Lanny G. Thieme

Glenn Research Center, Cleveland, Ohio

Friction Factor Characterization for HighPorosity Random Fiber Regenerators

NASA/TM—2001-211098

August 2001
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NASA/TM—2001-211098

August 2001

National Aeronautics and

Space Administration

Glenn Research Center

Lanny G. Thieme

Glenn Research Center, Cleveland, Ohio

Friction Factor Characterization for HighPorosity Random Fiber Regenerators
Acknowledgments

The author would like to express his appreciation for the support provided by Andrea Clary and the NASA Glenn

Flow Calibration Laboratory, operated by Cortez III Service Corporation (presently InDyne, Inc.), which completed

the flow testing on the regenerator samples. Also, the author would like to thank Maury White and Songgang Qiu

of Stirling Technology Company (STC) and Steve Welty, formerly of STC, for their efforts in providing the

regenerator samples, the flow test fixture, and the desired flow ranges. This work was performed in

part under Interagency Agreement SAA3–198 with the Department of Energy, between

November 1997 to March 1999.

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Available electronically at http://gltrs.grc.nasa.gov/GLTRS
NASA/TM—2001-211098 1

FRICTION FACTOR CHARACTERIZATION FOR HIGH-POROSITY

RANDOM FIBER REGENERATORS

Lanny G. Thieme

National Aeronautics and Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Summary

NASA Glenn Research Center, the Department of Energy (DOE), and Stirling Technology

Company (STC) of Kennewick, WA are developing a Stirling convertor for a high-efficiency

Stirling Radioisotope Power System to provide spacecraft on-board electric power for NASA

deep space missions. Stirling is also now being considered for unmanned Mars rovers, especially

for missions of long duration. STC is developing the 55-We Technology Demonstration

Convertor (TDC) under contract to DOE. NASA Glenn is conducting an in-house technology

project to assist in developing the convertor for readiness for space qualification and mission

implementation. NASA Glenn is also evaluating key technology issues through the use of NASA

Phase II Small Business Innovation Research (SBIR) contracts with STC and providing technical

consulting for the DOE effort under an Interagency Agreement.

As part of the Interagency Agreement, NASA Glenn performed a review of the TDC design.

The HFAST computer code was used to compare projected convertor performance to that

predicted by the GLIMPS code used by STC to design the convertor. These comparisons

showed a large difference in the regenerator pressure drop losses due to significantly different

regenerator friction factors used by the two codes. Neither code's friction factor correlations

appeared to be based on regenerator test data at the regenerator porosities that were being

considered for the design (90-96%). Therefore, NASA Glenn recommended that steady-flow

pressure drop tests be conducted to better determine the friction factor for these high-porosity

regenerators.

STC fabricated a flow test fixture and three random fiber regenerator test samples, one each at

approximately 80%, 88%, and 96% porosities. The flow tests were then completed by the

NASA Glenn Flow Calibration Laboratory, and the data reduced to Reynolds number and

friction factor. The results showed that the 80% and 88% porosity samples had similar

characteristics while the 96% porosity sample had significantly higher friction factors for given

Reynolds numbers compared to the samples with lower porosities. Comparisons were also made

between the test data and existing correlations. STC used this data to derive a modified

regenerator friction factor correlation for use in GLIMPS for porosities greater than 88%. Using

this new correlation, the final optimized regenerator design porosity was reduced from 96% to

90%.
NASA/TM—2001-211098 2

It is important to note that no adjustments were made to the heat transfer correlation used in

GLIMPS for the higher regenerator porosities. Heat transfer test data would be very worthwhile

to obtain but are difficult to measure. It was felt that the straightforward steady-flow pressure

drop tests would give at least some idea of the similarity of high-porosity regenerators to those

for which both friction factor and heat transfer data exist. In the future, an existing NASA Glenn

regenerator test rig may be used to perform heat transfer testing on high-porosity random fiber

regenerator samples.

Introduction

NASA Glenn Research Center, the Department of Energy (DOE), and Stirling Technology

Company (STC) of Kennewick, WA are developing a Stirling convertor for an advanced

radioisotope power system to provide spacecraft on-board electric power for NASA deep space

missions. Stirling is being evaluated as an alternative to replace RTG’s (Radioisotope

Thermoelectric Generators) with a high-efficiency power source and has been identified for

potential use on the Europa Orbiter and Solar Probe missions. Stirling is also now being

considered for unmanned Mars rovers, especially for missions of long duration. The efficiency of

the Stirling system, in excess of 20%, will reduce the required amount of isotope by a factor of at

least 3 compared to RTG’s. This significantly reduces radioisotope cost, radiological inventory,

and system cost and provides efficient use of scarce radioisotope resources.

STC has designed, fabricated, and completed first testing of the 55-We Technology

Demonstration Convertor (TDC) under contract to DOE [1,2]. TDC’s are now being tested

singly and in dynamically-balanced opposed pairs by STC. The design power of 55 We and an

efficiency of about 25% have been demonstrated for TDC operating conditions of 650∞C hot-end

temperature and 120∞C cold-end temperature. The TDC’s have been mapped over a range of

temperatures and strokes. NASA Glenn is providing technical consulting for this effort under an

Interagency Agreement with DOE.

NASA Glenn is conducting an in-house technology project to assist in developing the convertor

for readiness for space qualification and mission implementation [3]. As part of this effort, the

TDC has been characterized for electromagnetic interference/electromagnetic compatibility

(EMI/EMC) and also successfully passed launch environment random vibration testing at

qualification levels while operating at full stroke and full power. An independent performance

verification and mapping of multiple TDC’s is now being done. Heater head life assessment and

NdFeB magnet aging characterization tasks are underway. Substitute organic materials for the

linear alternator for use in a high radiation environment have been identified and have been

incorporated by STC in TDC’s recently built for GRC. Electromagnetic and thermal FEA for the

linear alternator are also being conducted.

As part of the overall radioisotope Stirling development, NASA Glenn is evaluating key

technology issues through the use of two NASA Phase II SBIR contracts with STC [4]. Under

the first SBIR, STC demonstrated a synchronous connection of two thermodynamically
NASA/TM—2001-211098 3

independent Stirling convertors. Synchronization was achieved over a wide operating range, and

a 40 to 50 fold reduction in vibrations compared to an unbalanced convertor was shown. System

operation was also demonstrated with the synchronized convertors feeding a battery charger

load. This connection method is now being used to connect the TDC’s. The second SBIR

contract is for the development of an Adaptive Vibration Reduction System (AVRS) that will

further reduce vibration levels under normal operating conditions and will add the ability to adapt

to any changing convertor conditions over the course of a mission.

As part of the Interagency Agreement, NASA Glenn performed a review of the TDC design. As

part of this review, the HFAST computer code was used by NASA Glenn to analyze the TDC

performance. HFAST was developed by Mechanical Technology, Inc. (MTI), in part, during the

NASA effort to develop Stirling for space power for the SP-100 program. NASA Glenn has

unrestricted rights to use and distribute HFAST. Comparisons were made to the STC GLIMPS

computer code predictions for the TDC. GLIMPS was the primary code used by STC for design

purposes. NASA Glenn also owns a license to use the GLIMPS code and has completed

previous comparisons between HFAST and GLIMPS. NASA Glenn’s past experience in using

the two codes has not revealed any clear superiority of one code over the other. Although there

are differences between them, both have been found to give reasonable overall results.

Overall comparisons of the GLIMPS and HFAST projections for the TDC showed that the two

codes predicted similar performance with an adjustment for friction factor in the regenerator to

make the two codes use similar regenerator friction factors. Without this adjustment, HFAST

predicted much lower performance than did GLIMPS due to higher pressure drop losses through

the regenerator.

The friction factor correlations used in each code were evaluated to understand these differences

in pressure drop losses. This then led to a recommendation to complete steady-flow pressure

drop tests to better determine the friction factor for the high-porosity regenerator that is used in

the TDC design. NASA Glenn performed these tests in the NASA Glenn Flow Calibration

Laboratory. This report describes the evaluation of the GLIMPS and HFAST friction factor

correlations, the steady-flow testing and data reduction procedures, and the test results and

comparisons to existing correlations.

Comparison of the HFAST and GLIMPS Friction Factor Correlations

STC was considering porosities of about 90-96% for the TDC random fiber regenerator design.

Both GLIMPS and HFAST include a porosity dependence in their friction factor correlations.

However, as shown by figures 1 and 2, HFAST has a much higher sensitivity to porosity than

does GLIMPS, especially for screen regenerators. The agreement between the two codes is

better for 94% random fiber regenerators as shown in figure 3, but the codes still vary by about

40%. The friction factor correlations for both codes agree well at 78% porosity for both types of

regenerators.
NASA/TM—2001-211098 4

0

20

40

60

80

0 50 100 150 200

Re

f

GLIMPS

HFAST

Figure 1 - GLIMPS and HFAST Friction Factor (f) vs. Reynolds Number (Re) for 

 94% Porosity Screen Regenerators.

0

5

10

15

20

0 50 100 150 200

Re

f

GLIMPS

HFAST

Figure 2 - GLIMPS and HFAST Friction Factor (f) vs. Reynolds Number (Re) for 

 78% Porosity Screen Regenerators.

Gedeon, in his final report on regenerator pressure drop and heat transfer testing in oscillating

flow done at Ohio University [5], concluded that he could not determine any porosity

dependence for the range of screens and felts (random fiber) that were tested in that project.

These tests covered porosities of 62-78% for screens and 69-84% for felts. The HFAST manual

states that its screen regenerator friction factor is based on Kays and London data and appears to

be the same as used in an earlier version of GLIMPS. Kays and London show that their test

data were taken for a range of porosities of 60-83% for screens [6]. GLIMPS (version 4.0) uses

relationships for screens and random fibers that are based, in part, on earlier testing at Ohio

University [7]. Pressure drop tests for steady and oscillating flow were also completed by
NASA/TM—2001-211098 5

0

5

10

15

20

25

30

0 50 100 150 200

Re

f

GLIMPS

Figure 3 - GLIMPS and HFAST Friction Factor (f) vs. Reynolds Number (Re) for 

 94% Porosity Random Fiber Regenerators.

Sunpower, Inc. with the same rigs that were later moved to Ohio University [8]. These tests

included regenerator porosities of 61-68% for screens and 80-84% for random fibers.

So it appears that neither code's friction factor correlations are based on regenerator test data at

the regenerator porosities that were being considered for the design (90-96%). Due to this

concern, NASA Glenn recommended that STC consider running a steady-flow pressure drop test

on a high-porosity regenerator sample to get good empirical data on the friction factor for these

regenerators. Gedeon indicated that steady-flow testing should be adequate for determining

friction factors for typical regenerators [7]. Heat transfer test data would also be very important

but are much more difficult to obtain. It was felt that the straightforward pressure drop tests

would give at least some idea of the similarity of high-porosity regenerators to those for which

both friction factor and heat transfer data exist.

Steady-Flow Pressure Drop Tests

STC agreed with the recommendation to conduct steady-flow pressure drop tests to determine

the friction factor for a high-porosity regenerator sample. It was determined that the Flow

Calibration Laboratory at NASA Glenn could do these tests in a quick, economical, and accurate

manner.

STC selected and fabricated three random fiber regenerator test samples, one each at

approximately 80%, 88%, and 96% porosities. The 80% porosity sample was chosen to give a

comparison to the correlations used in GLIMPS and HFAST at a porosity level where empirical

test data exist. The wire diameter used in all samples was 0.0009 in (22 microns). Each test

sample consisted of two disks that were stacked in the sample holder. STC provided the length,

diameter, and porosity of each disk. The values of diameter and porosity for the two disks in

HFAST
NASA/TM—2001-211098 6

each sample were averaged and the lengths of the two disks were added to arrive at the following

sample characteristics:

Sample Ave. diameter, cm (in) Ave. porosity Length, cm (in)

80%, disks 1,2 2.22 (0.875) 0.797 2.57 (1.011)

88%, disks 3,4 2.22 (0.873) 0.878 2.53 (0.995)

96%, disks 5,6 2.21 (0.872) 0.957 2.42 (0.952)

STC also designed a test fixture, with inputs from NASA Glenn, and then fabricated this fixture

to hold the samples for testing. The test fixture and the three test samples are shown in figure 4.

The pressure taps can be seen on each half of the test fixture. A coarse wire screen was used on

each half of the test fixture to help straighten the flow on each end of the regenerator sample.

Photomicrographs of sections of each of the three test samples are shown in figure 5.

Consideration was given for flow testing with helium, nitrogen, or air. The TDC uses helium at

about 2.41 MPa (350 psia) absolute mean pressure; the maximum flow rate in the regenerator

predicted by GLIMPS was about 3.6 g/sec (0.008 lbm/sec). Based on discussions with the

NASA Glenn Flow Calibration Laboratory and STC, it was decided that testing with air at about

0.69 MPa (100 psia) absolute inlet pressure provided the best combination of meeting the desired

flow rates and producing the data in a timely, economical manner. STC provided their desired

flow rates for testing. These were chosen to both cover the range of Reynolds numbers as

appropriate for the TDC and to include higher flow rates that may be applicable to future

convertor designs.

Figure 4 - Regenerator test samples and flow test fixture.
NASA/TM—2001-211098 7

96% Porosity

80% Porosity 88% Porosity

Figure 5 - Random Fiber Regenerator Samples at 50x Magnification.

The flow tests were then completed by the NASA Glenn Flow Calibration Laboratory. The test

data are included in Appendix A. A test was also run with no sample to determine the effect of

the coarse screens that were used as flow straighteners. There was no measurable pressure drop

for this test until the flow rate reached 5.4 g/sec (0.012 lbm/sec). At the highest flow rate,

11.8 g/sec (0.026 lbm/sec), the pressure drop was only 0.17 kPa (0.025 psid). It was felt that

this pressure drop was negligible, and it was ignored in the data reduction.

Figure 6 shows the measured steady-flow pressure drop as a function of mass flow rate for each

of the three samples. Testing was done with air at 0.69 MPa (100 psia) absolute inlet pressure

for all samples. Flow conditions were chosen to include the range of Reynolds numbers that

were expected to occur in the actual convertor. Tests were also run in each of the two different

flow directions for the 96% porosity sample. These results are shown in figure 7 and can be seen

to be essentially identical. Flow directions 5-6 and 6-5 refer to the regenerator disk numbers 5

and 6, which were the two 96% porosity disks that were used in this sample.
NASA/TM—2001-211098 8

0

40

80

120

160

0 2 4 6 8 10 12 14

Mass Flow, g/sec

Pressure Drop, kPa

80% Porosity

88% Porosity

96% Porosity

Figure 6 - Pressure Drop vs. Mass Flow for Random Fiber Regenerator Samples.

0

4

8

12

16

20

0 2 4 6 8 10 12 14

Mass Flow, g/sec

Pressure Drop, kPa

0.38 MPa, flow 5-6

0.69 MPa, flow 5-6

0.69 MPa, flow 6-5

Figure 7 - Pressure Drop vs. Mass Flow for 96% Porosity Random Fiber Regenerator 

 Sample for Different Inlet Pressures and Different Flow Directions.

A test was also run at 0.38 MPa (55 psia) absolute inlet pressure for the 96% porosity sample to

check the effect of DP/P, and these pressure drop results are compared to those for the 0.69 MPa

(100 psia) absolute inlet pressure in figure 7. An expansion factor correction based on the DP/P

[9], calculated using inlet pressure, was made on one of these sets of data to correct it back to the

data at the other pressure level. The thought was to then use this type of correction on any data

points that had high ratios of DP/P. However, it was found that similar results were obtained by

using the average of the inlet and outlet pressures when calculating the density of the fluid so this

method was used for all data and assumed to be satisfactory for any data points that had a high

ratio of DP/P. In general, it was preferred to maintain the DP/P below 0.1. Appendix A shows

that most of the test data had a DP/P of less than 0.06.
NASA/TM—2001-211098 9

The measured flow data were provided to STC. STC and NASA Glenn first independently

reduced this data to friction factor versus Reynolds number and then resolved any significant

differences. The Reynolds numbers and friction factors as calculated by NASA Glenn are

included in Appendix A. These values were obtained from the test data by using the following

equations:

Re = mdot * Dh / (m * Asample * p)

Dh = p * dw / (1-p)

where:

Re – Reynolds number

mdot – mass flow rate, lbm/sec

Dh – regenerator sample hydraulic diameter, ft

m - fluid absolute viscosity, lbm/ft-sec

Asample – total cross-sectional area of the regenerator sample, ft2

p - regenerator sample porosity

dw – regenerator sample wire diameter, ft

f = DP * Dh * (Asample * p)2 * r * 2gc * 144 / (L * mdot2)

where:

f – friction factor

DP – pressure drop, psi

Dh – regenerator sample hydraulic diameter, ft (as defined in previous 

equation)

Asample – total cross-sectional area of the regenerator sample, ft2

p - regenerator sample porosity

r - fluid density, lbm/ft3

gc – gravitational conversion factor = 32.2 lbm-ft/(lbf-sec2)

L – regenerator sample length, ft

mdot – mass flow rate, lbm/sec

Friction factor versus Reynolds number (based on NASA Glenn’s data reduction) is shown for

each of the samples in figure 8. The curves for the 80% and 88% porosity samples are very

similar while the friction factor is significantly higher for the 96% porosity sample. Figure 9

shows the friction factor versus Reynolds number results for the two different pressure levels

run for the 96% porosity sample. They are identical for most of the Reynolds number range

with significant variations at the lower Reynolds numbers. These variations appear to be caused
NASA/TM—2001-211098 10

0

4

8

12

16

20

24

0 300 600 900

Re

f

80% Porosity

88% Porosity

96% Porosity

Figure 8 - Friction Factor (f) vs. Reynolds Number (Re) for Random Fiber 

 Regenerator Samples.

0

2

4

6

8

10

12

14

0 300 600 900

Re

f

0.38 MPa

0.69 MPa

Figure 9 - Friction Factor (f) vs. Reynolds Number (Re) for 96% Porosity Random Fiber 

 Regenerator Sample for Different Inlet Pressures.

by errors in the measurement of pressure drop as the values of the pressure drop are very low for

these data points.

Estimated errors for all data are shown in figure 10. Errors were calculated based on the following

[10]:

wR = [((∂R/∂x1)w1)

2

 + ((∂R/∂x2)w2)

2

 + o + ((∂R/∂xn)wn)

2

]

1/2
NASA/TM—2001-211098 11

1

10

100

0 300 600 900

Re

Error in f, %

80% Porosity

88% Porosity

96% Porosity - 0.69 MPa

96% Porosity - 0.38 MPa

Figure 10 - Percent Error in the Friction Factor (f) vs. Reynolds Number (Re) for Random Fiber 

 Regenerator Flow Tests (the error in Reynolds number is 1.0% of reading for all points).

where:

wR – uncertainty of the calculation, units of the calculation

∂R/∂x1, ∂R/∂x2, ..., ∂R/∂xn – partial derivatives of the calculation with respect to each

independent variable in the calculation

w1, w2, ..., wn – uncertainties of the independent variables, units of the independent

variables

The measurement error for the mass flow rate was 1% of reading for all data points. The error in

Reynolds number was taken as 1% of reading based on just this error in the mass flow rate.

Uncertainties in the pressure drop, mass flow rate, inlet pressure, and temperature were included

in the calculation of uncertainty for the friction factor. Figure 10 shows the error in the friction

factor as a function of Reynolds number for each of the three samples; curves are shown for each

pressure level for the 96% porosity data. Most of the errors in friction factor are less than 10%.

Significantly higher errors occur for the low Reynolds number points for the 96% porosity

curves. These larger errors appear to explain the difference in friction factor for the two different

pressure levels at these low Reynolds numbers for the 96% porosity sample.

The friction factor curves for the three samples are compared with three correlations in figures

11-13. The three correlations shown are those for GLIMPS, HFAST, and the latest correlation

based on test data taken at Ohio University [5]. All three correlations agree well with the test

data for the 80% porosity sample (figure 11). Figure 12 shows that the GLIMPS correlation and

the correlation based on test data taken at Ohio University agree well with the test data for the

88% porosity sample while the HFAST correlation yields a higher friction factor. Finally, figure

13 shows the same comparison for the 96% porosity sample. Now, HFAST compares the best

with the test data (data shown is for the 0.69 MPa (100 psia) absolute inlet pressure only) at the
NASA/TM—2001-211098 12

0

5

10

15

20

25

30

35

0 50 100 150 200

Re

f

Flow Test Data

GLIMPS

HFAST

Ohio U.

Figure 11 - Friction Factor (f) vs. Reynolds Number (Re) for 80% Porosity Random Fiber 

 Regenerator - Comparison of Test Data with Correlations.

0

2

4

6

8

10

12

14

16

18

0 100 200 300

Re

f

Flow Test Data

GLIMPS

HFAST

Ohio U.

Figure 12 - Friction Factor (f) vs. Reynolds Number (Re) for 88% Porosity Random Fiber 

 Regenerator - Comparison of Test Data with Correlations.

lower Reynolds numbers, 0-300, which was the expected range for the TDC design with a 96%

porosity regenerator.

Following analyses of these results, STC decided to use the GLIMPS correlation for all

regenerator porosities up to 88%. They then derived a curve based on the GLIMPS friction

factor for 88% porosity and the 96% porosity test data (average of the curves for 0.38 MPa

(55 psia) and 0.69 MPa (100 psia) absolute inlet pressures) that extrapolates between these for

porosities from 88-96%. Figure 14 shows the GLIMPS friction factor curve for 88% porosity

and the two test data curves for the 96% porosity sample over the Reynolds number range of

0-350.
NASA/TM—2001-211098 13

0

2

4

6

8

10

12

14

0 300 600 900

Re

f

Flow Test Data

GLIMPS

HFAST

Ohio U.

Figure 13 - Friction Factor (f) vs. Reynolds Number (Re) for 96% Porosity Random Fiber 

 Regenerator - Comparison of Test Data with Correlations.

0

2

4

6

8

10

12

14

0 50 100 150 200 250 300 350

Re

f

96% Data - 0.69 MPa

96% Data - 0.38 MPa

88% GLIMPS

Figure 14 - Input Curves for STC Correlation for Friction Factor for Random Fiber 

 Regenerator Porosities Between 88% and 96%.

Based on these overall results and recognizing that heat transfer data does not exist for the higher

porosities, STC decided to limit the design regenerator porosity to a value no greater than 90%.

STC GLIMPS results with the new friction factor input for 88-96% porosities showed that the

final design optimized around 90% porosity (with no constraint on the porosity), and this is the

regenerator porosity that was then used for the TDC. It should be kept in mind that no

adjustments were made to the heat transfer correlation used in GLIMPS for the higher porosities.

In the future, an existing NASA Glenn regenerator test rig may be used to perform heat transfer

testing on high-porosity random fiber regenerator samples.
NASA/TM—2001-211098 14

Conclusions

Prior to the testing discussed in this report, the random fiber regenerator for the DOE/STC TDC

design was optimizing at porosities of about 96%. Comparisons of the GLIMPS and HFAST

computer codes showed large differences in the regenerator friction factor correlations for these

porosities although the correlations compared well for porosities around 80%. It was felt that

the large differences for the higher porosities were due to the correlations being extrapolated too

far from existing regenerator test data on which the correlations were based. The highestporosity regenerator flow test data from which the GLIMPS and HFAST correlations were

derived appear to be for porosities of around 84%. Thus, it was recommended to perform flow

tests on high-porosity random fiber regenerators to better determine the friction factor.

Steady-flow tests were run for 80%, 88%, and 96% porosity random fiber regenerator samples,

and the data were reduced to Reynolds number and friction factor. The results showed that the

80% and 88% porosity samples had similar characteristics while the 96% porosity sample had

significantly higher friction factors for given Reynolds numbers compared to the lower porosities.

STC used this data to derive a modified regenerator friction factor correlation for use in GLIMPS

for porosities greater than 88%. Using this new correlation, the final regenerator design

optimized at a porosity of 90%.

It is important to note that no adjustments were made to the heat transfer correlation used in

GLIMPS for the higher regenerator porosities. Heat transfer test data would be very worthwhile

to obtain but are difficult to measure. It was felt that the straightforward pressure drop tests

would give at least some idea of the similarity of high-porosity regenerators to those for which

both friction factor and heat transfer data exist. In the future, an existing NASA Glenn

regenerator test rig may be used to perform heat transfer testing on high-porosity random fiber

regenerator samples.

References

1. White, M.A.; Qiu, S.; and Augenblick, J.E.: Preliminary Test Results from a Free-Piston

Stirling Engine Technology Demonstration Program to Support Advanced Radioisotope Space

Power Applications, Proceedings of the Space Technology and Applications International

Forum, 2000.

2. White, M.; Qiu, S.; Augenblick, J.; Peterson, A.; and Faultersack, F.: Positive Results from a

Free-Piston Stirling Engine Technology Demonstration Program for Advanced Radioisotope

Space Power Systems; Proceedings of the 35th Intersociety Energy Conversion Engineering

Conference, paper no. AIAA–2000–3023, 2000.

3. Thieme, L.G. and Schreiber, J.G.: NASA GRC Technology Development Project for a

Stirling Radioisotope Power System, Proceedings of the 35th Intersociety Energy Conversion

Engineering Conference, paper no. AIAA–2000–2840, NASA/TM—2000-210246, 2000.
NASA/TM—2001-211098 15

4. Thieme, L.G.; Qiu, S.; and White, M.A.: Technology Development for a Stirling

Radioisotope Power System, Proceedings of the Space Technology and Applications

International Forum - 2000, NASA/TM—2000-209791, 2000.

5. Gedeon, D. and Wood, J.G.: Oscillating-Flow Regenerator Test Rig: Hardware and Theory

With Derived Correlations for Screens and Felts, NASA CR–198442, 1996.

6. Kays, W.M. and London, A.L.: Compact Heat Exchangers, 2nd Edition, McGraw-Hill, Inc.,

1964.

7. Gedeon, D. and Wood, J.G.: Oscillating-Flow Regenerator Test Rig: Woven Screen and Metal

Felt Results, Ohio University Center for Stirling Technology Research, status report for NASA

grant NAG3–1269, 1992.

8. Koester, G.; Howell, S.; Wood, G.; Miller, E.; and Gedeon, D.: Oscillating Flow Loss Test

Results in Stirling Engine Heat Exchangers, NASA CR–182288, 1990.

9. Flow of Fluids Through Valves, Fittings, and Pipe; Engineering Division of the Crane Co.,

Chicago; Technical Paper No. 410, 1957.

10. Holman, J.P.: Experimental Methods for Engineers, 2nd Edition, McGraw-Hill, Inc., 1971.
Appendix A – Steady-Flow Test Data and Reduced Data

Sample: 80% Porosity - Disks 1,2

Flow Direction: 1-2 Date: 3/3/98

Inlet

Pressure

Inlet

Pressure Flow Rate Flow Rate

Pressure

Drop

Pressure

Drop Delta P/P Temp. Temp. Re f (Darcy)

psia kPa lbm/sec g/sec psid kPa degrees F degrees C

99.93 689.0 0.00152 0.689 0.30 2.1 0.003 75.3 24.1 10.5 22.8

100.22 691.0 0.00332 1.51 0.81 5.6 0.008 75.5 24.2 22.9 12.8

99.97 689.3 0.00474 2.15 1.32 9.1 0.013 75.5 24.2 32.8 10.2

100.14 690.5 0.00660 2.99 2.11 14.5 0.021 75.5 24.2 45.6 8.4

100.11 690.2 0.00825 3.74 2.92 20.2 0.029 75.4 24.1 57.0 7.4

100.02 689.6 0.00997 4.52 3.90 26.9 0.039 75.1 23.9 68.9 6.7

100.02 689.6 0.0129 5.86 5.86 40.4 0.059 74.9 23.8 89.2 6.0100.00 689.5 0.0199 9.00 12.12 83.5 0.121 75.2 24.0 137 5.0

100.09 690.1 0.0260 11.8 19.94 137.4 0.199 75.5 24.2 180 4.62

100.01 689.5 0.0264 12.0 20.56 141.8 0.206 75.5 24.2 183 4.60

Sample: 88% Porosity - Disks 3,4

Flow Direction: 3-4 Date: 3/3/98

Inlet

Pressure

Inlet

Pressure Flow Rate Flow Rate

Pressure

Drop

Pressure

Drop Delta P/P Temp. Temp. Re f (Darcy)

psia kPa lbm/sec g/sec psid kPa degrees F degrees C

100.33 691.7 0.00162 0.735 0.10 0.7 0.001 74.9 23.8 18.7 15.5

100.11 690.2 0.00331 1.50 0.27 1.8 0.003 74.7 23.7 38.2 9.5

100.40 692.3 0.00494 2.24 0.46 3.2 0.005 74.7 23.7 57.1 7.3

100.46 692.6 0.00658 2.98 0.69 4.7 0.007 74.9 23.8 76.0 6.2

100.15 690.5 0.00837 3.80 0.98 6.7 0.010 75.0 23.9 96.7 5.4

99.96 689.2 0.00991 4.50 1.26 8.7 0.013 75.2 24.0 114 5.0

100.00 689.5 0.0132 5.97 1.96 13.5 0.020 75.3 24.1 152 4.38

100.05 689.8 0.0198 8.96 3.79 26.1 0.038 75.4 24.1 228 3.72

99.97 689.3 0.0260 11.8 6.05 41.7 0.060 75.6 24.2 300 3.39

NASA/TM—2001-21109816
Sample: 96% Porosity - Disks 5,6

Flow Direction: 5-6 Date: 3/3/98

Inlet

Pressure

Inlet

Pressure Flow Rate Flow Rate

Pressure

Drop

Pressure

Drop Delta P/P Temp. Temp. Re f (Darcy)

psia kPa lbm/sec g/sec psid kPa degrees F degrees C

100.35 691.9 0.00158 0.717 0.02 0.2 0.0002 76.0 24.4 51.9 13

100.58 693.5 0.00343 1.56 0.06 0.4 0.001 76.1 24.5 113 7.8

100.36 691.9 0.00488 2.21 0.10 0.7 0.001 76.4 24.7 160 6.4

100.59 693.5 0.00652 2.96 0.16 1.1 0.002 76.6 24.8 214 5.5

100.31 691.6 0.00823 3.73 0.22 1.5 0.002 76.6 24.8 270 4.9

100.42 692.4 0.00981 4.45 0.29 2.0 0.003 76.6 24.8 322 4.5

100.10 690.1 0.0131 5.92 0.45 3.1 0.005 76.6 24.8 429 4.0

100.49 692.9 0.0194 8.81 0.86 5.9 0.009 76.6 24.8 638 3.38

100.00 689.5 0.0265 12.0 1.44 9.9 0.014 76.6 24.8 870 3.04

55.01 379.3 0.00143 0.649 0.02 0.2 0.0004 75.4 24.1 47.0 9

56.52 389.7 0.00370 1.68 0.11 0.8 0.002 74.9 23.8 122 6.9

56.13 387.0 0.00565 2.56 0.22 1.5 0.004 74.8 23.8 186 5.6

55.48 382.5 0.00799 3.62 0.37 2.6 0.007 74.7 23.7 262 4.8

55.01 379.3 0.0102 4.61 0.55 3.8 0.010 74.6 23.7 334 4.3

55.23 380.8 0.0154 7.00 1.07 7.4 0.019 74.6 23.7 507 3.6654.98 379.1 0.0168 7.63 1.24 8.5 0.022 74.6 23.7 552 3.5455.02 379.3 0.0206 9.33 1.73 11.9 0.031 74.7 23.7 676 3.3055.06 379.6 0.0222 10.1 1.96 13.5 0.036 74.9 23.8 728 3.2154.91 378.6 0.0258 11.7 2.55 17.5 0.046 75.2 24.0 848 3.06

NASA/TM—2001-21109817
Sample: 96% Porosity - Disks 5,6

Flow Direction: 6-5 Date: 3/3/98

Inlet

Pressure

Inlet

Pressure Flow Rate Flow Rate

Pressure

Drop

Pressure

Drop Delta P/P Temp. Temp.

psia kPa lbm/sec g/sec psid kPa degrees F degrees C

100.14 690.5 0.00146 0.662 0.02 0.2 0.0002 75.8 24.3

100.16 690.6 0.00329 1.49 0.06 0.4 0.001 75.7 24.3

100.19 690.7 0.00816 3.70 0.22 1.5 0.002 75.8 24.3

101.04 696.7 0.0143 6.48 0.52 3.6 0.005 75.9 24.4

100.31 691.6 0.0166 7.53 0.67 4.6 0.007 75.9 24.4

100.02 689.6 0.0226 10.3 1.11 7.7 0.011 76.0 24.4

100.06 689.8 0.0268 12.1 1.47 10.1 0.015 76.0 24.4

104.52 720.6 0.0164 7.44 0.63 4.3 0.006 76.1 24.5

101.47 699.6 0.00848 3.85 0.23 1.6 0.002 76.1 24.5

100.07 690.0 0.00256 1.16 0.05 0.3 0.0004 76.2 24.6

NASA/TM—2001-21109818
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24

Friction Factor Characterization for High-Porosity Random Fiber Regenerators

Lanny G. Thieme

Stirling engines; Friction factor; Regenerators

Unclassified -Unlimited

Subject Categories: 20 and 44 Distribution: Nonstandard

This work was performed in part under Interagency Agreement SAA3–198 with the Department of Energy, between

November 1997 to March 1999. Responsible person, Lanny G. Thieme, organization code 5490, 216–433–6119.

NASA Glenn Research Center, the Department of Energy (DOE), and Stirling Technology Company (STC) of

Kennewick, Washington are developing a Stirling convertor for a high-efficiency Stirling Radioisotope Power System to

provide electric power for NASA Space Science missions. STC is developing the 55-We Technology Demonstration

Convertor (TDC) under contract to DOE. Steady-flow tests were completed to determine the friction factor for the highporosity regenerators that are used in the TDC. STC fabricated a flow test fixture and three random fiber regenerator test

samples, one each at approximately 80, 88, and 96 percent porosities. The flow tests were then completed by the NASA

Glenn Flow Calibration Laboratory, and the data reduced to Reynolds number and friction factor. The results showed that

the 80 and 88 percent porosity samples had similar characteristics while the 96 percent porosity sample had significantly

higher friction factors for given Reynolds numbers compared to the samples with lower porosities. Comparisons were

also made between the test data and existing correlations. STC used this data to derive a modified regenerator friction

factor correlation for use in the Stirling design code GLIMPS for porosities greater than 88 percent. Using this new

correlation, the final optimized regenerator design porosity was reduced from 96 to 90 percent.