” 

DOEINASAI4 105-4 

NASA CR-I 82248 

NASA Lewis Stirling Engine 

Computer Code Evaluation 

Timothy J. Sullivan 

Sverdrup Technology, Inc. 

NASA Lewis Research Center Group 

January 1989 

N 89-24741 

Unclas 

(NASA-CR-182248) NASA LEVIS STIRLING ENGINE 

COHPUTER CODE EVALUATION final Report 

ISverdrup Technology) 43 p 

G3/44 0217214 

Prepared for 

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION 

Lewis Research Center 

Under Contract NAS3-24105 

for 

U.S. DEPARTMENT OF ENERGY 

Conservation and Renewable Energy 

Office of Vehicle and Engine R&D 
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DOElNASN4105-4 

NASA CR-182248 

NASA Lewis Stirling Engine 

Computer Code Evaluation 

Timothy J. Sullivan 

Sverdrup Technology, Inc. 

NASA Lewis Research Center Group 

January 1989 

Prepared for 

National Aeronautics and Space Administration 

Lewis Research Center 

Cleveland, Ohio 441 35 

Under Contract NAS3-24105 

for 

Conservation and Renewable Energy 

Office of Vehicle and Engine R&D 

Washington, D.C. 20545 

Under Interagency Agreement DE-AI01 -85CE50112 

b U.S. DEPARTMENT OF ENERGY 
NASA LEWIS STIRLING ENGINE COMPUTER CODE EVALUATION 

Veh 

anc 

In suDDort of th 

Timothy J. Sullivan 

Sverdrup Technology, Inc. 

NASA Lewis Research Center Group 

Cleveland, Ohio 44135 

SUMMARY 

U.S. Department of Energy's Stirling E gine Highway 

icle Systems program, the NASA Lewis Stirling engine nodal-analysis performe code was evaluated by comparing code predictions without engine-specific 

calibration factors to Stirling engine test data. Stirling engine test data 

was obtained from the GPU-3, P-40, and RE-1000 Stirling engines, over a wide 

range of operating conditions. The code evaluation process included: an 

investigation of prediction error trends for changes in the operating conditions, an investigation into the cause of the power prediction errors, and an 

evaluation of the possible computer model shortcomings. 

The error in predicting power output was -11 percent for the P-40 and 

12 percent for the RE-1000 at design conditions and 16 percent for the GPU-3 

at near-design conditions (2000 rpm engine speed versus 3000 rpm at design). 

The efficiency and heat rate predictions showed better agreement with engine 

test data than did the power predictions. Concerning all data points, the 

GPU-3 prediction errors were much greater than those for the P-40 or RE-1000. 

The GPU-3 power error significantly increased with decreasing power level and 

when using helium working fluid (compared to hydrogen). 

inaccuracy in predicting the pressure phase angle. 

prediction error was mainly a result of inaccuracy in predicting the pressure 

amplitude. 

pressure amplitude and phasing was difficult because of relatively large errors 

in measuring the working-fluid pressure phase angle. 

0 

co 

m 

d 

I 

w The error in predicting the GPU-3 brake power was mainly a result of 

The RE-1000 indicated power 

The analysis of P-40 performance prediction errors with respect to 

Analysis into the GPU-3 pressure phase angle prediction error suggested 

that improvements to the hysteresis loss model could have a significant effect 

on overall Stirling engine performance predictions. Improvements in predicting other loss mechanisms such as gas leakage by the pistons, effects of oscillating flow on pressure drops and heat transfer, and appendix gap losses will 

undoubtedly improve performance predictions as well. 

INTRODUCTION 

This study was done in support of the U.S. Department of Energy (DOE) 

Stirling Engine Highway Vehicle Systems program. The NASA Lewis Research Center, through interagency agreement DE-AI01-85CE50112 with DOE, is responsible 

for management of the project under the program direction of the DOE Office of 

Transportation Systems, Heat Engine Propulsion Division. 

This report deals with the evaluation of the NASA Lewis Stirling engine 

nodal-analysis performance code. This study was completed by comparing code 

predictions to Stirling engine test data. The objectives for this evaluation 
were (1) to determine the extent of agreement of the computer model with a wide 

range of Stirling engine test data from a variety of engines, using no enginespecific calibration factors and (2) to identify shortcomings of the model. 

The Stirling engine computer model, described in reference 1, is a nodalanalysis, time marching simulation. This thermodynamic performance code is 

designed for simulating engine performance under steady periodic operating 

conditions. 

The simulation of Stirling engine performance is difficult because common 

simplifying assumptions can't be made when dealing with the working fluid 

dynamics. The fluid flow is unsteady, compressible, mainly turbulent, and 

multidimensional, with varying properties. With the present state of the art 

on modeling these complex flows, the complete solution to the governing equations would require a large amount of computer time (on a "supercomputer"). 

The alternative is to make simplifying assumptions and test the validity of 

those assumptions by comparing the computer model predictions with test data. 

In the past, efforts have been made to validate the NASA Lewis Stirling 

engine computer model. Tew (ref. 2) compared and calibrated single-cylinder 

Stirling engine computer model predictions with test results. Tew found that 

code predictions could be improved by increasing the pressure drop prediction. 

Allen (ref. 3) compared test results of a 40-kW Stirling engine to computer 

model predictions and speculated that the over predictions in brake power were 

caused by piston-seal leakage not being accounted for in the computer model. 

Free-piston Stirling engine computer model predictions from the NASA Lewis 

code were compared to test data by Tew (ref. 4). The performance prediction 

error was decreased by mainly increasing the predicted pressure drop and 

decreasing the displacer gas-spring leakage factor. Geng (ref. 5) calibrated 

a slightly different version of the free-piston Stirling engine computer 

model. Large increases in the expansion and compression-space heat transfer 

coefficients were found to improve performance predictions. 

The code evaluation process reported here used engine test data that 

represented a wide range of operating conditions, for different types of Stirling engines. All engine test data was collected at NASA Lewis. The Stirling 

engines used for this study were the GPU-3, P-40, and RE-1000. The GPU-3 is a 

6-kW single-cylinder, rhombic-drive Stirling engine, described in reference 6. 

The P-40 is a 40-kW four-cylinder double-acting Stirling engine, described in 

reference 7. The RE-1000 is a 1-kW single-cylinder free-piston Stirling 

engine, described in reference 8. A variable-stroke Stirling engine, the 

Advenco, was initially included in this study; however, because of the uncertainty in the mechanical loss, reasonable comparisons with the test data could 

no be completed. 

Predictions were then made with the computer model using operating conditions identical to those used in the test cell. Predicted and actual engine 

performance were then compared and analyzed. The evaluation of the Stirling 

engine computer model included: an investigation of prediction error trends 

for changes in operating conditions, a summary of Stirling engine prediction 

errors, and investigation into the cause of the power.predict,ion errors, and 

finally an evaluation of the possible computer model "shortcomings". 

I 

2 
PROCEDURE AND ANALYSIS 

Description of Stirling Engine Computer Model 

The NASA Lewis Stirling engine computer model is a nodal-analysis, time 

marching simulation. The nodes, or control volumes, are used to simplify the 

solution of the governing equations, for each time step. Reference I describes 

the code, which was initially designed for predicting steady periodic performance for a kinematic Stirling engine. 

The NASA Stirling engine computer model has been modified by both Mechanical Technology Incorporated (ref. 9) and Tew, of NASA, (ref. 4) to model the 

free-piston Stirling engine. The thermodynamics of the free-piston Stirling 

engine are similar to that for the kinematic Stirling engine. The free-piston 

Stirling engine does not couple the displacer and piston mechanically; rather, 

the motion of the displacer and piston is governed by working fluid and gasspring pressure forces. The displacer and piston gas springs and gas leakage 

paths are accounted for in the free-piston Stirling engine simulation. 

The free-piston version of the NASA Lewis Stirling engine computer model 

was improved by Geng (ref. 5). Notable improvements were made in the cooler 

heat exchanger model, gas leakage model, and displacer gas-spring model. 

Sullivan (the author of this report) also made various improvements to the kinematic version of the computer model. Major improvements, over that presented 

in reference 4, were made in the regenerator heat exchanger model and the overall flow-path pressure drop model. Improvements to the overall flow-path pressure drop model are described in reference 10. 

Prior to evaluating the computer model, engine-specific calibration factors that were used to force code predictions to agree with engine test data 

were removed. The removal of these calibration factors was necessary for an 

unbiased evaluation of the computer model. 

A list of possible computer model shortcomings was made prior to the comparisons. These possible shortcomings are as follows: 

(1) Auxiliary and mechanical loss uncertainty 

(2) Inadequate or no gas leakage loss model 

(3) Primitive appendix gap (displacer-cylinder gap) loss model 

(4) Inadequate hysteresis (cylinder heat transfer) loss model 

(5) Use of steady flow friction factor and heat transfer coeff 

(6) Simplified treatment of the momentum equation and energy e 

(7) Finite number of nodes and increments per cycle 

relations (as well as 1-D fluid flow approximation) 

The importance of these computer model shortcomings was readdressed 

lyzing results from this study. 

Experimental Stirling Engine Testing 

cient coruation 

when anaThe Ground Power Unit (GPU) Stirling engine was built by the General 

Motors Research Laboratory; it is referred to as the GPU-3 since it was meant 

to deliver 3 kW of electrical energy from the unit as a whole. The GPU-3 is a 

6-kW. single-cylinder, rhombic-drive Stirling engine, described in reference 6 

and pictured in figure 1. The GPU-3 test data used in this study included a 

3 
range of average heater-tube gas temperatures, mean working-space gas pressures, and engine speeds with both helium and hydrogen working fluids. Engine 

testing details are given in references 6 and 11. GPU-3 design operating conditions are given in table I. 

The P-40 Stirling engine was built by United Stirling of Sweden. The 

P-40 is a 40-kW, double-acting, four-cylinder Stirling engine, described in 

reference 7 and shown in figure 2. The P-40 test data used in this study was 

for a range of mean working-space gas pressure and engine speeds. The working 

fluid was hydrogen and the average heater-tube wall temperature was held fixed. 

further P-40 testing details are in reference 3. Engine design operating conditions are shown in table I. 

The RE-1000 freeRE-1000 is a single cy 

described in reference 

lected using a dashpot 

gas pressures, average 

temperatures. Details 

fluid was helium. REThe GPU-3, P-40, 

iston Stirling engine was built by Sunpower, Inc. The 

inder Stirling engine capable fo 1-kW output and is 

8 and shown in figure 3. The engine test data was colload, for a range of piston strokes, mean working-space 

heater-tube wall temperatures, and average coolant inlet 

of the engine testing are in reference 12. The working 

000 design operating conditions are shown in table I. 

nd RE-1000 Stirling engine dimensions are listed in 

tables A.1, A.11, A.111, and A.IV of appendix A. The engine test data that 

were used in this study are shown in tables 6.1, B.11, B.111 of appendix B. 

All engine test data were taken at NASA Lewis. 

Stirling Engine Performance Predictions 

Necessary inputs to the computer model are defined in table 11. Space 

and time increment specifications for the computer model were chosen to result 

in a predicted error in the energy balance of roughly 1 percent or less. Code 

options used for this study included: working fluid was modeling using real 

properties (instead of ideal); average heater-tube wall temperature was input 

for the P-40 and RE-1000, and heater-tube gas temperature was input for the 

GPU-3. Also the RE-1000 piston and displacer motions were input to the computer model. 

The Stirling engine operating conditions that were used in the computer 

model matched those for the experimental engine testing. The mean gas pressure 

input to the model was the experimental mean compression-space gas pressure. 

Various heater-tube wall (or heater-tube gas) temperature mean compressionspace gas pressure. Various heater-tube wall (or heater-tube gas) temperature 

measurements were spatially averaged and input into the computer model. Also 

averaged were various engine component temperatures, such as cylinder wall temDerature (used for conduction calculations). 

The GPU-3 averaged heater-tube gas temperature was the average temperature 

measurement from three thermocouples, each located inside a separate heater 

tube. Two heater-tube wall temperatures were input for the P-40 simulation: 

one to represent the heater-tubes in the back row and one to represent the 

heater-tubes in the front row. These two-heater-tube wall temperatures were 

based on a total of twelve thermocouple readings with the thermocouples located 

thermocouples were mounted on the coolest surface (circumferentially) of the 

, 

I at various locations along the outside heater-tube wall. The P-40 heater-tube 

4 
heater tube so corrections had to be made to these readings to obtain an average (circumferentially) tube temperature. These corrections depended on the 

fuel flow rate and were based on data from United Stirling of Sweden. The 

RE-1000 average heater-tube wall temperature was an average of twelve thermocouple readings. 

Indicated power was used for the RE-1000 prediction-experimental comparison; brake power was used for the GPU-3 and P-40 comparison. The GPU-3 and 

P-40 beat inputs were defined as the energy input from the fuel minus the 

burner losses (the burner losses were calculated from energy balances). The 

RE-1000 heater tubes were electrical conductors; the heat input was defined as 

the voltage drop across the heater tubes times the current. 

Throughout this report the term "pressure amplitude" was redefined to be 

the difference between the maximum gas pressure and minimum gas pressure. Normally the gas pressure amplitude is defined as maximum minus the mean gas 

pressure. 

Use of the Pressure-Wave Curve-Fit (PWCF) Code 

Prediction errors for the power output and heat input depend on the gaspressure-wave amplitude (pressure amplitude) error, the gas-pressure-wave/ 

piston-position phase angle (pressure phase angle) error, and the mechanical 

loss error (when considering the brake power prediction error). The power output and heat input prediction errors also depend on any error in simulating 

the engine volume variations, but the simulated volume variations used for this 

study were considered perfectly accurate. 

It was desired to determine which pressure parameter prediction error 

(amplitude or phase angle) was responsible for the power output and heat input 

prediction errors; attention was also given to the effect of a mechanical loss 

error. Due to the nature of the NASA Lewis Stirling engine computer simulation, it is unable to perform this type of investigation. Thus, the PWCF code 

was written for this purpose. 

tor and a detailed description of the PWCF code can be found in appendix C. 

PWCF stands for Pressure-Wave Curve-Fit IntegraThe following procedure was used to investigate Stirling engine perforrnance sensitivity to prediction errors in the pressure parameters: 

(1) Input experimental pressure parameters (both amplitude and phase 

angle) to the PWCF code and calculate performance. 

(2) Calculate performance again, now substituting either the predicted 

pressure amplitude or the predicted phase angle. 

(3) Compare the two calculated performances to determine the effect of the 

difference between the predicted and the measured pressure amplitude or phase 

angle. 

Note from appendix C that the calculations from the PWCF code for brake 

power agree well with predictions from the NASA Lewis Stirling engine computer 

simulation. However, agreement for the heat input was not acceptable and thus, 

the PWCF code could not be used to analyze errors in heat input. 

5 
I RESULTS AND DISCUSSION 

This section covers the following: investigation of trends in prediction 

errors for each Stirling engine, summary of Stirling engine prediction errors, 

investigation into the effects of pressure amplitude and phasing on the power 

output prediction errors, and evaluation of the computer model shortcomings. 

Throughout this report the prediction "error" refers to an error based on percentages and is defined as the predicted value minus the experimental value 

divided by the experimental value. 

considered all operating conditions for each Stirling engine and are accompanied with representative figures showing the trends. 

The prediction error trends discussed below 

Comparisons for the GPU-3 Stirling Engine 

The following GPU-3 operating conditions were varied: engine speed, mean 

compression-space gas pressure, average heater-tube gas temperature, and working fluid. Design operating conditions are shown in table I. The coolant 

inlet temperature was held constant at 20 OC for all GPU-3 data points used in 

this study. Brake power versus engine speed, for a fixed heater-tube gas temperature and mean pressure, is shown in figure 4. Brake power is seen to be 

overpredicted. The error in predicting brake power increases with engine 

speed and is larger when the working fluid is helium. Figure 5 shows brake 

power versus engine speed, for various mean pressures. The working fluid is 

helium and the heater-tube gas temperature is held fixed. The brake power prediction error (remember this is a percentage error) decreases with increasing 

mean pressure; similar results occurred when using hydrogen working fluid. 

Brake power variation with engine speed and heater-tube gas temperature is 

shown in figure 6. 

power prediction error is considered insignificant. 

The effect of the heater-tube gas temperature on the brake 

Heat input versus engine speed for hydrogen and helium working fluids is 

shown in figure 7. The heater-tube gas temperature and mean pressure are held 

fixed. Heat input is over predicted for both gases. Figure 8 shows heat 

input versus engine speed, for a variation in mean pressure for helium working 

fluid. The error in predicting heat input is relatively insensitive to changes 

in the engine speed and mean pressure. Figure 9 shows heat input for variations in the engine speed and heater-tube gas temperature. The mean pressure 

is held fixed and the working fluid is hydrogen; the results are similar when 

using helium working fluid. Notice the prediction error increases as the 

neater-tube gas temperature rises. 

The compression-space pressure amplitude versus engine speed, for various 

heater-tube gas temperatures and for hydrogen working fluid, is shown in figure 10; remember the pressure amplitude is defined as the maximum pressure 

minus the minimum pressure. Notice that the error increases with the heatertube gas temperature. The prediction error proved to be insensitive to mean 

pressure. These trends are about the same for the expansion-space gas pressure 

amplitude as well as when using helium working fluid. The absolute prediction 

error was greater for helium working fluid than for hydrogen. Although the 

pressure amplitude error is insensitive to mean pressure and relatively insensitive to engine speed, the GPU-3 brake power error depends on pressure and 

increases with engine speed; this suggests that the GPU-3 brake power error is 

not a result of inaccuracy in the prediction of the pressure amplitude. 
Comparisons for the P-40 Stirling Engine 

Variations in the P-40 engine operating conditions were accomplished by 

changing the mean gas pressure and the engine speed. The working fluid was 

hydrogen for all P-40 tests. P-40 design operating conditions are shown in 

table I. Figure 11 shows brake power versus engine speed, for variations in 

mean pressure. Brake power is underpredicted with the error increasing 

slightly with increasing engine speed and decreasing slightly with increasing 

mean pressure; these variations in the P-40 brake power prediction error are 

significantly smaller than those for the GPU-3. Allen's comparison of code 

predictions to engine test data (ref. 3) showed that P-40 brake power was 

slightly overpredicted. Prior to this study, the dead volumes that were input 

to the computer model were updated based on recent engine measurements. This 

improvement caused the change in P-40 predictions relative to Allen's 

comparison. 

Heat input versus engine speed, for various mean pressures, is shown in 

figure 12. Heat input agreement is very good with no apparent trends in the 

prediction error (percentage error). Figure 13 shows the compression-space 

pressure amplitude versus engine speed, for various mean pressures. The agreement again is very good with respect to both engine speed and mean pressure. 

Comparisons for the RE-1000 Stirling Engine 

The following RE-1000 operating conditions were varied: piston stroke, 

mean gas pressure, average heater wall temperature, and coolant inlet temperature; while one of these parameters was varied, the other three were held at 

design conditions. Engine design operating conditions are shown in table I. 

The working fluid is helium. Measurement error bands are shown on the figures. 

Indicated power versus piston stroke is shown in figure 14. Indicated 

power is over predicted with the prediction error increasing with piston 

stroke. Figures 15 and 16 show indicated power versus mean pressure and heater 

wall temperature, respectively. The indicated power prediction error decreases 

with mean pressure and increases with heater wall temperature. Indicated power 

versus coolant inlet temperature is shown in figure 17. The error decreases 

with increasing coolant inlet tenperature. These variations in the RE-1000 

indicated power prediction error are significantly smaller than those for the 

GPU-3. 

Heat input versus piston stroke is shown in figure 18. Figures 19 and 20 

show heat input versus mean pressure and heater wall temperature, respectively. 

Heat input versus coolant inlet temperature is shown in figure 21. Considering 

all data points, the error in predicting heat input can be considered insensitive to variations in all four parameters. 

Compression-space pressure amplitude versus heater wall temperature is 

shown in figure 22. The error increases with increasing heater wall temperature. Considering a variation in all the independent parameters, a variation 

in the heater wall temperature had the biggest effect on the prediction error 

in the compression-space arnplitude. 

7 
Summary of Stirling Engine Prediction Errors 

Eng ne performance prediction errors for design (or near-design) and low 

power conditions, are shown in table 111. Two low power conditions are shown 

for the RE-1000, at low piston stroke and at low mean gas pressure. For each 

engine, the errors for the low power condition shown are typical of other low 

power condition errors, not shown on the table. 

The GPU-3 power error is the largest, when comparing errors of all 

engines. The GPU-3 error is larger with helium working fluid than with hydrogen and also when decreasing the power level. The efficiency prediction generally shows better agreement to engine test data than does the power prediction. 

This is due to the value of the heat input prediction error. The heat input 

and heat out of the engine errors are generally lower than the power prediction 

errors; they are generally larger for the GPU-3 engine, when compared to the 

other engines. When compared to the power errors, these errors in heat input 

and heat out are relatively insensitive to power level. 

The errors in gas temperature were based on time-averaged gas temperatures. The predicted gas temperatures for the GPU-3 and RE-1000 engines compare well with the test data; the prediction errors for the P-40 are larger. 

For each engine, the errors in the expansion and compression-space pressure amplitudes are lower than the power errors. The GPU-3 pressure amplitude 

errors are significantly lower than the power errors; this seems to suggest 

that the error in predicting the pressure amplitude is not responsible for the 

GPU-3 power prediction error. The P-40 pressure amplitudes are over predicted. 

The maximum and minimum P-40 gas pressures, used to determine the pressure 

amplitudes, were measured (with large strain gage transducers) in the P-40 vent 

and pressurization lines, respectively; these pressure amplitude measurements 

are considered sufficiently accurate. The fact that the P-40 pressure amplitudes are over predicted and the P-40 brake power is under predicted suggests 

an inconsistency, which will be discussed later in this report. 

The absolute error in the compression-space pressure phase angle is seen 

to be relatively large for the GPU-3 and negligible for the RE-1000. The 

GPU-3 phase angle absolute errors are approximate because of uncertainty in 

the measurement of the actual engine pressure phase angle. The heat exchanger 

pressure-drop amplitude was measured on the RE-1000 engine; the pressure-drop 

amplitude prediction errors are large. 

Pressure Parameters Effects on Power Prediction Errors 

The investigation into the power prediction errors was accomplished by 

using the PWCF code, described in the PROCEDURE AND ANALYSIS section and in 

appendix C. Prior to using the PWCF code for the GPU-3 and P-40 engines, the 

accuracy of the mechanical loss model input to the code had to be considered. 

The GPU-3 brake power prediction error may have been caused by a large underprediction in the mechanical loss. The mechanical loss used for the GPU-3 

mechanical loss was considered to be the sum of the heat rejected to the oil 

and the buffer-space cooling water (ref. 11). An attempt was also made to 

measure the mechanical loss more directly by doing "motoring tests" (ref. 11). 

I predictions was derived from experimental data for the energy balance. The 

I 8 
a 

The mechan 

upperbound 

cal loss derived from the motoring test was considered to be an 

for the true GPU-3 mechanical loss. 

Figure 23 shows the effect that this motoring test data has on the brake 

power prediction compared to the baseline prediction (using the energy balance 

mechanical loss). Analysis of all GPU-3 data showed that, when using the 

motoring test mechanical loss for hydrogen working fluid, the prediction error 

decreased by an average of 18 percent at low engine speeds and 60 percent at 

high engine speeds. When helium working fluid was used, the use of the motoring test mechanical loss resulted in the prediction error increasing by an 

average of 11 percent at low speeds and decreasing by an average of 30 percent 

at high engine speeds. 

Using the PWCF code, figure 24 shows the effect on brake power due to the 

prediction error in the pressure amplitude or pressure phase angle, for various 

operating conditions. 

marily accounted for by a phase angle prediction error. 

seen for hydrogen working fluid. Tew (ref. 2) found that GPU-3 performance 

prediction accuracy could be greatly improved by increasing the regenerator 

pressure drop by a factor of four for helium working fluid. 

ing the predicted GPU-3 regenerator pressure drop, which accounts for the 

majority of the flow path pressure drop, resulted in a negligible change in 

the pressure phase angle. Therefore, inaccuracy in the regenerator pressuredrop prediction (or entire working space pressure-drop prediction) does not 

account for the poor predictions in the GPU-3 brake power as it doesn't improve 

the agreement for the pressure phase angle. 

The error in predicting the GPU-3 brake power was priSimilar results were 

However, increasThe use of measured P-40 pressure parameters in the PWCF code produced a 

value for indicated power that was below the measured value of brake power. 

The P-40 pressure phase angles were measured using miniature, dynamic, strain 

gage pressure transducers. Because the P-40 pressure amplitude is considered 

to be accurately measured, the measured P-40 pressure phase angles must have 

been in error. Using the PWCF code, the pressure phase angle measurement 

error was estimated equal to -7O. Two main problems plagued the measurement 

of the P-40 gas pressure phase angle: uncertainty of the crank angle and sensitivity errors of the miniature, dynamic, strain gage pressure transducers. 

Allen's (ref. 3) speculation that the inaccuracy in the predicted P-40 brake 

power was caused by not modeling the piston-seal leakage was based on the 

dynamic pressure measurement and thus, this speculation may be incorrect. 

pressure amplitude measurements (based on measurements of maximum and minimum 

pressures) may lead to a better understanding of the P-40 brake power prediction error. The P-40 brake power prediction error increased slightly with 

increasing engine speed, yet the pressure amplitude error was insensitive to 

variations in engine speed. This seems to suggest that the brake power error 

is attributed to an error in predicting the pressure phase angle. 

An examination of error trends based on the power measurements and the 

Using the results of the PWCF code, figure 25 shows the effect of the 

RE-1000 indicated power due to the error in the pressure amplitude or pressure 

phase angle, for various operating conditions. The error in predicting the 

indicated power was primarily accounted for by the pressure amplitude prediction error. 

9 
Evaluation of Computer Model Shortcomings 

Sensitivity to computer model precision - Computer model precision was 

varied to determine its effect on the Stirling engine performance prediction 

error. Computer model parameters were altered to obtain a "high precision" 

computer model. Then these predictions were compared to predictions from the 

"standard" computer model, for all three engines at design conditions. Alterations to the code were as follows: number of heat exchanger control volumes, 

number of time increments per cycle, and the number of engine cycles were 

increased to their asymptotic limit. The number of heat exchanger control 

volumes was increased from 3 to 25 (per heat exchanger). The number of increments per cycle was increased from 360 to 900 and the number of engine cycles 

was increased from 30 to 100. Also, "two passes" through the calculations 

were made, which approximate 

Increasing the computer 

"high" precision resulted in 

slight decrease in heat inpu 

puter model precision caused 

increase; therefore, increas 

for the observed performance 

y coupled the' momentum and-energy equations. 

model precision from "standard" precision to 

a slight increase in the predicted power and a 

and heat-out predictions. The increase of comthe GPU-3 and RE-1000 power prediction errors to 

ng the computer model precision does not account 

prediction errors. 

Parameters that effect the pressure phase angle - The largest power prediction error occurred for the GPU-3 and was caused primarily by inaccuracy in 

predicting the pressure phase angle. For the GPU-3, the maximum gas pressure 

occurred at approximately 300°, but is predicted at 312O. Using the Equation 

of State and assuming that gas pressure is a function of time only: 

dP = -P @! V+ lx(Ti dMi) + lx(Mi dTi) 

where P is gas pressure, V is engine volume, R is gas constant, Ti is gas 

temperature in ith control volume in engine, and Mi is mass of gas in 

ith control volume. 

When the pressure wave reaches a maximum or minimum, dP = 0; at these 

points, 

The two sides of this equation are plotted in figure 26; the curves shown were 

calculated with the computer model for the GPU-3 Stirling engine at the indicated conditions. For these operating conditions, the computer model predicted 

dP = 0 (maximum gas pressure) at 312O. Notice that the curves cross at approximately 312O; this agreement with the crank angle at which the maximum pressure 

occurs offers confidence in the above "pressure variation" equation. In order 

for the predicted pressure phase angle to agree with the measured value, the 

curves should cross at approximately 300O. If the 

I curve were to rise, P would have to increase by a factor of approximately 3 

(assuming that the volumes and volume variations are correct); the magnitude 

of P could not be in error by a factor of 3. Thus, the 

10 
terms will have to decrease by a factor of 3. 

From an "order of magnitude" analysis, 

simp1 ifies to 

R v (Te dMe + Tc dMc + Mh dTh) 

where subscripts e denotes expansion-space, c denotes compression-space, and 

h denotes hot side of the engine. Thus, the error in predicting the GPU-3 

pressure phase angle is primarily due to an error in predicting dMe, dMc, or 

dTh. 

Relationship of dMe, dMc, and dTh to computer model shortcomings - 

Smith (ref. 13) suggested that the temperature difference between the gas and 

the wall in the cylinder and the heat transfer rate (hysteresis loss) should 

be out of phase. In the NASA Lewis Stirling engine computer model, the gaswall temperature difference and the heat transfer rate are modeled with no 

phase difference. If the predicted cylinder heat transfer was not modeled in 

phase with the gas-wall temperature difference, the points of maximum and minimum heat transfer would shift to different crank angles. This shift in the 

cylinder heat transfer wave would have an effect on the phasing of the cylinder gas temperature wave resulting in a variation in dTh; this could cause 

the two curves of figure 26 to intersect at a point near a crank angle of 300O. 

Improving the accuracy of the hysteresis loss model may improve the GPU-3 pressure phase angle prediction, which in turn will improve the GPU-3 performance 

prediction accuracy. 

Geng (ref. 5) found that increasing the heat transfer coefficient in the 

expansion and compression spaces improved RE-1000 performance predictions. 

The expansion-space heat transfer coefficient was increased by a factor of 230; 

the compression-space heat transfer coefficient was increased by a factor of 

50. These variations resulted in a reduction in the gas temperature amplitude, 

which reduced the predicted pressure amplitude (while the pressure phase angle 

changed by only 0.2O). 

error in predicting the indicated power to be reduced from 12 to 3 percent. In 

this author's study, the pressure amplitude error was found to be mainly 

responsible for the error in predicting the RE-1000 indicated power. 

The reduction of the pressure amplitude caused the 

This author increased the predicted heat transfer coefficients for the 

GPU-3 by the same amount as Geng had. The effect on predicted performance was 

different than that observed by Geng. For the GPU-3, the phase angle of the 

gas temperature changed (the temperature amplitude was insensitive), resulting 

in a variation in dTh. The error in predicting the pressure phase angle was 

consequently reduced, which resulted in the brake power prediction error being 

reduced from 16 to 12 percent. Earlier, this investigation showed that the 

primary reason for the GPU-3 brake power error was inaccuracy in predicting the 

11 
pressure phase angle. Note that increasing the cylinder heat transfer coefficient improved the prediction accuracy for the appropriate pressure parameter 

for each engine (pressure amplitude for the RE-1000, pressure phase angle for 

the GPU-31, which in turn decreased the error in predicting power. This seems 

to support the speculation that inaccuracy in the hysteresis loss model 

accounts for at least part of the Stirling engine prediction error. 

Another possible error was inaccuracy in predicting dMe and dMc. Gas 

leakage past the displacer and piston seals would relate to the prediction of 

dMe and dM,. This gas leakage is grossly accounted for in the GPU-3 model 

and not accounted for in either the P-40 or RE-1000 models. Therefore, the 

gas leakage model also needs to be addressed, but it is not known what effect 

this improvement will have on overall performance predictions. 

Computer model shortcomings revisited - The list of possible computer 

model shortcomings was introduced in the PROCEDURE AND ANALYSIS section. From 

this investigation, we know: 

(1) Auxiliary and mechanical loss - Uncertainty does not account for the 

majority of the Stirling engine performance prediction error with the possible 

exception of the high-speed points for the GPU-3. 

(2) Gas leakage loss model - Inaccuracy in the gas leakage loss model may 

have a significant effect on the Stirling engine performance prediction error. 

(3) Appendix gap loss model - Significance of possible inaccuracy was not 

evaluated and is still unknown. 

(4) Hysteresis loss model - Inaccuracy in the hysteresis loss model may 

have a significant effect on the Stirling engine performance prediction error. 

(5) Friction factor and heat transfer coefficient correlations - Significance of possible inaccuracy was not evaluated and is still unknown (referring 

to steady flow and 1-D assumptions). 

(6) Momentum and energy equations - Numerical treatment of these equations 

does not account for the majority of the Stirling engine performance prediction 

error for the engines considered. 

(7) Number of nodes and increments per cycle - Approximations due to using 

the standard number of nodes and time increments per cycle does not result in a 

significant error in predicting Stirling engine performance. 

SUMMARY OF RESULTS 

The major results from the evaluation of the NASA Lewis Stirling engine 

computer simulation are presented below. Computer model predictions were compared to Stirling engine test data for the GPU-3, P-40, and RE-1000 Stirling 

engines. 

1. The error in predicting power at design* conditions was 16 percent for 

, the GPU-3, -11 percent for the P-40, and 12 percent for the RE-1000. The GPU-3 

~ 

*Near-design conditions for the GPU-3. 

I 12 
error significantly increased with decreasing power level or when using helium 

as the working fluid instead of hydrogen. 

2. The efficiency, heat input, and heat out of the engine predictions 

generally showed better agreement with engine test data than did the power 

prediction. 

3. The percentage errors in the GPU-3 and P-40 brake power predictions 

increased with increasing engine speed and decreasing mean gas pressure; the 

brake power prediction error was attributed to an inaccuracy in predicting the 

pressure phase angle. 

4. The percentage error in the RE-1000 indicated power prediction was 

attributed to an error in predicting the pressure amplitude. 

5. The average gas temperatures had negligible prediction errors for the 

GPU-3 and RE-1000; the errors in predicting the average gas temperature were 

larger for the P-40. 

6. The computer model precision in terms of the number of nodes, cycles, 

and time increments per cycle was not a significant factor in the difference 

between predictions and test data. 

7. For the GPU-3, increasing the cylinder heat transfer coefficients 

resulted mainly in a correction to the pressure phase angle prediction. For 

the RE-1000, the same change resulted in a correction to the pressure amplitude 

prediction. The increased accuracy in predicting the GPU-3 pressure phase 

angle and the RE-1000 pressure amplitude reduced the power prediction errors 

for both engines. 

CONCLUSIONS 

The main objective of this study was to compare predictions from the NASA 

Lewis Stirling engine performance code to Stirling engine test data, for a 

variety of Stirling engines using no engine-specific calibration factors. 

Then, analyze these differences to try to determine shortcomings in the computer model. 

The engines used for this study were the GPU-3, P-40, and RE-1000. The 

error in predicting the GPU-3 brake power was a result of the inaccuracy in 

predicting the working fluid's pressure phase angle; the pressure phase angle 

is the pressure phasing with respect to the piston position. The error in predicting the RE-1000 indicated power was determined to be a result of inaccuracy 

in predicting the gas pressure amplitude. 

In doing this study, a relatively large measurement error was detected in 

the P-40 pressure phase angle. The pressure phase angle could not be used in 

the analysis and thus an accurate understanding of the P-40 prediction discrepancy was impossible. The required level of measurement accuracy needs to be 

carefully considered when measuring performance parameters, such as the working 

fluid's pressure amplitude and phase angle, needed for comparisons of predictions to test data. 

13 
Errors in predicting Stirling engine performance could be caused by unsatisfactory computer model precision, which relates to approximations made to 

simplify the solution of the governing conservation equations. 

mations included finite difference approximations to these equations and the 

decoupling of the momentum and energy equations in the NASA Lewis computer 

model. When considering these approximations, this study concluded that the 

treatment of these governing equations does not account for the inaccuracy 

seen in predicting engine performance. 

than that for the P-40 or RE-1000 Stirling engines and, therefore, work went 

into understanding the pressure phase angle prediction error. The accuracy in 

predicting the GPU-3 pressure phase angle was found to be closely related to 

the accuracy in predicting the working fluid mass variation in the expansion 

space and compression space and the accuracy in predicting the gas temperature 

variation for the "hot-side" of the Stirling engine. 

These approxiGenerally, the percentage error in predicting the GPU-3 power was larger 

Modeling of the piston and displacer mass leakage past the seals could 

have an impact on the mass variation prediction; currently this effect is 

accounted for crudely or not at all (depending on the specific engine) in the 

Stirling engine computer code. Also, past work suggests that improvements to 

the hysteresis (cylinder heat transfer) model would alter the "hot-side" gas 

temperature variation prediction. 

The cylinder hysteresis loss was increased for the GPU-3 and RE-1000 by 

increasing the heat transfer coefficients in the expansion and compression 

spaces. As a result, accuracy improved in power predictions for both engines 

because of decreases in the GPU-3 pressure phase angle error and the RE-1000 

pressure amplitude error. Notice that an improvement was made in the prediction of the pressure parameter that was mainly responsible for the respective 

engine's power prediction error. This sensitivity study supports the suggestion that an improvement in the hysteresis loss model could significantly benefit stirling engine performance predictions. One recommendation of this study 

is to improve the modeling of this hysteresis loss. 

Much work remains to be done to understand the true physics of the Stirling engine. The different loss mechanisms need to be investigated in greater 

depth and their effort on engine performance understood. These loss mechanisms include: cylinder hysteresis loss, gas leakage loss, effect of oscillating flow on pressure drop and heat transfer, appendix gap loss, and velocity 

and temperature maldistributions. Currently, a significant "loss understanding" effort is being made in the area of oscillating flow effects. 

;tudies are beginning on multidimensional analysis of the gas flow path. 

Also, 

14 
APPENDIX A 

ENGINE DIMENSIONS 

Tables A.1, A.11, A.111, and A.IV give GPU-3, P-40, and RE-1000 Stirling 

engine dimensions and other operating parameters. 
TABLE A.1 . GPU-3 ENGINE DIMENSIONS AND PARAMETERS (FROM REF . 6) ’ Miscellaneous: 

Number of cylinders ............... Typeof engine .................. Type of drive .................. Type of shaft seals ............... Cylinder bore with liner. cm (in.) ........ Cylinder bore above liner (top of displacer seal at 

of liner at displacer top.dead.center) . cm (in.) 

Stroke. cm (in.) ................. Displacement maxim m change in total working-space 

volume). cms (in.’) .............. Piston-rod diameter. cm (in.) .......... Displacer-rod diameter. cm (in.) ......... Displacer diameter. cm (in.) ........... Displacer wall thickness. cm (in.) ........ Expansion-space clearance. cm (in.) ....... Compression-space clearance. cm (in.) ...... 

........ 

........ 

........ 

........ 

........ 

top 

........ 

........ 

........ 

........ 

........ 

........ 

....... 

........ 

........ 

...... 1 

. . Displacer 

... Rhombic 

. 6.99 (2.75) 

. 7.01 (2.76) 

. 3.15 (1.24) 

119.6 (7.30) 

2.22 (0.875) 

0.953 (0.375) 

. 6.96 (2.74) 

0.159 (0.0625) 

0.163 (0.064) 

0.030 (0.012) 

... Sliding 

Cooler: 

Tube length. cm (in.) ....................... 4.60 (1.81) 

Tube inside diameter. cm (in.) ................. 0.108 (0.0425) 

Tube outside diameter. cm (in.) ................ 0.159 (0.0625) 

Number of tubes per cooler ......................... 39 

Heat-transfer length. cm (in.) ................... 3.56 (1.40) 

Number of tubes per cylinder ........................ 312 

Heater: 

Mean tube length. cm (in.) 

Regenerator side ........................ 12.90 (5.08) 

Cylinder side ......................... 11.63 (4.58) 

Heat-transfer length. cm (in.) ................... 7.77 (3.06) 

Tube inside diameter. cm (in.) .................. 0.302 (0.119) 

Tube outside diameter. cm (in.) ................. 0.483 (0.190) 

Number of tubes per cylinder (consider tubes to 

regenerator and cylinder separately) ................... 80 

Regenerators: 

Length (inside). cm (in.) . Diameter (inside). cm (in.) 

Number per cylinder .... Matrix: 

Wire-cloth material ... Cloth mesh per 2.5 cm (1 in 

Wire diameter . cm (in.) . Number of layers ..... Filler factor. percent . . 

.................... 2.26 (0.89) 

.................... 2.26 (0.89) 

......................... 8 

................ 304 stainless steel 

) .................... 200x200 

................. 0.00406 (0.0016) 

........................ 308 

....................... 30.3 

Drive: 

Connecting-rod length. cm (in.) .................. 4.60 (1.81) 

Crank radius. cm (in.) ...................... 1.38 (0.543) 

Eccentricity. cm (in.) ....................... 2.08 (0.82) 

Insulation coverc: 

Cross-sectional area. cm2 (in.2) .................. 6.45 (1.00) 

Length between thermocouples. cm (in.) ............... 1.27 (0.50) 

16 
TABLE A.11 . GPU-3 ENGINE DEAD VOLUMES (FROM REF . 6) 

[AII volumes in cm3 (in.’).] 

Expansion space clearance volume: 

Clearance around displacer ......................... 3.34 (0.204) 

Clearance above displacer ......................... 7.41 (0.452) 

Volume from end of heater tubes into cylinder ............... 1.74 10.1061 

Insulated portion of tubes leading to expansion space ........... 9.68 (0.591) 

Heated portion fo tubes .......................... 47.46 (2.896) 

Insulated portion of tubes leading to regenerator ............. 13.29 (0.811) 

Additional volume in four tubes used for instrumentation .......... 2.74 (0.167) 

Volume in header .............................. 7.67 (0.468) 

Total .... 12.49 (0.762) 

Heater dead volume: 

Total .... 80.84 (4.933) 

Regenerator dead volume: 

Volume between regenerators and heater tubes ................ 8.75 (0.534) 

Volume within matrix ............................ 50.60 (3.088) 

Volume between regenerators and cooler tubes ................ 6.16 l0.37hl 

Total .... 65.51 (3.998) 

Volume in cooler tubes ........................... 13.14 (0.802) 

Volume in connecting passages from cooler tubes to 

Cooler dead volume: 

Compressi on-space clearance volume: 

compression space ............................ 12.57 (0.767) 

Clearance around power piston ....................... 7.36 (0.449) 

Clearance between displacer and power piston ................ 10.077) 

Total .... 21.19 (1.293) 

Total dead volume ............................. 193.2 (1 1.79) 

Minimum live volume (power piston at TOC) ................ 39.2 (2.391 

Calculated minimum total working-space volume .............. 232.4 (14.18) 

17 
Mi scel laneous : 

Number of cylinders ...................... 4 (square 4 arrangement) 

Overall dimensions . cm (in.) ............... 7 8 . 5 ~ 6 5 . 5 ~ 5 8 . 0 ( 3 0 . 9 ~ 2 5 . 8 ~ 2 2 . 8 ) 

Heater type .............................. Involute tabular 

Number ot heater tubes ................................ 18 

Heater tube material ........................... Multimet N-155 

1 Heater tube outside didmeter. on (in.) .................. 0.450 (0.1772) 1 Heater tube Inside diameter. cm (in.) ................... 0.30 (0.1181) 

i Icni (in.) ................................. 25.18 (9.913) 

' Regenerators: 1 Number of regenerators ................................. 2 

Reyenerator material ................. 304 stainless steel wire ine5h qauz t. 

Regenerator natrix diameter. cm (in.) ................... 5.70 (2.244) 

Regenerdtor lnatrix length. cm (in.) .................... 3.90 (1.535) 

Reqenerdtor matrix wire diameter . cin (in.) ............... 0.0050 (0.001968) i Reg~nerator [natrix porosity ............................ 0.58 

' Coolers: 

! 

1 

Heater tube leiqth . I:m (in.) ........................ 28.07 (11.05) 

Ettective heater tube length for heat transter . 

Number of coolers ................................... 2 

Number of cooler tubes per cooler .......................... 192 

Cooler tube outside diameter . cm (in.) .................. 0.150 (0.05906) 

Cooler tube inside diameter. cm (in.) .................. 0.10 (0.03937) 

Cooler tube length. cm (in.) ........................ 8.000 (3.150) 

Effective cooler tube length. cm (in.) ................... 6.721 (2.646) 

Effective c001.ng wa er tlow area through 

1.ooler-s . emz (in.') ........................... 20.10 (3.116) 

Connecting ducts: 

Average heater-tube manifold inside diameter. cm (in.) ........... 0.50 (0.1968) 

Average expansion spacelheater-tube manifold 

flow path length. cm (in.) ........................ 1.20 (0.4724) 

Average heater-tube/regenerator mani fold flow 

path length. cm (in.) .......................... 1.30 (0.5118) 

Coo:er/comprescion-space connecting duct 

Cooler/coiiiprrssion-spdce connecting duct 

lenath . cm (in.) ............................. 3.40 (3.307) 

Cooler casing inside diameter. cm (in.) .................. 4.80 (1.890) 

diameter . cm (in.) ............................ 1.40 (0.5512) 

Piston stroke. cm (in.) .......................... 4.000 (1.575) 

Piston diameter. cm (in.) ......................... 5.406 (2.128) 

I Engine dead volumes: 

I Exparsion-space clearance volume. cm3 ( in.3) ......... j Efipansion-\pace/heater_conne ting duct volume. cm3 (in.3) . . ' 1 tieater dead volume. cmJ (in: 5 ) 

Heater/regenerators connecti g duc s volume. cm3 (in.3j .... 

Qegenerator/cooler conn cting ducts volume. cm3 (in.3) 5' . ~ Coolers dead volume. cm (in.3) ............... 

' Yot appendix yap volume. cm3_( in . ............. Cold appendix gas volume. cmJ (in.3) 

............... 

~ Qeqenerators dead volume. cm9 ( in.$) ........... 

~ Compression-space clearance volumtj. cm? (in . 8 ........ 

.... 

~oolers/compression-space connecting d cts v lume. em3 ( in.3) 

............. 

.... 

...... 

...... 

...... 

...... 

...... 

...... 

...... 

..... 

1.810 (0.1104) 

4.409 (0.2690) 

. 35.71 (2.179) 

. 16.66 (1.016) 

. 115.5 (7.045) 

5.099 (0.3111) 

. 24.13 (1.472) 

. 49.87 (3.043) 

7.270 (0.4435) 

7.220 (0.4405) 

0.7220 (0.04405) 

ORIGINAL PAGE IS 

OF POOR QUALITY 
TABLE A.IV . DESCRIPTION OF THE GEOMETRY OF THE RE-1000 (FROM REF . 8) 

Mi scel 1 aneous : 

Number of cy1 inders .................................. 1 

Housing weight. kg (lb) ............................ 416 (917) 

Type ............................... Free-piston with dashpot 

Design working fluid ................................ Helium 

Design frequency. Hz .................................. 30 

Design pressure. MPa ................................ 7.0 

Bounce space volume. cm3 ...................... 20. 500 (1250) 

Design power. W ................................... 1000 

Cylinder bore. cm (in.) .......................... 5.722 (2.2527) 

Maximum displacer 1 stroke. cm (in.). ..................... 4.01 (1.579) 

Displacer 1 length. cm (in.) ......................... 15.21 (5.99) 

Maximum displacer 2 stroke. cm (in.) ..................... 5.18 (2.039) 

Displacer 2 length. cm (in.) ......................... 14.05 (5.53) 

Maximum power piston stroke. cm (in.) .................... 4.35 (1.713) 

Description ......................... 135 rectangular gas passages 

Passage width. cm (in.) .......................... 0.0508 (0.020) 

Passage depth. cm (in.) .......................... 0.376 (0.148) 

Length. cm (i ) ............................. 7.92(3.118) 

Wetted per’meter cm (in.) ......................... 115.2 (45.354) 

20.42 ( 1 . 246) 

Design displacer phase angle. deg ........................... 45 

Cool er : 

Flow area. cm”(in:2j ............................ 2.58 (0.400) 

Volume. cmJ ( in . 3, ............................. 

Heater: 

Description ................................... Tabu1 ar 

Tube material ................................ Inconel 718 

Number of tubes .................................... 34 

Tube length. cm (in.) ........................... 18.34 (7.220) 

Tube inside diameter. mm (in.) ....................... 2.362 (0.093) 

Tube outside diameter. mm (in.) ....................... 3.175 (0.125) 

Design maximum wall temperature. OC (OF) .................... 650 (1202) 

Length containing wire mesh. cm (in.) ................... 6.446 (2.538) 

Outside diameter. cm (in.) .......................... 7.18 (2.825) 

Inside diameter. cm (in.) .......................... 6.07 (2.391) 

Inner wall thickness. cm (in.) ........................ 0.13 (0.05) 

Matrix material ............................... 304SS Metex 

Wire diameter . mm (in.) ......................... 0.0889 (0.0035) 

Porosity. regenerator 1. percent ........................... 75.9 

Porosity. regenerator 2. percent ........................... 81.2 

Weight of matrix. regenerator 1. g (lb) .................... 139 (0.31) 

Weight of matrix. regenerator 2. g (lb) .................... 108 (0.24) 

Standard power piston oscillating mass. kg (lb) ............... 5.97 (13.17) 

Power piston diameter. cm (in.) ...................... 5.718 (2.2514) 

Displacer 1 mass. kg (lb) ......................... 0.426 (0.939) 

Displacer I diameter . cm (in.) ........................ 5.b7 (2.232) 

Displacer 1 rod diameter. cm (in.) ..................... 1.663 (0.6548) 

Displacer 1 bore. cm (in.) ......................... 1.666 (0.6560) 

Displacer 2 mass. kg (lb) ......................... 0.381 (0.840) 

Displacer 2 diameter. cm (in.) ........................ 5.67 (2.232) 

Oisplacer Z rod diameter. cm (in.) ..................... 1.806 (0.7110) 

Displacer 2 bore. cm (in.) ......................... 1.808 (0.7118) 

Regenera tor: 

Pistons: 

Light power piston oscillating mass. kg (lb) ................. 3.48 (7.67) 

19 
TABLE A.IV - Concluded. 

Dead volumes: 

................. 9.83 (0.60) 

3i- 1.64 (0.10) 

Di spl acer l/cyl i nder annular gap, 

8.36 (0.5 1 ) 

Expansion-space o hea er tube junction, cmii;;n.j) ............. 3.80 (0.23) 

Di s p l a c e r 2 / c y l i nder annular gap, ................ Expansion-space instrumentation .............. 

Heater tubes, cm5 (in.S) ........................... '27.4 (1.67) 

Heater tube to regenerator ple um ju ction, cm' (in.3) 

Regenerator hot end plenum. cm9 (in.3) ........ Regenerator plenum ring, cm3 (in. ) .... Instrumentation p rts ( eater/regenerator), cm3 iii.3)' 

Regenerator 1, cm9 ( in .9) .............. Regenerator 2. cm3 ( in .3) 

Regenerator cold end plenum, cm3 (in.3) . . .. ~nstrument tion gorts (regenerator/cooler), cm3 iin.3) 

-3.:: Cooler, cm3 (in. ) 

Cooler plenum at the compression space, ~m~~iin. 

Compression-space nstru entation ports, cm (in.') . Cy1 i nder ports, cmj ( in .?) .............. Piston/spider clearance, cm3 ........ Annular ring around the spide cm (in.3) ...... 

Power piston center port, cm (in.3) ......... 

.............. 

........... 

Displacer Lvor core, 03 (in,'; .......... 

............ 

............ 

............ 

............ 

............ 

............ 

............ 

............ 

............ 

............ 

............ 

............ 

............ 

............ 

............ 

............ 

5.90 (0.36) 

4.10 (0.25) 

0.83 (0.05) 

1.64 (0.10) 

56.1 (3.42) 

69.1 (3.67) 

4.23 (0.26) 

3.41 (0.21) 

20.42 (1.25) 

7.15 (0.44) 

3.15 (0.19) 

1.21 (0.07) 

18.0 (1.21) 

3.82 (0.23) 

2.95 (0.18) 

5.90 (0.36) 

Ma teri a1 s : 

Heater head 

Regenerator outer cy1 inder .............. Expansion-space dome ................. Regenerator inner cy1 i nder wall ........... Oi spl acer ....................... Cooler ......................... Cy1 i nder 

Power piston ..................... 

Displacer ...................... 

Standard power piston ................. 

Light power piston ................... 

....... 316 stainless steel 

....... 316 stainless steel ....... 316 stainless steel 

....... 321 stainless steel 

............ 6061-T6 A1 

...... 6016-T6 A1 with chrome 

oxide coating 

..... 304 stainless steel with 

oxide coating 

6061-T6 A1 body with Xylan coating 

and mild steel mass 

6061-T6 A1 body with Xylan coating 

and A1 mass 

Diametral clearances: 

Displacer 1 rod/rod cylinder, mm (in.) ................... 0.030 (0.0012) 

Displacer 1 body/displacer cylinder, mm (in.) ............... 0.381 (0.015) 

Displacer 2 rod/rod cylinder, mm (in.) ................... 0.020 (0.0008) 

Displacer 2 body/displacer cylinder, mm (in.) ............... 0.381 (0.015) 

Power piston/piston cylinder, inm (in.) ................... 0.033 (0.001) 

Displacer gas spring: 

No. 1 design mean volume, cm3 (in.3) ..................... 31.79 (1.94) 

No. 2 design mean volume, cm3 (in.3) ..................... 18.8 (1.147) 

No. 1 rod diameter. cm (in.) ....................... 1.663 (0.655) 

No. 2 rod diameter, cm (in.) ........................ 1.806 (0.711) 

Center ports: 

Power piston port location (distance from inward 

Displacer 1 (distance from expansion space limit to 

Disoiacer 2 (distance from expansion space limit to 

l;mit to center port opening position ), cm (in.) ............. 2.05 (0.81) 

position where the center port opens), cm (in.) .............. 1.90 (0.75) 

position where the center port opens), cm (in.) .............. 2.64 (1.04) 

Center port diameter (power piston), mm (in.) ................ 1.1 (0.042) 

1 Center port diameter (displacers), mm (in.) ................. 1.0 (0.040) 

I 

I 1 

20 
APPENDIX 6 

ENGINE TEST DATA 

Tables 6.1, B.11, and 6.111 give the GPU-3, P-40, and RE-1000 Stirling 

engine test data used for this study computer code evaluation. All the engine 

test data were taken at NASA Lewis Research Center. 

21 
TABLE B.1 - 

2.13 

2.04 

1.33 

2.71 

2.39 

1.50 

4.47 

2.93 

2.30 

5.24 

4.16 

Mean 

pressure, 

MPa 

18.5 11.52 

24.4 8.39 

22.0 6.04 

24.2 11.23 

26.7 8.97 

24.3 6.19 

28.3 15.79 

29.1 10.07 

30.8 7.48 

33.3 15.72 

34.5 12.08 

Engine 

speed, 

rPm 

I 

Average 

heatertube 

gas temperature, 

"C 

HE 1 -41A 

H3 1 -43A 

HE 1 -45A 

HE3-41B 

HE3-436 

HE3-45A 

HE3-6 1 A 

HE3-62A 

HE3-64B 

HE3-81A 

HE3-82A 

Brake 

power, 

kW 

2.86 3516 593 

2.84 2506 580 

2.84 1501 574 

2.90 3494 698 

2.86 2520 70 1 

2.86 1515 70 1 

4.28 3499 68 3 

4.23 3009 698 

4.20 1995 706 

5.61 3512 685 

5.63 3019 690 

Brake 

thermal 

efficiency, 

percent 

Heat 

input, 

kW 

Heat 

to 

cooler 

cool ant , kW 

Cool ant 

AT 

across 

cooler , 

"C 

Run 

identity 

2 

Hydrogen 

2.86 

2.84 

2.85 

2.86 

2.85 

2.86 

4.23 

4.25 

4.25 

6.98 

7.02 

3495 

2499 

1492 

3519 

2499 

1471 

3516 

2002 

1501 

1999 

1504 

7.4 

5.3 

3.4 

7.3 

5.4 

3.6 

10.5 

6.0 

4.7 

9.2 

7.1 

580 

584 

58 1 

68 1 

669 

679 

68 7 

652 

659 

663 

659 

H 1-438 

H 1-456 

H3-41A 

H3-43A 

H3-45A 

H3-61A 

H25-648 

H25-656 

tl25- 1 04A 

H25-105A 

11.5 

6.6 

5.2 

9.8 

7.6 

He1 i um 

0.26 

0.94 

0.92 

0.95 

1.53 

1.25 

2.03 

2.58 

2.40 

3.42 

3.77 

2.7 

12.8 

17.6 

8.8 

19.0 

10.0 

12.6 

18.3 

23.4 

18.1 

20.8 

9.59 

7.34 

5.24 

10.81 

8.07 

6.24 

16.17 

14.11 

10.26 

18.92 

18.09 

8.1 

5.6 

3.5 

8.3 

5.9 

3.8 

9.1 

6.3 

4.0 

9.0 

6.4 

4.1 

11.4 

9.9 

6.5 

14.4 

12.4 

13.5 

11.9 

8.4 

18.5 

16.3 

TABLE 6.11 - 

Run 

identity 

Mean 

pressure, 

MPa 

Engine 

speed, 

rPm 

Brake 

power, 

kW 

Brake 

thermal 

efficiency, 

percent 

Heat 

input, 

kW 

Heat 

to 

cooler 

coolant, 

kW 

Cool ant 

AT 

across 

cooler, 

"C 

2.0 

2.3 

2.1 

2.5 

3.6 

4.0 

4.3 

4.5 

5.7 

5.6 

5.7 

6.7 

388 

395 

396 

387 

393 

397 

386 

394 

389 

39 1 

392 

390 

5.12 

5.11 

5.13 

5.10 

10.12 

10.08 

10.13 

10.15 

15.13 

15.08 

15.09 

15.17 

947 

2000 

3002 

3918 

997 

2000 

3003 

400 1 

1413 

2002 

2999 

4000 

4.78 

9.47 

13.11 

15.02 

9.95 

19.18 

26.14 

31.29 

21.70 

27.79 

37.48 

43.21 

28.3 

32.0 

32.7 

28.7 

33.6 

35.7 

33.4 

31.9 

36.9 

36.4 

34.3 

30.3 

11.3 

19.0 

25.6 

35.1 

18.9 

33.4 

50.5 

64.4 

36.2 

47.3 

69.8 

96.7 

58.8 

76.4 

109.3 

142.5 ~~ 

aAmpl i tude - peak-to-peak values. 

22 
~~ ______

 

GPU-3 TEST DATA 

557 

569 

553 

643 

61 7 

634 

660 

638 

623 

655 

637 

Expansionspace 

heater 

duct gas 

temperature, 

working fluid 

72 

61 

52 

70 

62 

53 

86 

68 

63 

80 

72 

compression- space space 

ture, 

1.78 

1.82 

1.80 

1.82 

1.82 

1.84 

2.63 

2.70 

2.70 

4.42 

4.43 

OC I 

300 

300 

3 300 

300 

300 

300 

300 

304 

306 

300 

303 

1.96 300 

1.90 300 

1.88 300 

2.00 300 

1.94 300 

1.76 305 

2.46 300 

2.87 300 

2.85 300 

3.66 300 

3.68 300 

working fluid 

30 0 

295 

300 

300 

300 

305 

300 

300 

300 

300 

300 

572 

548 

55 1 

677 

668 

674 

67 7 

677 

672 

67 1 

674 

Coolercompressionspace duct 

gas temperature 

OC 

98 

82 

66 

95 

80 

70 

117 

106 

87 

123 

113 

Maxi mum 

compressionspace 

pressure, 

MPa 

1.84 

1.76 

1.74 

1.84 

1.82 

1.72 

2.73 

2.54 

2.49 

4.22 

4.23 

Minimum 

compressionspace 

pressure, 

MPa 

Expansionspace 

pressure 

phase 

angl e, b 

deg 

Compression- Compressionspace space 

pressure pressure 

ratio ampl i tude, a 

MPa 

6.27 

6.26 

6.30 

~ 6.30 

~ 12.53 

12.50 

12.57 

12.49 

18.86 

18.79 

18.65 

18.73 

1.74 

1.69 

1.80 

1.82 

1.86 

1.88 

2.77 

2.77 

2.81 

3.53 

3.64 

Compressionspace 

pressure 

b phase 

angl e, 

deg 

300 

300 

300 

300 

300 

300 

300 

300 

303 

300 

304 

Energy 

balance 

error, 

percent 4 

6.2 

2.5 

8.1 

1.3 

2.5 

5.0 

-1.3 

2.8 

-1.5 

1.4 

0.6 

1 

' 0.4 

-1 .o 

1.8 

1.9 

-1.6 

5.3 

4.8 

1 .o 

2.5 

-1.6 

1.5 

P-40 TEST DATA 

Expansionspace heater 

duct gas 

temperature , "C 

657 

659 

654 

646 

660 

639 

628 

613 

640 

623 

597 

575 

57 

57 

57 

59 

59 

60 

62 

63 

62 

63 

65 

69 

3.89 

3.86 

3.85 

3.83 

7.73 

7.69 

7.71 

7.68 

11.55 

11.50 

11.45 

11.51 

1.60 

1.61 

1.62 

1.63 

1.61 

1.62 

1.62 

1.62 

1.63 

1.63 

1.62 

1.62 

2.38 

2.41 

2.44 

2.47 

4.81 

4.82 

4.87 

4.81 

7.32 

7.29 

7.19 

7.22 

23 
TABLE B.111 - RE-1000 

Mean 

pressure, 

M Pa 

Run 

i denti ty 

Piston 

stroke, 

Clll 

1006 

1010 

1012 

1017 

1024 

1030 

1070 

1079 

1121 

1200 

7.04 

7.03 

7.05 

7.06 

7.05 

7.06 

5.53 

4.01 

7.07 

7.03 

1.80 

2.60 

3.00 

2.60 

2.60 

2.60 

2.61 

2.61 

2.61 

2.60 

Average 

heater 

wall 

temperature, 

"C 

600 

599 

599 

550 

500 

450 

599 

599 

600 

600 

Cool i ng 

water 

inlet 

temperature, 

"C 

25 

25 

25 

25 

25 

25 

25 

25 

40 

55 

Engine 

f reHZ quency . 

30.2 

30.1 

30.2 

30.2 

30.2 

30.2 

26.9 

23.0 

30.3 

30.2 

Ind i cated 

power, 

W 

570 

939 

1100 

846 

765 

643 

759 

520 

907 

837 

Indicated 

efficiency , percent 

24.4 

25.8 

24.6 

24.7 

22.8 

20.4 

26.4 

24.7 

25.2 

24.0 

Heat 

input, 

W 

2338 

3643 

4467 

3424 

3348 

3159 

2879 

2109 

3599 

3493 

Expansionspace gas 

cool er t emoe racool ant , W 

1892 

2736 

3265 

2713 

268 1 

2595 

2137 

1242 

2532 

2108 

ture, 

"C 

568 

558 

552 

51 1 

462 

415 

555 

553 

557 

558 ~ 

aAmpl i tude - peak-to-peak values. 

bPhase angle - angle between the maximum gas pressure and minimum working space volume. 

cP - gas pressure. 

24 
TEST DATA 

Regeneratorcooler gas 

temperature, 

"C 

Regeneratorheater gas 

temperature, 

"C 

Compression- Compressionspace gas space 

temperature, pressure 

"C amp1 i tude.a 

564 

548 

540 

507 

46 1 

416 

555 

560 

559 

559 

91 

91 

93 

92 

90 

89 

80 

70 

109 

123 

40 

56 

65 

53 

54 

55 

49 

42 

64 

75 

kPa I 

792 

1147 

1344 

1166 

1176 

1181 

910 

645 

1171 

1161 

Compressionspace 

pressure 

b phase 

angl e, 

deg 

-19.8 

-15.7 

-14.0 

-14.1 

-12.5 

-10.3 

-18.0 

-19.7 

-14.9 

-13.7 

Cooler 

WP,C 

kPa 

3 

7 

10 

7 

7 

7 

4 

3 

6 

6 

Regenerator 

kPa 

WP,C 

40 

60 

60 

60 

60 

60 

40 

30 

60 

50 

Di spl acer 

kPa 

WP.C 

70 

100 

100 

100 

100 

100 

70 

50 

100 

90 

25 
APPENDIX C 

DESCRIPTION OF THE PWCF CODE 

The Pressure-Wave Curve-Fit (PWCF) computer code was used to calculate the 

Stirling engine power given mean gas pressures, pressure amplitudes, and pressure phase angles for both the expansion space and compression space. 

The gas pressure parame 

P= 

e 

P= 

C 

ers were curve-fit 

'em + z P ea sin[a + 

pcm + - 1 P sin[a + 2 ca 

n the following manner: 

where Pem is the mean expansion-space gas pressure, Pea is the expansionspace gas pressure amplitude (defined as maximum pressure - minimum pressure), 

a is the engine crank angle or piston angular position, Be is the expansionspace pressure phase angle, 13 varies linearly with a in order to simulate 

the nonharmonic nature of the Stirling engine gas pressure variation with time, 

and the subscript c indicates compression-space gas pressure parameters. 

Having a mathematical relationship for the Stirling engine gas pressure, 

it was straightforward to calculate the Stirling engine indicated power and 

heat input. Work per cycle is $(Pe dVe + P, dV,>. Heat input was approximated as $(Pe dVe). The integration was accomplished numerically and both 

expressions were multiplied by engine frequency to arrive at power or energy 

f 1 ow rate . 

The accuracy of the PWCF code was evaluated by comparing the PWCF code's 

calculated value of Stirling engine indicated power to that predicted from the 

NASA Stirling engine computer simulation. Indicated power errors resulting 

from the use of this PWCF code at design conditions are 

GPU-3 error :- 1 percent 

P-40 error = 8 percent 

RE-1000 error = 1 percent 

Thus, the PWCF code was considered sufficiently accurate for calculating indicated power. 

Heat input calculated with the PWCF code was compared to that predicted 

from the NASA Stirling engine computer simulation. The discrepancy was 40 to 

50 percent for all three engines, and thus this PWCF code was not considered 

accurate enough for calculating heat input. 

26 
1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 

10. 

11. 

12. 

13. 

REFERENCES 

Tew, R.C., Jr.: Computer Program for Stirling Engine Performance Calculations. NASA TM-82960, DOE/NASA/51040-42, 1983. 

Tew, R.C., Jr.; Thieme, L.G.; and Miao, D.: Initial Comparison of Single 

Cylinder Stirling Engine Computer Model Predictions With Test Results. 

Allen, D.; and Cairelli, J.: Test Results of a 40kW Stirling Engine and 

Comparison With the NASA-Lewis Computer Code Predictions. Energy For the 

Twenty-First Century (20th IECEC), Vol. 3, SAE, 1985, pp. 3.238-3.243. 

Tew, R.C., Jr.: Comparison of Free-Piston Stirling Engine Model Predictions with RE-1000 Engine Test Data. NASA TM-83650, DOE/NASA/1005-3, 

1984. 

Geng, S.M.: Calibration and Comparison of the NASA Lewis Free-Piston 

Stirling Engine Model Predictions with RE-1000 Test Data. NASA TM-89853, 

1987. 

Thieme, L.G.: Low-Power Baseline Test Results for the GPU-3 Stirling 

Engine. NASA TM-79103, DOE/NASA/1040-79/6, 1979. 

Kelm, G.G.; Cairelli, J.E.; and Walter, R.J.: Test Results and Facility 

Description for a 40-Kilowatt Stirling Engine. NASA TM-82620, 

DOE/NASA/51040-27, 1981. 

Schreiber, J.G.: Testing and Performance Characteristics of a 1-kW FreePiston Stirling Engine. NASA TM-82999, 1983. 

Giansante, J.E.: A Free Piston StirlingHEngine Performance Code. Report 

81TR17, Mechanical Technology, Inc., Latham, NY, Nov. 1980. 

Sullivan, T.J.: Comparison of NASA Lewis Performance Code's Pressure-Drop 

Model Predictions to Stirling Engine Working-Space Flow Test Data. NASA 

Thieme, L.G.: 

Stirling Engine. NASA TM-82646, DOE/NASA/51040-31, 1981. 

Schreiber, J.G.; Geng, S.M.; and Loren2,G.V.: RE-1000 Free-Piston Stirling Engine Sensitivity Test Results. NASA TM-88846, DOE/NASA/1005-11, 

1986. 

Faulkner, H.B.; and Smith, J.L., Jr.: Instantaneous Heat Transfer During 

Compression and Expansion in Reciprocating Gas Handling Machinery. Energy 

for the Marketplace (18th IECEC), Vol. 2, AIChE, 1983, pp. 724-730. 

NASA TM-79044, DOE/NASA/1040-78/30, 1979. 

(NASA TM-87050.) 

CR-182215. 1988. 

High-Power Baseline and Motoring Test Results for the GPU-3 

27 
t 

TABLE I . . STIRLING ENGINE DESIGN OPERATING CONDITIONS 

GPU-3 I 

Gas mean pressure. MPa ........... 6.9 

Engine speed. rpm ............ 3000 

Average heater gas temperature. "C ..... 677 

Coolant inlet temperature. "C ....... 20 

Coolant ................. Water 

Working fluid H2 

P-40 

............... 

t 

Gas mean pressure. MPa .......... 15.0 

Engine speed. rpm ............ 4000 

Average heater wall temperature. OC .... 720 

Coolant inlet temperature. OC ....... 50 

Coolant ................. Water 

Working ............... fluid H2 

I RE- 1000 

Gas mean pressure. MPa ........... 7.0 

Piston stroke. cm ............. 2.6 

Average heater wall temperature. OC .... 600 

Engine frequency. Hz ............ 30 

Coolant inlet temperature. "C ....... 25 

Coolant ................. Water 

Working fluid ............... He 

28 
TABLE 11. - STIRLING ENGINE COMPUTER MODEL INPUTS 

~____ ~~~~ 

Engine geometry 

Code space and time specifications: 

Number of engine cycles 

Number of control volumes for each component 

Number of time steps per cycle 

Code options: 

Working fluid - real, ideal (real used for this study) 

Gas type - Hz, He, mixture 

Heater temperature - wall, gas 

RE-1000 - input piston motion or solve for piston motion (input used for this study) 

Engine operating conditions: 

Mean gas pressure 

Engine speed 

Heater wall or average gas temperature 

Cy1 i nder wall and regenerator wall temperatures 

Coolant flow rate 

Coolant inlet temperature 

29 
TABLE 111. 

Operating conditions Power,b 

(a) percent 

Efficiency, Heat 

percent input, 

percent 

P = 2.8 MPa, W = 2500 rpm 38.0 

P = 6.9 MPa, W = 2000 rpm (near design) 16.0 

- STIRLING 

cool ant, 

percent 

14.8 20.1 23.4 

-1.6 17.9 21.6 

P = 5 MPa, W = 1000 rpm -8.8 

P = 15 MPa. W = 4000 rprn (design) -1 1.4 

P = 2.8 MPa, W = 2500 rpm 

P = 5.5 MPa, W 3500 rpm 

-14.6 6.8 7.5 

-3.9 -7.8 -17.3 

129.1 78.2 28.6 I 80.1 1 45.1 I 24.1 I ’::; I 

P = 4 MPa, St = 2.6 cm 

P 7 MPa, St = 1.8 cm 

P = 7 MPa, St = 2.6 cm (design) 

20.1 8.9 10.3 27.5 

1.5 -4.1 5.8 -5.4 

12.4 -.8 13.0 5.4 

30 
ENGINE PREDICTION ERRORS 

Expansionspace gas 

temperature, 

OC 

Compressionspace gas 

temperature, 

OC 

Expansionspace 

pressure 

ampl i tude, 

percent 

Compressionspace 

pressure 

phase angle, 

deg 

Compressionspace 

pressure 

ampl i tude, 

percent 

Heat 

exchanger 

pressure 

drop 

ampl i tude, 

percent 

-1 

-7 

7 7.4 7.7 -6 --- 12 12.8 9.0 -6 --- 

5 

-1 1 

4 17.8 12.1 -7 --- 7 10.8 15.8 -5 -- 

30 

11 

31 

5 -- 4.0 -- --- 

24 9.0 2.7 ---- --- 

2 2 --- 11.3 1.4 

4 5 ---- 5.4 -1.3 

-1 6 ---- 7.1 -0.1 

-49 

-5 1 

-4 7 
.REGENERATOR 

FIGURE 1. - CROSS-SECTIONAL VIEW OF GPU-3 SINGLE-CYLINDER STIRLING ENGINE. 

THE HYDROGEN CWRESSOR VAS RmVED FRCH THE NASA TEST €KINE. 

ORIGINAL PAGE 

BLACK AND WHITE PHOTOGRAPH 

32 
lORIGINAL PAGE 

BLACK AND WHITE PHOTOGRAPH 

PREHEATER-COMBUSTOR ASSEMBLY 

:AD 

SEMBLY 

?OR 

33 
FIGURE 3. - CROSS-SECTIONAL VIEW OF RE-1000 FREE-PISTON 

STIRLING ENGINE. 

I I 

6 

I 

WORKING GAS 

0 HYDROGEN 

- 

0 HELIUM 

PREDICTED PERFORMANCE 

ENGINE TEST DATA 

--. \cl 

0. ----aDW 

u, 

0 

1000 1500 2000 2500 3000 3500 9000 

ENGINE SPEED, RPM 

FIGURE 4. - GPU-3 BRAKE POWER VERSUS ENGINE SPEED FOR HYDRWN AND HELIUM WORKING FLUIDS. 

GAS TEIPERATURE. 690 OC: MEAN CWRESSIOW-SPACE GAS PRESSURE. 2.8 WA. 

AVERAGE HEATER-TUBE 

EAN CWRESSIONSPACE GAS PRESSURE. 

MPA 

0 5.5 

0 9.1 

A 2.8 

- 

- PREDICTED PERFORWNCE 

- --- ENGINE TEST DATA e0 

1000 1500 2000 2500 3000 3500 4000 

ENGINE SPEED. RPM 

FIGURE 5. - GPU-3 BRAKE POWER VERSUS ENGINE SPEED FOR VARIOUS MEAN CWRESSION-SPACE PRESSURES. 

6As TEMPERATURE, 690 OC: WORKING GAS. HELILW. 

AVERAGE HEATER-TUBE 

AVERAGE KATER-TUBE 

GAS TERf'ERATURE. 

OC 

0 690 

0 580 

- 

- PREDICTED PERFORMANCE 

--- ENGINE TEST DATA 

/e----- 0- 

FIGURE 6. - GPU-3 BRAKE POWER VERSUS ENGINE SPEED FOR VARIOUS HEATER-TUBE GAS PERATURES. MEAN CWRESSION-SPACE 

PRESSURE. 2.8 WA; YORKING 6AS. HYDROEN. 

ORIGINAL PAGE 

BLACK A'ND WMTE PHOTOGRAP).) 34 
WORKING GAS 15 - 0 HYDROGEN 

ENGINE TEST DATA 

3 

11 - c' 

a 

5 

1000 1500 2000 2500 3000 3500 4ooO 

ENGINE SPEED. RPM 

F'dIRE 7. - GPU-3 HEAT INPUT VERSUS ENGINE SPEED FOR HYDROGN 

I I 

AND HELIUM WORKING FLUIDS. 

ATURE. 690 OC: MEAN MS PRESSURE, 2.8 RA. 

AVERAGE HEATER-TUBE GAS TENPERMEAN CWRESSIONSPACE GAS PRESSURE. 

MPA 

0 5.5 

20 0 4.1 

io00 1500 2000 2500 3000 3500 4& 

ENGINE SPEED. RPM 

FIGURE 8. - GPU-3 HEAT INPUT VERSUS ENGINE SPEED FOR VARIOUS MEAN CONPRESSION-SPACE PRESSURES. AVERAGE HEATERTUBE GAS TEMPERATURE. 690 OC: WORKING GAS, HELIUM. 

15 

13 

3, 

c' a n

L 

z9 

Y 

11 

7 

AVERAGE HEATER-NE 

GAS TEWERATURE, 

OC 

0 690 

PREDICTED PERFORNANCE 

ENGINE TEST DATA 

- 

e-- 

5 

1000 1500 2000 2500 3000 3500 4ooO 

ENGINE SPEED, RPM 

I I I 

FIGURE 9. - GPU-3 HEAT INPUT VERSUS ENGINE SPEED FOR VARIOUS HEATER-TUBE GAS TEMPERATURES. MEAN CONPRESSION-SPACE 

PRESSURE IS 2.8 RA. WORKIN6 GAS. HYDROGEN. 

AVERAGE HEATER-TUBE 

GAS TEMPERATURE, 

OC 

0 690 

- 0 580 PREDICTED PERFORMNCE 

--- ENGINE TEST DATA 

----- = -- -0 9,- ----- 

--% 

1.7 

1000 1500 2000 2500 3000 3500 4000 

ENGINE SPEED, RPM 

FIGURE 10. - GPU-3 COMPRESSION-SPACE PRESSURE MPLITUDE 

(PEAK TO PEAK VALUES) VERSUS ENGINE SPEED FOR VARIOUS 

HEATER-TUBE GAS TEMPERATURES. MEAN COMPRESSION-SPACE 

PRESSURE. 2.8 RA: WORKIE 6AS. HYDROGEN. 

35 
0 

50 1 0 

A 

j /.: 20 10

rn YORKICSPACE PRESSURE. 

RA 

5 

10 

- 

15 

PREDICTED PERFORMANCE 

--- ENGINE TEST DATA 

0/ 

a 

w'/ 

150 

3 100 

cz 

c 

50 

EAR WORKINGSPACE PRESSURE. 

RA 

0 5 

-0 10 

- 

A 15 

PREDICTED PERFORMANCE / 

--- ENGINE TEST DATA 

- 

0 

500 1000 1500 2000 2500 3000 3500 4000 4500 

ENGINE SPEED, RPM 

FIGURE 12. - P-40 HEAT INPUT VERSUS ENGINE SPEED FOR VARIOUS KAN WORKING-SPACE PRESSURES. MEAN HEATER WALL TV)- 

PERATURE, 720 OC . 

KAN WORKINGSPACE PRESSURE, 

WA 

0 5 

0 10 

- 

A 15 

PREDICTED PERFORMANCE --- ENGINE TEST DATA 

0 

500 1000 1500 ZOO0 2500 3000 3500 4000 4500 

ENGINE SPEED. RPM 

FIGURE 13. - P-40 CWRESSIM-SPACE PRESSURE WLITUDE 

(PEAK TO PEAK VALUES) VERSUS ENGINE SPEED FOR VARIOUS 

ATWE. 720 'C. 

EAN WORKING-SPACE PRESSURES. EAN HEATER WALL TEMPER- 

+ PREDICTED PERFORMNCE 

-0- ENGINE TEST DATA 

1200 

3 

g 1000 

p. 

P 

f 

600 

36 
1200 

loo0 

3 

s p.

n 800 

u 

n 

L 

W c- 4 

600 

400 

1200 

r 

$ 1000 

n 

n 

W cf 

800 

- 

-0- PREDICTED PERFORMANCE 

-0- ENGINE TEST DATA 

I ERROR BAND 

- 

- 

- 

8' 

I I I I 

- PREDICTED PERFORMANCE 

-0- ENGINE TEST DATA I ERROR BAND 

600 

-7 

~ 

PREDICTED PERFORMANCE 1100 r 

800 I I I I I I 

20 25 30 35 40 45 50 55 60 

COOLANT INLET TEMPERATURE. OC 

FIGURE 17. - RE-1000 INDICATED POWER VERSUS COOLANT INLET 

TEMPERATURE. PISTON STROKE, 2.6 CM; MEAN WORKING-SPACE 

PRESSURE. 7.0 WA; EAN HEATER WALL TEMPERATURE, 600 OC. 

5000 

3 4oo0 

s ' 3000 

- 

PREDICTED PERFORMANCE 

-0- ENGINE TEST DATA A/." I ERROR BAND 

- AI I I I I I I I I I I I I I 

37 
+ PREDICTED- 

-0- ENGINE TEST DATA I ERROR BAND 

P0 

3 4 5 6 7 8 2000 

EAR WORKING-SPACE PRESSURE, WA 

FIGURE 19. - RE-1000 HEAT INPUT VERSUS EAN WORKING-SPACE 

PRESSURE. 

ATURE. 600 OC; COOLANT INLET TEFERATURE. 25 OC. 

PISTON STROKE, 2.6 cM; EAN HEATER WALL TMI 3'- 

A 

3000 I I I I I 

400 450 500 550 600 650 

MEAN HEATER WALL TEMPERATURE, OC 

FIGURE 20. - RE-1000 HEAT INPUT VERSUS EAN HEATER WALL TW'ERATURE. PISTON STROKE. 2.6 CM; EAN YORKING-SPACE PRESSURE. 

7.0 RA; cm IuT mm. 25 OC. 

4500r 7 PREDlCTEDPERFORllAmE 

-0- ENGINE TEST DATA 

ERROR BAND 

1 4000 

+-- '-3- I 

+------ c 

3500 

20 25 30 35 40 45 50 55 60 

COOLANT INLET EWERATURE. OC 

FIGURE 21. 

ATURE. 

7.0 WA; MEAN HEATER WALL TEPIPERATURE. 600 OC. 

- RE-1000 HEAT INPUT VERSUS COOLANT INLET TEFERPISTON STROKE. 2.6 CM: EAR WORKING-SPACE PRESSURE. 

1300 

s 

E9 1200 XI' 

6s 

af 1100 % % 

- --$-e PREDICTED PERFORMNCE 

-e- ENGINE TEST DATA 

T ERROR BAND 

I I I I I 

400 450 500 550 600 650 

EAR HEATER WALL TEFERATURE. OC 

1000 

FIGURE 22. - RE-1000 CWRESSIOW-SPACE PRESSURE WLITUDE (PEAK 

TO PEAK VALUES) VERSUS EAN HEATER WALL TENPERATURE. PISTON 

ANT INLET TEMPERATURE, 25 OC. 

STROKE, 2.6 CM; RAN WORKING-SPACE PRESSURE, 7.0 MPA; COOL5 

4 

1 

WORKING GAS 

0 HYDROGEN 

0 HELIUM 

TAILED SYRBOLS DENOTE ENERGY BALANCE ECHANICAL LOSS - SOLID SYMBOLS DENOTE MOTORING ECHANICAL LOSS 

- PREDICTED PERFORMANCE 

--- ENGINE TEST DATA - 

- 

- 

t38 
PRESSURE AWLITUDE 

PRESSURE PHASE ANGLE 

ERROR ONLY 

ERROR ONLY 

fi .5 84 

f 

V !lo 

-.5 ' 

2.8 2.8 4.1 5.5 

MEAN COMPRESSION-SPACE GAS PRESSURE. P. MPA 

1500 3500 2000 3000 

ENGINE SPEED. W. RPM 

DICTION ERRORS IN THE PRESSURE ANPLITUDE OR PHASE 

ANGLE. WORKING GAS. HELIUM. 

FIGURE 24. - GPU-3 BRAKE POWER SENSITIVITY DUE TO PREI PRESSURE WLITUDE 

PRESSURE PHASE ANGLE 

ERROR ONLY 

ERROR ONLY 

-50 ' 

DESIGN PISTON PRESSURE. COOLANT 

CONDITIONS. STROKE; 4 WAC TEWERA2.6 CM TURE. 55 OC* 

OPERATING CONDITIONS 

FIGURE 25. - RE-1000 INDICATED POWER SENSITIVITY DUE TO 

PREDICTION ERRORS IN THE PRESSURE AMPLITUDE OR PHASE 

ANGLE. DESIGN CONDITIONS: PRESSURE. 7 MPA: PISTON 

STROKE, 2.6 CM: COOLANT INLET TEMPERATURE, 25 OC: 

AVERAGE HEATER WALL TEMPERATURE. 600 OC. 

OTHER PARlllETERS HELD AT DESIGN CONDITIONS. 

- dV PV 

- R (Ti dMi) + + (fli d~i) 

V 16 c --- 

4 

300 302 304 306 308 310 312 314 316 

ENGINE CRANK ANGLE, DEG 

FIGURE 26. - GPU-3 PHASE ANGLE GOVERNING EQUATION CURVES. 

ENGINE SPEED. 3500 RPM: PEAN CWRESSION-SPACE PRESSURE. 

4.1 WA: AVERAGE HEATER-TUBE GAS TEHPERATURE, 690 'C: 

WORKING GAS. HYDROGEN. 

39 
2. Government Accession No. 3. Recipient's Catalog No. ' N' NASA CR-182248 

DOE/NASA/4 105-4 

I 

I 

NASA Lewis Stirling Engine Computer Code Evaluation 

1 4. Title and Subtitle 

January 1989 

5. Report Date 

7 Author($ 

Timothy J. Sullivan 

~ 

16. Abstract 

8. Performing Organization Report No. 

E4580 

10. Work Unit No. 

778-35-13 

In support of the U.S. Department of Energy's Stirling Engine Highway Vehicle Systems program, the NASA 

Lewis Stirling engine performance code was evaluated by comparing code predictions without engine-specific 

calibration factors to GPU-3, P-40, and RE-1000 Stirling engine test data. The error in predicting power output 

was - 11 percent for the P-40 and 12 percent for the RE-1000 at design conditions and 16 percent for the GPU-3 

at near-design conditions (2000 rpm engine speed versus 3000 rpm at design). The efficiency and heat input 

predictions showed better agreement with engine test data than did the power predictions. Concerning all data 

points, the error in predicting the GPU-3 brake power was significantly larger than for the other engines and was 

mainly a result of inaccuracy in predicting the pressure phase angle. Analysis into this pressure phase angle 

prediction error suggested that improvements to the cylinder hysteresis loss model could have a significant effect 

on overall Stirling engine performance predictions. 

9 Performing Organization Name and Address - 

I 

Sverdrup Technology, Inc. 

NASA Lewis Research Center Group 

Cleveland, Ohio 44135-3191 

12 Sponsoring Agency Name and Address 

U.S. Department of Energy 

Office of Vehicle and Engine R&D 

Washington, D.C. 20545 

I 

19. Security Classif. (of this report) 20. Security Classif. (of this page) 1 21. NO ofqP2ages 22. Price' 

Unclassified Unclassified 1 A03 

11. Contract or Grant No. 

NAS3-24105 

13. Type of Report and Period Covered 

Contractor Report 

Final 

14. Sponsoring Agency 

'For sale by the National Technical Information Service, Springfield, Virginia 221 61 NASA FORM 1626 OCT 86 

17 Key Words (Suggested by Author@)) 

Stirling engine 

Computer predictions 

18. Distribution Statement 

Unclassified - Unlimited 

Subject Category 44 

DOE Category UC-96