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68, №3, 2015
532.613.5
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Key words: wave, corks, fluid, gas.
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Grigoryan Sh.A., Ohanyan G.G., Sahakyan S.L.
The propagation of pressure wave in closed channel filed of periodic alternate corks with the gas–liquid mixture and gas
The propagation of wave in closed channel filed of corks is considered. It is supposed that the discrete structure of corks is periodic. The dispersion equation of the Bloch wave number dependence on wave numbers of corks is derived. It is obtained the frequencies bands of transmitting waves.
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2
1 1 10
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1
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1
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,
1
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(1.1) : 2 22 2 0
2 2 2 2
2 2
2 2 2
20 2 20
V
1
0,
0,
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c
t
x
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(1.2)t
– ,x
– ,,
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– ,
– ,c
– ё-. (1.1)
. 0, 1 2
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1, 2
i t
i i i i
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x t
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e
i
– , (1.1), (1.2):
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2 2 2 2 2
1 1 2
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1 1 1 20 2 1 2
0,
0,
1
1
V
V
,
,
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ar
d P
d P
P
P
dx
c
dx
c
d
k
d
k
i
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i
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k
k
dx
c
dx
c
c
c
(1.3) , .0
x
,
1
0
20 ,
V 0 =V 0
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1 2
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a
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(1.3) :
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2 2 2 2
1 1 1 1 1 1
1 1 1
2 2 2 2 2 2
20 2
1
,
V
1
,
V
ik x ik x ik x ik x
ik x ik x ik x ik x
P x
A e
B e
x
A e
B e
c
P x
A e
B e
x
A e
B e
c
(1.6)
,
1, 2
i i
A B
i
– .(1.4) (1.5),
1
A
,A
2,B
1,B
2 :1 1 2 2
0
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1 1 2 2
1 1 1 1 1 1 20 2 20 2
1
1
1
1
0
A
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A
B
c
c
c
c
1 1 2 2
1 1 2 2
0
ik a ik a ik b ik b
A e
B e
lA e
lB e
1 1 2 2
1 1 2 2
1 1 1 1 1 1 20 2 20 2
1
1
0
ik a ik a
l
ik bl
ik bA e
B e
A e
B e
c
c
c
c
, 1A
,A
2,B
1,B
2. ,l
:
20 2
1 1 1
1 2 1 2
20 2 1 1 1
1
1
1
cos
cos
sin
sin
2
2
c
c
l
k a
k b
k a
k b
l
c
c
q
, :20 2
1 1 1
1 2 1 2
20 2 1 1 1
1
cos
cos
cos
sin
sin
2
c
c
qL
k a
k b
k a
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a
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cos
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2. и и ии.
(1.1). .
1 2
,
k a
k b
, ё. (1.3)
(
k
1
/
c
1,k
2
/
c
2,
1 ) 22 20 2 1 1
20 2 1 1
1
cos
1
1
sin
2
c
c
qL
c
c
,c
1(1
)
L
(2.1)(1
)
a
L
,b
L
.k a
1
k b
2 10
,
20
20
1 2
2 10
1
1
1
c
c
c
, (2.1) ,
, , ( ).
.
.1 ( ),
(2.1) , .
и 1
0
0.1
P
,
1.4
,L
2
0.66 0.005 [25, 748] [799, 1522] [1573, 2296] 0.73 0.01 [27, 673] [716, 1351] [1405, 2040] 0.81 0.025 [31, 597] [659, 1225] [1287, 1853]
0
0.2
P
,
1.4
,L
2
0.6 0.005 [34, 896] [965, 1826] [1895, 2756] 0.77 0.025 [40, 683] [764, 1407] [1487, 2130]
.1 ,
, .
,,
P
0( ) .
.1 .
qL
P
0
0.2
,0.025,
.1 1
qL
0
0.2
P
P
0
0.1
,ё [6]. .1 1 ,
,
. .1.
(1.7), :
20 2 1 1
1 2 20 2 1 1 1 2
1
cos
cos
cos
sin
sin
2
c
c
a
b
a
b
qL
c
c
c
c
c
c
(2.2). 2 2 ,
(2.2) .
.
и 2
, (P
0
0.05
,
1.4
,L
2
)0.001
0.7 [19, 668] [670, 1331] [1338, 1386] 0.8 [21, 585] [586, 1170] [1171, 1754]
и 2
, (P
0
0.05
,
1.4
,L
2
)0.005
0.7 [19, 613] [621, 668] [675, 1237] 0.8 [21, 584] [586, 928] [932, 1170]
. 2 2 ,
-
.
.3 3 ,
-
, , .200 400 600 800 1000 1200 2
3 4 5
qL
.1 .
qL
0
0.1
и 3
, (P
0
0.2
,
1.4
,L
2
)0.001
0.7 [37, 814] [817, 1629] [1632, 2442] 0.8 [42, 713] [716, 1426] [1428, 2139]
и 3
, (P
0
0.2
,
1.4
,L
2
)0.005
0.7 [37, 812] [817, 1237] [1243, 1629] 0.8 [42, 712] [716, 1422] [1428, 1855]
3 2 3 2 , 0
P
., ё
,
P
0
.
.P
0
.3. и и и ии. ё
(1.7), ё .
20 2
1 1 1 1 1
1 2 20 2 1 1 1 1 2
1
cos
cos
cos
sin
sin
2
c
a
b
c
a
b
qL
c
c
c
c
c
c
(3.1)
221
1
1
ar
. 4 4 ,
(3.1) .
и 4
, (R
7 10
3 ,
0.001
,
1.4
,L
2
)0
0.05
P
0.7 [19, 668] [670, 1151] [1153, 1337]
0.8 [21, 585] [586, 1169] [1171, 1468]
и 4
, (R
7 10
4 ,
0.001
,
1.4
,L
2
)0
0.05
P
, , . .
, .
, . 5 5 .
и 5
, (R
7 10
3 ,
0.001
,
1.4
,L
2
)0
0.2
P
0.7 [37, 814] [817, 1629] [1632, 2300]
0.8 [42, 713] [716, 1426] [1428, 2139]
и 5
, (R
7 10
3 ,
0.005
,
1.4
,L
2
)0
0.2
P
0.7 [37, 812] [817, 1186] [1991, 1629]
0.8 [42, 712] [716, 1422] [1428, 1696]
. . 5 4 ,
0
P
.. 4 2 ,
.
.,
,
P
0.
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1. Martin C.S., Padmanabhan M. Pressure Pulse Propagation in Two–Component Slug
Flow // Trans. of the ASME. Vol.101. №1. 1979. –
.
// . ё . 1979. .101. №1. .161-171.
2. . ., . ., . . -
. .: Э , 1990. 248 .
3. . ., . .
// . . VIII .
., 22-26, 2014, – . , 2014. .340-344.
4. ., . .
.: , 1959. 448 .
5. . ., . ., . .
-ё . .: , 1989. 288 .
6. . .. . ., . . . .: , 1979.
384 .
7. . . . .1. .: , 1987. 464 .
и :
и и , . .- . ., «
-. » - ( ) .
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E-mail: grig-shushanik@rambler.ru
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E-mail: ssahakyan@ysu.am
