PSI - Issue 20

Tatiana Fesenko et al. / Procedia Structural Integrity 20 (2019) 284–293

287

Tatiana Fesenkoet al. / Structural Integrity Procedia 00 (2019) 000–000

4

where k е 2 . Note that the velocity induced by the j-th impenetrable profile presence located in the external flow will decrease with the distance from it no slower than 2 1 j r and correction to i Ф potential associated with the presence of the j th profile will be of the 2 ij е order. It is convenient to identify two potential components in i Ф : , ~ i i i       (9) Ф describes the flow caused by small profile oscillations. As a zero approximation, we take the potential created by i -th profile in a boundless liquid: ..... , i i        , 4 2 2 1 0 0 е е i i. e. the order of the main member in k i Ф is equal to where potential i _ Ф is connected with the current approaching from infinity, and potential i ~

_ 0

_ 0

0 V r i

и

i  

 

cos

,

(10)

i

i

_ 0   i 

0,

(11)

_ 0

i    

V

, cos и

 

(12)

ix

i

r r a

i

i

0 _ 0   i  when

,  i r

(13)

~ 0 ~ 0 i i   

,

(14)

~ 0   i 

0,

(15)

~

   

V

V и 

и

i

N

cos

sin

,

1,...,

,





(16)

ix

i

iy

i

r r a

i

i

0 ~ 0   i  when

.  i r

(17)

Symbols (10) and (14) are done for further expressions recording convenience. From (10) – (17) can be found:

   

_ 0             i _ 0 i i

2

0 r V r a  i

, cos и

i

i

2

0 r V r a 

, cos и

(18)

i

i

2

2

~ 0

. sin и

iy r V a и  i

ix r V a

cos

i   

(19)

i

i

i