Patent Publication Number: US-2021180885-A1

Title: Representative volume elements for heat exchangers with flow area control

Description:
BACKGROUND 
     This disclosure relates generally to component volumes partitioned by representative volume elements (RVEs) that define unequal cross-sectional flow areas, and more particularly to forming a heat exchanger core formed by representative volume elements (RVEs) in which the RVEs define different cross-sectional flow areas expressed as an area ratio. 
     Heat exchanger design often seeks to maximize the transmission of heat flux from one fluid to another or among multiple fluids within the heat exchanger core. To this end, many heat exchanger designs increase the surface area in contact between fluids within the heat exchanger core. Heat exchanger core designs having a relatively high surface area to volume ratio, or heat exchanger density, are referred to as compact heat exchangers. While large surface areas in compact heat exchangers increase heat transfer efficiency, the resulting relatively small fluid passage size is more susceptible to fouling and high pressure losses, which can be undesirable in some applications. 
     Recent attempts to address these disadvantages include forming heat exchanger cores by replicating representative volume elements (RVE), also known as representative elementary volumes (REV), within the core volume of heat exchangers. A representative volume element (RVE) or representative elementary volume (REV) is the smallest unit volume representation of a more complicated geometry. For periodic structures and materials, the RVE is the smallest unit volume that can be replicated in at least one direction of three-dimensional space to produce the overall structure. RVEs that can be replicated in three orthogonal directions are termed triply periodic structures. Some of these triply periodic RVE structures produce dissimilar boundary faces and require a particular orientation, or crystalline structure, with respect to the adjacent RVEs to form a unitary structure. Other RVEs have identical boundary faces, permitting the RVE to be rotated with respect to the adjacent RVEs while maintaining a unitary structure otherwise known as orientation independent structures. 
     In some applications, RVE geometry utilizes, or is derived from, a minimal surface. Minimal surfaces are surfaces with a minimized local area. In other words, a minimal surface is a surface that has the smallest possible surface area for a given boundary. Additionally, minimal surfaces have a zero mean curvature, i.e., the sum of the principle curvatures at each point is zero. One subset of such RVEs are triply periodic minimal surfaces (TPMS) that are RVEs in which the dividing surface is a minimal surface that produces a triply periodic unit structure. Examples of triply periodic unit structures based on TPMS surfaces include the structures based on Schwarz-D, Schoen-G, Schwarz-P, and Schoen IWP surfaces (depicted by  FIGS. 1A, 1B, 1C, and 1D , respectively) known in the art, each structure being based on a thickened minimal surface. 
     While RVEs have improved fouling performance and reduced pressure loses in compact heat exchangers, conventional RVE configurations, such as those based on a thickened minimal surface, produce equal cross-sectional flow areas. However, in some heat exchanger applications, heat exchanger efficiency can be improved by biasing the cross-sectional flow area between two fluid paths, or among multiple fluid paths. As such, a need exists for producing RVE-based components and, in particular, heat exchanger cores with unequal RVE divisions and unequal cross-sectional flow area divisions. 
     SUMMARY 
     In one example, a component can be formed by representative volume elements (RVEs) in which each RVE includes a first dividing structure partitioning the RVE into two discrete regions. The first dividing structure is bounded by first and second surfaces defined by offsetting a parting surface in opposite directions. The parting surface is defined by a mathematical expression that equals a non-zero first constant. Characteristically, the mathematical expression defines a triply periodic surface or, in some embodiments, a triply periodic minimal surface if the mathematical expression equals zero. In a further example, a heat exchanger can include a core formed by the above component, which places two fluids in a heat exchange relationship and biases the cross-sectional flow areas of the heat exchanger core in favor of one of the two fluid paths. 
     In another example, the component can include a second dividing structure that cooperates with the first dividing structure to partition each RVE into three discrete regions. The second dividing structure is also based on a parting surface defined by the mathematical expression, but differs in that the mathematical expression equals a non-zero second constant different from the first constant. A heat exchanger core constructed from the above component permits cross-sectional flow area ratios between the first and second regions and between the second and third regions to be greater than or less than 1.0 at the boundary faces of the RVEs. In a particular example in which two fluids are placed in a heat exchange relationship, an area ratio equal to the summation of the first and third outer cross-sectional flow areas of the RVE divided by the inner cross-sectional flow area of the second region can be greater than or less than 1.0 or, in other words, biased in favor of one of the two fluid paths. 
     In another example, the component can include a third dividing structure to partition each RVE into four discrete regions. The third dividing structure is based on a third parting surface defined by the mathematical expression equal to a non-zero third constant different from the first constant and different from the second constant. Heat exchanger cores formed by components of this type permit area ratios between two of any of the four regions to be greater than or less than 1.0. In a particular example of this type, two of the regions can be disposed between regions containing fluid to form buffer zones. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1A  is an isometric view of a representative volume element (RVE) having a dividing structure based on a Schwarz-D surface. 
         FIG. 1B  is an isometric view of a representative volume element (RVE) having a dividing structure based on a Schoen-G surface. 
         FIG. 1C  is an isometric view of a representative volume element (RVE) having a dividing structure based on a Schwarz-P surface. 
         FIG. 1D  is an isometric view of a representative volume element (RVE) having a dividing structure based on a Schoen IWP surface. 
         FIG. 2A  is an isometric view of a representative volume element (RVE) having a dividing structure based on a Schwarz-D surface but is offset within the RVE to define two regions with unequal cross-sectional flow areas. 
         FIG. 2B  is an enlarged isometric view of zone A depicted in  FIG. 2A . 
         FIGS. 2C and 2D  are isometric views of each of the regions defined by the RVE depicted in  FIG. 2A . 
         FIG. 3A  is an isometric view of a representative volume element (RVE) having two dividing structures based on a Schwarz-D surface except each structure is offset by a different amount within the RVE relative to the Schwarz-D surface to define three discrete regions of unequal cross-sectional flow areas. 
         FIG. 3B  is an enlarged isometric view of zone B depicted in  FIG. 3A . 
         FIGS. 3C, 3D, and 3E  are isometric views of each of the regions defined by the RVE depicted in  FIG. 3A . 
         FIG. 4  is a schematic view of a representative volume element (RVE) having three dividing structures based on a Schwarz-D surface except each structure is offset by a different amount within the RVE relative to the Schwarz-D surface to define four discrete regions. 
         FIG. 5A  is a schematic view of an exemplary system implementing a heat exchanger core formed by a plurality of RVEs depicted by  FIGS. 2A-2D . 
         FIG. 5B  is a schematic view of an exemplary system implementing a heat exchanger core formed by a plurality of RVEs depicted by  FIGS. 3A-3E . 
         FIG. 5C  is a schematic view of an exemplary system implementing a heat exchanger core formed by a plurality of RVEs depicted by  FIG. 4 . 
         FIG. 6  is a flow chart describing steps for forming a component comprising a plurality of RVEs. 
     
    
    
     DETAILED DESCRIPTION 
     As disclosed herein are components formed by representative volume elements (RVEs) characterized by discrete regions having unequal cross-sectional flow areas. Each representative volume element includes at least one dividing structure bound by two surfaces, each surface offset from opposite sides of a parting surface. The parting surface is a surface defined in three-dimensional space by a mathematical expression that equals a constant. Further, the selected mathematical expression is one that defines a triply periodic surface, or a triply periodic minimal surface (TPMS), when the expression equals zero. When the mathematic expression of the parting surface equals zero, the dividing structure bound by surfaces offset from the parting surface has a shape and contour that is similar to the parting surface and bounds discrete regions of equal volume and equal cross-sectional flow area of the RVE. However, in other embodiments, the mathematical expression equals a non-zero constant to offset the parting surface within the RVE such that the dividing structure bounds discrete regions of unequal volume and unequal cross-sectional flow area of the RVE. 
     Additional dividing structures can be added to the RVE to create additional discrete regions within the RVE, each additional dividing structure defined in a similar manner to the first dividing structure. As a result, the RVE can include one or more dividing structures that partition the RVE into multiple discrete regions and cross-sectional flow areas, the proportions of which can be varied by selecting different constants that equal the mathematical expression. When such components are used to construct heat exchanger cores, the fluid paths can be tailored to application-specific requirements of the heat exchanger. For instance, using RVE with unequal cross-sectional flow areas, the cross-sectional flow area ratio between two fluid paths can be tailored to account for differences in fluid viscosity, flow rate, temperature, pressure, and the like, and to improve heat exchanger efficiency. 
       FIG. 2A  is an isometric view of representative volume element (RVE)  10  that includes dividing structure  12 . Dividing structure  12  extends within RVE  10  to divide the internal volume of RVE  10  into two discrete regions  14  and  16  as noted along boundary faces  18   a ,  18   b ,  18   c ,  18   d ,  18   e , and  18   f , which enclose RVE  10 . Region  14  defines a flow path within RVE  10  that does not fluidly communicate with region  16 . That is to say, fluid flowing through region  14  does not mix with fluid flowing within region  16 . 
     Further, dividing structure  12  is a triply periodic structure such that RVE  10  can be replicated along mutually orthogonal X, Y, and Z axes of coordinate system  17  to form a component. As depicted in  FIG. 2A , the X-axis of coordinate system  17  is normal to boundary surfaces  18   b  and  18   d . The Y-axis of coordinate system  17  is normal to boundary surfaces  18   a  and  18   c , and the Z-axis of coordinate system  17  is normal to surfaces  18   e  and  18   f . Replicating RVE  10  along one or more axis of coordinate system  17  will produce a component defined by an array or assembly of a plurality of representative volume elements  10 , adjacent elements having abutting boundary faces. Dividing structures of adjacent representative volume elements  10  form continuous dividing structures through the component, regions  14  and  16  communicating with corresponding regions  14  and  16  of adjacent RVEs  10  in order to from continuous and discrete flow paths through the component. 
     While the depicted dividing structure  12  is derived from the Schwarz-D surface, dividing structure  12 , or any of the other dividing structures disclosed herein, can be based on a different implicit surface expression or an explicit surface expression. For instance, dividing structure  12  can be based on a Schoen-G, Schwarz-P, or Schoen-IWP surfaces, among other possible minimal surfaces as well as explicitly defined surfaces of any shape so long as the surface has the required periodic characteristic. The Schwarz-D, Schoen-G, Schwarz-P, and Schoen IWP surfaces are given by equations 1, 2, 3, and 4 below expressed as a mathematical expression that equals zero. These base surfaces, sometimes referred to as zero surfaces, are triply periodic minimal surfaces. 
       Schwarz-D cos( x )cos( y )cos( z )−sin( x )sin( y )sin( z )=0  (Equation 1)
 
       Schoen-G cos( x )sin( y )+cos( y )sin( z )+cos( z )sin( x )=0  (Equation 2)
 
       Schwarz-P cos( x )+cos( y )+cos( z )=0  (Equation 3)
 
       Schoen IWP 2 cos( x )cos( y )+2 cos( x )cos( z )+2 cos( y )cos( z )−cos(2 x )−cos(2 y )−(2 z )=0  (Equation 4)
 
       FIG. 2B  is an enlarged view of zone A encompassed by the corner of RVE  10  defined by the intersection of boundary faces  18   c ,  18   d , and  18   e . Dividing structure  12  is bound by surfaces  20   a  and  20   b . Surface  20   a  defines region  14 , surface  20   b  defines region  16 , and each of surfaces  20   a  and  20   b  is offset from parting surface  22  in opposite directions such that each point on surface  20   a  and each point on surface  20   b  is offset along a vector normal to corresponding points on parting surface  22 . All points along surface  20   a  are offset by the same amount from parting surface  22 , and similarly, all points along surface  20   b  are offset by the same amount from parting surface  22 . Accordingly, surfaces  20   a  and  20   b , and thus dividing structure  12 , have a similar shape and a similar contour profile as parting surface  22 . 
     An exemplary process for offsetting surfaces  20   a  and  20   b  from parting surface  22 , or any other of the surfaces described herein that are offset from respective parting surfaces, is described by U.S. patent Ser. No. 16/353,206 entitled “METHOD OF CREATING A COMPONENT VIA TRANSFORMATION OF REPRESENTATIVE VOLUME ELEMENTS” and filed on Mar. 14, 2019 with the United States Patent and Trademark Office, which is incorporated by reference in its entirety. In this exemplary process, each parting surface of the representative volume element is mapped into the target, or component domain. For example, the component domain may be a heat exchanger core volume. Subsequently each parting surface is thickened to form a dividing structure (i.e. a solid wall) separating the fluid regions. Bounding surfaces of the dividing structure that are opposite each other along the thickness direction form surfaces offset from the parting surface (e.g., surfaces  20   a  and  20   b ). In this way, the thickness of the dividing structure is uniform throughout the representative volume element and, therefore, uniform through the component domain. A similar process can be applied to produce RVEs with additional dividing structures and, hence, components with additional parting walls, as will be described in further detail in subsequently-described embodiments. 
     In the embodiment depicted by  FIGS. 2A, 2B, 2C, and 2D , parting surface  22  is an implicit surface defined by a mathematical expression that equals a non-zero constant. The mathematical expression selected for parting surface  22  is one that defines a triply periodic minimal surface when the expression equals zero (e.g., a surface defined by one of equations 1, 2, 3, and 4, among other possible triply periodic surfaces). In the example depicted by  FIGS. 2A and 2B , equation 5 defines parting surface  22  where K is a non-zero constant. When non-zero constant K equals zero, the mathematical expression defines a Schwarz-D surface. 
       Parting Surface 22 cos( x )cos( y )cos( z )−sin( x )sin( y )sin( z )= K   (Equation 5)
 
       FIGS. 2C and 2D  are isometric views of regions  14  and  16 , respectively, shown without dividing structure  12 . Region  14  intersects boundary faces  18   a ,  18   b ,  18   c ,  18   d ,  18   e , and  18   f  to define cross-sectional flow areas  24   a ,  24   b ,  24   c ,  24   d ,  24   e , and  24   f , respectively, although only areas  24   a ,  24   b , and  24   e  associated with boundary faces  18   a ,  18   b , and  18   e  are shown in  FIG. 2C . Similarly, region  16  intersects boundary faces  18   a ,  18   b , and  18   e  to define cross-sectional flow areas  26   a ,  26   b , and  26   e  shown in  FIG. 2D , but also intersects hidden boundary faces  18   c ,  18   d , and  18   f  to define cross-sectional flow areas  26   c ,  26   d , and  26   f  not shown in  FIG. 2D . 
     Since the dividing structure  12  is triply periodic, features of dividing structure  12 , region  14 , and region  16  defined at a boundary face of RVE  10  are identical to corresponding features of dividing structure  12 , region  14 , and region  16  defined at an opposite boundary face of RVE  10 . For example, cross-sectional flow area  24   a  of region  14  is identical to cross-sectional flow area  24   c  on hidden face  18   c  of RVE  10 . Similarly, cross-sectional flow areas defined on boundary face  18   b  are identical to corresponding cross-sectional flow areas on hidden boundary face  18   d , and cross-sectional flow areas defined on boundary face  18   e  are identical to corresponding cross-sectional flow areas on hidden boundary face  18   f . Likewise, faces of dividing structure  12  defined at boundary faces  18   a - 18   f  are identical to faces of dividing structure defined at an opposite boundary face. 
     The volume of region  14  is greater than the volume of region  16  as a result of offsetting parting surface  22  from the Schwarz-D base surface via selecting non-zero constant K. Further, as depicted, the cross-sectional flow areas of region  14  defined at boundary faces  18   a - 18   f  are greater than cross-sectional flow areas of region  16  defined at corresponding faces. For example, cross-sectional flow area  24   a  of region  14  is greater than corresponding cross-sectional area  26   a  of region  16  both defined at boundary face  18   a . An area ratio defined at any one of the boundary faces  18   a - 18   f  of RVE  10  is equal to the cross-sectional flow area of region  14  divided by the cross-sectional flow area of region  16  defined at the selected boundary face. For instance, the ratio of area  24   a  divided by area  26   a , or the area ratio taken at any of the other boundary faces  18   b - 18   f , is greater than 1.0 as depicted in  FIGS. 2C and 2D . Accordingly, the cross-sectional flow area of RVE  10  defined at boundary face  18   a  is biased in favor of region  14  and thus, area  24   a  of region  14  is greater than area  26   a  of region  16 . Although, by varying the non-zero constant K of equation 5, other embodiments of RVE  10  can be formed in which the ratio of area  24   a  to area  26   a , or the area ratio taken at any of the other boundary faces  18   b - 18   f , can be less than one. 
     In other embodiments, RVE  10  can include one or more additional dividing structures to divide the volume of RVE  10  into three or more discrete regions. For example,  FIG. 3A  depicts representative volume element (RVE)  100  enclosed by boundary faces  110   a ,  110   b ,  110   c ,  110   d ,  110   e , and  110   f . RVE  100  includes dividing structures  112  and  114 , which are offset from a Schwarz-D base surface and spaced from each other to partition RVE  100  into three discrete regions  116 ,  118 , and  120  as indicated along the boundary faces of RVE  100 . As shown in  FIG. 3A , region  118  is disposed between regions  116  and  120 . Further, each of regions  116 ,  118 , and  120  is fluidly isolated from the other regions such that fluid within one region does not communicate with the fluid of the other regions. For instance, fluid supplied to region  116  does not enter region  118  or region  120 . Similarly, fluid within region  118  does not fluidly communicate with regions  116  or region  120 , and fluid within region  120  does not fluidly communicate with regions  116  and region  118 . 
     Dividing structures  112  and  114  are triply periodic structures such that RVE  100  can be replicated along mutually orthogonal X, Y, and Z axes of coordinate system  119  to form a component. As depicted in  FIG. 3A , the X-axis of coordinate system  119  is normal to boundary surfaces  110   b  and  110   d . The Y-axis of coordinate system  119  is normal to boundary surfaces  110   a  and  110   c , and the Z-axis of coordinate system  119  is normal to surfaces  110   e  and  110   f . Replicating RVE  100  along one or more axis of coordinate system  119  will produce a component defined by an array or assembly of a plurality of representative volume elements  100 , adjacent elements having abutting boundary faces. Dividing structures of adjacent representative volume elements  100  form continuous dividing structures through the component, regions  116 ,  118  and  120  communicating with corresponding regions  116 ,  118 , and  120  of adjacent RVEs  100  in order to from continuous and discrete flow paths through the component. 
       FIG. 3B  is an enlarged isometric view of RVE  100  showing the corner formed by the intersection of boundary faces  110   c ,  110   d , and  110   e  and indicated in  FIG. 3A  by zone B. Dividing structures  112  and  114  are defined by parting surfaces  122  and  124 , respectively, each parting surface  122  and  124  being defined by a mathematical expression that equals non-zero constants M and N, respectively Like the mathematical expression defining parting surface  22  of RVE  10 , the mathematical expression defining each of parting surfaces  122  and  124  also defines a triply periodic minimal surface when constants M and N equal zero. For instance, parting surfaces  122  and  124  shown in  FIG. 3B  are based on a Schwarz-D surface expressed by equations 6 and 7 below, respectively, and in which M and N are non-zero constants. 
       Parting Surface 122 cos( x )cos( y )cos( z )−sin( x )sin( y )sin( z )= M   (Equation 6)
 
       Parting Surface 124 cos( x )cos( y )cos( z )−sin( x )sin( y )sin( z )= N   (Equation 7)
 
     Parting surfaces  122  and  124  are offset from the Schwarz-D, or zero surface, by a different amount to produce regions  116 ,  118 , and  120  shown in  FIG. 3A . As depicted by FIGS.  3 A and  3 B, non-zero constant M does not equal non-zero constant N. In some embodiments, both constants M and N are positive values, or negative values, of different magnitude, offsetting parting surfaces  122  and  124  from the same side of the Schwarz-D surface. In other embodiments, one of constants M and N is positive while the other constant is negative to offset parting surface  122  and  124  from opposite sides of the Schwarz-D surface. For example, in one particular embodiment, constants M and N have opposite sign and equal magnitude to offset parting surfaces  122  and  124  the same amount from opposite sides of the Schwarz-D surface. From these variations, it is evident that constants M and N can be any two non-zero and different values within the domain of the mathematical expression to produce three discrete regions. 
     Dividing structures  112  and  114  themselves are bound by surfaces offset from opposite sides of each parting surface  122  and  124 . For instance, dividing structure  112  is bound by surfaces  126   a  and  126   b . Each point along surfaces  126   a  and  126   b  are offset along a vector normal to a corresponding point on parting surface  122 , albeit in opposite directions along the normal vector. Similarly, dividing structure  114  is bound by surfaces  128   a  and  128   b  in which each point along surfaces  128   a  and  128   b  are offset in opposite directions along a vector normal to a corresponding point on parting surface  124 . Accordingly, dividing structures  112  and  114  as well as bounding surfaces  126   a ,  126   b ,  128   a , and  128   b  have a shape and contour profile that is similar to the triply periodic minimal surface expressed by the mathematical expression, which in the depicted case, is a Schwarz-D surface. 
       FIGS. 3C, 3D, and 3E  are isometric views of regions  116 ,  118 , and  120  depicted without dividing structures  112  and  114 . Each of regions  116 ,  118 , and  120  intersect boundary faces  110   a - f  of RVE  100  to form cross-sectional flow areas. For example, region  116  intersects boundary faces  110   a ,  110   b ,  110   c ,  110   d ,  110   e , and  110   f  to form cross-sectional flow areas  130   a ,  130   b ,  130   c ,  130   d ,  130   e , and  130   f  of which flow areas  130   a ,  130   b , and  130   e  are visible in  FIG. 3C . Similarly, region  118  intersects boundary faces  110   a - f  to define cross-sectional flow areas  132   a - f , and region  120  intersects boundary faces  110   a - f  to define cross-sectional flow areas  134   a - f  of which areas  132   a ,  132   b , and  132   e  of region  118  are shown in  FIG. 3D  and areas  134   a ,  134   b , and  134   e  of region  120  are shown in  FIG. 3E . 
     Dividing structures  112  and  114  are also triply periodic like dividing structure  12  of RVE  10 . As such, features of dividing structure  112 , dividing structure  114 , region  116 , region  118 , and region  120  defined at a boundary face of RVE  100  are identical to corresponding features of dividing structure  112 , dividing structure  114 , region  116 , region  118 , and region  120  defined at an opposite boundary face of RVE  100 . For example, cross-sectional flow area  130   a  of region  116  is identical to cross-sectional flow area  130   c  on hidden face  110   c  of RVE  100 . Similarly, cross-sectional flow areas defined on boundary face  110   b  are identical to corresponding cross-sectional flow areas on hidden boundary face  110   d , and cross-sectional flow areas defined on boundary face  110   e  are identical to corresponding cross-sectional flow areas on hidden boundary face  110   f . Likewise, faces of dividing structures  112  and  114  defined at boundary faces  110   a - 110   f  are identical to faces of respective dividing structures  112  and  114  defined at an opposite boundary face. 
     Representative volume elements partitioned into three discrete regions by two dividing structures, such as RVE  100 , permit the cross-sectional flow area ratio between any two regions to be greater than or less than 1.0 or, in other words, to be biased towards one of the two regions. For applications that fluidly connect regions  116  and  120  to a single fluid source and fluidly connect region  118  to a different fluid source, the cross-sectional flow area ratio at boundary face  110   a  can be defined as the summation of cross-sectional areas  130   a  and  134   a  divided by cross-sectional flow area  132   a . The cross-section flow area ratios of RVE  100  can be selected by varying non-zero constants M and N within the domain of the mathematical expression until the desired flow area ratio is achieved. As shown in  FIGS. 3A-3E , cross-sectional flow areas of region  116  at each boundary face  110   a - 110   f  are approximately equal to corresponding cross-sectional flow areas of region  120 . Further, cross-sectional flow areas of region  118  at each boundary face  110   a - 110   f  are less than corresponding cross-sectional flow areas of either region  116  or region  120 . 
       FIG. 4  is a schematic view of the boundary faces of representative volume element (RVE)  200 . Dividing structures  212 ,  214 , and  216  partition RVE  200  into four discrete regions  218 ,  220 ,  222 , and  224 . Each of dividing structures  212 ,  214 , and  216  is bound by surfaces offset from opposite sides of respective parting surfaces in the same manner as dividing structures  112  and  114  of RVE  100  and dividing structure  12  of RVE  10 . In the example shown in  FIG. 4 , each parting surface is defined by a mathematical expression that equals first, second, and third non-zero constants and each non-zero constant is different from every other non-zero constant. In the depicted embodiment, the mathematical expression defines a Schwarz-D triply periodic minimal surface when equal to zero. Accordingly, dividing structures  212 ,  214 , and  216  have surfaces that have a similar shape and similar contour profile to the Schwarz-D surface but are offset away from the Schwarz-D within RVE  200 . 
     With this arrangement, regions  218 ,  220 ,  222 , and  224  intersect boundary faces  110   a ,  110   b ,  110   c ,  110   d ,  110   e , and  110   f  of RVE  200  to define cross-sectional flow areas.  FIG. 4  shows cross-sectional flow areas  226   a ,  226   b , and  226   e  defined by the intersection of region  218  with boundary faces  110   a ,  110   b , and  110   e , respectively. While cross-sectional flow areas  226   c ,  226   d , and  226   f  are not shown in  FIG. 4 , it is evident that cross-sectional flow areas  226   c ,  226   d , and  226   f  are defined by the intersection of region  218  with hidden boundary faces  210   c ,  210   d , and  210   f , respectively. Similarly, cross-sectional flow areas  228   a - f ,  230   a - f , and  232   a - f  are defined by intersections of regions  220 ,  222 , and  224  with boundary faces  210   a - f , the letter portion of each cross-sectional area reference number shared with the letter portion of each boundary face reference number. Of these cross-sectional areas, areas  228   a ,  230   a , and  232   a  are shown on boundary face  210   a ; areas  228   b ,  230   b , and  232   b  are shown on boundary face  210   b ; and areas  228   e ,  230   e , and  232   e  area shown on boundary face  210   e . Like RVE  10  and RVE  100 , dividing structures  212 ,  214 , and  216  of RVE  200  are triply periodic and enable replication of RVE  200  along mutually orthogonal X, Y, and Z axes of coordinate system  234  to produce a component comprising a continuous structure defined by a repeating pattern of RVEs  200 . 
     Any of the foregoing representative volume elements as well as other representative volume elements based on a different implicit or explicit surface may be used to form a component comprising a plurality of represent volume elements, and in some embodiments, the component is used to form a heat exchanger core. For example, RVE  10  can be replicated as previously described to create heat exchanger core  300  for use in system  310  schematically depicted by  FIG. 5A . 
     Heat exchanger core  300  includes a plurality of RVEs  10  and consequently, a plurality of dividing structures  12  defining parting wall  312  through which fluid within first fluid path  314  is placed in a heat exchange relationship with another fluid within second fluid path  316 . Fluid paths  314  and  316  are defined by parting wall  312  and, more specifically, are formed by a plurality of regions  14  and a plurality of regions  16  interconnected via abutting RVEs  10 . 
     First fluid path  314  is placed in fluid communication with fluid source  318 , and second fluid path is placed in fluid communication with fluid source  320 , wherein fluid source  318  and fluid source  320  are of different temperature and may be of different material. For example, fluid source  318  may be air while fluid source  320  may be CO 2 . Communication between fluid source  318  and inlet  321  of first fluid path  314  is provided with supply line  322  and communication between outlet  323  of first fluid path  314  and fluid source  318  is provided by scavenge line  324 . Similarly, supply line  326  fluidly connects source  320  with inlet  327  of second fluid path  316 , and scavenge line  328  fluidly connects outlet  329  of second fluid path  316  to fluid source  320 . 
     A first fluid flows from source  318  to first fluid path  314  of heat exchanger core  300  via supply line  322  and returns to fluid source  318  from first fluid path  314  via scavenge line  324 . Similarly, a second fluid flows from source  320  to second fluid path  316  of heat exchanger core  300  via supply line  326  and returns to fluid source  320  from second fluid path  316  via scavenge line  328 . With this configuration, thermal energy stored within the first fluid flowing through first fluid path  314  can be discharged to the second fluid flowing within second fluid path  316  through parting wall  312 . It is understood that thermal energy may be passed from either the first fluid to the second fluid, or from the second fluid to the first fluid, depending on the relative temperatures of each fluid. 
     As indicated by the flow arrows shown in  FIG. 5A , the heat exchanger core has a cross-flow configuration. However, other heat exchanger configurations could be used, for example, a parallel-flow arrangement could be formed by reversing the connections of supply line  326  and scavenge line  328  to second fluid path  316 . Additionally,  FIG. 5A  depicts a simplified and schematic depiction of fluid flows through heat exchanger core  300  as implemented in a closed loop system. An open-loop system is also possible whereby fluid does not return to fluid source  318  and fluid source  320  and, instead, flows through discharge lines  330  and  332 , respectively. It shall be understood that systems implementing heat exchanger core  300  shall include one or more of pumps, valves, filters, accumulators, or other components common to heat exchanger systems, but are not shown in  FIG. 5A , to facilitate operation of the system. 
     Further, because dividing structure  12  of RVE  10 , from which parting wall  312  of heat exchanger core  300  is formed, partitions RVE  10  into unequal volumes and unequal cross-sections flow areas, the cross-sectional flow area ratio of first fluid path  314  divided by second fluid path  316  can be greater than or less than 1.0 and can be tailored to a particular application. In a particular example where first fluid source  318  is a liquid and second fluid source  320  is a gas, the ratio of cross-sectional flow area through first path  314  divided by the cross-sectional flow area through second path  316  and taken at a common location can be less than 1.0. Thus, more of the available cross-sectional flow area through heat exchanger core  300  can be apportioned to the gaseous flow path (i.e., second path  316 ) than to the liquid flow path (i.e., first path  314 ). 
       FIG. 5B  is a schematic representation of system  400  utilizing heat exchanger core  410  formed by a plurality of RVEs  100  and defining first fluid flow path  412 , second fluid flow path  414 , and third fluid flow path  416 . In the depicted embodiment, a first fluid flowing through first fluid path  412  and third fluid flow path  416  is placed in a heat exchange relationship with a second fluid flowing through second fluid flow path  414  by exchanging heat through parting walls  418  and  420 . Supply lines  422  provide fluid communication from fluid source  424  to inlet  425   a  of first fluid path  412  and to inlet  425   b  of third fluid path  416 . Scavenge lines  426  place outlet  427   a  of first fluid path  412  and outlet  427   b  of third fluid path  416  in fluid communication with fluid source  424 . Similarly, supply line  428  places fluid source  430  in fluid communication with inlet  431  to second fluid path  414 , and scavenge line  432  returns fluid from outlet  433  of second fluid path  414  to fluid source  424 . 
     Each parting wall  418  and  420  is formed by a plurality of dividing structures  112  and a plurality of dividing structures  114 , respectively. Likewise, first, second, and third fluid paths  412 ,  414 , and  416  are formed by a plurality of regions  116 ,  118 , and  120 , respectively. As such, second fluid path  414  is disposed between first fluid path  412  and third fluid path  416 . The cross-sectional flow area ratio between the first fluid flow path and the second fluid flow path can be expressed as the summation of cross-sectional areas of first fluid path  412  and third fluid flow path  416  divided by the cross-sectional area of second fluid path  414 , which in the depicted example, is greater than 1.0. 
       FIG. 5C  is schematic representation of system  500  that includes heat exchanger core  510  formed by a plurality of RVEs  200  and defining first, second, third, and fourth fluid paths  512 ,  514 ,  516 , and  518 . Due to the periodic structure of RVE  200 , first, second, third, and fourth fluid paths  512 ,  514 ,  516 , and  518  are formed by pluralities of first, second, third, and fourth regions  218 ,  220 ,  222 , and  224 , respectively. Similarly, parting walls  520 ,  522 , and  524  are defined by pluralities of dividing structures  212 ,  214 , and  216 , respectively. As such, parting wall  520  divides first fluid path  512  from second fluid flow path  514  and, when viewed in light of  FIG. 4 , divides first fluid path  512  from fourth fluid path  518 . Parting wall  522  divides second fluid path  514  from third fluid path  516 , and parting wall  524  divides third fluid path  516  from fourth fluid path  518 . 
     In the depicted embodiment, fluid flowing through first fluid path  512  is placed in a heat exchange relationship with fluid flowing through third fluid flow path  514 . Additionally, second fluid path  514  and fourth fluid path  518  are supplied with an inert gas (e.g., nitrogen or air), or inert fluid. For this purpose, fluid source  526  is placed in fluid communication with inlet  527  of first fluid path  512  via supply line  528  and returns from outlet  529  of first fluid path  512  to fluid source  526  via scavenge line  530 . Fluid from fluid source  532  is delivered to inlet  533  of third fluid path  516  via supply line  534  and returns from outlet  535  of third fluid path  526  via scavenge line  536 . Supply lines  538  provide inert gas or fluid from source  540  to inlets  541   a  and  541   b  of second and fourth fluid paths  514  and  518 . Scavenge lines  542  return the inert gas or fluid from outlets  543   a  and  543   b  of second and fourth fluid paths  514  and  518  to source  540 . 
     Alternatively, fluid from source  526  and fluid from source  532  are not required to return through scavenge lines  530  and  536  and, instead, may be discharged from the heat exchanger system via lines  544  and  546  as shown. Further, fluid originating from source  540  may stagnate within second and fourth flow paths  514 ,  518 , eliminating the need for scavenge lines  542 . Alternatively, fluid from source  540  may be discharged through one or more lines  548  in an open loop arrangement. 
     With any of the foregoing arrangements of system  500 , a volatile or combustible fluid (e.g., fuel) can be separated from another fluid (e.g., lubricating oil). Furthermore, second and fourth fluid paths  514  and  518  can be equipped with sensors to detect leakage of one or both of the first fluid and second fluid into second and fourth fluid paths. 
     Any of the foregoing components or heat exchanger cores can be manufacturing using additive manufacturing techniques such as selective laser sintering (DLS), direct metal laser sintering (DMLS), and selective laser melting (SLM) techniques, among other additive manufacturing techniques known in the art. 
       FIG. 6  is a schematic representation of method  600  summarizing steps forming a component comprising a plurality of any one of the foregoing representative volume elements. Method  600  includes defining a representative volume element in step  610  and creating a component by replicating the representative volume element along each of three mutually orthogonal directions in step  612 . Defining the representative volume element in step  610  can be further refined by including any one or more of the following steps  614 ,  616 , and  618 . 
     In step  614 , a triply periodic surface is selected to define a general shape and contour profile of the dividing structure of the representative volume element. In some embodiments, the surface is a triply periodic minimal surface. In both instances, the periodic surface can be defined by a mathematical expression that defines a surface in three-dimensional space and equals zero, sometimes referred to as a zero surface. When the periodic surface divides the representative volume element into equal volumes and equal cross-sectional areas, a triply periodic minimal surface can be used. Example triply periodic minimal surfaces suitable for this method include the Schwarz D, Schoen-G, Schwarz-P, and Schoen IWP surfaces given by equations 1, 2, 3, and 4, although other triply periodic minimal surfaces could be derived for this purpose. 
     In step  616 , at least one parting surface is defined using the mathematical expression selected during step  614 . For example, RVEs  10 ,  100 , and  200  are all based on the Schwarz-D surface given by equation 1. The parting surface is defined by offsetting the Schwarz-D surface, or the zero surface, in the RVE by setting the mathematical expression of a Schwarz-D surface equal to a non-zero constant. If additional parting surfaces are desired, each additional parting surface is defined by setting the same mathematical expression equal to different non-zero constants. The number of parting surfaces and the non-zero constants defining each parting surface can be selected based on the desired area ratio or ratios between cross-sectional flow areas of two regions of the RVE. 
     The dividing structure associated with each parting surface is defined by thickening the parting surface in step  618 . In other words, bounding surfaces of each dividing structure are defined by offsetting points on the parting surface in opposite directions along a vector normal the parting surface such that each point on the bounding surfaces is spaced from the parting surface by the same distance. 
     Representative volume elements formed in accordance with method  600  have two or more discrete regions of unequal volume and unequal cross-sectional flow areas. Such RVEs facilitate building components with cross-sectional flow area ratios greater than or less than 1.0, and are particularly useful for constructing heat exchanger cores. Such heat exchanger cores provide relatively high surface area available for heat transfer while reducing pressure losses produced by flows through the heat exchanger core and benefiting from the efficiency improvements of heat exchangers with cross-sectional flow area ratios greater than or less than 1.0. 
     DISCUSSION OF POSSIBLE EMBODIMENTS 
     The following are non-exclusive descriptions of possible embodiments of the present invention. 
     A component according to an exemplary embodiment of this disclosure, among other possible things, includes a plurality of representative volume elements. Each of the plurality representative volume elements abuts at least one other representative volume element of the plurality of representative volume elements to form the component. Additionally, each of the plurality of representative volume elements includes a first dividing structure. 
     The component of the preceding paragraph can optionally include, additionally and/or alternatively, any one or more of the following features, configurations and/or additional components: 
     A further embodiment of the foregoing component, wherein the first dividing structure can be bound by a first surface defined by a first parting surface offset in a first direction and a second surface defined by the first parting surface offset in a second direction opposite the first direction. 
     A further embodiment of any of the foregoing components, wherein the first parting surface can be defined by a mathematical expression that equals a first constant. 
     A further embodiment of any of the foregoing components, wherein the first constant can be equal to a non-zero first constant. 
     A further embodiment of any of the forgoing components, wherein the first dividing structure can partition each of the plurality of representative volume elements into discrete first and second regions. 
     A further embodiment of any of the forgoing components can further comprise a second dividing structure. 
     A further embodiment of any of the forgoing components, wherein the second dividing structure can be bound by a third surface defined by a second parting surface offset in the first direction and a fourth surface defined by the second parting surface offset in the second direction. 
     A further embodiment of any of the foregoing components, wherein the second parting surface is defined by the mathematical expression that equals a second constant different from the first constant to define the second parting surface. 
     A further embodiment of any of the foregoing components, wherein the second constant can be equal to a non-zero second constant. 
     A further embodiment of any of the foregoing components, wherein the first and second dividing structures partition each of the plurality of representative volume elements into discrete first, second, and third regions. 
     A further embodiment of any of the foregoing components can further include a third dividing structure. 
     A further embodiment of any of the foregoing components, wherein the third dividing structure can be bound by a fifth surface defined by a third parting surface offset in the first direction and a sixth surface defined by the third parting surface offset in the second direction. 
     A further embodiment of any of the foregoing components, wherein the third parting surface can be defined by the mathematical expression that equals a third constant different from each of the first and second constants. 
     A further embodiment of any of the foregoing components, wherein the third constant can be equal to a non-zero third constant. 
     A further embodiment of any of the foregoing components, wherein the first, second, and third dividing structures can partition each of the plurality of representative volume elements into discrete first, second, third, and fourth regions. 
     A further embodiment of any of the foregoing components, wherein each of the first and second constants can be positive values or negative values. 
     A further embodiment of any of the foregoing components, wherein one of the first and second constants can be a positive value and the other one of the first and second constants can be a negative value. 
     A further embodiment of any of the foregoing components, wherein the first and second constants can have the same magnitude. 
     A further embodiment of any of the foregoing components, wherein the component forms a heat exchanger core. 
     A system according to another exemplary embodiment of this disclosure, among other possible things, includes a heat exchanger core formed by a plurality of representative volume elements. Each of the plurality of representative volume elements abuts at least one other representative volume element of the plurality of representative volume elements to form the heat exchanger core. Each of the plurality representative volume elements includes a first dividing structure. 
     The system of the preceding paragraph can optionally include, additionally and/or alternatively, any one or more of the following features, configurations and/or additional components: 
     A further embodiment of the foregoing system, wherein the first dividing structure can be bound by a first surface defined by a first parting surface offset in a first direction and a second surface defined by the first parting surface offset in a second direction opposite the first direction. 
     A further embodiment of any of the foregoing systems, wherein the first parting surface can be defined by a mathematical expression that equals a first constant. 
     A further embodiment of any of the foregoing systems, wherein the first constant can equal a non-zero first constant. 
     A further embodiment of any of the forgoing systems, wherein the first dividing structure can partition each of the plurality of representative volume elements into discrete first and second regions. 
     A further embodiment of any of the forgoing systems can further comprise a second dividing structure. 
     A further embodiment of any of the forgoing systems, wherein the second dividing structure can be bound by a third surface defined by a second parting surface offset in the first direction and a fourth surface defined by the second parting surface offset in the second direction. 
     A further embodiment of any of the foregoing systems, wherein the second parting surface is defined by the mathematical expression, and wherein the mathematical expression equals a second constant different from the first constant to define the second parting surface. 
     A further embodiment of any of the foregoing systems, wherein the second constant can be a non-zero second constant. 
     A further embodiment of any of the foregoing systems, wherein the first and second dividing structures partition each of the plurality of representative volume elements into discrete first, second, and third regions. 
     A further embodiment of any of the foregoing systems can further include a third dividing structure. 
     A further embodiment of any of the foregoing systems, wherein the third dividing structure can be bound by a fifth surface defined by a third parting surface offset in the first direction and a sixth surface defined by the third parting surface offset in the second direction. 
     A further embodiment of any of the foregoing systems, wherein the third parting surface can be defined by the mathematical expression, and wherein the mathematical expression equals a third constant different from each of the first and second constants to define the third parting surface. 
     A further embodiment of any of the foregoing systems, wherein the third constant can be a non-zero third constant. 
     A further embodiment of any of the foregoing systems, wherein the first, second, and third dividing structures can partition each of the plurality of representative volume elements into discrete first, second, third, and fourth regions. 
     A further embodiment of any of the foregoing systems, wherein each of the first and second constants can be positive values or negative values. 
     A further embodiment of any of the foregoing systems, wherein one of the first and second constants can be a positive value and the other one of the first and second constants can be a negative value. 
     A further embodiment of any of the foregoing systems, wherein the first and second constants can have the same magnitude. 
     A further embodiment of any of the foregoing systems can further include a first fluid source and a second fluid source. 
     A further embodiment of any of the foregoing systems, wherein the first fluid source fluidly communicates with the first region of at least one of the plurality of representative volume elements and the second fluid source fluidly communicates with the second region of the at least one of the plurality of representative volume elements or the second fluid source fluidly communicates with the first region of at least one of the plurality of representative volume elements and the first fluid source fluidly communicates with the second region of the at least one of the plurality of representative volume elements. 
     A further embodiment of any of the foregoing systems, wherein the first region can intersect a boundary face of each of the plurality representative volume elements to define a first cross-sectional area, and wherein the second region can intersect the boundary face of each of the plurality of representative volume elements to define a second cross-sectional area, and wherein an area ratio of the first cross-sectional area divided by the second cross-sectional area is greater than or less than 1.0. 
     A further embodiment of any of the foregoing systems, wherein the first fluid source can be in fluid communication with the first and third regions of at least one of the plurality of representative volume elements, and wherein the second fluid source can be in fluid communication with the second region of the at least one of the plurality of representative volume elements or wherein the first fluid source can be in fluid communication with the second region of at least one of the plurality of representative volume elements, and wherein the second fluid source can be in fluid communication with the first and third regions of the at least one of the plurality of representative volume elements. 
     A further embodiment of any of the foregoing systems, wherein the second region can be disposed between the first and third regions, and wherein the first, second, and third regions can intersect a boundary face of each of the plurality of representative volume elements to define first, second, and third cross-sectional areas, respectively, and wherein an area ratio equal to the summation of the first and third cross-sectional areas divided by the second cross-sectional area is greater than or less than 1.0. 
     A further embodiment of any of the foregoing systems, wherein the first fluid source can be in fluid communication with the first region of at least one of the plurality of representative volume elements, and wherein the second fluid source can be in fluid communication with the third region of the at least one of the plurality of volume elements, and wherein a third fluid source can be in fluid communication with the second and fourth regions of the at least one of the plurality of representative volume elements. 
     A further embodiment of any of the foregoing systems, wherein the second region can be disposed between the first and third regions and the fourth region can be disposed between the first and third regions, and wherein the first, second, third, and fourth regions intersect a boundary face of each of the plurality of representative volume elements to define first, second, third, and fourth cross-sectional areas, respectively, and wherein an area ratio can equal to the first cross-sectional area divided by the third cross-sectional area is greater than or less than 1.0. 
     A further embodiment of any of the foregoing systems, wherein the second cross-sectional area can be equal to the fourth cross-sectional area. 
     A further embodiment of any of the foregoing systems, wherein each of the second cross-sectional area and the fourth cross-sectional area are less than each of the first cross-sectional area and the third cross-sectional area. 
     A method of manufacturing a component comprising a plurality of representative volume elements according to another exemplary embodiment of this disclosure, among other possible things, includes defining a representative volume element of the plurality of representative volume elements and creating the component by replicating the representative volume element along each of three mutually orthogonal directions. 
     The method of the preceding paragraph can optionally include, additionally and/or alternatively, any one or more of the following features, steps, configurations and/or additional components: 
     A further embodiment of the foregoing method, wherein defining the representative volume element can further include selecting a triply periodic surface expressed as a mathematical expression that equals zero. 
     A further embodiment of the foregoing method, wherein defining the representative volume element can further include selecting a triply periodic minimal surface expressed as a mathematical expression that equals zero. 
     A further embodiment of any of the foregoing methods, wherein defining the representative volume element can further include defining a first parting surface expressed as the mathematical expression that equals a first constant. 
     A further embodiment of any of the foregoing methods, wherein the first constant can be a non-zero first constant. 
     A further embodiment of any of the foregoing methods, wherein defining the representative volume element can further include defining a first surface of a first dividing structure by offsetting the first parting surface in a first direction. 
     A further embodiment of any of the foregoing methods, wherein defining the representative volume element can further include defining a second surface of the first dividing structure by offsetting the first parting surface in a second direction that is opposite the first direction. 
     A further embodiment of any of the foregoing methods, wherein defining the representative volume element can further include defining the first dividing structure of the representative volume element based on the first surface and the second surface. 
     A further embodiment of any of the foregoing methods, wherein defining the representative volume element can further include selecting the first constant based on an area ratio equal to a first cross-sectional area divided by a second cross-sectional area, and wherein the first dividing structure partitions the representative volume element into discrete first and second regions, and wherein the first and second regions intersect a boundary face of the representative volume element to define the first cross-sectional area and the second cross-sectional area, respectively. 
     A further embodiment of any of the foregoing methods, wherein defining the representative volume element can further include defining a second dividing structure. 
     A further embodiment of any of the foregoing methods, wherein defining the representative volume element can further include defining a second parting surface defined by the mathematical expression equal to a second constant different from the first constant. 
     A further embodiment of any of the foregoing methods, wherein the second constant can be a non-zero second constant. 
     A further embodiment of any of the foregoing methods, wherein defining the representative volume element can further include defining a third surface of the second dividing structure by offsetting the second parting surface in the first direction. 
     A further embodiment of any of the foregoing methods, wherein defining the representative volume element can further include defining a fourth surface of the second dividing structure by offsetting the second parting surface in the second direction. 
     A further embodiment of any of the foregoing methods, wherein the second dividing structure can be defined based on the third and fourth surfaces. 
     A further embodiment of any of the foregoing methods, wherein defining the representative volume element can further include selecting the first and second constants based on an area ratio equal to the summation of first and third cross-sectional areas divided by a second cross-sectional area, and wherein the first and second dividing structures partition the representative volume element into discrete first, second, and third regions, and wherein the first, second, and third regions intersect a boundary face of the representative volume element to define the first, second, and third cross-sectional areas, respectively. 
     A further embodiment of any of the foregoing methods, wherein defining the representative volume element can further include defining a third dividing structure. 
     A further embodiment of any of the foregoing methods, wherein defining the representative volume element can further include defining a third parting surface defined by the mathematical expression equal to a third constant different from the first constant and different from the second constant. 
     A further embodiment of any of the foregoing methods, wherein the third constant can be a non-zero third constant. 
     A further embodiment of any of the foregoing methods, wherein defining the representative volume element can further include defining a fifth surface of the third dividing structure by offsetting the third parting surface in the first direction. 
     A further embodiment of any of the foregoing methods, wherein defining the representative volume element can further include defining a sixth surface of the third dividing structure by offsetting the third parting surface in the second direction. 
     A further embodiment of any of the foregoing methods, wherein defining the third dividing structure can be based on the fifth surface and the sixth surface. 
     A further embodiment of any of the foregoing methods, wherein defining the representative volume element can further include selecting the first, second, and third constants based on an area ratio equal to a first cross-sectional area divided by a third cross-sectional area, and wherein the first, second, and third dividing structures partition each representative volume element into discrete first, second, third, and fourth regions, and wherein the second region is disposed between the first and third regions, and wherein the fourth region is disposed between the first and third regions, and wherein the first, second, third, and fourth regions intersect a boundary face of the representative volume element to define the first, second, third, and fourth cross-sectional areas, respectively. 
     A further embodiment of any of the foregoing methods, wherein defining the representative volume element can further include selecting first, second, third, and fourth constants based on equal second and fourth cross-sectional areas. 
     While the invention has been described with reference to an exemplary embodiment(s), it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted for elements thereof without departing from the scope of the invention. In addition, many modifications may be made to adapt a particular situation or material to the teachings of the invention without departing from the essential scope thereof. Therefore, it is intended that the invention not be limited to the particular embodiment(s) disclosed, but that the invention will include all embodiments falling within the scope of the appended claims.