Xiao-Yen J. Wang and James Yuko

Glenn Research Center, Cleveland, Ohio

Orion Active Thermal Control System Dynamic 

Modeling Using Simulink/MATLAB

NASA/TM—2010-216252

May 2010

AIAA–2010–0810
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Xiao-Yen J. Wang and James Yuko

Glenn Research Center, Cleveland, Ohio

Orion Active Thermal Control System Dynamic 

Modeling Using Simulink/MATLAB

NASA/TM—2010-216252

May 2010

AIAA–2010–0810

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Prepared for the

48th Aerospace Sciences Meeting

sponsored by the American Institute of Aeronautics and Astronautics

Orlando, Florida, January 4–7, 2010
Acknowledgments

The authors thank Thomas Haregot at Lockheed Martin for providing critical data for the modeling effort and Stephen Miller at 

the NASA Johnson Space Center for providing the attitude defi nition for the 45-hr nominal mission timeline.

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subject to revision as analysis proceeds.
Orion Active Thermal Control System Dynamic Modeling Using 

Simulink/MATLAB 

Xiao-Yen J. Wang and James Yuko 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Abstract 

This paper presents dynamic modeling of the crew exploration vehicle (Orion) active thermal control 

system (ATCS) using Simulink (Ref. 1). The model includes major components in ATCS, such as heat 

exchangers and radiator panels. The mathematical models of the heat exchanger and radiator are 

described first. Four different orbits were used to validate the radiator model. The current model results 

were compared with an independent Thermal Desktop (Ref. 2) (TD) model results and showed good 

agreement for all orbits. In addition, the Orion ATCS performance was presented for three orbits and the 

current model results were compared with three sets of solutions—FloCAD (Ref. 3) model results, 

SINDA/FLUINT (Ref. 4) model results, and independent Simulink model results. For each case, the fluid 

temperatures at every component on both the crew module and service module sides were plotted and 

compared. The overall agreement is reasonable for all orbits, with similar behavior and trends for the 

system. Some discrepancies exist because the control algorithm might vary from model to model. Finally, 

the ATCS performance for a 45-hr nominal mission timeline was simulated to demonstrate the capability 

of the model. The results show that the ATCS performs as expected and approximately 2.3 lb water was 

consumed in the sublimator within the 45 hr timeline before Orion docked at the International Space 

Station. 

Introduction 

The Orion project is under the Constellation program for the space exploration vision initiated by 

President Bush in 2004. The Constellation program is responsible for providing the elements that will 

transport humans and cargo to both the International Space Station (ISS) and the Moon. These elements 

are the crew exploration vehicle (Orion), the crew launch vehicle (Ares I), the lunar surface access 

module (Altair), and the cargo launch vehicle (Ares V). Orion, with a crew of up to four astronauts, will 

launch on Ares I and then use its main engine to insert itself into a safe orbit to either dock with the ISS or 

with Altair. For ISS missions, Orion will be responsible for separation, entry, descent, and landing. For 

lunar missions, Orion also will have to maintain itself in low lunar orbit and perform a trans-Earth 

injection maneuver to return from the Moon. Orion consists of the launch abort system (LAS), crew 

module (CM), service module (SM), and spacecraft adapter (SA). The CM is a capsule design that 

provides the primary structure for crew support, incorporates the bulk of the avionics systems, and 

provides the capability for entry and parachute landing. The LAS will safely extract the CM from the 

launch configuration in the event of an early launch abort. The SM, the structure on which the CM rests, 

interfaces with Ares I. It will perform in-space flight propulsion operations and power generation and 

provide the heat rejection for the Orion active thermal control system. 

This study focuses on Orion’s ATCS. The purpose of the ATCS is to control the crew environment 

inside the CM, while maintaining the temperature of all avionics under their temperature limits. As shown 

in Figure 1, two CM fluid loops will pass through the CM, take heat generated inside the CM and from all 

electronics, then pass the heat to the SM fluid loops through two interface heat exchangers (IFHXs). The 

SM fluid loops will carry the heat to the radiator panels and radiate the heat to space. On the CM side, 

there will be a phase-change 

NASA/TM—2010-216252 1 
material (PCM) heat exchanger (HX) and a sublimator for the purpose of thermal topping. The control 

loop will have several set points, such as the fluid temperature entering the CM and the maximum 

temperature at the cold plates associated with the batteries on the SM. There will be a bypass flow path at 

the upstream of the IFHX on the CM side and a bypass flow path before the regenerative heat exchanger 

(Regen HX) on the SM side. 

The current modeling effort is part of independent validation and verification (IV&V) of the analysis 

results. Simulink and MATLAB are used to build a dynamic model independently to simulate the Orion

ATCS. The model includes all major components in the ATCS, such as the cabin HX and cold plates on 

both CM and SM sides, IFHX, Regen HX, and the radiator with fluid loops on the SM side. The control 

system also is modeled to meet the thermal requirement for the ATCS. The user must define the initial 

conditions and provide the ambient radiation sink temperature for the radiator. This model focuses on the 

thermal performance of the ATCS. The hydraulic performance of the pump and the pressure drop at each 

component in the ATCS are not reported here. 

In the following sections, the mathematical models of the HX and the radiator with the fluid loops are 

described first, followed by the validation of the ATCS radiator model using four different orbits. The 

numerical results are compared with the corresponding results from independent resources. The performance of the ATCS is presented for a 45-hr nominal mission timeline; then conclusions are drawn. 

Nomenclature 

A heat transfer area 

Ap radiator panel area 

Ap,i area of the three sections on the panel (where i = 1, 2, 3) 

cp,c specific heat of cold fluid in heat exchanger 

cp,f specific heat of fluid in heat exchanger 

cp,HX specific heat of heat exchanger 

cp,h specific heat of hot fluid in heat exchanger 

cp,r specific heat of radiator panel 

Dh hydraulic diameter of the fluid channel 

hAcold heat transfer rate for cold fluid in heat exchanger 

hAhot heat transfer rate for hot fluid in heat exchanger 

k thermal conductivity of the fluid 

NASA/TM—2010-216252 2 
mc mass of cold fluid in heat exchanger 

mf,1, mf,2 mass of fluid in the two loops 

mHX mass of heat exchanger 

mh mass of hot fluid in heat exchanger 

mi mass of the three sections on the panel (where i = 1, 2, 3) 

mc  mass flow rate of cold fluid in heat exchanger 

mh  mass flow rate of hot fluid in heat exchanger 

21 , mm  mass flow rates of the two loops 

Pr Prandtl number 

Qa total heat flux on the radiator panel from solar, albedo, and planetshine 

Qhot2wall heat flux from the hot stream to the wall 

Qwall2cold heat flux from wall to the cold stream 

q1, q2 heat flux

R1, R'1 convection resistances between fluid and channel wall 

R2, R'2 conduction resistances through panel thickness 

R3, R4 conduction resistances along panel 

R5, R6, R7 adiation resistances between panel surface and ambient environment 

Ta equivalent ambient or sink temperature 

Tc,e cold-stream exit temperature 

Tc,i cold-stream inlet temperature 

Th,e hot-stream exit temperature 

Th,i hot-stream inlet temperature 

Twall wall temperature 

Ti,1, Ti,2 fluid inlet temperatures for the two fluid loops 

Tp,a temperature at panel between the two fluid channels 

Tp,1, Tp,2 temperatures at panel right above the fluid channel 

Tw,1 Tw,2 wall temperatures of fluid channel 

Re Reynolds number 

T1,i, T2,i, fluid inlet temperatures

T1,o, T2,o fluid exit temperatures 

t time

ε surface emissivity 

σ Stefan-Boltzmann constant 

β the angle between the solar vector and the orbit plane 

Mathematical Models of the Heat Exchanger and Radiator 

One-Dimensional Transient Model for the Heat Exchanger 

The heat exchanger considered here is a typical compact HX with plain-fin surfaces as shown in 

Figure 2. It is in a counter-flow arrangement. 

NASA/TM—2010-216252 3 
The inlet and exit temperatures are Th,i and Th,e, respectively, for the hot-stream, Tc,i and Tc,e. for the 

cold-stream. Given the inlet temperature of both sides, Th,e, Tc,e , and the wall temperature Twall can be 

solved through the following ordinary differential equations: 

( ) ( ) ( )

( ) ( ) ( )

( ) ( ) HXpHX

cpceciccpc ec

hphehihhph

eh

Q Q cm

dt

dT

Q cmTTcm

dt

dT

Q cmTTcm

dt

dT

hot2wall wall2cold , wall

wall2cold ,,, , ,

hot2wall ,,, , ,

= −

= + −

+−= −





where 

(( ) )

( ) ( ) 2

2

wall2cold ,,wallcold

hot2wall ,,hot wall

ecic

ehih

Q TTThA

Q TTThA

= +−

= + −

t is time; Qhot2wall and Qwall2cold are the heat flux from the hot stream to the wall and from the wall to the 

cold stream; hAhot and hAcold are the heat transfer rates for the hot and cold fluids; mh, mc, and mHX are the 

masses of the hot fluid, cold fluid, and the heat exchanger itself; cp,h, cp,c, and cp,HX are the specific heats of 

the hot fluid, cold fluid, and heat exchanger; and are the mass flow rates of the hot and cold 

fluids, respectively. 

mm ch and 

One-Dimensional Transient Model of the Radiator Panel With Fluid Loops 

The radiator panel has a thin surface with fluid channels attached at its interior surface. The interior 

surface is covered by multilayer insulation (MLI) blankets. The exterior surface is coated with material 

that has high emissivity. The fluid loop will come into the header and split the flow through a number of 

channels along the panel. For the two-loop (A and B) flow configuration, the channel will flow alternately 

along fluid loops A and B. The flow condition in the two loops can be different. A cross section of the 

radiator panel in the flow direction (sketched in Fig. 3) shows the two neighboring fluid channels denoted 

as loop A and loop B. On the exterior surface of the radiator panel, Tp,1 and Tp,2 are the temperatures at the 

panel right above the fluid channel, Tp,a is the temperature at the panel between the two fluid channels, 

and Tw,1 and Tw,2 are the wall temperatures of the fluid channel. 

NASA/TM—2010-216252 4 
The corresponding thermal circuit is plotted in Figure 4. R1 and R'1 are the convection resistances 

between the fluid and the channel wall; R2 and R'2 are the conduction resistances through the panel and 

the adhesive layer thickness; R3 and R4 are the conduction resistances along the panel; R5, R6, and R7 are 

the radiation resistances between the panel surface and the ambient environment; Ti,1 and Ti,2 are the fluid 

inlet temperatures for the two fluid loops (assumed to be given); and Ta is the equivalent ambient or 

radiation sink temperature. In space, the radiator panel is exposed to the Sun, the planet, and deep space. 

For this model, Qa is the total heat flux from the Sun, albedo, and planetshine on the radiator panel. It is 

assumed that with Ap being the radiator panel area, σ the Stefan-Boltzmann Constant, and 

ε the surface emissivity. Then the radiation sink temperature Ta can be used to represent the ambient 

condition. For all cases, the sink temperatures were computed using a separate Thermal Desktop model 

and were used as input to the Simulink model. The Thermal Desktop model performed full threedimensional transient analysis for orbit heating on all the radiator panels and averaged the results over the 

entire panel to generate one sink temperature for each panel. Radiation between the large structures, such 

as solar arrays and radiator panels, is included in the model. 

, 4 σε= TAQ apa

In the model, mi and Ap,i (where i = 1, 2, 3) denote the mass and the area of the three sections of the 

panel; cp,r and cp,f are the specific heats of the radiator panel and the fluid, mf,1 and mf,2 are the masses of 

the fluid in the two loops, and are the mass flow rates of the two loops. The equations for 21 and mm 

NASA/TM—2010-216252 5 
solving the three panel wall temperatures, Tp,1, Tp,2, and Tp,a, and two fluid exit temperatures, T1,o and T2,o, 

follow: 

( ) ( )

( ) ( )

( ) ( ) ( )

( )

( ) oifp o fpf

oifp o fpf

aapp

appappap

rp

p p a p apprp

p p a p apprp

TTcmq

t

T

cm

TTcmq

t

T

cm

TTA

R

TT

R

TT

t

T

cm

TTA

R

TT

q

t

T

cm

TTA

R

TT

q

t

T

cm

,2,2,22

,2

,2,

,1,1,11

,1

,1,

44,3,

4

,2,

3

, ,1,

,3

4 4 2, 2, 4

,2,

2

2,

,2

4 4 1, 1, 3

,1,

1

1,

,1

2 2

2

2

+−= − ∂

∂

+−= − ∂

∂

−σε− − + − = ∂

∂

−σε− − −= ∂

∂

−σε− − −= ∂

∂





where 

(( ) )

( ) ( ) 2 ,2,2 2,

1 ,1,1 1,

2

2

poi

poi

TTThAq

TTThAq

−+=

= + −

with 

hA = 7.54 kA/Dh for Re ≤ 2000 

hA = 0.023*Re0.8Pr0.333 kA/Dh for Re > 2000 (Colburn equation) 

where q1 and q2 are the heat flux from the stream to the panel, A is the heat transfer area, Re is the 

Reynolds number, Pr is the Prandtl number, k is the thermal conductivity of the fluid, and Dh is the 

hydraulic diameter of the fluid channel. 

Validation of the Radiator Mathematical Models 

Since the radiator will be one of the major components in the ATCS, the transient model must be 

validated. The radiator studied here is a cylindrical surface divided into eight panels. Two flow loops go 

through all seven panels in series as shown in Figure 5. The eighth panel does not have flow channels 

attached to it and remains a panel to close out the structure. Four cases were used for the validation and 

described as follows. 

The first case was low Earth orbit (LEO) hot case at an altitude of 230 km, β = 56°, aft to the Sun, 

with pitch/yaw/roll/ (P/Y/R) angles of 5°/–5°/0°. The Thermal Desktop results of the non-dimensional 

sink temperature and the equivalent heat flux from the environment were plotted in Figures 6(a) and 6(b) 

for one orbit cycle time of 1.5 hr. With a given mass flow rate and the inlet fluid temperature, the 

computed results of the non-dimensional fluid temperature at the exit of the last panel and the total heat 

rejection were plotted in Figures 6(c) and 6(d) in comparison with the corresponding Thermal Desktop 

(TD) results. The maximum difference between the current result and the TD result was less than 2 to 3 

percent in the fluid temperature and total heat rejection. 

The second case was LEO hot case at the altitude of 230 km, β = 75°, nose forward, with P/Y/R 

angles of 0°/0°/0°. The environmental heat fluxes were similar to the first case except that the average 

seven-panel heat flux had abrupt changes for the first case. The corresponding results were plotted in 

Figure 7 showing a similar agreement as in the first case. 

NASA/TM—2010-216252 6 
The third case was lunar transit, aft to the Sun, with P/Y/R angles of 0°/0°/0°. It was a cold steadystate case. The non-dimensional fluid exit temperature maximum difference between the two solution sets 

was within 1.5 percent as shown in Figure 8. 

The fourth case was low lunar orbit (LLO) hot case at an altitude of 90 km, β = 0°, nose forward, with 

P/Y/R angles of 0°/0°/0°. The non-dimensional sink temperautre and the equivalent orbit heating flux 

were plotted in Figure 9 for an orbit time of 2 hr. It can be seen that the environment is more severe and 

could be extremely hot and cold. The computed fluid temperature and heat rejection results show similar 

trend as shown in TD results. 

NASA/TM—2010-216252 7 
 

NASA/TM—2010-216252 8 
 

NASA/TM—2010-216252 9 
 

NASA/TM—2010-216252 10 
In summary, the one-dimensional transient model results agree reasonably well with the threedimensional Thermal Desktop model results for all four orbits. It can be concluded that the onedimensional transient model for the radiator can capture the radiator performance accurately. 

Active Thermal Control System Model Validation 

The ATCS for the ISS mission will have an eight-panel radiator with no PCM HX, whereas the 

ATCS for the lunar mission will have a seven-panel radiator with a PCM HX since the LLO environment 

is generally much worse than that in LEO. 

Three orbit cases were used for validation. The first case was for an ISS mission, LEO aft-to-Sun hot 

at an altitude of 230 km, β = 75o, P/Y/R angles of 5o/–5o/0o, and a power load of 4683 W; The second case 

was for a lunar mission, LLO nose-nadir hot at an altitude of 75 km, β = 0o, P/Y/R angles of –20o/20o/0o, 

and a power load of 2571 W; and the third case also was for a lunar mission, LLO aft-to-Sun cold at an 

altitude of 400 km, β = 90o, P/Y/R angles of 0o/0o/0o, and a power load of 1725 W. 

Four sets of solution were compared: (1) current Simulink model results, (2) an independent Simulink 

model results, (3) SINDA/FLUINT model results, and (4) FloCAD model results. The modeling details of 

the other three models were not available. The current Simulink model uses the same heat transfer 

characteristic of all HXsin the ATCS as those used in other three models. The SINDA/FLUINT model 

has a full three-dimensional radiator model. All models use a similar mathematical approach. Simulink is 

a commercial tool for modeling, simulating and analyzing multidomain dynamic systems. 

SINDA/FLUINT is a comprehensive finite-difference, lumped parameter (circuit or network analogy) 

tool for heat transfer design analysis and fluid flow analysis in complex systems. FloCAD is a Thermal 

Desktop module that allows a user to develop and integrate both fluid and thermal systems within a CAD 

based environment. Like Thermal Desktop, FloCAD is a graphical user interface for SINDA/FLUINT. 

In the current Simulink/MATLAB model, 20 mesh points are used in the flow direction for the IFHX, 

30 mesh points are used in the flow direction for the Regen HX, and two mesh points are used in the flow 

direction for the sublimator and PCM HX. The heat transfer rate for the IFHX, Regen HX, sublimator, 

and PCM HX were referred to in Reference 5. For the cabin HX and cold plate for the CM and SM sides, 

a constant heat load based on the power load was imposed. For the radiator, two mesh points were used 

for each panel, and all panels were modeled. 

The solver used in the Simulink model is ODE45(Dormand-Prince) with a variable time step. The 

maximum Δt was 0.5 s, otherwise the result would have diverged. The model took approximately 20 min 

to simulate a three-orbit (4.5-hr) run. 

For each case, the non-dimensional fluid temperatures on the CM side (including the cabin inlet, SM 

cold plate inlet, IFHX inlet, PCM inlet, and sublimator inlet) and the fluid temperatures on the SM side 

(including the IFHX cold side exit, Regen HX exit, and radiator exit temperature) were plotted. The IFHX 

bypass flow fraction and Regen HX bypass flow fraction also were plotted. Four sets of solution were 

plotted side by side for comparison. 

Figure 10 shows plots of the non-dimensional Thermal Desktop results of the sink temperature for the 

eight radiator panels for the LEO aft-to-Sun hot case. Figures 11 and 12 show plots of the all four model 

results for both the CM and SM sides. The non-dimensional sink temperature changed from –1.70 to 0.55, 

showing a mild orbit heating environment. All four model results show similar trends for the IFHX 

bypass flow changes and a similar on-and-off pattern for the sublimator. Some oscillations exist in the 

FloCAD model because of the algorithm for turning the sublimator water on and off. On the SM side, all 

four models show that the Regen HX is not used. 

NASA/TM—2010-216252 11 
NASA/TM—2010-216252 12 
Figures 13 to 15 show the corresponding results for the second case. The sink temperature varied 

from –2.50 to 1.20. On the CM side, all models show a maximum IFHX bypass flow rate of 50 to 54 

percent. On the SM side, all models show a similar pattern of Regen HX bypass flow changes. The 

maximum Regen HX flow rate was 40 to 65 percent. The fluid temperature drop across the radiator was 

similar for all the models: there was a 0.33 to 0.34 drop when the Regen HX was operating at the 

maximum flow rate. The difference in the Regen HX flow percentage could be due to the varying 

performance of the Regen HX. However, the total heat rejection should be similar for all models. When 

the Regen HX has no flow passing through, each model has different ways of book keeping the Regen 

cold exit temperatures, as shown in Figure 15. The Regen cold exit temperature is not used in the model 

when no flow goes through regen HX. 

For the third case—a steady-state cold case—very good agreement was achieved, as shown in 

Figures 16 to 18. The sink temperature changed from –1.60 to –0.60. On the CM side, all models show a 

68- to 69-percent IFHX bypass flow. On the SM side, the current model and SINDA/FLUINT model 

show 78 to 80 percent flow to the Regen HX flow, FloCAD data show 90 percent flow to the Regen HX. 

For all models, the temperature drop across the radiator panel was approximately 0.20. 

NASA/TM—2010-216252 13 
NASA/TM—2010-216252 14 
NASA/TM—2010-216252 15 
NASA/TM—2010-216252 16 
In summary, there is reasonable agreement among the four models with the possible exception that 

the control algorithm in each model might be different, which would cause the transient phenomena to be 

slightly different, as shown in the first and second cases. All four models show simiar trends and 

performance for the ATCS. 

ATCS Performance for a 45-hr Nominal Mission Timeline 

To further demonstrate the capability of this model, a timeline for the 45-hr nominal mission timeline 

was simulated to show the ATCS performance. During the mission timeline, the attitude of Orion and 

power loads on the ATCS vary with time. With defined attitude and power load timelines, the ATCS 

performance is computed and the non-dimensional fluid temperature variations on both the CM and SM 

sides are plotted in Figures19 and 20. The non-dimesnional heat rejection is shown in Figure 21. During 

the first 45 hr before docking, the ATCS was relatively “cool” compared with some hot cases studied 

previously. The radiator fluid inlet temperature was within 0.40 to 0.60 most of the time. The Regen HX 

was on most of the time, whereas the maximum regenerative flow rate was approximately 50 percent. The 

sublimator turned off at t = 18 min and stayed off. The total sublimated water was 2.3 lbm. Note that 

ascent heating was not included here. The model took approximately 3 hr to simulate for the 45-hr run. 

NASA/TM—2010-216252 17 
NASA/TM—2010-216252 18 
Conclusions 

A dynamic Simulink model of the Orion ATCS was presented. Details of the mathematical models of 

the heat exchanger and radiator were described. The active thermal control system model was validated 

using three different orbits by comparing the corresponding three results from independent resources. The 

agreement of the results for all four models is reasonable. All four models predict similar ATCS behavior 

for all three cases. Some unexplained discrepancies exist among the four models and are thought to be 

due to possible variations in the control algorithm used in each model. Control algorithm details were not 

available for this study. 

References 

1. Simulink, developed by The MathWorks. 

2. Thermal Desktop®, PC/CAD-based thermal model builder, developed in Cullimore & Ring (C&R) 

Technologies. 

3. FloCAD®, PC/CAD-based thermal/fluid model builder, developed in C&R Technologies. 

4. SINDA/FLUINT, a generalized thermal/fluid network-style solver. 

5. NASA and Lockheed Martin Orion thermal technical interchange meeting (TIM), Dec. 2008. 

NASA/TM—2010-216252 19 
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Orion Active Thermal Control System Dynamic Modeling Using Simulink/MATLAB 

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13. SUPPLEMENTARY NOTES

14. ABSTRACT

This paper presents dynamic modeling of the crew exploration vehicle (Orion) active thermal control system (ATCS) using Simulink 

(Simulink, developed by The MathWorks). The model includes major components in ATCS, such as heat exchangers and radiator panels. 

The mathematical models of the heat exchanger and radiator are described first. Four different orbits were used to validate the radiator 

model. The current model results were compared with an independent Thermal Desktop (TD) (Thermal Desktop, PC/CAD-based thermal 

model builder, developed in Cullimore & Ring (C&R) Technologies) model results and showed good agreement for all orbits. In addition, 

the Orion ATCS performance was presented for three orbits and the current model results were compared with three sets of solutionsFloCAD (FloCAD, PC/CAD-based thermal/fluid model builder, developed in C&R Technologies) model results, SINDA/FLUINT 

(SINDA/FLUINT, a generalized thermal/fluid network-style solver ) model results, and independent Simulink model results. For each case, 

the fluid temperatures at every component on both the crew module and service module sides were plotted and compared. The overall 

agreement is reasonable for all orbits, with similar behavior and trends for the system. Some discrepancies exist because the control 

algorithm might vary from model to model. Finally, the ATCS performance for a 45-hr nominal mission timeline was simulated to 

demonstrate the capability of the model. The results show that the ATCS performs as expected and approximately 2.3 lb water was

consumed in the sublimator within the 45 hr timeline before Orion docked at the International Space Station. 

15. SUBJECT TERMS

Active thermal control system; Dymanic modeling; Spacecraft 

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