PSI - Issue 59

Viktoriia Ihnatieva et al. / Procedia Structural Integrity 59 (2024) 487–493 Viktoriia Ihnatieva / Structural Integrity Procedia 00 (2019) 000 – 000

491

5

2 r r S n e  ,

(7)

where r n – is the number of filtration channels; e – is the distance between neighbouring fibres. Assuming that the fibres are a mesh structure, the number of channels is:

2 c

h dx

.

(8)

n



r

 2



d e 

The distance e is determined by the fill degree 1  , which can be represented as a product of 1 1 2      ,

(9)

where 1  – is the structural characteristic а . The structural characteristic is determined by the type of fibre packing and is numerically equal to the degree of filling at maximum packing density. At filtration of the binder in the radial direction the best is hexagonal structure. It provides a large value of the gap between the fibres. Then 1 0 907 ,   . 2  – geometric characteristic. The geometric characteristic defines the relationship between the distance between the fibres e and the degree of filling:

1 1 k 

e

,

.

k

2  



2





d

2

B

Then the distance between the fibres is calculated by the formula

   

   

1 0 907 , 

1

e d 

.

(10)



B

Substituting the values (8) and (10) into (7), we obtain:

2

   

   

1 0 907 , 

.

(11)

2 2 S , h 

1

dx



1 

r

c

On the basis of equations (3), (4) and (6) we make the equation of balance of flows. Then

2

   

   

0 907 ,

3

1

xdx



1 

1 

dp

xdx

,

(12)







 

 1 c 2



p x

b



1 

2

   

   

0 907 ,

3

1



1 

1  

where

.

(13)





 1 c 2



b

1 