Maxwell H. Briggs

Glenn Research Center, Cleveland, Ohio

Implementation of a Sage-Based Stirling Model Into 

a System-Level Numerical Model of the Fission 

Power System Technology Demonstration Unit

NASA/TM—2011-217203

December 2011

NETS–2011–3271
NASA STI Program . . . in Profi le

Since its founding, NASA has been dedicated to the 

advancement of aeronautics and space science. The 

NASA Scientifi c and Technical Information (STI) 

program plays a key part in helping NASA maintain 

this important role.

The NASA STI Program operates under the auspices 

of the Agency Chief Information Offi cer. It collects, 

organizes, provides for archiving, and disseminates 

NASA’s STI. The NASA STI program provides access 

to the NASA Aeronautics and Space Database and 

its public interface, the NASA Technical Reports 

Server, thus providing one of the largest collections 

of aeronautical and space science STI in the world. 

Results are published in both non-NASA channels 

and by NASA in the NASA STI Report Series, which 

includes the following report types:

• TECHNICAL PUBLICATION. Reports of 

completed research or a major signifi cant phase 

of research that present the results of NASA 

programs and include extensive data or theoretical 

analysis. Includes compilations of signifi cant 

scientifi c and technical data and information 

deemed to be of continuing reference value. 

NASA counterpart of peer-reviewed formal 

professional papers but has less stringent 

limitations on manuscript length and extent of 

graphic presentations.

• TECHNICAL MEMORANDUM. Scientifi c 

and technical fi ndings that are preliminary or 

of specialized interest, e.g., quick release 

reports, working papers, and bibliographies that 

contain minimal annotation. Does not contain 

extensive analysis.

• CONTRACTOR REPORT. Scientifi c and 

technical fi ndings by NASA-sponsored 

contractors and grantees.

• CONFERENCE PUBLICATION. Collected 

papers from scientifi c and technical 

conferences, symposia, seminars, or other 

meetings sponsored or cosponsored by NASA.

• SPECIAL PUBLICATION. Scientifi c, 

technical, or historical information from 

NASA programs, projects, and missions, often 

concerned with subjects having substantial 

public interest.

• TECHNICAL TRANSLATION. Englishlanguage translations of foreign scientifi c and 

technical material pertinent to NASA’s mission.

Specialized services also include creating custom 

thesauri, building customized databases, organizing 

and publishing research results.

For more information about the NASA STI 

program, see the following:

• Access the NASA STI program home page at 

http://www.sti.nasa.gov

• E-mail your question via the Internet to help@

sti.nasa.gov

• Fax your question to the NASA STI Help Desk 

at 443–757–5803

• Telephone the NASA STI Help Desk at

 443–757–5802

• Write to:

 NASA Center for AeroSpace Information (CASI)

 7115 Standard Drive

 Hanover, MD 21076–1320
Maxwell H. Briggs

Glenn Research Center, Cleveland, Ohio

Implementation of a Sage-Based Stirling Model Into 

a System-Level Numerical Model of the Fission 

Power System Technology Demonstration Unit

NASA/TM—2011-217203

December 2011

NETS–2011–3271

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Prepared for the

Nuclear and Emerging Technologies for Space (NETS-2011)

cosponsored by the ANS Aerospace Nuclear Science and Technology Division, the ANS Trinity Section, 

and the American Institute of Aeronautics and Astronautics

Albuquerque, New Mexico, February 7–10, 2011
Acknowledgments

The author would like to acknowledge the support of the Thermal Energy Conversion Branch at the NASA Glenn Research 

Center; the Enabling Technology Development and Demonstration (ETDD) project for fi nancial support of this work; the

work of Ross Radal, Sandia National Labs, and Lee Mason, NASA Glenn Research Center, for contributions to the

system-level modeling effort; and David Gedeon, Sunpower, Inc., for the development of the Sage model of the

Power Conversion Unit (PCU).

Available from

NASA Center for Aerospace Information

7115 Standard Drive

Hanover, MD 21076–1320

National Technical Information Service

5301 Shawnee Road

Alexandria, VA 22312

Available electronically at http://www.sti.nasa.gov

Trade names and trademarks are used in this report for identifi cation 

only. Their usage does not constitute an offi cial endorsement, 

either expressed or implied, by the National Aeronautics and 

Space Administration.

Level of Review: This material has been technically reviewed by technical management. 
NASA/TM—2011-217203 1 

Implementation of a Sage-Based Stirling Model Into a System-Level 

Numerical Model of the Fission Power System Technology 

Demonstration Unit 

Maxwell H. Briggs 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Abstract 

The Fission Power Systems (FPS) project is developing a Technology Demonstration Unit (TDU) to 

verify the performance and functionality of a subscale version of the FPS reference concept in a relevant 

environment and to verify component and system models. As hardware is developed for the TDU, 

component and system models must be refined to include the details of specific component designs. This 

paper describes the development of a Sage-based pseudo-steady-state Stirling convertor model and its 

implementation into a system-level model of the TDU. 

Introduction 

The Fission Surface Power (FSP) project at the NASA Glenn Research Center (GRC) is developing 

technology to enable the option for fission power for planetary exploration. The FSP reference baseline 

concept consists of a 186-kWt fission reactor, which provides heat to four 12-kWe free-piston Stirling 

Power Conversion Units (PCUs). The waste heat from the convertors is then rejected through four 

cooling loops, each capable of radiating 35 kWt through titanium-water heat pipes to radiator panels 

(5 per cooling loop). Current system-level models of the FSPS estimate that such a system could deliver 

40 kW of reliable, round-the-clock electrical power with an estimated mass of 5820 kg (Fission Surface 

Power Team, 2010). 

The FSP team is currently developing a Technology Demonstration Unit (TDU), which will consist of 

an electrically heated core simulator capable of producing up to 100-kWt, a single 12-kW Stirling PCU, and 

a single 35-kWt cooling loop. Thus, full-scale prototypes of components will be used in a quarter-scale 

system and operated in thermal vacuum. Since the TDU uses full-scale FSPS components operating in a 

relevant environment, verifying TDU system models is a key step in verifying FSPS system models. Prior to 

the completion of the design of the TDU components, system-level models of the TDU did not include 

detailed component models. However, as the TDU components are designed and fabricated, the detailed 

designs of these components can be included in detailed component models, which can be integrated into 

the system-level model. This will add fidelity to both TDU and FSPS system models. 

Sage-Based PCU Model 

Overview 

System-level models of both the TDU and FSPS have modeled the PCU using either a Schmidt-cycle 

analysis or by simply assuming that the convertors would reach a fixed percentage of the Carnot 

efficiency at the design condition. While both of these techniques provide quick closed-form solutions 

and are useful for estimating performance near the design operating point, they are much less useful in 

predicting off-nominal performance required in transient and off-nominal steady-state simulations, and 

both are subject to somewhat subjective evaluations of convertor performance, which are not physics 

based. 
NASA/TM—2011-217203 2 

In contrast, Sage models the physics of the actual convertor, coupling the solutions of heat transfer 

through the heat exchangers, gas volume pressure, and mass-spring-damper systems (Gedeon 2010). In 

addition, this model includes several parasitic losses commonly seen in actual convertors, including 

appendix gap losses, conduction losses, heat exchanger ineffectiveness, pressure drop, and alternator 

inefficiency. As a result, the Sage-based model, provided by Sunpower, gives the most accurate 

prediction currently available for convertor performance during both nominal and off-nominal operations. 

One disadvantage with using a Sage-based model is the loss of a closed-form solution. In addition, 

embedding a Sage model directly into a system-level model introduces an additional subsolver, which is 

called repeatedly by a top-level solver. This has been shown to dramatically increase computational time. 

To eliminate this requirement, the Sage model is run independently of the system model over the entire 

range of the intended operation, generating a comprehensive performance map, analogous to compressor 

or turbine maps used in Brayton cycle analysis. These performance maps can then be referenced by multidimensional interpolation functions in the system model, eliminating the need for nested solvers. The 

current performance map, which has more than 114,000 data points, was generated in approximately 

1 week on a commercial laptop central processing unit (CPU). Since this performance map is design 

specific, any changes to the design of the PCU will require that a new performance map be generated. 

Sage-Based Map Generation 

The Sage model consists of a free displacer, a constrained piston, a rejector, a regenerator, and an 

acceptor, as well as expansion, compression, and buffer spaces. The rejector model contains a model of 

the water heat exchanger and therefore is defined by boundary conditions on the water mass flow and 

water temperature, both of which are inputs from the system-level solver during a given iteration. The 

cold-end heat exchanger on the PCU flows water circumferentially around the rejector. Since Sage can 

only resolve the axial dimension, it cannot apply the circumferential temperature gradient that is seen in 

the real convertor. To compensate for this, Sunpower uses a degradation factor that increases the cold-end 

temperature above the levels that would be predicted if this gradient were axial, providing a conservative 

estimate of convertor performance. The acceptor model does not contain a corresponding NaK heat 

exchanger model, so for the purpose of performance mapping, the boundary conditions that define the hot 

end are the metal temperatures at the inlet and outlet of the acceptor. The system level model then 

incorporates a NaK heat exchanger and iterates to determine the correct relationship between NaK inlet 

temperature, NaK flow rate, NaK outlet temperature, and heat input to the convertor. 

The performance maps were generated using the commercial mathematics programming environment 

MATLAB to call Sage within a nested loop structure throughout the entire range of intended operation. 

Inputs to the map include hot-end temperature, hot-end axial temperature difference, water temperature, 

water mass flow rate, and amplitude. The outputs are net heat input, electrical output, heat rejected, and 

thermal efficiency. The hot-end temperature ranged from 250 to 950 K in 25 K increments, hot-end 

temperature difference from 0 to 150 K in 15 K increments, water temperature from 250 to 450 K in 25 K 

increments, water mass flow from 0.01875 to 0.5875 kg/s in increments of .05 kg/s, and piston amplitude 

ranged from 8 to 20 mm in increments of 2 mm, resulting in approximately 114,000 performance map 

points covering a five dimensional parametric space. In addition to this, better resolution was obtained in 

specific areas of interest. It should be noted that each PCU consists of two Stirling generators in a 

symmetric, thermodynamically coupled, dual-opposed configuration. Therefore the Sage analysis is 

performed on one-half of the convertor, and the results are applied to both convertors in the system 

model. 
NASA/TM—2011-217203 3 

Results 

The charts below are a selection of data points taken from the performance maps. Figure 1 shows 

power output plotted against piston amplitude at various hot-end temperatures for one Stirling generator 

(one-half the full PCU). The trend appears to become increasingly linear as the convertor approaches its 

design operating temperature, with some curvature introduced at low hot-end temperatures. This trend is 

consistent with measured values taken during prior testing on kilowatt-class Stirling convertors (Briggs, 

2010). Figure 2 shows efficiency plotted against piston amplitude at the same operating conditions. The 

peak efficiency appears to occur at piston amplitudes well below the nominal amplitude of 16 mm. This is 

not entirely unexpected, as the PCU was not designed for optimum efficiency due, in part, to system-level 

trades that allow the radiator mass to decrease as the cooling water temperature, which can be 

accomplished by increasing the amount of waste heat rejected by the convertors. 

1000

2000

3000

4000

5000

6000

7000

8000

9000

6 8 10 12 14 16 18 20 22

P

o

w

e

r

O

u

t

p

u

t

(

W

a

t

t

s

)

Piston Amplitude (mm)

PowerOuput vs Amplitude Over a Range of Hot End Temperature Differences

850_28_383_.1875

800_28_383_.1875

750_28_383_.1875

700_28_383_.1875

Design Point: 6100 Watts

Figure 1.—Power output vs. piston amplitude at various hot-end temperatures for one Stirling 

generator (half of the PCU) operating with a 28 K hot-end temperature drop, a 383 K inlet water 

temperature, and a 0.1875 kg/s mass flow rate. 

0.12

0.14

0.16

0.18

0.2

0.22

0.24

0.26

0.28

0.3

0.32

6 8 10 12 14 16 18 20 22

E

f

f

i

c

i

e

n

c

y

Piston Amplitude (mm)

Efficiency vs Amplitude Over a Range of Hot End Temperature Differences

850_28_383_.1875

800_28_383_.1875

750_28_383_.1875

700_28_383_.1875

Design Point: 28% Efficiency

Figure 2.—Efficiency vs. piston amplitude at various hot-end temperatures for a convertor 

operating with a 28 K hot-end temperature drop, a 383 K inlet water temperature, and a 

0.1875 kg/s mass flow rate. 
NASA/TM—2011-217203 4 

Figure 3 shows the power output of one Stirling convertor plotted against the hot-end temperature 

difference at various piston amplitudes for one Stirling generator operating at a 850 K hot-end 

temperature, a 383 K inlet water temperature, and a 0.1875 kg/s mass flow rate. This plot shows that the 

power output is more sensitive to hot-end temperature difference at high amplitudes. This indicates that 

especially, at high amplitudes, it is important to provide sufficient NaK mass flow to the convertor. As 

discussed previously, determination of the appropriate relationship between hot-end temperature 

difference, net heat input to the convertor, and NaK mass flow rate will be left to a system-level solver, 

which will incorporate a component model of the NaK heat exchanger. Figure 4 shows the efficiency 

plotted against a hot-end temperature drop for the same set of operating conditions. Again, we see that the 

convertor attains higher efficiencies at lower piston amplitudes, and that increasing the temperature drop 

across the hot end results in a reduction in the efficiency of the convertor. 

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

0 50 100 150

P

o

w

e

r

O

u

p

u

t

(

W

a

t

t

s

)

Hot‐End Temperature Difference (K)

PowerOuput vs Hot‐End Temperature Difference at

VariousAmplitudes

850_383_.1875_20

850_383_.1875_16

850_383_.1875_12

850_383_.1875_8

Design Point: 6100 Watts

Figure 3.—Power output vs. piston amplitude at various amplitudes for one Stirling 

generator (half of the PCU) operating at 850 K hot-end temperature, a 383 K inlet 

water temperature, and a 0.1875 kg/s mass flow rate. 

0.15

0.17

0.19

0.21

0.23

0.25

0.27

0.29

0.31

0.33

0 50 100 150

E

f

f

i

c

i

e

n

c

y

Hot‐End Temperature Difference (K)

Efficiency vs Hot‐End Temperature Differenceat Various

Hot‐End Temperatures

850_383_.1875_20

850_383_.1875_16

850_383_.1875_12

Design Point: 28% Efficiency 850_383_.1875_8

Figure 4.—Efficiency vs. piston amplitude at various amplitudes for a convertor operating at 

a 850 K hot-end temperature, a 383 K inlet water temperature, and a 0.1875 kg/s mass 

flow rate. 
NASA/TM—2011-217203 5 

Conclusion 

System-level models of the Fission Power System (FPS) Technology Demonstration Unit (TDU) are 

being updated with detailed component-level codes as hardware designs are completed and fabrication 

begins. These updated models will be used to improve the accuracy of steady-state performance and 

transient response predictions for the TDU system, beyond what was previously available using 

simplified modeling techniques. Verification of detailed system-level TDU models with test data will 

allow for improvements to be made in system-level models of the FSPS, which can be used to verify 

performance claims as well as transient response analyses. A detailed performance map of the PCU has 

been generated using a Sage model provided by Sunpower, the designer of the PCU hardware. This 

performance map is currently being integrated into a system level model, allowing for improved accuracy 

while maintaining sufficient computational speed. 

References 

Fission Surface Power Team, “Fission Surface Power System Initial Concept Definition,” NASA/TM—

2010-216772 and NASA/TM—2010-216772, 2010. 

Gedeon, Sage User’s Guide, Gedeon Associates 7th Edition, Athens, Ohio, 2010. 

Briggs, M., Geng, S., Robbie, M., “Status of Kilowatt-Class Power Conversion Using a Pumped NaK 

Loop for Thermal Input,” NASA/TM—2010-216265. 
REPORT DOCUMENTATION PAGE Form Approved 

OMB No. 0704-0188 

The public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the 

data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this 

burden, to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports (0704-0188), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302. 

Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid OMB 

control number. 

PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. 

1. REPORT DATE (DD-MM-YYYY)

01-12-2011 

2. REPORT TYPE

Technical Memorandum 

3. DATES COVERED (From - To)

4. TITLE AND SUBTITLE

Implementation of a Sage-Based Stirling Model Into a System-Level Numerical Model of the 

Fission Power System Technology Demonstration Unit 

5a. CONTRACT NUMBER

5b. GRANT NUMBER

5c. PROGRAM ELEMENT NUMBER

6. AUTHOR(S)

Briggs, Maxwell, H. 

5d. PROJECT NUMBER

5e. TASK NUMBER

5f. WORK UNIT NUMBER

WBS 463169.04.03.01.02 

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration 

John H. Glenn Research Center at Lewis Field 

Cleveland, Ohio 44135-3191 

8. PERFORMING ORGANIZATION

 REPORT NUMBER

E-17603 

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration 

Washington, DC 20546-0001 

10. SPONSORING/MONITOR'S

 ACRONYM(S)

NASA 

11. SPONSORING/MONITORING

 REPORT NUMBER

NASA/TM-2011-217203 

12. DISTRIBUTION/AVAILABILITY STATEMENT

Unclassified-Unlimited 

Subject Category: 20 

Available electronically at http://www.sti.nasa.gov 

This publication is available from the NASA Center for AeroSpace Information, 443-757-5802

13. SUPPLEMENTARY NOTES

14. ABSTRACT

The Fission Power System (FPS) project is developing a Technology Demonstration Unit (TDU) to verify the performance and functionality 

of a subscale version of the FPS reference concept in a relevant environment, and to verify component and system models. As hardware is 

developed for the TDU, component and system models must be refined to include the details of specific component designs. This paper 

describes the development of a Sage-based pseudo-steady-state Stirling convertor model and its implementation into a system-level model 

of the TDU. 

15. SUBJECT TERMS

Fission; Power conversion; Numerical modeling; Fission surface power; Stirling power conversion 

16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF

 ABSTRACT

UU 

18. NUMBER

 OF 

 PAGES

11 

19a. NAME OF RESPONSIBLE PERSON

STI Help Desk (email:help@sti.nasa.gov) 

a. REPORT

U 

b. ABSTRACT

U 

c. THIS 

PAGE

U 

19b. TELEPHONE NUMBER (include area code)

443-757-5802 

Standard Form 298 (Rev. 8-98)

Prescribed by ANSI Std. Z39-18