Khảo sát hiệu quả của tấm phẳng điều khiển dòng chảy qua tiết diện cầu bằng phương pháp số

iv

TÓM TT

D
 
 
  

thích xoáy và 

. 
          
.

v

ABSTRACT

The study of the aerodynamic stability of long-span suspension bridge is very
important in design state. One of control methods is to change the flow over the
bridge deck, so that the aerodynamic forces will be changed. This study investigates
the effectiveness of control surface attached to bridge deck by using the immersed
boundary method. The results show that the values of the aerodynamic forces are
reduced after controlling the control surfaces.

vi

MỤC LỤC




 i
 ii
 iii
 iv
ABSTRACT v
 vi
 viii
 ix
DANH SÁCH CÁC HÌNH x
Chương 1. TỔNG QUAN 1
 1
 2
 4
1 5
Chương 2. TỔNG QUAN V PHNG PHÁP BIểN NHÚNG 6
Chương 3. PHNG PHÁP BIểN NHÚNG CHO BIểN CỨNG 8
 8
 9
 9
 10
-stokes 11
 11
 12
 13
vii

 14
 16
 18

 19
Chương 4. CU TRÚC HÀM DIRAC DELTA 21
Chương 5. KT QU TệNH TOÁN 26
 26
 28
Chương 6. KT LUN VÀ HNG PHÁT TRIN 42
 42
 43
 44
THE 2012 INTERNATIONAL CONFERENCE ON GREEN TECHNOLOGY
AND SUSTAINABLE DEVELOPMENT 45
NUMERICALLY STUDY EFFECTIVENESS OF CONTROL SURFACE ON
AERODYNAMIC OF BRIDGE DECK BY USING IMMERSED BOUNDARY
METHOD 46
INVESTIGATING THE FLOW OVER BRIDGE DECK CONTROLLED BY
CONTROL SURFACES BY USING IMMERSED BOUNDAY METHOD 51


viii

KÝ HIU KHOA HC


        
kk
YXtsYtsXts ,,,,, X

c cho bi t cm
trên biên


t hàm c dài cung s và thi gian t-1

   
 
tsFtsF
yx
,,,F
là lc biên (boundary force density)

        
kk
VUtsVtsUts ,,,,, U
là vn tc ci Lagrangian

   
 
tftf
yx
,,, xxf 
là lc vt th c tích h-Stokes

 
yx,x
là t i Eulerian

      
tvtut ,,,, xxxu 
là vn tc ct ( theo 2 chiu x, y)

 

tp ,x
là áp sut ct.


là khng riêng ct


 nht
 u* là vn tng vn tc)
 p là gradient áp sut.

là toán t Laplace


 (.t ký hic dùng : (

.) thay vì
(vi grap,div c s dng trong toán t laplace)
 L
b
là chiu dài cng cong khép kín Γ
 

  

, 


= 


  



y  Y

là hàm Dirac Delta.


2
2
2
2
yx














yx
grap





,
+=∇.=
yδ
δ
xδ
δ
div
ix

DANH SÁCH CÁC BNG

Bng 5.1:  27
Bng 5.2:  27
Bng 5.3: C
D
37
Bng 5.4: C
L
38
Bng 5.5: C
M
40

x

DANH SÁCH CÁC HÌNH

Hình 1.1:  2
Hình 1.2:  3
Hình 1.3:  3
Hình 1.4:  3
Hình 2.1:  6
Hình 3.1:  
 10
Hình 3.2:  13
Hình 4.1:  25
Hình 5.1:  26
Hình 5.2: θ=30
0
26
Hình 5.3:  α là 0
0
28
Hình 5.4: t = 6.6s 31
Hình 5.5:  α = 0
0
33
Hình 5.6: θ=30
0
α = 0
0
33
Hình 5.7: α 37
Hình 5.8:  α 39
Hình 5.9:  α 40

1

Chương 1
TỔNG QUAN

1.1 GII THIU CHUNG
D 
 thì

  
, 
     ,        
. M 
  V
               . Thí
, 






     


           

Dynamics--Structure Interaction-


(Immersed Boundary Methods - 

2


 




Tron        

. 

1.2 LCH S NGHIểN CỨU TRONG VÀ NGOÀI NC

          ichi MIYACHI, Masahiro
YONEDA và Katsuya EDAMOTO.
  
ình 1.1

Hình 1.1: 

 b = 20 mm. Thí
θ θ = 30
0

và góc θ = 45
0
.
3


Hình 1.2: 

 
là u 
 là α = + 3
0
.

Hình 1.3: 


Hình 1.4:  có  

, ba 

4


.
θ = 30
0

.
3. 

dC
M
/ dcác thí 


moment dC
M
/ d.

1.3 PHNG PHÁP BIểN NHÚNG IBM




cho quá trình tính toán.



               
            
Method).




, thì 
    

5


 







 

, t


1.4 NHIM VỤ CỦA LUN VĂN
Các :
- V  tính toán, 
   tính toán và

- Tính âng 
.
- 

-   .
- 
 
 

6

Chương 2:
TỔNG QUAN V PHNG PHÁP BIểN NHÚNG
IMMERSED BOUNDARY METHOD (IBM)

2.1 PHNG PHÁP BIểN NHÚNG
à  
ng tác

làm 
 P
                
Largange.

Hình 2.1: 

 


range





7

 IMB  công    

            Euler và Largange, có liên
quan   ng trình  tác. T  các     rac
Delta  




 S 
là c             

 T



8

Chương 3
PHNG PHÁP BIểN NHÚNG CHO BIểN CỨNG

3.1 PHNG TRỊNH ĐNG LỢNG
 
 
 di . Các
              



ng khép kín

(Hình 3.1a). 

     :
 
,,tsX
,0
b
Ls 

   
tLt
b
,,0 XX 
.  
b
L
là


, và
 
ts,X
là hàm vector 


s t. 
 f  Navier-Stokes.
 Navier-Stokes   


. , 
. ng


( )
fuuu
u
+=∇+.∇+
∂
∂
μpρ
t
ρ
(3.1)
0 u
(3.2)

 
yx,x
và
 
YX,X
,
      
tvtut ,,,, xxxu 
 và
 
tp ,x
là
. 

và



. 
     
 
tftft
yx
,,,, xxxf 
hay
      


 dststst ,,, XxFxf

(3.3)

9


     
 
tsFtsFts
yx
,,,, F
         biên nhúng và
      
YyXxts 

,Xx
là hàm Dirac delta. 


 
         





xXxxuXuU
X
dtstttsts
t
ts
,,,,,
,

(3.4)
 (3.3) và (3.4) . Trong
(3.3)  
 (3.4) .

  
ts,Xx 

( 4)
  
1, 


xXx dts


(3.5)
     
0,, 


xXxXx dtsts

(3.6)
  X 

X
.

        
 
 
 dstsddststsdt ,,,, FxXxFxxf

(3.7)
3.2 PHNG PHÁP SỐ
3.2.1 Rời rc không gian vƠ thời gian.
 nhúng -
 
 
3
.1b.       :         
Eulerian,  Lagrangian.

10


],0[],0[
yxf
ll 
và
yx
NN 

Eulerian 
yx
hhh 
, và
yyxxyx
NlNlhh // 
. 
u
ij
     u    (i,j).    
b
N
 
Lagrangian (
bb
NLs /
).  F
k
  F
 k.  k Lagrangian  X
k
. 

              
   
tn
n
 ,xuxu
và
   
tnss
n
 ,XX
.
a) b)
Hình 3.1: a)   
. b)  Eulerian (ch
sáng)  Lagrangian ()
3.2.2 Gii vt th


 
 



b
N
k
k
n
ji
n

jih
n
k
n
ji
st
1
,,,
XxFf

(3.8)

 
x
h

là  Dirac, delta.
 














h
y
h
x
h
h

2
1
x
(3.9)


 :

11

 
 
 

















r
rrrr
rrrr
r
2,0
21,412725
8
1
10,44123
8
1
2
2

(3.10)
 NavierStokes 

1
,
n
ji
p
  

1
,
n
ji
u
    

[3]. 

 



ji
n
kjih
n
ji
n
k
n
k
hdtd
,
21
,
1
,
11
/ XxuUX


(3.11)
3.2.3 Gii h phương trình Navier-stokes
 Navier-Stokes 
 ( (3.1)-(3.2)) là
 









0u
fuuu
u

p
t
(3.12)

























































































0
2
2
2
22
2
2
2
22
y
v
x

u
f
y
v
x
v
y
v
x
uv
y
p
t
v
f
y
u
x
u
y
uv
x
u
x
p
t
u
y
x



(2.13)
Chúng ta tìm 
 
st
n 1
:
3.2.3.1 X lý phi tuyn đ nht
C

12

 





















0
1
1
1
1
1
n
n
n
nnnn
n
p
t
t
u
uu
fuuu
uu



(3.14)
3.2.3.2 Hiu chnh áp sut
T (

u
)  gradient 

1n
p

.
1
1
1





n
n
p
t

uu
(3.15)

1n
p
, :
11
111






nn
p
tt

uu
(3.16)
 (

) 
:
11
111





nn
p
tt

uu
(3.17)



 u
t
p
n

11
1

(3.18)
(
0
1

n
u
)
  Poisson cho 
1n
p
 
 
st
n 1
.   
 
st
n 1
.
 Bước 1: Tính

 uF

 
nn
vu ,

.
 Bước 2:  Poisson (3.18)  
1n
p
.

13

  3: 
 
11
,
 nn
vu

11 



nn
p
t

uu


1n
p
.
3.2.3.3 Lưi so le

 Navier-Stokes, t
f

  
 p  u 
  v 
.
Xét
yx
nn 
    p,  u và v  
     .      

 . Nh 
3.2   , trong khi
.

Hình 3.2: 

14

3.2.3.3.1 Đo hƠm xp x
 Đạo hàm cấp 2

ji
u
,
 Laplace:
2
1,,1,

2
,1,,1
,
2
2
2
2
,
22
h
uuu
h
uuu
y
u
x
u
u
jijijijijiji
ji
ji




















(3.19)
2
1,,1,
2
,1,,1
,
2
2
2
2
,
22
h
vvv
h
vvv
y
v
x
v

v
jijijijijiji
ji
ji



















(3.20)
 Đạo hàm bậc nhất

h
uu
x
u

jiji
ji
2
,1,1
,











(3.21)

x
u



ji
u
,
, 

ji
u

,1
và
ji
u
,
. :
h
uu
x
u
jiji
ji
,,1
,
2
1












(3.22)
 Thành phần phi tuyến (sai phân trung tâm)

 
.  uv 
 u và v . 
 u, chúng t
xu  /
2
và
yuv  /
.
, 
. 
2
u

, và uv .

15

 
2
,1,
,
2
1
2
2













jiji
ji
uu
u
(3.23)
 
2
1,,
2
1
,




jiji
ji
uu
u
(3.24)
 
2

,1,
,
2
1
jiji
ji
vv
v




(3.25)
 v. 
.  x 
,   
y 
:
 
y
vu
x
u
t
uu
xyx










2
(3.26)
 
y
v
x
vu
t
vv
yxy









2
(3.27)

   
   
2

2
2

2
,1,
2
1
,
,1,
2
1
,
,,1
,
2
1
,,1
,
2
1
jiji
ji
y
jiji
ji
y
jiji
ji
x

jiji
ji
x
vv
v
uu
u
vv
v
uu
u
















(3.28)
 Thành phần phi tuyến (sai phân tiến)


  v 
 h là quá thô.  
 .              
  
. S

16

∈ [0, 1]
:




1,max,maxmax2.1min
,
,
,
,
ji
ji
ji
ji
vut 

(3.29)
 γ 
 1.2,  1.  1.2 

[3].


:
   
   
2
~

2
~
2
~

2
~
,1,
2
1
,
,1,
2
1
,
,,1
,
2
1
,,1
,
2
1

jiji
ji
y
jiji
ji
y
jiji
ji
x
jiji
ji
x
vv
v
uu
u
vv
v
uu
u

















(3.30)
.26) và (3.27) :
 
 
 
y
uvvu
x
uuu
t
uu
yxxyxxx









~~
2


(3.31)
 
 
 
y
vvv
x
vuvu
t
vv
yyyxyxy









~~
2

(3.32)
  
 
3.2.3.3.2 Điu kin biên
 

chúng. , 

u  v . 
 . Biên phía

17

  u. 
ji
u
,
và
1, ji
u
, 

N
u
. :
NORTHjijiNORTH
jiji
uuuu
uu
2
2
1,,
1,,




(3.33)

SOUTHiiSOUTH
ii
uuuu
uu
2
2
1,0,
1,0,


(3.34)
EASTjijiEAST
jiji
vvvu
vv
2
2
,1,
,1,




(3.35)
WESTjjWEST
jj
vvvu
vv
2
2

,1,0
,1,0


(3.36)
 Điều kiện biên không trượt
0
0
,,,
,,,


SOUTHNORTHEASTWEST
SOUTHNORTHEASTWEST
v
u
(3.37)
 Điều kiện trượt tự do

tiêu cùng v:























0
0
00
0,
1,
,1,0
SOUTH
iSOUTH
NORTH
jiNORTH
jiEAST
EAST
jWEST
WEST
v
uu
v
uu

vv
u
vv
u

(3.38)
 Điều kiện dòng chảy ra

:































0,
0,
1,
1,
,1
,1
,0
,0
iSOUTH
iSOUTH
jiNORTH
jiNORTH
jiEAST
jiEAST
jWEST
jWEST
vv
uu
vv
uu
vv

uu
vv
uu

(3.39)
 Điều kiện dòng chảy vào

18



3.2.3.3.3 Phương trình Poisson
  Poisson            
gian.         Laplace.
           .   
, 























11
11
2
1
121
121
1
1
a
a
h
K

(3.40)
 a
11

Dirichlet (
2
11
a
):
































2
0
2
1
2
0
0
2
21
2
11
1
2
210
11
00
2
2
2
2
h
g
f
h
uu
h
g
f
h
uu

f
h
guu
f
h
uug
gu
gu
N
NN
N
NNNNN
(3.41)
Neumann (
1
11
a
):














































N
NNNNNN
N
NN
N
N
f
h
uuu
f
h
uuu
hguu
hguu
g
h
uu
g
h
uu
g
x
u
g
x
u
2
11

1
2
210
11
120
11
1
02
1
1
2
2
2
2
2
2