Patent Publication Number: US-2022213790-A1

Title: Thermodynamic cycle process performing transfer between mechanical and heat energies

Description:
FIELD OF THE INVENTION 
     The invention relates to the field of thermodynamic cycle process, performing transfer between mechanical and heat energies, by changing a state of a fluid. 
     BACKGROUND OF THE INVENTION 
     According to a first classical prior art, it is known a thermodynamic cycle process comprising a fluid expansion performed by an expansion valve. However, the energy produced during this fluid expansion is lost. 
     According to a second prior art, for example described in U.S. Pat. No. 4,208,885, or for example described in JP 2011127879, it is known a thermodynamic cycle process using a cyclic free piston expander to retrieve energy from this fluid expansion. However, this thermodynamic cycle process using this cyclic free piston expander uses either two different fluid flows or one fluid flow with one or more opening and closing valves so as to push it in two opposite sliding directions. Hence, this makes its control mechanism too complex and/or too fragile to alternatively change the sliding directions for the free piston sliding. 
     SUMMARY OF THE INVENTION 
     The object of the present invention is to alleviate at least partly the above mentioned drawbacks. 
     It is an object of the invention to propose an improvement of such a control mechanism in order to make it simpler and/or more robust, thereby improving the compromise between simplicity and robustness for the control mechanism of the cyclic free piston expander used by the thermodynamic cycle process, while keeping efficient the energy retrieval from expansion. 
     Therefore, the invention proposes a modification of a thermodynamic cycle process using a cyclic free piston expander both by introducing into free piston expander a fluidic communication between its two surfaces alternatively so as to push it in two opposite sliding directions with a single fluid flow and by making very simple and robust the mechanism to alternatively open and close this fluidic communication so as to control in a simple and efficient way the alternative change of sliding directions for the free piston sliding. 
     This object is achieved with a thermodynamic cycle process, performing transfer between mechanical and heat energies, by changing a state of a fluid, comprising: an expansion of said fluid, an energy retrieval from said fluid expansion, a step of powering a liquid pump or a gas compressor with said retrieved energy, using a cyclic free piston expander which alternatively changes direction of said free piston sliding: by alternatively: closing said fluidic communication between said both opposite sides of said free piston, so as to make different from each other the pressures applied respectively thereon, so that said free piston then slides in a first direction, opening a fluidic communication between both opposite sides of said free piston, so as to make equal to each other the pressures applied respectively thereon, so that said free piston then slides in a second direction opposite to said first direction, said free piston sliding, directly and mechanically, opening and closing, said fluidic communication. 
     The free piston sliding, directly and mechanically, opening and closing, said fluidic communication, means, first that it is the sliding itself of the free piston which opens and closes the fluidic communication, not by an intermediate control mechanism detecting the sliding of the free piston, and second that the action of the free piston sliding which directly opens or closes the fluidic communication is a mechanical action and not a mechanical trigger of another non mechanical action like would be the trigger of an electric or electronic actuator. Indeed, it is the sliding of the free piston which opens and closes the fluidic communication, in a direct and mechanical way. 
     According to embodiments of the invention, neither valve, nor other distribution mechanism, nor any other control system, is needed. 
     Preferably, indeed, this object is achieved with a thermodynamic cycle process, performing transfer between mechanical and heat energies, by changing a state of a fluid, comprising: an expansion of said fluid, an energy retrieval from said fluid expansion, a step of powering a liquid pump or a gas compressor with said retrieved energy, using a cyclic free piston expander which comprises a free piston sliding in a sliding chamber, which free piston comprises a free piston head and a free piston pin or rod, and which alternatively changes direction of said free piston sliding: by alternatively : closing said fluidic communication between said both opposite sides of said free piston head, so as to make different from each other the pressures applied respectively thereon, so that said free piston then slides in a first direction, opening a fluidic communication between both opposite sides of said free piston head, so as to make equal to each other the pressures applied respectively thereon, so that said free piston then slides in a second direction opposite to said first direction, said free piston sliding, directly and mechanically, opening and closing, said fluidic communication. This helps making opening and closing of the fluidic communication simpler and more automatic, the simple sliding of free piston changing position of the end of fluidic communication being open and closed, respectively by sliding in a portion of the chamber with increased internal diameter and a portion of the chamber with reduced internal diameter. 
     Preferably, in one embodiment, said fluidic communication is closed and open, respectively by an end of an admission channel located within the free piston and sliding against the sliding chamber wall with a reduced diameter and by same end of the admission channel opening into a space with an increased diameter of a sliding chamber wall. 
     Preferably, in another embodiment, said fluidic communication is closed and open, respectively by an end of an admission channel located within the sliding chamber wall and relatively sliding against the free piston head and by same end of the admission channel opening into a space with an increased diameter of a sliding chamber wall. 
     Preferred embodiments comprise one or more of the following features, which can be taken separately or together, either in partial combination or in full combination, with the previous object of the invention or with one or more of the preferred options related to the previous object of the invention. 
     Preferably, said fluidic communication includes one or more, preferably only one, communicating channel(s) located within the body of said free piston. 
     Hence, the compromise between simplicity and robustness for the control mechanism of the cyclic free piston expander used by the thermodynamic cycle process is still more improved, since the communicating channel which is a fragile element per se is well protected by its location within the bulky body of the free piston itself. 
     Preferably, said communicating channel is a bent channel, has a major part of its length, preferably at least 70%, extending axially with respect to said sliding directions of said free piston, preferably extending along a symmetry axis of said free piston, and has a minor part of its length, preferably at most 30%, extending radially with respect to said sliding directions of said free piston. 
     Hence, the free piston remains well balanced, during all its sliding, in either of first and second directions. 
     Preferably, axial length end of said communicating channel opens into said expansion space, radial length end of said communicating channel: opens into said admission space at end of free piston sliding stroke when said free piston slides in said first direction, leads against sliding chamber wall during the major part of free piston sliding stroke from beginning when said free piston slides in said first direction, opens into said admission space at beginning of free piston sliding stroke when said free piston slides in said second direction, leads against sliding chamber wall during the major part of free piston sliding stroke until end when said free piston slides in said second direction. 
     Hence, opening of this radial length end of the communicating channel into the admission space is enough to start braking the free piston sliding in the first direction, before inverting this free piston sliding in the second direction, and closing of this radial length end of the communicating channel by the sliding chamber wall is enough to start braking the free piston sliding in the second direction, once internal pressure of expansion space has dropped by opening exhaust outlet, before inverting this free piston sliding in the first direction. 
     Preferably, said free piston slides within a sliding chamber, said fluidic communication includes one or more, preferably only one, communicating channel(s) located within the wall of said sliding chamber. 
     Hence, the free piston is more balanced than in former case where the communicating channel was located within the bulky body of the piston itself, but the required volume in the sliding chamber wall is somewhat bigger, at least in one radial direction. 
     Preferably, said communicating channel is a doubly bent channel, has a major part of its length, preferably at least 55%, extending axially with respect to said sliding directions of said free piston, and has a minor part of its length, preferably at most 45%, extending radially with respect to said sliding directions of said free piston. 
     Hence, the required volume in the sliding chamber wall to locate the communicating channel is somewhat lower. 
     Preferably, axial length of said communicating channel is located between two radial lengths of said communicating channel, end of one radial length of said communicating channel: opens into said expansion space at end of free piston sliding stroke in said first direction, end of the other radial length of said communicating channel: opens into said admission space at end of free piston sliding stroke when said free piston slides in said first direction, leads against free piston external wall during the major part of free piston sliding stroke from beginning when said free piston slides in said first direction, opens into said admission space at beginning of free piston sliding stroke when said free piston slides in said second direction, leads against free piston external wall during the major part of free piston sliding stroke until end when said free piston slides in said second direction. 
     Hence, opening of one of these radial length ends of the communicating channel into the admission space is enough to start braking the free piston sliding in the first direction, before inverting this free piston sliding in the second direction, and closing of this same radial length end of the communicating channel by the sliding chamber wall is enough to start braking the free piston sliding in the second direction, once internal pressure of expansion space has dropped by opening exhaust outlet, before inverting this free piston sliding in the first direction. 
     Preferably, in said step of powering a liquid pump or a gas compressor with said retrieved energy, said cyclic free piston expander alternatively changes direction of said free piston sliding: by alternatively: closing said fluidic communication between said both opposite sides of said free piston, so as to make different from each other the pressures applied respectively thereon, so that said free piston then slides and accelerates in a first direction, opening a fluidic communication between both opposite sides of said free piston, so as to make equal to each other the pressures applied respectively thereon, so that said free piston then slides and accelerates in a second direction opposite to said first direction, said free piston sliding and accelerating, directly and mechanically, opening and closing, said fluidic communication. 
     Hence, since said free piston is not only sliding but also accelerating, the momentum acquired by the free piston helps the free piston stroke to be longer and the alternation between opening and closing the fluidic communication to be more dynamic. 
     Preferably, toward a first direction of said free piston sliding, a first pressure is applied on a first surface of a first side of said free piston, toward a second direction of said free piston sliding, a second pressure is applied on a second surface of a second side of said free piston opposite to said first side, said first surface being smaller than said second surface, a ratio between said first surface and said second surface being preferably less than 70%, first product of said first pressure by said first surface being higher than second product of said second pressure by said second surface, during a major part of said free piston sliding stroke in said first direction, preferably during most of said free piston sliding stroke in said first direction, first product of said first pressure by said first surface being lower than second product of said second pressure by said second surface, during a major part of said free piston sliding stroke in said second direction, preferably during most of said free piston sliding stroke in said second direction. 
     Hence, the compromise between simplicity and robustness for the control mechanism of the cyclic free piston expander used by the thermodynamic cycle process is still better improved, since this size difference between first and second surfaces allows, not only for using the same fluid flow to switch between the two sliding directions of the free piston, but also for using this same fluid flow without modifying the way or the intensity to apply it on the first surface of the free piston and without associated modifying mechanism to do so. 
     Preferably, said free piston slides within a sliding chamber, said first surface of said free piston is in an admission space of said sliding chamber having a first variable volume, said second surface of said free piston is in an expansion space of said sliding chamber having a second variable volume, said second volume decreasing when said first volume increases and said second volume increasing when said first volume decreases. 
     Hence, this is quite a simple mechanism for the free piston to perform the alternation between opening and closing the fluidic communication. 
     Preferably, said free piston includes a shoulder reducing its diameter, said free piston shoulder being said first surface, said sliding chamber comprises a shoulder reducing its diameter, said admission space is located between said free piston shoulder and said sliding chamber shoulder. 
     Hence, the admission space is located on the periphery of the free piston, and therefore can more easily be connected to an outside compressed fluid flow. 
     Preferably, said admission space has the shape of an annular compartment of a height which is variable and which height direction is parallel to said sliding directions of said free piston. 
     Hence, the direction of the thrust provided by such an admission space first is parallel to the direction of the free piston sliding and second is well distributed around this direction of the free piston sliding. This makes the control mechanism of the cyclic free piston expander used by the thermodynamic cycle process still more efficient and better balanced, thereby more robust over time. 
     Preferably, said admission space is connected to an outside compressed fluid flow, via a simple and preferably via a single inlet through a wall of the sliding chamber, said inlet being preferably located so as to remain open during all free piston sliding. 
     Hence, the compromise between simplicity and robustness for the control mechanism of the cyclic free piston expander used by the thermodynamic cycle process is still better improved, since transmission of compressed fluid flow toward admission space is made shorter and simpler. 
     Preferably, said expansion space is located between on a one hand a free side of a head of said free piston, said free piston head being opposite to a pin of said free piston, a free side of said free piston pin either exerting a force toward pumping liquid of said liquid pump or toward compressing gas of said gas compressor at an open extremity of said sliding chamber, and on the other hand a closed extremity of said sliding chamber. Free piston pin preferably has the shape of a free piston rod. 
     Hence, the direction of the thrust provided by such an expansion space first is parallel to the direction of the free piston sliding and second takes advantage of the whole free piston head surface available. This makes the control mechanism of the cyclic free piston expander used by the thermodynamic cycle process still more efficient. 
     Preferably, said expansion space is connected to an outside expanded fluid flow, via a simple and preferably via a single outlet through a wall of the sliding chamber, said outlet being preferably located so as to remain closed during a major part of said free piston sliding stroke, preferably during more than 80% of said free piston sliding stroke. 
     Hence, the compromise between simplicity and robustness for the control mechanism of the cyclic free piston expander used by the thermodynamic cycle process is still more improved, since transmission to expanded fluid flow from expansion space is made shorter and simpler. 
     Preferably, said free piston expander, which is located between a compressed fluid flow and an expanded fluid flow of the thermodynamic cycle process, has all of its pieces which are static except only one piece which is moving, that is the free piston which slides within the static sliding chamber. 
     Hence, the compromise between simplicity and robustness for the control mechanism of the cyclic free piston expander used by the thermodynamic cycle process is well optimized. 
     Preferably, said fluid is: water, or carbon dioxide, or air, or natural gas, or organic fluid, or ammoniac (NH 3 ), or any mixture comprising carbon dioxide, and/or air, or and/natural gas, or organic fluid, and/or ammoniac (NH 3 ), or any mixture comprising water and/or ethanol and/or any organic fluid. 
     Preferably, said fluid is carbon dioxide. 
     Hence, the global efficiency of the thermodynamic cycle process is even higher. 
     Preferably, said free piston pin either exerting a force toward pumping liquid of said liquid pump or toward compressing gas of said gas compressor at an open extremity of said sliding chamber via an extension arm sliding in a tube having a smaller internal diameter than an internal diameter of said sliding chamber, a ratio of said internal diameter of said tube by said internal diameter of said sliding chamber being preferably less than 60% and advantageously more than 20%. 
     Hence, the stroke of the pumping or of the compressing is longer and multiplied as compared to the stroke of the free piston sliding. 
     Preferably, a ratio of a fluid high pressure before said fluid expansion by a fluid low pressure after fluid expansion, is greater than 20, preferably greater than 30, more preferably greater than 40. 
     Hence, this thermodynamic cycle process works well even for very high expansion ratio. 
     Preferably, a fluid high pressure before said fluid expansion, is greater than 50 bars, preferably greater than 80 bars, more preferably greater than 100 bars. 
     Hence, this thermodynamic cycle process works well even for very high fluid pressures before fluid expansion. 
     Preferably, said free piston sliding has an oscillation frequency, said free piston has a mass which has a value such that said oscillation frequency ranges from 20 Hz to 150 Hz, preferably ranges from 30 Hz to 120 Hz, more preferably ranges from 50 Hz to 90 Hz. 
     Hence, this is an optimized compromise between on one hand the global efficiency of the thermodynamic cycle process and on the other hand the mechanical resistance of the whole structure kept as simple and as robust over time as possible. 
     Preferably, a fluid temperature during said fluid expansion, goes under 80° C., preferably 0° C., more preferably −40° C. Temperature may range for instance from −40° C. to 10° C. for refrigeration and for heat pump. Temperature may range for instance from 30° C. to 80° C. for use of ORC cycle. 
     Preferably, a fluid temperature during said fluid expansion, goes under −100° C., preferably under −150° C. 
     Hence, this thermodynamic cycle process works well even for very low fluid temperatures during fluid expansion. 
     Preferably, said powering step powers a positive displacement pump or a positive displacement compressor with said retrieved energy. 
     Thermodynamic cycle process according to the invention is especially efficient for positive displacement pump or a positive displacement compressor having a more important fluid compression. 
     Preferably, the thermodynamic cycle includes a phase of adiabatic expansion. 
     Hence, the proportion of retrieved energy is somewhat higher. 
     Preferably, said adiabatic expansion phase is more than a half of the whole expansion phase. 
     Hence, the proportion of retrieved energy is even higher. 
     Preferably, at the beginning of said adiabatic expansion phase, said fluid is: in a liquid state, or in a mixed state including both liquid and vapor, or in a super-critical fluid state. 
     Preferably, at the beginning of said adiabatic expansion phase, said fluid is in a super-critical fluid state. 
     Hence, the global efficiency of the thermodynamic cycle process is even higher. 
     Preferably, said thermodynamic cycle process is used: in a refrigerator, or in a heat pump, or in an air conditioner. 
     Preferably, said thermodynamic cycle process includes a main powering step, said powering step of said free piston expander is re-used to perform part of said main powering step in said thermodynamic cycle process. 
     Hence, the retrieved energy is directly reused. 
     Preferably, said thermodynamic cycle process comprises a compression step, in said powering step, a compressing portion of said free piston expander performs part of said compression step, said free piston expander compressing portion being preferably disposed in parallel to a compressor performing major part of said compression step, or said free piston expander compressing portion being preferably disposed in series to a compressor performing major part of said compression step. 
     Preferably, said thermodynamic cycle process is: a Rankine cycle, or an organic Rankine cycle. 
     Further features and advantages of the invention will appear from the following description of embodiments of the invention, given as non-limiting examples, with reference to the accompanying drawings listed hereunder. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  shows an application to a heat pump or to a refrigerating machine of a thermodynamic cycle process according to first classical prior art, with a simple expansion valve. 
         FIG. 2  shows an example of an application to a heat pump or to a refrigerating machine of a thermodynamic cycle process according to an embodiment of the invention, with a free piston expander disposed in parallel with a compressor. 
         FIG. 3  shows another example of an application to a heat pump or to a refrigerating machine of a thermodynamic cycle process according to an embodiment of the invention, with a free piston expander disposed in series with a compressor. 
         FIG. 4  shows another example of an application to an organic Rankine cycle or to a Rankine cycle of a thermodynamic cycle process according to an embodiment of the invention, with a free piston expander powering a hydraulic pump or a piston compressor. 
         FIG. 5  shows another example of an application to an organic Rankine cycle or to a Rankine cycle of a thermodynamic cycle process according to an embodiment of the invention, with the free piston expander disposed in parallel with a hydraulic motor. 
         FIG. 6  shows another example of an application to an organic Rankine cycle or to a Rankine cycle for the energy powering stage of the free piston expander and to a heat pump for the energy providing stage of the free piston expander, of a thermodynamic cycle process according to an embodiment of the invention, with the free piston expander powering a compressor, with separate condensers for both stages. 
         FIG. 7  shows another example of an application to an organic Rankine cycle or to a Rankine cycle for the energy powering stage of the free piston expander and to a heat pump for the energy providing stage of the free piston expander, of a thermodynamic cycle process according to an embodiment of the invention, with the free piston expander powering a compressor, with a common condenser for both stages. 
         FIG. 8  shows an example of a structure of a free piston expander, of a thermodynamic cycle process according to an embodiment of the invention. 
         FIG. 9  shows another example of a structure of a free piston expander, of a thermodynamic cycle process according to an embodiment of the invention. 
         FIG. 10  shows an example of a first phase of operation of the free piston expander, according to an embodiment of the invention. 
         FIG. 11  shows an example of a corresponding first phase in a diagram pressure volume in the expansion chamber of the free piston expander, according to an embodiment of the invention. 
         FIG. 12  shows an example of a second phase of operation of the free piston expander, according to an embodiment of the invention. 
         FIG. 13  shows an example of a corresponding second phase in a diagram pressure volume in the expansion chamber of the free piston expander, according to an embodiment of the invention. 
         FIG. 14  shows an example of a third phase of operation of the free piston expander, according to an embodiment of the invention. 
         FIG. 15  shows an example of a corresponding third phase in a diagram pressure volume in the expansion chamber of the free piston expander, according to an embodiment of the invention. 
         FIG. 16  shows an example of a fourth phase of operation of the free piston expander, according to an embodiment of the invention. 
         FIG. 17  shows an example of a corresponding fourth phase in a diagram pressure volume in the expansion chamber of the free piston expander, according to an embodiment of the invention. 
         FIG. 18  shows an example of diagram of a thermodynamic cycle process, according to an embodiment of the invention. 
         FIG. 19  shows another example of diagram of a thermodynamic cycle process, according to an embodiment of the invention. 
         FIG. 20  shows an example of a performance gain improvement when using a free piston expander in a thermodynamic cycle process, according to an embodiment of the invention. 
         FIG. 21  shows an example of a diagram pressure volume in the expansion chamber of the free piston expander, according to an embodiment of the invention. 
         FIG. 22  shows an example of a diagram pressure volume in the compression cycle of the compressor, according to an embodiment of the invention. 
         FIG. 23  shows an example of a detailed structure, with precise dimensions given in cm, of a free piston expander chamber, according to an embodiment of the invention, corresponding to  FIG. 9 . 
         FIG. 24  shows an example of a detailed structure, with precise dimensions given in cm, of a free piston expander piston, according to an embodiment of the invention, corresponding to  FIG. 9 . 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     In the following text, unless explicitly stated to the contrary, “connected” means “fluidically connected” i.e. connected together such that a fluid may go from one to the other. 
       FIG. 1  shows an application to a heat pump or to a refrigerating machine of a thermodynamic cycle process according to first classical prior art, with a simple expansion valve. 
     The thermodynamic machine comprises a condenser  1  connected to both a compressor  3  and an expansion valve  4 . The thermodynamic machine also comprises an evaporator  2  connected to both the compressor  3  and the expansion valve  4 . The compressor  3  compresses a gas at low pressure coming from the evaporator  2  and sends this gas at high pressure toward the condenser  1 . The condenser  1  changes the gas into liquid and sends the liquid toward the expansion valve  4 . The expansion valve  4  sends the liquid, after being expanded, toward the evaporator  2  which changes the liquid into gas. The condenser  1  performs a high temperature cooling. The evaporator  2  performs a low temperature heating. An external source of energy, not represented, is powering the compressor  3 . 
       FIG. 2  shows an example of an application to a heat pump or to a refrigerating machine of a thermodynamic cycle process according to an embodiment of the invention, with a free piston expander disposed in parallel with a compressor. The thermodynamic cycle process is used for example either in a refrigerator, or in a heat pump, or in an air conditioner. 
     The thermodynamic machine comprises a condenser  1  connected to both a compressor  3  and a free piston expander  5  including a free piston  7  sliding in a sliding chamber  6 . The condenser  1  is connected to the free piston expander  5  energy powering stage directly and to the free piston expander  5  energy providing stage via a high pressure valve  8 . 
     The thermodynamic machine comprises an evaporator  2  connected to both the compressor  3  and the free piston expander  5 . The evaporator  2  is connected to the free piston expander  5  energy powering stage directly and to the free piston expander  5  energy providing stage via a low pressure valve  9 . Free piston expander  5  can provide energy at its energy providing stage because he receives energy that it retrieves from the fluid expansion of the thermodynamic machine. 
     The compressor  3  compresses a gas at low pressure coming from the evaporator  2  and sends this gas at high pressure toward the condenser  1 . An external source of energy, not represented, is powering the compressor  3 . The free piston expander  5  helps the compressor  3  to compress the gas at low pressure coming from the evaporator  2  and to send this gas at high pressure toward the condenser  1 . Therefore, less energy is required from the external source of energy to power the compressor  3 . The free piston expander  5  is disposed in parallel to the compressor  3 . 
     The condenser  1  changes the gas into liquid and sends the liquid toward the free piston expander  5 . The free piston expander  5  sends the liquid, after being expanded, toward the evaporator  2  which changes the liquid into gas. The condenser  1  performs a high temperature cooling. The evaporator  2  performs a low temperature heating. 
     For example, a ratio of a fluid high pressure before fluid expansion by a fluid low pressure after fluid expansion, can be greater than 20, greater than 30, greater than 40. 
     For example, a fluid high pressure before fluid expansion, can be greater than 50 bars, greater than 80 bars, greater than 100 bars. 
     For example, a fluid temperature during fluid expansion, can go under −100° C., even under −150° C. 
       FIG. 3  shows another example of an application to a heat pump or to a refrigerating machine of a thermodynamic cycle process according to an embodiment of the invention, with a free piston expander disposed in series with a compressor. 
     The thermodynamic machine comprises a condenser  1  connected to a free piston expander  5 . The condenser  1  is connected to the free piston expander  5  energy powering stage directly and to the free piston expander  5  energy providing stage via a high pressure valve  8 . 
     The thermodynamic machine comprises an evaporator  2  connected to both the compressor  3  and the free piston expander  5 . The evaporator  2  is connected to the free piston expander  5  energy powering stage directly. The compressor  3  is also connected to the free piston expander  5  energy providing stage via a low pressure valve  9 . 
     The compressor  3  compresses a gas at low pressure coming from the evaporator  2  and sends this gas at high pressure toward the low pressure valve  9 . An external source of energy, not represented, is powering the compressor  3 . The free piston expander  5  helps the compressor  3  to compress the gas at low pressure coming from the compressor  3  via low pressure valve  9  and to send this gas at high pressure toward the condenser  1  via high pressure valve  8 . Therefore, less energy is required from the external source of energy to power the compressor  3 . The free piston expander  5  is disposed in series to the compressor  3 . 
     The condenser  1  changes the gas into liquid and sends the liquid toward the free piston expander  5 . The free piston expander  5  sends the liquid, after being expanded, toward the evaporator  2  which changes the liquid into gas. The condenser  1  performs a high temperature cooling. The evaporator  2  performs a low temperature heating. 
       FIG. 4  shows another example of an application to an organic Rankine cycle or to a Rankine cycle of a thermodynamic cycle process according to an embodiment of the invention, with a free piston expander powering a hydraulic pump or a piston compressor. 
     The thermodynamic machine comprises a condenser  1  connected to both a pump  10  and a free piston expander  5  including a free piston  7  sliding in a sliding chamber  6 . The condenser  1  is connected to the free piston expander  5  energy powering stage directly. The free piston expander  5  energy providing stage can be connected either to a hydraulic pump or to a piston compressor, both not represented on the figure. This connection from free piston expander  5  either to a hydraulic pump or to a piston compressor may be either direct or via a rod capable of transmitting mechanical effort. 
     The thermodynamic machine comprises an evaporator  2  connected to both the pump  10  and the free piston expander  5 . The evaporator  2  is connected to the free piston expander  5  energy powering stage directly. 
     The pump  10  pumps a liquid coming from condenser  1  and sends this liquid toward the evaporator  2 . An external source of energy, not represented, is powering the pump  10 . The free piston expander  5  provides energy toward either a hydraulic pump or toward a piston compressor. Heat, coming for example from waste heat recovery or from solar heating or from biomass combustion, is brought to the evaporator  2 . The condenser  1  provides cooling. 
     The condenser  1  changes the gas coming from the free piston expander  5  into liquid and sends the liquid toward the pump  10 . The pump  10  sends the liquid toward the evaporator  2  which changes the liquid into gas. The free piston expander  5  receives gas at high pressure coming from the evaporator  2 , and sends gas at low pressure toward the condenser  1 , gas being expanded when going through the free piston expander  5 . 
       FIG. 5  shows another example of an application to an organic Rankine cycle or to a Rankine cycle of a thermodynamic cycle process according to an embodiment of the invention, with the free piston expander disposed in parallel with a hydraulic motor. 
     The thermodynamic machine comprises a condenser  1  providing cooling to outside and an evaporator  2  receiving heating from outside (for example from an external heat source). 
     The evaporator  2  is connected to both a hydraulic motor  11  providing mechanical energy toward outside and a free piston expander  5  including a free piston  7  sliding in a sliding chamber  6 , this free piston  7  being connected by a rod  12  to a pump  13  energy powering stage, the rod  12  transmitting mechanical effort from free piston  7  to pump  13 . This pump  13  has a diameter D which is reduced as compared to the diameter of free piston  7  rod at its energy providing stage, the diameter D is for example of 1 cm, as compared to a diameter of free piston comprised between 2 and 3 cm, hence a reduction factor ranging from 2 to 3. The evaporator  2  is connected to the free piston expander  5  energy powering stage directly. The evaporator  2  is connected to the pump  13  energy providing stage via a high pressure valve  8 . 
     The condenser  1  is connected to both the hydraulic motor  11  and the free piston expander  5 . The evaporator  2  is connected to the free piston expander  5  energy powering stage directly. The evaporator  2  is connected to the pump  13  energy providing stage via a low pressure valve  9 . 
     The pump  13  pumps a liquid at low pressure coming both from the condenser  1  and the hydraulic motor  11  via low pressure valve  9 , and sends it at high pressure both toward the evaporator  2  and toward the hydraulic motor  11  via high pressure valve  8 . 
     The condenser  1  changes the gas coming from free piston expander  5  energy powering stage into liquid and sends the liquid toward the low pressure valve  9 . The evaporator  2  changes the liquid into gas and then sends the gas at high pressure toward the free piston expander  5  energy powering stage where this high pressure gas is expanded into a low pressure gas which is then sent toward the condenser  1 . 
       FIG. 6  shows another example of an application to an organic Rankine cycle or to a Rankine cycle for the energy powering stage of the free piston expander and to a heat pump for the energy providing stage of the free piston expander, of a thermodynamic cycle process according to an embodiment of the invention, with the free piston expander powering a compressor, with separate condensers for both stages. 
     The main thermodynamic machine comprises a condenser  1  connected to both a pump  10  and a free piston expander  5  including a free piston  7  sliding in a sliding chamber  6 . The condenser  1  is connected to the free piston expander  5  energy powering stage directly. 
     The main thermodynamic machine comprises an evaporator  2  connected to both the pump  10  and the free piston expander  5 . The evaporator  2  is connected to the free piston expander  5  energy powering stage directly. 
     The pump  10  pumps a liquid coming from condenser  1  and sends this liquid toward the evaporator  2 . An external source of energy, not represented, is powering the pump  10 . The free piston expander  5  provides energy toward an auxiliary thermodynamic machine. Heat, at high temperature, coming for example from waste heat recovery or from solar heating or from biomass combustion, is brought to the evaporator  2 . The condenser  1  provides cooling at medium temperature. 
     The condenser  1  changes the gas coming from the free piston expander  5  into liquid and sends the liquid toward the pump  10 . The pump  10  sends the liquid toward the evaporator  2  which changes the liquid into gas. The free piston expander  5  energy powering stage receives gas at high pressure coming from the evaporator  2 , and sends gas at low pressure toward the condenser  1 , gas being expanded when going through the free piston expander  5  energy powering stage. 
     The auxiliary thermodynamic machine comprises a condenser  14  providing cooling at medium temperature to outside and an evaporator  15  receiving heating at low temperature from outside. 
     The evaporator  15  is connected to both an expansion valve  16  and the free piston expander  5  energy providing stage via a low pressure valve  9 . The condenser  14  is connected to both the expansion valve  16  and the free piston expander  5  energy providing stage via a high pressure valve  8 . 
     The free piston expander  5  energy providing stage compresses gas at low pressure coming from the evaporator  15  via low pressure valve  9 , and sends it at high pressure toward the condenser  14  via high pressure valve  8 . 
     The condenser  14  changes the gas coming from free piston expander  5  energy providing stage via high pressure valve  8  into liquid and sends the liquid toward the expansion valve  16  where it is expanded. The evaporator  15  changes the liquid coming from the expansion valve  16  into gas and then sends the gas at low pressure toward the free piston expander  5  energy providing stage where this low pressure gas is compressed into a high pressure gas. 
       FIG. 7  shows another example of an application to an organic Rankine cycle or to a Rankine cycle for the energy powering stage of the free piston expander and to a heat pump for the energy providing stage of the free piston expander, of a thermodynamic cycle process according to an embodiment of the invention, with the free piston expander powering a compressor, with a common condenser for both stages. 
     The main thermodynamic machine and the auxiliary thermodynamic machine are similar to the ones shown on  FIG. 6 , except that they share a common condenser  17 . This common condenser  17  receives gas coming from both energy powering stage and energy providing stage of free piston expander  5 , via high pressure valve  8  from free piston expander  5  providing stage. This common condenser  17  changes gas into liquid and sends the liquid toward both the pump  10  of the main thermodynamic machine and the expansion valve  16  of the auxiliary thermodynamic machine. 
     On  FIGS. 8, 9, 10, 12, 14 and 16 , there are represented two sliding directions for the free piston, which are a first direction D 1  and a second direction D 2 . Second direction D 2  is from chamber bottom  66  toward free space  65 . First direction D 1  is from free space  65  toward chamber bottom  66 . 
       FIG. 8  shows an example of a structure of a free piston expander, of a thermodynamic cycle process according to an embodiment of the invention. 
     The free piston expander  5  comprises a free piston  7  sliding, alternatively first in a first sliding direction then in a second direction opposed to the first direction, in a sliding chamber  6 . There is an admission inlet  62  receiving compressed gas from thermodynamic cycle machine main circuit (including evaporator and condenser represented on  FIGS. 1 to 7 ) and an exhaust outlet  64  sending expanded gas toward thermodynamic cycle machine main circuit (including evaporator and condenser represented on  FIGS. 1 to 7 ). 
     Free piston  7  comprises a cylindrical body including a cylindrical piston head  71  and a cylindrical piston rod  72  with an annular piston shoulder  77  for the surface of cylindrical piston head  71  extending over cylindrical piston rod  72  at the level of the junction between cylindrical piston head  71  and cylindrical piston rod  72 . At the level of free extremity of piston head  71 , there is a circular piston head surface  76  which is notably larger than the annular piston shoulder surface  77 . Within the body of the free piston  7 , there is an admission canal  73  including on the one hand an axial canal  74  extending over the whole length of the piston head  71  and extending over part of the axial length of the piston rod  72 , and on the other hand a radial canal  75  extending over part of the radial width of the piston rod  72 . Preferably, the axial canal  74  extends axially along the axis of symmetry of the free piston  7  body, the whole free piston body  7  being thereby better balanced. Preferably, the radial canal  75  extends radially from axis of symmetry of the piston rod  72  body until periphery of the piston rod  72 . 
     Sliding chamber  6  is cylindrical and has a cylindrical chamber wall  60  with two different internal diameters separated by a chamber shoulder  70 , so that piston head  71  slides on one side of this chamber shoulder  70  against chamber wall  60  and piston rod  72  slides on the other side of this chamber shoulder  70  against chamber wall  60 . There is an annular admission chamber  61  located between piston shoulder  77  and chamber shoulder  70  as well as between chamber wall  60  and piston rod  72  periphery. This admission chamber  61  receives compressed gas from admission inlet  62 . At closed axial extremity of sliding chamber  6 , on the side of piston head  71 , there is a chamber bottom  66  of the sliding chamber  6 . There is a cylindrical expansion chamber  63  located between chamber bottom  66  and piston head surface  76  as well as inside cylindrical chamber wall  60 . This expansion chamber  63  sends expanded gas toward exhaust outlet  64 . At open axial extremity of sliding chamber  6 , on the side of piston rod  72 , there is a free space  65  which may contain a gas to be compressed or a fluid to be pumped by the free extremity of piston rod  72 . All canals  73 ,  74  and  75  are channels allowing fluidic communication through them. 
     Variable volume of expansion chamber  63  decreases when variable volume of admission chamber  61  increases, and variable volume of expansion chamber  63  increases when variable volume of admission chamber  61  decreases. 
     Only one admission channel  73  has been represented on  FIG. 8 , what corresponds to a preferred embodiment; nevertheless the fluidic communication may also include more than one communicating channel located within the body of free piston  5  or even outside the body of free piston  5 , for instance within the chamber wall  60 . 
     The axial admission canal  74  length is more than 70% of the full length of the admission canal  73 . The radial admission canal  75  length is less than 30% of the full length of the admission canal  73 . 
     The ratio between annular piston shoulder surface  77  and circular piston head surface  76  is less than 70%. 
     In the step of powering a liquid pump or a gas compressor with retrieved energy from fluid expansion, free piston expander  5  alternatively changes direction of free piston  7  sliding: by alternatively: opening an admission canal  73  between both opposite sides of free piston  7 , so as to make equal to each other the pressures applied respectively thereon, so that free piston  7  slides and accelerates in second sliding direction from chamber bottom  66  toward free space  65 , closing admission canal  73  between both opposite sides of free piston  7 , so as to make different from each other the pressures applied respectively thereon, so that free piston  7  slides and accelerates in first direction opposite to said second direction, i.e. from free space  65  toward chamber bottom  66 , this free piston  7  sliding and accelerating, directly and mechanically, opening and closing, admission canal  73 . This will be explained in more details with respect to  FIGS. 10, 12, 14 and 16 . 
     Free piston expander  5 , which is located between a compressed fluid flow and an expanded fluid flow of the thermodynamic cycle process, has all of its pieces which are static except only one piece, free piston  7  body (including free piston head  71  and free piston rod  72  which move jointly as a single piece and which are advantageously made together of one single piece) which is moving, that is the free piston  7  which slides within the static sliding chamber  6 . 
       FIG. 9  shows another example of a structure of a free piston expander, of a thermodynamic cycle process according to an embodiment of the invention. 
     The free piston expander  5  of  FIG. 9  is similar to the free piston expander  5  of  FIG. 8 , except for the admission canal  73  located within the body of free piston  7  which is replaced by an admission canal  67  located within the chamber wall  60 . 
     Within the chamber wall  60 , there is an admission canal  67  including on the one hand an axial canal  68  extending axially partly over the length of the chamber wall  60  over part only of the chamber wall  60  located between chamber bottom  66  and chamber shoulder  70 , and on the other hand two radial canals  69  extending radially outward from chamber wall  60 . The axial canal  68  is located between both radial canals  69 . 
     Only one admission channel  67  has been represented on  FIG. 9 , what corresponds to a preferred embodiment; nevertheless the fluidic communication may also include more than one communicating channel located within the chamber wall  60 . 
     Axial admission canal  68  length is more than 55% of full length of admission canal  67 . The sum of lengths of radial admission canals  69  is less than 45% of full length of admission canal  67 . 
       FIG. 10  shows an example of a first phase of operation of the free piston expander, according to an embodiment of the invention. 
     Compressed gas arrives into admission chamber  61  from admission inlet  62 . This compressed gas increases the variable volume of admission chamber  61  by moving piston shoulder  77  apart from chamber shoulder  70 , thereby making free piston  7  sliding within sliding chamber  6  in a first direction from free space  65  to chamber bottom  66 , thereby reducing the variable volume of expansion chamber  63 , thereby pushing away gas from expansion chamber  63  toward exhaust outlet  64 . There is a fluidic communication between admission inlet  62  and admission chamber  61 , since admission inlet  62  opens into admission chamber  61 . There is no fluidic communication between admission canal  73  and admission chamber  61 , since free extremity of radial canal  75  is closed by chamber wall  60 . There is a fluidic communication between admission canal  73  and expansion chamber  63 , since free extremity of axial channel  74  opens into expansion chamber  63 . There is a fluidic communication between exhaust outlet  64  and expansion chamber  63 , since exhaust outlet  64  opens into expansion chamber  63 . 
       FIG. 11  shows an example of a corresponding first phase in a diagram pressure volume in the expansion chamber of the free piston expander, according to an embodiment of the invention. 
     Within the variable volume of expansion chamber  63 , gas pressure remains at a low level Pexh since free piston  7  moving simply makes gas contained within expansion chamber  63  exhaust out of expansion chamber  63  as free piston  7  moves along first sliding direction toward chamber bottom  66 . This volume reduction at constant pressure is noted thermodynamic phase  21 . 
       FIG. 12  shows an example of a second phase of operation of the free piston expander, according to an embodiment of the invention. 
     Compressed gas continues to arrive into admission chamber  61  from admission inlet  62 . This compressed gas continues to increase the variable volume of admission chamber  61  by moving piston shoulder  77  further apart from chamber shoulder  70 , thereby making free piston  7  continuing and sliding within sliding chamber  6  in first direction from free space  65  to chamber bottom  66 , thereby further reducing the variable volume of expansion chamber  63 , thereby compressing gas within expansion chamber  63  once exhaust outlet  64  has been closed by periphery of sliding piston head  71 . There is a fluidic communication between admission inlet  62  and admission chamber  61 , since admission inlet  62  opens into admission chamber  61 . There is no fluidic communication between admission canal  73  and admission chamber  61 , since free extremity of radial canal  75  is closed by chamber wall  60 . There is a fluidic communication between admission canal  73  and expansion chamber  63 , since free extremity of axial channel  74  opens into expansion chamber  63 . There is no more fluidic communication between exhaust outlet  64  and expansion chamber  63 , since exhaust outlet  64  is now closed by sliding piston head  71 . 
       FIG. 13  shows an example of a corresponding second phase in a diagram pressure volume in the expansion chamber of the free piston expander, according to an embodiment of the invention. 
     Within the variable volume of expansion chamber  63 , gas pressure increases from low level Pexh toward high level Padm (high pressure in admission chamber  61 ) since free piston  7  moving now compresses gas contained within expansion chamber  63  which cannot anymore exhaust out of expansion chamber  63  as free piston  7  moves along first sliding direction toward chamber bottom  66 . This volume reduction with pressure increase is noted thermodynamic phase  22 . 
       FIG. 14  shows an example of a third phase of operation of the free piston expander, according to an embodiment of the invention. 
     Compressed gas continues to arrive into admission chamber  61  from admission inlet  62 . This compressed gas continues to increase the variable volume of admission chamber  61  by moving piston shoulder  77  further apart from chamber shoulder  70 , thereby making free piston  7  continuing and sliding within sliding chamber  6  in first direction from free space  65  to chamber bottom  66 , thereby further reducing the variable volume of expansion chamber  63 , thereby compressing gas within expansion chamber  63  since exhaust outlet  64  has been closed by periphery of sliding piston head  71 , until admission canal  73  opens into admission chamber  61  by free end of radial canal  75  opening into admission chamber  61 . Then, there is a pressure balancing between admission chamber  61  and expansion chamber  63  by pressure equalizing through admission canal  73 . There is a fluidic communication between admission inlet  62  and admission chamber  61 , since admission inlet  62  opens into admission chamber  61 . There is now fluidic communication between admission canal  73  and admission chamber  61 , since free end of radial canal  75  opens into admission chamber  61 . There is a fluidic communication between admission canal  73  and expansion chamber  63 , since free end of axial channel  74  opens into expansion chamber  63 . There is no more fluidic communication between exhaust outlet  64  and expansion chamber  63 , since exhaust outlet  64  is now closed by sliding piston head  71 . 
       FIG. 15  shows an example of a corresponding third phase in a diagram pressure volume in the expansion chamber of the free piston expander, according to an embodiment of the invention. 
     Within the variable volume of expansion chamber  63 , after establishing of a fluidic communication between admission chamber  61  and expansion chamber  63  through admission canal  73 , there is a further brutal gas pressure increase until high level Padm (high pressure in admission chamber  61 ) because of the pressure equalizing between admission chamber  61  and expansion chamber  63 . This volume reduction with pressure increase is noted thermodynamic phase  23 . Afterwards, there is still a volume reduction at constant pressure which is noted thermodynamic phase  24  and which comes from the inertia of the free piston  7  body which does not instantly stop its travel, but which curtails progressively before inverting its move toward second sliding direction opposed to first sliding direction, moving then away from chamber wall  66  toward free space  65  during next phase of operation described in  FIGS. 16 and 17 . 
       FIG. 16  shows an example of a fourth phase of operation of the free piston expander, according to an embodiment of the invention. 
     Compressed gas starts being expelled from admission chamber  61  toward admission inlet  62 , until piston head  71  periphery stops closing exhaust outlet  64  and piston head surface  76  goes past exhaust outlet  64  to let again exhaust outlet  64  opening into expansion chamber  63 , because there are the same pressures within admission chamber  61  and expansion chamber  63  whereas the piston head surface  76  on which this common pressure applies is notably more important, at least by a factor 1.5, preferably by at least a factor 2, more preferably at least a factor 3, than the piston shoulder surface  77  on which this same common pressure applies too since there is fluidic communication through admission canal  73  between admission chamber  61  and expansion chamber  63 . Free piston  7  has inverted its move toward second sliding direction opposed to first sliding direction, moving thereby away from chamber wall  66  toward free space  65 . 
     The variable volume of admission chamber  61  is reduced by moving piston shoulder  77  toward chamber shoulder  70 , thereby making free piston  7  continuing and sliding within sliding chamber  6  in second direction from chamber bottom  66  toward free space  65 , thereby increasing the variable volume of expansion chamber  63 , thereby expanding gas within expansion chamber  63  until piston head surface  76  reaches and goes past exhaust outlet  64  making then this exhaust outlet  64  opening again into expansion chamber  63 . At beginning of free piston  7  sliding in second sliding direction, fluidic communication between admission canal  73  and admission chamber  61  rapidly becomes closed since free end of radial canal  75  becomes closed by chamber wall  60 , and this happens before exhaust outlet  64  again opens into expansion chamber  63 . Then, there is no more pressure balancing between admission chamber  61  and expansion chamber  63 . 
     There is a fluidic communication between admission inlet  62  and admission chamber  61 , since admission inlet  62  opens into admission chamber  61 . There is no more fluidic communication between admission canal  73  and admission chamber  61 , since free end of radial canal  75  is now closed by chamber wall  60 . There is a fluidic communication between admission canal  73  and expansion chamber  63 , since free end of axial channel  74  opens into expansion chamber  63 . There is again fluidic communication between exhaust outlet  64  and expansion chamber  63 , since exhaust outlet  64  again opens into expansion chamber  63 . 
       FIG. 17  shows an example of a corresponding fourth phase in a diagram pressure volume in the expansion chamber of the free piston expander, according to an embodiment of the invention. 
     Within the variable volume of expansion chamber  63 , after inverting sliding direction of free piston  7  move, there is first a volume augmentation at constant high pressure Padm until admission canal  73  becomes closed again by chamber wall  60  closing free end of radial canal  75  (again noted thermodynamic phase  24  but from right to left on  FIG. 17 , whereas it was from right to left on  FIG. 15 ), then there is a gas pressure progressive decrease because of gas expansion within increasing variable volume of expansion chamber  63 , then followed by a further brutal gas pressure decrease (with constant volume) until low level Pexh (low pressure in expansion chamber  63 ) because of the pressure drop caused by the again opening of exhaust outlet  64  into expansion chamber  63  thereby rapidly expelling gas outside expansion chamber  63 . This volume reduction with pressure decrease is noted thermodynamic phase  25 , and is followed by the brutal drop pressure at constant volume which is noted thermodynamic phase  26 . Then, there is a volume increase at constant low pressure Pexh noted thermodynamic phase  21  (from left to right on  FIG. 17 , whereas it was from right to left in  FIG. 11 ). 
     Free piston  7  sliding has an oscillation frequency, and free piston  7  has a mass which has a value such that this oscillation frequency ranges from 20 Hz to 150 Hz, preferably ranges from 30 Hz to 120 Hz, more preferably ranges from 50 Hz to 90 Hz. 
       FIG. 18  shows an example of diagram of a thermodynamic cycle process, according to an embodiment of the invention. 
     The fluid may be chosen among: water, or carbon dioxide, or air, or natural gas, or organic fluid. The thermodynamic cycle includes a phase of adiabatic expansion. This adiabatic expansion phase is more than a half of the whole expansion phase in length on the diagram of  FIG. 18 . At the beginning of this adiabatic expansion phase, the fluid may be: in a liquid state, or in a mixed state including both liquid and vapor, or in a super-critical fluid state. 
     Diagram of  FIG. 18  corresponds to thermodynamic cycle of  FIG. 2  (or even  FIG. 3 ) and shows temperature T as a function of entropy S. There is a curve  30  limiting different regions corresponding to different states of the fluid used in the thermodynamic cycle. Point  31  is the point of critical temperature and of critical pressure. In region  32 , fluid is in liquid state. In region  33 , fluid is in a mix of liquid state and gas state. In region  34 , fluid is in gas state. Above critical point  31 , in an intermediate region between regions  32  and  34 , fluid is in a supercritical state. 
     All segments of cycle will now be described, the cycle being performed anticlockwise. At beginning of segment  35 , fluid is at output of compressor and at input of condenser. At end of segment  37 , fluid is at output of condenser. At beginning of segment  39 , fluid is at input of evaporator. At end of segment  39 , fluid is at output of evaporator and at input of compressor. 
     Within condenser, first there is segment  35 , where fluid remains at gas state and its temperature and entropy both decrease, then there is segment  36  where progressively fluid changes from gas state to a mix of gas state and liquid state to liquid state and its entropy decreases at constant temperature, at last segment  37 , where fluid remains in liquid state and both its temperature and entropy decrease. 
     Within thermodynamic cycle, there is an expansion phase, represented by segment  38 , which is an isenthalpic expansion phase in an optional non-preferred embodiment, where fluid temperature decreases and fluid entropy increases, while fluid state progressively changes from liquid state to a mix of liquid state and gas state. 
     Instead of this isenthalpic expansion phase  38 , there could be two phases, a first phase  41  of adiabatic expansion (still within free piston expander) followed by a second phase  42  of isothermal evaporation (within evaporator), in a preferred embodiment. Instead, there could be another less preferred embodiment, where there are successively, a first phase  41  of adiabatic expansion followed by a second phase  38  of isenthalpic expansion (both within free piston expander) and then followed by a third phase  42  of isothermal evaporation (within evaporator), where it is preferred that length of adiabatic expansion  41  is more than length of isenthalpic expansion  38 . 
     Within evaporator, there is segment  39 , where fluid entropy increases at constant temperature, while fluid state progressively changes from a mix of liquid state and gas state to gas state. 
     Within compressor, there is segment  40 , where fluid remains in gas state and is compressed at constant entropy. 
       FIG. 19  shows another example of diagram of a thermodynamic cycle process, according to an embodiment of the invention. 
     The fluid may be chosen as being carbon dioxide. At the beginning of the adiabatic expansion phase, the fluid is in a super-critical fluid state. 
     Diagram of  FIG. 19  corresponds to thermodynamic cycle of  FIG. 2  (or even  FIG. 3 ) and shows temperature T as a function of entropy S. There is a curve  30  limiting different regions corresponding to different states of the fluid used in the thermodynamic cycle. Point  31  is the point of critical temperature and of critical pressure. In region  32 , fluid is in liquid state. In region  33 , fluid is in a mix of liquid state and gas state. In region  34 , fluid is in gas state. Above critical point  31 , in an intermediate region between regions  32  and  34 , fluid is in a supercritical state. 
     All segments of cycle will now be described, the cycle being performed anticlockwise. At beginning of segment  45 , fluid is at output of compressor and at input of condenser. At end of segment  45 , fluid is at output of condenser. At beginning of segment  47 , fluid is at input of evaporator. At end of segment  48 , fluid is at output of evaporator and at input of compressor. 
     Within condenser, there is (curved) segment  45  going from point B to point C, where fluid goes from gas state toward liquid state via supercritical state, and its temperature and entropy both decrease. 
     Within free piston expander, there is an expansion phase, represented by segment  46 , going from point C to point D, which is an adiabatic expansion phase, where fluid temperature decreases at constant entropy, while fluid state progressively changes from liquid state to a mix of liquid state and gas state. 
     Within evaporator, there is first segment  47  from point D, where fluid entropy increases at constant temperature, while fluid state progressively changes from a mix of liquid state and gas state to gas state, then followed by segment  48  until point A, where both temperature and entropy of fluid increase slightly while fluid remains at gas state. 
     Within compressor, there is segment  49  from point A to point B, where fluid remains in gas state and is compressed. 
     In  FIG. 19 , following conditions are set up:
         Compression efficiency settled at 70%,   Expansion efficiency settled a 50%,   Super heating of 5° C. considered at input of compressor,   Evaporation temperature settled at 0° C.,   Temperature at output of condenser settled at 30° C.,   Condenser pressure varying between 73 bars and 120 bars.       

       FIG. 20  shows an example of a performance gain improvement when using a free piston expander in a thermodynamic cycle process, according to an embodiment of the invention. 
     There is a curve  43  showing an example of a performance gain when using a free piston expander in a thermodynamic cycle process, under the conditions of  FIG. 19 , when using a simple expansion valve instead of a free piston expander (related to  FIG. 2  with an expansion valve instead of the free piston expander). 
     There is a curve  44  showing an example of a performance gain when using a free piston expander in a thermodynamic cycle process, under the conditions of  FIG. 19 , when using a free piston expander instead of a simple expansion valve (with a thermodynamic machine as the one on  FIG. 2 ). 
     The distance existing between curve  43  and curve  44  represents the performance gain improvement when using a free piston expander instead of a simple expansion valve. The horizontal axis represents the evaporation pressure expressed in bars. The vertical axis represents a performance coefficient (COP=coefficient of performance) expressed in a number without unity. 
       FIG. 21  shows an example of a diagram pressure volume in the expansion chamber of the free piston expander, according to an embodiment of the invention. 
     The horizontal axis represents the expansion volume expressed in cm 3 . The vertical axis represents the expansion pressure expressed in bars. The diagram of  FIG. 21  is performed clockwise. The different steps are performed successively:
         Segment  51  from right to left: volume reduction at constant pressure,   (curved) segment  52 : compression (pressure increase with volume reduction),   Segment  53 : further pressure increase at constant volume,   Segment  54  from right to left: volume reduction at constant pressure,   Segment  54  from left to right: volume increase at constant pressure,   Segment  55 : pressure drop at constant volume,   (curved) segment  56  and then practically vertical segment  57 : expansion (pressure drop with volume increase),   Segment  51  from left to right: volume increase at constant pressure.       

     Segments  51  and  54  lengths are related to the inertia caused by the non-negligible mass of the moving free piston. 
       FIG. 22  shows an example of a diagram pressure volume in the compression cycle of the compressor, according to an embodiment of the invention. 
     The horizontal axis represents the compression volume expressed in cm 3 . The vertical axis represents the compression pressure expressed in bars. The diagram of  FIG. 21  is performed anticlockwise. The different steps are performed successively:
         (curved) segment  161 : compression (pressure increase with volume reduction),   Segment  162  from right to left: volume reduction at constant pressure,   Segment  163 : expansion (pressure drop with volume increase),   Segment  164  from left to right: volume increase at constant pressure.       

       FIG. 23  shows an example of a detailed structure, with precise dimensions given in cm, of a free piston expander chamber, according to an embodiment of the invention, corresponding to  FIG. 9 . 
     Axial admission canal  68  length value is 3.99 cm, length of each radial canal  79  value is 1 cm, admission canal  67  diameter value is 0.5 cm. 
     Diameter of sliding chamber has a value of 2.6 cm for receiving piston rod  72  (or slightly more to ensure smooth sliding), diameter of sliding chamber has a value of 3 cm for receiving piston head  71  (or slightly more to ensure smooth sliding). Diameter of admission inlet  62  has a value of 0.9 cm, diameter of exhaust outlet  64  has a value of 0.5 cm. 
     Length of sliding chamber has a value of 5 cm for receiving piston rod  72 . Depth of expansion chamber  63 , between middle of exhaust outlet  64  and chamber bottom  66 , has a value of 2.25 cm. 
       FIG. 24  shows an example of a detailed structure, with precise dimensions given in cm, of a free piston expander piston, according to an embodiment of the invention, corresponding to  FIG. 9 . For a free piston expander as on  FIG. 8 , all dimensions are the same except for axial admission canal  74  length which value is 4.8 cm, radial canal length  75  which value is 1.3 cm, admission canal  73  diameter which value is 0.5 cm. 
     Diameter of free piston head  71  has a value of 3 cm (or slightly less to ensure smooth sliding), diameter of free piston rod  72  has a value of 2.6 cm (or slightly less to ensure smooth sliding). Length of piston head  71  has a value of 2.5 cm, length of piston rod  72  has a value of 5 cm, full length of free piston  7  has a value of 7.5 cm. 
     Free piston body may be made of ceramics (alumina or zirconium oxide), graphite or aluminum, possibly with sliding guiding parts in ceramics or in graphite. For applications at rather low temperatures, this free piston body may be made of either Teflon (PTFE) or PEEK (polyetheretherketone). Chamber wall may be made of ceramics (alumina or zirconium oxide), stainless steel (inox 314 or inox 316), or spheroidal graphite cast iron. 
     The invention has been described with reference to preferred embodiments. However, many variations are possible within the scope of the invention.