Improving Performance of the Stirling Converter: Redesign of the
Regenerator with Experiments, Computation and Modern Fabrication
Techniques
Quarterly Report for the Period July – September 2001
Mounir Ibrahim – CSU
Terry Simon - UMN
David Gedeon - Gedeon Associates
Roy Tew - NASA Glenn RC
Cleveland State University
1983 East 24th Street
Fenn Tower 1010
Cleveland, Ohio
Date Published – October 2001
PREPARED FOR THE UNITED STATES
DEPARTMENT OF ENERGY
Under Financial Assistance Award
No. DE-FC36-00G010627
Table of Contents
Page
1.0 Summary……………………………………………………………………………...2
2.0 Experimental Effort at the University of Minnesota ............................................... 3
2.1 Test Section Description…………………………………………………………... 3
2.2 Instrumentation…………………………………………………………………… 5
2.2.1 Thermocouples…………………………………………………….5
2.2.2 Hot-Wire Anemometery…………………………………………..6
2.2.3 TDC and Shaft Encoders…………………………………………6
2.3 Literature Review…….……………………………………………………………..6
2.4 Upcoming Activities…..…………………………………………………………… 7
3.0 CFD Modeling ......................................................................................................... …8
3.1 Multi-Cylinder (Cross-Rods Matrix) Modeling…………………………………....8
3.2 UMN Test Rig CFD Simulation…………………………………………………....9
3.3 Porous Media, Momentum Resistance Modeling………………………………... 9
4.0 CSU-SLRE Fabrication for Future Regenerator Testing ....................................... 9
5.0 Submittal of a Research Proposal on Stirling Regenerator .................................... 9
6.0 NASA Support........................................................................................................... 13
7.0 References .................................................................................................................. 13
DOE-4th QRT Progress Report
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1.0 Summary
This is the 4th quarterly report for the period July-September 2001. During this
period our work focused on:
1) Literature review.
2) Fabrication of the University of Minnesota (UMN) test rig according to our
design parameters which came from the consideration of a representative engine, the
need for support of the development of computational models and the desire to take
measurements in details.
3) Design and construction of the electrical heating and cooling auxiliary systems
for the facility at the UMN.
4) UMN development of the instrumentation package for flow and heat transfer
measurements, including hot-wire anemometer, thermocouple data acquisition, stepper
motor controllers, and shaft encoder and TDC photo detector for synchronizing data
acquisition.
5) CFD simulations of multi-cylinder (cross-rods matrix) using: a) Laminar Flow
Model, b) Turbulent Flow with High-Reynolds-Number k- Model and c) Large Eddy
Simulations (LES) with High-Reynolds-Number k- as a subgrid Model.
6) CFD simulation of the UMN test rig.
7) Fabrication of the Cleveland State University- Stirling Laboratory Research
Engine (CSU-SLRE), for future regenerator testing.
8) Submittal of a research proposal (on Stirling Engine Regenerators) to U.S. Egypt Joint Board on Scientific and Technology Cooperation.
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2.0 Experimental Effort at the University of Minnesota
2.1 Test Section Description
We have now completed fabrication of the test rig. The following is the complete
description. Please refer to Figure 1 that shows the test section and Figure 2 that shows
the drive.
Heater
Regenerator
Clearance space
Cooler
Cylinder
Screen
Flow distributor
Piston
Figure 1 General View of Test Section - UMN Test Rig
Adjacent to the piston cylinder assembly(shown only partially at the right) is a
volume to allow better distribution of the flow coming from the piston space to uniformly
enter the cooler tubes. It is made of a steel tube with length 290mm (11.5 inch) and
inside diameter 203mm (8.0 inch) welded between two, 3–mm-thick steel plates. As part
of our qualification experiments, we will see if the velocity of the flow coming out of the
cooler tubes is sufficiently uniform from one tube to the next.
Further from the drive is the cooler. It is of a shell-and-tube type construction
consisting of 9, 18.9 mm (0.745 inch) inside diameter by 914 mm (36.0 inch) long copper
tubes glued between two, 12.9 mm (0.5 inch) acrylic flange plates. The tubes, which are
parallel to the flow displacement, carry the air. The layout of the 9 tubes is described by
the ratio of the spacing between any two tubes to the diameter of the tubes, a parameter
set to 3.0, as recommended by Stirling Technology Company (STC). An acrylic tube
with an inside diameter of 190mm (7.5 inch) is used as the shell of the cooler section heat
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exchanger. Using an existing water tank and pump, a cooling water circulation system
was built to hold the water temperature quite stable. City water will be supplied into the
system as makeup to maintain constant temperature. Overflow will go to the city sewer
system. The makeup flow rate will be very small because of the small energy release
rate. In order to assure no water leakage from the cooler, we modified the existing
cooling water circulation system to make the cooler operate under a sub-atmospheric
pressure.
Beyond the cooler, moving from the drive end, is the regenerator made of an
acrylic tube with an inside diameter of 190 mm (7.5 inch). Two hundred pieces of 4mesh stainless steel 304 screens are stacked within the regenerator holder in such a way
that each layer is rotated 45 from the adjacent layer and such that the regenerator has
90% porosity. Finding how to arrange the screens to obtain effective heat transfer while
decreasing pressure drop through the regenerator is a key element of our mission. The
wire diameter of the screens is 0.813mm (0.032inch), which results in the hydraulic
diameter of 7.32mm (0.288inch). This is smaller than the turbulent eddy viscosity
penetration depth required to make the flow quasi-steady under our intended operation
conditions, as demonstrated in our previous monthly report. The wire diameter is
sufficiently small that the heat transfer is also quasi-steady, as also previously
documented.
On each side of the regenerator is a 0.0625-inch-thick stainless steel washer that is
bolted to the acrylic tube to hold the screens axially and to provide spacing between the
regenerator and the adjacent heat exchangers. Between the cooler exit plane and the
regenerator screen inlet plane is a clearance space. This is used for studying the effect of
this space on the velocity distribution of the flow emerging from each cooler tube. This
space will be of 190mm (7.5 inch) diameter and of an axial thickness that can be varied.
This gap is an important test parameter that will be studied. Several rings with an inside
diameter of 190 cm (7.5 inch) will be made to create different dimensions for that space.
The following relationship that equates a radial-flow area to the axial-flow area gives the
axial length of this space for our base-case design:
d 
d 2
4
where d is the diameter of cooler tubes. This gives a thickness of the rings,  , of d/4.
Multiple rings could be combined to vary this space in multiples of d/4. The minimum
distance is d/4. In our base case, the thickness of one ring plus one washer bolted to the
regenerator will give us the minimum axial space of ¼ inch, which allows a single hotwire with the probe stem diameter of 3/16 inch to go into the flow to take velocity
measurements within that plenum.
At the far end of the test section from the drive is the hot end isolation duct. It
consists of an acrylic tube with the same inside diameter as that of the regenerator holder
and a length of 2600 mm (102 inches). This length results in an Amplitude Ratio (AR) of
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0.47 to make the air oscillate completely within the heater duct. Many through-holes are
drilled in the wall of the duct, spaced along the axial direction. The air will jet into the
tube at  = 0º, 120º and 240º and will be drawn from the tube at  = 60º, 180º and 360º
through the holes, which will mix the air effectively. The holes are spaced axially at the
following distances from the heater end: 6, 12, 24, 36, 48, 66 and 84 inches.
Between the regenerator and the isolation duct are four electrical heating coils
employed to heat the air going back to the regenerator during that half period of the
oscillation cycle. The heating power is about 300 W, regulated by a variable transformer.
Each heating coil is of the same construction, having the heating wire stretched within its
frame with a spacing of ¼ inch, the same as that of the screens within the regenerator.
Each successive heating coil will be rotated 90 from its neighbor. This configuration
will attempt to reproduce the hydrodynamics of the screened assembly.
To prevent the heater from overheating under conditions of loss of flow (such as
popping of the slip clutch on the drive), we installed a temperature controller that will
shut down the power to the heating element when the air temperature is above a set
temperature.
2.2 Instrumentation
Measurements will be of unsteady temperature within the regenerator, including
the flow and the matrix material. The high porosity of the matrix allows thermocouple
wires to traverse between two screens. Such temperature measurements can be taken
more easily in our test section than in the real engine because of the larger scale and
longer period of flow oscillation. Such measurements will be conducted with fine-wire
thermocouples (about 0.003 inch diameter) that can follow the thermal transients. We
will measure turbulence quantities of the flow departing the regenerator on the heater side
to document the streamwise turbulent diffusion of momentum in that region. We will
also try to measure the turbulent heat transfer in that same region with a probe that can
measure the instantaneous velocities and temperature.
Finally, we will try to measure unsteady velocities in the regenerator region where
the flow diffuses upon entry to the regenerator from the cooler tubes.
2.2.1 Thermocouples
The E-type thermocouple with the diameter of 76  m (0.003 inch) was calibrated
and will be used for the temperature measurement. A second-order polynomial curve is
fitted to the measured temperature and thermocouple voltage data:
Temp=A0+A1*(Voltage)+A2*(Voltage)2
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2.2.2 Hot-Wire Anemometery
A hot-wire probe is calibrated in a wind tunnel where the velocity is adjusted by
changing the speed of a fan. A pitot tube is used to measure the velocity. A King’s law
relationship between the hot-wire voltage and the velocity is used for the calibration and
could be expressed as:
(Velocity)n=C0+C1*(Voltage)2
where 0.45-0.5 is the recommended value range for n. We are constructing an onsite
calibration facility for hot-wire sensors. For this, a straight pipe with length of at least 80
diameters will be set up underneath the rail of our test section to provide a fully
developed flow. The velocity and turbulence characteristics of fully developed pipe flow
are well known. Such a pipe will facilitate our calibration of other types of hot-wire
probes that might be used in our future experiments.
2.2.3 TDC and Shaft Encoders
TDC and shaft encoders are important to our work. TDC gives us a signal that
identifies the beginning point of one cycle. The shaft encoder generates 720 pulses per
cycle. Through counting the number of pulse since a cycle starts, we should be able to
know exactly the crank angle of the cycle at any given time. We can use this to trigger a
device for taking measurements, either velocity or temperature, or for ensemble
averaging of measurements.
2.3 Literature Review
A literature survey has just started. It begins with a NASA contractor’s report
(Simon and Seume, 1988). This report supplied the Remax-Va and AR-Remax maps of
heaters, coolers and regenerators of Stirling engines. Several valuable references on
regenerator performance of that time were listed. The work of Simon and Seume went on
to construct a facility that allowed operation of a heat exchanger tube over a wide range
of Remax and Va to study oscillatory flow in a pipe. It was found (Seume et al. 1992) that
in the region on the Remax-Va map over which transition is expected, transition is twice
per cycle. Regenerators were not addressed in the experimental component of that study.
Ohmi (1982) investigated transition to turbulence and evolving velocity
distributions in an oscillating pipe flow. Although the critical Reynolds number for the
transition to turbulent flow could not agree well with the other research results, it is clear
that at high Reynolds numbers, the flow is turbulent most of the time. The results of this
study are useful for thinking of the effects of flow oscillations but they do not apply
directly to regenerators.
Gedeon and Wood (1996) did many experiments on oscillatory flow within
various regenerator matrix-geometrics, including stainless steel woven wire screens and
metal felts. They derived friction factor and heat transfer correlations based upon their
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experimental data. Because there are no published data of flow through porous media
under oscillatory flow conditions, they compared their results to the steady flow results of
Kays and London(1984). They found no essential difference between steady and
oscillatory flow in the Valensi number range they investigated.
Unfortunately, most of investigations in our present literature focus on oscillatory
flow in a pipe. In order to understand further the performance of the Stirling engine,
attention must be paid to heat transfer and pressure drop in a regenerator matrix, such as
the effect of thermal and hydrodynamic entry length and the temperature and velocity
distributions within the matrix. We are particularly interested in the unsteady flows in the
entry regions of the regenerator.
2.4 Upcoming Activity
1.
We will start to take the flow temperature measurement within the regenerator
matrix in a base case by the middle of November.
2.
We will design and fabricate a straight pipe in order to get a fully developed flow
for hot-wire calibrations. (We intend to complete it by the end of November).
Cylinder
Flywheels
Counterweight
Figure 2 Oscillatory Flow Drive - UMN Test Rig
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3.0 CFD Modeling
Cleveland State University worked on CFD in their efforts to develop a multidimensional computer model of a portion of the regenerator matrix. Work on the
modeling effort continued in the following areas: 1) Multi-Cylinder (Cross-Rods Matrix)
Modeling, 2) UMN Test Rig CFD Simulation, and 3) Porous Media Modeling. Each one
of these sections is covered below:
3.1 Multi-Cylinder (Cross-Rods Matrix) Modeling
The same code used before, Fluent Commercial CFD code, was utilized to
simulate this case. The computational simulation (a continuation to earlier activities)
were done for 9 wires in cross flow arrangements, three in each row. Each wire is 1 mm
in diameter and 9.35 mm long. The transverse pitch = 4.675, while the wires touch each
other in the flow direction. This arrangement resulted in a porosity = 0.832.
Several CFD runs were made simulating this case as: a) Laminar Flow Model, b)
Turbulent Flow using High-Reynolds-Number k- model and c) Large Eddy Simulations
(LES) with High-Reynolds-Number k- as a subgrid model. This is done due to the
absence of sufficient information from the experimental data, describing the flow whether
it is laminar or turbulent. Also the current literature (to the authors knowledge) does not
provide any guidance on the type flow (laminar/turbulent) in these complex geomtries
based on the Reynolds number (calculated using the hydraulic diameter). Figure 3 shows
the mean friction factor versus the Reynolds number for: a) Experimental data from Kays
& London (1984), from Re= 4,000 to 100,000, b) Laminar flow results in the range of
Re=4,000 to 60,000, c) Turbulent flow results in the range of Re=20,000 to 50,000, c)
LES flow results at Re=40,000. The results indicates clearly that further computations are
still needed. These will follow the guidelines below:
I.
Since the data are good in the low Reynolds number range using the Laminar
Flow Model, more computations will be conducted at this end (Re=4,000) using
this model only.
II.
Similarly, since the data are good in the high Reynolds number range using the
Turbulent Flow Model, more computations will be conducted at this end
(Re=60,000) using the Turbulent Flow and/or LES Models.
III.
In each of the above cases the following issues will be examined:
IIIa. Change the grid number and distribution for more accurate and economical
CFD calculations.
IIIb. Change the discretization order (1st, 2nd or higher)
IIIc. Examine the Periodic Boundary Condition applied so for. This will require
expanding the computation domain to include all the nine wires (at this point
we are using a sub-cell to allow using the largest number of grids in our PC).
Also, this will require using a higher computer hardware than available at
CSU, e.g. using the Ohio Super Computer (OSC) facilities.
IIId. Apply unsteady flow conditions
IIIe. Conduct heat transfer calculations.
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3.2 UMN Test Rig CFD Simulation
CFD-ACE+ Commercial CFD code was utilized to simulate the UMN test rig.
Figure 4. shows the CFD simulation for a quadrant of the rig. Components shown in the
figure (left to right) are: Piston, Cylinder, Flow Distributor, Cooler, and Regenerator. The
figure shows the velocity contours/vectors in m/s for the flow in the axial direction and
at 21.6 Crank Angle degree while the piston moving from TDC to BDC. This figure is
one of several generated from the video animation for the test rig. The CFD animation
allows visualizing the global flow characteristics. Detailed examination of velocity
profiles at certain sections of the rig can be done and compared with the experimental
data (as soon as they become available).
3.3 Porous Media, Momentum Resistance Modeling
CFD-ACE+ Commercial CFD code has a feature for modeling porous media via
momentum resistance modeling. This modeling involves adding source terms to the
momentum equation. This type of modeling is currently under consideration.
4.0 CSU-SLRE Fabrication for Future Regenerator Testing
Figure 5. shows the Cleveland State University test rig known as CSUSLRE (Stirling Laboratory Research Engine). Figure 5a shows a photo of the test rig. It
is designed and fabricated as a horizontally-opposed, two piston, single-acting engine
with a split crankshaft drive mechanism. The engine is electric motor-driven and, thus,
will run as a cooler. A photo-electric sensor is used to sense top dead center and a shaft
angle encoder is used to trigger data acquisition. Figure 5b shows a test module where
different inserts can be introduced for testing the regenerator (or regenerator like)
matrices.
5.0 Submittal of a Research Proposal on Stirling Regenerator
A joint research proposal was submitted by CSU & AUC (American University in
Cairo) to U.S. - Egypt Joint Board on Scientific and Technology Cooperation. The
proposal is entitled "Experimental & Computational Investigations of Random-Fiber
Matrices for Stirling Engine Regenerator". The U.S. cooperator is Dr. Mounir Ibrahim
(CSU) and the Egyptian cooperator is Dr. Mohy Mansour (AUC). The proposal if funded
will provide:
1) Additional financial assistance ($25K for U.S. side & $25K for Egypt side) to
conduct further experiments on regenerator matrices using LDV (Laser Doppler
Velocimetry) techniques.
2) Additional manpower assistance: Dr. Mansour who is expert in LDV system and two
graduate students (one from the U.S. & one from Egypt).
3) Provide an opportunity to open a market (in Egypt) for the U.S. industry utilizing the
Solar Dish/ Converter Technology.
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0.4
0.35
Exp. Kays & London, 1984
CFD-Laminar
CFD-Turbulent
CFD-LES
f
0.3
0.25
0.2
0.15
0.1
1000
10000
100000
Reynolds Number (Based on Hydraulic Diameter)
Figure 3. Comparison of the Mean Friction factor (f),
Experiment, Kays & London (1984), CFD: Laminar, Turbulent & LES.
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Figure 4. CFD Simulation (Velocity contours/vectors in m/s, axial flow direction)
of the UMN test Rig near the Bottom Dead Center,
Components (left to right): Piston, Cylinder, Flow Distributor, Cooler, and Regenerator
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a) Photo of Test Rig
b) Test Module
Figure 5. CSU-SLRE: a) Photo of Test Rig, b) Test Module
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6.0 NASA Support
NASA Glenn’s (GRC’s) participation this quarter was as follows: (1) GRC
participated in several telecons to discuss regenerator research test rig design (both Roy
Tew and Jim Cairelli have participated in these telecons). (2) Documents and e-mails are
rather routinely exchanged between the various team members; these must be studied and
responded to. (3) GRC (Roy Tew) & Cleveland State (Mounir Ibrahim) participated in
the 36th Intersociety Energy Conversion Engineering Conference, cosponsored by the
ASME, IEEE, AIChE, ANS, SAE & AIAA, Savannah, Georgia, July 29-August 2, 2001.
Two papers were presented in the conference (Ibrahim et al. 2001& Tew and Ibrahim
2001). The two papers also, appeared as NASA/TMs. (4) Several trips have been made to
Cleveland State University (these are trips downtown by private automobile) to
participate in reviews of the computational fluid dynamics regenerator work that is being
done at Cleveland State.
7.0 References
Gedeon, D. and Wood, J.G. (1996): “Oscillating-Flow Regenerator Test Rig:
Hardware and Theory With Derived Correlations for Screens and Felts.” NASA
Contractor Report 198442.
Ibrahim, M. B., Tew, R.C., Jr, Zhang, Z., Gedeon, D. and Simon, T.W. " CFD
Modeling of Free-Piston Stirling Engines", NASA/TM-2001-211132 & IECEC2001CT-38.
Kays, W. M. and London, A.L. (1984) Compact Heat Exchanger.
Ohmi, M. and Iguchi, M. (1982): “Transition to Turbulence and Velocity Distribution
in an Oscillating Pipe Flow.” Bulletin of the JSME, Vol.25, No. 201, pp.365-371.
Seume, J., Friedman, G. and Simon, T.W. (1992): “ Fluid Mechanics Experiments in
Oscillating Flow Volume I- Report.” NASA Contractor Report 189127.
Simon, T.W. and Seume, J. (1988): “A Survey of Oscillating Flow in Stirling Engine
Heat Exchanger.” NASA Contractor Report 182108.
Tew, R.C., Jr. and Ibrahim, M.B., "" Study of Two-Dimensional Compressible NonAcoustic Modeling of Stirling Machine Type Components", NASA/TM-2001-211066
& IECEC2001-CT-27.
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