RELATED APPLICATIONS

This application is related to U.S. Application Serial No. 12/773,431, entitled "HEAT ENGINE WITH CACSADED CYCLES", filed May 4, 2010, U.S.

Provisional Application Serial No, 60/719,327, entitled "PIEZOELECTRIC

SELECTABLY ROT AT ABLE BEARING," filed on September 21 , 2005, U.S. Provisional Application Serial No. 60/719,328, entitled "SOLAR HEAT ENGINE SYSTEM," filed on September 21 , 2005, U.S. Application Serial No. 1 1/512,568, entitled "SOLAR HEAT ENGINE SYSTEM," filed on August 30, 2006, and U.S. Application Serial No. 12/246127, entitled "HEAT ENGINE IMPROVEMENTS," filed on October 6, 2008, each of which are herein incorporated by reference in its entirety.

BACKGROUND

This disclosure relates to the conversion of heat energy to another form of energy, e.g. mechanical energy. The disclosure further relates to such conversion where the heat energy source is concentrated solar energy or a low grade or waste heat source.

Several different types of heat engines have been used in practice to convert concentrated solar radiation to mechanical power, notably Stirling cycle engines and Rankine cycle engines, however, all such known engines have had disadvantages relating to complexity, cost or low efficiency, Apparatus which convert heat energy into mechanical energy, namely the heat energy of concentrated beam of solar radiation into the movement of a piston through the explosion or expansion of a droplet of substantially uncompressed liquid targeted by the concentrated solar beam are described in patent application No. 11/512,568, referred to above. In patent application No, 1 1/512,568, (granted patent no 7,536,861) a method of utilizing a droplet or thin film of water or other liquid, which is heated and explosively expanded in a six-sided expander, is described. The six-sided expander absorbs substantially all of the energy in the droplet and converts a large fraction of that energy to mechanical power through the motion of a linear piston. Mechanical power is in turn converted to electrical power by a linear generator on each of the six sides complete with field excitation and output coil.

In theoretical, conventional Rankine cycles, expansion of working fluid takes place under reversible adiabatic conditions. Also in conventional Rankine cycles as applied to solar energy conversion, the fluid is first vaporized in a boiler then passed into an expander.

Methods whereby liquid is injected into a working space above a piston have also been described. Conventionally, the hot liquid vaporizes at the point of injection, with consequent loss of available energy or exergy. Some of the initial energy loss on vaporization of liquid injected into the cylinder may be regained as heat transferred from the compressed vapor already within the cylinder; however, the energy thus transferred comprises no net heat addition from outside but merely constitutes energy re-circulated within the system. Such recirculation cannot, of itself, produce a useful energy output by the system.

Thus, in the liquid injection prior art, fluid is injected, with exergy loss into a chamber, during which relatively uncontrolled vaporization takes place reducing the amount of available energy, then work is done by adding heat back into the already partially expanded vapor to cause the further expansion of the vapor which moves a piston to perform useful work.

SUMMARY OF THE INVENTION

In one practical embodiment, a concentrated beam of solar radiation is directed through a high temperature resistant window, for example, of sapphire or any other suitable material, onto a thin film or droplet of water. The thin film or droplet can be sitting on or near a "target" disk or plate. The target disk or plate can be a material with high absorptivity, low emissivity in the near and far infra red range and very high surface area. The thin film or droplet of liquid is heated and subsequently expanded or exploded, to provide mechanical power. Some embodiments use a boiler-less, thermodynamic cycle in which the working fluid is heated in contact with the expansion system and the expansion takes place whilst heat input is still going on. Fluid heating takes place at near constant volume, and with substantially no pre-compression resulting in achievement of pressures much higher than conventional Rankine cycles. Also, uniquely, expansion and heating take place on the constant pressure, constant temperature line in the liquid T s and h - s diagrams, unlike in conventional, Rankine cycle devices hitherto described in the prior art.

According to some embodiments, another part of the cycle comprises a constant volume heat recovery which pre-heats the unexpanded working fluid, while the exhausted, expanded working fluid experiences a constant pressure and constant temperature compression back to the liquid state. Due to the aforementioned heat recovery step whilst exhausting, in a particularly efficient embodiment, the cycle will receive input energy during the expansion process only. According to an embodiment, an engine comprises a chamber defined by at least one fixed wall and at least one movable wall, the volume of the chamber variable with movement of the movable wall; an injector arranged to inject liquid into the chamber while the chamber has a substantially minimum volume; apparatus through which energy is introduced that is absorbed by the fluid which then explosively vaporizes, performing work on the movable wall; and apparatus which returns the movable wall to a position prior to the work being performed thereon so the chamber has the substantially minimum volume, substantially evacuating the chamber of vaporized fluid without substantially compressing the vaporized fluid.

According to another embodiment, a method of converting energy from one form to another in a system comprises confining a quantity of substantially unexpanded liquid within a chamber; adding energy to the system, so as to heat the liquid sufficiently to vaporize the liquid and expand a resulting vapor; and receiving mechanical energy from the expanding vapor in a form of movement of a wall of the chamber responsive to the expansion. According to yet another embodiment, a method of converting energy from one form to another by passing a working material through a closed liquid-vapor thermodynamic cycle, comprises expanding the working material from a liquid phase into a vapor phase by addition of heat; recovering heat from the working material in the vapor phase so as to condense the working material from the vapor phase into the liquid phase to await expansion; and adding the recovered heat to working material awaiting expansion, without changing the phase thereof.

According to another embodiments, an engine is disclosed including: a chamber defined by at least one fixed wall and at least one movable wall, the volume of the chamber variable with movement of the movable wall; an injector arranged to inject liquid without expansion into the chamber while the chamber has a substantially minimum volume; an apparatus constructed and arranged to introduce energy into the chamber at a rate sufficient to explosively vaporize the liquid, performing work on the movable wall; an apparatus constructed and arranged to return the movable wall to a position prior to the work being performed thereon so the chamber has the substantially minimum volume; and a valve constructed and arranged to

substantially evacuate the chamber of vaporized fluid without substantially compressing the vaporized fluid.

In some embodiments, the apparatus configured and arranged to introduce energy into the chamber is further configured and arranged to deliver energy to a target disk in contact with the liquid.

In some embodiments, the apparatus through which energy is introduced includes a window of a material with high transmissivity, low reflectivity and low absorptivity. In some embodiments, the window is sapphire. In some embodiments, the apparatus configured and arranged to introduce energy into the chamber includes a textured surface in thermal contact with target disk. In some embodiments, the textured surface is in thermal contact with a heat exchanger with flow passages on the outside of the chamber. In some embodiments, the apparatus configured and arranged to introduce energy into the chamber includes a porous block fitted between the moveable wall and the at least one fixed wall. In some embodiments, the porous block is constructed and arranged such that it may be heated by applying heat external to the cylinder, which is then transferred through a head of the cylinder into the block.

Some embodiments include a series of heat pipes embedded in the head of the cylinder.

In some embodiments, the moveable wall includes a face of a piston, the piston including a groove, the piston configured such that the groove is aligned with an exhaust port in the fixed wall of the chamber after work is performed on the moveable wall. In some embodiments, the apparatus constructed and arranged to return the movable wall to a position prior to the work being performed thereon includes a spring constructed and arranged to exert a force on the piston in a direction toward a portion of the fixed wall. In some embodiments, the spring is constructed and arranged to rotate the piston upon a movement of the piston through the chamber. In some embodiments, the spring includes a plurality of fixed length members, the spring mechanically coupled to a shaft of the piston and constructed and arranged to convert a lateral motion of the piston into a rotational motion of the piston. In some embodiments, the engine includes: a valve; and an actuator mechanically coupled to the valve; the valve disposed on a piston, a surface of the piston including the moveable wall.

In some embodiments, actuator includes a solenoid or a mechanical lifter.

In some embodiments, the vaporized fluid is condensed during a time period when work is performed on the moveable wall. Some embodiments include a heat exchanger mounted within an area defined by the fixed wall, an input to the heat exchanger in fluid communication with the valve, and an output of the heat exchanger in fluid communication with the injector. In some embodiments, the heat exchanger includes a variable bypass. Some embodiments include a valve formed from the combination of a slot in a piston, a surface of the piston including the moveable wall, and a slot disposed in a sleeve disposed to the outside of the piston, the sleeve and piston constructed and arranged to rotate relative to one another.

Some embodiments include a heat recovery jacket surrounding at least a portion of the engine and in fluid communication with a heat exchanger, an input to the heat exchanger in fluid communication with the valve, and an output of the heat exchanger in fluid communication with the injector.

Some embodiments include a bypass splitter in fluid communication with the injector, the heat recovery jacket, and a bypass line, the bypass splitter constructed and arranged to divide a portion of the liquid to be injected into the chamber into a portion flowing through the heat recovery jacket and a portion flowing through the bypass line.

In some embodiments, the fluid is water.

In some embodiments, the engine has a rotary configuration. Some such embodiments may include an epitrochoid-shaped chamber and/or a roughly triangular rotor,

According to another embodiment, a method is disclosed of converting energy from one form to another in a system, including: confining a quantity of substantially unexpanded liquid within a chamber; adding energy to the system, so as to heat the liquid sufficiently to vaporize the liquid in the absence of a chemical reaction and expand a resulting vapor; and receiving mechanical energy from the expanding vapor in a form of movement of a wall of the chamber responsive to the expansion. In some embodiments, receiving mechanical energy from the expanding vapor further includes rotating the wall of the chamber relative to a second wall of the chamber.

In some embodiments, expanding the vapor includes expanding the vapor to a volume of over 80 times that of the unexpanded liquid.

Some embodiments include performing a closed liquid-vapor thermodynamic cycle in which one or more or all of the following hold: the liquid is not compressed in the chamber prior to expanding the vaporized liquid; the liquid heating takes place at near constant volume; the liquid is vaporized at a constant temperature and pressure; the expansion takes place while heat is being input; the vapor is exhausted from the chamber at a constant pressure; heat is recovered from the vapor with the vapor maintained at a constant temperature and pressure; the vapor phase is condensed at a constant pressure and temperature; and heat is recovered from the vapor by transferring the recovered heat to liquid awaiting expansion while maintaining a constant volume of the liquid awaiting expansion. In some embodiments, the temperature of the system during the expansion is maintained at a constant level as energy is added to the system, and the input of heat during the expansion results in substantially no change of internal energy to the system.

In some embodiments, the method includes performing a closed liquid-vapor thermodynamic cycle in which one or more or all of the following hold: the liquid is not compressed in the chamber prior to expanding the vaporized liquid; the liquid heating takes place at near constant volume; the liquid is vaporized whilst doing work; the expansion takes place while heat is being input; the vapor is exhausted from the chamber at a constant pressure; heat is recovered from the vapor during the expansion, with a change in internal energy; the vapor phase is condensed at a constant pressure and temperature; and heat is recovered from the vapor by transferring the recovered heat to liquid awaiting expansion while maintaining a constant volume of the liquid awaiting expansion.

In some embodiments, the thermodynamic cycle receives input energy during the expansion process only. In some embodiments, the liquid is water.

According to another embodiment, a method of converting energy from one form to another by passing a working material through a closed liquid-vapor thermodynamic cycle, is disclosed including: expanding at least a portion of the working material from a liquid phase into a vapor phase by addition of heat; recovering heat from the working material after expanding; condensing the working material, after recovering heat, from the vapor phase into the liquid phase, in a condenser, thus restoring the working material to a state where the working material awaits expansion to start a new cycle; varying the quantity of heat recovered by varying a bypass of the working material during recovering heat from the working material, so as to vary thermodynamic efficiencies and select desired specific work output; and adding the recovered heat to working material awaiting expansion, without changing the phase thereof; whereby efficiency of the method is improved over a method lacking recovering heat. In some embodiments, the working material is expanded within a chamber and the working material is not compressed in the chamber prior to expanding the working material.

In some embodiments, heating the working material in the liquid phase takes place at near constant volume and the expansion takes place while heat is being input. In some embodiments, expanding the working material from a liquid phase into a vapor is performed at a constant temperature and pressure. In some embodiments, expanding the working material from a liquid phase into a vapor is performed in a reversible, adiabatic cycle, where internal energy within the cycle is converted to mechanical work. Some embodiments include exhausting working material in the vapor phase from the chamber, the working material in the vapor phase maintaining at a constant volume.

In some embodiments, recovering heat from the working material in the vapor phase is performed with the working material in the vapor phase maintained at a constant temperature and pressure. In some embodiments, recovering heat from the working material in the vapor phase is performed with the working material in the vapor phase maintained at a constant volume.

In some embodiments, the working material in the vapor phase is condensed at a constant pressure and temperature.

In some embodiments, recovering heat from the working material in the vapor phase includes adding the recovered heat to working material awaiting expansion while maintaining a constant volume of the working material awaiting expansion.

In some embodiments, the temperature of the system is maintained at a constant level as energy is added to the system.

In some embodiments, varying a bypass of the working material during recovering heat from the working material includes varying a ratio of feed liquid mass flow in a heat recovery jacket to a total feed liquid mass flow, the heat recovery jacket surrounding a portion of an engine in which the method is performed. Some embodiments include decreasing a specific power output of the engine while increasing the thermodynamic efficiency of the engine by increasing the ratio of feed liquid mass flow in the heat recovery jacket to the total feed liquid mass flow.

In some embodiments, the working material is water.

Some embodiments including putting the water in a supercritical state. According to another embodiments, an engine is disclosed including: a chamber defined by at least one fixed wall and at least one movable wall, the volume of the chamber variable with movement of the movable wall; an injector arranged to inject liquid into the chamber while the chamber has a substantially minimum volume; an apparatus constructed and arranged to introduce energy into the chamber while the chamber has a substantially minimum volume at a rate sufficient to explosively vaporize the liquid, where the movable wall is adapted to move in response to work performed by the vaporized liquid, thereby increasing the volume of the chamber; an apparatus constructed and arraneed to return the movable wall to a position prior to the work being performed thereon so the chamber has the substantially minimum volume; and a valve constructed and arranged to substantially evacuate the chamber of vaporized fluid without substantially compressing the vaporized fluid.

According to another embodiment, a method of converting energy from one form to another in a system is disclosed, including: confining a quantity liquid within a chamber at a constant minimum volume; adding energy to the system while maintaining the chamber at the constant minimum volume, so as to heat the liquid sufficiently to vaporize the liquid; expanding a resulting vapor; and receiving mechanical energy from the expanding vapor in a form of movement of a wall of the chamber responsive to the expansion.

In some embodiments, adding energy to the system while maintaining the chamber at the constant minimum volume, so as to heat the liquid sufficiently to vaporize the liquid includes vaporizing the liquid in the absence of a chemical reaction.

According to another embodiment a method of converting energy from one form to another by passing a working material through a closed liquid-vapor thermodynamic cycle, including: expanding at least a portion of the working material from a liquid phase into a vapor phase by addition of heat; recovering heat from the working material after expanding; condensing the working material, after recovering heat, from the vapor phase into the liquid phase, in a condenser, thus restoring the working material to a state where the working material awaits expansion to start a new cycle; and adding the recovered heat to working material awaiting expansion, without changing the phase thereof.

In one aspect, a method is disclosed of converting thermal energy into another energy form using a thermodynamic cycle, the method including the steps of:

pressurizing a working fluid; supplying thermal energy to heat the working fluid from a liquid or substantially liquid state to a supercritical fluid state; in a first expander, substantially isentropically expanding the working fluid to yield energy in the other energy form; separating the expanded working fluid to form a first portion of the fluid diverted to a second expander and a second portion of the working fluid diverted to bypass the second expander; in the second expander, substantially isentropically expanding the first portion of the working fluid to yield energy in the other energy form; condensing the expanded first portion of the working fluid to a liquid or substantially liquid state; and recombining the first and second portions of the working fluid to be recirculated in the cycle.

In some embodiments, in the first expander, the working fluid is progressively dried during at least a portion of the expansion. In some embodiments, in the second expander, the first portion of the working fluid is progressively dried during at least a portion of the expansion.

In some embodiments, the other form of energy includes mechanical energy.

In some embodiments, the first expander or the second expander includes a turbine expander. In some embodiments, the first expander or the second expander includes a piston expander.

In some embodiments, the working fluid is an organic fluid. In some

embodiments,the organic fluid includes at least one fluid from the list consisting of: ammonia, benzene, butane, isobutane, carbon tetrachloride, HCFC-123, propane, R- 245fa, R-245ca, and toluene. In some embodiments, the organic fluid has a critical temperature of about 200 degrees C or less. In some embodiments, the organic fluid has a critical temperature of about 175 degrees C or less. In some embodiments, the organic fluid has a critical temperature of about 150 degrees C or less. In some embodiments, the organic fluid has a critical temperature in the range of 150-200 degrees C.

In some embodiments, the step of condensing the expanded first portion of the working fluid to a liquid or substantially liquid state includes rejecting heat from the cycle at a temperature of about 45 degrees C or more.

In some embodiments, the step of heating the working fluid include accepting heat from a heat sources at a temperature of about 200 degrees or less (e.g. 175 degrees C or less, 150 degrees C or less, etc).

In some embodiments, the cycle has a Carnot efficiency of about 30% or more.

In some embodiments, the efficiency of the first expander and the second expander is about 80% or more. In some embodiments, the net cycle efficiency in about 15% or more.

In some embodiments, the specific net work output of the cycle is about 20 kJ/Kg or more.

In some embodiments, the step of separating the working fluid includes separating the working fluid with a bypass ratio of about 50%.

In some embodiments, in the step of in a first expander, substantially isentropically expanding the working fluid, the expansion is characterized by an expansion ratio of in the range of 4: 1 and 8:1.

In some embodiments, in the step of, in a second expander, substantially

isentropically expanding the first portion of the working fluid, the expansion is characterized by an expansion ratio in the range of 4: 1 and 12: 1.

Some embodiments further include the step of: after condensing the expanded first portion of the working fluid and prior to recombining the first and second portions of the working fluid, substantially isentropically pressurizing the first portion of the working fluid.

In some embodiments, the step of recombining the first and second portions of the working fluid, the first portion of the working fluid is at a lower temperature than the second portion of the working fluid.

In some embodiments, the step of recombining the first and second portions of the working fluid includes transferring heat from the second portion to the first portion by direct contact of the first and second portions of the working fluid.

Some embodiments further include the step of: after the step of separating the expanded working and prior to the step of recombining the first and second portions of the working fluid, extracting heat from the second portion of the working fluid. Some embodiments further include using the heat extracted from the second portion of the working fluid to drive a secondary thermodynamic cycle to convert the heat to another form of energy.

In some embodiments, the secondary cycle converts the heat extracted from the second portion of the working fluid to mechanical work. In some embodiments, the secondary thermodynamic cycle includes a trilateral flash cycle or a Rankine cycle.

In some embodiments, the secondary thermodynamic cycle operates on an organic working fluid. In some embodiments, the secondary thermodynamic cycle operates on an inorganic working fluid.

In some embodiments, the step of supplying thermal energy to heat the working fluid from a liquid or substantially liquid state to a supercritical fluid state includes: injecting a quantity of the working fluid in the liquid or substantially liquid state into a chamber without substantially expanding the fluid; and holding the chamber at fixed volume while introducing energy to the quantity of the working fluid to vaporize the quantity of the working fluid.

In some embodiments, introducing energy to the quantity of the working fluid includes introducing optical energy to the quantity of the working fluid through at least one light transmissive region of the chamber.

In some embodiments, the quantity of working fluid is explosively vaporized without a chemical reaction.

Some embodiments further include:prior to condensing the expanded first portion of the working fluid, transferring heat from the expanded first portion of the working fluid to the recombined the first and second portions of the working fluid to be recirculated in the cycle.

Some embodiments include using a heat exchanger to transfer the heat from the expanded first portion of the working fluid to the recombined the first and second portions of the working fluid to be recirculated in the cycle.

In some embodiments, the heat exchanger does not mix the expanded first portion of the working fluid with thee combined the first and second portions of the working fluid. Some embodiments include separating the first portion of expanded working fluid from the second expander to form a third portion of the fluid diverted to a third expander and a forth portion of the working fluid diverted to bypass the third expander.

Some embodiments include, in the second expander, substantially isentropically expanding the first portion of the working fluid to yield energy in the other energy form.

In another aspect, an apparatus for converting thermal energy into another energy form including a closed cycled heat engine including: a first pump configured to pressurize a working fluid; a first heat exchanger configured to supply thermal energy for a heat source to heat the working fluid from a liquid or substantially liquid state to a supercritical fluid state; a first expander configured to receive the heated working fluid in the supercritical state and substantially isentropically expand the working fluid to yield energy in the other energy form; and a bypass mechanism configured to separate the expanded working fluid to form a first portion of the fluid diverted to a second expander and a second portion of the working fluid diverted to bypass the second expander; the second expander configured to substantially isentropically expand the first portion of the working fluid to yield energy in the other energy form; a condenser configured to reject heat from the expanded first portion of the working fluid to condense the expanded first portion of the working fluid to a liquid or substantially liquid state; and a combining mechanism configured to recombine the first and second portions of the working fluid and directed the combined working fluid to the first pump to be recirculated in the cycle.

In some embodiments, in the first expander, the working fluid is progressively dried during at least a portion of the expansion. In some embodiments, in the second expander, the first portion of the working fluid is progressively dried during at least a portion of the expansion.

In some embodiments, the other form of energy includes mechanical energy.

In some embodiments, the first expander or the second expander includes a turbine expander. In some embodiments, the first expander or the second expander includes a piston expander.

In some embodiments, the working fluid is an organic fluid. In some embodiments, the organic fluid includes at least one fluid from the list consisting of: ammonia, benzene, butane, isobutane, carbon tetrachloride, HCFC-123, propane, R-245fa, R- 245ca, and toluene. In some embodiments, the organic fluid has a critical temperature of about 200 degrees C or less. In some embodiments, the organic fluid has a critical temperature of about 200 degrees C or less. In some embodiments, the organic fluid has a critical temperature of about 175 degrees C or less. In some embodiments, the organic fluid has a critical temperature of about 150 degrees C or less. In some embodiments, the organic fluid has a critical temperature in the range of 150-200 degrees C.

In some embodiments, the condenser is configured to reject heat at a temperature of about 45 degrees C or more.

In some embodiments, the heat source is at a temperature of about 200 degrees or less. In some embodiments, the cycle has a Carnot efficiency of about 30% or more. In some embodiments, the efficiency of the first expander and the second expander is about 80% or more. In some embodiments, the net cycle efficiency in about 15% or more. In some embodiments, the specific net work output of the cycle is about 20 kJ/ g or more.

In some embodiments, the bypass mechanism separates the working fluid with a bypass ratio of about 50%.

In some embodiments, the first expander is characterized by an expansion ratio in the range of 4:1 to 8: 1 In some embodiments, the second expander is characterized by an expansion ratio in the range of 4: 1 to 12:1.

Some embodiments further include: a second pump configured to receive the first portion of the working fluid from the condenser, isentropically pressurize the first portion of the working fluid, and direct the pressurized first portion of the working fluid to the combining mechanism. In some embodiments, the combining mechanism receives the first portion of the working fluid at a lower temperature than the second portion of the working fluid. In some embodiments, the combining mechanism includes a direct contact heat exchanger configured to transfer heat from the second portion to the first portion of the working fluid by direct contact of the first and second portions of the working fluid.

Some embodiments include: a second heat exchanger configured to extract heat from the second portion of the working fluid.

Some embodiments include: a secondary thermodynamic cycle heat engine which receives the heat extracted from the second portion of the working fluid and converts the heat to another form of energy.

In some embodiments, the secondary thermodynamic cycle heat engine converts the heat extracted from the second portion of the working fluid to mechanical work.

In some embodiments, the secondary thermodynamic cycle heat engine includes a trilateral flash cycle heat engine or a Rankine cycle heat engine.

In some embodiments, the secondary thermodynamic cycle heat engine operates on an organic working fluid.

In some embodiments, the secondary thermodynamic cycle heat engine operates on an inorganic working fluid.

In some embodiments, the first heat exchanger includes: an injector configured to introduce a quantity of the working fluid in the liquid or substantially liquid state into a chamber without substantially expanding the fluid; and a heating mechanism for introducing energy to the quantity of the working fluid to vaporize the quantity of the working fluid while holding the chamber at fixed volume.

In some embodiments, the heating mechanism includes at least one light transmissive region of the chamber configured to transmit optical energy to the quantity of the working fluid.

In some embodiments, in response to the introduced energy, the quantity of working fluid is explosively vaporized without a chemical reaction. In some embodiments, the at least one light transmissive region includes a material of relatively high transmissivity and relatively low absorptivity to solar radiation.

In some embodiments, the at least one light transmissive region includes a material low emissivity at wavelengths in the near infrared an infrared portions of the spectrum.

In some embodiments, the closed cycle heat engine further includes a recuperating heat exchanger configured to transfer heat from the expanded first portion of the working fluid to the condensed working fluid which has exited the condenser.

In some embodiments, the closed cycle heat engine further includes a second bypass mechanism configured to separate the first portion of expanded working fluid from the second expander to form a third portion of the fluid diverted to a third expander and a forth portion of the working fluid diverted to bypass the third expander; the third expander configured to substantially isentropically expand the first portion of the working fluid to yield energy in a form other than heat.

Some embodiments include a second combining mechanism configured to combine the third and fourth portions of the expanded first portion of the working fluid

In another aspect, a method is disclosed of converting thermal energy into another energy form including the steps of: converting thermal energy to another energy form using a first trilateral flash cycle operating on a first working fluid, where the first trilateral flash cycle receives heat from a source at a first temperature Tl and rejects heat at a second temperature T2 lower that the first temperature; converting thermal energy to another energy form using a second trilateral flash cycle operating on a second working fluid, where the second trilateral flash cycle receives heat rejected from the first trilateral flash cycle at a third temperature T3 equal to or lower than T2 and rejects heat at a fourth temperature T4 lower than T3.

In some embodiments, the working fluid is an organic fluid. In some embodiments, the organic fluid includes at least one fluid from the list consisting of: ammonia, benzene, butane, isobutane, carbon tetrachloride, HCFC-123, propane, R-245fa, R- 245ca, and toluene. In some embodiments, the organic fluid has a critical temperature of about 200 degrees C or less. In some embodiments, the organic fluid has a critical te.rrmeratiire nf abmit 900 decrrp.es C. nr less Tn some emhnHiments the organic fluid has a critical temperature of about 175 degrees C or less. In some embodiments, the organic fluid has a critical temperature of about 150 degrees C or less. In some embodiments, the organic fluid has a critical temperature in the range of 150-200 degrees C.

In some embodiments, the converting thermal energy to another form using the first and second trilateral flash cycles includes, respectively: substantially isentropically pressurizing the respective first or second working fluid; supplying thermal energy to heat the respective first or second working fluid; in a respective first or second expander, substantially isentropically expanding the respective heated first or second working fluid to yield energy in the other energy form; condensing the expanded respective first or second working fluid exhausted from the respective first or second expander; and recirculating the condensed respective first or second working fluid for recompression.

In some embodiments, the other form of energy includes mechanical work.

In some embodiments, the first and second expanders include reciprocating piston expanders.

Some embodiment use the first and second piston expanders to drive a common shaft.

In some embodiments, Tl is about 300 degrees C or less. In some embodiments, T2 is about 100 degrees C or more. In some embodiments, T3 is about 100 degrees C or less. In some embodiments, T4 is about 40 degrees C or more.

In some embodiments, the first cycle and second cycles are characterized by a net efficiency of about 10% or greater.

In some embodiments, at least one of the first and second expanders includes a turbine expander.

In some embodiments, for at least a respective one of the first and second trilateral flash cycles, the converting thermal energy to another form using the respective trilateral flash cycle includes: prior to the isentropic expansion, injecting a quantity of the heated respective first or second working fluid into a chamber without substantially expanding the fluid; and holding the chamber at fixed volume while introducing energy to the quantity of the working fluid to vaporize the quantity of the working fluid.

In some embodiments, introducing energy to the quantity of the working fluid includes introducing optical energy to the quantity of the working fluid through at least one light transmissive region of the chamber.

In another aspect, an apparatus is disclosed for converting thermal energy into another energy form including: a first trilateral flash cycle heat engine operating on a first working fluid configured to convert thermal energy to another energy form using a first trilateral flash cycle, where, during operation, the first trilateral flash cycle heat engine receives heat from a source at a first temperature Tl and rejects heat at a second temperature T2 lower that the first temperature; and a second trilateral fiash cycle heat engine operating on a first working fluid configured to convert thermal energy to another energy form using a first trilateral flash cycle, where, during operation, the second trilateral flash cycle heat engine receives heat rejected from the first trilateral flash cycle heat engine at a third temperature T3 equal to or lower than T2 and rejects heat at a fourth temperature T4 lower than T3.

In some embodiments, the first working fluid has a higher boiling point that the second working fluid.

In some embodiments, the first working fluid includes water and the second working fluid includes an organic fluid.

In some embodiments, the organic fluid includes at least one fluid from the list consisting of: ammonia, benzene, butane, isobutane, carbon tetrachloride, HCFC- 123, propane, R-245fa, R-245ca, and toluene. In some embodiments, the organic fluid has a critical temperature of about 200 degrees C or less. In some

embodiments, the organic fluid has a critical temperature of about 200 degrees C or less. In some embodiments, the organic fluid has a critical temperature of about 175 degrees C or less. In some embodiments, the organic fluid has a critical temperature of about 150 degrees C or less. In some embodiments, the organic fluid has a critical temperature in the range of 150-200 degrees C. In some embodiments, the first and second trilateral flash cycles include,

respectively: a respective first or second pump configured to substantially isentropically pressurize the respective first or second working fluid; a respective first or second heat exchanger configured to supply thermal energy to heat the respective first or second working fluid: a respective first or second expander configured to substantially isentropically expand the heated respective first or second working fluid to yield energy in the other energy form; a respective first or second condenser configured to condense the expanded respective first or second working fluid exhausted from the respective first or second expander; and a conduit configured to recirculate the condensed respective first or second working fluid for recompression.

In some embodiments, the other form of energy includes mechanical work.

In some embodiments, the first and second expanders include reciprocating piston expanders.

In some embodiments, the first and second piston expanders to drive a common shaft.

In some embodiments, the common shaft drives a generator to convert mechanical work to electrical energy.

In some embodiments, Tl is about 300 degrees C or less. In some embodiments, T2 is about 100 degrees C or more. In some embodiments, T3 is about 100 degrees C or less. In some embodiments, T4 is about 40 degrees C or more. In some

embodiments, the first cycle and second cycles are characterized by a net efficiency of about 10% or greater. In some embodiments, at least one of the first and second expanders includes a turbine expander.

In some embodiments, at least a respective one of the first and second trilateral flash cycle heat engine includes: an injector configured to inject a quantity of the heated respective first or second working fluid into a chamber without substantially expanding the fluid; and a mechanism for holding the chamber at fixed volume while introducing energy to the quantity of the working fluid to vaporize the quantity of the working fluid prior to expansion in the respective first or second fvxnanHe.r Tn snmfi pmhnrlimpnts hp mpr.liankm inHiii-lpc at 1<=>a«t ntip li oht transmissive region of the chamber configured to transmit optical energy to the quantity of the working fluid through at least one light transmissive region of the chamber.

In some embodiments, the first expander is characterized by an expansion ratio of in the range of 4: 1 to 8 : 1. In some embodiments, the first expander is characterized by an expansion ratio in the range of 4: 1 to 12: 1.

Various embodiments may include an of the above features, elements, steps, or techniques, either alone or in any suitable combination.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings are not intended to be drawn to scale. In the drawings, each identical or nearly identical component that is illustrated in various figures is represented by a like numeral. For purposes of clarity, not every component may be labeled in every drawing. In the drawings:

FIG. 1 is an overall schematic of a system implementing a proposed thermodynamic cycle showing the major elements;

FIG. 2 depicts the thermodynamic cycle laid out on a steam T - s diagram;

FIG. 3 is a graph of a typical measured and predicted expansion curve derived from experimental rig operation;

FIG. 4 is a schematic showing a solar beam entering an exemplary expansion chamber through a sapphire window;

FIG. 5 is a perspective view of a cylinder and piston system showing a valving method according to some embodiments;

FIG. 6 is a schematic block diagram of a system implementing a proposed thermodynamic cycle including a variable bypass; FIG. 7 depicts the variable bypass thermodynamic cycle laid out on a steam T - s diagram; FIG. 8 depicts the variable bypass thermodynamic cycle for the special case of a bypass ratio of 1 : 1 laid out on a steam T - s diagram;

FIG. 9 is a pressure - volume graph showing the effect of a 50% bypass ratio; FIG. 10 is an overall schematic of another system implementing a proposed

thermodynamic cycle showing the major elements; and

FIG 10: Is a block diagram for a supercritical cycle

FIG. 11 depicts the thermodynamic cycle laid out on a steam T s diagram.

FIG. 12 depicts a thermodynamic cycle featuring feed preheating laid out on a steam T s diagram. FIG. 13 illustrates an exemplary heat engine corresponding to the thermodynamic cycle of FIG. 12.

FIG. 14 is a plot of efficiency versus temperature for the heat engine of FIG. 13.

FIG. 15 is an illustration of an exemplary heat engine suitable for use with a low grade heat source. FIG. 15 A is a plot of cycle efficiency as a function of heat source return temperature for an exemplary heat engine.

FIG. 15B. is an illustration of an exemplary heat engine suitable for use with a low grade heat source featuring a heat recuperator.

FIG. 15C is an illustration of an exemplary heat engine suitable for use with a low grade heat source featuring three expanders and heat recuperator.

FIG. 16 depicts the thermodynamic cycle of the heat engine of FIG. 15 laid out on an organic fluid T s diagram.

FIG. 16A is a schematic of the thermodynamic cycle of the heat engine of FIG. 15 accounting for imperfectly isentropic expansion. FIG. 17 is an illustration of an exemplary heat engine suitable for use with a low grade heat source featuring a secondary cycle.

FIG. 18 depicts the thermodynamic cycle of the heat engine of FIG. 17 laid out on an organic fluid T s diagram. FIG. 19 is an illustration of the secondary cycle of the heat engine of FIG. 17.

FIG. 20 is an illustration of a heat engine device featuring cascaded cycles.

FIG. 21 depicts the upper thermodynamic cycle of the heat engine of FIG. 20 laid out on a steam T s diagram.

FIG. 22 depicts the upper thermodynamic cycle of the heat engine of FIG. 20 laid out on an organic fluid Pressure-Enthalpy diagram.

FIG. 23 is a schematic of an exemplary embodiment of a heat engine device featuring cascaded thermodynamic cycles as depicted in FIGs. 21 and 22.

DETAILED DESCRIPTION

This invention is not limited in its application to the details of construction and the arrangement of components set forth in the following description or illustrated in the drawings. The invention is capable of other embodiments and of being practiced or of being carried out in various ways. Also, the phraseology and terminology used herein is for the purpose of description and should not be regarded as limiting. The use of "including," "comprising," or "having," "containing," "involving," and variations thereof herein, is meant to encompass the items listed thereafter and equivalents thereof as well as additional items.

A single sided expander and its working cycle is now described. The single sided expander includes an oscillating piston and linear electrical generator. The single sided expander is derived from actual experimental rig results. It will be understood that expanders operating on the principles illustrated by the single sided expander but employing more than one moveable wall element are possible. Moreover, the single sided expander is described in the context of a cylindrical chamber having a piston which moves to vary the size of the chamber; however, it will be understood that other expander configurations are possible, for example based on a rotary configuration similar to the Wankel internal combustion engine, which also has an expansion chamber having a single side which moves to vary the size of the chamber. Any suitable expander chamber configuration in which the expander chamber varies in size responsive to the force of the expanding vapor within and which is returned to a starting position by excess energy temporarily stored in a flywheel or other device for the purpose.

The operating thermodynamic cycle for the expanders, according to various embodiments, is a closed cycle, having relatively high conversion efficiency. It will be contrasted with a conventional Rankine thermodynamic cycle. It is based on the heating and expansion of a droplet or thin film of any suitable liquid, without any substantial precompression of the liquid or any substantial pre-compression of any gas surrounding the liquid.

Reference will now be made to FIG. 1 , which is a schematic and FIG. 2, a thermodynamic cycle diagram superimposed on a Temperature - entropy (T - s) diagram. Referring to FIG. 1 , the heat engine comprises four main elements, a piston type expander 101 , a heat exchanger 102, a vapor condenser 103, a liquid pump 104 an incoming concentrated solar beam 105 and a linear generator 106.

Each element is more fully described below. Points of transition on the T - s diagram of FIG. 2 denoted by single-digit reference numbers are also indicated in

FIG. 1 at locations which indicate where in the exemplary apparatus each point in the thermodynamic cycle is achieved.

The Expander 101 includes a piston 107 in a cylinder 108, the piston having a piston top 109, which forms a suitable cavity boundary, together with the cylinder 108 and a cylinder head 110. When it is in top dead centre (TDC) position a water droplet or film 1 11 is injected into this cavity, with necessary propellant force being provided by the liquid pump 104.

A concentrated solar beam 105 is applied intermittently through a sapphire window 112 or other means provided in the cylinder head 1 10, such that the trapped water droplet or film 111 is vaporized and expands against the piston top 109, producing mechanical power, during an expansion stroke. See also FIG. 4. The expansion stroke, also referred to herein as Process 1- 2, is depicted as a line 1 - 2 in the T - s chart in FIG. 2. This expansion stroke is initiated by and continues during the input of heat to the working fluid to produce mechanical power through PdV work on the piston. In contrast, Rankine cycle engines separate the input of heat energy to the working fluid (e.g., in a boiler) and the extraction of mechanical work therefrom (e.g., in an expansion cylinder).

In addition to utilizing a beam of concentrated solar radiation, any other suitable method of introducing heat into the chamber may be used. For example, a heat exchanger with flow passages on the outside of the chamber may be configured to heat up a flat surface or surface with enhanced area (e.g., textured to have additional surface area), which is directly in contact with the water film inside the cylinder and trapped between piston and cylinder head. Alternatively, a porous block or plate may be fitted between the piston and cylinder head. The porous block, which, as a result of its porosity, has a very substantial surface to volume ratio, can be heated by applying heat externally, which is then transferred through the cylinder head into the block. In yet another alternative, a series of heat pipes embedded in the cylinder head, may enable heat to be transferred at a very high rate from external sources. This last alternative can be combined with the use of the porous block or heat transfer surface explained above.

Exhaust of spent vapor at point 2 on the T-s diagram is carried out by a rotation of the piston such that exhaust ports 122 on the cylinder wall line up with grooves 120a and 120b in the piston, as shown in FIGs. 4 and 5. Rotation of the piston, as well as its return to TDC, is achieved by means of springs 118a and 1.18b configured to provide rotation as they flex along the axis of the piston 107. Spent vapor is exhausted through heat exchanger 102, which enables recovery of heat from spent vapor into condensed liquid awaiting injection into the cylinder 108. Spent vapor exhaust, also referred to herein as Process 2 - 3, is indicated as a constant volume process by line 2 - 3 in the T - s diagram. In addition to piston rotation, any other suitable method for exhausting spent vapor may be used. For example, a poppet type valve can be disposed in the cylinder head, operated by a solenoid, mechanical lifters or any other suitable means.

Alternatively, a valve can comprise a combination of a slot in the piston together with a slot disposed in a rotating sleeve disposed to the outside of the piston. The rotating sleeve may comprise the whole of the cylinder. A cyclical rotation of the sleeve can alternately bring into alignment and take out of alignment the slot in the piston wall in relation to the corresponding slot in the cylinder wall. In yet another alternative, a poppet valve may be disposed on the top surface of the piston, exhausting spent vapor to the area behind the piston. This last alternative has some advantages, notably that the constant pressure condensation step (step 3- 4 in FIG. 4) can take place during the expansion step. The heat recovery heat exchanger can, in this alternative, be installed within the expander, leading to greater compactness and lowered weight. Spent vapor must be condensed, also referred to herein as Process 3 - 4, prior to reinjection into the cylinder, for example, in condenser 103. The process pathway is given as line 3 - 4 in the T - s diagram. The spent vapor condensation, Process 3 - 4, is represented as a constant pressure process. At point 4, the spent vapor is wholly in liquid form, ready for injection into the expander cylinder to start a new cycle. Thus, a continually refreshed supply of working fluid is not required, as the cycle is closed.

Condensed liquid from the condenser 103 is pumped up to injection pressure by means of pump 104, through heat exchanger 102 and then injected into cylinder 108 as a liquid droplet or thin film. The heat exchanger 102 permits otherwise wasted heat in the vapor to be recovered for the useful purpose of increasing the energy available in the next expansion cycle, rather than simply disposing of waste heat. This part of the cycle is indicated as lines 4 - 5 (liquid pumping, Process 4 5) and 5 - 6 (constant volume heat gain, Process 5 - 6), in the T - s diagram. Notably, because the heat recovered by the heat exchanger 102 provides insufficient energy to the liquid to vaporize the liquid prior to or dining injection into the cylinder 108, the full energy of expansion of the liquid into expanded vapor after adding some quantum of externally supplied heat is available to perform work on the piston 107.

The inventive cycle is distinguished from conventional Rankine cycles in part by eliminating the boiler and also because inward heat transfer occurs while the working fluid is in the cylinder 108. Other differences include the presence of two constant volume heat transfer processes, (1) Process 2 - 3, and (2) Process 5 - 6, in the T - s diagram, and a low pressure compression step, 3 - 4. The portion 6 - 1 is an external heat addition step, because the total recovered heat in the 5 - 6 step is insufficient to heat the condensed fluid awaiting expansion to the fluid's saturation temperature at point 1.

In comparison with conventional Rankine cycles, the ability to do external work during the heat addition process has not previously been considered practical by those skilled in this art, possibly because of the difficulty of implementation. The described and heretofore unknown embodiment, and the variations suggested herein, each demonstrate a way to accomplish this useful result.

In contrast with conventional Rankine cycles a very high expansion ratio is achieved by embodiments in a single cylinder. Because the working fluid is expanding directly from a condensed liquid state to vapor within the cylinder of the expander, expansion ratios of over 80: 1 may be achieved in a single cylinder with a four inch diameter and 5 inch stroke. See FIG. 3. This is quite remarkable compared to conventional steam reciprocating engines, which barely achieve expansion ratios of between 5:1 or 8: 1 in a single cylinder; and also compared to internal combustion engines achieve at best expansion ratios of between 12: 1 or 15: 1. High conversion efficiency in internally heated cycles depends on two main elements; a high initial gas phase temperature and pressure and a high expansion ratio. In the present cycle, a very high expansion ratio has been achieved in one single cylinder with a relatively short stroke.

Embodiments further employ a single piston on a rod; to the opposite end of this rod a linear generator 106 is mounted, capable of absorbing mechanical energy produced and converting that mechanical energy in the form of motion to electrical energy, at high efficiency. The linear generator consists of permanent magnet 116 and/or coil 114 type system for excitation field and a coil 114 based electrical output system, with necessary software based field current control for production of sinusoidal power output. A rotary crank and suitable connecting rod can also permit connection to a conventional, rotary generator.

In general terms, the invention consists of a unique liquid film-based, constant- temperature, wet-region, expansion heat engine device, running on a unique, hitherto unexploited thermodynamic power cycle, with heating during expansion resulting in an expansion with no internal energy change, constant volume heat transfer, isothermal compression, leading to very high conversion efficiency,

The theoretical basis for the operation of the inventive engine is now presented using non-flow, 1 ^st Law analyses. The theoretical underpinning of each of the processes discussed above is given.

Process 1— 2:

In the general case, δΗ is non zero. Therefore, rearranging, the heat input during Process 1-2 is

Process 2 - 3 :

Q ₂ . ₃ = (h ₂ -h ₃ )

Process 3 - 4:

Q _3-4 - W _3- 4 = n4-h ₃

Process 4 - 5:

This process constitutes pressurization of the liquid to operating pressure PI and is a work input term. Since the pressurization is being done on a liquid and not vapor, the magnitude of this term is usually low,

W ₄ . ₅ = (P,-P ₃ ) x vl Process 5 - 6:

This process constitutes a constant volume heat gain to the pressurized liquid and receives heat from the heat output process of process 2 - 3. No external or internal work is done, in this process. This is the transfer of heat from spent vapor which is to be condensed back to liquid (for subsequent injection into the expander), into the liquid that is presently awaiting injection into the expander, thus recovering heat that would otherwise be discarded as waste heat. Since the working fluid at 6 is in liquid form whereas the working fluid at 2 is a mixture of vapor and liquid, the total quantum of heat that may be recovered and introduced to the liquid in the process 5 - 6 is limited by the fluid temperature at 2.

Therefore, Q _5-6 = Q ₂ ' _-3 ,

where point 2' represents the liquid condition pertaining to the pressure and temperature at point 6. Therefore the enthalpy at 6 is given by h ₆ = ( r- ) + h ₅

Generally U ₅ = U ₄ , hence

h ₆ = h ₂

To bring the working fluid up to the working temperature and pressure, additional heat input, for example by transferring into the expansion chamber concentrated solar energy, is required, as follows:

Hence

Therefore total heat input to the cycle is

Qin total - Qe-l + Ql-2,

Or

Qin total = (h, - h ₂ >) + Wi _-2 +(h ₂ -U,).

Hence, 'in total

Qin total - W _1-2 + (h ₂ - h ₂ .).

Net work output from the cycle is given by

I W _{0Ut net} = W _1-2 - (W _3- 4 + w _4-5 ).

output plus a difference in the recovered energy in the constant volume heat transfer and the net work output is equal to gross work out less the low pressure vapor compression work and the liquid compression work.

Part of the heat available at point 2 of the cycle, after expansion, is recovered and utilized for preheating of the fluid prior to commencement of the cycle, at point 1 of the cycle, with additional heat addition to make up any shortfall,

One example of a novel thermodynamic cycle has been described, above. Further specific, novel modifications of a general class of cycles, based on the above cycle, are now presented.

The novel thermodynamic cycle described above, and the related cycles described now are part of a general class of cycles characterized by the Trilateral Flash Cycle described in US Patent Number 5,833,446, issued to Smith et al. The Trilateral Flash Cycle is presented in FIG. 6 and may be identified as follows:

Process 1- 2 Heat Addition at constant pressure

Process 2 - 3 Adiabatic, reversible expansion from saturated liquid state at 2 Process 3 - 4 Constant pressure condensation

The work described in the Smith at al. patent indicates the Trilateral Flash Cycle is suitable for low grade and geothermal heat recovery and highly suited to utilization with organic fluids. Smith et al. were unable to identify any wider range of suitable application for the particular cycle they describe. During any Rankine cycle process in the wet vapor region, heat may be recovered during expansion. The quantity of heat recovered affects the improvement achieved in the power output and the efficiency.

According to an aspect of an embodiment, as illustrated by FIG. 6, a mixing valve 124 and a heat recovery jacket 128 can be employed for purposes of varying heat quantity recovered during expansion. A representation of the resulting process on a conventional T - s diagram is given in FIG. 7. One parameter helpful to defining the general class of cycles to which embodiments of the invention belong is the bypass ratio, which is defined as the ratio of feed liquid mass flow in the heat recovery jacket to the total feed liquid mass flow.

This bypass ratio may theoretically vary from 0 to 1 but very low bypass ratios result in low specific power outputs hence a more practical approach would be in the range 0.2 to 1.0. The expansion processes resulting from finite stepwise variation of bypass flow is generally shown as lines 2 - 3a, 2 - 3b, 2 - 3c etc. In each of these cases,

There is a progressive increase in specific power output and a decrease in overall efficiency as the line from 2 - 3n approaches vertical (not shown).

To describe the cycle more fully, feedwater at point 1 is pressurized by the pump (see FIG. 6) and sent to bypass splitter 126 where the flow is divided into a portion flowing through the heat recovery jacket and a portion flowing through a bypass line. The two flows are mixed at point 2' and the mixed flow proceeds to the heater. As mentioned the bypass ratio may be varied to let more or less liquid flow through the heat recovery jacket, resulting in varying quantities of heat recovered by and introduced into the feedwater flow. As a result of varying bypass flow, point 2' on the feedwater or pressurized liquid side of the cycle varies up and down, in relation to point 2 where the expansion starts. Low bypass ratio results in the point 2' being raised and coming closer to point 2 (higher efficiency, lower specific power output); whereas higher bypass ratio results in lowering of point 2' in relation to 2 (lower efficiency, higher specific power output). Process 2' - 2 represents the heat added in the heater. The Trilateral Flash Cycle identified by Smith et al. is a special case of the general class of liquid to vapor expansion bypass cycles, with a bypass ratio equal to 1, thereby resulting in a high specific power output but a low overall efficiency, for this class of cycles. A conventional Rankine cycle calculation may be applied to the liquid to vapor expansion bypass cycle; the resulting pressure volume diagram is given in FIG. 9. The calculation is carried out in a finite number of steps and consists of a pair of calculations in each step, namely a reversible, isentropic expansion followed by a constant volume heat recovery, by means of the heat transfer through the cylinder jacket to the feedwater. Typical results obtained were as follows, utilizing water as the working fluid:

Although it was not apparent to Smith et al, we have discovered that lower bypass ratios lead to a substantial efficiency increase. As a result of these high efficiencies water, which is readily available in many locales, may be used as the working fluid, whereas Smith et al. propose organic fluids due to perceived low efficiencies using water. Low efficiency using water in the trilateral cycle appears unavoidable in the literature, but we have discovered that low bypass ratio cycles lift this ceiling and permit consideration of water as a working fluid,

The new cycle with bypass may be logically and rationally extended to the supercritical region of the fluid, see FIG. 10 for a schematic and FIG. 1 1 for the cycle diagram. The method of operation of the system is exactly the same as in the wet region, except for much higher pressures and significantly higher temperatures. Because there is no constant pressure liquid to vapor conversion, the cycles are seamlessly changeable just in terms of pressure and temperature, with the same bypass heat recovery system applicable in all cases. The new cycle when extended to the superheated region shows higher efficiency than in the wet vapor region, in keeping with Carrot efficiency temperature dependence correlations. There is, however, substantial improvement in work done per unit mass of fluid, which is clearly apparent from the fact that internal energy and enthalpy are much higher in the supercritical region. A cycle with a reversible, adiabatic expansion directly from point 2 down to condensing temperature and pressure, as in the case of the trilateral flash cycle of FIG. 9, is possible and once again becomes a special case, with a bypass ration of 1. There is no art known to this inventor suggesting the special case of a supercritical cycle bypass ratio 1 expansion (reversible adiabatic) to condensing temperature.

The general class of liquid to vapor expansion cycles in the wet vapor and supercritical region with bypass constitute a new class of thermodynamic cycles and provides enhanced efficiency possibilities in a multitude of applications: fixed bypass ratio systems may be used in constant output applications such as geothermal power generation; and, variable bypass ratio systems may be considered for hybrid vehicle applications, wherein a low bypass ratio is used during cruising only to charge a battery at a high efficiency, with a momentary high bypass ratio used to produce higher power output for overtaking, etc.

In another embodiment, instead of recovering heat from a jacket external to the expansion cylinder, it is possible to recover heat by splitting the working fluid into two parts after a first expansion process, see Figs. 12 and 13. In such a case, the cycle diagram is shown in Fig 12.

The cycle process steps are as follows. In process 1 - 2 the working fluid is preheated by means of extracted working fluid from an expansion process, in heat exchanger 131. In process 2 - 3 heat is added to the preheated working fluid from outside source in a heat exchanger. In process 3 - 4, a primary expansion of all of the working fluid occurs, e.g. in piston/cylinder expander 1 12. As shown, the primary expansion is isentropic (i.e. reversible and adiabatic). In some

embodiments, the primary expansion may take place in any other suitable type of expander, e.g. a turbine expander. In some embodiments, mechanical work

extracted durine the nrimarv exnansinn nrnne.ss (e, frnm nistnn eynanHer 1 1 9 mav be used for any suitable application, e.g. to drive the shaft of a generator (e.g. a linear generator as shown) to generate electrical energy.

The working fluid is then exhausted at point 4 and divided into two parts in the flow splitter 129. A first portion of the working fluid, having a fluid fraction k where 0 <k<l is diverted into heat exchanger 131 , as a heating fluid used to preheat the working fluid as described above. In process 4 - 2' - 1 heat is transferred in exchanger 131 from the first portion (i.e. the diverted portion) of the working fluid to the condensed and pressurized working fluid moving from condenser 103 through pump 104. A second portion of the working fluid, having fluid fraction 1 - k, is sent to a second expander 130. As shown expander 130 is a piston expander, but any other suitable expander (e.g. a turbine expander) may be used. In process 4 - 5 the second portion of the working fluid undergoes further expansion to the condition at the fluid condenser 103 denoted as point 5, with production of additional work. In process 5 - 6 the second portion of the working fluid is condensed in the condenser 103.

In process 6 - 6' the first (diverted) and second (undiverted) portions of the working fluid are mixed at the suction entrance to the pump. In process 6 - 1 the combined fluid is pressurization by the pump, and is ready to be recirculated to start new cycle

By utilizing a fraction k of the working fluid to preheat all of the working fluid, a significant efficiency gain is achieved in the thermodynamic cycle. Not wishing to be bound by theory, the inventors have found that the overall cycle efficiency may be calculated by the formula:

(h3 -(l-k) h5) - h4 k Efficiency =

(h3 - h2) Where h3 is enthalpy at point 3, h5 is enthalpy at point 5, h2 is the liquid enthalpy at point 2, h4 is the liquid vapor mix enthalpy at point 4, k is the fraction of working fluid diverted to be used in preheating, and T4 is the temperature at point 4. This simple but elegant formula provides a convenient method of calculating ideal cycle efficiency.

Fig. 14 shows an efficiency curve as a function of temperature T4 for a high pressure cycle with fluid extraction. In this case the temperature T4 is the intermediate temperature after the first expansion in expander 112, The basic cycle parameters are as follows:

Notably, as shown in Fig. 14, the efficiency of the cycles is improved relative to a cycle without extraction for preheating over a wide range of intermediate temperatures T4.

A cycle of this type may have it's highest temperature and pressure point in the supercritical or subcritical region, in Fig 12, the presentation is given in the subcritical region. As described in detail below, a similar construction is applicable in the supercritical region. The cycle is highly advantageous in that the primary heat exchanger providing "heat input" and the condenser 103 may both be much smaller than in a comparable Rankine cycle, also a higher efficiency is achieved with just one stage of extraction type feedheating. In typical applications, a Rankine cycle requires six to nine or more stages of extraction feedheating, to achieve high efficiencies,. Referring to Figs. 15, an exemplary heat engine 200 suitable for use with a low grade heat source (for example at a temperature of less than 250 degrees C, less than 200 degrees C, or even less, e.g. in the range of 150-250 degrees C) is illustrated. The corresponding thermodynamic cycle diagram for the heat engine 200 is shown in Fig, 16. As with the embodiment shown in Figs. 12 and 13, the heat engine 200 recovers heat for feed fluid preheating by splitting the working fluid into two parts after a first expansion process. However, the heat engine 200 preferably operates on an working fluid (e.g. an organic fluid) having a relatively low critical point temperature, for example less than 250 degrees C, less than 200 degrees C, less than 175 degrees C, less than 150 degrees C, or even less. In some embodiments, the working fluid critical temperature is in the range of 150 to 200 degrees C. As detailed below, such a low critical point working fluid may be readily heated to a supercritical state prior to expansion using heat from a low grade source.

Referring to Fig. 15, the heat engine includes a heat exchanger 201 for transferring sensible heat from an incoming fluid (e.g. heated water from a collector field) to the pressurized cycle working fluid (as shown, organic working fluid R-245fa having a critical temperature of about 154 degrees C). As shown the incoming fluid is at a temperature T=190 degrees C. This heat transfer is represented in Fig. 16 as process 1-2. As shown, the pressurized fluid is heated from a liquid state to a supercritical fluid state at a temperature T ₂ = 180 degrees C.

The heated supercritical working fluid undergoes an isentropic expansion process 2- 3 in the first high pressure expander 202. As shown the first expander is a turbine expander, but any suitable expander (e.g. a reciprocating piston expander) may be used. Work W _hP (e.g. mechanical work) is extracted during the expansion process. Referring to Fig. 16, note that the saturated vapor states of the organic working fluid has a region of positive gradient. Accordingly, the working fluid R-245fa becomes progressively drier during expansion process 1-2. As will be understood by those skilled in the art, this is advantageous, e.g., in that smaller, less costly expanders may be used to expand a relatively dry vapor than would be required to expand a wet vapor. The working fluid exhausted from the first expander 202 enters a flow splitter 203 which directs a first portion of the working fluid to second low pressure expander 204, as indicated by process 3-4. The flow splitter 203 directs a second portion of the working fluid to bypass the second expander 204, as indicated by process 3-6. The first portion of the working fluid undergoes an isentropic expansion process 4-5 in the second low pressure expander 205. As shown the first expander is a turbine expander, but any suitable expander (e.g. a reciprocating piston expander) may be used. Work W _lp (e.g. mechanical work) is extracted during the expansion process. As in the first expansion process, the working fluid becomes progressively drier, which, in some embodiments, may advantageously allow for the use of smaller, less costly expanders.

In some embodiments, mechanical work extracted from the first and second expanders 202 and 204 may be used to drive a common shaft, e.g., which may in turn drive a generator to produce electrical energy. In other embodiments, the work generated by each of the expanders may be directed to separate applications.

Each of the first and second expanders may have expansion ratios greater than 1 :1, 2: 1 : 4: 1, 8:1 ; 12: 1 or more, e.g. in the range of 4:1 to 8:1 or 4:1 to 12: 1 or any other suitable value. In some embodiments the expansion ration of the first expander may be greater than less than or equal to that of the second expander. The first portion of the working fluid exhausted from the second expander 204 is directed to condenser 205. The condenser condenses the expanded vapor back to a liquid or substantially liquid state in process 5-7. The condenser rejects heat to the surrounding environment (as shown at temperature T ₇ =45 degrees C).

The condensed first portion of the working fluid is directed to the first low pressure pump 206, which isentropically pressurized the condensed fluid. The pressurized fluid is them mixed with the second portion of working fluid that was diverted to bypass the second low pressure expander 204. The first and second portions of the working fluid are mixed in direct contact heat exchanger 207 (point 6 in Figs. 15 and 16). The second portion of the working fluid is at a higher temperature than the first portion, and thus operates to preheat the first portion, as shown in process 8-9.

In process 9-10 the combined fluid is pressurization by the second high pressure pump 208. In process 10-1, the mixed, preheated, pressurized working fluid is recirculated to start new cycle.

A cyclic power generation process of this type with heat acceptance at a higher temperature and heat rejection at a lower temperature is governed by the Second Law of Thermodynamics and the maximum possible efficiency is the Carnot efficiency which is 1 - T2/T1 where Tl and T2 are absolute temperatures of the heat source (e.g. the temperature of incoming water) and heat sink (i.e. the temperature in the condensing process 5 -7) respectively. For the general conditions given in Fig. 16, Carnot efficiency is 31.3%. The other performance values for this exemplary embodiment are shown in the chart below.

An isentropic or expander efficiencies of 80% or more are achievable for organic fluids such as R-245fa. Because these fluids become drier as expansion proceeds, the expansion process can proceed to temperatures near ambient without the fluid becoming two-phase. This avoids the complications of and the reductions in expander efficiency of operation in the two phase region. Therefore utilizing this type of fluid leads to a high cycle efficiency. Suitable fluids include organic ammonia, benzene, butane, isobutane, carbon tetrachloride, HCFC 123, HCFC 134a, propane, R-245fa, R-245ca, toluene, or any other suitable fluid. Not wishing to be bound by theory, the inventors have found that a formula for the theoretical efficiency η for this type of cycle may be derived, as:

T T.

77 = 1 ^c - InH

in out out Where T _c is the temperature at which the cycle rejects heat (i.e. T ₇ as shown in Fig. 15), Tin is the temperature of the heat source (T _A as shown in Fig. 15), and T _out is the temperature at which fluid is returned to the heat source (T _B as shown in Fig. 15). Fig. 15A shows a plot of ideal efficiency η for the cycle shown in Fig. 15 as a function of T _ou t. As T _ou t increases from a value of T _out =T _c =45 degrees C to a value degrees C, the ideal efficiency is seen to increase approximately linearly from about 17% to about to Carnot efficiency of 31 %. In general, the ideal efficiency η may be used as a figure of merit to evaluate the performance of a given thermodynamic cycle.

The above formula for cycle efficiency assumes a perfectly isentropic (i.e., reversible) expansion process (i.e. process 2-5 as shown in Fig. 16). However, a modified formula may be used to calculate the efficiency of a cycle where the expansion process is not perfectly isentropic.

The isentropic efficiency r i _sen t for any gas expansion process, may be defined as the actual enthalpy change divided by ideal enthalpy change possible in the process and applies to reversible, adiabatic processes. Fig. 16A shows a modification of a thermodynamic cycle of the type shown in Fig. 16 to include some irreversibility in the expansion process. On the T - s diagram as shown, the vertical solid line Tj _n -T _c is an isentropic expansion line, and the dashed line is an imperfect expansion line, such that the ratio of the enthalpy differences is the isentropic efficiency. The temperature after irreversible expansion is Tout' and temperature after partial heat recovery is T _ou t" - Ideally, the total amount of heat available for recovery, represented as a temperature difference, is (T _ou t' - T _ou t). However, this whole amount may not available due to imperfect heat exchanger efficiencies. In such cases, the actual heat recovered is may represented by the difference between T _out " and T _out , given by (Τ _οΛ "-Τ _ου where k ⁼ Ω-Qut' '-Toutl

Therefore k is a proportionality factor, where 0<k<l , which accounts for less- than- perfect heat recovery in an actual heat exchanger .

Taking into account the isentropic expansion efficiency r i _sen t and the heat recovery factor k, the cycle efficency η may be calculated as: n = i - _F(T (fr - a - ¾-)0 - k)

V in out ' on! where

F = ((l - k) + k _isenl ) .

Note that for the special case k=l and ??isent ⁼ l, the above efficiency formula reduces to that derived in the case of perfect expansion efficiency and heat recovery.

As will be understood by those skilled in the art, the above described heat engines may be modified to employ and of the devices or techniques described herein. For example, the heating process 1-2 may include the injection of quantity of working fluid into a chamber (e.g. of a piston), and the introduction of energy (e.g. via concentrated solar energy directed through a transparent window in the chamber) to the quantity of working fluid to vaporize the fluid, as described in detail above. Although in the examples above, 50% of the working fluid was diverted to bypass the second expander 204, any other suitable bypass ratio may be used. In some embodiments, the bypass ratio may be adjust to improve or maximize one or more operating parameters of the cycle (e.g. net cycle efficiency, work output, etc.). In various embodiments, one or more of these operating parameters may be monitored via a suitable sensor, and the bypass ratio adjusted based on the sensor measurement (e.g. using a servo loop in real time).

In some embodiments, heat engine 200 may be modified to include one or more additional components. For example, referring to Fig 15B, in one embodiment a further modification of the cycle of Fig 15 as described above incorporates another heat exchanger, called a recuperator 209, to recover additional heat after the end of the expansion process in the second expander 204. The heat engine cycle is identical to that shown in Fig. 15, except that the fluid at point 5, instead of being sent directly to the condenser 205, is first diverted through recuperator 209, for transfer of residual heat to the fluid stream after condensation and prior to direct contact heat exchanger 207 (processes 5— 5A and 8— 8A). The temperature at point 5 is higher than condensing temperature at 5A and hence heat may be usefully recovered. In this manner additional heat recovery is facilitated, leading to increase in cycle efficiency over and above cycle in Fig 15.

The calculated efficiency the heat engine 200 depicted in Fig 15 B for a variety of exemplary operating parameters is given in the table below (all temperatures are in degrees C). The table shows cycle efficiencies for various values of the efficiency of the following cycle components: the recuperator 209, the pumps 206 and 208 , and the expanders 202 and 204.

Working Fluid

R245fa

C C C

Recuperato >rr PPuummpp EExxppaannddeerr Ambient Cycle efficiency efficiency efficiency T ₂ T ₇ Temp. efficiency

0.9 0.8 0.6 200 45 35 0.1491

0.9 0.8 0.7 200 45 35 0.1755

0.9 0.8 0.8 200 45 35 0.2008

0.9 0.8 0.9 200 45 35 0.2249

0.95 0.8 0.6 200 45 35 0.151

0.95 0.8 0.7 200 45 35 0.1776

0.95 0.8 0.8 200 45 35 0.2029

0.95 0.8 0.9 200 45 35 0.2271

0.95 0.8 0.6 200 40 35 0.1582

0.95 0.8 0.7 200 40 35 0.1854

0.95 0.8 0.8 200 40 35 0.2113

0.95 0.8 0.9 200 40 35 0.2359

0.9 0.8 0.6 200 40 35 0.1561

0.9 0.8 0.7 200 40 35 0.1832

0.9 0.8 0.8 200 40 35 0.209

0.9 0.8 0.9 200 40 35 0.2337

Generally the incorporation of both feed water heating and recuperation after final expansion has result in a significant practical cycle efficiency improvement. Note that cycle efficiencies of greater than 17%, e.g., up to about 24% or more may be achieved. In some embodiments, the efficiency may approach the theoretical Carnot efficiency (equal to 1-T ₂ /T ₇ ). In some embodiments, the cycle efficiency may be in the range of about 15% to about 25%.

Referring to Fig. 15 C, in one embodiment, heat engine 200 includes a third, still lower pressure expander 210 positioned after low pressure expander 204. A second flow splitter 203 A is positioned between expanders 204 and 210. Flow splitter 203 A directs a portion of the working fluid exiting the second expander 204 to bypass the third expander 210. This portion of the working fluid is directed to feed water heater 207A, to direct contact heat exchanger 207A, which is paired with pump 208A. As will be evident to one skilled in the art, any number of additional heat expanders

may be included in a similar fashion, each capable of extracting mechanical work

Flow splitters positioned between some or all of the expanders to allow extraction of working fluid to be used for feed fluid heating.. The calculated efficiency the heat engine 200 depicted in Fig 15C for a variety of

exemplary operating parameters is given in the table below (all temperatures are in

degrees C). The table shows cycle efficiencies for various values of the efficiency

of the following cycle components: the recuperator 209, the pumps 206 208 and

208 A , and the expanders 202, 204, and 210. Generally the incorporation of both feed water heating and recuperation after final

expansion has resulted in a significant practical cycle efficiency improvement. Note that cycle efficiencies of greater than 17%, e.g., up to about 24% or more may be

achieved. In some embodiments, the efficiency may approach the theoretical Carnot efficiency (equal to 1-T ₂ /T ₇ ). In some embodiments, the cycle efficiency may be in

the range of about 15% to about 25%.

recup eff Pump eff Exp eff T2 cycle T7 cycle T ambient

0.9 0.8 0.6 200 45 35 0.1514

0.9 0.8 0.7 200 45 35 0.1774

0.9 0.8 0.8 200 45 35 0.2024

0.9 0.8 0.9 200 45 35 0.2266

0.95 0.8 0.6 200 45 35 0.1533

0.95 0.8 0.7 200 45 35 0.1792

0.95 0.8 0.8 200 45 35 0.2044

0.95 0.8 0.9 200 45 35 0.2282

0.95 0.8 0.6 200 40 35 0.160i

0.95 0.8 0.7 200 40 35 0.187f

0.95 0.8 0.8 200 40 35 0.213;

0.95 0.8 0.9 200 40 35 0.2381

0.9 0.8 0.6 200 40 35 0.158

0.9 0.8 0.7 200 40 35 0.185(

0.9 0.8 0.8 200 40 35 0.21 V

0.9 0.8 0.9 200 40 35 0.236: Referring to Figs. 17 and 18, in some embodiments the heat engine 200 may be modified to include a secondary thermodynamic cycle heat engine (labeled C) which converts the thermal energy from the diverted second portion of the working fluid to other form of energy (e.g. mechanical work). As shown, heat exchanger 301 transfers heat at a first temperature (e.g. about 100 deg C) from the diverted fluid to drive cycle C to generate mechanical work W _c . Cycle C rejects heat to the surrounding environment at a lower temperature (e.g. 45 degrees C).

As will be understood by one skilled in the art, an increased amount of mechanical work extracted from the diverted fluid will lead to a decreased cycle efficiency for heat engine 200. Referring to Fig. 18, the dashed arrows indicate the operation of the cycle of heat engine 200 at different values of work extracted. As more work is extracted, less feed fluid preheating is provided by the diverted fluid, leading to a decrease in cycle efficiency. Suitable values for the amount of extracted work can be selected based on the application at hand. Fig. 19 shows a more detailed view of an exemplary embodiment of secondary cycle C. As shown, cycle C is a single expander trilateral flash cycle. In process 1-2, the second portion of working fluid from the primary cycle transfers heat to the working fluid of secondary cycle C. In the example shown, the incoming fluid is at a temperature of 130 degrees C, and heats the working fluid to a temperature of 120 degrees C. In process 2-3, the heated working fluid is directed to an expander (a piston or turbine expander). In process 3-4, the heated working fluid undergoes isentropic expansion in the expander to yield mechanical work. In process 4-5, the expanded working fluid is condensed, rejecting heat to the surrounding environment at a temperature of 45 degrees C. In process 5-6, the condensed working fluid is repressurized, and in process 6-1 the repressurized fluid is recirculated to start the cycle anew.

Although Fig. 19 shows a trilateral flash cycle, any suitable thermodynamic cycle may be used to extract mechanical work from the second portion of the working fluid of heat engine 200. Other heat engine types include a Stirling cycle, a Rankine cycles, or any of the cycles described herein. The cycles may use any suitable rCTPmi r* rtr innronni r ¹ flni H inrOnrl-in cT -flnirJc l-ip»rmn Tn various embodiments the working fluid can be heated to a state in the liquid-vapor region, or in the supercritical region.

Referring to Fig. 20, a heat engine device 400 includes multiple cascaded

thermodynamic cycles (two are shown). An upper cycle operating on a first working fluid accepts heat from a heat source at a first temperature Tl , rejects heat at a second lower temperature T2, and yields work (e.g. mechanical work.) The lower cycle accepts heat rejected by the upper cycle at a temperature T3 less than or about equal to T2. The lower cycle rejects heat into the surrounding environment (or yet another lower cycle) at a lower temperature T4. Accordingly, the lower cycle generates useful work from rejected heat from the upper cycle that otherwise may have simply gone to waste.

In some embodiments, the first working fluid of the upper cycle has a relatively high boiling point, while the second working fluid of the lower cycle has a relatively low boiling point. For example, the first working fluid may be pressurized water/steam, while the second working fluid is a low boiling point fluid, e.g. an organic fluid such as HCFC 123 or HCFC 134a. In other embodiments, the organic working fluid may include organic ammonia, benzene, butane, isobutane, carbon tetrachloride, propane, R-245fa, R-245ca, toluene, or any other suitable fluid. Accordingly, the lower cycle is able to operate efficiently using the relatively low temperature heat rejected from the upper cycle.

Fig. 23 shows an exemplary heat engine device 500 featuring upper and lower cascaded trilateral flash cycles. The upper cycle operates on a pressurized water/steam working fluid and is depicted in the temperature-entropy T-s steam table of Fig. 21. The lower cycle operates on a an organic HCFC 123 fluid pressure- enthalpy diagram of Fig. 22.

Considering first the upper cycle, in process 5-1, a liquid pump 150 isentropically compresses the water working fluid to upper working pressure. In process 1-2 , a heat exchanger 135 transfers heat from a primary heat source to the compressed water working fluid. As shown, the heat source is waste heat from a coal power station at 140 degrees C, which heats the compressed working fluid from a temperature of about 32 degrees C to a temperature of 120 degrees C.

In process 2-3 the heated working fluid undergoes isentropic ( reversible, adiabatic) expansion in an expander 136, and is cooled to a temperature of 102 degrees C. As shown, expander 136 is a reciprocating piston expander. However, in other embodiments, other suitable expanders may be used, e.g. a turbine expander.

In process 3-4 heat is recovered from the expanded water vapor exhausted from the expander and transferred to the HCFC 123 working fluid of the lower cycle using a heat exchanger 151. In process 4-5 the water vapor working fluid exiting the heat exchanger 151 is condensed back tot the liquid state using a steam vapor condenser 137. Note that, in some embodiments, the heat rejected during this process may also be transferred to heat the lower cycle working fluid. The condensed water working fluid is then recirculated to the pump 150 to begin the cycle anew.

Considering the lower cycle, this cycle of the heat engine operates as a conventional trilateral flash cycle on the HCFC 123 working fluid. In process 6 -7 a liquid pump 150 isentropically compresses the HCFC 123 working fluid to upper working pressure. In process, 7-8, the pressurized HCFC 12 working fluid is heated to a temperature of 82 degrees C in heat exchanger 151 using heat rejected from the upper cycle. In process 8-9 the heated HCFC 123 working fluid undergoes isentropic ( reversible, adiabatic) expansion in an expander 139, and is cooled to a temperature of about 40 degrees C. As shown, expander 139 is a reciprocating piston expander. However, in other embodiments, other suitable expanders may be used, e.g. a turbine expander. In process, 9-6 the expanded working fluid exhausted from the expander 139 is condensed in fluid condenser 140, rejecting heat into the surrounding environment. Note that in some embodiments, the heat rejected by the lower cycle may be used to drive a tertiary cycle, etc. As shown, all of the mechanical output of both types of expanders, upper

water/vapor based expander 136 and lower low boiling point organic based expander 139 is integrated into a common shaft 152 which is then used to turn a single alternator 153 to generate electrical energy. In embodiments described herein, two trilateral flash cycles, the upper one using water and the lower using a working fluid with a lower boiling point, are cascaded for purposes of achieving higher efficiency. In a typical example, recovery useful energy from the waste heat of a coal power plant stack gas, input and output parameters were as follows:

Therefore useful power generation from waste heat may be carried out using low grade heat sources, utilizing the proposed cascaded thermodynamic cycle

While in both exemplary cycles described above the working fluid was heated into the wet vapor region, in other embodiments, the working fluid in one or more cycle may be heated to a supercritical fluid state. As will be understood by those skilled in the art, the above described heat engine may be modified to employ and of the devices or techniques described herein. For example, the heating processes may include the injection of quantity of working fluid into a chamber (e.g. of a piston), and the introduction of energy (e.g. via concentrated solar energy directed through a transparent window in the chamber) to the quantity of working fluid to vaporize the fluid, as described in detail above. Any of the cycles may include multiple expanders and/or bypass preheating devices and techniques described herein Having thus described several aspects of at least one embodiment of this invention, it is to be appreciated various alterations, modifications, and improvements will readily occur to those skilled in the art. Such alterations, modifications, and improvements are intended to be part of this disclosure, and are intended to be within the spirit and scope of the invention. Accordingly, the foregoing description and drawings are by way of example only.