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TitleQuantification of Reactor Kinetics Parameters during Reactor Transients using Cherenkov Light ...
LanguageEnglish
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Document Text Contents
Page 95

78







Next, the impact of angular offset and stand-off distance on the photodiode response

was investigated to provide a foundation for desktop experiments using a transient

LED light intensity in a similar fashion to OSTR transients. Figure 6-4 provides the

normalized voltage response of the Thorlabs PDA25K at a gain setting of 70 dB as a

function of position from the LED light source illuminating the space at a constant

output intensity calculated for each photodiode position per Figure 6-2. As expected,

voltage intensity decreases with increasing distance from the LED. For all test

positions, the photodiode was positioned normal to the “distance along” axis. As a

result, the photodiode response decreases quickly with increased distance along, since

the solid angle of the photodiode’s surface decreases.





Figure 6-4. Contour plot for normalized photodiode response



To provide values of uncertainty for each photodiode response, Figure 6-5 provides a

selection of individual row data, per the positions defined by Figure 6-2. The

uncertainty in the photodiode response is calculated with the standard deviation at of

the photodiode response during the constant output intensity portion of the Figure 6-3

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79







data. As a result, the ranges of the uncertainty bars in Figure 6-5 are extremely small.

Additional photodiode response curves as a function of position may be found in

Appendix A.





Figure 6-5. Normalized PD response with associated uncertainty (A-D)



6.1.3 Simulations

It is imperative to explore the viability of an experimental situation with

computational simulations to confirm the physical phenomena observed by

instrumentation, and confirmation allows the further simulation of experiments with

confidence.



Figure 6-6 provides the theoretical photon flux at each detector position (at 1 inch

intervals) from a constant light source with a given dispersion angle (33 degrees) to

match the Thorlabs M365FP1 LED solid angle at the emission point of the light. The

data for Figure 6-6 were acquired with Monte Carlo N-Particle (MCNP6.1.1 [95]) to

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172








        

      

2 2 4 3

2 2 1 2 2 1 2 1

2
2 2 2

1
1 2 1 2 1

3 $ 1 $ 1 $ 1 2 $ 1 $ 1

$
$ 1 $ 1 $ 1

I I Il

I I


       




   

(13-4)


        

      

2 2 4 3

1 1 2 1 1 2 1 2

2
2 2 2

2
1 2 2 2 1

3 $ 1 $ 1 $ 1 2 $ 1 $ 1

$
$ 1 $ 1 $ 1

I I Il

I I


       




   

(13-5)


 

       

3

2

2 22
1 1 2 1 2 1

2 $ 1

$ 1 $ 1 $ 1 $ 1

l

I I


  


     

(13-6)


 

       

3

1

2 22
2 2 2 1 2 1

2 $ 1

$ 1 $ 1 $ 1 $ 1

l

I I


 


     

(13-7)

The uncertainty in the β/l ratio may be then calculated using the Taylor error

propagation method (13-8).


1 2 1 2

1
2 2 2 2 2

$ $

1 2 1 2
$ $

I I
l

l l l l

I I


   

    

                                                 

(13-8)

Based on rod worth values provided by the OSTR staff, reactivity insertions are

performed based on percentage of full rod withdrawal height in increments of 0.1

inch. A distance of 0.1 inch is approximately equal to $0.003, so this is the value

assigned to σ$ when computing the uncertainty associated with the β/l ratio.

13.2 Proliferation Resistance

In Section 7.1, the potential for material diversion is assessed based on a case study of

the OSTR experiments using the data with the lowest quantified uncertainty acquired

with the CRANK system (P-29 and P-30). The lower limit of detection based on the

CRANK methodology is dependent on the reactivity insertion values, the

instrumentation uncertainty, and the mathematical sensitivity to the expressions used.

In the case of material diversion, the instrumentation uncertainty and reactivity

insertion uncertainty are previously described in Section 13.1. However, the

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173







mathematical uncertainty with regards to H is yet to be addressed. Through a

manipulation of (3-33), it is possible to ascertain the value of H in (13-9).


   

2

2 1
1

$ 1 $ 1

l
H

I

 
     

(13-9)

H is dependent on four independent variables, so the uncertainty in H is calculated

through (13-10) with the associated partial derivatives in (13-11) through (13-14)

with the Taylor error propagation method. The calculated uncertainty in H is then

used to obtain a maximum deviation using (H + 2σH) to determine a value of the

detectable fraction of the β/l ratio in (7-7).


1 2 1 2

1
2 2 2 2 2

$ $

1 2 1 2
$ $

H I I

H H H H

I I
    

           
           
            

(13-10)


      

    

2 2

2 1 2 2 1

2
3 3

1
1 1 2 2

$ 1 $ 1 $ 1 $ 1

$ 1 $ 1

IH

I
I I

       



  

(13-11)


      

    

2 2

1 1 2 2 1

2
3 3

2
1 1 2 2

$ 1 $ 1 $ 1 $ 1

$ 1 $ 1

IH

I
I I

       



  

(13-12)


       

    

3 2 32

1 1 1 2 1 2 1 2 2

2
3 3

1
1 1 2 2

2 $ 1 3 $ 1 $ 1 $ 1

$
$ 1 $ 1

I I I I IH

I I

     



  

(13-13)


      

    

3 2 32

2 2 1 2 1 2 1 2 1

2
3 3

2
1 1 2 2

2 $ 1 3 $ 1 $ 1 $ 1

$
$ 1 $ 1

I I I I IH

I I

     



  

(13-14)

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