Maxwell H. Briggs and Nicholas A. Schifer

Glenn Research Center, Cleveland, Ohio

Evaluation of Advanced Stirling Convertor

Net Heat Input Correlation Methods Using

a Thermal Standard

NASA/TM—2012-217293

March 2012

AIAA–2011–5578
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Maxwell H. Briggs and Nicholas A. Schifer

Glenn Research Center, Cleveland, Ohio

Evaluation of Advanced Stirling Convertor

Net Heat Input Correlation Methods Using

a Thermal Standard

NASA/TM—2012-217293

March 2012

AIAA–2011–5578

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

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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. 

This report contains preliminary fi ndings, 

subject to revision as analysis proceeds.
NASA/TM—2012-217293 1 

Evaluation of Advanced Stirling Convertor Net Heat Input 

Correlation Methods Using a Thermal Standard 

Maxwell H. Briggs and Nicholas A. Schifer 

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. In an effort to improve net heat input predictions, numerous tasks 

have been performed which provided a more accurate value for net heat input into the ASCs, including 

testing validation hardware, known as the Thermal Standard, to provide a direct comparison to numerical 

and empirical models used to predict convertor net heat input. This validation hardware provided a 

comparison for scrutinizing and improving empirical correlations and numerical models of ASC–E2 net 

heat input. This hardware simulated the characteristics of an ASC–E2 convertor in both an operating and 

non-operating mode. This paper describes the Thermal Standard testing and the conclusions of the 

validation effort applied to the empirical correlation methods used by the Radioisotope Power System 

(RPS) team at NASA Glenn. 

Nomenclature 

ASC advanced Stirling convertor 

CSAF cold side adapter flange 

EL environmental losses, W 

FEA finite element analysis 

HET hot-end temperature, K 

HST heat source temperature, K 

GHI gross heat input 

NHI net heat input, W 

R thermal resistance between the heat source and hot end, K / W 

1.0 Introduction 

Convertor efficiency is a crucial performance parameter that must be accurately measured in order to 

guarantee that the Advanced Stirling Convertor (ASC) will meet its performance specifications. Central to 

the determination of convertor efficiency is an accurate estimate of net heat input (NHI) to the convertor. 

The NHI of an operating convertor cannot be measured directly, because the amount of heat being leaked 

to the environment (environmental losses (EL)) cannot be distinguished from the heat input to the 

thermodynamic cycle. However, stalled (non-operating) convertors have no contribution from the 

thermodynamic cycle, making it possible to estimate what portion of the gross heat input (GHI) that is 
NASA/TM—2012-217293 2 

attributed to EL. Therefore, correlations for EL can be made based on non-operating data. These 

correlations can then be applied to operating convertors as long as the relationship between EL and the 

correlation parameters does not change substantially once the piston is in motion. Several different 

parameters including cold-end temperature and GHI were initially considered as potential inputs to the 

environmental loss correlation, but hot-end temperature (HET) and heat source temperature (HST) were 

found to be the only substantial contributors and will be the only ones discussed in this paper. The 

correlation methodology is described mathematically below: 

 EL non-operating = f (HET and/or HST) non-operating (1) 

 EL operating = f (HET and/or HST) non-operating + Difference (2)

 NHI = GHI – EL operating (3) 

Where EL is environmental losses, HET is the hot-end temperature, HST is heat source temperature, 

Difference is the inaccuracy resulting from applying the non-operating correlation to operating data, NHI 

is net heat input, and GHI is the gross heat input measured directly as the electrical power to the heat 

source. For this method to be used effectively, EL of the non-operating convertor must be accurately 

characterized using the chosen correlation parameters (typically HET, HST, or some linear combination 

of the two) and the difference term in Equation (2) must be within an acceptable tolerance. The Thermal 

Standard can be used to test both of these assumptions. 

A commonly used method of developing correlations for the EL of a non-operating convertor was 

referred to as the alumina disk testing. This test involved placing a convertor into the insulation package, 

with a thin alumina disk between the heat source and the hot end, and measuring the GHI required to 

achieve various HETs and HSTs. During alumina disk testing, the GHI to the heaters minus the amount of 

heat conducted through the convertor to the cold-side adapter flange (CSAF) is calculated as the EL. The 

heat conducted through the convertor can be calculated using relatively simple conduction equations, and 

the electric input to the heaters can be directly measured, so the heat lost through the insulation at a given 

operating condition can be calculated. The limitation of this method is that when the convertor is not 

operating and it is not pulling heat out of the heater, there is a very small temperature difference across the 

alumina disk from the heat source to the hot end. Operating convertors see a much larger temperature 

difference across these components, with HSTs of around 1000 °C for a nominal HET of 842 °C. Because 

the insulation package sees a much different temperature gradient across the convertor during operation than 

it does during the alumina disk testing, it is possible that Equation (2) will not be satisfied. Specifically one 

would expect empirical correlations based on HET data of a non-operating convertor using an alumina disk 

to underpredict EL, because the correlation assumes that both the HST and HET are close to the hot-end 

operating temperature of 842 °C. Likewise, empirical correlations based on HSTs are expected to 

overpredict EL, because these correlations assume that the heat source and HET are both close to the HST 

of 1000 °C. In addition to these biases, temperature limitations on the ASC–E2 heater head prevent data 

from being taken on a non-operating convertor with the heat source near its expected operating temperature 

of 1000 °C. Therefore, empirical correlations based on the HST must be extrapolated to predict the EL of 

operating convertors, which is expected to result in some additional error. 

Another empirical modeling method, referred to as thermal barrier testing, simulates the heat-sourceto-hot-end temperature difference of an operating convertor while testing a non-operating convertor. 

During thermal barrier testing, ceramic paper insulation is inserted between the heat source and the 

convertor hot end. Introducing this insulation creates a substantial temperature difference between the 

heat source and convertor hot end, similar to that seen in an operating convertor, even though the 

convertor is idle. This makes it more likely that the difference term in Equation (2) is sufficiently small, 

and eliminates the need to extrapolate the HST-based correlations as is required in alumina disk testing. 

The primary limitation of thermal barrier testing is that in order to run an ASC–E2 convertor after a 

thermal barrier test, the insulation package must be partially disassembled to remove the barrier prior to 

operating the convertor. This could result in changes in the setup of the insulation package that could 

change the difference term in Equation (2). 
NASA/TM—2012-217293 3 

To resolve the limitations of thermal barrier testing, a new method was developed in which heat lost 

through the insulation was calculated numerically using finite element analysis (FEA). This modeling 

methodology begins with a generic model of the GRC insulation package. This generic insulation model 

is then tuned to the specific insulation package using alumina disk test data. This tuned insulation model 

is then used to predict the heat lost through the insulation for an operating convertor, based on 

temperature profiles measured during convertor operation. This method allows the EL and NHI to be 

calculated without disassembling the insulation package and does not require empirical EL correlations to 

be generated and/or extrapolated. The disadvantage of using an FEA model for calculation of EL and NHI 

is the time that it takes to set up, calibrate, and run the model, which can delay the results. Real-time 

estimates of NHI will have to be made using empirical correlations described above in order for convertor 

operators to set operating points, and these estimated values will have to be refined at a later time using 

the FEA model. 

By simulating both non-operating and operating convertors and allowing for NHI to be calculated in 

both cases, the Thermal Standard allows the predictions of each of the correlation methods described 

above to be compared to test data, thus quantifying any inaccuracies. The application of the Thermal 

Standard to FEA model validation can be found in Reference 1. 

1.1 Thermal Standard Design 

The design of the Thermal Standard is based on the mock heater head concept and the lessons learned 

from a series of mock heater head tests (Ref. 2). These lessons learned resulted in several improvements 

in the design of the Thermal Standard. These improvements include precise replication of ASC–E2 heater 

head external geometry, closer replication of the ASC–E2 heat transfer path, improved instrumentation, 

the ability to compensate for uncertain values of contact resistance, and the use of the high-temperature, 

high-conductivity material GRCCop-84 (Refs. 3 and 4) to remove heat from the Stirling hot end. 

Conceptually, the Thermal Standard is a replica of an ASC–E2 heater head assembly brazed to a 

modified CSAF. A schematic of the Thermal Standard can be seen in Figure 1; because of export control 

restrictions, a corresponding schematic of the ASC–E2 heater head is not included. To reduce cost and 

schedule, the Mar-M portions of the heater head were replaced with 316L stainless steel. 316L stainless 

steel was chosen because it has a thermal conductivity that is close to Mar-M, and because it resists 

oxidation at the required temperatures. The variable thickness wall of the ASC–E2 heater head was 

replaced with a constant thickness wall for ease of fabrication and to allow for simple one-dimensional 

hand calculations of heat flow through the wall to be made. The internal acceptor on the inside of the 

heater head was replaced with a piece of solid nickel with a conical hole. This conical hole provides a 

high surface area mate for a cylindrical rod with a conical tip, which is put in place to conduct heat, 

simulating the thermodynamic heat draw of an operating convertor. 

The cylindrical rod that interfaces with the Thermal Standard is designed to conduct the same amount 

of heat that passes through the acceptor of an operating ASC–E2 convertor. Figure 2 shows a full 

assembly of the Thermal Standard with rod and heat exchanger in place. During testing, the actual heat 

throughput of the rod can be calculated using simple one-dimensional conduction equations based on a 

measured temperature gradient. It should be noted that the most accurate measurement available for the 

conductivity of the rod based on a laser flash method performed by the Thermophysical Properties 

Research Laboratory was +4 percent. Consequently, each calculation of heat through the rod based on 

temperature measurements also has an uncertainty of +4 percent.

The Thermal Standard closely replicates the geometry, heat transfer path, and temperature profile seen 

in an actual convertor, it is placed inside an ASC–E2 insulation package, and it allows for simulation of both 

a non-operating and an operating convertor. Therefore, NHI models can be compared directly to NHI 

calculations made from measured temperature gradients on parts with a simple and well-defined geometry. 
NASA/TM—2012-217293 4 

Figure 1.—Cross-section of Thermal Standard heater head. 

Figure 2.—Cross-section of Thermal Standard in the simulated operation configuration. 

 

Stainless Steel constant 

Thickness Wall 

Nickel acceptor 

with conical mating 

surface 

Heat collector body 
NASA/TM—2012-217293 5 

2.0 Methodology 

The Thermal Standard went through the same test sequence as an actual ASC–E2 convertor. The 

ASC-E2 test sequence begins with alumina disk testing, in which heat is applied to a non-operating 

convertor through a range of HETs. Heat flow within the convertor is then calculated by measuring 

convertor temperatures and using conduction and radiation equations to determine cold-end losses 

through the heater head walls, regenerator, helium gas, and displacer. These losses typically total 

approximately 17 W. Subtracting these cold-end losses from the measured GHI gives the EL of a nonoperating convertor at a given HST and HET. These results are then used to tune FEA models and build 

empirical correlations for individual ASC-E2 convertors. 

Alumina disk testing was simulated on the Thermal Standard by measuring temperatures and heat 

flows through a range of HETs without a rod in place, as shown in Figure 3. With no rod to conduct heat, 

the only available heat transfer paths are through the heater head wall and through the insulation package 

to the environment. The temperature gradient on the heater head wall was measured, and Fourier’s law 

was used to calculate the conduction through the walls, which was typically around 20 W. This allows the 

EL to be calculated as the difference between the GHI and the heat conducted through the wall using 

methods very similar to those used during ASC-E2 alumina disk testing. 

Similarly, thermal barrier testing is accomplished on ASC-E2 convertors by inserting insulation 

between the heat source and the Thermal Standard hot end and operating through a range of HSTs 

without a rod in place. EL can then be calculated in the same way as alumina disk testing. To simulate 

thermal barrier testing on the Thermal Standard, the alumina disk was replaced by the same thermal 

insulation used during ASC-E2 thermal barrier testing. The Thermal Standard was then run through a 

range of HSTs with no rod in place. 

Figure 3.—Cross-section of the Thermal Standard in the simulated non-operating configuration. 

Fire rods 

ASC–E2 

i li

Thermal Standard 

without rod 

ASC–E2 

insulation housing 

Heat source block 
NASA/TM—2012-217293 6 

Figure 4.—Thermal Standard in simulated operation configuration. 

TABLE 1.—COMPARISON OF ASC-E2 AND THERMAL STANDARD TEST SEQUENCES 

ASC-E2 convertor Thermal standard 

Test title Interface 

material 

Piston 

status 

EL calculation 

method 

Test title Interface 

material 

Rod/No 

rod 

EL calculation method 

Alumina disk Alumina 

disk 

Stalled Conduction 

calculation 

Simulated 

alumina disk 

Alumina 

disk 

No rod Conduction 

calculation 

Thermal 

barrier 

Ceramic 

paper 

Stalled Conduction 

calculation 

Simulated 

thermal barrier 

Ceramic 

paper 

No rod Conduction 

calculation 

Nominal 

operation 

Alumina 

disk 

Moving Correlation based 

on Alumina disk / 

thermal barrier 

testing 

Simulated 

nominal 

operation 

Alumina 

disk 

Rod-in Correlation based on 

alumina disk/thermal 

barrier testing and 

conduction calculation 

Following alumina disk testing and/or thermal barrier testing at GRC, ASC–E2 convertors are 

typically run at some nominal operating condition and empirical correlations are used to predict the NHI 

of the convertor in real time. To simulate an operating convertor, the Thermal Standard was run with a 

rod in place, as shown in Figure 4. The rod was insulated from the heater head wall to prevent radial heat 

transfer that would invalidate the use of one-dimensional heat flow calculations. In this configuration, the 

temperature profile on the wall and the rod were measured, and Fourier’s law is once again used to 

determine both the heat conducted through the wall and the heat conducted through the rod, and the sum 

of these two is analogous to the NHI into an ASC–E2 convertor. The difference between the GHI, and the 

sum of the heat through the rod, and the heat through the heater head wall is then calculated was the EL. 

Empirical models were validated by using the correlations based on simulated non-operating data 

(with no rod in place) to predict the EL during simulated operation (with rod in place). The NHI was then 

calculated as the difference between the measured GHI and the predicted EL. These values are then 

compared to the sum of the values for heat input through the rod and the heater head as calculated from 

measured temperature gradients on the Thermal Standard hardware to validate models and to quantify 

bias and error introduced by the correlations. Table 1 summarizes the ASC-E2 thermal loss test sequence 

and the Thermal Standard simulation method for each test. 
NASA/TM—2012-217293 7 

3.0 Results 

3.1 Replication of ASC–E2 Behavior 

It is not necessary to have an exact replica of ASC–E2 to validate a modeling method, but the 

validation is certainly more applicable the closer the Thermal Standard is to an ASC–E2 heater head. 

Although the Thermal Standard design is very similar to the ASC–E2 heater head design, there are 

differences in materials and internal geometry. It is therefore useful to compare data from the Thermal 

Standard data taken on ASC–E2 convertors. Comparisons of Thermal Standard simulated operating data 

and actual ASC–E2 operating data are difficult to make because NHI cannot be directly measured on 

operating convertors, however comparisons of EL can be made to non-operating convertors using alumina 

disk and thermal barrier data. 

Figures 5 through 8 show comparisons Thermal Standard data with no rod in place compared to 

thermal barrier and alumina disk data from various ASC–E2 convertors. Thermal barrier data was 

collected on five convertors, while alumina disk data was collected on three convertors. As shown in 

Figure 6, the relationship between HST and EL appears to be well within the range of what is expected of 

a convertor during thermal barrier testing, comparing very well with what was observed on ASC–E2 #3 

and #4. Likewise, Figure 7 shows that the relationship between HST and HET during thermal barrier 

testing. Thermal Standard again appears to be well within the range of what is seen during thermal barrier 

testing on ASC–E2 convertors. 

Figure 7 shows a comparison between alumina disk data taken on the Thermal Standard and alumina 

disk data taken on various convertors. The Thermal Standard EL are lower than those seen on ASC–E2 #5 

and #6 by approximately 7 W. This is not surprising because the EL calculated for the Thermal Standard 

were also approximately 7 W lower than those of ASC–E2 #5 and #6 during thermal barrier testing, as 

shown in Figure 6. Figure 8 shows the relationship between HET and HST for the Thermal Standard 

compared to various convertors. The difference between the HST and HET on the Thermal Standard is 

larger than what is seen on the ASC–E2 convertors by approximately 9°. This is likely caused by more 

heat flowing through the thicker, constant wall thickness of the Thermal Standard heater head compared 

to the thinner variable thickness wall of the ASC–E2 convertors. 

Figure 5.—Environmental losses of Thermal Standard compared to ASC–E2 convertors during thermal 

barrier testing. 

0.0

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180.0

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Environmental losses (W)

Heat Source Temperature (°C)

E2 #1 (GRC) ‐ Thermal Barrier

E2 #3 (GRC) ‐ Thermal Barrier

E2 #4 (GRC) ‐ Thermal Barrier

E2 #5 (GRC) ‐ Thermal Barrier

E2 #6 (GRC) ‐ Thermal Barrier

Thermal Standard ‐ Thermal Barrier
NASA/TM—2012-217293 8 

Figure 6.—Relationship between hot-end and heat source temperature on the Thermal Standard 

and ASC–E2 convertors during thermal barrier testing. 

Figure 7.—Environmental losses of Thermal Standard compared to ASC–E2 convertors during 

alumina disk testing. 

Figure 8.—Relationship between hot-end and heat source temperature on the Thermal Standard and 

ASC–E2 convertors during alumina disk testing. 

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Heat Source Temperature (°C)

E2 #1 (GRC) ‐ Thermal Barrier

E2 #3 (GRC) ‐ Thermal Barrier

E2 #4 (GRC) ‐ Thermal Barrier

E2 #5 (GRC) ‐ Thermal Barrier

E2 #6 (GRC) ‐ Thermal Barrier

Thermal Standard ‐ Thermal

Barrier

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Environmental losses (W)

Heat Source Temperature (°C)

E2 #2 (GRC) ‐ Alumina Disk

E2 #5 (GRC) ‐ Alumina Disk

E2 #6 (GRC) ‐ Alumina Disk

Thermal Standard ‐ Alumina Disk

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Heat Source Temperature (°C)

E2 #2 (GRC) ‐ Alumina Disk

E2 #5 (GRC) ‐ Alumina Disk

E2 #6 (GRC) ‐ Alumina Disk

Thermal Standard ‐ Alumina Disk
NASA/TM—2012-217293 9 

The Thermal Standard replicates the trends in both EL and HET versus HST for both alumina disk 

and thermal barrier testing. In addition to matching trends, the Thermal Standard matches the absolute 

value of both HET and EL test data when plotted against HST for ASC–E2 convertors during thermal 

barrier testing. The absolute value of EL and HET plotted against HST are within 7 W and 9 C, 

respectively, of ASC–E2 test data taken during alumina disk testing. The matching of trends, as well as 

modest differences in absolute values of characterizing parameters suggests that the Thermal Standard 

sufficiently mimics the characteristics of an ASC–E2 convertor and can be used to validate empirical 

correlations as well as numerical models.

3.2 Combined Thermal Barrier and Alumina Disk Correlations 

When analyzing thermal barrier and alumina disk datasets independently, the approximate 

relationship between the HET and the HST is given by: 

 HET ~ HST – (NHI)(R) (4) 

where R is the thermal resistance between the heat source and the hot end. Because the thermal resistance is 

close to constant within a given test (it is approximately equal to either the alumina disk resistance or the 

thermal barrier resistance depending on the test), and the NHI is itself correlated to the HST, there is a 

strong cross correlation between the HET and the HST, which can be seen in Figures 6 and 8. This cross 

correlation masks the fact that one parameter may actually be more strongly correlated to EL than the other. 

Analyzing alumina disk data and thermal barrier data together decouples the HET from the HST 

because different thermal resistances are used in each test, making it easier to distinguish how they 

independently effect the EL. Figures 9 and 10 show the heat source and hot-end best fit curves, 

respectively, plotted against the combined alumina disk and thermal barrier EL. These figures show how 

well each correlation parameter fits simulated non-operating data, they do not show how well the 

correlations do at predicting the environmental losses during simulated operation. The comparison to 

simulated operating data can be found in the results section of this paper. 

Figure 9.—Goodness of fit of a heat source temperature correlation fit to combined alumina disk and thermal barrier 

testing (simulated non-operating data). 

y = 0.1739x ‐ 31.029

R2 = 0.9973

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Environmental Loss (Watts)

Heat Source Temperature (C°)

Alumina Disk

Thermal Barrier Data
NASA/TM—2012-217293 10 

Figure 10.—Goodness of fit of a hot-end temperature correlation fit to combined alumina disk and thermal barrier 

testing (simulated non-operating data). 

The heat-source-based correlation fits the combined alumina disk and thermal barrier data far better 

than the hot-end correlation. The fact that two distinct sets of points are present (one for thermal barrier 

and one for alumina disk) when using a HET correlation suggests that Equation (1) is not valid when 

considering HET as the only correlation parameter. This is not always obvious because when the alumina 

disk and thermal barrier datasets are considered individually the cross-correlation between HET and HST 

can mask the fact that HET alone does not adequately correlate with EL. Conversely, the fact that both 

alumina disk points and thermal barrier points lie close to a single curve when plotted versus HST 

suggests Equation (1) is valid when correlations are built on HST alone. It also suggests that it may be 

unnecessary to perform both thermal barrier and alumina disk testing to generate HST correlations. 

These conclusions might lead one to suspect that the HST-based correlations would be a better 

predictor of EL and NHI during simulated operation than HET correlations. However, when these two 

models are used to predict EL for simulated operation, as shown in Figures 11 and 12, the heat source 

correlation overpredicts EL by 14.8 W on average, while the correlation based on HET correlation 

underpredicts EL by 3.8 W on average. A line of slope equal to one and intercept equal to zero represents 

a perfect model, and is plotted for reference. 

Although the HET correlations have been shown, in this case, to be more accurate predictors of the 

EL than the HST correlations, it is highly recommended that HET correlations not be used to predict the 

EL of operating ASC–E2 convertors. The ability of these correlations to fit Thermal Standard data 

accurately is likely coincidental. It is highly unlikely that HET correlations will generalize to different 

values of piston amplitude and GHI when applied to operating ASC–E2 convertors. 

For example, if an ASC–E2 convertor operating at a constant HET underwent a piston amplitude 

increase, the GHI and the HST would both increase. If the correlation used to calculate EL in Equation (2) 

only considers HET then the estimated EL would not change and the net heat input would be equal to the 

change in gross heat input. However, this analysis ignores the fact that the HST has also increased, 

resulting in an increase in environmental losses, and Figure 10 shows that ignoring changes in the HST 

can result in substantial errors in the calculation of EL and corresponding errors in the calculation of net 

heat input. Therefore, it is recommended that the HST be used in all single parameter environmental loss 

correlations and HET correlations are not discussed further in this paper. 

y = 0.1899x ‐ 26.755

R2 = 0.8374

0.0

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0.0 100.0 200.0 300.0 400.0 500.0 600.0 700.0 800.0 900.0

Environmental Loss (Watts)

Hot‐End Temperature (C°)

Alumina Disk

Thermal Barrier Data
NASA/TM—2012-217293 11 

Figure 11.—Predicted vs. measured environmental losses for simulated operation using heat source 

temperature correlation based on alumina disk and thermal barrier data. 

Figure 12.—Predicted vs. measured environmental losses for simulated operation using hot-end 

temperature correlation based on alumina disk and thermal barrier data. 

 

0

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Predicted Environmental Loss (W)

Measured Environmental Loss (W)

0

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160

Predicted

0.0 20.0 40.0 60.0 80.0 100.0 120.0 140.0

Environmental Loss

(W)

Measured Environmental Loss (W)
NASA/TM—2012-217293 12 

When using heat source correlations based on combined thermal barrier and alumina disk testing to 

predict the EL during simulated operation, the difference term as described by Equation (2) is 14.8 W. If 

this bias is tolerable, then these correlations can be used directly. If not, it may be possible to take 

advantage of the fact that this difference is unidirectional bias and not random scatter, to calculate a more 

accurate value. Equation (2) could be modified to include the estimated bias as calculated during thermal 

standard testing 

 EL operating ASC = f (HST) non-operating ASC + (Estimated Bias) Thermal Standard (5)

This would allow environmental loss correlations based on ASC-E2ASC–E2 operating data to be 

corrected by an estimated bias from Thermal Standard testing, potentially producing a more accurate 

result. However, this must be done with caution because it uses an unverifiable assumption that the bias 

seen during Thermal Standard testing is similar to what would be seen on ASC–E2 convertors. Since the 

Thermal Standard closely mimics the behavior of an operating convertor, this does not appear to be a bad 

assumption, but it is an unverifiable assumption. 

Another technique previously used to build correlations for ASC–E2 convertors was to use weighted 

average temperatures or a multi-parameter fit, using both hot-end and HST as correlation parameters. The 

weighting that fits the combined alumina disk and thermal barrier datasets best was a 93 percent heat 

source weighting and a 7 percent hot-end weighting. This correlation offers some improvement over the 

heat-source-only correlation; again it overpredicts EL, this time by 13.5 W on average. 

Using a weighted average or multi-parameter fit is not recommended unless both alumina disk and 

thermal barrier data are both available because of the strong cross correlation between hot-end and HST 

that exists when only one or the other data set is available. Multi-parameter fits based on highly cross 

correlated data can inappropriately magnify, reduce, or ignore the contributions of certain parameters. 

3.3 Alumina Disk Correlations 

As described previously, alumina disk correlations based on HST are expected to overpredict EL of 

operating convertors because correlations based on HST assume that the heat source and HET are both 

close to the higher HST. Figure 13 is a plot of predicted EL from the alumina disk HST correlation 

against the Thermal Standard measured EL. On average, the heat source model overpredicted 

environmental loss by 13.9 W, which would result in an underprediction of NHI of the same amount. This 

test confirms and quantifies the intuitive suspicion that heat-source-based correlations build on alumina 

disk data overpredict EL. 

3.4 Thermal Barrier Correlations 

Correlations based on thermal barrier testing are expected to have less error than correlations based on 

alumina disk testing because the relationship between hot-end and HST is closer to what is seen on 

operating convertors, and because these correlations eliminate the need for extrapolation. Figure 14 is a plot 

of predicted EL from a HST correlation using thermal barrier data against the Thermal Standard measured 

EL. Heat source correlations based on thermal barrier data alone were found to overpredict EL by 14.1 W 

on average, showing no substantial improvement over the predictions based on alumina disk testing. 
NASA/TM—2012-217293 13 

Figure 13.—Predicted environmental losses vs. measured environmental losses for a heat source 

temperature correlation based on alumina disk testing. 

Figure 14.—Predicted environmental losses vs. measured environmental losses for a heat source 

temperature correlation based on thermal barrier testing. 

0

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NASA/TM—2012-217293 14 

4.0 Conclusions 

The Thermal Standard was used to scrutinize the methods used at NASA Glenn to calculate the net 

heat input of the ASC–E2 convertor using empirical correlations. In order for these methods to be 

considered acceptable, the correlation parameters must adequately correlate to the EL of a non-operating 

convertor (i.e., Eq. (1) must be valid), and correlations based on non-operating data must be applicable to 

operating convertors (i.e., the Difference term in Eq. (2) must be sufficiently small). 

The validity of Equation (1) was tested by considering both thermal barrier and alumina disk datasets 

simultaneously, which eliminated the cross correlation between the HET and the HST. This analysis 

showed that Equation (1) is not valid when using HET as the only correlation parameter. Considering 

only HET and ignoring the effects of HST, resulted in poor correlations when analyzing combined 

thermal barrier and alumina disk data. This analysis also showed that Equation (1) is valid when using 

HST as the only correlation parameter. Based on this, it is recommended that the HST be the only 

parameter used in single-parameter correlations on ASC–E2 convertors. Alternatively, a multi-parameter 

correlation, or weighted average temperature correlation can be used, but only if both alumina disk and 

thermal barrier datasets are available, otherwise cross correlation between the hot-end and HSTs is too 

high to accurately distinguish their independent contributions to EL. For the Thermal Standard, the 

optimal weighting for the weighted average temperature based on combined alumina disk and thermal 

barrier data was 93 percent HST and 7 percent HET, once again showing the dominance of the heat 

source in the environmental loss correlations. 

Thermal barrier and alumina disk data were shown to collapse onto a single curve when plotted 

against HST, which suggested that conducting thermal barrier and alumina disk tests may be redundant if 

a correlation based only on heat-source temperature will be used. Because alumina disk testing does not 

require disassembly of the insulation package, it may be advantageous to build correlations based on 

alumina disk testing only. 

The difference term in Equation (2) was quantified for HST correlations based on thermal barrier 

testing, alumina disk testing, and both tests combined. HST correlations based on thermal barrier data 

were shown to underpredict net heat input by 14.1 W on average. HST correlations based on alumina disk 

data were shown to underpredict net heat input by 13.9 W on average. HST correlations based on 

combined thermal barrier and alumina disk data was shown to underpredict net heat input by 14.8 W on 

average. A weighted average temperature correlation based on combined thermal barrier and alumina disk 

data was shown to underpredict net heat input by 13.5 W on average. 

The difference term associated with each of these correlations appears as unidirectional bias, not 

random scatter. Therefore, if the difference terms quantified above are not small enough to be considered 

useful, it is possible that the unidirectional bias measured during Thermal Standard testing could be 

applied the NHI correlations used on operating ASC–E2 convertors. However, this assumes that the bias 

measured during Thermal Standard testing is close the bias that would be seen on an operating convertor, 

which cannot be verified.

References 

1. Reid, T., et al., “Computational Methodology for Simulating Thermal Loss Testing of the 

Advanced Stirling Convertor,” IECEC 2011, AIAA (submitted for publication) 

2. Schifer, N., Briggs, M., “Environmental Loss Characterization of an Advanced Stirling Convertor 

(ASC-E2) Insulation Package using a Mock Heater,” IECEC 2011, AIAA (submitted for 

publication)

3. Ellis, David L., and Keller, Dennis J., “Thermophysical Properties of GRCop-84,” 

NASA/CR—2000-210055, 2000.

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

NASA/TM—2005-213566, 2005.
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Evaluation of Advanced Stirling Convertor Net Heat Input Correlation Methods Using a 

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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 highefficiency 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. In an effort to improve net heat input predictions, 

numerous tasks have been performed which provided a more accurate value for net heat input into the ASCs, including testing validation 

hardware, known as the Thermal Standard, to provide a direct comparison to numerical and empirical models used to predict convertor net 

heat input. This validation hardware provided a comparison for scrutinizing and improving empirical correlations and numerical models of 

ASC-E2 net heat input. This hardware simulated the characteristics of an ASC-E2 convertor in both an operating and non-operating mode. 

This paper describes the Thermal Standard testing and the conclusions of the validation effort applied to the empirical correlation methods 

used by the Radioisotope Power System (RPS) team at NASA Glenn.

15. SUBJECT TERMS

Stirling cycle; Stirling engines; Thermodynamic efficiency; Energy conversion efficiency; Regression analysis 

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