Three-dimensional surface structure for reduced friction resistance and improved heat exchange

Abstract

In order to improve the flow properties of a surface, a surface along which a medium flows is provided. The medium consisting of a gas, a liquid, a two-phase mixture, or a mixture of multiple phases and the surface comprises dimples, the edges of which are rounded, thereby forming a central dimple area and at least one curvature area for each dimple. The at least one curvature area continuously connects the dimple to the surrounding surface.

1 . A surface along which a medium flows, said medium consisting of a gas, a liquid, a two-phase mixture, or a mixture of multiple phases, said surface comprising: 
 dimples, wherein edges of each of said dimples are rounded, thereby forming a central dimple area and at least one curvature area for each dimple, said at least one curvature area continuously connecting the dimple to a surrounding surface, wherein said curvature area comprises at least a first curvature area and a second curvature area, said first curvature area having a different curvature than said second curvature area.    
   
   
       2 . The surface according to  claim 1 , wherein said central dimple area essentially has the form of a section of a sphere or an ellipsoid.  
   
   
       3 . (canceled)  
   
   
       4 . The surface according to  claim 1 , wherein said first curvature area is rounded with a first rounding radius and said second curvature area is rounded with a second rounding radius.  
   
   
       5 . The surface according to  claim 4 , wherein said central dimple area essentially has the form of a section of a sphere, and the form of the central dimple area, of the first curvature area and of the second curvature area in a cross section perpendicular to said surrounding surface and through a center of the dimple is defined by the following parameters: 
 d 1 : Diameter of the central dimple area,    d 2 : Outer diameter of the first curvature area,    t 1 : Outer diameter of the second curvature area,    R 1 , C 1 : Radius and center point of the sphere, the section of which forms the surface of the central dimple area,    R 2 , C 2 : Radius and center point of the rounding radius of the first curvature area,    R 3 , C 3 : Radius and center point of the rounding radius of the second curvature area,    P 1 : Transition point from the central dimple area to the first curvature area,    P 2 : Transition point from the first curvature area to the second curvature area,    P 3 : Transition point from the second curvature area to the surrounding surface,    h 1 : Difference in height between the lowest point of the central dimple area and the outer rim of the central dimple area,    h 2 : Difference in height between the inner rim of the first curvature area and the outer rim of the first curvature area,    h 3 : Difference in height between the inner rim of the second curvature area and the outer rim of the second curvature area,    α 1 : Angle between the y-axis and a line connecting C 2  and C 3 ,    α 2 : Angle between the x-axis and a line connecting C 1  and C 2 ,    f: Parameter related to the portion of the surface covered by the central dimple area in relation to the combined area of central dimple area and curvature areas, 
 wherein a set of parameters, in particular the parameters comprising d 1 , α 1 , α 2 , R 2 /R 1  and f, are chosen and a remaining set of parameters are calculated by the following equations with a tolerance of ±10% for each parameter:  
             R   1     =       d   1         2   ·   sin     ⁢           ⁢     α   1           ,     
     ⁢       R   2     =         R   2       R   1       ·       d   1         2   ·   sin     ⁢           ⁢     α   1             ,     
     ⁢       R   2     =         t   1     -         d   1     2     ·       R   2       R   1       ·       (     1   -     sin   ⁢           ⁢     α   1         )       sin   ⁢           ⁢     α   2               sin   ⁢           ⁢     α   2           ,     
     ⁢       h   1     =         d   1     2     ·       (     1   -     cos   ⁢           ⁢     α   1         )       sin   ⁢           ⁢     α   1             ,     
     ⁢       h   2     =       R   2     ·     (       cos   ⁢           ⁢     α   2       -     cos   ⁢           ⁢     α   1         )         ,     
     ⁢       h   3     =       R   3     ·     (     1   -     cos   ⁢           ⁢     α   2         )         ,     
     ⁢     H   =       h   1     +     h   2     +     h   3         ,     
     ⁢       t   1     =         π     6   ·   f         ·     d   1         ,     
     ⁢       C   1     =         (       X     C   ⁢           ⁢   1       ,     Y     C   ⁢           ⁢   1         )     ⁢           ⁢   with   ⁢           ⁢     X     C   ⁢           ⁢   1         =   0       ,       Y     C   ⁢           ⁢   1       =       R   1     -   H       ,     
     ⁢       C   2     =         (       X     C   ⁢           ⁢   2       ,     Y     C   ⁢           ⁢   2         )     ⁢           ⁢   with   ⁢           ⁢     X     C   ⁢           ⁢   2         =         d   1     2     ·     (     1   +       R   2       R   1         )           ,     
     ⁢       Y     C   ⁢           ⁢   2       =       R   3     +         X     C   ⁢           ⁢   3       -     X     C   ⁢           ⁢   2           tg   ⁢           ⁢     α   2             ,     
     ⁢       C   3     =         (       X     C   ⁢           ⁢   3       ,     Y     C   ⁢           ⁢   3         )     ⁢           ⁢   with   ⁢           ⁢     X     C   ⁢           ⁢   3         =       t   1     2         ,       Y     C   ⁢           ⁢   3       =     -     R   3         ,     
     ⁢       P   1     =         (       X     P   ⁢           ⁢   1       ,     Y     P   ⁢           ⁢   1         )     ⁢           ⁢   with   ⁢           ⁢     X     P   ⁢           ⁢   1         =       d   1     2         ,       Y     P   ⁢           ⁢   1       =     H   -     h   1         ,     
     ⁢       P   2     =         (       X     P   ⁢           ⁢   2       ,     Y     P   ⁢           ⁢   2         )     ⁢           ⁢   with   ⁢           ⁢     X     P   ⁢           ⁢   2         =         t   1     2     -         R   3     ·   sin     ⁢           ⁢     α   2             ,     
     ⁢       Y     P   ⁢           ⁢   2       =       R   3     ·     (       cos   ⁢           ⁢     α   2       -   1     )         ,     
     ⁢       P   3     =         (       X     P   ⁢           ⁢   3       ,     Y     P   ⁢           ⁢   3         )     ⁢           ⁢   with   ⁢           ⁢     X     P   ⁢           ⁢   3         =       t   1     2         ,       Y     P   ⁢           ⁢   3       =   0     ,         
 said equations being defined in a two-dimensional coordinate-system with an x-axis in the plane of said surrounding surface and with the a y-axis through the center of the dimple and perpendicular to said surrounding surface.  
   
   
   
       6 . The surface according to  claim 1 , wherein said dimples are arranged periodically on said surrounding surface.  
   
   
       7 . The surface according to  claim 5 , wherein the centers of three adjoining dimples form a triangle, a first distance between two neighboring dimples of said triangle having a constant value t 1 , and a second distance between two rows of the dimples having a constant value t 2 .  
   
   
       8 . The surface according to  claim 7 , wherein the at least one curvature areas of said three adjoining dimples are in contact with each other.  
   
   
       9 . The surface according to  claim 7 , further comprising additional dimples of a different size than said dimples, which are located in the center of three respective adjoining dimples.  
   
   
       10 . A surface along which a medium flows, said medium consisting of a gas, a liquid, a two-phase mixture, or a mixture of multiple phases, comprising: 
 dimples having a diameter of d and a depth of h with a ratio between said depth and said diameter of h/d less than or equal to 0.1, wherein edges of each of said dimples are rounded, thereby forming a central dimple area and at least one curvature area for each dimple, said at least one curvature area continuously connecting the dimple to a surrounding surface.    
   
   
       11 . A surface along which a medium flows, said medium consisting of a gas, a liquid, a two-phase mixture, or a mixture of multiple phases, said surface comprising: 
 dimples having a diameter of d and a depth of h with a ratio between said depth and said diameter of h/d greater than or equal to 0.1, wherein edges of each of said dimples are rounded, thereby forming a central dimple area and at least one curvature area for each dimple, said at least one curvature area continuously connecting the dimple to a surrounding surface.    
   
   
       12  and  13 . (canceled).  
   
   
       14 . The surface according to  claim 1 , wherein said surrounding surface comprises a locomotive device selected from the group consisting of a car, a truck, a train, an airplane, a helicopter and a ship.  
   
   
       15  and  16 . (canceled).  
   
   
       17 . The surface according to  claim 1 , wherein said surrounding surface comprises an inner surface of a transport channel.  
   
   
       18 . The surface according to  claim 17 , wherein said transport channel is a pipe.  
   
   
       19 . (canceled)  
   
   
       20 . The surface according to  claim 1 , wherein said surrounding surface comprises a device for heat exchange between a the medium and at least one surface of the device.  
   
   
       21 . (canceled)  
   
   
       22 . The surface according to  claim 1 , wherein said surrounding surface comprises a container for cooking and/or for keeping warm, said surrounding surface being located at an outside surface of a bottom wall of the container and/or an outside surface of side walls of the container.  
   
   
       23 . A layer for applying on a surface, comprising: 
 a surface with dimples wherein edges of each of said dimples are rounded, thereby forming a central dimple area and at least one curvature area for each dimple, said at least one curvature area continuously connecting the dimple to a surrounding surface, and wherein said curvature area comprises at least a first curvature area and a second curvature area, said first curvature area having a different curvature than said second curvature area.    
   
   
       24 . The layer according to  claim 23 , further comprising a first side and a second side, wherein said first side comprises said surface and said second side is self-adhesive.  
   
   
       25 . A method for producing a surface with reduced friction resistance and/or improved heat exchange with a surrounding medium, comprising the step of: 
 forming a layer having a first side with dimples and a second side with an adhesive, wherein edges of each of said dimples are rounded, thereby forming a central dimple area and at least one curvature area for each dimple, said at least one curvature area continuously connecting the dimples to a surrounding surface, wherein said curvature area comprises at least a first curvature area and a second curvature area, said first curvature area having a different curvature than said second curvature area; and    applying a said second side of said layer onto said surface.    
   
   
       26 . The method according to  claim 25 , further comprising the steps of: 
 imprinting said dimples into said first side.    
   
   
       27 . A method for producing a surface with reduced friction resistance and/or improved heat exchange with a surrounding medium, comprising the steps of: 
 providing a casting mold with at least one structured surface; and    molding a workpiece with at least one surface in contact with said at least one structured surface to define comprising dimples, on the workpiece, wherein edges of each of said dimples are rounded, thereby forming a central dimple area and at least one curvature area for each dimple, said at least one curvature area continuously connecting the dimples to a surrounding surface, wherein said curvature area comprises at least a first curvature area and a second curvature area, said first curvature area having a different curvature than said second curvature area.    
   
   
       28 . (canceled)