Scott D. Wilson, Terry V. Reid, Nicholas A. Schifer, and Maxwell H. Briggs

Glenn Research Center, Cleveland, Ohio

Overview of Heat Addition and Effi ciency

Predictions for an Advanced Stirling Convertor

NASA/TM—2012-217292

March 2012
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Scott D. Wilson, Terry V. Reid, Nicholas A. Schifer, and Maxwell H. Briggs

Glenn Research Center, Cleveland, Ohio

Overview of Heat Addition and Effi ciency

Predictions for an Advanced Stirling Convertor

NASA/TM—2012-217292

March 2012

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Prepared for the

9th International Energy Conversion Engineering Conference (IECEC)

sponsored by the American Institute of Aeronautics and Astronautics

San Diego, California, July 31–August 3, 2011
Acknowledgments

This work is funded through the National Aeronautics and Space Administration (NASA) Science Mission Directorate and the 

Radioisotope Power Systems Program Offi ce. The authors wish to acknowledge the many people who supported this testing 

and analysis effort including Art Atherton, Kamran Daryabeigi, Wayne Gerber, Dave Gubics, Nissim Lugasy, and the vision and 

guidance of Jeff Schreiber.

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Level of Review: This material has been technically reviewed by technical management. 

This report is a formal draft or working 

paper, intended to solicit comments and 

ideas from a technical peer group.

This report contains preliminary fi ndings, 

subject to revision as analysis proceeds.
NASA/TM—2012-217292 1 

Overview of Heat Addition and Efficiency Predictions for an 

Advanced Stirling Convertor 

Scott D. Wilson, Terry V. Reid, Nicholas A. Schifer, and Maxwell H. Briggs 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Abstract 

The U.S. Department of Energy (DOE) and Lockheed Martin Space Systems Company (LMSSC) 

have been developing the Advanced Stirling Radioisotope Generator (ASRG) for use as a power system 

for space science missions. This generator would use two high-efficiency Advanced Stirling Convertors 

(ASCs), developed by Sunpower Inc. and NASA Glenn Research Center (GRC). The ASCs convert 

thermal energy from a radioisotope heat source into electricity. As part of ground testing of these ASCs, 

different operating conditions are used to simulate expected mission conditions. These conditions require 

achieving a particular operating frequency, hot end and cold end temperatures, and specified electrical 

power output for a given net heat input. Microporous bulk insulation is used in the ground support test 

hardware to minimize the loss of thermal energy from the electric heat source to the environment. The 

insulation package is characterized before operation to predict how much heat will be absorbed by the 

convertor and how much will be lost to the environment during operation. In an effort to validate these 

predictions, numerous tasks have been performed, which provided a more accurate value for net heat 

input into the ASCs. This test and modeling effort included: (a) making thermophysical property 

measurements of test setup materials to provide inputs to the numerical models, (b) acquiring additional 

test data that was collected during convertor tests to provide numerical models with temperature profiles 

of the test setup via thermocouple and infrared measurements, (c) using multidimensional numerical 

models (computational fluid dynamics code) to predict net heat input of an operating convertor, and (d) 

using validation test hardware to provide direct comparison of numerical results and validate the 

multidimensional numerical models used to predict convertor net heat input. This effort produced high 

fidelity ASC net heat input predictions, which were successfully validated using specially designed test 

hardware enabling measurement of heat transferred through a simulated Stirling cycle. The overall effort 

and results are discussed. 

Nomenclature 

ASC(–E2) Advanced Stirling Convertor (for the second generation Engineering Unit) 

ASRG(–EU) Advanced Stirling Radioisotope Generator (Engineering Unit) 

CFD computational fluid dynamic 

CSAF cold-side adapter flange 

DOE Department of Energy 

EU Engineering Unit 

FEA finite element analysis 

GPHS General Purpose Heat Source 

GRC Glenn Research Center 

LaRC Langley Research Center 

LMSSC Lockheed Martin Space Systems Company 

RPS Radioisotope Power System 

TPRL Thermophysical Properties Research Laboratory Inc. 
NASA/TM—2012-217292 2 

1.0 Introduction 

Stirling power conversion technology is being developed for space flight by the U.S. Department of 

Energy (DOE), Lockheed Martin Space Systems Company (LMSSC), Sunpower, Inc., and the NASA 

Glenn Research Center (GRC). NASA GRC has been testing high-efficiency free-piston Stirling 

convertors for potential use in Radioisotope Power Systems (RPSs) since 1999. The current effort is in 

support of the Advanced Stirling Radioisotope Generator (ASRG), which has demonstrated significantly 

higher system efficiency in comparison to radioisotope thermoelectric generators, reducing the amount of 

fuel (Pu238) required by a factor of four (Ref. 1). 

Convertor and generator testing is carried out in tests designed to characterize convertor performance 

when subjected to environments intended to simulate launch and space conditions. These conditions 

require maintaining a particular operating frequency, piston amplitude, and convertor temperatures (hot 

end, cold end, and alternator) while achieving a specified electrical power output for a given net heat 

input. Figure 1 shows a simplified example of how net heat input can be calculated if all values for heat 

flux are known. More complex formulations involving internal surfaces of heat exchangers can be used to 

calculate net heat input but are not discussed here. Stirling convertor net heat input is defined as the sum 

of heat energy supplied to the Stirling cycle and heat energy lost from the hot end to the cold end of the 

machine (known as cold end losses). Inherent to all heat engines, cold end losses are minimized by design 

but still play a significant role in the power budget. In this example, net heat input is the heat energy not 

lost back to the environment before it is consumed by the cycle or lost to the cold end. Testing involves 

developing support hardware that enables 24/7 unattended operation and data collection, including control 

and data acquisition systems, heating and cooling components, and general mounting and insulation 

packages. Microporous bulk insulation is used in the ground support test hardware to minimize the loss of 

thermal energy from the electric heat source to the environment. 

Before operation, the insulation package is subjected to various temperature conditions during 

insulation loss characterization to quantify how much heat will be absorbed by the convertor and how 

much will be lost to the environment during operation. This characterization enables the calculation of net 

heat input to the convertor and efficiency at a given operating point. Calculation of net heat input has 

historically been done by curve fitting the insulation loss characterization data, but such a method has 

never been validated. In an effort to validate net heat input predictions, numerous tasks have been 

(1)

(2)

(3)

Simplified Example of Net Heat Input to Convertor 

(1) – Heat addition to Heater Head from Heat Source 

(2) – Heat Loss from Collector to Support Hardware 

(3) – Heat Loss from Cylinder to Support Hardware 

Example calculation: 

 (1) – (2) – (3) = Net Heat Input 

220 W – 10 W – 1 W = 209 W 

Figure 1.—Simplified example of net heat input. 
NASA/TM—2012-217292 3 

performed that provided a more accurate value for net heat input to the Advanced Stirling Convertors 

(ASCs). These tasks, discussed in more detail in later sections, include a) making thermophysical 

property measurements of test setup materials to provide inputs to the numerical models, b) acquiring 

additional test data that is collected during convertor tests to provide numerical models with temperature 

profiles of the test setup, c) using multidimensional numerical models to predict net heat input of an 

operating convertor, and d) using validation test hardware to provide direct comparison between 

measured data and numerical results to validate the multidimensional numerical models used to predict 

convertor net heat input (and efficiency). 

2.0 Convertor Testing 

The ASC was developed by Sunpower, Inc., under contract to NASA GRC with technical support 

from GRC. It was designed to produce a nominal 80 We from 250 W gross heat input when integrated 

into a generator. The ASC–E convertors utilize Inconel 718 heater heads while the ASC–E2, -E3, and 

Flight convertors utilize MarM-247 heater heads, which operate at a maximum hot end temperature of 

650 and 850 °C, respectively. The cold end temperature operating range is 40 to 90 °C for the ASC–E. 

The operating range has been expanded significantly to 15 to 124 °C for the ASC–E2. A heat collector is 

attached to the hot end of the heater head, which interfaces to an electric heat source during laboratory 

operation. A conductive flange called the cold side adapter flange has been attached to the heat rejection 

zone of the convertor that allows attachment of cooling loops. 

2.1 Ground Support Hardware 

Figure 2 shows ASC–E2s mounted in a vertical orientation and dual-opposed configuration. The 

ground support hardware was developed to provide proper heating and cooling of the convertor while 

supporting a single convertor in vertical orientation (heater head up) or a dual-opposed pair of convertors 

in either horizontal or vertical orientation (Ref. 2). Electric heaters and fluid cooling loops are used to 

control the temperatures of the hot and cold ends of the Stirling convertor. As the convertor design 

transitioned from the ASC–E, which has an Inconel heater head to the ASC–E2 and future units that all 

have MarM heater heads, the convertor hot end temperature increased from 650 to 850 °C. The electric 

heat source temperature required to maintain the 850 °C hot end temperature in ground tests increased 

(approaching 1,000 °C) as well. This proved to be problematic with standard cartridge heaters because 

they were not rated for operation above 760 °C. As such, the heat sources typically only lasted a few 

hundred hours, which delayed testing of convertors at the desired conditions. To enable long-duration 

HT Firerod 

cartridge heaters 

Microsil microporous 

bulk insulation

Kaowool blanket 

insulation

Heat source spring 

load mechanism 

Surface 

thermocouples 

Insulation 

enclosure

Figure 2.—Insulation package for ASC–E2 testing. ASC–E2s #3 and #4 shown mounted in a vertical orientation 

and dual-opposed configuration (left) and ASC–E2 #4 shown at different stages of insulation assembly.
NASA/TM—2012-217292 4 

Figure 3.—ASC–E2 HT Firerod heat source. HT Firerod 

cartridge heaters (red) and nickel block (green) 

shown. 

850 °C convertor tests, a high-temperature heat source development activity was initiated. In addition to 

down selecting to a new heat source design, the insulation package was redesigned to minimize heat loss 

from the heat source to the environment during operation. Also shown in Figure 2 are the HT Firerod 

cartridge heaters, insulation package, heat source load mechanism, and insulation enclosure. 

The insulation enclosure is used for mounting the convertor and many test components including the 

heat source, cooling plumbing, and bulk insulation. The enclosures, machined from aluminum, have been 

designed to the representative size and general shape of the ASRG–EU housing. The enclosures house the 

Microsil microporous insulation used to minimize heat loss from the heat source to the environment 

during operation. The insulation package is made of several different types of insulation including 

microporous insulation, ceramic paper, and Kaowool (Morgan Thermal Ceramics) blanket insulation. 

Figure 3 shows the different areas where each type of insulation was used and how the heat source locates 

against the hot end of the Stirling convertor heater head (labeled “ASC–E2 Head”). The heat source is 

spring loaded against the convertor heater head using a Cotronics Rescor ceramic load stud, which has a 

temperature limit of 1150 °C. Firerod heat source temperatures can exceed 1,000 °C when operating with 

an 850 °C acceptor temperature due to the roughly 90 W of additional heat energy lost to the environment 

compared to a completely enclosed, yet shorter life, version of the heat source. The Microsil microporous 

insulation has a temperature limit of 1,000 °C, so the Kaowool blanket and ceramic paper insulations, 

which have a temperature limit of above 1100 °C, were used to separate the Microsil from heat source. 

Thermocouples were located inside the test setup to monitor internal temperatures and gather data for 

thermal modeling tasks. 

2.2 Insulation Loss Characterization 

Performance tests are used to test convertors for acceptance and characterization. Before performance 

testing can begin, insulation loss characterization is performed to determine environmental losses for 

different convertor temperature profiles. The heat source and convertor are subjected to various 

temperature profiles and convertor parasitic losses, or cold end losses (parasitic heat losses transferred 

from the hot end to the cold end of the convertor through conduction, convection, and radiation) are 

calculated via one-dimensional models. The cold end losses are subtracted from the measured gross heat 

input to the electric heaters to calculate the environmental loss. Calculation of net heat input has 

historically been achieved by curve fitting the environmental loss to a reference temperature. Typically, 

the heat source is chosen as a reference temperature due to its strong influence on thermal gradients in the 

test setup. However, these curve fits are limited because they rely on the assumption that the cold end 

losses and temperature profiles are accurately represented for an operating convertor during a 

nonoperating test. Single parameter and multiparameter correlations have been shown to contain a bias 

error of around 13 W, despite using a weighted average reference temperature over a heat source 
NASA/TM—2012-217292 5 

reference temperature (Ref. 3). Also, it is assumed that the closed form equations used to calculate 

convertor parasitic losses accounted for all of the static and dynamic losses present in an operating 

convertor. Actually, thermodynamic second law available energy losses in an operating convertor are of 

the following general types: (1) mass flow across a pressure difference (viscous dissipation), (2) heat 

transfer across a temperature difference, and (3) mixing of fluids at different initial temperatures (Refs. 4 

and 5). Viscous dissipation losses in the regenerator and heat exchangers, displacer shuttle losses, 

regenerator thermal dispersion, and losses from mixing of fluids at different initial temperatures have not 

typically been included in the calculation of cold end losses while heat transfer across a temperature 

difference has typically been accounted for. A greater limitation of using curve fits is the dependence on 

the assumption that nonoperating test data accurately represents the temperature profile of an operating 

convertor. The convertor and insulation package temperature profiles, used to calculate heat conduction 

through the convertor to the cold side adapter flange (CSAF), change when the convertor is operating so 

there is an unquantifiable error associated with curve fitting environmental losses to a reference 

temperature, despite which temperature is chosen as a reference. 

3.0 Predictions of Convertor Net Heat Input 

Net heat input cannot be directly measured on an operating convertor. The validation effort focused 

on being able to actually predict net heat input on a devise with a temperature profile very similar to that 

of an operating convertor. Figure 4 outlines the measured and predicted values of net heat input available 

from test and numerical methods. The Thermal Standard and Stirling convertors share all available 

methods except measured net heat input on an operating convertor. One key assumption made by the 

validation effort is that validating numerical models of the Thermal Standard provides confidence in the 

results from numerical models used to represent an operating convertor. 

Paramount to the convertor modeling effort was the assumption that the predicted temperature profile 

governed the resulting heat transfer through modeled components. With that in mind, one major goal was 

to match predicted temperatures to measured temperatures by adjusting the various resistance paths 

inherent to the materials and component interfaces present in the model. Resistance paths were tuned by 

adjusting the interface resistance between two mating solid components. The interface resistance was 

modified only between the heat source/heat collector plate interface for convertor models and between the 

Insulation Loss Test

 Measured NH Input

 Predicted NH Input

Operating Point Test

 Measured NH Input (N/A)

 Predicted NH Input

Insulation Loss Test

 Measured NH Input

 Predicted NH Input

Operating Point Test

 Measured NH Input

 Predicted NH Input

Thermal

Validation

Figure 4.—Net heat input values available from testing and analysis.

Measurement of convertor net heat input is not possible. 

Stirling

Convertor
NASA/TM—2012-217292 6 

heat source/heat collector plate interface and internal acceptor/conduction rod interface for the Thermal 

Standard model. Resistance paths were also tuned by offsetting thermal conductivity for a given 

insulation material. Figure 3 shows several types of insulation used in the test setup, including Microsil 

microporous insulation, Kaowool blanket, magnesium oxide (heaters), and ceramic paper. Each of the 

insulation materials had a corresponding thermophysical property data available from literature. In the 

case of the bulk microporous insulation, test measurements were made to acquire a more accurate value 

of the temperature-dependent thermal conductivity. This material test value had an inherent 7 percent 

uncertainty according to Thermophysical Properties Research Laboratory Inc. (TPRL). Furthermore, the 

geometric size of an insulation component decreases slightly, or shrinks, and effectively changes the 

optical transparency of the insulation to radiation heat transfer. As new insulation pieces are exposed to 

high-temperature parts during tests, the thermal conductivity increases until the package stops shrinking, 

which is expected to happen at around 4 percent volume decrease for the type of insulation used in ASC 

ground tests. 

Leading up to the validation, numerous tasks were performed, which provided more accurate inputs 

and boundary conditions for numerical models. Thermophysical property measurements were made of the 

microporous bulk insulation used to insulate the hot components in the Thermal Standard test setup and to 

provide more accurate inputs for the materials. Additional temperatures were acquired throughout the 

ASC test setup (external surfaces and internal probes) to provide numerical models with temperature 

profiles. These test temperatures were used as boundary conditions and as targets for which the numerical 

results could be compared. Nonlinear temperature profiles were also acquired via infrared images of the 

heater assembly components surfaces exposed to air and, therefore, affected by natural and forced 

convection. These inputs were used in multidimensional numerical models designed to predict net heat 

input of an operating convertor. 

In an effort to improve input into the numerical model, insulation material testing was performed. 

Figure 5 shows results provided by TPRL and NASA Langley Research Center (LaRC). The vendor data 

is also shown (Zircar M-sil 2). The tests were performed on various microporous insulations used in ASC 

tests. The thermophysical properties measured using the laser flash method (ASTM E1461), included 

density, specific heat, thermal diffusivity, and thermal conductivity (Ref. 6). Thermal conductivity 

was measured for the microporous insulation materials used in GRC tests (Microsil Type 2, M-sil 2) and 

in Sunpower tests (Microsil Type 1, M-sil 1). There are three curves that represent the M-sil 1 material 

used in convertor tests performed at Sunpower, Inc. Similarly, there are four curves that represent the 

M-sil 2 insulation material used in convertor tests performed at NASA GRC. The M-sil 2 labels 

correspond to unaged and aged conditions: aged data from TPRL, unaged data from TPRL, and unaged 

data from LaRC.

Figure 5.—Thermal conductivity measurements. 

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.10

0.11

0 250 500 750 1000

Thermal Conductivity, W/m‐K

Temperature, °C

Thermal Conductivity for Various  

Microporous Insulations TPRL M‐sil 1

TPRL M‐sil 2

(Aged)

TPRL M‐sil 2

(Un‐aged)

LaRC M‐sil 2

(Un‐aged)

Zircar M‐sil 2
NASA/TM—2012-217292 7 

Prior to having received the aged insulation material test data, the Microsil thermal conductivity was 

increased in the numerical model by an arbitrary amount required to get resulting temperatures to match 

measured temperatures. It was later revealed, after having received the aged data, that the thermal 

conductivity used and the thermal conductivity from the aged insulation were within 5 percent, suggesting 

that the aged data well represents the condition of the insulation used in the test. The lesson learned was 

that the insulation should be baked out prior to use in testing in order to accelerate degradation. This 

aging process was performed at 800 °C for 12 hr, which was expected to shrink the insulation from 2 to 

4 percent. This technique bypasses the slow aging that would normally happen due to exposure of the heat 

source after a test has started. 

4.0 Validation Effort 

In addition to high-fidelity computational fluid dynamic (CFD) models, a validation effort was 

performed to provide evidence that the CFD models were grounded in reality and, in turn, quantify the 

accuracy of ASC net heat input predictions. Validation test hardware provided direct comparison between 

measured data and numerical results to validate the multidimensional numerical models used to predict 

convertor net heat input. This effort consisted of two separate test assemblies, the Mock Heater Head and 

Thermal Standard. Test conditions were used that attempted to simulate the temperature profile of an 

operating convertor using static heat conduction through solid components. This enabled direct 

calculation of heat transferred through the test setup and provided a comparison to numerical results. The 

test data was also used to constrain the numerical models. For example, the measured heat addition to the 

cartridge heater assembly was used as the gross heat input to the model. The measured temperatures from 

exterior surfaces of the convertor, insulation, and support hardware were also used as model boundary 

conditions. This included infrared images used to represent the temperature profiles for the heater 

assembly surfaces exposed to air. Each convertor and test point was treated as an individual case. The 

data was collected from convertor tests and used in 1) the insulation loss test case, which was used to tune 

heat transfer resistance values for various materials and interfaces and 2) the operating point test case, 

which was used to acquire the proper net heat input. For both modeled cases, the success criteria was to 

achieve a close match of predicted and measured temperatures. Thermocouples were placed at key 

locations throughout the test setup, as shown in Figure 6, to enable tuning of various interface resistances 

and bulk thermal conductivities. These temperature measurements were matched at least within the 

measurement error, but of often much better, of the temperature readings ranging from 300 to 1,000 °C. 

Figure 6.—Thermal standard thermocouple diagram. 
NASA/TM—2012-217292 8 

4.1 Mock Heater Head 

Prior to the design of the Thermal Standard, a test setup was designed using an existing version of the 

heater head used in past testing and some new components including a rod fabricated from a special type 

of high-strength copper and a CSAF fabricated from oxygen-free high-thermal conductivity copper. This 

hardware enabled conduction through a cylinder wall normally present in convertor testing and a rod, 

which was used to simulate the additional heat absorbed by the Stirling cycle (called the conduction rod). 

Testing was carried out over a number of hot end and CSAF temperatures (Ref. 7). The Mock Heater 

Head hardware served as a pathfinder for the Thermal Standard test, in that it enabled the selection of 

materials and coatings used for the conduction rod, identified desired design features for the heat 

collector, internal acceptor, and CSAF. It also identified the desired thermocouple locations for 

calculating heat conducted to the cold end, heat rejection system mounting method for ease of 

disassembly and shipment, and preferred test methods used for characterization, such as how to control 

the heat input. 

For the conduction rod, GRCop-84, a high-strength copper design at GRC was used as it has superior 

strength at expected temperatures compared to traditional copper (Refs. 8 and 9). The material has 

exceptional corrosion resistance up to 650 °C. To protect from planned exposure to higher temperatures, 

the rod was nickel plated. Small-diameter probe thermocouples were then tack welded onto the nickel 

plated surface. The Mock Heater Head test exposed the nickel plated GRCop-84 to an estimated 500 °C 

for over 1,500 hr while the Thermal Standard test exposed it’s rod to an estimated 700 °C for just under 

1,000 hr. The conduction rods were inspected after each test and were found to be in relatively good 

condition, meaning there was an insignificant oxide layer present. Additionally, diffusion bonding 

between the rod and heater head was prevented in both tests by installing a thin layer (0.010 in.) of 

Cotronics ceramic paper between the heater block and head. 

The Mock Heater Head test data was also used as boundary conditions in a finite element analysis 

(FEA) simulation to predict the contribution of environmental heat loss from the exposed portion of the 

heater assembly. Figure 7 shows the truncated model, which consisted of the hot surfaces of the heat 

source assembly, the electrical connections with ceramic beads, and the load plate that compressed the 

heater load stud during assembly. This model was used to provide an estimate of how much more heat is 

lost while simulating an operating convertor compared to insulation loss characterization. Originally 

believed to be large, the additional heat lost to the environment from the hot surfaces of the heater 

assembly was less than 3 W for an increase in gross heat input of 194 W, which is within 10 percent of 

the expected increase for a convertor. This same exercise was performed domains of the Thermal 

Standard and ASC–E2 #7 and the results were similar. 

 

Figure 7.—Firerod heat source assembly thermal analysis. Infrared 

image (left) and truncated domain used to represent surfaces 

affected by convection heat transfer (right). 

 
NASA/TM—2012-217292 9 

4.2 Net Heat Input Predictions for Thermal Standard 

The Thermal Standard, shown in Figure 8, is the test 

hardware designed to provide validation data for the 

modeling approach employed to predict net heat input for 

convertors. This test hardware allowed predicted values of 

net heat input to be compared directly to measured values. 

A computational model of the Thermal Standard hardware 

was used to perform calculations of net heat input (Ref. 10). 

These calculations used boundary conditions obtained 

during the testing of the Thermal Standard hardware in the 

GRC Stirling Research Laboratory. Test conditions 

included Insulation Loss Characterization, which were used 

to simulate a non-operating convertor, and simulated 

operation of a convertor. The Thermal Standard is a device 

that was constructed to simulate the thermal gradients that 

would exist in the ASC–E2. The total heat addition or net 

heat input into the Stirling convertor is difficult to measure 

experimentally due to the inability to accurately measure 

the environmental losses from the hot insulation package 

during operation. 

During lab experiments, Fourier’s Law was used to 

calculate the heat conducted through the copper rod based 

on test measurements. The corresponding rod heat transfer 

is 208.7 W where k = 316 W/m/K, D = 0.014 m, A = 

1.539E–04 m2

, ∆T = 309 °C, and ∆x = 0.072 m. The same calculation was performed for the stainless 

steel heater head cylinder wall, which resulted in 35.7 W. Operating conditions from the Thermal 

Standard resulted in 208.7 W of heat conducted through the rod, used to simulate the Stirling cycle, and 

35.7 W of heat conducted through the heater head cylinder, resulting in a net heat input value of 244.4 W. 

Similarly, the modeling approach resulted in 205.5 W of heat conducted through the rod and 34.8 W of 

heat conducted through the heater head cylinder wall. This resulted in a net heat input value of 240.3 W. 

Figure 8 also shows the resulting temperatures for the case discussed. The predicted value of net heat 

input was 1.7 percent less than that measured during testing. Enhancements were made to the model over 

time, which included adding additional heat transfer modes and improved boundary conditions. This 

resulted in a model with higher fidelity and robust boundary conditions. 

4.3 Net Heat Input Predictions for Stirling Convertors 

Convertor net heat input predictions were produced for several ASC-E2s during December 2010. After 

the validation effort had concluded in March 2011, several lessons learned during the validation exercise 

were applied to the previous convertor predictions. The lessons learned included the need for (a) 

enhanced heat transfer due to the inclusion of radiation heat transfer near the interior surfaces of the 

heater head, (b) separating the Kaowool blanket insulation surrounding the heat source and heater head 

into three sections to allow better control over the resulting temperatures at measured temperature 

locations, and (c) changing the magnesium oxide thermal conductivity present in the HT Firerod cartridge 

heaters from a constant input to a temperature dependent input. Net heat input and convertor efficiency 

was reported during December 2010 for the Beginning of Mission Low Reject operating point performed 

on ASC–E2 #7. The resulting net heat input reported was 213.9 W. The corresponding efficiency, based 

on a terminal power output of 84.9 W, was 39.7 percent. That case was updated using lessons learned 

during the validation exercise. The updated net heat input and corresponding efficiency were 216.3 W and 

39.3 percent. Figure 9 shows the resulting temperature profile for the updated case. 

Figure 8.—Thermal standard hardware (top) 

and predicted temperatures (bottom).
NASA/TM—2012-217292 10 

Figure 9.—Convertor computational domain 

and predicted temperatures. 

5.0 Conclusion 

Convertor and generator testing is carried out in tests designed to characterize convertor performance 

when subjected to environments intended to simulate launch and space conditions. These conditions 

require achieving a particular operating frequency, hot end and cold end temperatures, and power output 

for a given net heat input. The value of net heat input must be known to validate convertor efficiency. In 

an effort to improve the accuracy of the efficiency calculation, numerous tasks have been performed, 

which provided a more accurate value for net heat input into the Advanced Stirling Convertors (ASCs). 

This test and modeling effort included: (a) making thermophysical property measurements of test setup 

materials to provide inputs to the numerical models, (b) acquiring additional test data that was collected 

during convertor tests to provide numerical models with temperature profiles of the test setup via 

thermocouple and infrared measurements, (c) using multidimensional numerical models (CFD codes) to 

predict net heat input of an operating convertor, and (d) using validation test hardware to provide direct 

comparison of numerical results and validate the multidimensional numerical models used to predict net 

heat input. This effort produced high fidelity ASC net heat input predictions, which were successfully 

validated using specially designed test hardware enabling measurement of heat transferred through a 

simulated Stirling cycle. 

References 

1. Schreiber, J.G., Thieme, L.G., Wong, W.A., “Supporting Technology at GRC to Mitigate Risk as 

Stirling Power Conversion Transitions to Flight,” Proceedings of the Sixth International Energy 

Conversion Engineering Conference (IECEC 2008), American Institute of Aeronautics and 

Astronautics, 2008. 

2. Oriti, S., Wilson, S.D., “Advanced Stirling Convertor (ASC–E2) Performance Testing at NASA 

Glenn Research Center,” Proceedings of the First Nuclear and Emerging Technologies for Space 

(NETS 2011), Feb. 2011. 

3. Briggs, M.H., Schifer, N.A., “Evaluation of Advanced Stirling Convertor Net Heat Input 

Correlation Methods using a Thermal Standard,” Proceedings of the Ninth International Energy 

Conversion Engineering Conference (IECEC 2011), American Institute of Aeronautics and 

Astronautics, 2011. 

4. Tew, R.C., Overview of Heat Transfer and Fluid Flow Problem Areas Encountered in Stirling 

Engine Modeling, NASA TM–100131, Feb. 1988. 

5. Wilson, S.D., Dyson, R.W., Tew, R.C., Ibrahim, M.B., “Multi-D CFD Modeling of a Free-Piston 

Stirling Convertor at NASA GRC,” Proceedings of the Second International Energy Conversion 

Engineering Conference (IECEC 2004), American Institute of Aeronautics and Astronautics, 2004. 
NASA/TM—2012-217292 11 

6. Daryabeigi, K., Cunnington, G.R., Miller, S.D., Knutson, J.R., “Combined Heat Transfer in HighPorosity High-Temperature Fibrous Insulations: Theory and Experimental,” AIAA 2010–4660. 

Validation. 

7. Schifer, N.A., Briggs, M.H., “Environmental Loss Characterization of an ASC–E2 Insulation 

Package using a Mock Heater,” Proceedings of the Ninth International Energy Conversion 

Engineering Conference (IECEC 2011), American Institute of Aeronautics and Astronautics, 2011. 

8. Ellis, David L., and Keller, Dennis J., “Thermophysical Properties of GRCop-84,” NASA/CR—

2000-210055, 2000. 

9. Ellis, David L., “GRCop-84: A High-Temperature Copper Alloy for High-Heat-Flux Applications,” 

NASA/TM—2005-213566, 2005. 

10. Reid, T.V., Wilson, S.D, Schifer, N.A., Briggs, M.H., “A Computational Methodology for 

Simulating Thermal Loss Testing of the Advanced Stirling Convertor,” Proceedings of the Ninth 

International Energy Conversion Engineering Conference (IECEC 2011), American Institute of 

Aeronautics and Astronautics, 2011. 
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Overview of Heat Addition and Efficiency Predictions for an Advanced Stirling Convertor 

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Wilson, Scott, D.; Reid, Terry, V.; Schifer, Nicholas, A.; Briggs, Maxwell, H. 

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WBS 138494.05.02.04.01 

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

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14. ABSTRACT

The U.S. Department of Energy (DOE) and Lockheed Martin Space Systems Company (LMSSC) have been developing the Advanced Stirling Radioisotope Generator 

(ASRG) for use as a power system for space science missions. This generator would use two high-efficiency Advanced Stirling Convertors (ASCs), developed by Sunpower 

Inc. and NASA Glenn Research Center (GRC). The ASCs convert thermal energy from a radioisotope heat source into electricity. As part of ground testing of these ASCs, 

different operating conditions are used to simulate expected mission conditions. These conditions require achieving a particular operating frequency, hot end and cold end 

temperatures, and specified electrical power output for a given net heat input. Microporous bulk insulation is used in the ground support test hardware to minimize the loss of 

thermal energy from the electric heat source to the environment. The insulation package is characterized before operation to predict how much heat will be absorbed by the 

convertor and how much will be lost to the environment during operation. In an effort to validate these predictions, numerous tasks have been performed, which provided a 

more accurate value for net heat input into the ASCs. This test and modeling effort included: (a) making thermophysical property measurements of test setup materials to 

provide inputs to the numerical models, (b) acquiring additional test data that was collected during convertor tests to provide numerical models with temperature profiles of the 

test setup via thermocouple and infrared measurements, (c) using multidimensional numerical models (computational fluid dynamics code) to predict net heat input of an 

operating convertor, and (d) using validation test hardware to provide direct comparison of numerical results and validate the multidimensional numerical models used to 

predict convertor net heat input. This effort produced high fidelity ASC net heat input predictions, which were successfully validated using specially designed test hardware 

enabling measurement of heat transferred through a simulated Stirling cycle. The overall effort and results are discussed.

15. SUBJECT TERMS

Stirling convertor; Performance verification; Computational fluid dynamics (CFD); Heat addition predictions; Radioisotope power

system 

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