PSI - Issue 36

Volodymyr Sydorenko et al. / Procedia Structural Integrity 36 (2022) 318–325 Volodymyr Sydorenko, Sergiy Yeremenko, Viola Vambol et al. / Structural Integrity Procedia 00 (2021) 000 – 000

322

5

  

  

h

2

1

N  = = 1 i

exp

−

q

   

   

2

2

z 

1

1

   +

 −  

   −

  

L  0

i



( , )

C x y

erf

y L z

erf

y L dx z

=

(3)

i

2

2

z 

2

u



2

2

2

2

z 



y

where х' – coordinate of the emission source; σ z = σ z ( х – х' ), σ у = σ у 5( х – х' );

S = L x  L z – area of the radioactive emission source in the form of a rectangle. As a first approximation, a radioactive source of RСP contamination can be considered in the form of a circle with a radius R, with the origin in the center. Further, using the principle of superposition, the value of the integral coordinate of the RСP is determined from –  to +  in y:

      

      

  

  

  

  

h

h

2

2

1

N

exp

exp

=

−

−

2

q



2

2

y

y

2

2

( ) dx R x 2 1/ 2 2 − 

R 

x 

i

z

z

C

=

1

i

(4)

=

i

pu

y

y



R

x

−

z

z

Then, during the continuous inflow of radionuclides, the sector- averaged RСP concentration over a controlled time interval, which is formed by a source of radius R, is defined as: ( )    − = = =   −       − = R z M j j N i i i dx R x j h q n C 2 , exp 2 2 1/ 2 2 2 2 1 1 1    (5)

,

x

u

j





z 

R

j

 j – the frequency of occurrence of the j-th category during the emission of harmful substances; ū j – average wind speed in the j-th weather category; n – number of sectors; ζ – frequency with which the wind blows in the given azimuth sector; М = 6 – category of atmospheric stability.

where

4. Results and discussion For the simplest verification of the proposed mathematical method, the calculation of the surface concentration of 137Cs emitted into the atmosphere after a forest fire in the Chernobyl exclusion zone on an area of L 1  L 2 =5  15 m 2 was performed. The calculation results by formula (5) are presented in the form of isopleths in Fig. 3. The values of the quantities included in the formula (3) are as follows: u = 1 m/s, h = 1.7 m; the average temperature of the mixture is 300  K, the average temperature of the atmospheric air is 293  K; averaging time - 0.5 h; σ y = a 1 x b 1 ; σ t = a 2 x b 2 , where a1, a2, b1, b2 are empirical coefficients depending on the stability category of the atmosphere according to Pasquill-Guyford. Initial data on ω j and ū j are provided in Table 1.

Table 1. The value of repetitions of the categories of atmospheric stability and average wind speeds Values Atmospheric stability category j =1 j =2 j =3 j =4

j =5

j =6

2

2,5

3

5

2

3

ū j ω j

0,05

0,05

0,1

0,5

0,1

0,1