Performance of a transcritical or supercritical CO2 Rankin cycle engine

Abstract

A Rankine Expander System that converts low quality heat (heat usually at temperatures below 400 degrees Celsius) to electricity by using the properties of trans-critical CO.sub.2. The system is comprised of a compressor, an expander, three heat exchangers, and a permanent magnet alternator (PMA). It operates at pressures and temperatures that hold the CO.sub.2 above its critical point for the full cycle, and as such, attains high efficiencies even at low power. Under some conditions the efficiency can exceed 50%.

Claims

1. A closed-loop CO.sub.2 system for capturing waste heat comprising: a heat exchanger configured for transferring heat from a lower pressure part of said closed-loop system to a higher pressure part of said closed-loop system; a cooler configured for receiving lower pressure CO.sub.2 from said heat exchanger for exhausting waste heat from said closed-loop system and cooling the CO.sub.2 to a temperature below the critical temperature of CO.sub.2; a compressor configured for compressing lower pressure CO.sub.2 received from said cooler at a temperature below the critical temperature of CO.sub.2 into higher pressure CO.sub.2 for outputting supercritical CO.sub.2 to said heat exchanger; another heat exchanger configured to receive higher pressure CO.sub.2 from said heat exchanger and further configured for inputting additional heat energy obtained from outside said closed-loop system into the higher pressure CO.sub.2; and a piston expander comprising a plurality of piston pairs having opposing pistons, each piston pair being associated with a associated shared expansion chamber configured to support linear travel of said pistons and configured for receiving the higher pressure CO.sub.2 to convert the higher pressure CO.sub.2 into a lower pressure CO.sub.2 to output a rotational torque to drive a load, wherein the lower pressure CO.sub.2 output by said expander is input into said heat exchanger, wherein at all points the lower pressure CO.sub.2 is maintained at a pressure above the critical point pressure of CO.sub.2.

2. The system of claim 1, wherein at all points the higher pressure CO.sub.2 is maintained below 200 bar.

3. The system of claim 1, wherein said CO.sub.2 is maintained at a temperature between 0 C. and 400 C.

4. The system of claim 1, wherein said expander is comprised of a plurality of said pistons arranged around the circumference of one disk for oscillating the one disk for outputting said rotational torque.

5. The system of claim 1, wherein for the entire closed loop, said CO.sub.2 is maintained at a temperature between 0 C. and 400 C., and wherein for the entire closed loop, said CO.sub.2 is maintained between a pressure of at least about 80 bar and a pressure of no more than about 200 bar.

6. A closed-loop CO.sub.2 system for capturing waste heat comprising: a heat exchanger configured for transferring heat from a lower pressure part of said closed-loop system to a higher pressure part of said closed-loop system; a cooler configured for receiving lower pressure CO.sub.2 from said heat exchanger for exhausting waste heat from said closed-loop system and cooling the CO.sub.2 to a temperature below the critical temperature of CO.sub.2; a compressor configured for compressing lower pressure CO.sub.2 received from said cooler into higher pressure CO.sub.2 for outputting supercritical CO.sub.2 to said heat exchanger; another heat exchanger configured to receive higher pressure CO.sub.2 from said heat exchanger and also configured for inputting additional heat energy obtained from outside said closed-loop system into the higher pressure CO.sub.2; and an expander configured for receiving the higher pressure CO.sub.2 to convert the higher pressure CO.sub.2 into a lower pressure CO.sub.2 for outputting rotational torque, wherein the lower pressure CO.sub.2 is output by said expander for input into said heat exchanger, wherein for the entire closed loop, said CO.sub.2 is maintained between a pressure of at least about 80 bar and a pressure of no more than about 200 bar, and further wherein for the entire closed loop, said CO.sub.2 is maintained at a temperature between 0 C. and 400 C., wherein said expander is comprised of a plurality of paired opposed pistons configured for linear travel in a common expansion chamber, wherein for each piston pair, the opposing pistons are each installed on a circumference of a different disk in a configuration provided to oscillate the different disks in opposing directions both configured to provide a rotational torque to a shaft for driving a load, with the expander being configured for generating said rotational torque through the converting of the higher pressure CO.sub.2 into lower pressure CO.sub.2.

7. The system of claim 6, wherein said expander is comprised of a plurality of said pistons driving at least one oscillating disk for outputting said rotational torque.

8. A closed-loop CO.sub.2 system for capturing waste heat comprising: a first heat exchanger configured for transferring heat from a lower pressure part of said closed-loop system to a higher pressure part of said closed-loop system; a cooler configured for receiving lower pressure CO.sub.2 from said heat exchanger for exhausting waste heat from said closed-loop system and cooling the CO.sub.2 to a temperature below the critical temperature of CO.sub.2; a compressor configured for compressing lower pressure CO.sub.2 received from said cooler into higher pressure CO.sub.2 for outputting supercritical CO.sub.2 to said heat exchanger; a second heat exchanger configured to receive higher pressure CO.sub.2 from said first heat exchanger and also configured for inputting additional heat energy obtained from outside said closed-loop system into the higher pressure CO.sub.2; and an expander including a plurality of pistons arranged as pairs of opposed pistons configured to travel in a linear motion in a respective expansion chamber associated with the piston pair, each piston of said piston pair being severably installed on and driving a separate oscillating disk configured to output a rotational torque to a load, said expander being adapted to receive the heated CO.sub.2 from said second heat exchanger to convert the heated CO.sub.2 into lower pressure CO.sub.2 via an expansion process using said oscillating disks for outputting said rotational torque, wherein lower pressure CO.sub.2 is output by said expander for input into said first heat exchanger.

9. The system of claim 8, wherein at all points the lower pressure CO.sub.2 is maintained at a pressure above the critical point pressure of CO.sub.2.

10. The system of claim 8, wherein the pistons of said piston expander are arranged on a circumference of the disk and wherein said pistons travel in a linear motion tangential to the disk within an expansion chamber.

11. The system of claim 8, further comprising an electrical generator mechanically connected to said piston expander in a manner configured for transmitting a torque from said piston expander to said electrical generator.

12. The system of claim 6, wherein a plurality of the one or more pistons of said piston expander are arranged on a circumference of a disk and wherein said pistons travel in a linear motion tangential to the disk within an expansion chamber.

13. The system of claim 6, further comprising an electrical generator mechanically connected to said piston expander in a manner configured for transmitting a torque from said piston expander to said electrical generator.

14. The system of claim 1, wherein a plurality of the one or more pistons of said piston expander are arranged on a circumference of a disk and wherein said pistons travel in a linear motion tangential to the disk within an expansion chamber.

15. The system of claim 1, further comprising an electrical generator mechanically connected to said piston expander in a manner configured for transmitting a torque from said piston expander to said electrical generator.

16. A closed-loop CO.sub.2 system for capturing waste heat comprising: a first heat exchanger configured for transferring heat from a lower pressure part of said closed-loop system to a higher pressure part of said closed-loop system; a cooler configured for receiving lower pressure CO.sub.2 from said heat exchanger for exhausting waste heat from said closed-loop system; a compressor configured for compressing lower pressure CO.sub.2 received from said cooler into higher pressure CO.sub.2 for outputting to said heat exchanger; a second heat exchanger configured to receive higher pressure CO.sub.2 from said first heat exchanger and also configured for inputting additional heat energy obtained from outside said closed-loop system into the higher pressure CO.sub.2; and an expander including a plurality of pistons arranged as pairs of opposed pistons having a common expansion chamber associated with the piston pair, each piston of said piston pair being installed on a circumference of a different disk with said pistons being configured to travel in a linear motion within a respective static expansion volume for oscillating said disks in a manner configured to generate a rotational torque for driving a load, said expander being adapted for receiving the heated CO.sub.2 from the second heat exchanger to convert the heated CO.sub.2 into lower pressure CO.sub.2 via an expansion process using said pistons for generating said rotational torque, wherein lower pressure CO.sub.2 is output by said expander for input into said first heat exchanger.

17. The system of claim 16, wherein at all points the lower pressure CO.sub.2 is maintained at a pressure above the critical point pressure of CO.sub.2.

18. The system of claim 16, further comprising an electrical generator mechanically connected to said piston expander in a manner configured for transmitting a torque from said piston expander to said electrical generator.

19. A closed-loop CO.sub.2 system for capturing waste heat, said system comprising: a first heat exchanger configured for transferring heat from a lower pressure part of said closed-loop system to a higher pressure part of said closed-loop system; a cooler configured for receiving lower pressure CO.sub.2 from said heat exchanger for exhausting waste heat from said closed-loop system; a compressor configured for compressing lower pressure CO.sub.2 received from said cooler into higher pressure CO.sub.2 for outputting supercritical CO.sub.2 to said heat exchanger; a second heat exchanger configured to receive higher pressure CO.sub.2 from said first heat exchanger and also configured for inputting additional heat energy obtained from outside said closed-loop system into the higher pressure CO.sub.2; and an expander configured to receive the heated CO.sub.2 to convert the heated CO.sub.2 into lower pressure CO.sub.2 for outputting rotational torque to a load, wherein the lower pressure CO.sub.2 output by said expander is input into said first heat exchanger, wherein said expander includes at least one opposing pair of pistons sharing an expansion chamber configured such that said pistons travel in a linear motion, each piston being mounted on respective disks and configured to convert energy of the CO.sub.2 for oscillating the disks about an axis of the disks with a drive shaft passing through a hole in the axis of the disks for receiving the rotational torque; and an electrical generator mechanically connected to said drive shaft in a manner configured for transmitting the rotational torque to said electrical generator, wherein at all points the lower pressure CO.sub.2 is maintained at a pressure above the critical point pressure of CO.sub.2.

20. The system of claim 19, wherein said expander is configured with the drive shaft outputting the torque to the electrical generator.

21. A closed-loop CO.sub.2 system for capturing waste heat comprising: a first heat exchanger configured for transferring heat from a lower pressure part of said closed-loop system to a higher pressure part of said closed-loop system; a cooler configured for receiving lower pressure CO.sub.2 from said first heat exchanger for exhausting waste heat from said closed-loop system and cooling the CO.sub.2 to a temperature below the critical temperature of CO.sub.2; a compressor configured for compressing lower pressure CO.sub.2 received from said cooler at a temperature below the critical temperature of CO.sub.2 into higher pressure CO.sub.2 for outputting to said heat exchanger; a second heat exchanger configured to receive higher pressure CO.sub.2 from said first heat exchanger and further configured for inputting heat energy obtained from outside said closed-loop system into the higher pressure CO.sub.2; and an expander comprising a plurality of disks with at least one piston being mounted on each one of said disks, said pistons being configured in piston pairs each sharing a common expansion volume configured for the pistons traveling in a linear motion to drive said disks in opposing oscillating motions for rotating a shaft traveling through said disks for outputting a torque, wherein the expander is configured to receive the higher pressure CO.sub.2 from said second heat exchanger for converting into rotational torque, wherein lower energy CO.sub.2 output by said expander is input into said first heat exchanger for providing heat energy to said first heat exchanger and for supplying said lower pressure CO.sub.2 to said cooler.

22. The system of claim 21, wherein said expander is comprised of one or more pistons each associated with at least one expansion chamber, said one or more pistons being mounted on a circumference of at least one disk such that an oscillation of the one or more disks is converted into a rotational torque output from said expander to drive a load.

23. The system of claim 21, wherein at all points the lower pressure CO.sub.2 is maintained at a pressure above the critical point pressure of CO.sub.2.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The features and advantages of the examples described herein will become apparent to those skilled in the art to which this disclosure relates upon reading the following description, with reference to the accompanying drawings, in which:

(2) FIG. 1 shows a schematic of the six elements of the example Rankine Expander System;

(3) FIG. 2 shows a Molliere Diagram for CO.sub.2 plots of pressure versus enthalpy;

(4) FIG. 3 shows a Molliere Diagram for CO.sub.2 used for the Refrigeration Cycle;

(5) FIG. 4 shows a Molliere Diagram for an example CO.sub.2 refrigeration cycle run in reverse for creating work;

(6) FIG. 5 shows plots of example calculated efficiencies for the Expander cycle for a variety of maximum pressures and temperatures;

(7) FIG. 6 shows a Molliere Diagram for an example CO.sub.2 refrigeration cycle run in reverse using an internal heat exchanger;

(8) FIG. 7 shows a plot of example predicted efficiencies possible from a CO.sub.2 expander system for various values of pressure and temperature using an internal heat exchanger;

(9) FIG. 8 shows the example expander cycle with internal heat exchanger where the entire cycle is above the critical pressure;

(10) FIG. 9 shows the efficiency of the example Expander System as a function of the low end pressure for various values of the high end temperature;

(11) FIG. 10 shows the efficiency of the example Expander System as a function of the ambient temperature of the exhausted heat;

(12) FIG. 11 shows the efficiency of the example Expander System as a function of the temperature difference between the input and output at the low temperature end of the internal heat exchanger;

(13) FIG. 12 shows the efficiency of the example Expander System as a function of the external ambient temperature; and

(14) FIG. 13 shows one example embodiment of an engine that can be used as the expander 10 of FIG. 1;

(15) FIG. 14 is a schematic showing an example location of an exhaust port, fuel injector and spark plug for the example expander of FIG. 13; and

(16) FIG. 15 is a schematic showing an example location of the inlet and exhaust injectors for the example expander of FIG. 13.

DETAILED DESCRIPTION OF THE EXAMPLE EMBODIMENTS

(17) An example embodiment of the Rankine Expander System is made up of six parts as shown in FIG. 1. The system operates on a thermodynamic cycle using the properties of high pressure CO.sub.2 above its critical point. The CO.sub.2 critical point is at a temperature of 31.1 C. and a pressure of 73.8 bar (or 1070 psi). The Rankine Expander System can operate anywhere in the pressure range between 80 and 200 bar and the temperature range between ambient temperature (even below 0 C.) and 400 C. The actual pressure change and resultant temperature rise are set by the specific design parameters of the system which depend on the desired output power and efficiency. How these values are chosen is the main topic of this paper.

(18) The Rankine Expander System has a compressor 1 which takes CO.sub.2 at near ambient temperature and a pressure above 80 bar and compresses it to a higher pressure (but below 200 bar). For a high pressure of 170 bar, the temperature is raised by about 10 C. The high pressure CO.sub.2 then goes through an internal heat exchanger 2 where its temperature is raised by extracting heat from the higher temperature CO.sub.2 that comes from the example expander 10. Then, the CO.sub.2 passes through an external heater 3 (may be a second heat exchanger or other heat transmission source) that obtains heat generated from an outside source of energy. This heater/exchanger 3 raises the temperature of the CO.sub.2 to its maximum operating value (between 250 and 700 C. depending upon the chosen value). This high pressure, high temperature CO.sub.2 then enters the Rankine Expander 10 where the pressure drops to the starting pressure, the temperature drops by about 100 C., and the pressure change performs mechanical work. The Expander 10 converts the pressure of the expanding gas into a high torque rotational energy. The spinning shaft of the expander 10 drives a generator 4, such as a Permanent Magnet Alternator (PMA), which produces electricity. The trans-critical CO.sub.2 that comes out of the Expander 10, still in its trans-critical state, enters the internal heat exchanger 2 where it transfers much of its heat to the CO.sub.2 that is the output of the compressor 1. Finally, the CO.sub.2 enters a cooler 5 (e.g., another heat exchanger) which reduces the temperature back to ambient temperature, and the cycle repeats.

(19) The primary elements of the example Rankine Expander System, are thus the compressor 1, the expander 10, the permanent magnet alternator 4, and three separate heat exchangers 2, 3, and 5. External to the system is the heat source represented by Q.sub.in which will, in the example embodiment, provide high temperature liquid (e.g., mineral oil) to the input heat exchanger 3 and an electricity conversion module that converts the electricity from the PMA 4 into a form appropriate for the specific application.

(20) The CO.sub.2 Refrigerator:

(21) The Rankine Expander System depends on the properties of CO.sub.2 in its trans-critical phase for its proper function. These CO.sub.2 properties have been known for a long time, and the trans-critical behavior has been used in refrigerators since the early 1900's. The interest dropped with the introduction of more efficient refrigerant gases in 1930, but interest in CO.sub.2 has been renewed lately due to the increased awareness of the environmental impact of these refrigerant gases. CO.sub.2 has the desirable property that it is benign with respect to the environment.

(22) The Molliere diagram for CO.sub.2 is shown in FIG. 2. The commonly used Molliere diagram plots the properties of CO.sub.2 on a pressure vs. enthalpy grid, in this case the pressure is shown on a logarithmic scale compressing the features above the critical pressure. The plot shows lines of constant temperature (isotherms), constant entropy (adiabatic curves), and constant density (or specific volume). The liquid-vapor line 12 is shown as a thick black line. Below that line, the CO.sub.2 is a mixture of liquid and vapor and the term quality in this plot refers to the proportion of the mixture that is liquid and the portion that is vapor. (Note: a gas is a substance whose surface is defined by the container. A vapor is a substance that has a surface in contact with a liquid). Above the critical pressure, CO.sub.2 behaves like a viscous gas in that it does not have an identifiable surface, but it flows like a liquid.

(23) The utility of the Molliere diagram comes from three features of the refrigeration cycle, two of which are used in the Rankine Expander cycle disclosed herein. The refrigeration steps are shown in FIG. 3. During the compression step, the gas follows a curve of constant entropy. This is an adiabatic compression which FIG. 3: The Molliere Diagram for CO.sub.2 used for the Refrigeration Cycle is fast enough that negligible heat flows from the surrounding surfaces into the operating gas. During the two heat exchange steps, the gas remains at a constant pressure and therefore follows a horizontal line in the Molliere diagram. In the expansion step in the refrigeration cycle, the enthalpy remains constant as the gas passes through the expansion valve, and this shows as a vertical line in the Molliere diagram.

(24) A CO2 Expander System:

(25) Previous work with the CO.sub.2 cycle, in discussing its utility in an expander system, has been to emulate the refrigeration cycle except run in reverse. An example of this is shown in FIG. 4. Here, the cycle is shown by the solid line 14. The cycle starts at position 1 at a pressure of 62 bar and a temperature of 22 C. The CO.sub.2 is compressed to a pressure of 170 bar, which raises the temperature to 42 C. (position 2). Heat is added, keeping the pressure constant until the trans-critical CO.sub.2 is 150 C. at position 3. Next, the CO.sub.2 moves through an expander where it performs work as the pressure drops to 62 bar and drops the temperature to 59 C. (position 4). Finally, the CO.sub.2 is cooled (and condensed) to 22 C. and the cycle repeats.

(26) The utility of the Molliere diagram is in using the value of enthalpy to determine the efficiency of the cycle. The change in the value of the enthalpy gives a measure of the energy needed in each step. For example, if in going from state 2 to state 3 the enthalpy changes by 253.4 (=32.5(220.9)) kJ/kg (kilo-Joules per kilogram), and if the heat added to the system is 1 kW (kilo-Watt), then the flow of CO.sub.2 is 1/253.4 kg/sec=3.95 gm/sec (note: 1 kW=1 kJ/sec). Using the other enthalpy values in the cycle with this mass flow rate gives a compressor work output of 56.9 W, and expander work output of 221.3 W, and a heat exhausted of 836 W. For an expander/PMA efficiency of 0.85, the actual power generated is 188 W, and with a compressor efficiency of 0.80, the power consumed is 71 W, giving an overall system efficiency for this example of 11.7% (18871=117 W net to 1000 W input).

(27) The efficiencies for a variety of pressures and temperatures using this cycle have been studied in the past by several authors. FIG. 5 shows efficiencies for the Expander cycle for a variety of maximum pressures and temperatures, where the low pressure is 60 bar, and the condensing temperature is 22 C. There is no internal heat exchanger for these cases. For the cycle above with no internal heat exchanger, the efficiency is relatively low and tops out at less than 15% even at higher temperatures.

(28) The overall efficiency can be improved by adding an internal heat exchanger (as shown in FIG. 1) to the system. The internal heat exchanger transfers some of the heat that is normally exhausted to pre-heat the CO.sub.2 before it enters the main heater. This has the effect of reducing the amount of input heat needed to reach the desired high temperature, and thereby increases the ratio of net output energy to input energy. This is shown in FIG. 6, which shows an example expander cycle with internal heat exchanger. The heat exchanger reduces the amount of heat in required to raise the temperature of the CO.sub.2.

(29) With the internal heat exchanger, the four step process in FIG. 4 therefore becomes a 6 step process 16 as shown in FIG. 6. For this example, the high pressure is set at 170 bar and the high temperature is set at 350 C. with the low pressure still at 60 bar and the low temperature at 22 C. The compression phase from position 1 to position 2 is the same as FIG. 4. But with the internal heat exchanger, heat is added raising the temperature to 133 C. at position 6. Then the external heat (1 kW in this example) is added raising the temperature further to 350 C. at position 3. The CO.sub.2 moves through the expander performing work and cooling to 235 C. (position 4). This hot CO.sub.2 then enters the internal heat exchanger and gives up some of its heat further cooling to 47 C. at position 5. The enthalpy decrease between position 4 and 5 is equal to the enthalpy increase between positions 2 and 6. In this example, the internal heat exchanger moves 784 W from the low pressure side to the high pressure side. Finally, the CO.sub.2 goes through the external cooler to reduce the temperature to 22 C.

(30) The 1 kW of input heat results in a flow of 3.53 g/sec of CO.sub.2 (this number is the heat added divided by the enthalpy increase). This cycle shows that the ideal compressor requires 51 W, the ideal expander delivers 377.6 W, and the external heater supplies 1000 W for an ideal efficiency of 32.7%. If the assumed efficiency for the compressor is 80% and the assumed efficiency for the expander/PMA combination is 85%, then this efficiency drops to 25.7%.

(31) The efficiency increases as the maximum temperature and pressure is increased. This is shown in FIG. 7, which is a plot showing predicted efficiencies possible from a CO.sub.2 expander system for various values of pressure and temperature using an internal heat exchanger. For top pressures of 170 bar and temperatures of 400 C., the efficiency is shown to exceed 25%. This high efficiency is comparable to or exceeds systems based on solar cells. Hence, the renewed interest in the trans-critical CO.sub.2 cycle.

(32) There are three assumptions upon which these results depend. First is the assumption that the low end pressure is below the critical pressure. The critical pressure is 73.8 bar, and the examples in the literature are at 60 bar or below. This is the natural assumption for the refrigeration system where a phase change is desired to enhance the cooling step. But for the expander system, the low end pressure does not need to be below the critical pressure, and, in fact, the efficiency is much better when the low end pressure is higher. Second is the assumption that the low end temperature is 22 C. (this is 72 F.), or at least below the critical temperature of 31 C. This temperature is reached by blowing air (or flowing water) through a radiator to exhaust the waste heat. If the ambient temperature (or water temperature) is above 72 F., the efficiency of the system with these operating pressures drops quickly. Third is the assumption that the internal heat exchanger can transfer the heat in such a way that the exit temperature on the cold side (at position 5 in FIG. 6) is only 5 C. above the inlet temperature at position 2. If the internal heat exchanger is not that effective, or it is not very nearly 100% efficient, then the system efficiency again drops quickly. These three issues are discussed in more detail below, and is the material that is added with the Rankine Expander System.

(33) Variation with Pressure:

(34) For the expander system, the low end pressure is not restricted to be below the critical pressure. The expander will generate power even when all the pressures are above 73.8 bar. An example of this is shown in FIG. 8. For this example, the low end pressure is held at 100 bar while the upper pressure and temperature are the same as in FIG. 6. This figure shows that for an input of 1 kW heat, the expander extracts 644 W giving an output net power (after considering inefficiency and the power needed for the compressor) of 436 W. The predicted efficiency for this cycle is a startling value of 43.6%. The high efficiency is a result of the internal heat exchanger. Because of the shape of the isotherm lines, the internal heat exchanger is able to transfer a larger amount of heat energy from the exhaust of the expander to the output of the compressor.

(35) The efficiency of the Expander system with the internal heat exchanger improves as the low end pressure increases, all other parameters being held constant. This is shown in FIG. 9. Here, the high end pressure is held constant at 170 bar, the high end temperature is held constant at 350 C., and the low end ambient temperature is held constant at 22 C. The points at the low end pressure of 62 bar correspond with the values in FIG. 7 for the temperature of 350 C. While the earlier results of efficiencies above 20% renewed the interest in CO.sub.2 systems, the actual performance is even better, falling above 40%-45%. The rapid rise in the curves for low end pressures between 80 and 90 bar are a direct result of the shape of the isotherms in the Molliere diagram. This high efficiency is due entirely to the performance of the internal heat exchanger. In transferring heat from the expander output to a temperature within 5 C. of the compressor output temperature, the internal heat exchanger is able to transfer more heat energy as the low side pressure increases. The ability of the exchanger to do this is a key feature of the Rankine Expander System, and the importance will be discussed below.

(36) Variation with Low End Temperature:

(37) One of the difficulties with the predicted performance of the above expander system is the dependence upon a condensing temperature of 22 C. If the ambient temperature is above this temperature the efficiency of the system with these operating pressures drops quickly. This is shown in FIG. 10. Here, the top curve is the same as in FIG. 9 for the case where the high end temperature is 350 C. As the ambient temperature increases, the efficiency drops and the maximum moves toward higher low end pressures. But still the efficiencies are impressive. At an ambient temperature of 37 C. (98.6 F.) the efficiency is above 32% for a low end pressure of 130 bar.

(38) Variation with Internal Heat Exchanger Performance:

(39) The performance of the Expander System also depends strongly on the performance of the internal heat exchanger. In the literature.sup.3, the internal heat exchanger is assumed to give an outlet temperature on the low pressure side equal to only 5 C. above the inlet temperature on the high pressure side. Building a heat exchanger that performs this well with temperature differences from the front to back of nearly 200 C. is a significant design challenge. If the performance is not that good, the efficiency of the expander system is degraded. This is shown in FIG. 11. Here, again, the top curve is the same as the curve in FIG. 9 for the case of the top temperature being 350 C., and is the same as the top curve in FIG. 10 for the case of the ambient temperature being 22 C. FIG. 11 shows that as delta temperature at the outlet of the internal heat exchanger increases, the efficiency drops quickly. The high end temperature is 350 C. and the high end pressure is 170 bar for all plots.

(40) The heat exchanger is doing the important function of reusing the heat energy exhausted from the expander to pre-heat the CO.sub.2 that goes into the main heater. It is actually moving more heat energy between parts of the system than is input from the outside. For example, in the case where the efficiency is near 44%, the heat exchanger is transferring 6.35 kW of heat energy for every 1 kW of external heat added. If the delta temperature for the heat exchanger is 20 C., then the efficiency drops to 24% and the amount of heat transferred by the heat exchanger drops to 3.38 kW for every 1 kW of external heat added. The performance of the expander system directly depends on the amount of heat transferred by the heat exchanger, and hence its design is critical.

(41) For certain environments, the expander system can have truly astonishing efficiencies. For example, for northern latitudes with cold outside temperatures where commercial facilities have their own power generators, an add-on expander system can produce additional electricity very effectively. By using the waste heat from the power generation equipment, the expander system can very efficiently augment the power generation. This is shown in FIG. 12. For the case where the outside temperature is at freezing (0 C.), the expander efficiency can approach 60% for low outside temperatures making this system attractive for northern locations. Such high efficiency is unheard of in other power generation systems.

(42) Rankine Expander Design:

(43) The Rankine Expander System describe here based on the trans-critical properties of CO.sub.2 can produce electricity from low quality heat with good efficiency. The system is based on six elements, a compressor, an expander, a permanent magnet alternator, and three heat exchangers. This paper has shown that very high efficiencies can be realized when the system operates at pressures above the critical point. Key to the high efficiencies is an internal heat exchanger that moves significant amounts of heat energy from the output of the expander to the output of the compressor. Also important is the ambient temperature which sets the low end temperature of the cycle.

(44) A pressure adjustment feature to optimize efficiency of a CO.sub.2 Rankine cycle engine can be provided. FIGS. 9 and 12 show the relationship of ambient temperature and low end pressure to performance. Therefore it would also be desirable to optimize performance of the heat recovery to be able to adjust the low end pressure in day to day and season to season operation. Provided is a described variation of the CO.sub.2 Rankine cycle engine circuit that would perform this task. Included is a feature, not shown, that would be a variation of the circuit diagram of FIG. 1.

(45) On the High pressure side of the circuit, most likely after the compressor and/or before the expander, is a solenoid operated valve that can be opened and closed on command by a microprocessor, leading to the inlet opening of a reservoir tank. The compressor charges the high side circuit with a pressure of up to 200 bar or atmospheres of pressure and if the solenoid is open the reservoir tank would be charged with CO2. This would work in conjunction with the companion solenoid valve just before the expander that would shut off gas flow to the expander with the resulting action being to deplete the low pressure side of the circuit of CO2 working fluid while the compressor was operating. By opening and closing these valves the low end pressure can be adjusted to reach an optimum pressure to maximize conversion efficiency.

(46) FIG. 13 shows one embodiment of a piston expander that could be used for the expander 10 of FIG. 1, as disclosed in provisional application Ser. No. 61/625,940 filed on Apr. 18, 2012 and incorporated herein by reference. FIG. 13 shows a Polygon Oscillating Piston Engine with six chambers. This engine has the unique feature of providing very high torque and is therefore ideal to drive a PMA under high electrical load. The Polygon Oscillating Piston Engine is a derivative of the Toroidal Oscillating Piston Engine described in patent Ser. No. 13/074,510. However, almost any other configuration of piston engine could be used in the Waste Heat Electrical Generation System.

(47) FIG. 13 shows a Hexagonal Polygon Oscillating Piston Engine. There are six chambers 20 and six corner pieces 21 that form a closed polygon. The six pistons 27 move back and forth in the chambers with motion coordinated by having alternate pistons connected via two disks 26 (three pistons for each disk). The piston pegs on each disk ride on six piston sleeves 28 while the pistons move back and forth in their respective chambers. Each disk 26 rides on a cam on one of two crank shafts 22. Each crank shaft 22 is connected to the main shaft 24 via drive gears. The corner chambers 20 contain the inlet injector and the outlet exhaust valve. The timing of the inlet injector is critical for the operation of the engine as an expander.

(48) FIGS. 14-15 show some of the desired modifications to the polygon oscillating engine of FIG. 13. FIG. 14 shows the possible location of the exhaust port, the fuel injector and the spark plug for the two cycle embodiment of the Polygon Oscillating Piston Engine, whereas FIG. 15 shows the possible location of the inlet and exhaust injectors for the expander embodiment of the Polygon Oscillating Piston Engine.

(49) FIG. 14 shows for the two cycle embodiment of the Polygon Oscillating Piston Engine the location of the spark plug 39 and the fuel injector 40 which would be on each of the corner combustion chambers 52. Also shown is one possible location of the exhaust ports 38 which would be on every other piston cylinder 51. The two cycle embodiment can have both inlet and exhaust ports, or exhaust ports only with a fuel injector as shown in FIG. 14.

(50) FIG. 15 shows for the expander embodiment of the Polygon Oscillating Piston Engine the location of two separate injectors. Injector 40 is the inlet injector which is open for part of the stroke of the piston wherein hot high pressure gas enters the piston chamber. The inlet injector 40 then closes and the gas expands and cools as the piston continues toward the limit of its motion within piston cylinder 51. Then the exhaust injector 41 opens, and the cooler lower pressure gas is pushed out of the chamber as the piston returns to its top dead center position. Both injectors are located in the corner combustion chamber 52, although no combustion occurs in the expander embodiment.

(51) Additional discussion of the components discussed in FIG. 1 can be found in provisional application Ser. No. 61/636,236, filed on Apr. 20, 2012, and incorporated herein by reference in its entirety. Provisional application Ser. No. 61/477,762, filed on Apr. 21, 2011, and incorporated herein by reference, discusses a number of applications for the oscillating engines that are referenced by this document that can also be applied.

(52) Thus disclosed is a Rankine Expander System that converts low quality heat (heat usually at temperatures below 400 degrees Celsius) to electricity by using the properties of trans-critical CO2. The system is comprised of a compressor, an expander, three heat exchangers, and a permanent magnet alternator (PMA). It can operate at pressures and temperatures that hold the CO2 above its critical point for the full cycle, and as such, attains high efficiencies even at low power. Under some conditions the efficiency can exceed 50%. This makes the Rankine Expander System ideal for use with solar heat collectors, or using the waste heat from power generators, internal combustion engines, or even nuclear waste. This paper shows the operating conditions used to attain high efficiencies, and how these efficiencies can vary with controllable design parameters.

(53) The following documents are incorporated herein by reference:

(54) MegaWatSoft, inc. on www.carbon-dioxide-properties.com/default.aspx. The web site features a CO.sub.2 properties calculator.

(55) Transcritical R744 (CO2) heat pumps, Technician's Manual, put out by the CENTRE TECHNIQUE DES INDUSTRIES ARAULIQUES ET THERMIQUES (CETIAT) sponsored by SHERPA (Sustainable Heat and Energy Research for Heat Pump Applications), October 2007.

(56) Platell and Dudzik, Zero Energy Houses; in Proceedings of ES2007, Energy Sustainability Conference, Jun. 27, 2007, Long Beach, Calif.