the nozzle and subsequent boundary layer distortion caused by
the rapid reduction in local Reynolds number in the diverging section of the nozzle. We have demonstrated this
agreement through comparisons with measured Pitot pressure profiles in the freestream in several previous
publications
7,30
.
The nozzle code also uses the same excluded volume equation of state as does the CREST code, so that
results from CREST become consistent input boundary conditions to the subsonic inflow plane. Computed
freestream conditions from the nozzle code are also consistent with the model flowfield calculations done with
DPLR since both codes employ the same thermo-chemical models, constants, and rate coefficients. Thus, without
the excluded volume correction, we would expect the nozzle code and DPLR to produce the same result for the
nozzle flowfield.
IV. Analysis of Flow Conditions with Carbon Dioxide Test gas
A. Nominal Conditions on the Model
Because of the large negative heat of
formation of carbon dioxide, the definition
of total enthalpy in the flow can be
somewhat misleading. Thus, the
convention defined by Eqn (1) is used
throughout this publication. The effective
total enthalpy provided by the shock tunnel
is the net increase in energy from the initial
state in the driven tube, which is defined as 100% carbon dioxide at the measured wall temperature and driven tube
pressure in the lab. This convention insures that total enthalpy will always be a positive number, making it more
consistent with the expected results when one is testing in air or nitrogen. Also, since the reflected shock tunnel
facility does not see a significant increase in wall temperature during the run time, the term given in Eqn (1) is
useful and relevant in the aerothermal analysis to, for example, define the Stanton number.
Table 1. Reservoir Conditions for Run 8
P
0
29.5 MPa
ρ
38.30 kg/m
3
T
0
= T
V0
3,499 K c
CO2
0.7701
h
0
EFF
5.63 MJ/kg c
CO
0.1463
h
0
-3.09 MJ/kg c
O2
0.0798
h
INITIAL
-8.72 MJ/kg c
O
0.0037
INITIAL
EFF
hhh −=
00
(1)
As a typical, representative case, run 8 from
the MSL phase-two program has been selected for
further study. This run measured the phase-two
sphere-cone heating at zero degrees angle of attack
(an axisymmetric flowfield) at a relatively low total
pressure and freestream unit Reynolds number to
obtain fully laminar flow on the body. The total
enthalpy effective increase for this case was 5.63
MJ/kg. The complete set of equilibrium reservoir
conditions as computed by the CREST code is given
in Table 1.
Figure 3. Prediction of Vibrational Relaxation of CO
2
Gas in LENS Nozzle with Camac and Millikan-White
Rates
Calculations were performed with the nozzle
code tool to determine the freestream conditions for
all runs. A single set of values was used from the
centerline of each calculation at the axial station in
the test section where the nose of the model was
positioned. The degree of non-uniformity in the test
section of the facility is small enough that it is not
expected to be significant for this body shape. In
the nominal case, the vibration is treated with the
Landau-Teller model with a common vibrational
temperature using Camac rates. The result of this
5
