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The following article appeared in AIP Conference Proceedings and may be found at http://proceedings.aip.org/proceedings/confproceed/654.jsp

Advanced 35 W Free-Piston Stirling Engine

for Space Power Applications

J. Gary Wood and Neill Lane

Sunpower, Inc. 182 Mill Street Athens Ohio 45701

740-594-2221 ext. 509, wood@sunpower.com

Abstract. This paper presents the projected performance and overall design characteristics of a high efficiency, low mass

35 W free-piston Stirling engine design. Overall (engine plus linear alternator) thermodynamic performance greater than

50% of Carnot, with a specific power close to 100 W/kg appears to be a reasonable goal at this small power level.

Supporting test data and analysis results from exiting engines are presented. Design implications of high specific power

in relatively low power engines is presented and discussed.

INTRODUCTION

Recently there is a renewed interest in free-piston Stirling engine (FPSE) converters for use in space power

applications. The use of high efficiency FPSEs would allow a reduction in the radioisotope fuel by a factor of

roughly four compared to existing RTGs. Free-piston Stirling engines and cryocoolers are demonstrating long life

capability, and significant strides in performance of Stirling cycle machines have been made in the commercial

sector. The following presents the characteristics and performance of existing engines, and presents an advanced

design for a small engine designed for space power applications.

FPSE PERFORMANCE

The following plot presents the performance data available in the open literature for free-piston Stirling engines.

This plot also includes test data from the current Sunpower EG-1000 engine. For comparison with the free-piston

machines, performance of the Mod 2 automotive (kinematic) engine is also included. All machines use helium as the

working fluid, except for the Mod 2, which uses hydrogen. This plot presents engine efficiency only (not including

linear alternator efficiency) and is intended to show that engine efficiencies slightly exceeding 60 percent of Carnot

are reasonably achievable.

The Curzon-Ahlborn efficiency curve (Curzon 1975) shown on the plot is the maximum power efficiency of an

endoreversible heat engine system. This is not a limit to possible efficiency, but appears to be reasonable goal for

real machines. The most efficient free-piston engine to date is seen to be the Sunpower EG-1000 engine. This is a

prototype 1 kW machine designed for use in small domestic European cogeneration systems (Microgen 2001).

Although this machine is designed for low cost commercial production, the engine achieves 58 percent of Carnot

efficiency. With redesign it is expected that the machine would achieve greater than 60 percent of Carnot.

Calculations for data points in the figure are as follows:

• MTI Mod 2 (Ernst 1997) efficiency was calculated by reducing P-V efficiency by measured friction losses. The

peak efficiency upper bound occurs at 41% of maximum power point (lower bound).

• Sunpower EG-1000 efficiency was calculated by dividing P-V power by heat into the electrically-heated head.

P-V power was calculated from measured electric power output using a known alternator efficiency of 85%.

• MTI CPTC efficiency is the average of heat-to-water and heat-to-head methods of calculating efficiency. Heat-

to-head efficiency is 45% of Carnot efficiency and heat-to-water efficiency is about 54% of Carnot (Dhar

1997).

• MTI SPRE data was based on heat-to-water efficiency from the Dochat (1993) plot on page 92 of that report.

The maximum efficiency (upper point) occurs at 35 % of design power (lower point)

CP654, Space Technology and Applications International Forum--STAIF 2003 , edited by M.S. EL-Genk

• Stirling Technology Company (STC) 55 W test data is from NASA (2001). Alternator efficiency was assumed

to be 85%.

• Finally, the Sunpower 1979 model RE-1000 data point shown is from test point 602 in Schreiber (1986), which

represents approximately the highest measured efficiency point.

Note that for both the Sunpower EG 1000 and the STC 55 W engine-only efficiency has been calculated assuming

an 85% efficient alternator. The EG 1000 alternator efficiency is known. However if the efficiency of the STC

alternator is different than the assumed 85% the engine efficiency will be different than the values presented on the

plot.

0.8

0.7

Projected EG-1000

with improvements

MTI Mod 2

kinematic hydrogen (1987)

Curzon-Ahlborn Efficiency

(for reference only)

0.6

0.5

MTI SPRE (1990)

MTI CPTC (1993)

Sunpower EG-1000

(2000)

0.4

STC 55 W

(2000)

Sunpower RE-1000

(1979)

0.3

0.2

0.1

1.0

1.5

2.0

2.5

3.0

3.5

Temperature Ratio ( T heater / T rejector )

FIGURE 1. Comparison of Stirling Engine-Only Efficiencies (Curzon (1975); Dhar (1997); Dochat (1993); Ernst

(1997), NASA (2002); Schreiber (1986)).

FPSE LIFE AND RELIABILITY DEMONSTRATIONS

Much of the ongoing life and reliability testing of free piston machines is proprietary. Some information on the long

life capability of Stirling machines is publicly available and is summarized below.

A Sunpower M223 100 W Stirling-cycle refrigerator based on Sunpower’s patented gas bearing technology has been

on life test since 1995. This machine achieved 60,000 hours of maintenance free operation on September 9, 2002,

and the life test is continuing. A similar M223 flew on the Space Shuttle (MacDonald 1994). STC has a 10 W

Stirling engine, based on their flexure support technology, which achieved 66,000 degradation-free hours in 2002

(Qiu 2002).

SMALL ENGINE DESIGN

Under 2001 NASA SBIR Phase I funding, Sunpower optimized and designed the small FPSE converter shown in

the following figure. In this design, two dynamically opposed engines would operate on the heat supplied by a

single 250W General Purpose Heat Source (GPHS) module. The design is based on 120C reject temperature and

uses an 83 percent efficient alternator to minimize mass. The design is projected to produce 33 W for 115W of heat

input, and has a mass of only 305 gm.

Phase II of the SBIR that involves building and testing of the machine has just started. System optimization studies

are underway in conjunction with NASA-Glenn, which at present are indicating that the system optimizes at a lower

reject temperature and with a more efficient alternator. Reduction of the reject to 80C and the increase in alternator

efficiency to 90.9 percent will result in an converter of approximately 400 gm producing approximately 40 W with

the same 115 W heat input. The design presented here however is for the 33 W 305 gm machine. The final design

will likely fall between 33 W to 40 W depending of the final system optimization. For now we are referring to the

engine as an “Advanced 35 Watt Engine”.

FIGURE 2. Sunpower Advanced 35 W Free-Piston Engine, Shown With Ohio State Quarter.

The following table presents some details of the machine designed under the Phase I effort. The engine (without

alternator) is projected to have 60.8 percent of Carnot, which appears to be reasonable when considering the data

presented in Figure 1. Design considerations that influence Stirling engine efficiency when scaling to small sizes

will be discussed further below.

TABLE 1. Overall Performance and Design Parameters.

Parameter

Value

Electrical Power Output (W)

33.3

Hot End Metal Temperature (°C)

650

Rejector Metal Temperature (°C)

120

Projected Engine Efficiency (%)

34.9

Projected Engine % of Carnot Efficiency

60.8

Alternator Efficiency (%)

Projected Overall Efficiency (%)

29.0

Projected Overall % of Carnot Efficiency

50.5

Design Heat Input (W)

115

Total Mass (g)

305

Operating Temperature Ratio

2.35

Parameter

Value

Specific Power (W/kg)

109

Operating Frequency (hz)

100

Charge Pressure of helium (Mpa guage)

2.27

Piston Amplitude (mm)

4.0

Radial Running Clearances (microns)

The specific power projected for the design falls in the 100 W/kg range, which appears reasonable considering

Sunpower’s larger engine performance. The EG-1000 engine operates at 50 hertz and produces approximately

35 W/kg. Doubling the frequency of this machine would result in 70 W/kg. The existing engine also has flanges to

allow tear-down and is also designed to meet stringent pressure vessel codes. Removal of the flanges and thinning

the pressure vessel, as well as doubling the frequency, would put the EG-1000 in the 100 W/kg range. Thus specific

powers around 100 W/kg appear reasonable.

EFFECTS ON EFFICIENCY WHEN SCALING DOWN IN POWER

When designing the engine presented here, Sunpower performed numerous computer optimizations to arrive at the

best performance. Sunpower projects that the proposed engine will have higher efficiency than that of the EG1000,

and there are good reasons to expect higher efficiency in a small engine. The primary reasons are outlined in the

following

As engines are made smaller, the main difference is the increase in the ratio of the perimeter to cross sectional area

of the machine. Perimeter varies directly with diameter, whereas cross sectional area varies with the square of the

diameter. Power and associated heat flows into and out of the machine are proportional to the cross-sectional area of

the machine. If all the other lengths of the machine are held constant, then the heat transfer per unit of surface area

into and out of the machine decrease as the engine diameter is made smaller. Also as the diameter is decreased the

wall thickness of the vessel can be made proportionally thinner for the same pressure to maintain the same stress

level in the wall. Temperature drops through the wall therefore vary as the square of the diameter, with smaller

machines having much reduced temperature drops. This is the primary reason that large machines resort to tubular

or modular type heat exchangers, instead of simple monolithic heater heads where heat is transferred directly though

the wall of the main vessel.

The EG-1000 has a monolithic heater head, as does the small engine presented here. However the heater wall

temperature drop of the EG1000, due to its size, is 35 degrees C which in effect drops the temperature ratio of the

internal gas. This wall temperature drop reduces the design point effective temperature ratio from 2.55 to 2.44. This

results in an efficiency drop of more than 1 percentage point, or an efficiency penalty of more than 3 percent in

relative terms. Overall nominal thermal efficiency of this machine is 30 percent.

For the small engine presented here, the temperature drop through the wall is very much less significant than in the

high efficiency EG-1000 engine, which leads to higher efficiency. An additional factor that helps reduce this

temperature drop results from the increase in frequency of the small machine. Increasing frequency reduces the

required charge pressure of the machine, which in turn further reduces the required wall thickness of the vessel.

Because of the large total reductions in through the wall temperature drops, additional advantages are achieved

because the lengths of the internal acceptor and rejector can be reduced. These components can then be optimized

with length being very much independent to wall temperature drop effects. Typically the reduced lengths reduce the

internal heat exchanger surface areas, which in turn reduce thermal hysteresis losses arising from the pressure swing

of the machine.

The most effective and useful part of the internal acceptor and rejector of an engine are those areas adjacent to the

expansion space and compression space, respectively. These flow entry regions see the largest wall-to-gas

temperature difference and additionally have the highest rates of heat transfer because the flow is developing in

these regions. Typically these heat exchangers want to optimize at rather short lengths if wall temperature drops are

not significant. Small engines thus allow much freer optimization of the heat exchangers.

One might suspect that seal losses would become significant in small sizes, because of the increase in the ratio of

perimeter to area of the machine. However this turns out not to be a serious problem. Assuming that the piston

stroke and seal length remain fixed, it is instructional to look at the ratio of seal power loss to engine power. Seal

power loss varies as the diameter times the cube of the clearance gap, while engine power scales with the square of

the piston diameter. To maintain the seal loss at a fixed percentage of the piston power thus requires that the gap

vary as the diameter to the 1/3 power. Again advantage can be made in this area by increasing frequency while

reducing pressure to maintain engine power. Leakage power varies as the square of the pressure, thus reducing the

pressure has a significant effect on the leakage.

EFFICIENCY, MASS, AND REJECTION TEMPERATURE TRADEOFFS

Rejection temperature has a significant effect on the FPSE converter efficiency and power. Alternator efficiency is

largely a function of its mass. The design presented here has a 120C reject and utilizes an 83 percent efficient

alternator.

The following graph shows the relationship of output power at different machine masses (primarily driven by the

alternator mass) as a function of reject temperatures. Note that in this plot that the heat input is fixed so that

electrical power as presented is directly proportional to the conversion efficiency.

Power 40C

Power 80C

Power 120 C

270 280 290 300 310 320 330 340 350 360 370 380 390 400

Engine/Alternator Mass (gm)

Input Heat Fixed at 115 watts, engines optimized at each temperature

(Acceptor at 650 C)

FIGURE 3. Electrical Power Versus Converter Mass at Different Rejector Temperatures.

Data presented in the above plot is currently being input by NASA-Glenn into a total system model to determine the

optimal rejection temperature as well as converter mass. Early indications from that effort are that the system

optimizes near the 80C reject point, and at a mass in the vicinity of 400 grams. As seen in the above plot, the engine

alternator combination at that point will produce 40 W for a mass of 400 gm thus resulting in a specific power of

100 W/kg.

SUMMARY

This paper presents the design of an advanced small 35 Watt free-piston Stirling engine with integral linear

alternator for space power applications. Notable features of the design are high thermal to electric energy

conversion efficiencies (exceeding 50 percent of Carnot) and high specific power (~100 W/kg). The predictions in

efficiency and power are reasonable considering recently achieved gains in performance of the larger Sunpower EG-

1000 engine. As discussed in the paper, there are significant efficiency advantages when scaling Stirling engines

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