# Моделирование процесса измерения уровня жидкости акустическим методом, учитывающим факторы среды

• Published on
05-Apr-2017

• View
224

0

Embed Size (px)

Transcript

• http://www.ejta.org

2007, 10

. .

, , e-mail: an_gromov@rambler.ru

, 21.01.2007, 04.05.2007

, - . , , .

. [112], .

.

, .. . ,

. , , . , , . ,

- . . , . , , , , . . ,

mailto:an_gromov@rambler.ru

• 2007, 10 _________________________________________________________________________________________

2 (16)

, , . . [12], .

.

. Saab Saab Tank Control, , . , . 10 . . . [47]. ,

[1011]. , , , ,

c

12

L c t= ,

, , .

L c Const= t

, c Const= , . . , , . [3] , -, - , 5%. 1000 10.7 . , 80% . 4050

c Const=

. [1] ,

_________________________________________________________________________________________ . . ,

• 2007, 10 _________________________________________________________________________________________

3 (16)

. , L . , , , , .

[ L ,0 ]

, ( )

2P k P = , (1)

( )zck

= , .

(1)

( ) ( )00 0 0P P + = , ( ) ( ) 0LP L P L + = (2) 0 , L .

OZ( ) 0c z Const c= = , (1), (2) -

( 22 0k c = = ) ]. [14], , -,

[ L ,0

{ }n ,

=

lim

nn

nL

. (3)

{ }n , 0 0L = = , (3)

0

n

n cL

= , (4)

; 0c n .

(4) [2]. { }n , ( ) 0c z Const c= = , L

(3). ( ) Constzc (3) L , , , [1], L , . ( )c z ,

, { }n (1), (2). (1)

_________________________________________________________________________________________ . . ,

• 2007, 10 _________________________________________________________________________________________

4 (16)

( ) ( )00 0 0P P + = , ( ) ( ) 0LP L P L + = , (5) 0 0 0 .

{ }n (1), (5). [1] ,

( )c zL -

{ }n , { }n , .

1,2,...n =

{ }n , { }n , .

1,2,...n =

, [1], -, . , . [17]. [13], -

( ) { }n , 1,2,...n = . , . .

1.

( )c z c e Lz

= 0

, , [15]. (1), (2) . .

{ n} { }n , L . (1), (2)

-.

( )=z

tcdt

0 , ( ) ( )

( )zczPY 1= , (6)

; ( )Y . _________________________________________________________________________________________ . . ,

• 2007, 10 _________________________________________________________________________________________

5 (16)

( ) YYqY ~~ =+ , [ ]0, L , (7)

( ) ( )

2

0

0

2

cqL c

=

0

; . ~ = 2

(2)

( ) ( ) =Y h Y0 01~

, ( ) ( ) 0L LY HY + = , (8)

1 0 00.5h c

L = +

, 0

0.5LH c eL

= +

.

L L , (7), (8),

, (3)

lim

Ln

n

n

=

, (9)

n (7), (8).

(9), (6),

( )0 0

1 1L

tL

L e dt pc

= = , (10)

0

Lpc

= , = e .

[ ]0,x , (7), (8)

( ) [ ] + = Y q x Y Y x , 0, , (11)

( ) ( )2

21 = 4 1

L

qq x x

=

; 2

L

=

.

-. (8)

( )q x

( ) ( ) =Y h Y0 0 01 ( ) ( ) +, =Y HY 0 , (12)

( )

h hp

1 1

1=

~ ,

( )H H

p=

~ 1 ; p

(10).

_________________________________________________________________________________________ . . ,

• 2007, 10 _________________________________________________________________________________________

6 (16)

0 0L = = , (8), (10), (12)

h112

=

, H =1

2

. (13)

, (1)

01 222

=++ PPddP

dd

, (14)

z

Lpe

= . (14)

( ) ( ) ( )0 0P A J B Y = + , (15)

. ( ) (J Y0 0 , )

(11) (14) (6). (15), (11)

( )Y x AJ x BY x x=

+

0 0

12

1 1 1

, (16)

L

= .

( ),xY (16),

( ) ( ) 10, 1 , 0,Y Y = = h

)

, (17)

(13). 1h ( ,xY (12).

(11), (12) ( )R

( ) ( ) ( ), ,R Y HY = + , (18) H , (13). ( )nxY , , .

(16), (17), ,

...2,1,0=n

BA ,

( ) ( ) ( )( )( ) ( )( )

1 0

1 0

,2

,

Y x b Y b J b x

J b Y b x b x

=

(19)

_________________________________________________________________________________________ . . ,

• 2007, 10 _________________________________________________________________________________________

7 (16)

( ) ( )bYbJ 11 , ; a =

1

, b =1

.

(18),(19)

( ) ( ) ( )[ ( ) ( )]aYbJaJbYabR 11112 = . (20) (20)

{ } , 0n n

=

= 0 , ( ) ( ) ( ) ( )Y b J a J b Y a1 1 1 1 0 = , (21) , (19). ba, (19) = 0

( ) 21

0,

=

bxbxY , (22)

= =0 0 (11),(12). [13],

( )20

,n nY x dx

= , (23)

( ), nY x (11),(12). (19), (21), (23),

:

( ) ( ) ( ) ( )( ) n n n n n nb a J a Y b J b Y a=

2

12

22

0 1 1 0

2n, = 1 2 3, , .... (24)

0 ,

(22) (23)

( )100

12

b b x dx += = . (25)

_________________________________________________________________________________________ . . ,

• 2007, 10 _________________________________________________________________________________________

8 (16)

2.

085.0= . 10=L ,

50.

/ 4.29

{ }4000n n

=

,

, (21), (24), (25). 1.

{ }4000n n =

n n .

1.

n

n

n

n

n

n

0 0 3,01359204925 396 6,93642535e-07 1,57079633207

1 0,27434330e-03 1,57162227253 397 6,91895073e-07 1,57079633205

2 0,13729871e-03 1,57100315690 398 6,90156582e-07 1,57079633202

3 9,15482070e-05 1,57088827968 399 6,88426474e-07 1,57079633199

4 6,86652869e-05 1,57084805589 400 6,86705333e-07 1,57079633196

nF

Lnc

fn 20= ,

(4). n , 1,

(11) . , 2

nn

L

F

= . nnn fF = .

1n = 7.0111 = fF . 1 .

_________________________________________________________________________________________ . . ,

• 2007, 10 _________________________________________________________________________________________

9 (16)

0 100 200 300 4000

100

200

300

Hz n

n

. 1.

, ,

.

{ }4000n n

=

, { }4000n n = ,

. L ( )xq , .. -. , [1],

( )

q~4

324

2=

, (26)

( )2

L L

q q

=

.

( )Lz L = . LL z= . ( )xq , [13],

( ) ( ) ( ) ( ) (K x y F x y K x t F t y dt y xx

, , , ,+ + = 0

0 0 ) , (27)

( ),F x y ,

( ) ( ) ( )F x y x y D u D vnn

nn

, cos cos= + =

+

=

1 10

0 01 1

+ , (28)

( )D u u nunn

n =

12

1

cos cos , ( )D v v nvnn

n+ =

12

1

cos cos ,

u x y= , 0 u , v x y= + , 0 2 v .

_________________________________________________________________________________________ . . ,

• 2007, 10 _________________________________________________________________________________________

10 (16)

(27) (

x( )K x y, ,

) .

x

( ) xq

( ) ( )q x ddx

K x x = 2 , , (29)

(27). ( yxK , ) (28), (27), .

, ( )yxF , . , . [13],

:

( )q x

313 ...n

kknn n

= + + + , ...~~

2 44

22 +++=

nd

nd

n , (30)

n , n (11), (12).

, , , (30) , 1=n , (27).

2. 1 3 5 7, , ,k k k k 2 4 6, , ,d d d d8

2.

n

n2/1

1k 2,74682402284552 e-04 2d 1.67743442374836e-04

3k 3,40132335254744e-07 4d 4.61927618275191e-007

5k 9,44690448318419e-10 6d 2.1410365069608e-009

7k 8,58707037946961e-11 8d 1.65673220678243e-011 [13] , . 1k Tk

( )10

1 12T

k h H q t d

= + +

t , (31)

, 1h H (13).

_________________________________________________________________________________________ . . ,

• 2007, 10 _________________________________________________________________________________________

11 (16)

(31) . 1k

71 100% 1.8 10 %TT

k kk

.

. ,

, . 1k

( )uDn (. 28). ( )vDn+ . vu

3 513 5 ...n

k kkn n n

= + + , (32)

(30), , .

nn

uncos , (28),

cos cos cos sin sinn n nu u nu u= nu . (33)

(32), cos sin nu , nu n

( )cos n

ii

iu

c un

= +=

1 2 21

, ( )

sin ni

ii

us un

= =

2 12 11

, (34)

, , . ic2 12 is

(34)

( ) 22

12 2

uk

uc = , ( ) 4412314 241 ukukkuc += ,

( ) 6614331223516 7201

61

21 ukukkukkkuc +

+= ,

, ( ) ukus 11 = ( ) 33133 61 ukukus = , ( ) 551332155 120

121 ukukkukus += ,

( ) 7715341323152177 50401

241

21

21 ukukkukkkkukus +

+= ,

(35)

(32). 7531 ,,, kkkk

_________________________________________________________________________________________ . . ,

• 2007, 10 _________________________________________________________________________________________

12 (16)

(33), (34) n2/1 ,

( ) ( ) ( )

==

=

=

+

+

Nn

kkn

kkn

n rnnuuM

nnuuMuD cos sin=

122

1k 11212

1, (36)

Nr1ni

; ( )uM i

u . : ( )uM i

( )

+++= 1223221212 ...

1 sdsdsuM kkkk , ( ) kkkk dcdcuM 222222 ...

1+++=

, (37)

,..., 42 dd n2/1 .

[16],

=+

112

sin

nknnu ,

=12

cos

nknnu

. (36)

( ) ( ) ( ) ( ) =

+

=

+

Nkkk

k

nn ruM

uBk

uD 2!2

21-= 1k

12

1 , (38)

. ( )uBk (38), 7=k ,

( ) =

=

+ Nin

n rueuD14

0ii

1= , (39)

(37). 14,...,0, =iei . 3

(

).

ie

10 14,...,e e

3. ie

0e -0.000378324724177147 5e 5.29329003909441e-013

1e 0.00017204179135448 6e 1.42645001113616e-012

2e 2.60571505254777e-006 7e -1.54491479236586e-013

3e 3.4514805373702e-008 8e 6.98866109936978e-015

4e 4.58803525031662e-010 9e -2.26764572914655e-019

_________________________________________________________________________________________ . . ,

• 2007, 10 _________________________________________________________________________________________

13 (16)

(39) ( )vDn+ yx, ,

( ) ( ) ( ) ryxyxF ii

i += =

8

1, , (40)

r , (30). ( )xi , ( )xi

( ) =

+ =

14

2ki

2i

21 2

kikik xeCx , ( ) kk yx 21 =+ , 7,...,1,0=k , (41)

. knC

(40) r , , (27) 8 , .

( ) ( ) (=

=8

1,

iii yxfyxK ) , (42)

,

.

( )xfi

, ( )xfi , :

( )( ) ( )=

=+8

1ikikiki xxfx ( ) , (43)

ki ; . ( ) ( ) ( ) ki k ix

x y y= 0

dy

(41), ( ) ( )yy ik ( )xki x . (43) (41),(42) ( )xxK , , (29) . ( )xq ( ),TK x x ( )xxK , , (29)

(11)

( )1

1 3,8 1 8T

K x x x 1

= , (44)

, (10).

_________________________________________________________________________________________ . . ,

• 2007, 10 _________________________________________________________________________________________

14 (16)

(44) . . 2

( ) ( ) ( )( ), ,

,T

T

K x x K x xx

K x x

=

( )xxK , .

0 1 2 3 45 .10 4

0

5 .10 4

0.001

0.0015

x j( )

x j

. 2. (27)

. ( ) %106.20 7

( ) ( ) %1.0max = x . , (40) " . (29), (26).

4 10 . ( )xq

4. (26)

kz

( )kz

kz

( )kz

9.894 0.028668361 10.064 0.029140157 9.928 0.028762775 10.098 0.029234434 9.962 0.028857162 10.132 0.029328684 9.996 0.028951521 10.166 0.029422907 10.03 0.029045853 10.2 0.029517102

_________________________________________________________________________________________ . . ,

• 2007, 10 _________________________________________________________________________________________

15 (16)

4 , ( ) 028951521.0996.9 = , ,

. , 4 (

).

( ) 21 2.8963112 10L p = = L 996.9 L

% 04.0

, - . , . .

, . -. ,

- [17].

1. . . , . C XI , 2001, . 2, . 262265.

2. . ., . ., . ., .., - . . . . ., 2000, . 46, 3, . 320324.

3. . ., . ., . . -. . ., 2001, . 47, 4, . 564566.

4. . ., . ., . . . . ., 1999, . 45, 6, . 825831.

5. . . . 2064666, 1996.

6. Nyce D. S., Togneri M. G., Bulkowski R. S. Magnetostrictive position sensing probe with waveguide referenced to tip for determining fluid level in a container. US Patent 5848549, 1998.

_________________________________________________________________________________________ . . ,

• 2007, 10 _________________________________________________________________________________________

16 (16)

7. . ., . . . XI , 2001, . 2, . 265274.

8. . . , .: , 1969. 9. . ., . . , .: ,

1977. 10. . . -

. .: - -, 1989, 249 . 11. Stapleton et al. Ultrasonic liquid measuring device for use in storage tanks containing

liquids having a non-uniform vapor density. US Patent 5085077, 1992. 12. . ., . . . , , .

, 2006, 8. 13. . . -. .: , 1984. 14. . . . .: , 1984. 15. . ., . . . .: , 1989. 16. . ., . ., . . . .: ,

1981. 17. . ., . ., . ., . ., . .

- Fieldbus Foundation. , 2001, 11, . 1014.

_________________________________________________________________________________________ . . ,