Abstract:
A novel thermodynamic engines including a piston operating on a compressible fluid in a thermally insulated volume, which also includes a movable displacer which selectively divides the internal volume between a warm and a cold side, and a regenerator through which the fluid from the selectively divided volume passes and transfer its heat to or receives heat from, wherein the piston and displacer are each periodically moved in various complex motions according to the present invention to provide efficiency higher than Carnot efficiency. The resulting novel structures and methods, generally referred to as “Superclassical Cycle” engines, incorporate constant volume cooling and aspects of the “Proell Effect” (relative to cooling) to achieve improved efficiencies wherein the gas temperature on the cold side of a fluid displacer is below the lowest regenerator temperature due to “self-refrigeration.” Thus according to the apparatus and methods according to the present invention, the traditional principals of the Second Law is further refined and higher operating efficiencies achieved.

Description:
FIELD OF THE INVENTION 
     The present invention relates to thermodynamic heat engines, in particular to improved efficiency thermodynamic heat engines of at least three cycle steps. 
     BACKGROUND OF THE INVENTION 
     Prior thermodynamic engines of the Stirling cycle exchange a fluid that can be heated (or cooled) and compressed (or expanded) and have at least two different volumes or segregated portions or regions of a common volume in which the fluid is contained and moved. Typically, the fluid is generally heated to a first temperature T 1  by a temperature source, cooled to a lower temperature T 2  by a temperature sink and mechanical work extracted as a result of the displacement and expansion and compression of the fluid as it is cyclically exposed to the temperature source and sink. Notably, most of the heat received from the source is transferred to the sink, with a small portion (about 30%) being inefficiently converted to mechanical energy in a typical, good heat engine. 
     An exemplary reference Stirling cycle engine  50  is shown in FIG. 1 as a power piston and displacer system, with piston motion controlled by cam surfaces on the flywheel, but alternative methods of piston motion control may be incorporated by the Stirling cycle engine. As shown in FIG. 1, a volume contains the fluid (e.g. air) within a vessel  52  having thermal insulation there around. Typically, a displacer comprises a form of a baffle which divides the volume within the vessel  52  into two regions or portions of complementary varying size, specifically, a “cold” end 52 C cooled to temperature T 2  as provided by a heat sink  54  to the ambient temperature, and a “warm” (or heated) end 52W heated by source  56  to temperature T 1 . The displacer is fitted within the vessel sufficiently completely so that fluid moves between the warm and cold regions substantially entirely via a regenerator  58  which is disposed in and moved with the displacer  60  within the volume  52  by the displacer  60  and rod  62 . For simplicity, the piston and displacer rods in the exemplary embodiment of FIG. 1 are coaxial. That is, the displacer rod goes through the piston rod and the displacer rod goes over the flywheel axle ( 71  in FIG.  1 .), which can be stationary and have a bearing interfacing with the flywheel  70 . In this case, the axle or its assembly may be penetrated by the displacer rod. Alternate flywheel arrangements are possible in which the cam tracks do not cross and can be placed on opposite sides of the flywheel. 
     Mechanical energy output is provided by ‘power’ piston  64  which in this embodiment, also incorporates a heat conductive material and the heat sink  54  attached thereto. The mechanical energy from the power piston is transferred to a flywheel  70  via connecting rod  74  and cam track  68 , connected to or part of (together with the displacer cam track  72 ) the flywheel  70 . 
     Stirling Cycle engines include constant volume processes (e.g.  84 A and  88 A) and constant temperature processes (e.g.  82 B and  86 B) cycles, as illustrated by the graphs  80 A and  80 B of FIGS. 2A and 2B, respectively. Also typically, as in other embodiments of the Stirling ling Cycle engine, the cyclical power piston and displacer motions of the embodiment of FIG. 1 are generally identical in sinusoidal motion, but offset by 90°. The typical piston and displacer positions-versus-time over the cycle reference points A-D (also in graphs  80 A and  80 B) are illustrated by respective segments  92 P,  94 P,  96 P,  98 P and  92 D,  94 D,  96 D,  98 D in the graph  90  of FIG.  2 C. 
     SUMMARY OF THE INVENTION 
     The novel thermodynamic heat engines according to the present invention provide efficiencies higher than Carnot efficiency. In the present inventions, generally referred to as “Superclassical Cycle” engines, constant volume cooling with displacement and regeneration, and aspects of the “Proell Effect” (relative to cooling) are utilized. Moreover, the gas temperature on the cold side of a fluid displacer is below the lowest regenerator temperature due to “self-refrigeration.” 
     The “Proell Effect” (as described in The Thermodynamic Theory and Engineering Design of Supercarnot Heat Engines, by Wayne Proell, Cloud Hill Press, Las Vegas, N.Mex., 1984) incorporated by reference, refers to thermodynamic heat engine cycles and includes previous behavior of all gases in constant volume conditions with regeneration. The Proell Effect, by itself, conforms to the most rigorous definition of the Second Law of Thermodynamics which calls for zero or greater than zero entropy increases in isolated energy systems. However, the Proell Effect is unrecognized, unpredicted and not fully explored for traditional analyses of constant volume processes, such as in the Stirling cycle engines. The Proell Effect is not seem in the Stirling cycle because of the summetry created by two constant volume processes of opposite direction of fluid flow which cancels the Proell Effect. 
     Conventional thermodynamics identifies only one behavior of gases in a constant volume process, that is a change in internal energy directly proportional to its temperature, which equates to the heat added or removed, as its heat capacity at constant volume, C V , times the temperature change experienced, 
     
       
           Q=C   V (Δ T )  (1) 
       
     
     In addition to a description of gas behavior at constant volume as described by Equation 1, above, the constant volume environment and its energy flows become more complex when the constant volume is not at a uniform temperature and is divided by a displacer and the subdivided volumes are connected via a regenerator as illustrated by the engine  50  of FIG.  1 . 
     Further understanding may be provided by the Proell Effect, wherein the fluid is exemplified by a gas. In a constant volume process with regeneration, the change in volume of a gas displaced through a regenerator as a result of its change in temperature going from the hot side (T 1 ) of a constant volume to the cold side (T 2 ) of a constant volume, or vice-versa, the gas being separated in the constant volume and displaced from said hot and cold sides through a regenerator by a displacer, must be compensated by an equal and opposite volume change in the remainder of the gas not in the regenerator, in the hot and cold sides of said constant volume. The corresponding pressure-volume work energies involved with all localized volume changes within the constant volume transfer thermal energy between said regenerator and the gas of the hot and cold sides of the constant volume. This results in a temperature change experienced by the gas under adiabatic conditions in the hot and cold sides of the constant volume which will be greater than the temperature difference of said regenerator, up to a limit proportional to said gas&#39; heat capacity ratio, gamma. The pressure-volume work transfers heat inside the regenerator by heat capacity at constant pressure C P  and transfers heat by heat capacity at constant volume, C V , in said hot and cold sides of the constant volume. 
     The Proell effect may occur for fluid (gas) flow in either direction through the regenerator. When the gas going through the regenerator is heated, it expands, causing a compensatory compression in the remainder of the gas in the constant volume chamber. When the gas going through the regenerator is cooled, it compresses, causing a compensatory expansion in the remainder of the gas in the constant volume chamber. By normal gas behavior under adiabatic conditions, expansion is accompanied by a drop in temperature and compression is accompanied by a rise in temperature. These temperature changes are in addition to the temperature changes caused by intimate thermal contact with the regenerator while passing through the regenerator. 
     In the present invention, the final gas temperature on the cold side of the displacer in constant volume cooling is below the lowest regenerator temperature. The magnitude of how far below the conventional constant volume cooling temperature the gas goes depends upon the temperature difference of the regenerator and the degree of displacement. Such cooling beyond the conventionally predicted temperature is referred to as “self-refrigeration.” 
     When displacement from the hot side to the cold side is complete, half of the maximum self-refrigeration is created in the cold side. This is because compensatory cooling occurs in both the hot and cold side portions of the constant volume during the entire constant volume displacement. Summed throughout the entire stroke, the hot and cold sides contribute the same total heat flow and pressure-volume work. As an increment of gas passing through the regenerator cools, by the Ideal Gas Law, its volume decreases in direct proportion to the temperature decrease, 
     
       
           dV   increment =( nR/P   increment ) dT   regenerator ,  (2) 
       
     
     where n is the number of moles of gas, R is the gas constant, and pressure, P, is variable and incremental because the overall constant volume process will see a pressure decrease as the entire mass of gas is cooled from high to low temperature in a fixed total volume. When the incremental volume of gas going through the regenerator is insignificant relative to the total volume, P is essentially constant for that incremental passage. By this same equation (2), it is seen that as P reduces over the entire constant volume process, incremental V must increase. The pressure-volume work done on the cooling gas is incrementally constant during the entire constant volume stroke. This is supported in conventional thermodynamics; the difference between C P  and C V  is a constant, also called the gas constant, R. 
     The work contributions made by the hot and cold volumes outside the regenerator are linearly proportioned according to the hot and cold gas volumes which shift throughout the stroke. At the beginning of the constant volume stroke, all of the compensating expansion is provided by the hot side. Half way through the stroke, half of the expansion work comes from the hot side and half from the cold side. At the end of the stroke, all of the work comes from the cold side. Since the incremental compression work is constant throughout the stroke, the cold side self-refrigeration energy is merely half of the total pressure-volume work absorbed by the regenerator. The hot side portion of the gas must pass through the regenerator, giving its thermal condition to the regenerator. That gas leaves the regenerator at the lowest temperature of the regenerator and the self-refrigeration which it obtained on the hot side is no longer present as the gas enters the cold side. That self-refrigeration is stored in the hot side of the regenerator as a slight cooling of the hot entrance of the regenerator, to be fully reversed in the engine&#39;s heating stroke. 
     When the displacement from the hot side to the cold side is partial, and starts with some gas already on the cold side, more than half of the self-refrigeration is on the cold side. This larger self-refrigeration can approach gamma times the conventional constant volume cooling value proportional to C V . 
     The heat absorbed by the regenerator is, 
     
       
           Q=C   P (Δ T   regen ),  (3) 
       
     
     as a mass of gas going through the regenerator experiences nearly constant pressure and must absorb the work of compression from its volume decrease. The compression work absorbed is passed on to the regenerator as heat. 
     Since the gas being cooled in the regenerator can only provide heat to the regenerator at C V , the extra energy of C P  absorbed in the regenerator must come from the remainder of the gas, as mentioned above. This absorption of heat by the regenerator is also termed heat recovery or heat rejection (to the regenerator). 
     The compression work done inside the regenerator is the difference between C P  and C V :              W   =       (     Δ                   T   regen       )                     C   v                     (     γ   -   1     )               (   4   )                            =     P                     (        V     )     .                 (4A)                                
     The work was provided from the bulk of the gas outside of the regenerator under adiabatic conditions, so the work comes from the internal energy of the gas in the hot and cold zones, 
     
       
           W=C   V (Δ T   sr ).  (5) 
       
     
     The self refrigeration, ΔT sr , is summarized as follows, 
     
       
         Δ T   sr   =K   P (Δ T   regen )(γ−1).  (6) 
       
     
     For full displacement (proportionality fraction K P =0.5), 
     
       
         Δ T   sr =0.5(Δ T   regen )(γ−1).  (7) 
       
     
     For partial displacement, more complicated conditions apply, as reflected by the proportionality fraction. Since only part of the gas confined to constant volume is passed through the regenerator, not as much energy is transferred. Likewise, the amount of self-refrigeration energy removed from the cold side depends upon the proportion of the total gas which is always on the cold side and half of the gas which comes from the hot side, The self refrigeration temperature change becomes, 
     
       
         Δ T   sr =(min. cold side mass fraction+0.5 hot side mass fraction)×(mass fraction transferred)(Δ T   regen )(γ−1).  (8) 
       
     
     If the lowest temperature of the regenerator is room temperature, a constant volume cooling stroke with regeneration will result in the confined gas at a temperature below room temperature. Since this is accomplished by only the displacement of the gas from the hot side to the cold side, this uncommon form of refrigeration takes place at a very low cost to an engine cycle which incorporates it. Under reversible conditions, this refrigeration takes place with no work input, only a perturbation which approaches zero work. Under common, irreversible conditions, the friction and viscous drag of the displacer is very small. This uncommon cooling is applied in the present invention to create an ‘internal’ heat sink to which all heat flows and is then partially or completely sent to the regenerator over the range of temperatures in the regenerator. When partial displacement is used, the self-refrigeration is greater than what is needed to produce an internal heat sink to capture all compression energy and all friction and all thermal losses. Heat can flow to the internal heat sink from outside the engine, becoming part or all of the heat input to the engine, and a unity efficient engine becomes possible. 
     This novel engine efficiency is consistent with the Kinetic Theory of Heat, wherein the collisions of moving particles composing matter transfer kinetic energy, which is thermal energy which is never lost; thermal energy is perpetual. When work is created from this thermal energy, all energy leaving the thermal mass can become work. Conventional thermodynamics allows for processes to have complete conversion of heat into work, such as in the isothermal expansion of an ideal gas under reversible conditions; likewise, isentropic expansion is a unity efficient process, producing work from only the internal energy of the working gas. Such work may degrade back to thermal energy. Since work has no temperature, it may be dissipated back to heat at whatever the temperature of the receiving mass is. If this is the same mass which produced the work from thermal energy, the energy flow as heat has occurred with no net entropy increase. Conventional thermodynamics does not preclude this except by the general understanding of the Second Law of Thermodynamics. 
     Conventional thermodynamics can accommodate the present inventions with the following refinements to the Second Law of Thermodynamics: Work and heat may interchange perpetually, when first, since work has no entropy and may be dissipated as heat at any temperature, an energy system may have more than one equilibrium state, and second, when an engine creates an internal heat sink which is lower in temperature than the surrounding environment, and thus no heat will escape the engine. 
     Thus according to the apparatus and methods according to the present invention, the traditional Second Law requirement of energy losses in a heat engine is circumvented, and uses the Second Law&#39;s fundamental principle, e.g. that heat flows from higher temperature to lower temperature, to advantage. 
     The more observable distinctions of the method and apparatus of the present invention can be seen in the corresponding individual and relative motions of the piston and the displacer. By contrast with a typical (e.g. Stirling) cycle which have piston (and other mechanism) motions which are a pure sinusoid having a period equal to the cyclical rotation of the engine, the present invention has a more complex piston and/or displacer excursions that move in motions, or motion harmonics, more complex than a pure sinusoid motion. This is most clearly seen in portions of the cycle according to the various embodiments of the present invention discussed below, which include a stationary period. Furthermore, the piston and displacer motions are different motions, not just similar but phase-shifted motions as frequently found in prior art engines. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     These and further features of the present invention will be better understood by reading the following Detailed Description together with the Drawing, wherein 
     FIG. 1 is a partial cross-section elevation view of a typical Stirling Cycle engine; 
     FIGS. 2A and 2B are typical Pressure-Volume and Pressure-Enthalpy graphs of the Stirling Cycle engine of FIG. 1; 
     FIG. 2C is a typical Displacement-Time graph of the power piston and fluid displacer cycle motions for the Stirling Cycle engine of FIG. 1; 
     FIG. 3 is a partial cross-section elevation view of a first embodiment thermodynamic engine according to the present invention; 
     FIGS. 4A and 4B are typical Pressure-Volume and Pressure-Enthalpy graphs of the thermodynamic engine embodiment of FIG. 3; 
     FIG. 4C is a typical Displacement-Time graph of the power piston and fluid displacer cycle motions for the thermodynamic engine embodiment of FIG. 3; 
     FIG. 5 is a partial cross-section elevation view of a modified first embodiment thermodynamic engine according to the present invention having unity efficiency; 
     FIGS. 6A and 6B are typical Pressure-Volume and Pressure-Enthalpy graphs of the thermodynamic engine embodiment of FIG. 5; 
     FIG. 6C is a typical Displacement-Time graph of the power piston and fluid displacer cycle motions for the thermodynamic engine embodiment of FIG. 5; 
     FIG. 7 is a partial cross-section elevation view of a second embodiment thermodynamic engine according to the present invention; 
     FIGS. 8A and 8B are typical Pressure-Volume and Pressure-Enthalpy graphs of the thermodynamic engine embodiment of FIG. 7; 
     FIG. 8C is a typical Displacement-Time graph of the power piston and fluid displacer cycle motions for the thermodynamic engine embodiment of FIG. 7; 
     FIG. 9 is a partial cross-section elevation view of a third embodiment thermodynamic engine according to the present invention; 
     FIGS. 10A and 10B are typical Pressure-Volume and Pressure-Enthalpy graphs of the thermodynamic engine embodiment of FIG. 7; 
     FIG. 10C is a typical Displacement-Time graph of the power piston and fluid displacer cycle motions for the thermodynamic engine embodiment of FIG. 9; 
     FIG. 11 is a partial cross-section elevation view of a fourth embodiment thermodynamic engine according to the present invention; 
     FIGS. 12A and 12B are typical Pressure-Volume and Pressure-Enthalpy graphs of the thermodynamic engine embodiment of FIG. 7; 
     FIG. 12C is a typical Displacement-Time graph of the power piston and fluid displacer cycle motions for the thermodynamic engine embodiment of FIG. 11; 
     FIG. 13 is a partial cross-section elevation view of a fifth embodiment thermodynamic engine according to the present invention; 
     FIGS. 14A and 14B are typical Pressure-Volume and Pressure-Enthalpy graphs of the thermodynamic engine embodiment of FIG. 7; 
     FIG. 14C is a typical Displacement-Time graph of the power piston and fluid displacer cycle motions for the thermodynamic engine embodiment of FIG. 13; 
     FIG. 15 is a partial cross-section elevation view of a sixth embodiment thermodynamic engine according to the present invention; 
     FIGS. 16A and 16B are typical Pressure-Volume and Pressure-Enthalpy graphs of the thermodynamic engine embodiment of FIG. 15; and 
     FIG. 16C is a typical Displacement-Time graph of the power piston and fluid displacer cycle motions for the thermodynamic engine embodiment of FIG.  15 ; 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     The embodiments discussed below are chosen here for greatest similarity to the above-discussed prior art Stirling Cycle embodiment (FIG. 1) and for simplicity. Refinements made or the incorporation of equivalents by one of ordinary skill in the art are also included within the scope of the present invention. Moreover, the implementations according to the present invention (Superclassical Cycle) incorporate more advanced type of piston control instead of the sinusoidal motion typically used by the Stirling Cycle. Therefore, by utilizing the same exemplary hardware and motion control mechanism, the distinctions of the several implementations of the present invention over the prior art become clear. 
     The first exemplary embodiment  100  according to the present invention is shown in FIG. 3, and is composed of isovolumetric, isentropic, and isobaric processes, wherein regeneration between the isovolumetric and isobaric processes recycles more unconverted heat than previously believed possible. The constant volume cooling provided through the regenerator  58  in this embodiment occurs with a greater temperature change in the working fluid than conventionally provided. The Pressure-Enthalpy graph  130 B shows point B at a lower temperature than point D, the lowest temperature of the regenerator. The heat rejected from point B to point C on the graphs  130 A and  130 B is wasted heat and is not recoverable (i.e. by the regenerator). Moreover, the heat recycled in the constant volume portion  132 A, of the cycle beyond the temperature of point D to point B, is greater than all previously known regeneration schemes, allowing the Carnot efficiency limit to be exceeded. 
     The embodiment  100  of FIG. 3 utilizes complete displacement of the working fluid which results in only half of the extra heat being lifted, according to the Proell Effect as previously stated, by pressure-volume work from the gas at constant volume to the regenerator  58 . The displacements of the piston  64  and the displacer  60  over the cycle is shown in graph  140  of FIG. 4C by line segments  142 P,  144 P,  146 P, and  142 D,  144 D,  146 D, respectively. The piston  64  and displacer  60  motions are provided by corresponding cam tracks  138  and  122 , respectively. 
     The Pressure-Volume and Pressure-Enthalpy graphs  130 A and  130 B corresponding to the embodiment  100  of FIG. 3 demonstrate constant volume cooling by traces  132 A and  132 ′A (also  132 B and  132 ′B), constant entropy (isentropic) compression by trace  134 A (also  134 B), and constant pressure expansion by curve traces  136 A and  136 ′A (also  136 B and  136 ′B). 
     A modified embodiment  150  of the first exemplary embodiment ( 100 ) according to the present invention is shown in FIG. 5, and is also composed of isovolumetric, isentropic and isobaric processes, but does not reject any heat in the constant volume process. However, the embodiment  150  of FIG. 5 provides partial excursions of the piston  64  and the displacer  58 , and the ‘hot’ and ‘cold’ regions of the volume are interchanged. 
     Like the prior embodiment ( 100 ), regeneration between the isovolumetric and isobaric processes recycles more unconverted heat than previously believed possible. Partial displacement results in a larger portion of the extra heat of the Proell Effect to be transferred from the confined gas to the regenerator in the constant Volume cooling process. The transfer of the extra heat is large enough to prepare the gas for isentropic compression to Point C, the lowest temperature of the regenerator, and is large enough to create an internal heat sink to which energy losses may completely flow to and be recovered within the cycle. Moreover, there are no mandatory loss pathways in this embodiment. 
     As above, the constant volume cooling provided through the regenerator  58  in this embodiment occurs with a greater temperature change in the working fluid than conventionally provided. The Pressure-Enthalpy graph  180 B shows point B at a lower temperature than point C, the lowest temperature of the regenerator. Moreover, the heat recycled in the constant volume portion  182 A of the cycle beyond the temperature of point C to point B, is greater than all previously known regeneration schemes, allowing the Carnot efficiency limit to be exceeded. 
     Since the embodiment  150  of FIG. 5 creates an internal heat sink, it is possible to use the heat of the atmosphere, previously believed to be unavailable, to do useful work. Since the internal heat sink in the cold side  152 C captures heat influx across the cylinder walls, which is transferred to the regenerator by the action of constant volume cooling ( 182 A,  182 B) for use in constant pressure expansion ( 186 A,  186 B), a large part of the heat input to the cycle occurs in the cold zone, not across the piston  64 . 
     The displacements of the piston  64  and the displacer  60  over the cycle is shown in graph  190  of FIG. 6C by line segments  192 P,  194 P,  196 P, and  192 D,  194 D,  196 D, respectively. The piston  64  and displacer motions are provided by corresponding cam tracks  188  and  172 , respectively. 
     The Pressure-Volume and Pressure-Enthalpy graphs  180 A and  180 B corresponding to the embodiment  150  of FIG. 5 demonstrate constant volume cooling by traces  182 A (also  182 B), constant entropy (isentropic) compression by trace  184 A (also  184 B), and constant pressure expansion by curve traces  186 A (also  186 B). 
     Similar to the first embodiment  100 , the third exemplary embodiment  200  according to the present invention is shown in FIG. 7, but introduces an isentropic expansion step at the end of the isobaric expansion step. As with other embodiments of the present invention, the process and apparatus of FIG. 7 recycles more unconverted heat than previously believed possible, and achieves efficiency above Carnot. The constant volume cooling provided through the regenerator  58  in this embodiment occurs with a greater temperature change in the working fluid than conventionally provided. The heat wasted from point C to point D on the graphs  230 A and  230 B and is not recoverable. Moreover, the heat recycled in the constant volume portion  234 A and  234 B of the cycle from the temperature of point B to point C, is greater than all previously known regeneration schemes, allowing the Carnot efficiency limit to be exceeded. 
     The embodiment  200  of FIG. 7 utilizes complete displacement of the working fluid which results in only half of the extra heat being lifted, according to the Proell Effect as previously stated, by pressure-volume work from the gas at constant volume to the regenerator  58 . The displacements of the piston  64  and the displacer  60  over the cycle is shown in graph  240  of FIG. 8C by line segments  242 P,  244 P,  246 P,  248 P and  242 D,  244 D,  246 D,  248 D respectively. The piston  64  and displacer motions are provided by corresponding cam tracks  238  and  222 , respectively. 
     The respective Pressure-Volume and Pressure-Enthalpy graphs  230 A and  230 B, corresponding to the embodiment  200  of FIG. 7, demonstrate constant volume cooling by traces  234 A and  234 ′A (also  234 B and  234 ′B), constant entropy (isentropic) compression by trace  236 A (also  236 B), and constant pressure expansion by curve traces  238 A and  238 ′A (also  238 B and  238 ′B). 
     As the embodiment  100  of FIG. 3, and similarly the further embodiments discussed below, can be modified to provide the alternate embodiment  150 , of FIG. 5, so to can the embodiment  200  be modified by the use and apparatus to provide partial displacement of the fluid by the use of a more limited excursion of the piston  64  and the displacer  60 . Accordingly, the resulting alternate embodiment, provides a reduced power output. Moreover, more of the thermal energy spontaneously transmitted from the bulk of the fluid (e.g. gas) to the fluid inside the regenerator  58 , and therefore to the regenerator  58 , comes from the cold side of the displacer. Furthermore, a larger portion of the heat removed to the regenerator  58  from the cold side  152 C provides more of the Proell Effect self-refrigeration, thus allowing friction and low temperature heat to be captured in the engine&#39;s low temperature internal heat sink, and to be recycled. 
     Similar to the third embodiment  200 , the fourth exemplary embodiment  250  according to the present invention is shown in FIG. 9, includes an isothermal expansion step at the end of the and isobaric expansion step. As with other embodiments of the present invention, the process and apparatus  250  of FIG. 9 recycles more unconverted heat than previously believed possible, and achieves efficiency above Carnot. The constant volume cooling provided through the regenerator  58  in this embodiment occurs with a greater temperature change in the working fluid than conventionally provided. Heat rejected from point C to point D on the graphs  280 A and  280 B. Moreover, the heat recycled in the constant volume portion  284 A and  284 B of the cycle from the temperature of point B to point C, is greater than all previously known regeneration schemes, allowing the Carnot efficiency limit to be exceeded. 
     The embodiment  250  of FIG. 9 utilizes complete displacement of the working fluid which results in only half of the extra heat being lifted, according to the Proell Effect as previously stated, by pressure-volume work from the gas at constant volume to the regenerator  58 . The displacements of the piston  64  and the displacer  60  over the cycle is shown in graph  290  of FIG. 10C by line segments  292 P,  294 P,  296 P,  298 P and  292 D,  294 D,  296 D,  298 D respectively. The piston  64  and displacer motions are provided by corresponding cam tracks  288  and  272 , respectively. 
     The respective Pressure-Volume and Pressure-Enthalpy graphs  280 A and  280 B, corresponding to the embodiment  250  of FIG. 9, as with the embodiment  200  of FIG. 7, demonstrate constant volume cooling by traces  284 A and  284 ′A (also  284 B and  284 ′B), constant entropy (isentropic) compression by trace  286 A (also  286 B), and constant pressure expansion by curve traces  288 A (also  288 B). However, the constant entropy cycle portion illustrated by segment  232 A (and  232 B) of FIGS. 8A and 8B is now a constant temperature (isothermal) portion as illustrated by segment  282 A (and  282 B) of FIGS. 10A and 10B. 
     The fourth exemplary embodiment  300  according to the present invention is shown in FIG. 11, and is composed of isovolumetric, isentropic, isothermal and isobaric processes respectively, wherein regeneration between the isovolumetric and isobaric processes recycles more unconverted heat than previously believed possible. The constant volume cooling provided through the regenerator  58  in this embodiment occurs with a greater temperature change in the working fluid than conventionally provided. The heat rejected from point C to point D on the graphs  330 A and  330 B is wasted heat. Moreover, the heat recycled in the constant volume portion  332 A of the cycle from the temperature of point A to point B, is greater than all previously known regeneration schemes, allowing the Carnot efficiency limit to be exceeded. 
     The embodiment  300  of FIG. 11 utilizes complete displacement of the working fluid which results in only half of the extra heat being lifted, according to the Proell Effect as previously stated, by pressure-volume work from the gas at constant volume to the regenerator  58 . The displacements of the piston  64  and the displacer  60  over the cycle is shown in graph  340  of FIG. 12C by line segments  342 P,  344 P,  346 P,  348 P and  342 D,  344 D,  346 D,  348 D respectively. The curve between points B-C of FIG. 12A is constant entropy, and the curve between points C-D of FIG. 12C is constant temperature. The added step indicated by curve segment C-D is to waste heat and thus balance the cycle in reverse sequence of waste and compression than done in the embodiment  100  of FIGS. 4A and 4B, which first wastes heat with a step illustrated by segment B-C,  132 A and  132 B, above, before the constant entropy compression. The piston  64  and displacer motions are provided by corresponding cam tracks  338  and  322 , respectively. 
     The Pressure-Volume and Pressure-Enthalpy graphs  330 A and  330 B corresponding to the embodiment  300  of FIG. 11 demonstrate constant volume cooling by traces  332 A (also  332 B) constant entropy (isentropic) compression by trace  334 A (also  334 B) constant temperature (isothermal) cooling by trace  336 A (also  336 B), and constant pressure expansion by curve traces  338 A (also  338 B). The process and apparatus according to the embodiment  300  of FIG. 11 releases the rejected heat at a higher temperature T than the embodiment  100 , above. 
     The fifth exemplary embodiment  350  according to the present invention is shown in FIG. 13, and is composed of isovolumetric, isothermal, isentropic, and isobaric processes respectively, wherein regeneration between the isovolumetric and isobaric processes recycles more unconverted heat than previously believed possible. The constant volume cooling provided through the regenerator  58  in this embodiment occurs with a greater temperature change in the working fluid than conventionally provided. The heat rejected from point B to point C on the graphs  380 A and  380 B is wasted heat. Moreover, the heat recycled in the constant volume portion  382 A,  382 B of the cycle from the temperature of point A to point B, is greater than all previously known regeneration schemes, allowing the Carnot efficiency to be exceeded. 
     The embodiment  350  of FIG. 13 utilizes complete displacement of the working fluid which results in only half of the extra heat being lifted, according to the Proell Effect as previously stated, by pressure-volume work from the gas at constant volume to the regenerator  58 . The displacements of the piston  64  and the displacer  60  over the cycle is shown in graph  390  of FIG. 14C by line segments  392 P,  394 P,  396 P,  398 P and  392 D,  394 D,  396 D,  398 D respectively. Although the curves between points B-C an C-D of FIG. 14A in FIG. 14C have similar corresponding mechanical motions, the thermal characteristics respective to those curve portions are different, effected in this embodiment by different stroke rates. The piston  64  and displacer motions are provided by corresponding cam tracks  388  and  372 , respectively. 
     The Pressure-Volume and Pressure-Enthalpy graphs  380 A and  380 B corresponding to the embodiment  350  of FIG. 13 demonstrate constant volume cooling by traces  382 A (also  382 B) constant temperature (isothermal) compression by trace  384 A (also  384 B) constant entropy (isentropic) compression by trace  386 A (also  386 B), and constant pressure expansion by curve traces  388 A (also  388 B). The process and apparatus according to the embodiment  350  of FIG. 13 releases the rejected heat at a slightly lower temperature T than the embodiment  100 , above. 
     The embodiment  400  of FIG. 15 is similar to the embodiment  100  of FIG. 1 which utilizes complete displacement of the working fluid which results in only half of the extra heat being lifted, according to the Proell Effect as previously stated, by pressure-volume work from the gas at constant volume to the regenerator  58 . However, in this embodiment ( 400 ), an isobaric compression step B-C is used at the end of the displacer cooling stroke A-B, and also provides a cooling effect on the fluid by heat rejection into the regenerator. Moreover, the self-refrigeration cooling according to the Proell Effect in the isovolumetric cooling does not interfere with the isobaric compression which follows; the fluid (gas) in the cold zone remains at the same temperature and the heat removed during the isobaric compression is rejected from the engine via the regenerator without affecting the gas outside the regenerator  58 . 
     The displacements of the piston  64  and the displacer  60  over the cycle is shown in graph  440  of FIG. 16C by line segments  442 P,  444 P,  446 P,  448 P and  442 D,  444 D,  446 D,  448 D respectively. The piston  64  and displacer motions are provided by corresponding cam tracks  438  and  422 , respectively. 
     The Pressure-Volume and Pressure-Enthalpy graphs  430 A and  430 B corresponding to the embodiment  400  of FIG. 15 demonstrate constant volume cooling by trace  432 A (also  432 B), constant pressure (isobaric) compression by trace  434 A (and  434 B), constant entropy (isentropic) compression by trace  436 A (also  436 B), and constant pressure expansion by curve trace  438 A (also  438 B). 
     Further embodiments and modifications of the embodiments illustrated above are included within the scope of the present invention. Also included are alternate embodiments of the structures and processes shown and discussed above which incorporate partial displacement of the fluid and embodiments which additionally incorporate heat rejection to further improve efficiency. Moreover, novel cycles according to the present invention having additional cycle steps (e.g. five steps or more) are also included within the scope of the present invention.