[American Institute of Aeronautics and Astronautics AIAA Atmospheric Flight Mechanics Conference and...

American Institute of Aeronautics and Astronautics

1

Parametric Shape Study of Capsule-Type Vehicles

During Atmospheric Re-entry

Kamal M. Shweyk*, B.F. Tamrat

†, and Abdi Khodadoust

‡

Phantom Works, The Boeing Company, Huntington Beach, California, 92647

This paper describes research undertaken to validate specific computational tools that

predict the aerodynamic and, to a lesser extent, aerothermodynamic characteristics of blunt,

capsule-type vehicles during atmospheric re-entry. To this end, several candidate capsules

were considered, with varying side wall angles and symmetrical and asymmetrical heat

shields. The results illustrate the correlations obtained from analytical predictions against

actual test data collected through two separate wind tunnel tests that span the range of Mach

numbers of interest. The research also assessed the effects of critical Outer Mould Line

parameters on the aerodynamic performance of the vehicle, including its stability and

control characteristics, and compared the results against the historical Apollo configuration.

The candidate vehicles’ center of gravity envelopes for single trim attitudes during re-entry

were also determined to evaluate their monopole stability tendencies. The results show that,

for the configurations with symmetrical heat shields, an Apollo concept offered the best lift-

to-drag ratio and the highest trim angle of attack for a given center of gravity position. The

capsule configuration with the asymmetrical heat shield, while offering the best overall lift-

to-drag ratio, exhibited a relatively large trim angle of attack changes as a function of roll

attitude. The center of gravity longitudinal displacement required to achieve monopole

stability of a single angle of attack trim point, increased with decreasing side wall angle.

Nomenclature

α = Angle of Attack, Degrees

β = Angle of Sideslip, Degrees

φ = Roll or Bank Angle, Degrees

CL = Lift Coefficient

CD = Drag Coefficient

CY = Side Force Coefficient

Cm = Pitching Moment Coefficient

Cl = Rolling Moment Coefficient

Cn = Yawing Moment Coefficient

L/D = Lift to Drag Ratio

AEDC = Arnold Engineering Development Center

AFE = Aeroassist Flight Experiment

APAS = Aerodynamic Preliminary Analysis System

BCFD = Boeing Computational Fluid Dynamics

c.g. = Center of Gravity

LaRC = Langley Research Center

OML = Outer Mold Line

Re = Reynolds Number per Foot

TPS = Thermal Protection System

USA = Unified Solution Algorithm

X/d = Non Dimensional Distance, positive in the direction the pilot faces

Z/d = Non-Dimensional Distance, positive in the direction of pilot’s head

_________________________________ *Principal Engineer/Scientist, Stability, Control, and Flying Qualities, Phantom Works, The Boeing Company, AIAA Member.

†Associate Technical Fellow, Stability, Control, and Flying Qualities, Phantom Works, The Boeing Company, AIAA Member.

‡Aerodynamics Manager, Space Exploration Systems, The Boeing Company, AIAA Associate Fellow.

AIAA Atmospheric Flight Mechanics Conference and Exhibit21 - 24 August 2006, Keystone, Colorado

AIAA 2006-6140

Copyright © 2006 by The Boeing Company. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.


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I. Introduction

As part of NASA’s Vision for Space Exploration to return man to the moon in preparation for human exploration

of Mars and beyond, capsule-type re-entry vehicles have reemerged as the configuration of choice for space

transportation1, 2

, primarily due to their proven and arguably safer design and, thus, lower associated risks and costs.

Current engineering analytical tools were, thus, required to support conceptual design studies of atmospheric re-

entry capsules. Since many of these tools were largely used and validated for wing-type vehicles, such as the Space

Shuttle, the need to confirm their validity for re-entry capsules became apparent.

Early in 2005, an Internal Research and Development (IRAD) grant funded by Boeing NASA Systems was

secured to address this issue. In order to facilitate the objective of validating current tools for capsule-type vehicles,

several configuration concepts were tested at two separate wind tunnel facilities in order to provide the required

validation target data. The resulting wind tunnel test data also provided the opportunity to better understand the

effects of key configuration changes, such as side wall angles, symmetrical heat shield, and asymmetrical heat

shield, on the aerodynamic performance of the vehicle, as well as its stability and control characteristics, specifically

in terms of the ability to trim at a single angle of attack, or rather, monopole stability. The goal was to determine the

sensitivity of key aerodynamic parameters to changes in the Outer Mold Line of a typical capsule

II. Analytical Tools

Several computational tools were used for this study, including the Aerodynamic Preliminary Analysis System

(APAS), Boeing Computational Fluid Dynamics (BCFD), and Unified Solution Algorithm (USA). Other

engineering aeroheating analysis tools, such as XF0002, were also evaluated using the limited aeroheating test data

that were collected. The aeroheating results, however, will be mentioned only briefly in this paper, which is more

focused on the aerodynamic results of the study. The following paragraphs offer a brief description of the primary

computational tools used.

A. Aerodynamic Preliminary Analysis System (APAS)

The APAS low order aero prediction software is an industry-proven standard available to NASA and other

government establishments, as well as academia and private contractors. It has been used extensively within Boeing

for conceptual design of a wide range of aerodynamic configurations including fighter, bombers, Space Shuttle, and

numerous X-planes, such as the Space Launch Initiative (SLI) and the Orbital Space Plane (OSP). The APAS

program is designed to provide complete vehicle aerodynamic analysis through subsonic, supersonic, and

hypersonic speed regimes. The shell program allows the aerodynamicist to pre and post process the geometry,

specify the configurations and analysis options, review the geometry prior to the analysis, and post process the force

and moment data.

Within the software, a Unified Distributed Panel (UDP) program performs the subsonic and supersonic analysis

(0.0<Mach<0.98 and 1.05<Mach<3.0). The UDP code is formulated from linear small disturbance theory to

calculate a complete multiple vehicle configuration’s longitudinal and lateral forces and moments. The analysis is

supplemented by additional codes to calculate skin friction drag, base drag, and supersonic wave drag. For higher

speeds, the Hypersonic Arbitrary Body Program (HABP) performs the hypersonic analysis (4.0<Mach<25.0). The

HABP program represents the geometry as a series of quadrilateral panels that are analyzed by a series of

Newtonian Theory methodologies. The pressure coefficients, temperatures, and velocities are calculated from the

panel orientation.

Among the aerodynamic prediction tools used in this study, APAS provides the fastest turn-around. This is born

from linearization of the governing equations applied throughout the flight regime. The gain in computational

efficiency is usually accompanied by a sacrifice in accuracy of predictions, however. Typical execution times are

less then one minute per Mach number with a 20 angles of attack sweep. References 3 and 4 offer additional

information regarding APAS.

B. Boeing Computational Fluid Dynamics (BCFD)

The BCFD code is a general geometry and general purpose Euler and Navier-Stokes solver that operates in three

dimensions with unstructured grids and two and three dimensions with structured grids (patched and overlapping).

Any valid grid can be utilized (tet, hex, prism, and pyra-mid) with the BCFD code. A mature zone coupling

technique ensures continuity of the solution across zone boundaries. BCFD has a library of boundary condition

routines available on a point-by-point basis.

BCFD has been used for flows from nearly incompressible speeds (M~0.05) to hypersonic. The gas chemistry

can be modeled in ideal gas, thermally perfect, and multi-species (frozen, equilibrium, and finite-rate) modes. The


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species concentrations and reaction rates are read from data files at run time allowing flows of arbitrary chemical

mixtures to be predicted. For unstructured grids, the default time integration scheme is a first-order accurate, Guass-

Seidel implicit scheme. For steady-state flows, variable time steps based on local Eigen values are used to speed

convergence. A blend of second- and fourth-order dissipation and flux limiters may be activated for robustness and

convergence acceleration.

For the majority of the predictions carried out with BCFD during this study, the tool was used in the Euler mode.

This means that the governing equations represent the flow physics (in the averaged sense) except for viscous effects

in the flow field. This form of computation generally yields quite reasonable predictions, both in terms of turn-

around efficiency and accuracy. The solutions yield distributed loads on the vehicle OML, which are typically used

for structural loads estimates, and the integration of these distributed loads on the vehicle OML provides the

predicted forces and moments. Reference 5 offers additional information about BCFD, including details of the

turbulence models utilized for structured and unstructured grids.

C. Unified Solution Algorithm (USA)

The USA code is a very versatile 3-dimentional flow solver that can be used to compute numerical solutions to a

large class of aerodynamic and aerothermodynamic problems by solving the Euler or Reynolds-averaged Navier-

Stokes equations. The discretization is a Total Variation Diminishing (TVD) formulation for the inviscid fluxes (up

to third order for equal spaced grids) and second order central differencing for the viscous fluxes using a finite

volume framework. The TVD formulation allows the USA code to automatically handle flow discontinuities

without any extra dissipation operators. This allows the code to resolve the flow discontinuities (shocks, contact

surfaces) generally without oscillations. A multizonal structural grid bookkeeping method facilitates the treatment

of complex geometric topologies. The grid zones or blocks can be aligned or unaligned. For least numerical error,

unaligned interfaces should be kept to a minimum. A real gas approach based on a finite rate chemistry formulation

can be coupled or uncoupled with the fluid dynamics to treat reacting and nonreacting gaseous species.

The USA code can be used for a wide variety of situations, including unsteady and steady flows; low speed,

subsonic, transonic, supersonic, and hypersonic flows; perfect gas, equilibrium air curve fit, frozen, equilibrium and

finite-rate chemistry; viscous and inviscid flows; simple and complex geometries; and internal and external flows.

The code has been in use since the early 1980s and has been used on many projects such as the Space Shuttle,

SSME, NASP, RLV, X37, and Columbia Shuttle Accident Investigation. As the USA code was developed, a wide

range of calibrations and validations had been done where comparison to experimental data was considered good.

The USA code provided the slowest turn-around time compared to the other tools used in this study. This is due

to time-intensive calculations, such as the simulation of viscous effects, which is vital for complete characterization

of the aerodynamic heating flight environments. Additional details regarding the USA code are available via

References 6, 7, and 8.

D. Convective Heat Transfer Coefficient Predictor, XF0002

The XF0002 engineering code was formulated as a rapid turn-around, preliminary analytical design tool to

develop heat transfer rates and surface temperature design environments for supersonic through hypersonic, full

and/or model scale conditions. The roots of XF0002 can be traced back to the early years of the space program and

has been adapted over time to meet the changing needs of the various programs to which it was applied. It has been

calibrated using a variety of flight test and wind tunnel data (X-15, Apollo, Shuttle, NASP, X-37, etc.), along with a

number of CFD solutions. Results have been shown to agree favorably with other industry-accepted heating

prediction codes such as MINIVER and AEROHEAT.

XF0002 employs a fixed point solution technique on simple geometric shapes (cones, wedges, spheres, and

cylinders) which approximate a user input arbitrary vehicle geometry (local surface flow angles and wetted surface

running lengths). Industry accepted engineering flow field and heating theories are used to provide estimates of

external heating and local properties at particular body points as a function of input trajectory parameters (time,

altitude, velocity, angle of attack, etc.) The code can compute heating at 50 locations and 100 trajectory time cuts

per run with typical execution time in minutes and is well suited to perform trade studies and trajectory analyses.

Results of the aerodynamic heating analyses are generally presented in the form of 1) convective heating rate

time histories as a function of 4 fixed wall temperatures (Tw), 2) local pressure histories, and 3) radiative

equilibrium heating and temperature histories for each of the Body Points. Those data are used in the streamlined

aerothermal TPS sizing process employed to select types and determine thicknesses of TPS for the vehicle

configuration being studied. Predictions are typically provided in terms of heating rates, as a function of surface arc

length. Reference 9 offers additional information about the XF0002 code.


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III. Test Configurations and Plans

In order to fulfill the objective of validating the above analytical tools for capsule-type vehicles, five different

Command Modules (CM) configurations, including one that is representative of the Apollo capsule and one of the

Soyuz capsule, were defined. Selecting an Apollo configuration as one of the candidate shapes allowed the

researchers to utilize a large amount of already-existing data. The different test configurations, a side view of each

is given in Figure 1, reflect changes in key parameters, specifically side wall angle, side wall contour, and

symmetrical and asymmetrical heat shields. It should be noted that the asymmetrical heat shield that was modeled

reflects the Aeroassist Flight Experiement (AFE) concept, which is detailed in References 10 and 11. This particular

shape was evaluated as an option for the capsule base geometry since design information on this shape indicated

potential aerodynamic and aeroheating improvements.

As shown in Figure 1, each test configuration was labeled by a Command Module (CM) number and a base (B)

number, with B1 implying a symmetrical base and B2 implying an asymmetrical base. The CM1+B1 and CM4+B1

configurations are based on the Apollo and the Soyuz capsules, respectively, while the CM2+B1 (24.6 deg side

wall) and CM3+B1 (16.6 deg side wall) configurations represent intermediate side wall angles between the former

two.

Figure 1. Subject Test Configurations.

Table 1 lists key dimension for each wind test model, scaled to 3.8%, and includes an illustration of how each

parameter is measured. The dimensions are in degrees for angles and in inches for distances. Each model was

assembled in pieces and houses a three component balance that provided the required forces and moments.

B2=AFE base1.3543.6656.06424.60CM2+B2 (AFE)

Bottom Radius

=1.609 in1.3923.7736.01810.00CM4+B1 (Soyuz)

1.9243.6656.03216.60CM3+B1

1.3543.6656.06424.60

CM2+B1

(Baseline)

B1=Nominal base0.8863.4016.11032.52CM1+B1 (Apollo)

d1, IN.L, IN.d, IN.δ, δ, δ, δ, deg

CM=command module

Remark

Transfer Tunnel DiamLengthBase, Diam

Side AngleConfiguration

B2=AFE base1.3543.6656.06424.60CM2+B2 (AFE)

Bottom Radius

=1.609 in1.3923.7736.01810.00CM4+B1 (Soyuz)

1.9243.6656.03216.60CM3+B1

1.3543.6656.06424.60

CM2+B1

(Baseline)

B1=Nominal base0.8863.4016.11032.52CM1+B1 (Apollo)

d1, IN.L, IN.d, IN.δ, δ, δ, δ, deg

CM=command module

Remark

Transfer Tunnel DiamLengthBase, Diam

Side AngleConfiguration

Table 1. Test Configuration Dimensions and Definitions.

The aerodynamic characteristics of these shapes were evaluated over flight conditions ranging from low

supersonic to hypersonic conditions. The testing of the candidate shapes took place at the Unitary Plan Wind

Tunnel at NASA Langley Research Center in Hampton, Virginia, and the Hypersonic Tunnel 9 at the Arnold

Engineering Development Center in White Oaks, Maryland. The former tunnel provided aerodynamics data at

Mach 1.6 through 4.6, while the latter provided aerodynamics data at Mach 10 and 13.4. In addition to the basic

aerodynamics forces and moments, aeroheating data were collected at the higher Mach number in Tunnel 9, but for

a single test configuration only, namely CM2+B1. The test matrices are given in Tables 2 and 3.


5

A. NASA Langley Unitary Plan Wind Tunnel (UPWT) Test

The flight conditions simulated at the NASA LaRC UPWT ranged from low supersonic (M=1.6) to moderate

hypersonic (M=4.6). The closed-circuit, variable density tunnel is equipped with two test sections, both of which

were utilized to achieve the desired Mach range. The Reynolds number ranged from 6 to 11 million per foot. The

re-entry and abort environment characterization was carried out over a range of flight conditions, as shown in Table

2. The angle of attack sweep was typically 10 to 40 degrees in 2 degree increments,

The asymmetrical base configuration was tested with the base “bump” clocked at 0, 90 and 180 degrees in order

to assess its effects for re-entry. The test instrumentation comprised of a single six-component balance and limited

pressure instrumentation on the base and cavity of the model to record and correct the measured forces and

moments. Figure 2 provides a picture of each model mounted on the sting at the NASA LaRC test section.

αααα ββββ φφφφ 1.60 1.80 2.16 2.50 3.50 4.60

CM1+B1 A 0 - x x x x x x Side Angle Variation




CM2+B2 A 0 0 x x x x x x Asym Base Rotation



A: Alpha 10 to 40 degrees, in 2 degree increments

DegreesConfiguration Nomenclature Run Description

Mach Number

Table 2. NASA LaRC UPWT Test Matrix.

Figure 2. Test Models at the NASA LaRC WT Test Section.

B. AEDC Tunnel 9 Wind Tunnel Test

Tunnel 9 is a blowdown facility that uses pure nitrogen as the working fluid and is capable of achieving Mach 7,

8, 10, 14 and 16.512

. The test section is over 12 ft long and has a diameter of 5 ft, enabling testing of relatively large

models. The test comprised of both aerodynamic, as well as aero-heating measurements, and included Schlieren

pictures of the flow fields (Figure 3) that facilitated comparisons of shock waves with those predicted by the subject

computational tools. The test instrumentation comprised of a single six-component balance and limited pressure

instrumentation on the base of the model to assess base pressures.

The aerodynamic and aero-heating re-entry environments were simulated in the AEDC Tunnel-9 Wind Tunnel.

These flight conditions are given in Table 3. The aero-heating runs were conducted at two Reynolds numbers to

assess laminar and turbulent convective heating characteristics.

For the aerodynamic heating measurements, the model was instrumented with seventeen coaxial thermocouples

mounted on the surface of the symmetric base heat shield (BH1). The locations of the sensors were selected to

capture critical heating distributions based on analytical predictions. However, according to the predictions, the

peak heating was located at or close to the shoulder radius of the capsule vehicle, but due to the small size of the

shoulder radius on the model, it was not possible to place sensors at that location. There are also several

thermocouples mounted on the back side of the heat shield to measure and calibrate the wall temperature.


6

αααα ββββ φφφφ 10 14

CM1+B1 A2 - - 0.5 x x Side Angle Variation




CM2+B2 A2 - 180 0.5 x x Asym Base Rotation

CM2+B2 - B (90) 0.5 x x Asym Base Rotation

CM2+BH1 A1 - - 0.5 - x Sym Base with Heat Sensors

CM2+BH1 A1 - - 1.3 - x Sym Base with Heat Sensors

A1: Alpha 0 to 36 degrees, in 4 degree increments

A2: Alpha 8 to 40 degrees, in 4 degree increments

B: Beta 8 to 40 degrees, in 4 degree increments

BH1: B1 base with thermocouples

Re

(10^6/ft)

DegreesConfiguration Nomenclature Run Description

Mach Number

Table 3. AEDC Tunnel 9 Test Matrix.

Figure 3. Schlieren Images of the Test Articles at the AEDC T9 Facility.

The vehicle coordinate system is

illustrated in Figure 4. The right-handed axes

system is adopted, in which the x-axis is

positive towards the apex of the vehicle. All

moments reported are relative to the center of

the symmetric base at the OML

The objective of these wind tunnel tests

was to collect sufficient data to help calibrate

the subject Computational Fluid Dynamics

analysis tools. As noted earlier, another

important objective was to evaluate each

capsule’s aerodynamic performance, in terms

of Lift-to-Drag (L/D), and vehicle stability

and trim alpha. The goal was to determine

the sensitivity of such key parameters to

changes in the Outer Mold Line (OML) of a

typical capsule. The following section

presents a summary of these results, with

emphasis on the aerodynamics effects. Figure 4. Body and Stability Axis Coordinate System.

-C N

C A

C m

Relative Wind

−−−−αααα

+ y

+CY

+ x

+z

-CN

-CA

C llll

φφφφφφφφ

CY

CnRelative Wind

ββββ

Side View

Top View


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IV. Computational and Wind Tunnel Test Results

The results in this section are segregated into two groups, those being validation of the computational tools,

including comparisons of experimental data, and wind tunnel assessment of the effects of different capsule shapes

for the five configurations tested, including their monopole trim characteristics.

A. Computational Tool Results and Validation

In order to facilitate validation of specific predictive tools, corresponding numerical simulations of the test

environments for the subject shapes were performed and made available prior to the wind tunnel tests. As described

in Section II, the subject computational tools ranged in fidelity from low-order linear theory methods to complex

CFD simulations with gas species modeling.

The aerodynamic characteristics, in terms of normal force coefficient, axial force coefficient, Lift/Drag ratio, and

pitching moment, of a representative capsule shape (CM2+B1) are given in Figure 5. The figure shows comparisons

between collected wind tunnel data and corresponding predictions by APAS, BCFD, and USA.

The predicted trends and general magnitudes of the aerodynamic parameters compare reasonably well with

results from various computational tools. The linearized method APAS compares least favorably (at low Mach),

while the Reynolds-Average Navier Stokes method (USA) compared most favorably. For additional validation of

the quality of the experimental data, these results were also compared to Apollo heritage data of References 13 and

14, as well as measurements from a previous space programs, such as the Orbital Space Plane. The measurements

from this IRAD study generally compare well with past measurements, with notable differences at specific Mach

numbers. In certain regions of the flight regime, a breakdown in the correlation was observed, especially for the

linearized methods. For instance, and as anticipated for reasons described earlier, the results show that the normal

force and the Lift-to-Drag ratio predictions from APAS do not compare well at low Mach numbers.

CONFIGURATION COMPARISON vs MACH NUMBERNORMAL FORCE, CM2+B1 ALPHA = -20 DEGREES

-0.16

-0.14

-0.12

-0.10

-0.08

-0.06

-0.04

-0.02

0.00

0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0

MACH NUMBER, M

NO

RM

AL

FO

RC

E C

OE

FF

ICIE

NT

, C

N

USA N.S. Apollo AeroDatabook

CM2B1 WTT BCFD Euler

APAS HABP APAS HABP Adjusted

CFD ++ N.S.

USA Navier Stokes

is Nitrogen gas

above Mach 9

to match AEDC

WTT Conditions

CONFIGURATION COMPARISON vs MACH NUMBERAXIAL FORCE, CM2+ B1 ALPHA = -20 DEGREES

1.00

1.10

1.20

1.30

1.40

1.50

1.60

0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0

MACH NUMBER, M

AX

IAL

FO

RC

E C

OE

FF

ICIE

NT

, C

A

USA N.S. Apollo AeroDatabook

CM2B1WTT BCFD Euler


CFD ++ N.S.

USA Navier Stokes

is Nitrogen gas

above Mach 9

to match AEDC

WTT Conditions

CONFIGURATION COMPARISON vs MACH NUMBERLIFT / DRAG, CM2+B1 ALPHA = -20 DEGREES

0.24

0.26

0.28

0.30

0.32

0.34

0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0

MACH NUMBER, M

LIF

T / D

RA

G-L

OD

USA N.S.

Apollo AeroDatabook

CM2B1 WTT

BCFD Euler

APAS HABP

APAS HABP Adjusted

CFD ++ N.S.

USA Navier Stokes

is Nitrogen gas

above Mach 9

to match AEDC

WTT Conditions

CONFIGURATION COMPARISON vs MACH NUMBERPitching Moment, Configuratation CM2+B1 ALPHA = -20 DEGREES

0.04

0.05

0.06

0.07

0.08

0.09

0.10

0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0

MACH NUMBER, M

PIT

CH

ING

MO

ME

NT

-C

m

USA N.S.

Apollo AeroDatabook

CM2B1WTT

BCFD Euler

APAS HABP

CFD ++ N.S.

USA Navier Stokes

is Nitrogen gas

above Mach 9

to match AEDC

WTT Conditions

Figure 5. Comparisons of Predicted vs. Measured Aerodynamic Results for the CM2+B1 (αααα=-20

o).

Additional comparisons of aerodynamics wind tunnel test results, in terms of L/D as a function of angle of

attack, with corresponding predictions obtained from the USA computational tools, are shown in Figure 6. In

general, and over the range of alpha considered, the results show good agreements.


8

Wind Tunnel Test/ CFD Comparison, Mach 13.4

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

-45.0 -40.0 -35.0 -30.0 -25.0 -20.0 -15.0 -10.0 -5.0 0.0

Alpha

LIF

T T

O D

RA

G R

AT

IO, L

/D.. CM1B1

CM1B1, USA

CM2B1

CM2B1, USA

CM2B2180

CM2B2180, USA

Figure 6. CFD Performance Prediction and Wind tunnel Data Comparison, Mach 13.4

The hypersonic performance of the CM1+B1 is shown in Figure 7 for a representative re-entry angle (CM1+B1),

and is compared to the Apollo aero data. All of the computational tools predicted the trends and magnitudes

measured in the wind tunnel, with the exception of APAS, which over-predicting the axial force performance.

Interestingly, the Apollo database results differ both in normal force, (L/D) and pitching moment performance, but

not in axial force performance. One possible reason for this behavior is that the OML of the CM1+B1

configuration, although originally intended to be identical to the Apollo OML, has slight deviations from the true

Apollo OML. The “APAS Corrected” label on the figures indicates APAS predictions which have been adjusted for

the difference between the APAS predictions and the Apollo database results.

CONFIGURATION COMPARISON vs MACH NUMBER

CM1+B1 NORMAL FORCE, ALPHA = -25 DEGREES

-0.15

-0.10

-0.05

0.00

4.0 6.0 8.0 10.0 12.0 14.0

MACH NUMBER, M

NO

RM

AL

FO

RC

E C

OE

FF

ICIE

NT

, C

N

CM1B1 WTT USA N.S.

Apollo AeroDatabook BCFD Euler


USA Navier Stokes

is Nitrogen gas

above Mach 9

to match AEDC

WTT Conditions


CM1+B1 AXIAL FORCE, ALPHA = -25 DEGREES

1.00

1.10

1.20

1.30

1.40

1.50

1.60

4.0 6.0 8.0 10.0 12.0 14.0

MACH NUMBER, M

AX

IAL

FO

RC

E C

OE

FF

ICIE

NT

, C

A

CM1B1 WTT USA N.S.



USA Navier Stokes

is Nitrogen gas

above Mach 9

to match AEDC

WTT Conditions


CM1+B1 LIFT / DRAG, ALPHA = -25 DEGREES

0.30

0.35

0.40

0.45

0.50

4.0 6.0 8.0 10.0 12.0 14.0

MACH NUMBER, M

LIF

T /

DR

AG

CM1B1 WTT USA N.S.



OSP WTT

USA Navier Stokes

is Nitrogen gas

above Mach 9

to match AEDC

WTT Conditions


CM1+B1 PITCHING MOMENT (at Blunt Base), ALPHA = -25 DEGREES

0.04

0.05

0.06

0.07

0.08

0.09

0.10

4.0 6.0 8.0 10.0 12.0 14.0

MACH NUMBER, M

PIT

CH

ING

MO

ME

NT

-C

m

CM1B1 WTT USA N.S.


APAS HABP

USA Navier Stokes

is Nitrogen gas

above Mach 9

to match AEDC

WTT Conditions



-0.15

-0.10

-0.05

0.00

4.0 6.0 8.0 10.0 12.0 14.0

MACH NUMBER, M

NO

RM

AL

FO

RC

E C

OE

FF

ICIE

NT

, C

N

CM1B1 WTT USA N.S.



USA Navier Stokes

is Nitrogen gas

above Mach 9

to match AEDC

WTT Conditions



1.00

1.10

1.20

1.30

1.40

1.50

1.60

4.0 6.0 8.0 10.0 12.0 14.0

MACH NUMBER, M

AX

IAL

FO

RC

E C

OE

FF

ICIE

NT

, C

A

CM1B1 WTT USA N.S.



USA Navier Stokes

is Nitrogen gas

above Mach 9

to match AEDC

WTT Conditions



0.30

0.35

0.40

0.45

0.50

4.0 6.0 8.0 10.0 12.0 14.0

MACH NUMBER, M

LIF

T /

DR

AG

CM1B1 WTT USA N.S.



OSP WTT

USA Navier Stokes

is Nitrogen gas

above Mach 9

to match AEDC

WTT Conditions



0.04

0.05

0.06

0.07

0.08

0.09

0.10

4.0 6.0 8.0 10.0 12.0 14.0

MACH NUMBER, M

PIT

CH

ING

MO

ME

NT

-C

m

CM1B1 WTT USA N.S.


APAS HABP

USA Navier Stokes

is Nitrogen gas

above Mach 9

to match AEDC

WTT Conditions

Figure 7. Comparisons of Predicted vs. Measured Hypersonic Performance for the CM1+B1.


9

Similarly, the supersonic performance of the CM1+B1 is shown in Figure 8. The computational tools generally

did well in predicting the forces (L/D) and pitching moment, except for APAS at the lower range of supersonic

regime. The linearized force and moment equations do not adequately predict the magnitude and the trends, as

evidenced in this figure. BCFD-Euler predictions of the pitching moment performance also indicate that the tool did

not adequately capture the measured performance at the lower range of supersonic regime. The only tool that

predicted the pitching moment performance fairly well in this regime was USA. The USA code was run in the

viscous mode with a dense grid. As a result, adequate flow physics was captured to resolve vehicle center of

pressure which leads to a reasonable prediction of the pitching moment. A detailed identification of the pitching

moment for a typical re-entry capsule may become critical for assessment of single pole stability characteristics.



-0.15

-0.10

-0.05

0.00

1.6 2.0 2.4 2.8 3.2 3.6 4.0

MACH NUMBER, M

NO

RM

AL

FO

RC

E C

OE

FF

ICIE

NT

, C

N

CM1B1 WTT USA N.S.





1.00

1.10

1.20

1.30

1.40

1.50

1.60

4.0 6.0 8.0 10.0 12.0 14.0

MACH NUMBER, M

AX

IAL

FO

RC

E C

OE

FF

ICIE

NT

, C

A

CM1B1 WTT USA N.S.



USA Navier Stokes

is Nitrogen gas

above Mach 9

to match AEDC

WTT Conditions



0.30

0.35

0.40

0.45

0.50

1.6 2.0 2.4 2.8 3.2 3.6 4.0

MACH NUMBER, M

LIF

T / D

RA

G

CM1B1 WTT USA N.S.



OSP WTT

USA Navier Stokes

is Nitrogen gas

above Mach 9

to match AEDC

WTT Conditions



0.04

0.05

0.06

0.07

0.08

0.09

0.10

1.6 2.0 2.4 2.8 3.2 3.6 4.0

MACH NUMBER, M

PIT

CH

ING

MO

ME

NT

-C

m

CM1B1 WTT USA N.S.


APAS HABP

USA Navier Stokes

is Nitrogen gas

above Mach 9

to match AEDC

WTT Conditions



-0.15

-0.10

-0.05

0.00

1.6 2.0 2.4 2.8 3.2 3.6 4.0

MACH NUMBER, M

NO

RM

AL

FO

RC

E C

OE

FF

ICIE

NT

, C

N

CM1B1 WTT USA N.S.





1.00

1.10

1.20

1.30

1.40

1.50

1.60

4.0 6.0 8.0 10.0 12.0 14.0

MACH NUMBER, M

AX

IAL

FO

RC

E C

OE

FF

ICIE

NT

, C

A

CM1B1 WTT USA N.S.



USA Navier Stokes

is Nitrogen gas

above Mach 9

to match AEDC

WTT Conditions



0.30

0.35

0.40

0.45

0.50

1.6 2.0 2.4 2.8 3.2 3.6 4.0

MACH NUMBER, M

LIF

T / D

RA

G

CM1B1 WTT USA N.S.



OSP WTT

USA Navier Stokes

is Nitrogen gas

above Mach 9

to match AEDC

WTT Conditions



0.04

0.05

0.06

0.07

0.08

0.09

0.10

1.6 2.0 2.4 2.8 3.2 3.6 4.0

MACH NUMBER, M

PIT

CH

ING

MO

ME

NT

-C

m

CM1B1 WTT USA N.S.


APAS HABP

USA Navier Stokes

is Nitrogen gas

above Mach 9

to match AEDC

WTT Conditions

Figure 8. Comparisons of Predicted vs. Measured Supersonic Performance for the CM1+B1.

The results from this research contributed to updates of some of the subject computational tools, specifically the

BCFD. The latest production version of the BCFD code (version 4) is a fully rewritten FORTRAN 90 code

compared to the earlier FORTRAN 77 with embedded C modules. It reflects bug fixes and improved capabilities in

development versions. The updated code also includes several major algorithm changes relative to the earlier

production version. Additional enhancements include multigridding to accelerate convergence and corrections to

gradient computations, as well as numerical algorithm changes such as the inclusion of the HLLE flux differencing

scheme that reduces the artificial dissipation. Enthalpy preserving scheme has also been added to correctly model

the flow stagnation region at hypersonic Mach numbers. On the other extreme flow regime, the addition of low

Mach number pre-conditioning treatment enables efficient computations for very low Mach number flows.

Algorithm efficiency improvement also includes the implicit line Gauss-Seidel scheme with sub-iterations for

improved accuracy. The W-multigrid relaxation cycles significantly reduces the number of time steps taken to reach

convergence. Improved zonal boundary treatment compared to the earlier version of the code also improves the

domain-decomposed grids for parallel processing.


10

WTT vs. BCFD Predictions Post Code Updates

0

0.1

0.2

0.3

0.4

0.5

-50 -40 -30 -20 -10 0

Angle of Attack (Degrees)

Lif

t-to

-Dra

g R

ati

o

BCFD V4

AEDC WT Run 2927

Another major improvement is the inclusion

of the Newton iteration dual time stepping

algorithm for time-accurate solutions and

unsteady computations with specified time step

for solution advancement. Finally, several

compiler efficiency parameters associated with

the LINUX operating system have been applied

to significantly improve the parallel computing

efficiency on both 32-bit and 64-bit platforms

in cluster computing. Figure 9 provides a

sample of the improved match offered by the

updated BCFD relative to the wind tunnel

results for CM4+B1, which was the

configuration that provided some of the largest

disagreements between test and computational

data from the earlier version of BCFD. It was

postulated that the discrepancies with the earlier

BCFD results were driven by inaccuracies in

predicting the flow separation point along the

curved aft side wall of the Soyuz-like model.

As noted earlier, comparisons were made of the rather limited aeroheating test data that were collected at AEDC

T9. Figure 10 shows the heat rate test results versus computational results. The measured convective heating rate

for the CM2+B1 capsule is shown against predictions from USA, as well as the in-house engineering code XF0002.

Although the trends appear somewhat similar, there is a clear shift in the data particularly between the CFD results

(USA) and wind tunnel data, up to 25% at

certain locations. It is postulated that a denser

grid and one that better fits the shock may

explain some of these differences, but, due to

time and funding constraints, those possibilities

were not investigated. The differences between

the XF0002 predictions and wind tunnel data,

on the other hand, where the former appear

more conservative, were anticipated. This is

because the XF0002 heating (and pressure)

predictions are based on a composite maximum

of Apollo data over a range of alphas, not just

an average of those data. Interestingly, the

location of maximum convective heating does

not coincide with the location of maximum

pressure, which has strong implications for

structural design of the vehicle aero shell. It

may be noted that Accuracy of the aero-heating

instrumentation was reported by AEDC to be at

±6% of the measured values.

B. Effects of OML Variations on the Vehicles’ Aerodynamics Characteristics

Another objective of the study was to determine the effects of key configuration changes on the aerodynamic

characteristics of the capsule. The work presented herein further supports past parametric studies that are more

involved, such as that described in Reference 15. Specifically, the goal here was to assess the effects of changing

the side wall angles, as well as the heat shield base, on aerodynamic parameters such as CL, CD, Cm and L/D.

The configurations’ longitudinal stability and trimability comparison is shown in Figure 11a for Mach 13.4. A

negative slope in pitching moment versus angle of attack curve is the measure of the inherent longitudinal stability.

At the noted cg location, all of the configurations are shown to be stable. The trim angle of attack is realized at the

point where zero pitching moment is achieved. The inverted (φ=180 degrees) CM2+B2 configuration is shown to

provide the highest trim angle of attack of -39 degrees and the most non-linear Cm-alpha characteristics. The other

test configurations are shown to trim between about -27.5 and -30.0 degrees of angle of attack.

Figure 9. Results of Updated BCFD (Version 4) for CM4+B1.

Figure 10. Comparison of Predicted vs. Measured Aeroheating

Results for the CM2+B1 (M=13.4, Re=1.35E6, αααα=-24o).

CEV CM2-B1 Aft Heat Shield Heating Distribution

USA CFD: M = 13.414, Re = 1.35e6, Ho = 938 Btu/lbm

xf0002: M = 13.65, Re = 1.36e6, Ho = 935 Btu/lbm

α=24°, Vertical Centerline

0

10

20

30

40

50

60

-1.5 -1 -0.5 0 0.5 1 1.5

Arc Length / Radius

Heat

Rate

, q

-do

t (B

tu/f

t2/s

)

α=24 USA CFD

α=24 WT data

α=24 xf0002

φ =90°φ = 270°

ΦΦΦΦ=90

ΦΦΦΦ=270

Arc Length

CEV CM2-B1 Aft Heat Shield Heating Distribution

USA CFD: M = 13.414, Re = 1.35e6, Ho = 938 Btu/lbm

xf0002: M = 13.65, Re = 1.36e6, Ho = 935 Btu/lbm

α=24°, Vertical Centerline

0

10

20

30

40

50

60

-1.5 -1 -0.5 0 0.5 1 1.5

Arc Length / Radius

Heat

Rate

, q

-do

t (B

tu/f

t2/s

)

α=24 USA CFD

α=24 WT data

α=24 xf0002

φ =90°φ = 270°

ΦΦΦΦ=90

ΦΦΦΦ=270

Arc Length


11

The corresponding performance comparison, in terms of L/D, is shown in Figure 11b. It would appear that the

inverted CM2+B2 configuration is the most desirable for its larger trimmed L/D, but its trim angle of attack is

marginal (barely trims). The L/D ratio is shown to be directly proportional to the side wall angle, so that when the

latter reduces, so does the L/D. The resulting trim L/D and angles of attack values are listed in Table 4 for ease of

comparison. With the exception of the CM2+B2 configuration, the CM1+B1 (Apollo) configuration offers a better

L/D and higher trim angle of attack relative to the other configurations considered.

CEV Parametric Configurations Trim and Longitudinal Stability

Comparison, Mach=13.4, X/d=0.20, Z/d=-.059

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

-40 -35 -30 -25 -20 -15 -10 -5 0

Alpha

Pitc

hin

g M

om

ent,

Cm

CM1+B1

CM2+B1

CM3+B1

CM4+B1

CM2+B2, PHI=180

z

xα

Vx/d=0

z/d=0

z

xα

Vx/d=0

z

xα

V

z

x

z

xα

Vx/d=0

z/d=0

a) Pitching Moment Longitudinal Stability Comparisons b) Lift-to-Drag Performance Comparisons

Figure 11. Comparisons of Aerodynamic Characteristics at Mach 13.4

Test Configuration Trim Alpha Trim L/D

CM1+B1 -30.0 0.45

CM2+B1 -29.5 0.41

CM3+B1 -28.0 0.38

CM4+B1 -28.0 0.37

CM2+B2 (φ=180 deg) -39.0 0.53

Table 4. Comparison of Trim Angles of Attack and L/D Values for Various Test Configurations.

The effects of vehicle orientation (φ=0 and 180 degrees) of the CM2+B2 configuration (asymmetrical base) on

its stability and performance are shown in Figures 12a and 12b, respectively. The configuration, CM2+B2 (φ=180

degrees), has the highest trim angle of attack of -37.5 degrees. Also, the trim angle of attack range varies from -25

degrees for the upright orientation (φ=0 degrees) to -37.5 degrees for the inverted orientation (φ=180 degrees). Such

a relatively large trim change would drive up attitude control thruster propellant weight and may, therefore, be

unacceptable.

CEV Parametric Configurations Trim and Longitudinal Stability Comparison

Mach 4.6, X/d=.20, Z/d=-.059

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

-40 -35 -30 -25 -20 -15 -10 -5 0

Alpha

Pit

ch

ing

Mo

me

nt,

Cm

CM1+B1

CM2+B1

CM3+B1

CM4+B1

CM2+B2, PHI=0

CM2+B2, PHI=180 z

xα

Vx/d=0

z/d=0

CEV Parametric Configurations Trim and Longitudinal Stability Comparison

Mach 4.6, X/d=.20, Z/d=-.059

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

-40 -35 -30 -25 -20 -15 -10 -5 0

Alpha

Pit

ch

ing

Mo

me

nt,

Cm

CM1+B1

CM2+B1

CM3+B1

CM4+B1

CM2+B2, PHI=0

CM2+B2, PHI=180 z

xα

Vx/d=0

z/d=0

z

xα

Vx/d=0

z

xα

V

z

x

z

xα

Vx/d=0

z/d=0

a) Pitching Moment Longitudinal Stability Comparisons b) Lift-to-Drag Performance Comparisons

Figure 12. CM2+B2 Configuration Orientation Effects on Aerodynamic Characteristics at Mach 4.6

CEV Parametric Configurations Performance comparison

Mach=13.4, X/d=0.20, Z/d=-.059

0.00000

0.10000

0.20000

0.30000

0.40000

0.50000

0.60000

0.70000

-40 -35 -30 -25 -20 -15 -10 -5 0

Alpha

L/D

CM1+B1

CM2+B1

CM3+B1

CM4+B1

CM2+B2, PHI=180

z

xα

Vx/d=0

z/d=0

CEV Parametric Configurations Performance comparison

Mach=13.4, X/d=0.20, Z/d=-.059

0.00000

0.10000

0.20000

0.30000

0.40000

0.50000

0.60000

0.70000

-40 -35 -30 -25 -20 -15 -10 -5 0

Alpha

L/D

CM1+B1

CM2+B1

CM3+B1

CM4+B1

CM2+B2, PHI=180

z

xα

Vx/d=0

z/d=0

z

xα

Vx/d=0

z

xα

V

z

x

z

xα

Vx/d=0

z/d=0

CEV Parametric Configurations Performance Comparison

Mach 4.6, X/d=.20, Z/d=-.059

0.00000

0.10000

0.20000

0.30000

0.40000

0.50000

0.60000

-40 -35 -30 -25 -20 -15 -10 -5 0

Alpha

L/D

CM1+B1

CM2+B1

CM3+B1

CM4+B1

CM2+B2, PHI=0

CM2+B2, PHI=180 z

xα

Vx/d=0

z/d=0

CEV Parametric Configurations Performance Comparison

Mach 4.6, X/d=.20, Z/d=-.059

0.00000

0.10000

0.20000

0.30000

0.40000

0.50000

0.60000

-40 -35 -30 -25 -20 -15 -10 -5 0

Alpha

L/D

CM1+B1

CM2+B1

CM3+B1

CM4+B1

CM2+B2, PHI=0

CM2+B2, PHI=180 z

xα

Vx/d=0

z/d=0

z

xα

Vx/d=0

z

xα

V

z

x

z

xα

Vx/d=0

z/d=0


12

In summary, the trim angle of attack dependence on the roll angle orientation makes the CM2+B2 configuration

less desirable when compared to the other test configurations. The CM1+B1 (Apollo) configuration offers an

acceptable L/D, together with a higher trim angle of attack for a given cg location.

One-Alpha (Monopole) Longitudinal Stability and Trim Characteristics

A stable and monopole angle of attack longitudinal trim of a reentry capsule is a desired goal to ensure passive

stability in case of control system failure. The capsule entry attitude is determined by the Xcg and Zcg locations.

For illustration purposes, consider a reentry capsule, as that in the sketch of Table 1, with the Xcg placed at the apex

or at the base of the capsule. In either of these

extreme cases, the capsule will enter with the

apex first (alpha=0 degrees) when the Xcg is at

the apex, or with the base first (alpha=180

degrees) when the Xcg is at the base, no matter

what the initial entry attitude. In either of these

cases the vehicle will be stable and trimmed at a

single angle of attack, namely 0 or 180 degrees,

providing that there is no Zcg offset.

As the Xcg moves from apex to base, there

will be a range where the vehicle would be

trimmed in a base first or apex first orientation,

depending on the initial attitude when contacting

the credible atmosphere around 300,000 feet

altitude. Obviously, apex first entry can not be

allowed, thus the need to define the transition cg

boundary. The Zcg offset, on the other hand,

determines the entry angle of attack of the

capsule. Figure 13 illustrates the effects of Xcg

and Zcg variations on the pitching moment of the

CM2+B1 configuration at Mach 4.6.

The Apollo capsule has stable two trim angles of attack, at 10 degrees (apex first), and 145 degrees (base first),

as shown in Figure 14. The Apollo capsule base first, monopole-trim, cg boundary is defined by the method

described above.

Figure 11 Effect of CG on Apollo Capsule Longitudinal Trim and Stability

Mach 10

-0.14-0.12-0.10

-0.08-0.06-0.04-0.020.00

0.020.040.06

0

10 20 30

40 50 60 70 80 90

100

110

120

130

140

150

160

170

180

190

alpha

Pitch

ing M

om

ent, C

m

Xcg=1032.3, Zcg=-8.9

Xcg=1042.3, Zcg=-8.9

Xcg=1052.3, Zcg=-8.9

Xcg=1062.3, Zcg=-8.9

2 Trimmed and Stable Points For Nominal Apollo Capsule

CG Closer to base provides 1 trimmed and stable point

x/d=0.21

0.27

0.34

0.41

EFFECT of XCG on Apollo CM Longitudinal Trim and Stability

at CG=z/d=-.058, d (base diameter)=154 inches

z

xα

V

x/d=0

z/d=0

(α)(α)(α)(α)


Mach 10

-0.14-0.12-0.10

-0.08-0.06-0.04-0.020.00

0.020.040.06

0

10 20 30

40 50 60 70 80 90

100

110

120

130

140

150

160

170

180

190

alpha

Pitch

ing M

om

ent, C

m

Xcg=1032.3, Zcg=-8.9

Xcg=1042.3, Zcg=-8.9

Xcg=1052.3, Zcg=-8.9

Xcg=1062.3, Zcg=-8.9



x/d=0.21

0.27

0.34

0.41



z

xα

V

x/d=0

z/d=0

Mach 10

-0.14-0.12-0.10

-0.08-0.06-0.04-0.020.00

0.020.040.06

0

10 20 30

40 50 60 70 80 90

100

110

120

130

140

150

160

170

180

190

alpha

Pitch

ing M

om

ent, C

m

Xcg=1032.3, Zcg=-8.9

Xcg=1042.3, Zcg=-8.9

Xcg=1052.3, Zcg=-8.9

Xcg=1062.3, Zcg=-8.9



x/d=0.21

0.27

0.34

0.41



z

x

z

xα

V

x/d=0

z/d=0

(α)(α)(α)(α)


Mach 10

-0.14-0.12-0.10

-0.08-0.06-0.04-0.020.00

0.020.040.06

0

10 20 30

40 50 60 70 80 90

100

110

120

130

140

150

160

170

180

190

alpha

Pitch

ing M

om

ent, C

m

Xcg=1032.3, Zcg=-8.9

Xcg=1042.3, Zcg=-8.9

Xcg=1052.3, Zcg=-8.9

Xcg=1062.3, Zcg=-8.9



x/d=0.21

0.27

0.34

0.41



z

xα

V

x/d=0

z/d=0

(α)(α)(α)(α)


Mach 10

-0.14-0.12-0.10

-0.08-0.06-0.04-0.020.00

0.020.040.06

0

10 20 30

40 50 60 70 80 90

100

110

120

130

140

150

160

170

180

190

alpha

Pitch

ing M

om

ent, C

m

Xcg=1032.3, Zcg=-8.9

Xcg=1042.3, Zcg=-8.9

Xcg=1052.3, Zcg=-8.9

Xcg=1062.3, Zcg=-8.9



x/d=0.21

0.27

0.34

0.41



z

xα

V

x/d=0

z/d=0

Mach 10

-0.14-0.12-0.10

-0.08-0.06-0.04-0.020.00

0.020.040.06

0

10 20 30

40 50 60 70 80 90

100

110

120

130

140

150

160

170

180

190

alpha

Pitch

ing M

om

ent, C

m

Xcg=1032.3, Zcg=-8.9

Xcg=1042.3, Zcg=-8.9

Xcg=1052.3, Zcg=-8.9

Xcg=1062.3, Zcg=-8.9



x/d=0.21

0.27

0.34

0.41



z

x

z

xα

V

x/d=0

z/d=0

(α)(α)(α)(α)

Figure 14. Effect of Center of Gravity Location on the Apollo Longitudinal Stability and Trim.

Configuration CM2+B1 CG and Trim Characteristics, Mach=4.6

-0.15

-0.10

-0.05

0.00

0.05

0.10

10 15 20 25 30 35 40

Alpha

Pit

ch

ing

Mo

me

nt,

Cm

X/d=0, Z/d=0X/d=0.39, Z/d=0

X/d=0.83, Z/d=0X/d=0.39, Z/d=-0.033

X/d=0.24, Z/d=-0.059X/d=0.20, Z/d=-0.059

z

xα

Vx/d=0

z/d=0

Configuration CM2+B1 CG and Trim Characteristics, Mach=4.6

-0.15

-0.10

-0.05

0.00

0.05

0.10

10 15 20 25 30 35 40

Alpha

Pit

ch

ing

Mo

me

nt,

Cm

X/d=0, Z/d=0X/d=0.39, Z/d=0

X/d=0.83, Z/d=0X/d=0.39, Z/d=-0.033

X/d=0.24, Z/d=-0.059X/d=0.20, Z/d=-0.059

z

xα

Vx/d=0

z/d=0

z

xα

Vx/d=0

z

xα

V

z

x

z

xα

Vx/d=0

z/d=0

Figure 13. Effects of the Center of Gravity Location on

the Longitudinal Stability and Trim.


13

An assessment of the monopole stable trim cg locations for the first four capsule configurations shown in Figure

1, at the entry trim angle of attack of 25 degrees, was performed and is summarized in Figure 15. The monopole cg

locations were determined using aerodynamics generated via the aerodynamic analysis tool, APAS, described

previously. APAS puts the IRAD Apollo configuration (CM1+B1) cg inside the Apollo monopole-trim cg

boundary, suggesting the reasonableness of the predictions. The results indicate that the predicted monopole Xcg

(or X/d, nondimentionalized by the vehicle diameter) increases with decreasing configuration side angle, δ, for the

first three configurations. The fourth configuration (Soyuz-like), although different, appears to fit the trend.

Apollo One-Alpha Stable Trim Boundary (Apollo Database)

and Other Configuration One- Alpha Stable Trim Points (APAS)

-0.07

-0.06

-0.05

-0.04

-0.03

-0.02

-0.01

0

0 0.04 0.08 0.12 0.16 0.2 0.24 0.28 0.32 0.36

X/d

Z/d

One T

rimm

ed stable

Alpha R

egion

Tw

oTrim

med

stable

Alpha R

egion

CM4+B1CM1+B1

CM2+B1

CM3+B1

Apollo two-alpha Trim

Note: CM1+B1, CM2+B1, CM3+B1, CM4+B1 have analytically (APAS) been determined to have one-alpha trim

points at alpha 25 degrees. Note also that APAS prediction for Apollo (CM1+B1) falls inside the boundary

z

x

Vx/d=0

z/d=0

Soft constraint: present database does not contain dynamicStability derivative beyond this CG



-0.07

-0.06

-0.05

-0.04

-0.03

-0.02

-0.01

0

0 0.04 0.08 0.12 0.16 0.2 0.24 0.28 0.32 0.36

X/d

Z/d

One T

rimm

ed stable

Alpha R

egion

Tw

oTrim

med

stable

Alpha R

egion

CM4+B1CM1+B1

CM2+B1

CM3+B1






-0.07

-0.06

-0.05

-0.04

-0.03

-0.02

-0.01

0

0 0.04 0.08 0.12 0.16 0.2 0.24 0.28 0.32 0.36

X/d

Z/d



-0.07

-0.06

-0.05

-0.04

-0.03

-0.02

-0.01

0

0 0.04 0.08 0.12 0.16 0.2 0.24 0.28 0.32 0.36

X/d

Z/d

One T

rimm

ed stable

Alpha R

egion

Tw

oTrim

med

stable

Alpha R

egion

CM4+B1CM1+B1

CM2+B1

CM3+B1




z

x

z

x

Vx/d=0

z/d=0

Soft constraint: present database does not contain dynamicStability derivative beyond this CG

Figure 15. Predicted Monopole Trim Locations Relative to the Apollo capsule Trim Boundary.

V. Conclusion

Some of the key findings of the study are as follows.

1. The trends and general magnitudes of the aerodynamic computational predictions compared relatively well

with the test data obtained from wind tunnels. The Reynolds-Average Navier-Stokes method, USA,

provided the best matches, while APAS provided the most differences, particularly at low Mach Numbers.

The BCFD code was updated to more accurately predict capsule-type entry aerodynamics.

2. The aeroheating data were very limited. Although trends of heat rate predictions were similar to those

obtained from the wind tunnel test, differences were noted at certain heatshield locations. Further analysis

is recommended to better understand these differences.

3. The Apollo configuration offered the best L/D and the highest trim angle of attack for a given center of

gravity, when compared to the other symmetrical heat shield configurations considered.

4. The asymmetrical heat shield configuration, while offering the best L/D overall, exhibited large trim angle

of attack changes as a function of bank angle (between upright and inverted roll orientations).

5. The L/D ratio was shown to be directly proportional to the configuration side wall angle, and the monopole

angle of attack trim Xcg (or X/d) envelope was shown to increase with decreasing side wall angle.

Acknowledgments

The authors wish to acknowledge the contributions of many colleagues whose help and support made this

research possible. Special acknowledgements are extended to Tom Hamilton and Lee Spacht of Boeing, Phantom

Works, for their support with the aerodynamic test and analysis and to Yuk Woo and Charlie Petrilla of Boeing,

Phantom Works, for their support with the aerothermodynamic test and analysis. The CFD computational analyses

were performed by Karuna Rajagopal and Pichuraman Sundaram, whose knowledge and expertise proved most

valuable. Special acknowledgements are also extended to Michael Raftery, whose support was instrumental in

securing the required IRAD funding, and to the AEDC Tunnel 9 test team, led by Arnold Collier, and the NASA

LaRC UPWT test team, led by Greg Brauckman, for their support and dedication during the ground test evaluations.


14

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Module,” NASA-TN-D-4688, August 1968.

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