# Patent

## Title
System and method for determining the blackbody temperature of an electrical discharge

## Abstract

A method for determining a blackbody temperature of an electrical discharge may include providing a radiometer with a sensor aperture, positioning a viewing aperture sheet between the sensor aperture and the electrical discharge, and providing the viewing aperture sheet with a viewing aperture therethrough, determining an area of the viewing aperture, determining a distance of the sensor aperture from the viewing aperture, observing the electrical discharge with the sensor aperture through the viewing aperture to obtain radiometer data, and calculating the blackbody temperature based at least on the radiometer data, the area of the viewing aperture and the distance of the sensor aperture from the viewing aperture.

## Background
FIELD
This application relates to the analysis of electrical discharges and, more particularly, to systems and methods for determining the spectral energy and associated black body temperature of electrical discharges.
BACKGROUND
Certain materials, such as carbon fiber reinforced plastic (“CFRP”) materials, may be prone to damage from electrical discharges, such as lightning strikes. Therefore, those skilled in the art continue to seek techniques for reducing or eliminating damage to materials due to electrical discharges.
For example, various spectrally selective coatings and methods for minimizing the effects of electrical discharges, such as lightning, are disclosed in U.S. Ser. No. 12/474,965 filed on May 29, 2009, the entire contents of which are incorporated herein by reference. However, the design of coatings and materials capable of resisting electrical discharges may require, or may be improved by, knowing the spectral energy and associated blackbody temperature of the electrical discharge.
Currently, the blackbody temperature of a lightning strike may be assumed from published values. Unfortunately, the published values of lighting strike temperatures are far ranging in values from approximately 8,000° K to 25,000° K.
Blackbody temperatures may also be estimated based upon post lightning strike thermal analysis and the radiative temperatures required to cause similar damage levels. However, calculating the required blackbody temperature to duplicate lighting strike test damage to CFRP panels is an inaccurate and indirect way of determining the lighting plasma blackbody temperature, and requires accurate knowledge of material layer thermophysical properties during and after extreme erosion.
Photographic techniques are currently used to determine the presence and amount of electrical sparking. However, film and digital photographic techniques do not provide a measure of electrical discharge energy levels and, therefore, cannot be used to determine blackbody temperature.
Other measurement techniques involve the use of spectral radiometers to measure the spectral energy from an electrical discharge. A spectral radiometer may be used to measure the relative spectral energy levels associated with an electrical discharge, but spectral radiometers do not provide the blackbody temperature of the electrical discharge.
A spectral radiometer may also be used to measure absorption lines. The absorption lines occur as a result of atmospheric constituents interacting with the electrical discharge plasma. The characteristic measurement results in a curve showing energy versus wavelength with many narrow lines which rise above the nominal curve height. The width of these lines may be used to analytically provide equivalent blackbody temperature values. This method is highly indirect, requiring many assumptions, in part because the absorption lines are broader at the base than at the peak, and is not based upon accurate measurements of the physical quantities in question because the emission lines coincide with absorption lines. The emissions are also very readily absorbed and, therefore, not present at the sensor aperture in relation to the physical temperature of the arc source.
Accordingly, those skilled in the art continue to seek techniques for determining the blackbody temperature of an electrical discharge.
SUMMARY
In an embodiment, a method for determining a blackbody temperature of an electrical discharge, may include providing a radiometer with a sensor aperture, positioning a viewing aperture sheet between the sensor aperture and the electrical discharge, and providing the viewing aperture sheet with a viewing aperture therethrough, determining an area of the viewing aperture, determining a distance of the sensor aperture from the viewing aperture, observing the electrical discharge with the sensor aperture through the viewing aperture to obtain radiometer data, and calculating the blackbody temperature based at least on the radiometer data, the area of the viewing aperture and the distance of the sensor aperture from the viewing aperture.
In another embodiment, a method for determining a blackbody temperature of an electrical discharge may include providing a light-tight enclosure, providing a viewing aperture sheet received in the light-tight enclosure, the viewing aperture sheet having a first side and a second, opposite side, and defining at least one viewing aperture having a known area, providing a dielectric aperture/ground plane within the light-tight enclosure, providing a radiometer having a sensor aperture, the sensor aperture being received in the light-tight enclosure on the first side of the viewing aperture sheet, the sensor aperture being positioned a known distance from the viewing aperture, providing an electric current source having an electrode, the electrode being received in the light-tight enclosure on the second side of the viewing aperture sheet, observing the electrical discharge with the sensor aperture through the viewing aperture to obtain radiometer data, and calculating the blackbody temperature based at least on the radiometer data, the known area and the known distance.
In yet another embodiment, a method for determining a blackbody temperature of an electrical discharge may include providing a light-tight enclosure, placing a viewing aperture sheet in the light-tight enclosure, the viewing aperture sheet having a first side and a second, opposite side, and defining at least one viewing aperture therethrough, wherein the viewing aperture has a known area, forming a dielectric aperture/ground plane as a layered structure having a first layer that includes a dielectric material and a second layer that includes a conductive material, wherein the first layer defines at least one aperture therethrough, placing the dielectric aperture/ground plane generally perpendicular to the viewing aperture sheet, wherein the second layer is electrically coupled to ground, providing an electric current source having an electrode, the electrode being received in the light-tight enclosure on the second side of the viewing aperture sheet, providing a radiometer having a sensor aperture, the sensor aperture being received in the light-tight enclosure on the first side of the viewing aperture sheet, the sensor aperture being positioned a known distance from the viewing aperture, observing the electrical discharge with the sensor aperture through the viewing aperture to obtain radiometer data, and calculating the blackbody temperature based at least on the radiometer data, the known area and the known distance.
In yet another aspect, the disclosed method for determining a blackbody temperature of an electrical discharge may include the steps of (1) providing a light-tight enclosure, (2) providing a viewing aperture sheet received in the light-tight enclosure, the viewing aperture sheet having a first side and a second, opposite side, and defining at least one viewing aperture therein, wherein the viewing aperture has a known area, (3) providing a dielectric aperture/ground plane disposed generally perpendicular to the viewing aperture sheet, the dielectric aperture/ground plane being formed as a layered structure comprising a first layer that includes a dielectric material and a second layer that includes a conductive material, wherein the first layer defines at least one aperture therein, and wherein the second layer is electrically coupled to ground, (4) providing an electric current source having an electrode, the electrode being received in the light-tight enclosure on the second side of the viewing aperture sheet, (5) providing a radiometer having a sensor aperture, the sensor aperture being received in the light-tight enclosure on the first side of the viewing aperture sheet, the sensor aperture being positioned a known distance from the viewing aperture, (6) observing the electrical discharge with the sensor aperture through the viewing aperture to obtain radiometer data, and (7) calculating the blackbody temperature based at least on the radiometer data, the known area and the known distance.
Other aspects of the disclosed method for determining the blackbody temperature of an electrical discharge will become apparent from the following description, the accompanying drawings and the appended claims.



BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a block diagram of one aspect of the disclosed system for determining the blackbody temperature of an electrical discharge;
FIG. 2A is a plan view of a dielectric aperture/ground plane of the system shown in FIG. 1;
FIG. 2B is a side view of the dielectric aperture/ground plane of FIG. 2A;
FIG. 3A is a plan view of a viewing aperture sheet of the system shown in FIG. 1; and
FIG. 3B is a side view of the viewing aperture sheet of FIG. 3A.



DETAILED DESCRIPTION
Disclosed is a system and method for the direct measurement and radiative characterization of an electrical discharge. Specifically, the disclosed system and method utilize a dielectric aperture of known geometry for viewing an electrical discharge with a calibrated spectral radiometer. The collected data may then be used to determine the blackbody temperature of the electrical discharge.
Referring to FIG. 1, one aspect of the disclosed system for determining the blackbody temperature of an electrical discharge, generally designated 10, may include a light-tight enclosure 12, a radiometer 14 (e.g., a spectral radiometer) having a sensor aperture 16 disposed at the distal end 18 of an optical fiber 20, an electric current source 22 electrically coupled to an electrode 24, a viewing aperture sheet 26 and a dielectric aperture/ground plane 28. The sensor aperture 16, the electrode 24, the viewing aperture sheet 26 and the dielectric aperture/ground plane 28 may be housed within the light-tight enclosure 12 to prevent ambient light from entering the sensor aperture 16 between electrical discharges, and such that the sensor aperture 16 is positioned on a first side 29 of the viewing aperture sheet 26 at a known distance R away from the viewing aperture sheet 26. The electrode 24 may be positioned on a second, opposite side 31 of the viewing aperture sheet 26.
The sensor 14 may be in communication with a processor 52, such as a personal computer. The sensor 14 and the processor 52 may be in a control room 54 that may be shielded from the electromagnetic pulse generated by the electrical discharge. An optional filter 50 may be positioned in front of the sensor aperture 16 to protect the sensor 14 from overexposure from the electrical discharge. For example, the sensor 14 may have a spectral sensitivity which may provide better accuracy over a primary spectral region. In such a case the filter 50 may be used to filter out all but a known and desired spectral band. As another example, the filter 50 may be desired to protect the sensor 14 from excessive UV.
The viewing aperture sheet 26 may be a generally planar sheet of dielectric material (e.g., phenolic resin) that defines at least one viewing aperture 30 therethrough. The use of dielectric material may prevent or inhibit spark attachment to the sheet 26. In one particular implementation, as shown in FIGS. 3A and 3B, the viewing aperture sheet 26 may define multiple viewing apertures 30, 32, 34 therethrough. Each viewing aperture 30, 32, 34 may have a known area ASourceAperture, which may be considered the source area of the electrical discharge when the electrical discharge fills the aperture, as discussed in greater detail below. For example, aperture 34 may be a circular aperture having a diameter of about 1⁄8 of an inch, aperture 30 may be a circular aperture having a diameter of about 1⁄4 of an inch, and aperture 32 may be a circular aperture having a diameter of about 3⁄8 of an inch.
At this point, those skilled in the art will appreciate that the array of viewing apertures as shown provide choices to the test director to help obtain the desired results of experimental data corresponding to the electrical discharge filling the entire viewing aperture. During any test, the adjacent unused viewing apertures may be covered over with non-transmissive material such as black tape.
As shown in FIGS. 2A and 2B, the dielectric aperture/ground plane 28 may be formed as a layered structure 36 having a first layer 38 of dielectric material positioned over a second layer 40 of electrically conductive material. The dielectric material of the first layer 38 may be fabricated from a high temperature dielectric material, such as phenolic resin. The electrically conductive material of the second layer 40 may be a high temperature metal alloy, such as tungsten alloy, to minimize or avoid melting and vaporization.
The first layer 38 of the dielectric aperture/ground plane 28 may define apertures 42, 44, 46 therethrough positioned to align with the viewing apertures 30, 32, 34 of the viewing aperture sheet 26. For example, aperture 42 may be a circular aperture having a diameter of about 1⁄4 of an inch, aperture 44 may be a circular aperture having a diameter of about 3⁄8 of an inch, and aperture 46 may be a circular aperture having a diameter of about 1⁄2 of an inch.
Referring back to FIG. 1, the dielectric aperture/ground plane 28 may be positioned generally perpendicular to the viewing aperture sheet 26 and the electrode 24 may be positioned generally perpendicular to and directly adjacent to the desired viewing aperture 30, 32, 34 of the viewing aperture sheet 26. The second layer 40 of the dielectric aperture/ground plane 28 may be electrically coupled to ground and, optionally, a current probe 48 may be positioned between the dielectric aperture/ground plane 28 and ground to obtain accurate measurements of the current associated with the measured electrical discharge.
Without being limited to any particular theory, it is believed that use of the dielectric aperture/ground plane 28 may be optional, but advantageous because the dielectric aperture/ground plane 28 is believed to contain the electrical discharge from the electrode 24 directly in front of the desired viewing aperture 30, 32, 34 of the viewing aperture sheet 26.
At this point, those skilled in the art will appreciate that the viewing apertures 30, 32, 34 of varying sizes may be provided such that a range of waveform current levels may be tested in order to obtain data with the viewing aperture 30, 32, 34 fully filled with the electrical discharge at varying discharge current levels for varying waveforms.
Accordingly, the electrical discharge from the electrode 24 may be viewed by way of the sensor aperture 16 through one of the viewing apertures 30, 32, 34 of the viewing aperture sheet 26. The electrical discharge arc initiation and pulse times may be synchronized with sensor aperture times. The sensor aperture measurement times may be greater than the electrical discharge arc time durations in order to capture the entire pulse radiative energy. Power may be determined by the prescribed and known pulse time and the measured spectral energy.
In one particular aspect, the electrode 24 may be placed adjacent to the viewing aperture 30 such that it would not be viewed by the sensor 14, leaving the aperture 30 open. When the electrical discharge occurs, the spark may be constrained between the electrode 24 and the ground plane aperture 44 adjacent to the viewing aperture 30 and opposite the electrode 24. Therefore the spark may be positioned across the viewing aperture 30. Although the electrode 24 and spark are contained within the overall light-tight enclosure 12, the only radiative path from the spark to the sensor 14 is through the selected viewing aperture 30.
Optionally, an in-scene calibration source may be used prior to the arc tests to confirm and calibrate the sensor response. Furthermore, a photographic or digital camera 56 (FIG. 1) may be used to provide visual corroboration of the electrical discharge arc event and to identify effects such as sparking into the enclosure, which may bias the experimental results of the measurement.
Analytical modeling may be performed to determine the effective blackbody temperatures of the electrical discharges based upon the experimental set-up and measured sensor responses. Analysis should reveal a leveling of calculated blackbody temperature as current levels increase for selected aperture sizes indicating the entire viewing aperture area is filled.
The following equations may be used to determine the arc source spectral energy and associated blackbody temperature:



  
    
      P
      PredictedSpectralPower
    
    =
    
      
        
          ∑
          λ
        
        ⁢
        
          
            L
            ⁡
            
              (
              
                λ
                ,
                T
              
              )
            
          
          ⁢
          
            A
            SourceAperture
          
          ⁢
          
            
          
          ⁢
          
            A
            SensorAperture
          
        
      
      
        R
        2
      
    
  




  
    
      L
      ⁡
      
        (
        
          λ
          ,
          T
        
        )
      
    
    =
    
      SpectralBlackbodyRadiance
      ⁢
      
        
      
      ⁢
      
        (
        
          watts
          
            
              cm
              2
            
            ⁢
            sr
          
        
        )
      
    
  




  
    
      P
      MeasuredSpectralPower
    
    =
    
      
        
          Q
          Measured
        
        ⁡
        
          (
          joules
          )
        
      
      
        t
        event
      
    
  



where:




  
    
      P
      Predicted
    
    =
    
      PredictedPower
      ⁡
      
        (
        watts
        )
      
    
  




  
    
      Q
      Measured
    
    =
    EnergyMeasuredatSensor
  




  
    λ
    =
    
      Wavelength
      ⁡
      
        (
        μm
        )
      
    
  




  
    T
    =
    
      
        
          AbsoluteTemperature
          ⁡
          
            (
            K
            )
          
        
        ⁢
        
          

        
        ⁢
        sr
      
      =
      
        
          
            steradian
            ⁡
            
              (
              SolidAngle
              )
            
          
          ⁢
          
            

          
          ⁢
          
            t
            event
          
        
        =
        
          
            
              DischargeTime
              ⁡
              
                (
                sec
                )
              
            
            ⁢
            
              

            
            ⁢
            
              L
              ⁡
              
                (
                
                  λ
                  ,
                  T
                
                )
              
            
          
          =
          
            
              
                
                  
                    C
                    1
                  
                  π
                
                
                  
                    λ
                    5
                  
                  ⁡
                  
                    (
                    
                      
                        exp
                        ⁡
                        
                          [
                          
                            
                              C
                              2
                            
                            
                              λ
                              ⁢
                              
                                
                              
                              ⁢
                              T
                            
                          
                          ]
                        
                      
                      -
                      1
                    
                    )
                  
                
              
              ⁢
              
                

              
              ⁢
              
                C
                1
              
            
            =
            
              
                2
                ⁢
                
                  
                
                ⁢
                π
                ⁢
                
                  
                
                ⁢
                h
                ⁢
                
                  
                
                ⁢
                
                  c
                  o
                  2
                
              
              =
              
                
                  37
                  ,
                  413
                  ⁢
                  
                    
                      watts
                      ⁢
                      
                        
                      
                      ⁢
                      
                        μm
                        4
                      
                    
                    
                      cm
                      2
                    
                  
                  ⁢
                  
                    

                  
                  ⁢
                  
                    C
                    2
                  
                
                =
                
                  
                    
                      hc
                      o
                    
                    
                      k
                      B
                    
                  
                  =
                  
                    
                      14
                      ,
                      388
                      ⁢
                      
                        
                      
                      ⁢
                      μmK
                      ⁢
                      
                        

                      
                      ⁢
                      h
                    
                    =
                    
                      
                        
                          Planck
                          '
                        
                        ⁢
                        sConstan
                        ⁢
                        
                          
                        
                        ⁢
                        t
                        ⁢
                        
                          

                        
                        ⁢
                        
                          k
                          B
                        
                      
                      =
                      
                        
                          BoltzmannCons
                          ⁢
                          
                            
                          
                          ⁢
                          tan
                          ⁢
                          
                            
                          
                          ⁢
                          t
                          ⁢
                          
                            

                          
                          ⁢
                          
                            A
                            SourceAperture
                          
                        
                        =
                        
                          
                            
                              SourceArea
                              ⁡
                              
                                (
                                
                                  cm
                                  2
                                
                                )
                              
                            
                            ⁢
                            
                              

                            
                            ⁢
                            
                              A
                              SensorAperture
                            
                          
                          =
                          
                            
                              
                                SensorArea
                                ⁡
                                
                                  (
                                  
                                    cm
                                    2
                                  
                                  )
                                
                              
                              ⁢
                              
                                

                              
                              ⁢
                              R
                            
                            =
                            
                              Distance
                              ⁡
                              
                                (
                                cm
                                )
                              
                            
                          
                        
                      
                    
                  
                
              
            
          
        
      
    
  



The radiative arc temperature may be determined by comparing the measured spectral power with the predicted equivalent temperature dependent spectral power at selected wavelength regions and sensor spectral integration specifications. The measured spectral power of the electrical discharge event requires knowledge of the measured electrical discharge temperal event and is thus calculated by dividing the measured spectral energy by the electrical discharge duration.
For simplicity, spectral energy is meant to define radiative energy associated with regions of spectral wavelengths. A given sensor 14 may provide only one integrated spectral energy measurement (radiometer) or many energy values at many wavelengths (spectral radiometer). The same methodology applies in all cases.
The calibrated sensor 14 measures radiometric energy within wavelengths which are within the sensitivity region of the sensor and with given accuracy. It follows from above that the predicted power equation may be equated to the measured power quantity. The predicted power may be summed across the same in-band range as the sensor used to derive the measured power quantities. Both the radiometer and spectral radiometer measure “in-band” radiometric energy where “in-band” refers to the energy within two wavelengths. The spectral radiometer just provides more spectral resolution of the radiometric quantities.
Since the sensor aperture 16 is placed at a distance R from the radiative source of a given area and the sensor aperture 16 has a known size ASensorAperture and spectral measurement characteristics, the measured power may be equated to the predicted power as follows:




  
    P
    MeasuredSpectralPower
  
  =
  
    
      
        ∑
        λ
      
      ⁢
      
        
          L
          ⁡
          
            (
            
              λ
              ,
              T
            
            )
          
        
        ⁢
        
          A
          SourceAperture
        
        ⁢
        
          
        
        ⁢
        
          A
          SensorAperture
        
      
    
    
      R
      2
    
  




where the temperature value, T may be parametrically varied to obtain energy agreement between measured and predicted values. The resultant temperature value required for energy agreement between the measured and predicted power emitted by the source and measured at the sensor is the quantity of interest.

Thus, use of the viewing aperture provides a known source area to the radiative arc which would otherwise not be quantified. This is only possible if the radiative arc is “filling” the entire viewing aperture area.
Accordingly, the disclosed systems and methods may be used to directly and accurately determine the spectral energy of an electrical discharge, as well as the blackbody temperature of the electrical discharge.
The electrical spark may be located closely behind the viewing aperture sheet. Those skilled in the art will appreciate that as the wavefront passes through the viewing aperture, the viewing aperture may act as a secondary radiometric blackbody source. This is known as Huygen's principle. The wavefront may propagate spherically from this constructed secondary source into the light-tight enclosure. Therefore, this test geometry may be equivalent to the desired, but otherwise impossible experimental condition of measuring the spark of known area, area geometry and distance to the sensor.
Although various aspects of the disclosed system and method for determining the blackbody temperature of an electrical discharge have been shown and described, modifications may occur to those skilled in the art upon reading the specification. The present application includes such modifications and is limited only by the scope of the claims.

## Claims

1. A method for determining a blackbody temperature of an electrical discharge, the method comprising:
providing a radiometer with a sensor aperture;
positioning a viewing aperture sheet between the sensor aperture and the electrical discharge, and providing the viewing aperture sheet with a viewing aperture therethrough;
determining an area of the viewing aperture;
determining a distance of the sensor aperture from the viewing aperture;
observing the electrical discharge with the sensor aperture through the viewing aperture to obtain radiometer data; and
calculating the blackbody temperature based at least on the radiometer data, the area of the viewing aperture and the distance of the sensor aperture from the viewing aperture.

2. The method of claim 1, wherein the radiometer is a spectral radiometer.

3. The method of claim 1, further comprising positioning an electrode adjacent the viewing aperture to form the electrical discharge.

4. The method of claim 1, further comprising housing the sensor aperture and the viewing aperture sheet within a light-tight enclosure; and wherein the observing is performed in the light-tight enclosure.

5. The method of claim 1, further comprising positioning a filter between the sensor aperture and the viewing aperture sheet.

6. The method of claim 1, further comprising positioning a camera toward the viewing aperture.

7. The method of claim 1, wherein the viewing aperture sheet defines an array of viewing apertures therethrough.

8. The method of claim 7, further comprising choosing the viewing aperture from the array of viewing apertures; and covering the unused viewing apertures with a non-transmissive material.

9. The method of claim 1, further comprising positioning a dielectric aperture/ground plane generally perpendicular to the viewing aperture sheet.

10. The method of claim 9, wherein positioning the dielectric aperture/ground plane includes forming a layered structure comprising a first layer that includes a dielectric material and a second layer that includes a conductive material.

11. The method of claim 10, further comprising electrically coupling the second layer of the dielectric aperture/ground plane to ground.

12. The method of claim 10, wherein forming the layered structure includes providing the first layer of the dielectric aperture/ground plane with at least one aperture therethrough.

13. The method of claim 10, wherein the dielectric material comprises phenolic resin.

14. The method of claim 10, wherein the conductive material comprises tungsten.

15. A method for determining a blackbody temperature of an electrical discharge, the method comprising:
providing a light-tight enclosure;
providing a viewing aperture sheet received in the light-tight enclosure, the viewing aperture sheet having a first side and a second, opposite side, and defining at least one viewing aperture having a known area;
providing a dielectric aperture/ground plane within the light-tight enclosure;
providing a radiometer having a sensor aperture, the sensor aperture being received in the light-tight enclosure on the first side of the viewing aperture sheet, the sensor aperture being positioned a known distance from the viewing aperture;
providing an electric current source having an electrode, the electrode being received in the light-tight enclosure on the second side of the viewing aperture sheet;
observing the electrical discharge with the sensor aperture through the viewing aperture to obtain radiometer data; and
calculating the blackbody temperature based at least on the radiometer data, the known area and the known distance.

16. A method for determining a blackbody temperature of an electrical discharge, the method comprising:
providing a light-tight enclosure;
placing a viewing aperture sheet in the light-tight enclosure, the viewing aperture sheet having a first side and a second, opposite side, and defining at least one viewing aperture therethrough, wherein the viewing aperture has a known area;
forming a dielectric aperture/ground plane as a layered structure having a first layer that includes a dielectric material and a second layer that includes a conductive material, wherein the first layer defines at least one aperture therethrough;
placing the dielectric aperture/ground plane generally perpendicular to the viewing aperture sheet, wherein the second layer is electrically coupled to ground;
providing an electric current source having an electrode, the electrode being received in the light-tight enclosure on the second side of the viewing aperture sheet;
providing a radiometer having a sensor aperture, the sensor aperture being received in the light-tight enclosure on the first side of the viewing aperture sheet, the sensor aperture being positioned a known distance from the viewing aperture;
observing the electrical discharge with the sensor aperture through the viewing aperture to obtain radiometer data; and
calculating the blackbody temperature based at least on the radiometer data, the known area and the known distance.