Timothy F. Regan and Edward J. Lewandowski

Sest, Inc., Middleburg Heights, Ohio

Development of a Stirling System Dynamic

Model With Enhanced Thermodynamics

NASA/CR—2005-214018

November 2005
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Timothy F. Regan and Edward J. Lewandowski

Sest, Inc., Middleburg Heights, Ohio

Development of a Stirling System Dynamic

Model With Enhanced Thermodynamics

NASA/CR—2005-214018

November 2005

National Aeronautics and

Space Administration

Glenn Research Center

Prepared under Contract NAS3–03064

Prepared for the

Space Technology and Applications International Forum (STAIF–2005)

sponsored by the University of New Mexico’s Institute for Space

and Nuclear Power Studies (UNM-ISNPS)

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Acknowledgments

This work was performed for NASA Headquarters, Office of Space Science (Code S) under the Prometheus

Program and was supported by the NASA Glenn Research Center Contract NAS3-03064. The authors gratefully

acknowledge the input and suggestions of Barry Penswick (consultant) and Jeff Schreiber, NASA Glenn Research

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NASA/CR—2005-214018 1 

Development of a Stirling System Dynamic Model 

With Enhanced Thermodynamics 

Timothy F. Regan and Edward J. Lewandowski 

Sest, Inc. 

Middleburg Heights, Ohio 44130 

Abstract 

The Stirling Convertor System Dynamic Model developed at NASA Glenn Research Center is a software model 

developed from first principles that includes the mechanical and mounting dynamics, the thermodynamics, the linear 

alternator, and the controller of a free-piston Stirling power convertor, along with the end user load. As such it 

represents the first detailed modeling tool for fully integrated Stirling convertor-based power systems. The 

thermodynamics of the model were originally a form of the isothermal Stirling cycle. In some situations it may be 

desirable to improve the accuracy of the Stirling cycle portion of the model. An option under consideration is to 

enhance the SDM thermodynamics by coupling the model with Gedeon Associates’ Sage simulation code. The 

result will be a model that gives a more accurate prediction of the performance and dynamics of the free-piston 

Stirling convertor. A method of integrating the Sage simulation code with the System Dynamic Model is described. 

Results of SDM and Sage simulation are compared to test data. Model parameter estimation and model validation 

are discussed. 

Introduction 

In recent years there has been significant development of free-piston Stirling convertors for potential use on NASA 

exploration missions (Schreiber and Thieme, 2004). In support of this development effort, a detailed nonlinear 

system-level dynamic model has been created, referred to as the Glenn Research Center (GRC) Stirling Convertor 

System Dynamic Model (SDM) (Lewandowski and Regan, 2004). While other Stirling models exist, none have the 

breadth and capability of the SDM. Governing equations of the model have been published previously, and 

therefore are not included in this paper. Figure 1 illustrates the fact that the SDM includes not only the Stirling 

Convertor Assembly (SCA) but it also includes many of the other key parts of the power system. The SDM models 

the Stirling cycle thermodynamics, heat flow, working fluid, mechanical mass-spring damper systems and the linear 

alternator. It also includes the entire system from the thermal energy input to thermal rejection, mounting dynamics, 

the controller and electrical load including the power distribution system. This allows one to study the interactions 

among the various subsystems comprising a Stirling convertor-based power system. Thermal, mechanical, fluid, 

magnetic, and electrical aspects can be studied in one model. The SDM is a non-linear time-domain model 

External 

structure loads

Stirling cycle 

thermodynamics

Case & mounting 

dynamics

Power 

management & 

distribution 

(PMAD)

End user 

load

Thermal 

losses

Heat sink/ 

environment

Gas dynamics

Heat 

source

Piston & 

displacer 

dynamics

Alternator 

electromagnetics Controller

External 

structure loads

Stirling cycle 

thermodynamics

Case & mounting 

dynamics

Power 

management & 

distribution 

(PMAD)

End user 

load

Thermal 

losses

Heat sink/ 

environment

Gas dynamics

Heat 

source

Piston & 

displacer 

dynamics

Alternator 

electromagnetics Controller

Figure 1.—SDM Model Structure.
NASA/CR—2005-214018 2 

containing sub-cycle dynamics, which simulates transient and dynamic phenomena that other models cannot. The 

entire range of convertor operation is modeled, from start-up to full power conditions. 

The SDM has been developed as a “bottom-up” model based on first principles. Components are separately 

modeled, then combined into subsystems and ultimately into the system. Very few calibration factors have been 

used to correlate SDM simulation results with test data. The SDM can be set up to include multiple convertors in 

various mechanical and electrical configurations, including dual-opposed, parallel electrical, and series electrical 

configurations. It is being used to model free-piston convertors from less than 100 W to over 10 kW. 

System Dynamic Model (SDM) 

SDM is a collection of inter-dependent circuit models of the various physical systems at work in a free-piston 

Stirling convertor. Circuit solutions obey conservation laws by their very nature. Circuit theory is a convenient 

framework for analysis in the electrical and mechanical domains because the through-quantities and acrossquantities remain confined to the machine elements modeled in the circuit model. The electrical currents in SDM’s 

electrical circuits remain confined to the conductors. In SDM’s mechanical circuits, the velocity and position are 

confined to their associated rigid moving masses in the axial direction. Modeling the free-piston Stirling convertor 

in the thermal domain and the fluid domain offer more challenges because the flow paths for thermal and fluid 

behavior are more than onedimensional. Indeed the 

working fluid encounters 

changing direction, changing 

temperatures and changing 

cross-sectional areas as it 

flows through the convertor in 

the cycle. Similarly, the flow 

of heat through the gas spaces 

and the various metal 

boundaries of the convertor 

encounters more degrees of 

freedom than a onedimensional circuit can 

accommodate. Nevertheless, 

by breaking the thermal and 

fluid flow paths up into 

segments with near-uniform 

characteristics, an adequate 

model can be made. 

In SDM, heat is modeled as 

flowing through the convertor’s structure from a source at the hot end to a rejection temperature sink connected to 

the cold end. The amount of heat flowing into the Stirling thermodynamic cycle is lumped into another heat source 

ExpPV connected to the heat sink, as shown in Fig. 2. The magnitude of the heat source is set equal to the 

expansion space PV power. The expansion space PV power is calculated from 

∫ PVpower = Pdv , (1) 

where P is the instantaneous pressure and v is the instantaneous volume of the expansion space. SDM reports a new 

value for ExpPV once per cycle. The temperature of the hot end results from the circuit solution of the thermal 

circuit. It is the temperature that is directly related to pressure through the ideal gas law. As an example of circuit 

operation, consider the case in which the input heat to a model operating at steady state is increased, the circuit 

solution for temperature yields a higher value. The pressure rises due to the ideal gas law. The PV power increases 

as a result. The increased PV power enters the thermal circuit of Fig. 2 through the heat source ExpPV and has the 

effect of reducing the rise in temperature until eventually, it reaches a new steady state solution. SDM assumes that 

the expansion space temperature can be determined solely from the input heat and the calculated PV power. This is 

 

 

Figure 2.—SDM Thermal Circuit with Sage inputs.
NASA/CR—2005-214018 3 

the major simplifying assumption of SDM. By this assumption, SDM assumes the thermal resistances Rhhx, Rexp, 

Rkhx, and Rcmp are equal to zero, neglecting temperature drops due to heat exchanger losses and losses to ambient 

through convection and radiation. Thus, SDM can dispense with all concern about heat exchanger performance, 

thickness of bounding surfaces and their materials of construction. Such a model suffers some inaccuracies as a 

result of the simplification and, of course, is of no use in gauging the effect of heat exchanger performance or 

materials of construction on dynamic performance. 

The flow of working fluid is not modeled as a circuit in SDM. A circuit model cannot adequately model the fluid 

flow in the convertor because the fluid velocity varies along that path due to temperature change. A circuit requires 

a uniform through-quantity in a series connection. SDM uses equations rather than a circuit solution to calculate 

flow. The equations consider temperature, pressure, volume and the rates of change of pressure and volume in 

calculating flow. The flow is important because it is used to calculate the viscous damping and consequent 

amplitude of the displacer. The fact that the working fluid flows through viscous elements implies that there is a 

pressure drop across the elements. The pressure used in the flow calculation is assumed uniform throughout all the 

working spaces. This is the second simplifying assumption of SDM. 

Comparison with test data shown in the graphs of Fig. 3 indicates the effect of the simplifying assumptions on the 

accuracy of the SDM. 

SDM Model Parameter Determination 

SDM does not require the user to make assumptions about values for the piston amplitude or operating frequency. 

These variables are determined based on the dynamics during the simulation. As a result, it is critical to the SDM to 

have accurate models for components such as the flexures, gas springs, moving masses, and the alternator. 

Flexures, if used, need to be modeled as nonlinear springs, since the nonlinear characteristics affect the dynamics 

and stability, especially at high piston and displacer amplitudes. The spring rate can be determined from static 

measurements. Testing has shown that for systems using multiple flexures, linear superposition of individual 

flexure spring rates can be used to determine the total effective spring rate. A 3rd-order curve fit of the test data of 

the form F = K1 X3 + K2 X is generally sufficient to model the spring rate. There is no X2 term, assuming the spring 

is symmetric about the null position. The spring rate is then K = K1 X2

 + K2.

Flexure spring rate can also be determined using finite element analysis (FEA) methods. However, unless the inner 

diameter and outer diameter clamping is accurately modeled, the spring rate can be in error by several percent. 

The effective masses for the piston and displacer can be determined by weighing the moving components. For 

flexures, the effective mass is approximately one third of the total mass when the inner diameter moves, and two 

thirds of the total mass when the outer diameter moves. It is recommended to use FEA to more accurately estimate 

the portion of the flexure mass to assign to the moving mass, especially when the flexure mass is significant. 

Statically determined mass and spring rates can be corroborated with dynamic data. Natural frequency 

measurements can be made at low and high amplitudes to verify model parameters. A measurement of oscillatory 

decay can provide an estimate of a portion of piston or displacer damping. 

The alternator magnet spring rate can be determined in a similar fashion to the method used for flexures. A 3rd-order 

equation of the form used to model the flexures can be used. Depending on the maximum amplitude of the 

alternator, though, end effects may need to be incorporated into the model. 

The alternator model includes a resistance, an inductance, and alternator constants relating current to force and 

velocity to voltage. The resistance measurement is straightforward, and can be readily adjusted for temperature 

effects through a linear correction factor. The inductance measurement is made at the operating frequency. The 

alternator constants can be derived from alternator performance data at various amplitudes, loads, and temperatures. 

In this way effects like the temperature effect on the magnets’ remanent flux density Br can be incorporated. The 

open loop voltage provides a good estimate of the alternator’s internal voltage, or EMF. If the alternator travel is 

not limited to the linear region, end effects at high amplitudes need to be incorporated. This is especially important 

when using the SDM to perform stability analysis. 
NASA/CR—2005-214018 4 

SDM model parameters have been determined using the methods described above for the 55-We Technology 

Demonstration Convertor (TDC) Stirling convertor at GRC. The TDC is designed and manufactured by Stirling 

Technology Company (STC) of Kennewick, WA. By accurately modeling dynamic characteristics associated with 

flexures, gas springs, magnets, masses, capacitors, thermal inertias and other components, including their 

nonlinearities, the SDM shows good correlation with test data even with the simplified Stirling cycle model 

assumptions. For example, the operating frequency is within 1 Hz of the actual operating frequency. The transient 

response and dynamic characteristics of the SDM have been reported in Regan and Lewandowski (2004). 

SDM Performance With Simplifying Assumptions 

When comparing the performance of a Stirling model to test data, a number of performance metrics can be 

examined. During steady-state simulation, variables like output power, displacer phase angle, pressure phase angle, 

pressure amplitude, piston amplitude, displacer amplitude, operating frequency, output current, output voltage, and 

various thermal, pressure, and power losses can be compared. However, as in the case of any evaluation process, 

great care must be exercised to insure that the potential errors in the test data are well understood. This is particulary 

true for free-piston systems due to the close interactions between the various components and the limited number of 

measured parameters available. This can lead to situations where portions of the measured data may be internally 

Figure 3.—SDM Model vs. Sage Model vs. Test Data. 

(a) Output Power at 6.0 mm Piston Amplitude and 80°C 

Cold End. 

(b) Output Power at 6 mm Piston Amplitude and 120°C 

Cold End. 

(d) Output Power at 5.4 mm Piston Amplitude and 120°C 

Cold End. 

(c) Output Power at 5.4 mm Piston Amplitude and 80°C 

Cold End. 

20

25

30

35

40

45

50

55

60

450 500 550

Heater temperature (°C)

Output power (We)

SDM simulation

Sage simulation

Test data

20

25

30

35

40

45

50

55

60

450 500 550 600 650

Heater temperature (°C)

Output power (We)

SDM simulation

Sage simulation

Test data

20

25

30

35

40

45

50

55

60

450 500 550

Heater temperature (°C)

Output power (We)

SDM simulation

Sage simulation

Test data

20

25

30

35

40

45

50

55

60

500 550 600 650

Heater temperature (°C)

Output power (We)

SDM simulation

Sage simulation

Test data
NASA/CR—2005-214018 5 

inconsistent. In addition, a number of the key components can have operating characteristics which vary 

significantly with relatively small changes in operating parameters, for example the linear alternator efficiency. This 

can lead to significant errors when attempting to extract internal component characteristics from external 

measurements. 

The SDM steady-state performance was validated by comparing model output with test data taken on the TDC at 

GRC. Figure 3 shows the SDM prediction of convertor output power vs. test data. Over the range of operating 

temperatures and piston amplitudes modeled, the output power predicted by SDM is between 6 and 31% high, with 

an average error of 20%. This error is attributed to SDM’s use of the simplifying assumptions described above. The 

thermal circuit of Fig. 2 yields a higher-than-actual working space temperature in the expansion space and a lowerthan-actual temperature in the compression space. 

Other variables were compared to test data. For the TDC convertor at the test conditions studied, the displacer phase 

angle predicted by SDM is 6° to 10° lower than actual. The pressure angle is about 5° to 15° higher than actual. 

The amplitude of the pressure wave is 5 to 25 kPa lower than actual. The differences in phase angles are attributed 

to the simplified treatment of fluid flow. This difference is explained in the section on Sage/SDM integration. 

Alternative models have been developed for the Stirling cycle besides the modified Schmidt’s analysis currently 

used by SDM. An adiabatic model, developed by Benvenuto and DeMonte (1992), generally gives a more accurate 

performance prediction than Schmidt’s analysis. A version of SDM is being developed for evaluation based on the 

adiabatic model. 

Sage Model 

Sage is a dedicated thermodynamic code for modeling Stirling-cycle based machines, developed by Gedeon 

Associates of Athens, OH (Gedeon, 1995). For the TDC, SDM models a Stirling convertor having coaxial piston 

and displacer and annular heat exchangers connecting the expansion space with the compression space. The 

corresponding Sage model is shown in Fig. 4. It comprises cylinders for the expansion and compression spaces. The 

construction materials and geometry of these cylinders as well as those of the heat exchangers and regenerator have 

been chosen to correspond with those of the TDC. The heat transfer properties are calculated by Sage for any 

operating temperature, pressure, frequency and piston motion entered into the Sage program as parameters. 

The power piston is modeled as what Sage refers to as a “phasor-constrained reciprocator.” The fact that it is 

phasor-constrained means that it is limited to sinusoidal motion with amplitude keyed into the graphical user 

interface by the user. The displacer is also kept to sinusoidal motion, but Sage will calculate its amplitude and phase 

Figure 4.—Sage Model Linked to SDM.
NASA/CR—2005-214018 6 

angle. Sage refers to such a construct as a “free reciprocator.” Its amplitude and phase angle relative to the piston’s 

motion are determined by the pressure forces acting on it and the spring force exerted by a spring connecting the 

displacer to the case. The displacer has child components including a cylinder and a flexure spring. The piston’s 

child components include a cylinder, a seal and an appendix gap. The Sage model is configured to calculate 

mechanical power, heat transfer, seal leakage losses, and flow losses for the specified operating condition. Unlike 

SDM, the Sage model simulation considers the heat transfer characteristics of the gas boundaries as specified by the 

user and calculates the temperature variation in the working spaces over the cycle. 

Sage output power was calculated by the model of Fig. 4 for the same conditions for which SDM and test results are 

plotted in Fig. 3. The Sage results are consistently closer to the true (test) values than SDM’s results. This indicates 

that incorporation the more sophisticated treatment of losses and working space temperatures in Sage results in a 

more accurate model. Fig 3 shows that in some of the simulations, the Sage calculations are very close to the test 

data. In other cases, especially at high values of temperature difference, the Sage results depart significantly from 

test data. Sage inaccuracies can be reduced through a more accurate determination of heat transfer and pressure drop 

coefficients (Qiu and Augenblick, 2004). When Sage’s temperatures, operating frequency and piston amplitude are 

valid, the resulting input and output powers are accurate. The SDM Sage interface will be able to supply Sage with 

these input parameters. Sage, in its turn, provides SDM with the time-varying temperatures in the expansion and 

compression spaces. These temperatures were calculated using Sage’s detailed modeling of the heat transfer at the 

gas boundaries. They are used to free SDM from its simplifying assumptions and allow more realistic model 

performance. 

Integrating Sage With the SDM 

It has been mentioned above that SDM 

lacks the ability to calculate the actual 

time-varying temperatures of the 

working spaces because it does not 

process any heat transfer characteristics 

at the gas boundaries in the convertor. 

It was also observed that Sage 

generally uses piston amplitude, 

operating frequency and mean working 

space pressure as inputs of the Sage 

model. A method of integrating SDM 

and Sage has been developed which 

uses the outputs of each model to 

supply what the other model lacks. 

Applying this method, the piston 

amplitude, operating frequency, mean 

working space pressure, and mean 

heater and cooler temperatures are 

passed to Sage from SDM. Sage 

results are then made available at the 

interface for use in SDM. In the 

specific method used as a test of the 

technique, the cyclic temperature 

variations in the expansion space and 

compression space are calculated by 

Sage and passed back to SDM. The 

temperature used by SDM to calculate 

its pressure wave is the sum of the 

mean temperature and the time-varying temperature. The thermal circuit model shown in Fig. 2 contains not only 

the means to solve for the mean expansion space temperature, already discussed, but it also has a temperature source 

for adding in the time-varying component of the expansion space temperature. This source is labeled SageFTe. Its 

output temperature is the sum of the mean temperature and the time-varying part that is obtained from Sage. The 

SDM

SDM determines:

Xp

Operating frequency 

Mean Pressure

Th and Tc

Sage calculates steady state solution 

from SDM input

Sage results available at interface:

Working space temperature variation

Expansion space pressure waveform

Compression space pressure waveform

Piston and displacer damping

Certain losses

SDM uses Sage data to integrate over 

the next operating cycle.

Stirling simulation begins in SDM. 

Continue until steady-state operation 

achieved.

Sage

Initialize SDM model parameters.

Send shared model parameters to Sage. Initialize Sage model parameters

For Each Operating Cycle 

Until Simulation End:

SDM

SDM determines:

Xp

Operating frequency 

Mean Pressure

Th and Tc

Sage calculates steady state solution 

from SDM input

Sage results available at interface:

Working space temperature variation

Expansion space pressure waveform

Compression space pressure waveform

Piston and displacer damping

Certain losses

SDM uses Sage data to integrate over 

the next operating cycle.

Stirling simulation begins in SDM. 

Continue until steady-state operation 

achieved.

Sage

Initialize SDM model parameters.

Send shared model parameters to Sage. Initialize Sage model parameters

For Each Operating Cycle 

Until Simulation End:

Figure 5.—Schematic of Sage Integration with SDM.
NASA/CR—2005-214018 7 

time-varying compression space temperature is handled in a similar fashion by the source labeled SageFTc in Fig. 2. 

A key element in the proposed approach will be insuring that the two simulations do not enter into an “infinite loop” 

situation in which true steady state conditions are never reached. 

Software Integration 

Gedeon Associates has provided an add-on to Sage to enable operation of the software outside of Sage’s normal 

graphical user interface. The add-on is called the Sage Stirling DLL. It is a Windows Dynamic Linked Library 

(DLL) which provides a number of functions callable from C or C++. The member functions contained in the DLL 

provide the ability to open and close a Sage model, to supply Sage with an input value and to get an output value 

from Sage. Sage will only supply outputs from solved models, so that if the model has not yet been solved when the 

function GetReal() for getting an output is called, it first solves the model and then sends the value to the function. 

SDM uses the Ansoft Simplorer platform which provides a C++ utility allowing development of custom elements 

coded from a convenient C++ template. A library of Sage interface modules developed using the C/C++ facility of 

Simplorer is envisioned. One element will be used to initialize the Sage model so that Sage and SDM are always 

considering the same model. Other elements will be used to pass the various values back and forth between Sage 

and SDM. 

More than one interface scheme is certainly possible and it is likely that some will perform better than others. The 

one that has been mentioned above – i.e., the working space dynamic temperature method – represents one of these 

approaches. The Sage interface calculates new values for the amplitude and phase angles of the time-varying 

portion of the expansion space and compression space temperatures based on SDM values for mean working space 

pressure, piston amplitude, mean temperatures of the expansion and compression space and operating frequency. 

The two models describe the same geometry and contain the same losses. The Sage model is a constrained-piston 

free-displacer type model. The temperatures calculated will correspond to a valid steady state operating point of the 

Sage model. The method does not depend upon making the solutions of the two models agree before proceeding 

with the simulation. Rather, Sage is treated as a subroutine of SDM that calculates the time-variation of the working 

space temperatures. Once SDM has obtained the temperature information, it proceeds with its simulation. 

The difference between SDM running in this mode and previous modes is that now the more sophisticated Stirling 

working space temperatures are used. They include the realistic effects of heat transfer to the gas boundaries 

without the need to calculate it in SDM. 

Other options include techniques such as a pressure factor-based approach, where piston and displacer are driven by 

a factored pressure wave. In this approach, the SDM would utilize pressure factors calculated by Sage to determine 

piston and displacer pressure forces. This approach and others will be investigated in the future as time and 

technical merit permit. 

Conclusions 

The GRC Stirling convertor SDM has been developed to evaluate the characteristics of fully integrated Stirling 

convertor based power systems. In some situations it has also been employed to model actual Stirling convertor test 

results over a wide range of operating conditions with varying levels of accuracy. The differences seen between 

SDM and test data are expected, due to a number of the fundamental assumptions employed. In an effort to improve 

SDM accuracy for these specific situations, a number of options are being investigated. The method discussed in 

this paper inserted working space temperatures calculated by Sage into the pressure wave calculation of SDM. The 

test cases run to date show significant improvement in fidelity of the model. The displacer phase angle, which had 

been low by 6° to 10° before the insertion of the Sage temperatures, was brought to no further than 1.5° from the 

Sage results after the insertion. The output power and pressure wave amplitude were brought closer to the Sage 

results as well. 

The integration of Sage working space temperatures into SDM represents one option which provided improved 

model accuracy. Other methods are under consideration and they may provide even greater improvements to SDM’s 

thermodynamic modeling. 
NASA/CR—2005-214018 8 

Nomenclature 

Br remanent flux density (T) 

ExpPV expansion space PV power (W) 

F force (N) 

HeatIn Heat input (W) 

HHheatCap heater head thermal capacitance (W*s/K) 

K spring rate (N/m) 

K1, K2 spring rate coefficients 

mGt  mass flow rate (kg/s) 

P pressure (Pa) 

Pphsr pressure phasor (Pa) 

Qstdy steady state heat flow (W) 

Rcmp thermal resistance into compression space (K/W) 

Rexp thermal resistance into expansion space (K/W) 

Rhhx heater thermal resistance (K/W) 

Rkhx cooler thermal resistance (K/W) 

RhhcondLoss heater head conduction loss (K/W) 

SageFTe expansion space temperature (K) 

SageFTc compression space temperature (K) 

Tc cooler temperature (K) 

Th heater temperature (K) 

To ambient temperature (K) 

V volume (m3

) 

Wnet displacer net work (W) 

Xd displacer position (m) 

Xp piston position (m) 

∆T temperature drop (K) 

References 

Benvenuto, G. and DeMonte, F., “An Adiabatic Approach for the Design and the Response-to-Load Evaluation of 

Free-Piston Stirling Engines,” 1992, SAE Paper No. 929066. 

Gedeon, D., “Sage: Object-Oriented Software for Cryocooler Design,” Cryocoolers 8, Edited by R.G. Ross, Jr., 

Plenum Press, New York, 1995, pp. 281-292.

Lewandowski, E.J. and Regan, T.F., “Overview of the GRC Stirling Convertor System Dynamic Model,” in 

proceedings of the Second International Energy Conversion Engineering Conference (IECEC 2004), American 

Institute for Aeronautics and Astronautics, 2004. AIAA-2004-5671. 

Qiu, S. and Augenblick, J.E., “Conceptual Design Update for an Improved Stirling Convertor,” in proceedings of the 

Second International Energy Conversion Engineering Conference (IECEC 2004), American Institute for 

Aeronautics and Astronautics, 2004. AIAA-2004-5623. 

Regan, T.F., Lewandowski, E.J., “Application of the GRC Stirling Convertor System Dynamic Model,” in 

proceedings of the Second International Energy Conversion Engineering Conference (IECEC 2004), American 

Institute for Aeronautics and Astronautics, 2004. AIAA-2004-5672. 

Schreiber, J.G, and Thieme, L.G., “Accomplishments of the NASA GRC Stirling Technology Development 

Project,” in Proceedings of the Second International Energy Conversion Engineering Conference (IECEC 

2004), American Institute for Aeronautics and Astronautics, 2004. AIAA-2004-5517. 
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NSN 7540-01-280-5500 Standard Form 298 (Rev. 2-89)

Prescribed by ANSI Std. Z39-18

298-102

Form Approved

OMB No. 0704-0188

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Unclassified Unclassified

Final Contractor Report

Unclassified

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National Aeronautics and Space Administration

Washington, DC 20546–0001

Available electronically at http://gltrs.grc.nasa.gov

November 2005

NASA CR—2005-214018

E–15333

WBS–22–972–20–01

NAS3–03064

14

Development of a Stirling System Dynamic Model With

Enhanced Thermodynamics

Timothy F. Regan and Edward J. Lewandowski

Stirling engines; Design analysis; Block diagrams; Electromechanics; Dynamic models;

Simulation; AC generators; Linear alternators; Stirling cycle

Unclassified -Unlimited

Subject Categories: 20 and 44

Sest, Inc.

18000 Jefferson Park Road

Suite 104

Middleburg Heights, Ohio 44130

Prepared for the Space Technology and Applications International Forum (STAIF–2005) sponsored by the

University of New Mexico’s Institute for Space and Nuclear Power Studies (UNM-ISNPS), Albuquerque,

New Mexico, February 13–17, 2005. Project Manager, Jeffrey G. Schreiber, Power and Electric Propulsion

Division, NASA Glenn Research Center, organization code RPT, 216–433–6014.

The Stirling Convertor System Dynamic Model developed at NASA Glenn Research Center is a software model

developed from first principles that includes the mechanical and mounting dynamics, the thermodynamics, the linear

alternator, and the controller of a free-piston Stirling power convertor, along with the end user load. As such it represents

the first detailed modeling tool for fully integrated Stirling convertor-based power systems. The thermodynamics of the

model were originally a form of the isothermal Stirling cycle. In some situations it may be desirable to improve the

accuracy of the Stirling cycle portion of the model. An option under consideration is to enhance the SDM

thermodynamics by coupling the model with Gedeon Associates’ Sage simulation code. The result will be a model

that gives a more accurate prediction of the performance and dynamics of the free-piston Stirling convertor. A method

of integrating the Sage simulation code with the System Dynamic Model is described. Results of SDM and Sage

simulation are compared to test data. Model parameter estimation and model validation are discussed.