Patent Publication Number: US-7708865-B2

Title: Vapor-compression evaporation system and method

Description:
RELATED APPLICATIONS 
     This application claims the benefit of Ser. No. 60/504,138 titled “Jet Ejector System and Method,” filed provisionally on Sep. 19, 2003. 
    
    
     TECHNICAL FIELD OF THE INVENTION 
     The present invention relates generally to the field of jet ejectors and, more particularly, to an improved, ultra-high efficiency jet ejector system and method. 
     BACKGROUND OF THE INVENTION 
     Typical steam jet ejectors feed high-pressure steam, at relatively high velocity, into the jet ejector. Steam is usually used as the motive fluid because it is readily available; however, an ejector may be designed to work with other gases or vapors as well. For some applications, water and other liquids are sometimes good motive fluids as they condense large quantities of vapor instead of having to compress them. Liquid motive fluids may also compress gases or vapors. 
     The motive high-pressure steam enters a nozzle and issues into the suction head as a high-velocity, low-pressure jet. The nozzle is an efficient device for converting the enthalpy of high-pressure steam or other fluid into kinetic energy. A suction head connects to the system being evacuated. The high-velocity jet issues from the nozzle and rushes through the suction head. 
     Gases or vapors from the system being evacuated enter the suction head where they are entrained by the high-velocity motive fluid, which accelerates them to a high velocity and sweeps them into the diffuser. The process in the diffuser is the reverse of that in the nozzle. It transforms a high-velocity, low-pressure jet stream into a high-pressure, low-velocity stream. Thus, in the final stage, the high-velocity stream passes through the diffuser and is exhausted at the pressure of the discharge line. 
     SUMMARY OF THE INVENTION 
     According to one embodiment of the invention, a vapor-compression evaporation system includes a plurality of vessels in series each containing a feed having a nonvolatile component, a mechanical compressor coupled to the last vessel in the series and operable to receive a vapor from the last vessel in the series, a pump operable to deliver a cooling liquid to the mechanical compressor, a tank coupled to the mechanical compressor and operable to separate liquid and vapor received from the mechanical compressor, a plurality of heat exchangers coupled inside respective ones of the vessels, the heat exchanger in the first vessel in the series operable to receive the vapor from the tank, at least some of the vapor condensing therein, whereby the heat of condensation provides the heat of evaporation to the first vessel in the series, and wherein at least some of the vapor inside the first vessel in the series is delivered to the heat exchanger in the next vessel in the series, whereby the condensing, evaporating, and delivering steps continue until the last vessel in the series is reached. 
     Embodiments of the invention provide a number of technical advantages. Embodiments of the invention may include all, some, or none of these advantages. An advantage of a jet ejector system according to one embodiment of the invention is that it blends gas streams of similar pressures; therefore, the velocity of each gas stream is similar. This leads to high efficiencies, even using traditional jet ejectors. The efficiency may be improved further by improving the design of the jet ejector. 
     A jet ejector according to one embodiment of the invention blends gas streams of similar velocities, but does not obstruct the flow of the propelled gas. This jet ejector may be used in many applications, such as compressors, heat pumps, water-based air conditioning, vacuum pumps, and propulsive jets (both for watercraft and aircraft). 
     An advantage of another jet ejector system according to one embodiment of the invention is it uses a high-efficiency liquid jet ejector in a cost-effective dewatering system. When combined with steam jet ejectors and multi-effect evaporators, any energy inefficiencies of the liquid jet system (liquid jet itself, pump, turbine) produce heat that usefully distills liquid. This liquid jet ejector may be used in water-based air conditioning. 
     In other embodiments, a heat exchanger is designed to facilitate a lower pressure drop than existing heat exchangers at low cost. Such a heat exchanger may include a plurality of plates (or sheets) inside a tube. The plates may be made of any suitable material; however, for some embodiments in which corrosion is a concern, the plates may be made of a suitable polymer. 
     Other technical advantages are readily apparent to one skilled in the art from the following figures, descriptions, and claims. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       For a more complete understanding of the invention, and for further features and advantages, reference is now made to the following description, taken in conjunction with the accompanying drawings, in which: 
         FIG. 1  illustrates a low-pressure vapor-compression evaporator system; 
         FIG. 2  illustrates a medium-pressure vapor-compression evaporator system; 
         FIG. 3  is a graphical correlation for standard jet ejectors; 
         FIG. 4  illustrates P motive /P inlet  (the inverse of the y-axis in  FIG. 3 ) as a function of compression ratio (P outlet /P inlet ) for each area ratio, AR; 
         FIG. 5  illustrates the slopes of  FIG. 4  on a log-log graph; 
         FIG. 6  illustrates m motive /m inlet  (the inverse of the x-axis in  FIG. 3 ) as a function of compression ratio (P outlet /P inlet  for each area ratio, AR; 
         FIG. 7  illustrates the slopes of  FIG. 6  on a log-log graph; 
         FIG. 8  illustrates a jet ejector system according to one embodiment of the invention; 
         FIGS. 9 through 20  illustrate the pressures and mass flows (using arbitrary units) according to various embodiments of the invention; 
         FIGS. 21 through 31  illustrate various jet ejector systems according to various embodiments of the invention; 
         FIG. 32  illustrates a jet ejector according to one embodiment of the invention; 
         FIG. 33  illustrates a jet ejector according to another embodiment of the invention; 
         FIGS. 34 and 35  illustrate a jet ejector according to another embodiment of the invention; 
         FIG. 36  illustrates a pattern of nozzle ducts according to one embodiment of the invention; 
         FIG. 37  illustrates a liquid jet ejector according to one embodiment of the invention; 
         FIG. 38  illustrates a liquid jet ejector according to another embodiment of the invention; 
         FIG. 39  illustrates a liquid jet ejector according to another embodiment of the invention; 
         FIG. 40  illustrates a liquid jet ejector according to another embodiment of the invention; 
         FIG. 41  illustrates a liquid jet ejector according to another embodiment of the invention; 
         FIGS. 42 through 51  illustrate various embodiments of an evaporator system that incorporates a liquid jet ejector according to various embodiments of the invention; 
         FIGS. 52 through 55  illustrate various embodiments of a vapor-compression evaporator system according to various embodiments of the invention; 
         FIG. 56  illustrates a cross-section of an example heat exchanger assembly including a shell and a sheet assembly disposed within the shell in accordance with an embodiment of the invention; 
         FIG. 57A  illustrates a three-dimensional view of the sheet assembly of the heat exchanger assembly of  FIG. 56  in accordance with one embodiment of the invention; 
         FIG. 57B  is a blown-up view of a corner area of the sheet assembly of  FIG. 57A  in accordance with an embodiment of the invention; 
         FIG. 57C  illustrates a side view of the corner of sheet assembly illustrated in  FIG. 57B ; 
         FIGS. 58A-58D  illustrate an example method of forming a particular sheet of the sheet assembly shown in  FIG. 57A  in accordance with one embodiment of the invention; 
         FIG. 59  illustrates various example manners for coupling the flange portions of adjacent sheets of the sheet assembly shown in  FIG. 57A  in accordance with one embodiment of the invention; 
         FIG. 60A  illustrates a method of aligning the molecules in a polymer for making polymer sheets in accordance with one embodiment of the invention; 
         FIG. 60B  illustrates a method of forming a sheet for a sheet assembly by joining a number of polymer sheets in accordance with one embodiment of the invention; and 
         FIGS. 61A-61D  illustrates another example sheet assembly in accordance with another embodiment of the invention. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       FIG. 1  illustrates a low-pressure vapor-compression evaporator system  2  performing desalination of salt water. A salt-containing feed  3  flows into an evaporator tank  4 , which in this embodiment is operated under vacuum. Although, in the illustrated embodiment, feed  3  is a salt-containing feed, a sugar-containing feed or suitable feed is also contemplated by the present invention. The salt-containing feed  3  boils, producing low-pressure vapors. These vapors are removed from evaporator tank  4  using a jet ejector  5 . The pressurized vapors exiting jet ejector  5  flow into a heat exchanger  6 , where they condense. Because of the interaction of heat exchanger  6  and evaporator tank  4 , the heat of condensation provides the heat of evaporation needed by the salt-containing feed  3 . Distilled liquid water  7  is recovered from heat exchanger  6  in any suitable manner, and concentrated salt solution  8  is removed from evaporator tank  4  using any suitable devices. The motive steam  9  added to jet ejector  5  may be condensed against cooling water; however, this condensation step may be eliminated if the product water is removed at a higher temperature than the feed water. A small vapor stream may be removed from evaporator tank  4  and sent to a condenser  10  to remove water vapor. The remaining gas is primarily noncondensibles, which may be removed using a vacuum pump (not explicitly illustrated). 
       FIG. 2  illustrates a medium-pressure vapor-compression evaporator system  20  according to an embodiment of the invention. System  20  operates similarly to system  2  in  FIG. 1 , except that an evaporator tank  22  operates at a moderate pressure, for example one atm. A motive steam  23  is added to a jet ejector  24  and exits evaporator tank  22  at moderate pressure and is useful for evaporating water. In the embodiment illustrated in  FIG. 2 , this medium-pressure steam may be used in a multi-effect evaporator  26 , although a multi-stage flash evaporator may be used as well. 
     In the illustrated embodiment, multi-effect evaporator  26  includes any suitable number of tanks  27   a ,  27   b ,  27   c  in series each containing a feed  28  having a nonvolatile component, such as salt or sugar. Jet ejector  24  coupled to evaporator tank  22  and receives a vapor from evaporator tank  22 . A heat exchanger  29  in evaporator tank  22  receives the vapor from jet ejector  24  where at least some of the vapor condenses therein. The heat of condensation provides the heat of evaporation to evaporator tank  22 . At least some of the vapor inside evaporator tank  22  is delivered to a heat exchanger  30   a  in tank  27   a , whereby the condensing, evaporating, and delivering steps continue through each tank until the last tank in the series (in this embodiment, tank  27   c ) is reached. 
     System  20  may also include a condenser  32  coupled to tank  27   c  for removing energy from system  20 , and a vacuum pump (not illustrated) for removing noncondensibles from system  20 . Any suitable devices may be utilized for removing concentrated feed  33  from tanks  22  and  27   a - 27   c , and a plurality of sensible heat exchangers  34  may be coupled to tanks  22  and  27   a - 27   c  for heating the feed  28  before entering the tanks  22 ,  27   a - 27   c . Sensible heat exchangers  34  may also be utilized for other suitable functions. 
     The pressure difference between the condensing steam and the boiling feed  28  depends upon the temperature difference between heat exchanger  29  and evaporator tank  22 . In addition, salts (or other soluble materials) depress the vapor pressure, which increases the pressure difference even further. Table 1 illustrates the required compression ratio for pure water (i.e., no salt) as a function of the temperature difference. 
                     TABLE 1                  Required compression ratio for water as a function of temperature       difference across the heat exchanger                         Temperature   Compression Ratio   Compression Ratio       Difference (° C.)   T evaporator  = 100° C.   T evaporator  = 25° C.               1   1.0362   1.0612       2   1.0735   1.1256       3   1.1119   1.1934       4   1.1514   1.2647       5   1.1921   1.3397       6   1.2340   1.4185       7   1.2770   1.5013       8   1.3210   1.5883                    
The required temperature difference depends upon the cost of heat exchangers and the cost of capital. In one embodiment, a temperature difference of 5° C. is considered economical. For a medium-pressure vapor-compression evaporator, such as system  20 , the required compression ratio is approximately 1.2.
 
       FIG. 3  illustrates a correlation for conventional jet ejectors. Table 2 illustrates the properties of a conventional jet ejector, based upon  FIG. 3 . Table 2 illustrates that using an area ratio of 100, 15.38-atm (226-psi) steam is able to evaporate 6.3 kg of water per kg of steam. Using system  20  ( FIG. 2 ) as an example, the steam exits the evaporator tank  22  at 1 atm and can evaporate more water in multi-effect evaporators  26  or a multi-stage flash evaporator. In industry, multi-stage flash evaporators typically evaporate 8 kg of water per kg of steam, so the entire medium-pressure vapor-compression system  20  can evaporate about 14 kg of distilled water per kg of steam. If the efficiency of jet ejector  24  can be improved, then the yield of distilled water may improve further. 
     
       
         
           
               
             
               
                 TABLE 2 
               
             
            
               
                   
               
               
                 Required pressure and motive steam consumption for ΔT = 5° C. and 
               
               
                 T evaporator  = 100° C. 
               
            
           
           
               
               
               
               
               
            
               
                 Compression Ratio 
                 Area Ratio 
                 
                   
                     
                       
                         
                           P 
                           inlet 
                         
                         
                           P 
                           motive 
                         
                       
                     
                   
                 
                 P motive (atm) 
                 
                   
                     
                       
                         
                           m 
                           inlet 
                         
                         
                           m 
                           motive 
                         
                       
                     
                   
                 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 1.2 
                 100 
                 0.065 
                 15.38 
                 6.3 
               
               
                 1.2 
                 50 
                 0.115 
                 8.70 
                 5.7 
               
               
                 1.2 
                 25 
                 0.200 
                 5.00 
                 4.5 
               
               
                   
               
            
           
         
       
     
     For optimization purposes, it is desirable to find equations that present the same information.  FIG. 4  illustrates P motive /P inlet  (the inverse of the y-axis in  FIG. 3 ) as a function of compression ratio (P outlet /P inlet ) for each area ratio, AR. As illustrated, each line is straight in  FIG. 4 .  FIG. 5  illustrates the slopes versus area ratio on a log-log graph. From  FIGS. 4 and 5 , the following equation relates the parameters: 
     
       
         
           
             
               
                 
                   
                     
                       P 
                       motive 
                     
                     
                       P 
                       inlet 
                     
                   
                   = 
                   
                     1 
                     + 
                     
                       0.9848 
                       ⁢ 
                       
                         
                           ( 
                           AR 
                           ) 
                         
                         0.9072 
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             
                               P 
                               outlet 
                             
                             
                               P 
                               inlet 
                             
                           
                           - 
                           1 
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
       FIG. 6  illustrates m motive /m inlet  (the inverse of the x-axis in  FIG. 3 ) as a function of compression ratio (P outlet /P inlet  for each area ratio, AR. Again, the lines are straight.  FIG. 7  illustrates the slopes versus area ratio on a log-log graph. From  FIGS. 6 and 7 , the following equation relates the parameters: 
     
       
         
           
             
               
                 
                   
                     
                       m 
                       motive 
                     
                     
                       m 
                       inlet 
                     
                   
                   = 
                   
                     5.1179 
                     ⁢ 
                     
                       
                         ( 
                         AR 
                         ) 
                       
                       
                         - 
                         0.4112 
                       
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           
                             P 
                             outlet 
                           
                           
                             P 
                             inlet 
                           
                         
                         - 
                         1 
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
     One reason jet ejectors may be inefficient is because they blend two gas streams with widely different velocities, which may occur when the motive pressure is significantly different from the inlet pressure. Thus, according to the teachings of one embodiment of the invention, the efficiency of jet ejectors may be improved substantially by developing jet ejectors and/or jet ejector systems that accomplish the required compression task by minimizing P motive /P inlet . 
       FIGS. 8 through 31  illustrate various embodiments of an improved design of a ultrahigh-efficiency jet ejector system that allows motive gas and propelled gas to be blended in a manner that minimizes the velocity differences between the two streams, thus optimizing efficiency. Some embodiments may also allow for the energy to be added in the form of work, rather than heat, which increases efficiency even further. 
       FIG. 8  illustrates a jet ejector system  50 , according to one embodiment of the invention, that minimizes P motive /P inlet . In the illustrated embodiment, system  50  includes a primary jet ejector  52  and one or more secondary jet ejectors  56   a ,  56   b ,  56   c  coupled to primary jet ejector  52  such that all of the jet ejectors are in a cascaded arrangement. As illustrated by various embodiments below in conjunction with  FIGS. 9-31 , this cascaded arrangement may be any suitable network of secondary jet ejectors  56  that receive a portion of a primary inlet stream  54  from primary jet ejector  52  and a motive steam  58  and process these streams before feeding a portion of the mixture of these streams back to primary jet ejector  52  for creation of primary outlet stream  55 . Primary jet ejector  52  is analogous to jet ejector  5  of  FIG. 1  or jet ejector  24  of  FIG. 2 . 
     In  FIG. 8 , a portion of primary inlet stream  54  is bled off and directed to secondary jet ejector  56   a  and, as described above, motive steam  58  is directed into secondary jet ejector  56   c . At each secondary jet ejector  56 , at least some of the portion of primary inlet steam  54  and at least some of motive steam  58  is received to create respective mixtures within secondary jet ejectors  56 . And at each secondary jet ejector  56  at least a portion of the respective mixture is directed to adjacent jet ejectors ( 57  or  56 ) in the cascaded arrangement. 
     For various embodiments of the invention utilizing the concept of  FIG. 8 , Tables 3 through 6 show the required P motive /P inlet  (Equation 1) and the resulting m motive /m inlet  (Equation 2) for each secondary jet ejector (also referred to as a stage) in the cascade.  FIGS. 9 through 20  illustrate the pressures and mass flows for each embodiment shown. Because any suitable operating parameters are contemplated by the present invention, the pressure units and mass units are arbitrarily shown in  FIGS. 9 through 20 ; however, it may be convenient to use atmospheres for pressure and kilograms for mass. 
     
       
         
           
               
             
               
                 TABLE 3 
               
             
            
               
                   
               
               
                 Analysis of jet ejector for compression ratio of 1.03. 
               
            
           
           
               
               
               
               
               
            
               
                 Area Ratio 
                 Stage 
                 
                   
                     
                       
                         
                           P 
                           outlet 
                         
                         
                           P 
                           inlet 
                         
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           P 
                           motive 
                         
                         
                           P 
                           inlet 
                         
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           m 
                           motive 
                         
                         
                           m 
                           inlet 
                         
                       
                     
                   
                 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 5 
                 1 
                 1.03 
                 1.127 
                 0.079 
               
               
                   
                 2 
                 1.13 
                 1.539 
                 0.335 
               
               
                   
                 3 
                 1.37 
                 2.552 
                 0.966 
               
               
                   
                 4 
                 1.86 
                 4.647 
                 2.271 
               
               
                   
                 5 
                 2.49 
                 7.319 
                 3.934 
               
               
                 4 
                 1 
                 1.03 
                 1.104 
                 0.087 
               
               
                   
                 2 
                 1.10 
                 1.360 
                 0.301 
               
               
                   
                 3 
                 1.23 
                 1.804 
                 0.671 
               
               
                   
                 4 
                 1.46 
                 2.607 
                 1.343 
               
               
                   
                 5 
                 1.78 
                 3.704 
                 2.260 
               
               
                   
                 6 
                 2.08 
                 4.741 
                 3.126 
               
               
                   
                 7 
                 2.28 
                 5.427 
                 3.699 
               
               
                 3 
                 1 
                 1.03 
                 1.080 
                 0.098 
               
               
                   
                 2 
                 1.08 
                 1.213 
                 0.261 
               
               
                   
                 3 
                 1.12 
                 1.331 
                 0.404 
               
               
                   
                 4 
                 1.33 
                 1.883 
                 1.078 
               
               
                   
                 5 
                 1.41 
                 2.105 
                 1.349 
               
               
                   
                 6 
                 1.49 
                 2.300 
                 1.588 
               
               
                   
                 7 
                 1.55 
                 2.457 
                 1.779 
               
               
                   
                 8 
                 1.59 
                 2.571 
                 1.919 
               
               
                   
                 9 
                 1.62 
                 2.649 
                 2.013 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 4 
               
             
            
               
                   
               
               
                 Analysis of jet ejector for compression ratio of 1.05. 
               
            
           
           
               
               
               
               
               
            
               
                 Area Ratio 
                 Stage 
                 
                   
                     
                       
                         
                           P 
                           outlet 
                         
                         
                           P 
                           inlet 
                         
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           P 
                           motive 
                         
                         
                           P 
                           inlet 
                         
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           m 
                           motive 
                         
                         
                           m 
                           inlet 
                         
                       
                     
                   
                 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 5 
                 1 
                 1.05 
                 1.212 
                 0.132 
               
               
                   
                 2 
                 1.21 
                 1.899 
                 0.560 
               
               
                   
                 3 
                 1.57 
                 3.405 
                 1.497 
               
               
                   
                 4 
                 2.17 
                 5.975 
                 3.097 
               
               
                   
                 5 
                 2.75 
                 8.421 
                 4.621 
               
               
                 4 
                 1 
                 1.05 
                 1.173 
                 0.145 
               
               
                   
                 2 
                 1.17 
                 1.599 
                 0.501 
               
               
                   
                 3 
                 1.36 
                 2.257 
                 1.051 
               
               
                   
                 4 
                 1.66 
                 3.269 
                 1.896 
               
               
                   
                 5 
                 1.97 
                 4.374 
                 2.819 
               
               
                   
                 6 
                 2.21 
                 5.205 
                 3.514 
               
               
                 3 
                 1 
                 1.05 
                 1.133 
                 0.163 
               
               
                   
                 2 
                 1.13 
                 1.355 
                 0.433 
               
               
                   
                 3 
                 1.20 
                 1.523 
                 0.638 
               
               
                   
                 4 
                 1.27 
                 1.731 
                 0.893 
               
               
                   
                 5 
                 1.36 
                 1.958 
                 1.169 
               
               
                   
                 6 
                 1.44 
                 2.173 
                 1.433 
               
               
                   
                 7 
                 1.51 
                 2.358 
                 1.658 
               
               
                   
                 8 
                 1.56 
                 2.499 
                 1.831 
               
               
                   
                 9 
                 1.6 
                 2.601 
                 1.955 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 5 
               
             
            
               
                   
               
               
                 Analysis of jet ejector for compression ratio of 1.1. 
               
            
           
           
               
               
               
               
               
            
               
                 Area Ratio 
                 Stage 
                 
                   
                     
                       
                         
                           P 
                           outlet 
                         
                         
                           P 
                           inlet 
                         
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           P 
                           motive 
                         
                         
                           P 
                           inlet 
                         
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           m 
                           motive 
                         
                         
                           m 
                           inlet 
                         
                       
                     
                   
                 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 5 
                 1 
                 1.10 
                 1.424 
                 0.264 
               
               
                   
                 2 
                 1.42 
                 2.798 
                 1.120 
               
               
                   
                 3 
                 1.97 
                 5.092 
                 2.548 
               
               
                   
                 4 
                 2.59 
                 7.751 
                 4.204 
               
               
                 4 
                 1 
                 1.10 
                 1.346 
                 0.289 
               
               
                   
                 2 
                 1.35 
                 2.198 
                 1.001 
               
               
                   
                 3 
                 1.63 
                 3.193 
                 1.832 
               
               
                   
                 4 
                 1.96 
                 4.308 
                 2.764 
               
               
                   
                 5 
                 2.20 
                 5.170 
                 3.485 
               
               
                 3 
                 1 
                 1.10 
                 1.267 
                 0.326 
               
               
                   
                 2 
                 1.27 
                 1.712 
                 0.869 
               
               
                   
                 3 
                 1.35 
                 1.936 
                 1.143 
               
               
                   
                 4 
                 1.43 
                 2.156 
                 1.412 
               
               
                   
                 5 
                 1.50 
                 2.345 
                 1.642 
               
               
                   
                 6 
                 1.56 
                 2.491 
                 1.821 
               
               
                   
                 7 
                 1.60 
                 2.595 
                 1.948 
               
               
                   
                 8 
                 1.63 
                 2.668 
                 2.036 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 6 
               
             
            
               
                   
               
               
                 Analysis of jet ejector for compression ratio of 1.2 
               
            
           
           
               
               
               
               
               
            
               
                 Area Ratio 
                 Stage 
                 
                   
                     
                       
                         
                           P 
                           outlet 
                         
                         
                           P 
                           inlet 
                         
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           P 
                           motive 
                         
                         
                           P 
                           inlet 
                         
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           m 
                           motive 
                         
                         
                           m 
                           inlet 
                         
                       
                     
                   
                 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 5 
                 1 
                 1.20 
                 1.848 
                 0.528 
               
               
                   
                 2 
                 1.85 
                 4.596 
                 2.239 
               
               
                   
                 3 
                 2.49 
                 7.306 
                 3.926 
               
               
                   
                 4 
                 2.94 
                 9.215 
                 5.115 
               
               
                 4 
                 1 
                 1.20 
                 1.693 
                 0.579 
               
               
                   
                 2 
                 1.69 
                 3.400 
                 2.006 
               
               
                   
                 3 
                 2.01 
                 4.491 
                 2.917 
               
               
                   
                 4 
                 2.24 
                 5.281 
                 3.577 
               
               
                   
                 5 
                 2.36 
                 5.718 
                 3.942 
               
               
                 3 
                 1 
                 1.20 
                 1.534 
                 0.652 
               
               
                   
                 2 
                 1.53 
                 2.422 
                 1.736 
               
               
                   
                 3 
                 1.58 
                 2.545 
                 1.886 
               
               
                   
                 4 
                 1.61 
                 2.630 
                 1.990 
               
               
                   
                 5 
                 1.63 
                 2.686 
                 2.059 
               
               
                   
                 6 
                 1.65 
                 2.724 
                 2.104 
               
               
                   
                 7 
                 1.66 
                 2.748 
                 2.134 
               
               
                   
               
            
           
         
       
     
     Table 7 illustrates the mass yield for various embodiments. The results indicate that the method works best when the per-stage compression ratio is small, which requires more stages. Further, the method works best when the area ratio is small, which also requires more stages. More stages allow the inlet pressures and motive pressures to be closely matched, thereby allowing streams with similar velocities to be blended. In some embodiments, extraordinarily high mass yields (kg water/kg steam) are possible. 
     
       
         
           
               
             
               
                 TABLE 7 
               
             
            
               
                   
               
               
                 Case studies for vapor-compression distillation. (T evaporator  = 100° C.) 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                 Overall 
                 Per-Stage 
                 Number 
                   
                 Per-Stage Mass 
                 Overall Mass 
               
               
                   
                 Compression 
                 Compression 
                 of 
                 Area 
                 Yield (kg 
                 Yield (kg 
               
               
                 ΔT (° C.) 
                 Ratio 
                 Ratio 
                 Stages 
                 Ratio 
                 water/kg steam) 
                 water/kg steam) 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 5 
                 1.2 
                 1.03 
                 6 
                 5 
                 119 
                 19.8 
               
               
                   
                   
                   
                   
                 4 
                 190 
                 31.6 
               
               
                   
                   
                   
                   
                 3 
                 425 
                 70.8 
               
               
                   
                   
                 1.05 
                 4 
                 5 
                 37.1 
                 9.3 
               
               
                   
                   
                   
                   
                 4 
                 49.3 
                 12.3 
               
               
                   
                   
                   
                   
                 3 
                 138 
                 34.5 
               
               
                   
                   
                 1.10 
                 2 
                 5 
                 11.1 
                 5.55 
               
               
                   
                   
                   
                   
                 4 
                 11.5 
                 5.75 
               
               
                   
                   
                   
                   
                 3 
                 18.2 
                 9.10 
               
               
                   
                   
                 1.20 
                 1 
                 5 
                 3.58 
                 3.58 
               
               
                   
                   
                   
                   
                 4 
                 3.72 
                 3.72 
               
               
                   
                   
                   
                   
                 3 
                 4.48 
                 4.48 
               
               
                   
               
            
           
         
       
     
     An advantage of utilizing a cascaded arrangement of jet ejectors, such as jet ejector system  50 , is that it blends gas streams of similar pressures; therefore, the velocity of each gas stream is similar. This leads to high efficiencies, even using traditional jet ejectors. Efficiency may be improved further by improving the design of the jet ejector, as is described in further detail below. 
       FIG. 21  illustrates a jet ejector system  60  according to another embodiment of the invention. In system  60 , a portion of a primary outlet stream  61  from primary jet ejector  62  is bled off and directed to one or more secondary jet ejectors  63 . This is in contrast to system  50  of  FIG. 8  in which a portion of primary inlet stream  54  was bled off. The rest of system  60  work in a similar manner to system  50 . 
       FIG. 22  illustrates a jet ejector system  70  according to another embodiment of the invention. In system  70 , a high-pressure steam, as indicated by reference numeral  71 , that powers the cascade of jet ejectors is produced by drawing a side stream  72  from one of the jet ejectors and compressing it with a suitable mechanical compressor  73 . In this case, the compressor is powered by a suitable steam turbine  74  via shaft  75  The waste steam  76  from turbine  74  may provide motive power to one or more of the jet ejectors, such as primary jet ejector  77 . 
       FIG. 23  illustrates a jet ejector system  80  according to another embodiment of the invention. System  80  is similar to system  70  except that in system  80  a compressor  81  is powered by a Brayton cycle engine  82  or other suitable engine. A suitable electric motor may also be utilized to power compressor  81 . 
       FIG. 24  illustrates a jet ejector system  90  according to another embodiment of the invention. In system  90 , multiple compression stages are employed by a plurality of primary jet ejectors  91   a ,  91   b ,  91   c  in series. Each primary jet ejector  91  is supported by its own independent cascade of secondary jet ejectors, which may operate according to one of the embodiments described above in  FIGS. 8 ,  21 ,  22  and/or  23 . 
       FIG. 25  illustrates a jet ejector system  100  according to another embodiment of the invention. In system  100 , multiple compression stages are employed by a plurality of primary jet ejectors  101   a ,  101   b ,  101   c  in series. However, system  100  differs from system  90  of  FIG. 24  in that some of the high-pressure secondary jet ejectors  102  from one cascade are shared with other primary jet ejectors  101  in the series. This reduces the number of secondary jet ejectors, thereby saving capital costs. 
       FIG. 26  illustrates a jet ejector system  110  according to another embodiment of the invention. In system  110 , multiple compression stages are employed by a plurality of primary jet ejectors  111   a ,  111   b ,  111   c  in series. In this embodiment, only the first primary jet ejector  111   a  in the series includes a cascade  112  of jet ejectors; however, each of the other primary jet ejectors  111   b ,  111   c  receive a stream from one of the secondary jet ejectors from cascade  112  (in this example, secondary jet ejector  112   a ). This again helps reduce the number of jet ejectors, thereby saving capital costs. 
       FIG. 27  illustrates a jet ejector system  120  according to another embodiment of the invention. In system  120 , multiple compression stages are employed by a plurality of primary jet ejectors  121   a ,  121   b ,  121   c  in series. In this embodiment, only the last primary jet ejector  121   c  in the series includes a cascade  122  of jet ejectors; however, each of the other primary jet ejectors  121   a ,  121   b  receive a stream from one of the secondary jet ejectors from cascade  122  (in this example, secondary jet ejector  122   a ). In addition, secondary jet ejector  122   a  is receiving a portion of outlet stream  124  from primary jet ejector  121   c.    
       FIG. 28  illustrates a jet ejector system  130  according to another embodiment of the invention. In system  130 , multiple compression stages are employed by a plurality of primary jet ejectors  131   a ,  131   b ,  131   c  in series. And an equal number of stages of secondary jet ejectors are included in each cascade. The secondary jet ejectors that comprise a particular stage are in series. In this embodiment, the stream for the cascades is drawn from a primary inlet stream  132  of the first primary jet ejector  131   a.    
       FIG. 29  illustrates a jet ejector system  140  according to another embodiment of the invention. System  140  is similar to system  130 , except the stream for the cascades is drawn from a primary outlet stream  142  of a primary jet ejector  141   c  in the series. 
       FIGS. 30 and 31  illustrate jet ejector systems  150 ,  160 , respectively, according to other embodiments of the invention. Systems  150 ,  160  are similar to systems  130 ,  140 , respectively; however, the flow arrangement in systems  150 ,  160  obtains a closer match of motive pressures to inlet pressures. Other suitable arrangements of both primary and secondary jet ejectors as well as arrangement of cascades are contemplated by the present invention. 
     Thus, an advantage of the jet ejector systems described above is that they blend gas streams of similar pressures; therefore, the velocity of each gas stream is similar. This leads to high efficiencies, even using traditional jet ejectors. The efficiency may be improved further by improving the design of the jet ejector, some embodiments of which are described below in conjunction with  FIGS. 32 through 41 . 
       FIGS. 32 through 36  illustrate various embodiments of an improved design of a jet ejector that allows large volumes of motive fluid to be added to propelled gas without obstructing the flow of the propelled gas. 
       FIG. 32  illustrates a jet ejector  200  according to one embodiment of the invention. Jet ejector  200  may have any suitable size and shape and may be formed from any suitable material. In the illustrated embodiment, jet ejector  200  includes a nozzle  202  having an upstream portion  203 , a downstream portion  204 , and a throat  205  disposed between upstream portion  203  and downstream portion  204 . A plurality of sets of apertures  206  are located in a wall of nozzle  202  in throat  205 , in which the plurality of sets are longitudinally spaced along the wall. Each set of apertures  206  has its apertures circumferentially located around the wall in any suitable pattern and spacing. Apertures  206  may be any suitably shaped apertures. For example, in the illustrated embodiment, apertures are in the form of circumferential slots. Jet ejector  200  also includes a device (not explicitly shown) that is operable to inject a motive fluid  207  through apertures  206  and into a first stream  208  flowing through nozzle  202 . Motive fluid  207  may be any suitable motive fluid, such as gas, vapor, liquid, and may be supplied through an annular space  211  in the wall of nozzle  202 . In such an embodiment, the pressure of motive gas  207  entering each set of apertures  206  is constant. In addition, motive fluid  207  enters first stream  208  at an angle with respect to the flow direction of first stream  208 . 
     In operation, first stream  208 , which may be any suitable propelled gas, such as low pressure vapor, enters upstream portion  203  of nozzle  202 . Throat  205  then initially accelerates first stream  208  when it enters throat  205 . The motive fluid  207  accelerates first stream  208  even further after entering throat  205  via apertures  206 . To minimize the velocity difference between motive fluid  207  and first stream  208 , it is advantageous to have the upstream most set of apertures  206   a  accelerate first stream  208  first, then the next set of apertures  206   b  accelerate first stream  208  second, and then the next set of apertures  206   c  accelerate first stream  208  last. The size of arrows  212  is meant to illustrate the accelerating of first stream  208  through nozzle  202 . 
       FIG. 33  illustrates a jet ejector  220  according to another embodiment of the invention. Jet ejector  220  is similar to jet ejector  200 ; however, in this embodiment, jet ejector  220  includes sets of apertures  226  in which each successive set of apertures  226  (as their location is farther downstream) is fed with a motive fluid  227  at increasingly higher pressures, which allows motive gas  227  exiting the later set of apertures  206  to have increasingly larger velocities. Thus, set of apertures  226   c  has a greater pressure than set of apertures  226   b , which has a greater pressure than set of apertures  226   c . Because a first stream  228  also has increasingly larger velocities, jet ejector  220  minimizes the velocity difference between the two streams, thereby improving efficiency. 
       FIGS. 34 through 36  illustrates a jet ejector  230  according to another embodiment of the invention. In this embodiment, a motive gas  237  enters a throat  235  of nozzle  232  through multiple point sources  236 , rather than through circumferential slots as in jet ejectors  200 ,  220 . Multiple point sources  236  may have any suitable configuration but are preferably small holes or slots.  FIG. 35A  is a cross-sectional view through the wall of throat  235  illustrating one of the point sources  236 .  FIG. 35B  illustrates a frontal view of the interior wall of throat  235 . As illustrated, point source  236  is coupled to a fan-shaped duct  239  that is defined by walls diverging in a downstream direction in order to introduce motive fluid  237  into throat  235  to entrain first stream  238  (i.e., propelled gas) flowing through nozzle  232 . In one embodiment, fan-shaped duct  239  is a NACA duct.  FIG. 36  is a two-dimensional view of the interior wall of nozzle  232  showing a staggered arrangement of multiple fan-shaped ducts  239 . However, the present invention contemplates any suitable arrangement of fan-shaped ducts  239 . 
     Thus, an advantage of the jet ejectors described in  FIGS. 32 through 36  is that they blend gas streams of similar velocities, but do not obstruct the flow of the propelled gas. These jet ejectors may be used in any suitable application, such as compressors, heat pumps, water-based air conditioning, vacuum pumps, and propulsive jets (both for watercraft and aircraft). 
       FIGS. 37 through 41  illustrate various embodiments of an improved design of a liquid jet ejector that allows motive liquid to be added to the propelled gas without obstructing the flow of the propelled gas. In some embodiments, the motive liquid may be added in stages, which increases efficiency. 
       FIG. 37  illustrates a liquid jet ejector  250  according to one embodiment of the invention. Liquid jet ejector  250  is similar to jet ejector  200  ( FIG. 32 ); however, the motive fluid in liquid jet ejector  250  is liquid. In operation, a first stream  258 , which may be any suitable propelled gas, such as low pressure vapor, enters an upstream portion  253  of nozzle  252 . A throat  255  then initially accelerates first stream  258  when it enters throat  255 . The motive fluid  257  accelerates first stream  258  even further after entering throat  255  via nozzles  256 . To minimize the velocity difference between motive fluid  257  and first stream  258 , it is advantageous to have the upstream most set of nozzles  256   a  accelerate first stream  258  first, then the next set of apertures  256   b  accelerate first stream  258  second, and then the next set of apertures  256   c  accelerate first stream  258  last. The size of arrows  251  is meant to illustrate the accelerating of first stream  258  through nozzle  252 . The motive liquid  257  may be supplied via an annular space  259  formed in the wall of nozzle  252 . Alternatively, each nozzle  256  could be supplied by its own pipe. In this embodiment, the pressure of the motive fluid  257  entering each nozzle  256  is constant. Similar to apertures  206  of jet ejector  200 , nozzles  256  may be circumferentially located around the wall in any suitable pattern and spacing. 
       FIG. 38  illustrates a liquid jet ejector  260  according to one embodiment of the invention. Liquid jet ejector  260  is similar to jet ejector  220  ( FIG. 33 ); however, the motive fluid in liquid jet ejector  260  is liquid and liquid jet ejector  260  includes nozzles  266  similar to nozzles  256  of liquid jet ejector  250  of  FIG. 37 . 
       FIG. 39  illustrates a liquid jet ejector  270  according to one embodiment of the invention. Liquid jet ejector  270  is similar to liquid jet ejector  250 , except that the motive liquid  277  enters a throat  275  of nozzle  272  through small tubes  276  that are tipped with nozzles. This embodiment facilitates the velocity of motive liquid  277  exiting the nozzles to be parallel to the velocity of a first stream  278  (i.e., the propelled fluid). Any suitable number and arrangement of tubes  276  is contemplated by the present invention. 
       FIG. 40  illustrates a liquid jet ejector  280  according to one embodiment of the invention. Liquid jet ejector  280  is similar to liquid jet ejector  270  except that the motive liquid  287  enters a throat  285  via tubes  286  at increasingly higher pressures as their location is farther downstream, which allows motive fluid  287  exiting the later set of tubes  286   c  to have increasingly larger velocities. Thus, motive fluid  287  exiting tubes  286   c  has a greater pressure than motive fluid  287  exiting tubes  286   b , which has a greater pressure than motive fluid  287  exiting tubes  286   a.    
       FIG. 41  illustrates a liquid jet ejector  290  according to one embodiment of the invention. Liquid jet ejector  290  includes a plurality of receptacles  291  coupled to the wall of nozzle  292  in order to collect the motive liquid  297 , thereby allowing the liquid to be readily collected and recycled. Receptacles  291  may be any suitable size and shape and are preferably located directly downstream from the nozzles of tubes  296 . The kinetic energy of the exiting liquid converts to pressure at the inlet to the pump, which reduces the required work input to the pump, thereby increasing efficiency. Although  FIG. 41  illustrates only one liquid stage along the axial length of nozzle  292 , multiple liquid stages may be employed. 
     Thus, advantages of the liquid jet ejectors of  FIGS. 37 through 41  are as follows: (1) the motive liquid may be added in stages, which increases system efficiency, and (2) the path of the propelled gas may be largely unobstructed by the nozzles that supply the motive liquid. These liquid jet ejectors may be used in any suitable applications, including compressors, heat pumps, water-based air conditioning, vacuum pumps, and vapor compression evaporators. Rather than propelling a gas, they could also be used to propel a liquid. If the outlet area of the jet ejector is less than its inlet area, then it may be used as a propulsive jet for watercraft. 
       FIGS. 42 through 51  illustrate various embodiments of an evaporator system that incorporates a liquid jet ejector according to various embodiments of the invention. 
       FIG. 42  illustrates an evaporator system  300  according to one embodiment of the invention. In the illustrated embodiment, system  300  includes a vessel  302  containing a feed  304  having a nonvolatile component (e.g., salt, sugar). The feed  304  may first be degassed by pulling a vacuum on it (equipment not explicitly shown). A liquid jet ejector  306  is coupled to vessel  302  and is operable to receive a vapor from vessel  302 . An example of liquid jet ejector  306  is one marketed by Hijet from Houston, Tex. A pump  308 , which may be driven by a suitable electric motor  310 , is operable to deliver a motive liquid  309  to liquid jet ejector  306 . A knock-out tank  312  is coupled to liquid jet ejector  306  and is operable to separate liquid and vapor received from liquid jet ejector  306  with the aid of a float  313  and a valve  317 . 
     A heat exchanger  314  is coupled inside vessel  302  and is operable to receive the vapor from knock-out tank  312 , at least some of the vapor condensing within heat exchanger  314 , thereby forming a distilled liquid such as distilled water if the feed is, for example, salt water. The heat of condensation provides the heat of evaporation to vessel  302  to evaporate feed  304 . Concentrated product  315  is removed from vessel  302  via any suitable method. Energy that is added to system  300  may be removed using a condenser  318 . Alternatively, if condenser  318  were eliminated, the energy added to system  300  will increase the temperature of concentrated product  315 . This is acceptable if the product is not temperature sensitive. To remove noncondensibles from system  300 , a small stream is pulled from vessel  302  and passed through a condenser  320 , and then sent to a vacuum pump (not explicitly illustrated). 
     In system  300 , motive liquid  309  may be a nonvolatile, immiscible, nontoxic, low-viscosity liquid (e.g., silicone oil) or it may be water. If it is water, the water will be in near equilibrium with the vapors discharged from jet ejector  306 . When this water is pumped, it may easily cavitate in pump  308 . In one embodiment, to overcome this problem, knock-out tank  312  is elevated relative to pump  308  so there is no cavitation. Ideally, if the system were perfect, the liquid water could be recycled indefinitely. However, in reality, energy is input into the circulating water (e.g., pump losses, pipe friction). This energy input causes the circulating water to evaporate, so make-up water should be added. In one embodiment, the make-up water is feed water, which has the following benefits: (1) the nonvolatile components increase the fluid density, which improves the efficiency of the jet ejector and (2) the waste thermal energy generated within the circulating fluid causes water to evaporate, which forms more product. 
       FIG. 43  illustrates an evaporator system  330  according to another embodiment of the invention. System  330  is similar to system  300 , except that a vessel  332  is operated at a higher temperature and pressure than vessel  302 . In system  330 , energy that is added to vessel  332  can cascade through a multi-effect evaporator  334 , which allows additional evaporation to occur. Only three stages are shown in  FIG. 43 , but more or less are contemplated by the present invention. Alternatively, a multi-stage flash evaporator could be employed rather than a multi-effect evaporator. In system  330 , noncondensibles may be removed in a manner similar to system  300 . A plurality of sensible heat exchangers  336  may be coupled to vessel  332  and the multi-effect evaporators for heating the feed or for other suitable functions. 
       FIG. 44  illustrates an evaporator system  340  according to another embodiment of the invention. System  340  is similar to system  300 , except that a pump  342  is driven by a Brayton cycle engine  344  or other suitable engines, such as a Diesel engine or Otto cycle engine. In one embodiment of system  340 , hot engine exhaust  346  is thermally contacted with the feed in the vessel  348 , which produces more product. 
       FIG. 45  illustrates an evaporator system  350  according to another embodiment of the invention. System  350  is a combination of system  340  ( FIG. 44 ), but includes a multi-effect evaporator  352 , which allows additional evaporation to occur. Only three stages are shown in  FIG. 45 , but more or fewer are contemplated by the present invention. Alternatively, a multi-stage flash evaporator could be employed rather than a multi-effect evaporator. 
       FIG. 46  illustrates an evaporator system  360  according to another embodiment of the invention. System  360  is similar to system  300  ( FIG. 42 ), except that a pump  362  is driven by a steam turbine  364 . Steam turbine may be a portion of a Rankine cycle. In this embodiment, the low-pressure steam  365  is sent to a steam jet ejector  366 , such as those described above. Although  FIG. 46  illustrates a single steam jet ejector  365 , system  360  may have multiple stages or it may have a cascade steam jet ejector system, such as those described above. Steam jet ejector  366  is in series with a liquid jet ejector  368 . In some embodiments, energy that is added to vessel  361  can cascade through a multi-effect evaporator, which allows additional evaporation to occur, similar to system  330  above. 
       FIG. 47  illustrates an evaporator system  370  according to another embodiment of the invention. System  370  is similar to system  360  ( FIG. 46 ), except that the steam jet ejector  372  is in parallel with the liquid jet ejector  374 . As such, steam jet ejector  372  also receives vapor from vessel  376  and compresses it before adding it to the vapor exiting a knock-out tank  378 , which then is sent to a heat exchanger  379  in vessel  376 . In some embodiments, energy that is added to vessel  376  can cascade through a multi-effect evaporator, which allows additional evaporation to occur, similar to system  330  above. 
       FIG. 48  illustrates an evaporator system  380  according to another embodiment of the invention. System  380  is similar to systems  360  and  370 , except that the waste low-pressure steam  382  from a turbine  384  is sent directly to the primary heat exchanger  386 . In some embodiments, energy that is added to vessel  381  can cascade through a multi-effect evaporator, which allows additional evaporation to occur, similar to system  330  above. 
       FIG. 49  illustrates an analysis of system  330  using the pump drive mechanism described in system  370 . This analysis illustrates that 1 kg of high-pressure steam fed to the turbine produces 78.2 kg of distilled water. The assumptions follow:
         Temperature difference in main heat exchanger=5° C.   Compression ratio=1.2   Number of multi-effect evaporators=8 (three shown in  FIG. 49 )   Steam jet ejector per-stage compression ratio=1.03   Steam jet ejector number of stages=6   Steam jet ejector number of cascade levels=3   Steam jet ejector area ratio=5   Liquid jet ejector efficiency=0.75   Pump efficiency=0.85 (appropriate for large industrial pumps)   Steam turbine efficiency=0.8 (relative to isentropic turbine)       
     The mass ratios shown for the cascade steam jet ejector are based upon the analysis presented above. 
     The mass flow through the liquid jet ejector is calculated as follows: 
               Steam   ⁢           ⁢   Through   ⁢           ⁢   Liquid   ⁢           ⁢   Jet   ⁢           ⁢   Ejector     =         η   pump     ⁢     η   ejector     ⁢     W   shaft             H   ^     cond     -       H   ^     evap               
where Ĥ cond  is the specific enthalpy of the condensing steam (1.2 atm), Ĥ evap  is the specific enthalpy of the evaporating steam (1.0 atm), η pump  is the pump efficiency, η ejector  is the liquid jet ejector efficiency, and W shaft  is the shaft work. The shaft work is calculated as follows:
   W   shaft =η turbine ( Ĥ   high   −Ĥ   low ) m   steam    
where m steam  is the mass of high-pressure steam, η turbine  is the turbine efficiency (compared to isentropic), Ĥ high  is the specific enthalpy of the high-pressure steam from the boiler, and Ĥ low  is the specific enthalpy of the low-pressure steam exiting the turbine. (Note: The conditions at the exit of the turbine correspond to an isentropic expansion.)
 
       FIG. 50  illustrates an analysis similar to the one shown in  FIG. 49 . All the assumption are identical, except that the steam jet ejectors use an area ratio of 3, and four cascade levels are employed. In this scenario, 1 kg of high-pressure steam produces 93.4 kg of distilled water. 
       FIG. 51  illustrates an analysis similar to the one shown in  FIGS. 49 and 50 , except that no steam jet ejector is employed. The waste steam from the turbine is directly sent to the condensing side of the primary heat exchanger. In this case, 1 kg of high-pressure steam produces 75.5 kg of distilled water, which is nearly identical to the case shown in  FIG. 49 , but not quite as good as the case presented in  FIG. 50 . This illustrates that there may be a benefit of using the jet ejectors only if they are very efficient (i.e., low area ratio with many stages). 
     The following table compares various options: 
                                         Energy (kJ/kg           Option   distilled water)   Effects*                                            Single-effect evaporator (100° C.)   2,256.58   1       FIG. 51   39.11   57.7       FIG. 49   37.80   59.7       FIG. 50   31.96   70.6       FIG. 44 (engine efficiency = 30%)   40.99   55.1       FIG. 44 (engine efficiency = 40%)   30.75   73.4       FIG. 44 (engine efficiency = 50%)   24.60   91.7       FIG. 44 (engine efficiency = 60%)   20.50   110.1       FIG. 45 (engine efficiency = 30%, 8 stages)   37.29   60.5       FIG. 45 (engine efficiency = 40%, 8 stages)   28.44   79.4       FIG. 45 (engine efficiency = 50%, 8 stages)   23.01   98.1       FIG. 45 (engine efficiency = 60%, 8 stages)   19.32   116.8               *Effect = Energy of single-effect evapor/Energy of the option            
This table illustrates that a simple liquid jet ejector combined with a high-efficiency engine ( FIGS. 44 and 45 ) may be the most attractive option. However, high-efficiency engines often require premium fuels, which can be expensive. The steam-turbine systems ( FIG. 46 through 48 ) may use low-cost fuels (e.g., coal), and may be the most economical system in some situations.
 
     An advantage is it uses a high-efficiency liquid jet ejector in a cost-effective dewatering system. When combined with steam jet ejectors and multi-effect evaporators, any energy inefficiencies of the liquid jet system (liquid jet itself, pump, turbine) produce heat that usefully distills liquid. This liquid jet ejector may be used in water-based air conditioning. 
       FIGS. 52 through 55  illustrate various embodiments of an improved design of a vapor-compression evaporator system. Some important features of the improved designs are (1) compressor equipment may be smaller due to lower vapor throughput, and (2) the systems may be tuned to the operating regions where the compressors are most efficient. 
       FIG. 52  illustrates a vapor-compression evaporator system  400  according to one embodiment of the invention. In the illustrated embodiment, system  400  includes a plurality of vessels  402   a - c  in series to form a multi-effect evaporator system. Each vessel contains a feed  404  having a nonvolatile component (e.g., salt, sugar). The feed  404  may first be degassed by pulling a vacuum on it (equipment not explicitly shown). A liquid jet ejector  406  is coupled to the last vessel in the series ( 402   c ) and is operable to receive a vapor therefrom. An example of liquid jet ejector  406  is one marketed by Hijet from Houston, Tex. A pump  408  is operable to deliver a motive liquid  410  to the liquid jet ejector  406  for compressing the vapors pulled from the coldest evaporator stage, vessel  402   c . A knock-out tank  412  is coupled to liquid jet ejector  406  and is operable to separate liquid and vapor received from liquid jet ejector  406 . A plurality of heat exchangers  414   a - c  are coupled inside respective vessels  402   a - c . Heat exchanger  414   a  is operable to receive the vapor from knock-out tank  412 , at least some of the vapor condensing therein, whereby the heat of condensation provides the heat of evaporation to vessel  402   a . At least some of the vapor inside vessel  402   a  is delivered to heat exchanger  414   b , whereby the condensing, evaporating, and delivering steps continue until the last vessel in the series is reached (in this embodiment, vessel  402   c ). 
     In  FIG. 52 , only three stages are shown (i.e., three vessels  402 ); however, more or fewer could be used. Concentrated product  416  may be removed from each of the vessels  402 . Energy that is added to system  400  may be removed using a suitable condenser  418 . Alternatively, if condenser  418  were eliminated, the energy added to system  400  will increase the temperature of concentrated product  416 . This is acceptable if the product is not temperature sensitive. To remove noncondensibles from system  400 , a small stream is pulled from each vessel  402  and passed through a suitable condenser  419  and is sent to a vacuum pump (not shown). 
     In system  400 , motive liquid  410  may be a nonvolatile, immiscible, nontoxic, low-viscosity liquid (e.g., silicone oil) or it may be water. If it is water, the water will be in near equilibrium with the vapors discharged from jet ejector  406 . When this water is pumped, it may easily cavitate in pump  408 . In one embodiment, to overcome this problem, knock-out tank  412  is elevated relative to pump  408  so there is no cavitation. Ideally, if the system were perfect, the liquid water could be recycled indefinitely. However, in reality, energy is input into the circulating water (e.g., pump losses, pipe friction). This energy input causes the circulating water to evaporate, so make-up water should be added. In one embodiment, the make-up water is feed water, which has the following benefits: (1) the nonvolatile components increase the fluid density, which improves the efficiency of the jet ejector and (2) the waste thermal energy generated within the circulating fluid causes water to evaporate, which forms more product. 
       FIG. 53  illustrates a vapor-compression evaporator system  430  according to another embodiment of the invention. System  430  is similar to system  400  above, except that the vapor-compression evaporator vessels  432  are operated at a higher temperature and pressure than in system  400 . In system  430 , energy that is added to the vapor-compression evaporator vessels  432  may cascade through a multi-effect evaporator  434  (three stages shown), which allows additional evaporation to occur. Alternatively, a multi-stage flash evaporator may be employed rather than a multi-effect evaporator. In system  430 , noncondensibles may be removed in a manner similar to system  400 . 
       FIG. 54  illustrates a vapor-compression evaporator system  440  according to another embodiment of the invention. System  440  is similar to system  400  above, except that the vapors are compressed using a mechanical compressor  442  driven by a suitable electric motor  443 . To reduce the superheat in compressor  445 , and thereby increase its efficiency, atomized liquid water  444  is added to compressor  445 . Preferably, the liquid water is feed water; as water evaporates from the feed water as it removes the heat of compression, it creates more distilled water and a concentrated product. Alternatively, if the compressor materials do not tolerate the nonvolatile components (e.g., salt) in the circulating cooling liquid  444 , then the cooling liquid  445  could be distilled water. 
       FIG. 55  illustrates a vapor-compression evaporator system  450  according to another embodiment of the invention. System  450  is similar to systems  440  except that energy that is added to vapor-compression evaporators  452  may cascade through a multi-effect evaporator  454 , which allows additional evaporation to occur, similar to system  430  above. 
     Thus, advantages of the vapor-compression evaporator systems of  FIGS. 52 through 55  are 1) because the vapor flow through the compressors is smaller, the compressors may be smaller than the compressors described in the evaporator systems above; and 2) the compression ratio may be adjusted so the compressor operates in its most efficient range. This is particularly important for a liquid jet ejector, which has lower efficiency at lower compression ratios. 
     Referring now to  FIGS. 56 through 61 , in general, a heat exchanger is provided that includes a shell and a sheet assembly disposed within the shell. The sheet assembly may include a number of substantially parallel rectangular sheets configured such that they define first passageways extending generally in a first direction and second passageways extending generally in a second direction perpendicular to the first direction. The sheet assembly may be configured such that communicating a first fluid through the first passageways and communicating a second fluid through the second passageways causes heat transfer between the first and second fluids. For example, the first fluid may comprise high pressure steam and the second fluid may comprise a liquid solution (such as saltwater, seawater, concentrated fermentation broth, or concentrated brine, for example) such that communicating the high-pressure steam and the liquid solution through the first and second passageways, respectively, causes at least a portion of the high-pressure steam to condense and at least a portion of liquid solution to boil off. 
       FIG. 56  illustrates a cross-section of an example heat exchanger assembly  500  including a shell  510  and a sheet assembly  512  disposed within shell  510  in accordance with an embodiment of the invention. Shell  510  may comprise any suitable shape and may be formed from any suitable material for housing pressurized gasses and/or liquids. For example, in the embodiment shown in  FIG. 56 , shell  510  comprises a substantially cylindrical portion  516  and a pair of hemispherical caps (not expressly shown) coupled to each end of cylindrical portion  516 . The cross-section shown in  FIG. 56  is taken at a particular point along the length of cylindrical portion  516 , which length extends in a direction perpendicular to the page. 
     In general, heat exchanger assembly  500  is configured to allow at least two fluids to be communicated into shell  510 , through passageways defined by sheet assembly  512  (such passageways are illustrated and discussed below with reference to  FIG. 57A ) such that heat is transferred between the at least two fluids, and out of shell  510 . Shell  510  may include any number of inlets and outlets for communicating fluids into and out of shell  510 . In the embodiment shown in  FIG. 56 , shell  510  includes a first inlet  520 , a first outlet  522 , a second inlet  524 , a second outlet  526  and a third outlet  528 . First inlet  520  and first outlet  522  are configured to communicate a first fluid  530  into and out of shell  510 . Second inlet  524 , second outlet  526 , and third outlet  528  are configured to communicate a second fluid  532  into and out of shell  510 . 
     Due to the transfer of heat between first fluid  530  and second fluid  532 , at least a portion of first fluid  530  and/or second fluid  532  may change state within shell  510  and thus exit shell  510  in a different state than such fluids  530  and/or  532  entered shell  510 . For example, in a particular embodiment, relatively high-pressure steam  534  enters shell  510  through first inlet  520 , enters one or more first passageways within sheet assembly  512 , becomes cooled by a liquid  540  flowing through one or more second passageways adjacent to the one or more first passageways within sheet assembly  512 , which causes at least a portion of the steam  534  to condense to form steam condensate  536 . The steam condensate  536  flows toward and through first outlet  522 . Concurrently, liquid  540  (saltwater, seawater, concentrated fermentation broth, or concentrated brine, for example) enters shell  510  through second inlet  524 , enters one or more second passageways within sheet assembly  512 , becomes heated by steam  534  flowing through the one or more first passageways adjacent to the one or more second passageways within sheet assembly  512 , which causes at least a portion of the liquid  540  to boil to form relatively low pressure steam  542 . The low pressure steam  542  escapes from shell  510  through second outlet  526 , while the unboiled remainder of liquid  540  flows toward and through third outlet  528 . 
     In some embodiments, heat exchanger assembly  500  includes one or more pumps  550  operable to pump liquid  540  that has exited shell  510  through third outlet  528  back into shell  510  through second inlet  524 , as indicated by arrows  552 . Pump  550  may comprise any suitable device or devices for pumping a fluid through one or more fluid passageways. As shown in  FIG. 56 , liquid  540  may be supplied to the circuit through a feed input  554 . In embodiments in which liquid  540  comprises a solution (such as a seawater solution, for example), a relatively dilute form of such solution (as compared with the solution exiting shell  510  through third output  528 ) may be supplied through feed input  554 . In addition, a portion of liquid  540  being pumped toward second inlet  524  of shell  510  may be redirected away from shell  510 , as indicated by arrow  556 . In embodiments in which liquid  540  comprises a solution (such as a seawater solution, for example), such redirected liquid  540  may comprise a relatively concentrated form of such solution (as compared with the diluted solution supplied through feed input  554 ). Although inlets  520 ,  524  and outlets  522 ,  526  and  528  are described herein as single inlets and outlets, each inlet  520 ,  524  and each outlet  522 ,  526  and  528  may actually include any suitable number of inlets or outlets. 
     Heat exchanger assembly  500  may also include a plurality of mounting devices  560  coupled to shell  510  and operable to mount sheet assembly  512  within shell  510 . Each mounting device  560  may be associated with a particular corner of sheet assembly  512 . Each mounting device  560  may be coupled to shell  510  in any suitable manner, such as by welding or using fasteners, for example. In the embodiment shown in  FIG. 56 , each mounting device  560  comprises a Y-shaped bracket into which a corner of sheet assembly  512  is mounted. Each mounting device  560  may extend along the length of shell  510 , or at least along the length of a portion of shell  510  in which fluids  530  and  532  are communicated, in order to create two volumes within shell  510  that are separated from each other. A first volume  564 , which includes regions generally to the left and right of sheet assembly  510 , as well as one or more first passageways defined by sheet assembly  510  (such first passageways are illustrated and discussed below with reference to  FIG. 57A ), is used to communicate first fluid  530  through heat exchanger assembly  500 . A second volume  566 , which includes regions generally above and below sheet assembly  510 , as well as one or more second passageways defined by sheet assembly  510  (such second passageways are illustrated and discussed below with reference to  FIG. 57A ), is used to communicate second fluid  532  through heat exchanger assembly  500 . 
     Since first volume  564  is separated from second volume  566  by the configuration of sheet assembly  512  and mounting devices  560 , first fluid  530  is kept separate from second fluid  532  within shell  510 . In addition, one or more gaskets  562  may be disposed between each Y-shaped bracket  560  and its corresponding corner of sheet assembly  512  to provide a seal between first volume  564  and second volume  566  at each corner of sheet assembly  512 . Gaskets  562  may comprise any suitable type of seal or gasket, may have any suitable shape (such as having a square, rectangular or round cross-section, for example) and may be formed from any material suitable for forming a seal or gasket. 
     Heat exchanger assembly  500  may also include one or more devices for sliding, rolling, or otherwise positioning sheet assembly  512  within shell  510 . Such devices may be particularly useful in embodiments in which sheet assembly  512  is relatively heavy or massive, such as where sheet assembly  512  is formed from metal. In the embodiment shown in  FIG. 56 , heat exchanger assembly  500  includes wheels  568  coupled to sheet assembly  512  that may be used to roll sheet assembly  512  into shell. Wheels  568  may be aligned with, and roll on, wheel tracks  570  coupled to shell  510  in any suitable manner. 
       FIG. 57A  illustrates a three-dimensional view of sheet assembly  512  of heat exchanger assembly  500  in accordance with one embodiment of the invention. Sheet assembly  512  includes a plurality of sheets  580  configured and coupled to each other to form a plurality of first passageways  582  extending in a first direction  584  alternating with a plurality of second passageways  586  extending in a second direction  588  perpendicular to the first direction  584 . Each passageway  582  and  586  is substantially defined by an adjacent pair of sheets  580 . In this embodiment, sheets  580  are aligned substantially parallel and, when positioned within shell  510 , the major surface of each sheet  580  extends in a plane substantially perpendicular to the direction of the length of cylindrical portion  516  of shell  510 . 
     As discussed above with reference to  FIG. 56 , first passageways  582  form a portion of first volume  564  and are thus used to communicate first fluid  530 , while second passageways  586  form a portion of second volume  566  and are thus used to communicate second fluid  532 . As fluids  530  and  532  pass through alternating first passageways  582  and second passageways  586 , respectively, heat is transferred from the higher temperature fluid  530  or  532  to sheets  580 , and then from sheets  580  to the lower temperature fluid  530  or  532 . In this manner, heat is transferred between fluids  530  and  532  via sheets  580 . 
     In the embodiments shown in  FIG. 57A , each sheet  580  has a substantially square shape having four edges  590 . In other embodiments, sheets  580  may comprise any suitable shape and configuration. For example, sheets  580  may have a generally rectangular, hexagonal, circular, or other geometric shape. In order to define alternating passageways  582  and  586 , each sheet  580  is coupled to an adjacent sheet  580  on one side at two of the four edges  590  and to an adjacent sheet  580  on the other side at the other two of the four edges  590 . For example, sheet  580   a , which is positioned between adjacent sheet  580   b  and adjacent sheet  580   c , is coupled to adjacent sheet  580   b  at opposite edges  590   a  and  590   b  of sheet  580   a , and is coupled to adjacent sheet  580   c  at opposite edges  590   c  and  590   d  of sheet  580   a.    
     Sheets  580  may be coupled to each other at edges  590  in any suitable manner, as discussed in greater detail below with reference to  FIG. 59 . In the embodiment shown in  FIG. 57A , each sheet  580  is folded near each edge  590  to form flanges  592  at each edge  590  which are then coupled to corresponding flanges  592  of adjacent sheets  580 .  FIG. 57B  is a blown-up view of a corner area of sheet assembly  512 , illustrating flanges  592  of adjacent sheets  580  being coupled to each other in accordance with an embodiment of the invention. As shown in  FIG. 57B , sheet  580   a  is folded twice at approximately 90 degree angles to form a flange  592   a  including a first flange portion  594   a  and a second flange portion  596   a . First flange portion  594   a  forms an approximately 90 degree angle with the major portion of sheet  580   a , indicated as  598   a , and second flange portion  596   a  forms an approximately 90 degree angle with first flange portion  594   a . Thus, the surface of second flange portion  596   a  is approximately parallel with the surface of major portion  598   a  of sheet  580   a . A triangular flap  600   a  is folded from first flange portion  594   a  and may be affixed to second flange portion  596   a  (such as by welding, for example). Similarly, sheet  580   b  is folded twice at approximately 90 degree angles to form a flange  592   b  including a first flange portion  594   b  and a second flange portion  596   b . First flange portion  594   b  forms an approximately 90 degree angle with the major portion of sheet  580   b , indicated as  598   b , and second flange portion  596   b  forms an approximately 90 degree angle with first flange portion  594   b . Thus, the surface of second flange portion  596   b  is approximately parallel with the surface of major portion  598   b  of sheet  580   b . A triangular flap  600   b  is folded from first flange portion  594   b  and may be affixed to second flange portion  596   b  (such as by welding, for example). 
       FIG. 57C  illustrates a side view of the corner of sheet assembly  512  illustrated in  FIG. 57B . 
       FIGS. 58A-58B  illustrate an example method of forming a particular sheet  580   a , including flanges  592 , of sheet assembly  512  in accordance with one embodiment of the invention.  FIG. 58A  illustrates a generally flat sheet  610  of material, such as sheet metal or one or more polymers, for example. The sheet  610  has a generally square shape including one or more notches removed from each corner. Cuts  612  are formed in each corner at approximately 45 degrees relative to the edges  590  of sheet  610  in order to form triangular flaps  600  in the resulting sheet  580   a . From sheet  610  formed as shown in  FIG. 58A , flanges  592   a  are formed by folding sheet  610  at each fold line  614  (indicated in  FIG. 58A  by dashed lines) at approximately 90 degree angles. For example, flange  592   a  may be formed by (a) folding the edge portion  590   a  of sheet  610  approximately 90 degree inward (out of the page and toward the center of sheet  610 ) at fold line  614   a  to form first flange portion  594   a , and (b) folding the remaining edge portion  590   a  of sheet  610  approximately 90 degree outward (to the left and down toward the page) at fold line  614   b  to form second flange portion  596   a . Thus, the resulting flange  592   a  extends generally out of the page. The flange  592  at opposing edge  590   b  may be formed in the same manner as flange  592   a . The flanges  592  at edges  590   c  and  590   d  may be formed in a similar, but opposite, manner such that the flanges  592  at edges  590   c  and  590   d  extend generally into the page. Triangular flaps  600  may then be folded down and connected (such as by welding) to second flange portions  596  to reinforce each flange  592 . For example, triangular flap  600   a  may be folded down and welded to second flange portion  596   a  to reinforce flange  592   a.    
       FIG. 58B  illustrates the resulting sheet  580   a , including flanges  592  at each edge  590   a - 590   d  of sheet  580   a . Flanges  592  at edges  590   a  and  590   b  of sheet  580   a  extend in a first direction (out of the page), such that they may be coupled to flanges  592  of adjacent sheet  580   b , while flanges  592  at edges  590   c  and  590   d  of sheet  580   a  extend in the opposite direction (into the page), such that they may be coupled to flanges  592  of adjacent sheet  580   c.    
     Sheets  580  may also include one or more protrusions for preventing passageways  582  or  586  between adjacent sheets  580  from being cut off, such as due to the distortion of sheets  580  during operation of heat exchanger apparatus  500  (such as due to the presence of high-pressure fluids, for example) and/or to provide additional strength or stiffening to sheets  580 . In the embodiment shown in  FIGS. 58A-58B , sheet  580   a  includes a plurality of stiffening ribs, or corrugations,  620  which strengthen sheet  580   a , as well as ensure that the second passageway  586  between sheets  580   a  and  580   b  remains intact during the operation of heat exchanger apparatus  500 . Sheet  580   b  may also include a plurality of stiffening ribs (not expressly shown) operable to engage stiffening ribs  620  of sheet  580   a . In a particular embodiment, such stiffening ribs of sheet  580   b  are oriented in a direction perpendicular to that of stiffening ribs  620  of sheet  580   a.    
       FIG. 58C  illustrates a cross-sectional view of sheet  580   a  taken along Cut A shown in  FIG. 58B .  FIG. 58D  illustrates a cross-sectional view of sheet  580   a  taken along Cut B shown in  FIG. 58B . Taken together with  FIG. 58B ,  FIGS. 58C and 58D  illustrate that, as discussed above, flanges  592  at edges  590   a  and  590   b  of sheet  580   a  extend in a first direction (out of the page), while flanges  592  at edges  590   c  and  590   d  of sheet  580   a  extend in the opposite direction (into the page). 
     As discussed above, in forming sheet assembly  512 , second flange portion  596   a  of flange  592   a  of sheet  580   a  may be coupled to second flange portion  596   b  of flange  592   b  of sheet  580   b  in any suitable manner.  FIG. 59  illustrates various example manners in which second flange portion  596   a  may be coupled to second flange portion  596   b . As shown in  FIG. 59 , second flange portion  596   a  may be coupled to second flange portion  596   b  by a weld  630 ; a brazed connection  632 ; a crimp clamp  634 ; one or more fasteners  636 , such as a rivet or screw for example; or a crimp connection  638 , for example. For some types of couplings, a gasket  640  may be inserted in order to assure a seal between second flange portion  596   a  and second flange portion  596   b  (and thus a seal between sheets  580   a  and  580   b  at the relevant edge of  580   a  and  580   b ). In embodiments in which one or more fasteners  636  are used, stiffeners  642  may be provided to strengthen or reinforce the connection. 
     As discussed above, sheets  580  may be formed from any suitable material, such as sheet metal or one or more polymers, for example. Table 1 compares various polymers that could be used for the sheet-polymer assemblies. The underlined value in Table 1 is used to calculate the overall heat transfer coefficient, U, which is determined as follows: 
             U   =       [       1     h   i       +     x   k     +     1     h   o         ]       -   1             
where
         h i =inside heat transfer coefficient =3000 Btu/(h·ft 2 ·° F.)(for boiling water)   h o =outside heat transfer coefficient =15,000 Btu/(h·ft 2 ·° F.)(dropwise condensation for polymer) =2,000 Btu/(h·ft 2 ·° F.)(filmwise condensation for metal)   k=thermal conductivity of material (Btu/(h·ft·° F.)   x=material thickness =0.01 in=500 mil=0.00083 ft       
     The overall heat transfer coefficient U is reported in the fifth column of Table 1. The cost of each polymer per square foot, C, is shown in the fourth column of Table 1. The ratio U/C is reported in the sixth column of Table 1, which is the overall heat transfer coefficient on a dollar basis, rather than an area basis. The ratio U/C may be referred to as the “figure of merit.” The polymers are listed in order, with the highest U/C appearing at the top and the lowest U/C appearing at the bottom. In the last column of Table 1, the U/C for each polymer is compared to that of stainless steel (SS) and titanium (Ti). Stainless steel resists corrosion for many solutions (e.g., sugar, calcium acetate), but titanium may be used for particularly corrosive solutions, such as seawater, for example. 
     The polymer with the highest U/C is HDPE (high-density polyethylene). Polypropylene is also very good, and it may perform well at slightly higher temperatures. Other polymers (polystyrene, PVC) may also be considered, but their U/C performance may not be quite as good as polyethylene or polypropylene. As a general rule, the thermal conductivity of the polymers is much lower than metals, but their U/C performance may be superior because of their low material cost relative to metals. In addition, polymers are typically less expensive to form into the final shape of sheets  580  and sheet assembly  512  than metals. Further, polymer structures may be easier to seal, providing an additional benefit over metals. 
     HDPE has a thermal conductivity comparable to stainless steel if the polymer molecules are aligned in the direction of heat flow (see third column, first row, Table 1).  FIG. 60A  illustrates an example method of aligning the molecules in a sample  650  of HDPE by drawing the polymer melt through a die  652 . The shear orients the HDPE molecules in the flow direction, thus forming a molecularly-oriented HDPE block  654 . By cutting polymer sheets  656  from such molecularly-oriented HDPE
         block  554  in which the molecules are aligned perpendicular to the sheet surface  658 , the heat transfer performance of the HDPE sheet may be increased or maximized.       

     In some situations, the desired size of sheets  580  for a sheet assembly  512  may be larger than the molecularly-oriented polymer (e.g., HDPE) block  654  that may be produced due to available manufacturing equipment, equipment limitations, cost or some other reason.  FIG. 60B  illustrates a method of forming a sheet  580  (e.g., a relatively large sheet  580 ) by joining a number of polymer sheets  656 . Such polymer sheets  656  may be joined in any suitable manner to form sheet  580 , such as welding or heating to a relatively low temperature, for example. 
     In addition to providing increased heat transfer per cost as compared with metal, polymers may be more corrosion-resistant, more pliable, and more easily formed into sheets  580  and sheet assembly  512 . 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 Comparison of polymers. 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 Material 
                 Max. Working Temp. ° F. 
                 k Thermal Conductivity Btu/(h · ft · ° F.) 
                 C $/ft 2  (10 mil thickness) 
                 U b  Btu/ (h · ft 2  · ° F.) 
                 U/C Btu/ (h · $ · ° F.) 
                 
                   
                     
                       
                         
                           
                             ( 
                             
                               U 
                               / 
                               C 
                             
                             ) 
                           
                           plastic 
                         
                         
                           
                             ( 
                             
                               U 
                               / 
                               C 
                             
                             ) 
                           
                           metal 
                         
                       
                     
                   
                 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 HDPE (high- 
                 160 c   
                 0.29 i   
                 0.12 a   
                 220 
                 2,000 
                 2.64 (SS) 
               
               
                 density 
                 175-250 e   
                 0.25 @ 70° F. k   
                 0.11 d   
                   
                   
                 5.93 (Ti) 
               
               
                 polyethylene) 
                   
                 0.20 @ 212° F. k   
               
               
                   
                   
                 4.9-8.1 m   
               
               
                 LDPE (low- 
                 185-214 d   
                 0.19i 
                 0.10 d   
                 158 
                 1,500 
                 1.98 (SS) 
               
               
                 density 
                 180-212 e   
                 0.17-0.24 j   
                   
                   
                   
                 4.45 (Ti) 
               
               
                 polyethylene) 
                   
                 0.20 @ 70° F. k   
               
               
                   
                   
                 0.14 @ 212° F. k   
               
               
                 Polypropylene 
                 225 d   
                 0.12 i   
                 0.09 a   
                 126 
                 1,400 
                 1.84 (SS) 
               
               
                   
                 225-300 e   
                 0.083-0.12 j   
                 0.10 d   
                   
                   
                 4.15 (Ti) 
               
               
                   
                   
                 0.12 @ 70° F. k   
               
               
                   
                   
                 0.11 @ 212° F. k   
               
               
                 HIPS (high- 
                 190 c   
                 0.083 l   
                 0.09 a   
                 104 
                 1,156 
                 1.52 (SS) 
               
               
                 impact 
                 140-175 e   
                   
                   
                   
                   
                 3.43 (Ti) 
               
               
                 polystyrene) 
               
               
                 Ultra-high MW 
                 180 d   
                 0.24 r   
                 0.50 a   
                 260 
                 1,037 
                 1.37 (SS) 
               
               
                 polyethylene 
                   
                   
                 0.25 d   
                   
                   
                 3.08 (Ti) 
               
               
                 PVC (polyvinyl 
                 140 d   
                 0.11 j   
                 0.14 d   
                 126 
                 900 
                 1.19 (SS) 
               
               
                 chloride) 
                 150-175 e   
                 0.10 k   
                   
                   
                   
                 2.67 (Ti) 
               
               
                 Acrylic 
                 209 c   
                 0.12 j   
                 0.28 a   
                 137 
                 489 
                 0.64 (SS) 
               
               
                   
                 180 d   
                   
                 0.40 d   
                   
                   
                 1.45 (Ti) 
               
               
                   
                 175-225 e   
               
               
                 ABS 
                 180 c   
                 0.074-0.11 p   
                 0.62 a   
                 126 
                 242 
                 0.32 (SS) 
               
               
                   
                 185 d   
                   
                 0.52 d   
                   
                   
                 0.72 (Ti) 
               
               
                   
                 160-200 e   
               
               
                 Acetal 
                 280 c   
                 0.25 @ 70° F. k   
                 1.03 d   
                 230 
                 223 
                 0.29 (SS) 
               
               
                   
                 195 e   
                 0.21 @ 2l2° F. k   
                   
                   
                   
                 0.66 (Ti) 
               
               
                 PET 
                 230 d   
                 0.08 w   
                 0.54 d   
                 93 
                 172 
                 0.23 (SS) 
               
               
                 (polyethylene 
                 175 e   
                   
                   
                   
                   
                 0.51 (Ti) 
               
               
                 terephthalate) 
               
               
                 PBT 
                 240 f   
                 0.17 t   
                 1.21 a   
                 189 
                 156 
                 0.21 (SS) 
               
               
                 (polybutylene 
                   
                   
                   
                   
                   
                 0.46 (Ti) 
               
               
                 teraphalate 
               
               
                 polyester, Hydex) 
               
               
                 CPVC 
                 215 d   
                 0.08 q   
                 1.92 a   
                 93 
                 125 
                 0.17 (SS) 
               
               
                   
                 230 e   
                   
                 0.74 d   
                   
                   
                 0.37 (Ti) 
               
               
                 Noryl 
                 175-220 e   
                 0.11 s   
                 1.07 a   
                 126 
                 117 
                 0.15 (SS) 
               
               
                 (polyphenylene 
                   
                   
                   
                   
                   
                 0.35 (Ti) 
               
               
                 oxide) 
               
               
                 Polycarbonate 
                 280 o   
                 0.13 @ 70° F. k   
                 1.86 a   
                 158 
                 85 
                 0.11 (SS) 
               
               
                   
                 190 d   
                 0.14 @ 212° F. k   
                   
                   
                   
                 0.25 (Ti) 
               
               
                   
                 250 e   
               
               
                 Teflon 
                 500 d   
                 0.14 j   
                 2.35 a   
                 158 
                 71 
                 0.094 (SS) 
               
               
                   
                 550 e   
                   
                 2.21 d   
                   
                   
                 0.21 (Ti) 
               
               
                 Polysulfone 
                 3400 
                 0.15 u   
                 3.42 a   
                 169 
                 49 
                 0.065 (SS) 
               
               
                   
                 300e 
                   
                   
                   
                   
                 0.15 (Ti) 
               
               
                 Polyurethane 
                   
                 0.13 v   
                 3.25 a   
                 147 
                 45 
                 0.060 (SS) 
               
               
                   
                   
                   
                   
                   
                   
                 0.13 (Ti) 
               
               
                 Nylon 
                 230 d   
                 0.14 j   
                 6.45 a   
                 158 
                 24 
                 0.032 (SS) 
               
               
                   
                 180-300 e   
                   
                   
                   
                   
                 0.071 (Ti) 
               
               
                 PEEK 
                 480 d   
                 0.15 q   
                 25.49 a   
                 168 
                 6.6 
                 0.009 (SS) 
               
               
                   
                   
                   
                   
                   
                   
                 0.02 (Ti) 
               
               
                 Stainless Steel 
                   
                 9.4 y   
                 1.68 g   
                 1,085 
                 759 
                 1.00 (SS) 
               
               
                   
                   
                   
                 1.49 d   
               
               
                   
                   
                   
                 1.43 n   
               
               
                 Titanium 
                   
                 12 x   
                 7.4 h   
                 1,108 
                 337 
                 1.00 (Ti) 
               
               
                   
                   
                   
                 3.29 o   
               
               
                   
               
               
                   a K-mac Plastics (www.k-mac-plastics.net) 
               
               
                   b h i  = 3000 BtU/(h · ft 2  · ° F.) 
               
               
                 h o  = 15,000 BtU/(h · ft 2  · ° F.) (dropwise condensation for plastic) 
               
               
                 h o  = 2,000 BtU/(h · ft 2  · ° F.) (filmwise condensation for metal) 
               
               
                 h m  = k/x 
               
               
                 x = 0.01 in = 0.00083 ft 
               
               
                   c Hubert Interactive 
               
               
                   d McMaster-Carr 
               
               
                   e Perry&#39;s Handbook of Chemical Engineering (Table 23-22) 
               
               
                   f K-mac Plastics 
               
               
                   g www.metalsdepot.com 
               
               
                   h www.halpemtitanium.com 
               
               
                   i R. M. Ogorkiewicz, Thermoplastics: Properties and Design, Wiley, London (1974) p. 133-135 
               
               
                   j R. M. Ogorkiewicz, Engineering Properties of Thermoplastics, Wiley, London (1970) 
               
               
                   k P. E. Powell, Engineering with Polymers, Chapman and Hall, London (1983), p. 242 
               
               
                   l Building Research Institute, Plastics in Building, National Academy of Sciences, 1955. 
               
               
                   m In the direction of molecular orientation, draw direction ratio of 25 www.electronics-cooling.com/html/2001_august_techdata.html Choy C. L., Luk W. H., and Chen, F. C., 1978, Thermal Conductivity of Highly Oriented Polyethylene, Polymer, Vol. 19, pp. 155-162. 
               
               
                   n Rickard Metals, rickardmetals.com ($3.50/lb) 
               
               
                   o Astro Cosmos, 888-402-7876 ($14/lb, Grade 2) 
               
               
                   p 3d-cam.com 
               
               
                   q boedeker.com 
               
               
                   r bayplastics.co.uk 
               
               
                   s sdplastics.com 
               
               
                   t tstar.com 
               
               
                   y plasticsusa.com 
               
               
                   v zae-bayern.de 
               
               
                   w toray.fr 
               
               
                   x efunda.com 
               
               
                   y Perry&#39;s Handbook of Chemical Engineering (Table 3-322) 
               
            
           
         
       
     
       FIGS. 61A-61D  illustrates another example sheet assembly  512 A in accordance with another embodiment of the invention.  FIG. 61A  illustrates a three-dimensional view of sheet assembly  512 A.  FIG. 61B  is a blown-up view of a corner area of sheet assembly  512 A, illustrating flanges  592 A of adjacent sheets  580 A being coupled to each other in accordance with an embodiment of the invention.  FIG. 61C  illustrates a side view of the corner of sheet assembly  512 A illustrated in  FIG. 61B .  FIG. 61D  illustrates the configuration of a flat sheet  610 A of material, such as sheet metal or one or more polymers, for example, that may be used to form each sheet  580 A of sheet assembly  512 A (such as by folding sheet  610 A, such as described above with regard to  FIGS. 3A-3B ). As shown in FIGS.  61 A- 61 D, sheet assembly  512 A is substantially similar to sheet assembly  512  shown in  FIG. 57A . However, unlike sheet assembly  512 , sheet assembly  512 A does not include triangular flaps  600  at the corners of each sheet  580 A. Thus, sheet assembly  512 A may be more simple to construct, and thus less expensive, than sheet assembly  512 . 
     Although embodiments of the invention and their advantages are described in detail, a person skilled in the art could make various alterations, additions, and omissions without departing from the spirit and scope of the present invention.