Pulse Electrothermal Deicing Of Complex Shapes

Abstract

A pulse electrothermal deicing apparatus comprises at least one complex shape characterized by a thickness profile configured to generate uniform power per unit area to melt an interfacial layer of ice. A method of optimizing thicknesses of complex shapes for a pulse electrothermal deicing system includes assigning initial estimates of the pulse electrothermal deicing system parameters. A temperature distribution, a temperature range and a refreezing time produced by a deicing pulse are modeled. Shape thicknesses are adjusted according to the temperature range, deicing pulse parameters are adjusted according to the deicing pulse, and the modeling and adjusting is repeated until the temperature range and the refreezing time are within predetermined limits.

1 . Pulse electrothermal deicing apparatus comprising at least one complex shape characterized by a thickness profile configured to generate uniform power per unit area to melt an interfacial layer of ice. 
   
   
       2 . Pulse electrothermal deicing apparatus of  claim 1 , further comprising a power supply and a switch to alternatively connect and disconnect the power supply from the complex shape. 
   
   
       3 . Pulse electrothermal deicing apparatus of  claim 1 , wherein the complex shape comprises a cone, and thickness t of the cone varies according to the 
     
       
         
           
             t 
             = 
             
               
                 ρ 
                 · 
                 
                   I 
                   0 
                   2 
                 
               
               
                 4 
                  
                 
                   
                     π 
                     2 
                   
                   · 
                   
                     x 
                     2 
                   
                   · 
                   
                     
                       tan 
                       2 
                     
                      
                     
                       ( 
                       θ 
                       ) 
                     
                   
                   · 
                   W 
                 
               
             
           
         
       
       wherein the cone is characterized by a linear dimension x along an x-axis and an angle θ with respect to the x axis, and the power supply supplies a current I 0  to provide a power W per unit area. 
     
   
   
       4 . Pulse electrothermal deicing apparatus of  claim 1 , wherein the complex shape comprises a sphere, and thickness t of the sphere varies according to the equation: 
     
       
         
           
             t 
             = 
             
               
                 ρ 
                 · 
                 
                   I 
                   0 
                   2 
                 
               
               
                 4 
                  
                 
                   
                     π 
                     2 
                   
                   · 
                   
                     R 
                     2 
                   
                   · 
                   
                     
                       sin 
                       2 
                     
                      
                     
                       ( 
                       θ 
                       ) 
                     
                   
                   · 
                   W 
                 
               
             
           
         
       
       wherein the sphere is characterized by a radius R and an angle θ with respect to an axis along which power is supplied, and the power supply supplies a current I 0  to provide a power W per unit area. 
     
   
   
       5 . Pulse electrothermal deicing apparatus of  claim 1 , wherein the complex shape comprises a crescent, and thickness t of the sphere varies according to the equation: 
     
       
         
           
             t 
             = 
             
               
                 ρ 
                 · 
                 
                   I 
                   0 
                   2 
                 
               
               
                 4 
                  
                 
                   
                     π 
                     2 
                   
                   · 
                   
                     
                       R 
                       2 
                     
                      
                     
                       ( 
                       x 
                       ) 
                     
                   
                   · 
                   W 
                 
               
             
           
         
       
       wherein the crescent is characterized by a linear dimension x and an offset value R(x), and the power supply supplies a current I 0  to provide a power W per unit area. 
     
   
   
       6 . Pulse electrothermal deicing apparatus of  claim 1 , the complex shape formed by one of die casting, injection molding, machining, and successive application of conductive layers. 
   
   
       7 . A method of optimizing thicknesses of complex shapes for a pulse electrothermal deicing system, comprising:
 assigning size and geometry to each shape of the pulse electrothermal deicing system and connectivity of the shapes;   assigning initial thicknesses to each shape;   assigning an initial estimate to a deicing pulse duration;   modeling a temperature distribution over the surface of each shape based upon the deicing pulse duration and the thickness of each shape;   determining a refreezing time for each shape after application of the deicing pulse;   adjusting the thickness of each shape based upon the modeled temperature distribution if the modeled temperature distribution is not within a desired tolerance;   adjusting the deicing pulse duration based upon the determined refreezing time and if the determined refreezing time is not within defined limits; and   repeating the steps of modeling, determining and adjusting until the temperature distribution is within the desired tolerance and the refreezing time is within defined limits.   
   
   
       8 . The method of  claim 7 , the step of adjusting the thickness comprising:
 increasing the thickness of the shape where the temperature distribution is higher than the desired tolerance; and   decreasing the thickness of the shape where the temperature distribution is lower than the desired tolerance.   
   
   
       9 . The method of  claim 7 , the step of assigning initial thicknesses to each shape comprising assigning a fixed thickness to each shape. 
   
   
       10 . The method of  claim 7 , the step of assigning initial thicknesses to each shape comprising assigning a variable thickness to each shape. 
   
   
       11 . The method of  claim 7 , the step of adjusting the deicing pulse duration comprising shortening the duration if the determined refreezing time is above the defined limits. 
   
   
       12 . The method of  claim 7 , the step of adjusting the deicing pulse duration comprising lengthening the duration if the determined refreezing time is below the defined limits. 
   
   
       13 . Pulse electrothermal deicing apparatus comprising at least one axially symmetric complex shape characterized by a thickness profile configured to generate uniform power per unit area to melt an interfacial layer of ice. 
   
   
       14 . Pulse electrothermal deicing apparatus of  claim 13 , further comprising a power supply and a switch to alternatively connect and disconnect the power supply from the axially symmetric complex shape. 
   
   
       15 . Pulse electrothermal deicing apparatus of  claim 13 , wherein the axially symmetric complex shape comprises a cone, and thickness t of the cone varies according to the equation: 
     
       
         
           
             t 
             = 
             
               
                 ρ 
                 · 
                 
                   I 
                   0 
                   2 
                 
               
               
                 4 
                  
                 
                   
                     π 
                     2 
                   
                   · 
                   
                     x 
                     2 
                   
                   · 
                   
                     
                       tan 
                       2 
                     
                      
                     
                       ( 
                       θ 
                       ) 
                     
                   
                   · 
                   W 
                 
               
             
           
         
       
       wherein the cone is characterized by a linear dimension x along an x-axis and an angle θ with respect to the x axis, and the power supply supplies a current I 0  to provide a power W per unit area. 
     
   
   
       16 . Pulse electrothermal deicing apparatus of  claim 13 , wherein the axially complex shape comprises a sphere, and thickness t of the sphere varies according to the equation: 
     
       
         
           
             t 
             = 
             
               
                 ρ 
                 · 
                 
                   I 
                   0 
                   2 
                 
               
               
                 4 
                  
                 
                   
                     π 
                     2 
                   
                   · 
                   
                     R 
                     2 
                   
                   · 
                   
                     
                       sin 
                       2 
                     
                      
                     
                       ( 
                       θ 
                       ) 
                     
                   
                   · 
                   W 
                 
               
             
           
         
       
       wherein the sphere is characterized by a radius R and an angle θ with respect to an axis along which power is supplied, and the power supply supplies a current I 0  to provide a power W per unit area. 
     
   
   
       17 . Pulse electrothermal deicing apparatus of  claim 13 , wherein the axially symmetric complex shape comprises a crescent, and thickness t of the sphere varies according to the equation: 
     
       
         
           
             t 
             = 
             
               
                 ρ 
                 · 
                 
                   I 
                   0 
                   2 
                 
               
               
                 4 
                  
                 
                   
                     π 
                     2 
                   
                   · 
                   
                     
                       R 
                       2 
                     
                      
                     
                       ( 
                       x 
                       ) 
                     
                   
                   · 
                   W 
                 
               
             
           
         
       
       wherein the crescent is characterized by a linear dimension x and an offset value R(x), and the power supply supplies a current I 0  to provide a power W per unit area. 
     
   
   
       18 . Pulse electrothermal deicing apparatus of  claim 13 , the axially symmetric complex shape formed by one of die casting, injection molding, machining, and successive application of conductive layers.