A Computer Simulation of Two Piston Stirling Engine Nicolae SOREA Ştefan cel Mare University Suceava, Romania nsorea@eed.usv.ro Abstract: This paper presents a computer simulation of two piston Stirling engine in Two Piston Stirling Engine Simulator software by JLB Enterprises and the influence of the phase angle on the operating characteristics. It also presents the conclusions regarding the phase angle influence on the p-v diagrams of this type of engine and the best position of the pistons for obtaining the best efficiency of the two piston Stirling engine. Keywords: Stirling engine, Stirling cycle, regenerator, p-v diagram, computer simulation. 1. Introduction On 27 September 1816, Church of Scotland minister Robert Stirling applied for a patent for his economizer in Edinburgh, Scotland. The device was in the form of an inverted beam engine, and incorporated the characteristic phase shift between the displacer and piston that we see in all Stirling engines today. The engine also featured the cyclic heating and cooling of the internal gas by means of an external heat source, but the device was not yet known as a Stirling Engine [4]. Stirling engines are unique among heat engines because they have a very high theoretical Carnot efficiency, in fact it is almost equal to their theoretical maximum Carnot efficiency. Stirling engines are powered by the expansion (heating) and contraction (cooling) of gas. The fixed amount of gas inside a Stirling engine is transferred back and forth between a hot end and a cold end, which cyclically expands and contracts the gas [1]. Robert Stirling continued to work on his engines throughout his life. In the 1820's he was joined by his younger brother James, whose major contribution was to suggest pressurizing the internal gas to increase the power output. Further improved design patents were applied for in 1827 and 1840. 2. The computer simulation of Stirling engine For computer simulation and examining the operating characteristics of the two piston Stirling engine, the software Two Piston Stirling Engine Simulator by JLB Enterprises was used. As the simulator runs, values are computed based on the specified parameters. These values include Hot Position: the position of the hot piston, for the current phase angle; zero is up. Cold Position: the position of the cold piston, for the current phase angle; zero is up. Pressure: the pressure inside the engine, for the current phase angle. More important than the pressure itself is whether the pressure is above or below the ambient pressure. This tells us whether the internal gas will be trying to push against the pistons, or pull the pistons. This is indicated by the trailing (+) or (-) [5]. Volume: the total volume in the two cylinders, for the current phase angle. This is the sum of the volumes of the hot and cold cylinders. It is expressed as a percent of the total possible engine volume. Hot N %: this is the percent of the gas in the engine which is in the hot cylinder, for the current phase angle. Cold N %: this is the percent of the gas in the engine which is in the cold cylinder, for the current phase angle. Maximum Pressure: This is the maximum pressure achieved at any time during
the engine cycle. It is the maximum over all phase angles. This value is not normalized [5]. Mean Pressure: This is the timeaveraged pressure in the engine. It is assumed that, over time, the pressure in the engine will try to equilibrate to the ambient pressure, because of small imperfections in the engine seals. We assume that the mean pressure and the ambient pressure will be the same. This value is not normalized. Net Work: As the engine turns, the pressure from the gas on the pistons is at times positive (in the same direction as the piston is moving) and sometimes is negative. If we sum all of the work (both positive and negative) over an entire engine cycle, we see whether the gases will push the pistons more than they pull them. This tells us whether the engine will put out net power for us, or will stop running completely. The configuration with the largest value should produce the most power. All values can be found in the graphs: The Piston Position Graph (Figure 1) shows the positions of the pistons at each point during the engine s cycle. The curves are simple sine waves, with the phase difference as specified by the Phase Offset parameter. yourself that this does not affect the volumes. Since we have two cylinders at different temperatures (and usually with different volumes), the pressure will depend on both how compressed the gas is relative to the rest volume (Total Volume vs. rest volume); but it will also depend on how much of the gas is in the hot cylinder and how much is in the cold cylinder. Consider the situation where the Hot and Cold Volumes are equal (pistons at the same position): if the temperatures are equal, there will be equal amounts of gas in each cylinder. But the hotter the hot cylinder is, the more gas gets forced out of the hot cylinder and into the cold cylinder. And the more gas gets forced out of the hot cylinder, the greater the pressure in both-cylinders. Fig. 2. Volume and pressure graph. Fig. 1. Piston position graph. The Volume and Pressure Graph (Figure 2) is derived from the Piston Position data. Once the position of each piston is known, we can easily compute the volume above each piston (the internal engine volume for each cylinder). This is the graphed Hot Volume and the Cold Volume. The Total Volume is just the sum of the Hot Volume and the Cold Volume at each phase angle. The three volumes are not affected by the temperatures, but they are affected by the phase offset and the stroke maximums and minimums. Play with these parameters and watch how they affect the volumes, until it begins to make sense to you. You can adjust the temperatures to assure The Gas Distribution Graph (Figure 3) shows where the gas is at each phase of the engine s operation. This is shown as a percentage of total gas in the engine. This graph depends not only on the stroke and phase angle parameters, but also on the temperature parameters. If you start with the default settings and increase the hot temperature, you will notice that the gas gets forced almost entirely into the cold cylinder around phase 270. When the hot temperature is reduced, this effect is reduced. Once we know how much gas is in each cylinder, and what the volume is of each cylinder, we can now compute the total pressure in the engine. The dark horizontal line shows the mean Pressure, which is assumed to be the ambient pressure. The graphed Pressure value is normalized. This means that it is scaled so that it goes from a value of zero to a value of one. The Work Graph (Figure 4) is the key to determining whether a particular engine configuration will generate energy (do work). As the pistons move in their cycles, at some moments the internal gas is at a higher pressure than the ambient pressure; at other moments,
the internal pressure is less than ambient. If a piston is moving down when the internal pressure is high, energy will be contributed to the flywheel; similarly if the piston is moving up when the internal pressure is low. If the reverse situation obtains (piston moving down with low internal pressure, or up with high pressure), the pistons take energy from the flywheel. If the engine contributes more energy to the flywheel over the entire cycle than it removes from the flywheel, the engine will continue to run; any excess energy is available to do work for us. Fig. 3. Gas distribution graph. The graphs are calculated as follows. At each phase angle, the internal engine pressure is determined and compared to the ambient/external pressure. If the internal pressure is higher, this is indicated with a (+) to the right of the Pressure value provided on the upper right of the screen [6]. The direction of the pistons is then noted, and if they are moving in the right direction, the engine pressure is deemed to be contributing to helping the engine work; the force is positive. Knowing whether the internal gas is helping the pistons is useful, but the amount of Work which the engine does is pressure (force) times distance. We compute how much work each piston contributes (or takes) by multiplying the internal pressure (relative to ambient) by the piston motion. The Work Graph shows how much each piston is contributing to helping the flywheel turn. This takes into account 1) the internal engine pressure, relative to the ambient pressure at each phase angle; 2) the direction in which each piston is moving at any given phase angle; 3) the amount the piston is moving at the given phase angle. The result is the red and blue lines; the dark line is the sum. Notice that the red and blue lines go through zero twice every cycle: this is the effect of the piston motion, described above. The blue Work curve goes through zero at 0 and 180 degrees, where the cold piston is at the end of its stroke. In addition, all three of the curves go through zero whenever the Pressure is equal to the ambient/mean pressure: this is because at that instant, the internal engine gas can neither push nor pull on the pistons. If you restore the engine parameters to their default values, you will see a Net Work value of 1.42 on the upper right part of the screen. This means that more energy is being put into the flywheel by this engine than is being taken out. This is the same as saying that, if you add up all of the values of the black (Sum) line on the Work Graph, across all phase angles, the sum is greater than zero. If you change the Phase Offset to be zero, the Net Work will change to 0.20: this engine produces no net energy. If you change the Phase Offset to be 90 degrees, the Net Work goes to 1.77: this engine is even worse! Now that you understand what the parameter controls do, what the displayed values represent, and what the graphs show you, you should be able to play with the parameters in order to gain a better understanding of the underlying physics of the two piston Stirling engine. Fig. 5. Work graph. Fig. 4. Wheel position. In the figures presented below (Figures 6, 7, 8, 9, 10, 11 and 12) we can observe the phase angle influence on the PV diagrams for the phase offset values: 0, 30, 60, 90, 120, 150, 180.
Fig. 6. PV diagram (phase angle is 0 ). Fig. 10. PV diagram (phase angle is 120 ). Fig. 7. PV diagram (phase angle is 30 ). Fig. 11. PV diagram (phase angle is 150 ). Fig. 8. PV diagram (phase angle is 60 ). Fig. 12. PV diagram (phase angle is 180 ). 3. Conclusion Fig. 9. PV diagram (phase angle is 90 ). This computer simulation was made to punctuate the advantages of Stirling engines: The engine as a whole is much less complex than other reciprocating engine types. No valves are needed. Fuel and intake systems are very simple. Most types of Stirling engines have the bearing and seals on the cool side; consequently, they require less lubricant and last significantly longer between overhauls than other reciprocating engine types [3].
They operate at relatively low pressure and thus are much safer than typical steam engines. Low operating pressure allows the usage of less robust cylinders and of less weight. They can be built to run very quietly and without air, for use in submarines. References [1]. N. Sorea, Stadiul actual al soluţiilor în domeniul motoarelor solare bazate pe conversia termomecanică - Referat I în cadrul stagiului de pregătire pentru doctorat. Conducător ştiinţific: prof. univ. dr. ing. Dorel Cernomazu, [2]. N. Sorea, Contribuţii teoretice şi experimentale preliminarii în domeniul motoarelor solare bazate pe conversia termomecanică - Referat II în cadrul stagiului de pregătire pentru doctorat. Conducător ştiinţific: prof. univ. dr. ing. Dorel Cernomazu, [3]. N. Sorea, Contribuţii privind realizarea unor noi motoare solare bazate pe conversia helio-termomecanică - Lucrare de disertaţie, Conducător ştiinţific: prof. univ. dr. ing. Dorel Cernomazu, [4]. N. Sorea, Stadiul actual al soluţiilor în domeniul motoarelor Stirling în: DOCT-US, Nr. 1, ISSN 2065-3247, Editura Universităţii Ştefan cel Mare, Suceava, pp. 97-102, 2009. [5]. N. Sorea, D. Cernomazu, A computer simulation of KS 90 Stirling engine In: 3rd International Symposium on Electrical Engineering and Energy Converters ELS 2009, September 24 25, Proceedings, ISSN 2066-853X, pp. 121-124, 2009. [6]. N. Sorea, D. Cernomazu, The phase angle influence on the operating characteristics of Gamma Stirling engine In: 3rd International Symposium on Electrical Engineering and Energy Converters ELS 2009, September 24 25, Proceedings, ISSN 2066-853X, pp. 125-130, 2009. [7]. Available on the Internet at the webpage: http://www.jonbondy.com/software.htm. Nicolae SOREA PhD student, Ştefan cel Mare University, Faculty of Electrical Engineering and Computer Science, PhD thesis: Theoretical and experimental contributions regarding the solar engines based on the thermomechanical conversion, PhD superviser Dorel CERNOMAZU, PhD.