Patent Publication Number: US-2017350251-A1

Title: Optimal expander outlet porting

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application is being filed on Dec. 29, 2015 as a PCT International Patent Application and claims the benefit of Indian Patent Application No. 4024/DEL/2014, filed on Dec. 30, 2014, the disclosure of which is incorporated herein by reference in its entirety. 
    
    
     TECHNICAL FIELD 
     The present disclosure relates to systems for recovering waste heat. More particularly, the present disclosure relates to waste heat energy recovery with a roots expander. 
     BACKGROUND 
     Waste heat energy is necessarily produced in many processes that generate energy or convert energy into useful work, such as a power plant. Typically, such waste heat energy is released into the ambient environment. In one application, waste heat energy is generated from an internal combustion engine. Exhaust gases from the engine have a high temperature and pressure and are typically discharged into the ambient environment without any energy recovery process. Alternatively, some approaches have been introduced to recover waste energy and re-use the recovered energy in the same process or in separate processes. However, there is still demand for enhancing the efficiency of energy recovery. 
     SUMMARY 
     An optimized mechanical expander or fluid expansion device with a delayed opening timing is disclosed. In one aspect, the expander includes a housing having an interior structure defining an interior volume, an inlet, and an outlet. The expander also includes a pair of parallel helical rotors disposed within the housing in a counter rotating non-contacting arrangement. Each of the rotors can have a plurality of lobes, wherein each lobe defines a cusp extending between a front end and a back end. The rotors are rotatable within the housing to form a transport volume between a leading lobe cusp, a trailing lobe cusp, and the housing interior structure. In the optimized design, the rotors alternatingly rotate sequentially through an intake position in which the transport volume is open to the housing inlet, a closed position in which the transport volume is closed to the housing outlet, and a discharge position in which the transport volume is open to the housing outlet. In one aspect, the rotors rotate from the closed position to the discharge position. During this rotational phase, a first opening forms between the housing interior structure and the leading lobe cusp proximate the front end. Subsequently, a second opening forms between the housing interior structure and the leading lobe cusp between the first opening and the leading lobe cusp back end, the second opening forming after the first opening has been at least partially formed. After further rotation, a third opening forms between the housing sidewall and the leading lobe cusp between the second opening and the leading lobe cusp back end, the third opening forming after the second opening has been at least partially formed. 
     In one aspect, the mechanical expander has an opening profile including an initial opening phase followed by a secondary opening phase, wherein only the first opening is formed and enlarged during the initial opening phase and both the first and second openings are enlarged during the secondary opening phase. In one example, the first rate of enlargement of a total opening area during the initial opening phase is less than a second rate of enlargement of the total opening area during the secondary opening phase to result in a delayed timing of the rotors. 
     A variety of additional aspects will be set forth in the description that follows. These aspects can relate to individual features and to combinations of features. It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the broad concepts upon which the embodiments disclosed herein are based. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic view of a vehicle having a volumetric fluid expansion device having features that are examples of aspects in accordance with the principles of the present disclosure. 
         FIG. 2  is a schematic side view of the fluid expansion device shown in  FIG. 1 . 
         FIG. 3  is a schematic end view of a stage inlet of the fluid expansion device shown in  FIG. 1 . 
         FIG. 4  is a schematic showing geometric parameters of the rotors of the fluid expansion device shown in  FIG. 1 . 
         FIG. 5  is a top perspective view of a physical example of the volumetric fluid expansion device depicted in  FIGS. 1-4 . 
         FIG. 6  is a bottom perspective view of the fluid expansion device shown in  FIG. 5 . 
         FIG. 7  is a top view of the fluid expansion device shown in  FIG. 5 . 
         FIG. 8  is a bottom view of the fluid expansion device shown in  FIG. 5 . 
         FIG. 9  is a front view of the fluid expansion device shown in  FIG. 5 . 
         FIG. 10  is cross-sectional view of the fluid expansion device shown in  FIG. 5 , taken along the line A-A shown in  FIG. 9 . 
         FIG. 11  is cross-sectional view of the fluid expansion device shown in  FIG. 5 , taken along the line B-B shown in  FIG. 9 . 
         FIG. 12  is cross-sectional view of the fluid expansion device shown in  FIG. 5 , taken along the line C-C shown in  FIG. 9 . 
         FIG. 13  is a bottom perspective view of a model of the fluid expansion device shown in  FIG. 5 , wherein the rotors in the fluid expansion device are in a first rotational position. 
         FIG. 13A  is a bottom perspective view of the model view shown in  FIG. 13 , but with the rotors removed such that only the interior surfaces of the fluid expansion device are shown. 
         FIG. 14  is a bottom view of the fluid expansion device model shown in  FIG. 13 . 
         FIG. 14A  is a bottom view of the model view shown in  FIG. 14 , but with the rotors removed such that only the interior surfaces of the fluid expansion device are shown. 
         FIG. 15  is a bottom perspective view of the fluid expansion device model shown in  FIG. 13 . 
         FIG. 16  is an enlarged bottom perspective view of the fluid expansion device model shown in  FIG. 13 , as indicated at  FIG. 15 . 
         FIG. 17  is a bottom view of the model of the fluid expansion device shown in  FIG. 13 , wherein the rotors in the fluid expansion device are in a second rotational position. 
         FIG. 18  is an enlarged bottom view of the fluid expansion device model shown in  FIG. 17 , as indicated at  FIG. 17 . 
         FIG. 19  is a bottom perspective view of the model of the fluid expansion device shown in  FIG. 13 , wherein the rotors in the fluid expansion device are in a third rotational position. 
         FIG. 20  is a bottom view of the fluid expansion device model shown in  FIG. 19  with the rotors in the third rotational position. 
         FIG. 21  is a bottom perspective view of the model of the fluid expansion device shown in  FIG. 13 , wherein the rotors in the fluid expansion device are in a fourth rotational position. 
         FIG. 22  is a bottom view of the fluid expansion device model shown in  FIG. 21  with the rotors in the fourth rotational position. 
         FIG. 23  is a bottom perspective view of the model of the fluid expansion device shown in  FIG. 13 , wherein the rotors in the fluid expansion device are in a fifth rotational position. 
         FIG. 24  is a bottom view of the fluid expansion device model shown in  FIG. 23  with the rotors in the fifth rotational position. 
         FIG. 25  is a graph showing an opening profile of the fluid expansion device shown in  FIG. 5 . 
     
    
    
     DETAILED DESCRIPTION 
     Modern demands for fuel efficient vehicles and power plants have led to development of hybrid power-generation and propulsion systems. Generally, such systems combine a power-plant, such as an internal combustion engine or a fuel cell, and an electric motor to drive the vehicle. Each of the internal combustion engine and fuel cell emits high temperature exhaust as a byproduct of the power-generation cycle employed therein. The high temperature exhaust constitutes energy that is lost from the power-generation cycle, which, if recaptured, could be employed to improve efficiency of the cycle, and, therefore, of the propulsion system employing the same. Improvements in other applications are also desired, for example in marine and agricultural industries. Another example is stationary generator sets. 
     Systems Including Fluid Expansion Devices 
     Referring to  FIG. 1 , a vehicle  10  is shown having wheels  12  for movement along an appropriate road surface. The vehicle  10  includes a power-generation system  14 . The system  14  includes a power-plant  16  employing a power-generation cycle. The power-plant  16  uses a specified amount of oxygen, which may be part of a stream of intake air, to generate power. The power-plant  16  also generates waste heat such in the form of a high-temperature exhaust gas in exhaust line  17  a byproduct of the power-generation cycle. In one embodiment, the power-plant  16  is an internal combustion (IC) engine, such as a spark-ignition or compression-ignition type which combusts a mixture of fuel and air to generate power. In one embodiment, the power-plant  16  may be or a fuel cell which converts chemical energy from a fuel into electricity through a chemical reaction with oxygen or another oxidizing agent. 
     The vehicle  10  may also include an energy recovery device, for example volumetric fluid expansion device  20 , which recovers waste heat from the power-plant  16  to improve the efficiency of the power-plant  16 . 
     In one embodiment, and as shown in  FIG. 1 , an organic Rankine cycle (ORC) is used to power the fluid expansion device  20 . In such an embodiment, a piping system  1000  including a heat exchanger  18  is provided that transfers heat from the exhaust gas line  17  to a working fluid  12  that is then delivered to the volumetric fluid expansion device  20 . The working fluid  12  may be a solvent such as ethanol, n-pentane, or toluene. A condenser  19  is also provided which creates a low pressure zone for the working fluid  12  and thereby provides a location for the working fluid  12  to condense. Once condensed, the working fluid  12  can be delivered to the heat exchanger  18  via a pump  17 . A more detailed description of an ORC system being utilized to drive an energy recovery device  20  is provided in Patent Cooperation Treaty (PCT) International Application Publication Number WO 2013/30774 entitled VOLUMETRIC ENERGY RECOVERY DEVICE AND SYSTEMS. WO 2013/30774 is hereby incorporated herein by reference in its entirety. The volumetric fluid expansion device  20  may also be utilized in a direct exhaust gas heat recovery process wherein the exhaust gas is the working fluid  12 , as disclosed in Patent Cooperation Treaty (PCT) International Application Publication Number Wo 2014/107407, the entirety of which is incorporated by reference herein. Additional expander systems are disclosed in Patent Cooperation Treaty (PCT) International Application Publication Number WO 2014/117159, the entirety of which is incorporated by reference herein. 
     In one aspect, the fluid expansion device  20  may also include a power output device  25  configured to transfer useful work from the fluid expansion device  20 . Such mechanical work generated by the rotation of the output shaft  38  (discussed later) of the fluid expansion device  20  may be delivered to any elements or devices as necessary. For example, the output shaft  38  can be directly or indirectly coupled to another power plant, another fluid expansion device, a turbocharger, a supercharger, a generator, a motor, a hydraulic pump, and/or a pneumatic pump via gears, belts, chains or other structures. In some examples, the recuperated energy may be accumulated in an energy storage device, such as a battery or an accumulator, and the energy storage device may release the stored energy on demand. In other examples, the recovered energy may return to the power plant  16  by mechanically coupling the output shaft of the device  20  to a power input location  17  (e.g. a crankshaft of an engine). A power transmission link  25  may also be employed between the volumetric fluid expander  20  and the power plant  16  to provide a better match between rotational speeds of the power plant  16  and the output shaft of the device  20 . In some embodiments, the power transmission link  25  can be configured as a planetary gear set to provide two outputs for the power plant  16  and a generator. 
     Fluid Expansion Device General Construction 
     Referring to  FIGS. 2-4 , a volumetric fluid expansion device  20  in accordance with the present teachings is shown in schematic form.  FIGS. 5-12  show a physical embodiment of the fluid expansion device  20 . As shown, the fluid expansion device  20  includes a main housing  102  that defines a first working fluid passageway  106  extending between a first inlet  108  and a first outlet  110 . The fluid expansion device  20  can also be provided with compartments  150 ,  152  to house bearings, timing gears, and/or step gears, for example, as explained in PCT Publication WO 2014/117159. Disposed within the working fluid passageway  106 , is a pair of meshed rotors  30 ,  32 . Each pair of meshed rotors  30 ,  32  is configured such that the rotors  30 ,  32  are overlapping or intermeshed, and rotate synchronously in opposite directions. 
     As the working fluid  12  passes through the inlet  108  across the meshed rotors  30 ,  32  and to the respective outlet  110 , the working fluid  12  undergoes a pressure drop which imparts rotational movement onto the rotors  30 ,  32 , thus creating mechanical work that can be input back into the power plant  16 . Accordingly, the inlet port  108  is configured to admit the working fluid  12  at an entering pressure whereas the corresponding outlet port  110  is configured to discharge the working fluid  12  at a leaving pressure lower than the entering pressure. In such a configuration, the working fluid  12  enters inlet  108  at a first pressure and leaves outlet  110  at a second pressure lower than the first. In one embodiment, the pressure drop from the inlet  108  to the outlet  110  is between about 2 bar and about 10 bar, for example 5 bar. 
     Each of the rotors  30 ,  32 , as most easily seen at  FIG. 3 , is provided with a plurality of lobes. As shown, each rotor  30 ,  32  can be provided with three lobes,  30 - 1 ,  30 - 2 ,  30 - 3  in the case of the rotor  30 , and  32 - 1 ,  32 - 2 ,  32 - 3  in the case of the rotor  32 . As shown, each of the lobes  30 - 1  to  30 - 3  and  32 - 1  to  32 - 3  form a respective tip or cusp edge  30 - 1   a  to  30 - 3   a  and  32 - 1   a  to  32 - 3   a.  Although three lobes are shown for each rotor  30  and  32 , each of the two rotors may have any number of lobes that is equal to or greater than two. For example, PCT Publication WO 2013/30774 shows a suitable rotor having four lobes. 
     As presented, the number of lobes is the same for each rotor  30  and  32 . This is in contrast to the construction of typical rotary screw devices and other similarly configured rotating equipment which have a dissimilar number of lobes (e.g. a male rotor with “n” lobes and a female rotor with “n+1” lobes). Furthermore, one of the distinguishing features of the expansion device  20  is that the rotors  30  and  32  are identical, wherein the rotors  30 ,  32  are oppositely arranged so that, as viewed from one axial end, the lobes of one rotor are twisted clockwise while the lobes of the meshing rotor are twisted counter-clockwise. Accordingly, when one lobe of the rotor  30 , such as the lobe  30 - 1  is leading with respect to the inlet port  24 , a lobe of the rotor  32 , such as the lobe  30 - 2 , is trailing with respect to the inlet port  24 , and, therefore with respect to a stream of the high-pressure fluid  12 . 
     As previously mentioned, the first and second rotors  30  and  32  are interleaved and continuously meshed for unitary rotation with each other. In one embodiment, the lobes of each rotor  30 ,  32  are twisted or helically disposed along the length L of the rotors  30 ,  32 . The length L can be defined as the distance between a first end  30   a,    32   a  and a second end  30   b,    32   b  of the respective rotors  30 ,  32 . Upon rotation of the rotors  30 ,  32 , the lobes, at the cusp edges, at least partially seal the fluid  12  against the interior structure or surface  33  of the housing  102  to define a transport volume  35 ,  37 , at which point expansion of the fluid  12  only occurs to the extent allowed by leakage which represents an inefficiency in the system. In contrast to some expansion devices that change the volume of the fluid when the fluid is sealed, the transport volume  35 ,  37  defined between the lobes and the interior structure or surface  33  of the housing is constant as the fluid  12  traverses the length of the rotors  30 ,  32 . Accordingly, the expansion device  20  is referred to as a “volumetric device” as the sealed or partially sealed fluid volume does not change wherein the working fluid  12  is generally not reduced or compressed. 
     In operation, rotor shafts  38 ,  40 , respectively attached to rotors  30 ,  32 , are rotated by the working fluid  12  as the fluid undergoes expansion from the higher first pressure working fluid  12  to the lower second pressure working fluid  12 . Accordingly, the shafts  38 ,  40  are configured to capture the work or power generated by the expansion device  20  during the expansion of the fluid  12  that takes place between the inlet port  108  and the respective outlet port  110 . As discussed previously, the work is transferred from the shafts  38 ,  40  as output torque from the expansion device  20  via output device  25 . 
     In one aspect of the geometry of the expansion device  20 , each of the rotor lobes  30 - 1  to  30 - 3  and  32 - 1  to  32 - 3  has a lobe geometry in which the twist of each of the first and second rotors  30  and  32  is constant along their substantially matching length L. Alternatively, the lobes  30 ,  32  can be provided without a twist although a drop in efficiency may be expected to occur. 
     As shown schematically at  FIG. 4 , one parameter of the lobe geometry is the helix angle HA. By way of definition, it should be understood that references hereinafter to “helix angle” of the rotor lobes is meant to refer to the helix angle at the pitch diameter PD (or pitch circle) of the rotors  30  and  32 . The term pitch diameter and its identification are well understood to those skilled in the gear and rotor art and will not be further discussed herein. As used herein, the helix angle HA can be calculated as follows: Helix Angle (HA)=(180/.pi.*arc tan (PD/Lead)), wherein: PD=pitch diameter of the rotor lobes; and Lead=the lobe length required for the lobe to complete 360 degrees of twist. It is noted that the Lead is a function of the twist angle and the length L of the lobes  30 ,  32 , respectively. The twist angle is known to those skilled in the art to be the angular displacement of the lobe, in degrees, which occurs in “traveling” the length L of the lobe from the rearward end of the rotor to the forward end of the rotor. In one embodiment, the twist angle is about 120 degrees, although the twist angle may be fewer or more degrees, such as 160 degrees. 
     Because the inlet port  108  introduces the fluid  12  to both the leading and trailing faces of each rotor  30 ,  32 , the fluid  12  performs both positive and negative work on the expansion device  20 . To illustrate,  FIG. 3  shows that lobes  30 - 2 ,  30 - 3 ,  32 - 2 , and  32 - 3  are each exposed to the fluid  12  through the inlet port opening  108 . Each of the lobes has a leading surface and a trailing surface, both of which are exposed to the fluid at various points of rotation of the associated rotor. The leading surface is the side of the lobe that is forward most as the rotor is rotating in a direction R 1 , R 2  while the trailing surface is the side of the lobe opposite the leading surface. For example, rotor  30  rotates in direction R 1  thereby resulting in side  30 - 1   a  as being the leading surface of lobe  30 - 1  and side  30 - 1   b  being the trailing surface. As rotor  32  rotates in a direction R 2  which is opposite direction R 1 , the leading and trailing surfaces are mirrored such that side  32 - 1   a  is the leading surface of lobe  32 - 1  while side  32 - 1   b  is the trailing surface. 
     In generalized terms, the fluid  12  impinges on the trailing surfaces of the lobes as they pass through the inlet port opening  24   b  and positive work is performed on each rotor  30 ,  32 . By use of the term positive work, it is meant that the fluid  12  causes the rotors to rotate in the desired direction: direction R 1  for rotor  30  and direction R 2  for rotor  32 . As shown, fluid  12  will operate to impart positive work on the trailing surface  30 - 1   b  of rotor  30 - 1 . The fluid  12  is also imparting positive work on the trailing surface  32 - 2   b  of rotor  32 - 2 . However, the fluid  12  also impinges on the leading surfaces of the lobes, for example surfaces  30 - 3   a  and  32 - 1   a,  as they pass through the inlet port opening thereby causing negative work to be performed on each rotor  30 ,  32 . By use of the term negative work, it is meant that the working fluid  12  causes the rotors to rotate opposite to the desired direction, R 1 , R 2 . 
     Optimized Fluid Expansion Device 
     The exemplary embodiment of the fluid expansion device  20  shown at  FIGS. 5-12  includes a housing outlet configuration which is optimized increase performance by defining and controlling the manner in which the transport volume  35 ,  37 , defined by the housing interior structure or surface  33  and the rotors  30 ,  32 , is opened to the housing outlet  110 . In operation, the fluid expansion device  20  rotors  30 ,  32  alternately rotate through an intake position in which the transport volume  35 ,  37  is open to the housing inlet, a closed position in which the transport volume  35 ,  37  is generally closed to the housing outlet, and a discharge position in which the transport volume  35 ,  37  is open to the housing outlet. As noted previously, some leakage of the working fluid  12  is possible between the lobe cusp edges and the interior structure or surface  33  of the housing  102 , since there may be a small clearance or gap therebetween. As such, by use of the terms “closed” or “sealed” with respect to the closed position of the rotors  30 ,  32 , it is meant to indicate that the working fluid  12  is prevented from exiting the transport volume  35 ,  37  through any pathway not due to the clearance between the rotors  30 ,  32  and housing  102 . 
       FIGS. 13-24  show the interaction between the rotors  30 ,  32  and the housing interior structure or surface  33  at various rotational points of the rotors  30 ,  32 , beginning at the closed position of the rotor  32 . For the purpose of clarity,  FIGS. 13-24  show the interior structure or surface  33  of the housing  102  as the outermost layer in the drawings with the portions of the housing  102  beyond the interior structure or surface  33  not shown. Additionally,  FIGS. 13A and 14A  are presented without the rotors  30 ,  32  being shown, such that the surface  33  and the below discussed related surface features can be more clearly understood. As configured, the housing  102  interior structure or surface  33  defines a chamber portion  300  within which the rotors  30 ,  32  are primarily disposed. In one aspect, the chamber portion  300  has an obround or race-track shaped cross-sectional profile to accommodate the two rotors  30 ,  32 . An outlet portion  302  is also provided as a portion of the interior structure or surface  33  and is oriented such that the outlet portion  302  overlays the end of the chamber portion  300  and such that the outlet portion  302  is generally orthogonally to the chamber portion  300 . 
     The interior structure or surface  33  is further provided with a dome portion  304  that further interconnects the chamber portion  300  and the outlet portion  302 . As shown, the dome portion  304  is generally v-shaped or tent-shaped and functions to control the timing of the opening of the rotors  30 ,  32  into the discharge position. The dome portion  304  also provides for increased volume for the working fluid  12  to evacuate from the transport volume  35 ,  37  and to the outlet  110 . 
     As most easily seen at  FIG. 13 , the dome portion  304  extends generally laterally across the width of the rotors  30 ,  32  from a first end  306  to lateral ends  308  and  310 . The dome portion  304  is further shown as extending from the first end  306  along the length of and away from the rotors  30 ,  32  towards an outlet end  312  proximate the outlet  110 . It is noted that each of the ends  306  to  312  can be formed as rounded ends that gradually converge with the surfaces of the chamber portion  300  and outlet portion  302 . In one aspect, the ends  306  and  308  define an interface line or zone  314  between the dome portion  304  and the chamber portion  300  while ends  306  and  310  define a second interface line or zone  316  between the dome portion  304  and the chamber portion  300 . Similarly, ends  306  and  312  form an interface line or zone  318  that forms an axis of symmetry for the dome portion  304  extending parallel to the length of the rotors  30 ,  32 . Ends  308  and  312  can form an interface line or zone  320  while ends  310  and  312  can form an interface line or zone  322 . As with the ends  306  to  310 , the interface lines or zones  314  to  322  can be formed with a generally rounded profile. In one aspect, the ends  306 ,  308 , and  312  which define interface lines or zones  314 ,  318 , and  320  can be said to define a first surface  304   a  of the dome portion  304  while the ends  306 ,  310 , and  312  which define interface lines or zones  316 ,  318 , and  322  can be said to define a second surface  304   b  of the dome portion  304 , wherein the first and second surfaces  304   a,    304   b  define the dome portion  304 . 
     As shown at  FIGS. 13-14 , the rotor  32  is rotated into the closed position such that the transport volume  37  is defined between lobes  32 - 2  (leading),  32 - 1  (trailing) and the chamber portion  300  of the interior structure or surface  33 . As such, the transport volume  37  is isolated from both the outlet portion  302  and the dome portion  304  such that no working fluid  12  can pass from the transport volume  37  to the outlet  110  of the fluid expansion device  20 . 
     Referring to  FIGS. 15-18 , the rotor  32  (and rotor  30 ) has been rotated by one degree (1 o) from the closed position towards the discharge position such that a first opening  400  forms between the leading lobe  32 - 2  and the interior structure or surface  33  proximate the outlet portion  302 . As shown, the first opening  400  is proximate the discharge end  32   b  of the rotor  32 . At this rotational position of the rotor  32 , the first opening  400  is the only opening between the transport volume  37  and the interior structure or surface  33  and represents about 10% of the maximal opening area for the first opening  400  before additional openings are created between the transport volume  37  and the outlet  110  by further rotation of the rotor  32 . 
     Referring to  FIGS. 19-20 , the rotor  32  (and rotor  30 ) has been further rotated by can be further rotated by another 12 degrees (12 o) for a total rotation of 13 degrees (13 o) which results in the first opening area  400  be further enlarged. However, the first opening area  400  still remains as the only opening between the transport volume  37  and the interior structure or surface  33 . In the position shown at  FIG. 19-20 , the first opening area  400  represents about 100% of the maximal opening area for the first opening  400  before additional openings are created between the transport volume  37  and the outlet  110  by further rotation of the rotor  32 . 
       FIGS. 21-22  show the rotor  32  (and rotor  30 ) having been rotated beyond the position shown in  FIGS. 19-20  such that a second opening  402  forms between the transport volume  37  and the interior structure or surface  33  and such that the first opening  400  is further enlarged. As shown, the rotor  32  (and rotor  30 ) has been rotated an additional 5 degrees (5 o) for a total rotation of 18 degrees (18 o) from the closed position. The second opening  402  is located at about the mid-point of the rotor  32  and the interior structure or surface  33  proximate the dome portion  304  at zone or line  316 . 
       FIGS. 23-24  show the rotor  32  (and rotor  32 ) having been rotated beyond the position shown in  FIGS. 21-22  such that a third opening  404  forms between the transport volume  37  and the interior structure or surface  33 , and such that the first and second openings  400 ,  402  are further enlarged. As shown, the rotor  32  (and rotor  30 ) has been rotated an additional 5 degrees (5 o) for a total rotation of 23 degrees (23 o) from the closed position. The third opening  404  is located at the inlet end  32   a  of the rotor and forms between the rotor  32  and the interior structure or surface  33  proximate the chamber portion  300 . 
     In one non-limiting example embodiment, the opening areas  400 ,  402 ,  404  at various rotational positions of the rotor  32  (or  30 ) are as shown in Table 1 below. 
     
       
         
           
               
               
               
               
               
             
               
                   
                 TABLE 1 
               
               
                   
                   
               
               
                   
                   
                 1 st   
                 2 nd   
                 3 rd   
               
               
                   
                 Rotational 
                 Opening 
                 Opening 
                 Opening 
               
               
                   
                 Position of 
                 Area  
                 Area 
                 Area 
               
               
                   
                 Rotor  
                 400 
                 402 
                 404 
               
               
                   
                 (degrees) 
                 (mm 2 ) 
                 (mm 2 ) 
                 (mm 2 ) 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 0° 
                 0 
                 0 
                 0 
               
               
                   
                 1° 
                 8.4 
                 0 
                 0 
               
               
                   
                 2° 
                 19.2 
                 0 
                 0 
               
               
                   
                 3° 
                 30 
                 0 
                 0 
               
               
                   
                 13°  
                 80.0 
                 0 
                 0 
               
               
                   
                 18°  
                 128.0 
                 57.5 
                 0 
               
               
                   
                 23°  
                 171.6 
                 154.4 
                 6.1 
               
               
                   
                   
               
            
           
         
       
     
     In comparison to a fluid expander having a standard outlet configuration, the disclosed fluid expansion device  20  is configured to have a delayed opening timing, meaning that the formation of the opening area between the transport volume  35 ,  37  and the outlet  110  occurs at a decreased rate in comparison to a standard design. Referring to  FIG. 25 , a graphical representation of the data shown in Table 1 is presented, wherein an opening profile  500  of the expansion device  20  is shown. The opening profile  500  can be characterized as having an initial opening phase  502  during which the first opening  400  enlarges and accounts entirely for the total open area between the rotor  32  and the interior structure or surface  33 . The initial opening phase  502  can be further characterized as having a first portion  502   a  and a second portion  502   b  in which the first portion  502   a  has a greater slope than the second portion  502   b,  meaning that the first opening  400  enlarges at a faster rate during the first portion  502   a  as compared to the second portion  502   b.  The opening profile  500  can be further characterized as having a secondary opening phase  504  during which the second and third openings  402 ,  404  develop and enlarge in conjunction with further enlargement of the first opening  400 . As can be seen, the secondary opening phase  504  has a significantly greater slope than the initial opening phase  502  which reflects that the opening area enlarges at a slower rate during the initial opening phase  502  as compared to the secondary opening phase  504 . 
     The difference in slopes of the phases  502 ,  504  can be referred to as creating a delayed opening timing of the rotors  30 ,  32 . Accordingly, with each degree of rotation of the rotor  30 ,  32 , the opening area of the optimized outlet expander  20  is smaller than that of an expander having a standard outlet. In some cases, the opening area of a non-optimized expansion device can be twice as much or more than that of the disclosed device  20  after only one degree of rotation from the closed position. This timing delay significantly increases the velocity of the working fluid  12  exiting the expansion device  20 . The resulting concentrated high velocity stream at the rotor exhaust creates an entrapment effect that results in a vacuum. This vacuum increases the delta pressure across the expander rotors  30 ,  32  which drives a higher output torque. Delaying venting at the front and back cusps of the rotor  30 ,  32  for a minimum of 2 to 3 degrees relative to the small pocket near the middle of the rotor maximizes torque output. 
     It is also noted that a standard outlet configuration can result in the opening between the rotors and the housing being initially formed near the middle of the rotor and then towards the inlet side of the rotor. This early opening towards the inlet end of the rotor can result in increased back pressure on the rotor by the working fluid which can cause negative work to be performed by the working fluid. In contrast, the disclosed fluid expansion device  20  opens first at opening  400  proximate the discharge end of the rotors  30 ,  32 , then the middle portion of the rotors  30 ,  32 , and then at the inlet end of the rotors  30 ,  32 . 
     The above cited differences are illustrated in Table 2 (below) which provides a comparison between a fluid expander having an unmodified or standard outlet and a fluid expander  20  in accordance with the above description. 
     
       
         
           
               
               
               
               
             
               
                   
                 TABLE 2 
               
               
                   
                   
               
               
                   
                   
                 Standard  
                 Optimized  
               
               
                   
                 Design 
                 outlet fluid  
                 outlet fluid 
               
               
                   
                 Parameter 
                 expander 
                 expander 20 
               
               
                   
                   
               
             
            
               
                   
                 Working Fluid 
                 Ethanol 
                 Ethanol 
               
               
                   
                 Expander Speed 
                 10000 
                 10000 
               
               
                   
                 Torque 
                 4.98 
                 5.13 
               
               
                   
                 Expander Power 
                 5.217 
                 5.363 
               
               
                   
                 Expander Press IN 
                 3.237 
                 3.237 
               
               
                   
                 Expander Press 
                 1.841 
                 1.841 
               
               
                   
                 OUT 
                   
                   
               
               
                   
                 Mass Flow of 
                 163.9 
                 162 
               
               
                   
                 Working Fluid 
                   
                   
               
               
                   
                 Expander Average 
                 246 
                 246 
               
               
                   
                 Inlet Temp 
                   
                   
               
               
                   
                 Expander Average 
                 222 
                 222 
               
               
                   
                 Outlet Temp 
                   
                   
               
               
                   
                 Working Fluid 
                   
                   
               
               
                   
                 Velocity at 1° 
                 403 
                 440 
               
               
                   
                 Opening (m/s) 
                   
                   
               
               
                   
                 Isentropic 
                 55.06% 
                 57.27% 
               
               
                   
                 Efficiency 
                   
                   
               
               
                   
                   
               
            
           
         
       
     
     By optimizing the outlet port as described above, the lowest level of vacuum draw that is possible created at the rotor exhaust event which subsequently maximizes efficiency and torque generation. As can be seen from the table above, the working fluid velocity at 1 degree of opening for the optimized expander is 440 meters per second, which represents about a 10 percent increase in working fluid velocity through the first opening  400 . This increased velocity of the disclosed design aids in developing the performance enhancing vacuum draw and has been shown to result in isentropic efficiency improvements of over 2 percent. These improvements are gained by controlling the location and timing of the initial opening between the transport volume and the interior structure or surface  33 . For example, the location of the initial opening (i.e. first opening  400  located at the front end of the rotor) is controlled such that positive work by the working fluid  12  is maximized. Additionally, by designing the rotors  30 ,  32  and housing interior structure or surface  33  such that the initial opening enlarges at as slow of a rate as possible through the first few degrees of rotation of the rotors  30 ,  32  out of the closed position. 
     From the forgoing detailed description, it will be evident that modifications and variations can be made without departing from the spirit and scope of the disclosure.