Dong nai bSng mo hinh toan so 1 va 2 chieu

ruyen tap Cdng trinh Hpi nghi Khoa hpc

Vffhpc Thuy khi Todn quoc, Phan Thiit, 2008 141

Tinh toan dong chay mang song Sai gon - Dong nai bSng mo hinh toan so 1 va 2 chieu

Le Song Giang, Nguyen Thj Phuong Dai hoc Bdch khoa, DHQG-HMC

Tom tdt. Bdl bdo trinh bdy vicjc tinh todn ddng chdy trong mang sdng Sal gon - Ddng nai bdng md hinh todn sd ket hap mat vd hai chieu. Phuang trinh Saint - Venant I vd 2 chieu dugc gidi theo phuang phdp the tich hiru han, trong do phuong trinh Saint - Venant 2 chieu dugc gidi cho cdc doan sdng quan trgng diing lirdi phi cdu true. Ket qud tinh dd duac kiem chdng vdi sd lieu do thuc te.

Abstract This paper presented the calculation of flow in the Saigon - Dongnal river network using combined ID and 2D numerical model. ID and 2D Saint - Venant equations are solved hy finite volume method. In wich 2D Saint - Venant equations are solved for major braches using unstructured grid. Computational results have been compared with field data.

1. Gioi thieu

Ddng chay trong mang sdng thudng dugc md hinh hoa thanh bai toan I chieu. Ly do la vi cd sir chcnh lech rat Idn giira chieu dai va chieu rdng sdng va su udn lugn phire tap ciia cac nhanh sdng. Tuy vay, tinh toan ddng chay nay bang md hinh 2 chieu hoac 3 chieu, cd le, la udc mudn cua khdng it ngudi trong gidi nghien ciru thiiy luc. Rd rang viec sir dung md hinh nhicu ban I chieu cho phcp thay ddng chay trong mang sdng rd net hon (sy khac biet ddng chay giiia 2 bd, ddng chay tai khu virc hgp luu va tai cac dgn cong,..) va dac biet cho thay ddng chay mot each loan bg, khdng chia cat. Dieu nay cd y nghia rat Idn trong nghien cuu cac bai loan mdi trudng, dicn bicn long dan,., ciia mang sdng,

Muc dich cua bai bao nay la trinh bay mdt sd ket qua ban dau linh loan ddng chay trong mang sdng Sai gdn - Ddng nai bang md hinh 2 chieu, ket hgp vdi md hinh 1 chieu cho cac nhanh sdng it quan trgng. Cac phuong trinh Saint - Venant 1 va 2 chieu dugc giai theo phuong phap the tich hiiu ban. Tai mat cat ndi bai md hinh, hai ddng chay lien ket vdi nhau ca bang muc nude lan van tdc. Ket qua tinh da dugc kiem chimg vdi sd lieu do thyc te.

2. M o ta m o hinh toan so

2.1 Phuong trinh cff bdn

Ddng chay trong sdng, nlu coi la 1 chilu, duoc md ta bdi phuang trinh Saint - Venant

dt ds

dQ^ d_

dt ds

^ dr\ . \Q\Q n. (2) ds K

142

Tinh todn ddng chdy mang sdng Sai Gdn-Ddng Nai hdng md hinh todn sd 1 vd 2 chieu Ddng chay trong sdng, neu coi la 2 chieu, dugc md ta bdi phuang trinh Saint - Venant 2 chieu:

dt dx dy ccj ^ rf(q) ^ cg{q]

ct ex cy = b(q]

0)

(4)

Trong dd:

q - muc nuoc;

Q, A va K - luu lugng, dien tich mat cat udt va module luu lugng cua ddng chay 1 chieu; q = [q^, g J = D\] - vector luu luang don vi cua ddng 2 chieu;

U = [z/,, u J - vector van tdc trung binh chieu san;

Z) - do sau;

f{q) = q^U ~ A^DcVldx va g(q) = g ^ U - A ^ ^ D r U / r y - vector thong lugng cua luu lugng don \i phuong x va y;

b(q)^

cx p p •' dy p p

-17"

- vector ngudn;

/ - tham sd Coriolis;

Twx va Ti„ - hai thanh phan ung suat tiep tren mat nude do gid;

Thx va Thy - hai thanh phan img suat ma sat day, dugc tinh thco cdng thirc Manning:

^ft-v ^fc-v I gn'

1 / 3

AH - he sd nhdt rdi, dugc tinh thco cdng thuc Elder [3]:

A„ =eu,D

Vdi u. - van tdc ma sat {ui = t ^ / p ); n - he sd nham Manning,

2.2 Phuang phdp gidi

Cac phuang trinh (1) - (4) dugc giai theo phuang phap thi lich hiru han va da dugc trinh bai trong lai lieu [1,2]. Phuang phap giai cd thi tdm tat nhu sau.

Ddng 1 chieu

Sdng dugc chia doan tinh nhu hinh H I . Dicn tich mat cat udt Aj o thdi dicm n+1/2 duac

(5)

(6)

^ / i-I

Hinh II. 1 Sa do doan sOng

fgSong Giang, Nguyen Thi Phuong 143

^'nh khi tich phan (1) tren the tich kiem soat ASj A n - i - l / 2

A;-"-^^^te..-.-<?;,-J

_As ⁽⁷⁾

Muc nude tai cac miit cat d thdi dicm linh loan dugc xac dmh tir quan he A=f(r^. Tich 'i)han (2) tren thi tich kiem soat la doan sdng 6Sj, la dugc dugc luu lugng o thdi dilm n + 1:

w

Q;:U2=-

^1.2-f" N i l -v9)^g^v^ki"-^r'1.

fa\

i+/^g4:v2\^.v^H^:^lff

⁽⁸⁾

(9a) (9b) Ddng 2 chieu

Miln linh 2 chieu ciing dugc chia thanh cac phin tir lir giac phi cau Iriic nhu tren hinh H.2, Muc nude dugc tinh tai cac nut cdn luu lugng don vi dugc tinh tai dicm giira canh cua cac phan tu, Tich phan (3) tren dien tich kiem soat xung quanh nut C (hinh H.3), ta dugc bilu thuc cho muc nude tai niit nay:

Con tich phan (4) tren dicn tich kicm soat xung quanh canh ict (hinh H,4), la dugc bilu thuc cho luu lugng don vi trong he tga do dia phuang tai canh nay:

Hinh H.2 LuM tinh 2 chieu

- -Vitri tinh q; O - Vi tri tbih T)

Hinh H.3 Dien tich kiem sodt ciia r\ Hinh 11.4 Dien tich kiem sodt cua q

144

Tinh todn ddng chdy mgng song Sdi Gdn-Dons Nai bdns md hinh todn sd l_yd_2 chieu

Q c "

'q^,+A/.F-|XF„jq"),]/il + ..AO (11)

Vdi

s -

g'^'

D

^2.333

Qx + 9?

r =

(12a)

(12b)

^gD^yl^yfq,

C:S p

-gD^ + '^-fq, ob p

Hinh H.5 Sadd ket ndt 1D-2D Kit ndi ddng I chieu vd ddng 2 chieu

Hinh H.5 la so dd kit ndi 2 md hinh. Nut J cua md hinh 1 chieu noi vdi mat I - I ciia mo hinh 2 chilu. Muc nude tai nut J va tai cac nut tren mat cat 1 - 1 dugc gia thiet bang

nhau va dugc tinh lu phuang trinh bao loan the lich: •

^r"-^r"

^{A^}

| 9 n 2 ^ ^ - Z ^ ^ "

1,2

.J (13)'

I

Vdi S - tdng dien tich nut J va dien tich cac nut 2D tren mat cat 1 - 1. Thanh phan tiep tuyln vdi mat cat 1 - 1 cua luu lugng don vi dugc gia thict bang khdng, cdn thanh phan phap tuyen dugc ndi suy vdi gia thiet van tdc phan bd deu:

X Q r + |<7.2^s

/,,,,

D.

2A,

⁽¹⁴⁾

3. Tinh toan dong chay trong mang song Sai gon - Dong nai

Hinh H.6 la so do ludi tinh mang sdng Sai Gdn - Ddng Nai. Cac kenh rach trong phan md hinh 1 chieu dugc chia thanh 1218 doan tinh vdi 1422 mat cat va 164 nut. Cac sdng rach chinh la sdng Sai Gdn, Ddng Nai, Nha Be, Vam Cd, Long Tau va viing bien d cua sdng dugc chia thanh 4700 phan tir tir giac vdi 5635 nut. Be ngang sdng ludn cd 4 phan tii. Dia hinh Idng sdng tham khao tir tai lieu cua Vien KHTL Miln Nam, cdn dia hinh day bien dugc lay theo Hai dd cua Hai Quan.

Dieu kien bicn cho bai loan dugc thiet lap nhu sau. Luu lugng chay vao cac niit thugng luu phan md hinh 1 chilu dugc dp dat:

Q-f{t) (15) Myc nude thiiy trieu dugc ap dat cho cac nut tren bien ngoai biln cua phhn md hinh 2D:

^^foit.s) (16) Muc nude thuy tricu nay dugc linh tir cac hang s6 thuy trilu cua Vung lau. Ngoai ra, tai

bien nay cdn can them 1 dieu kien bicn dao bam cho cac thanh phSn phap va tiip tuyln cua

luu lugng don vi:

r..

l£Song Giang, Nguyen Thi Phirang 145

dqJdn=Q va dqjcn = 0

(17)

^-^* -\ T'"

. ^ - . . - : . ' ^ • > - , ' ^ "

V --•

!

C-'

i ' . '• -

<•')

r. -

BI

1' ,'

- ))

200000 320000

46000-

162000 laOOO 1S6000 190000 192000 194000 196000 19BOO0

a) Todn bd luai tinh b) Ludi tinh doan sdng Nhd be Hinh H. 6 Ludi tinh he thong sdng rach Sdi gdn - Ddng nai Tren bien cimg ciia md hinh 2

chilu, khdng cd luu lugng chay xuyen qua va luu lugng dan vi tiip tuyen vdi bien truot tu do:

dqjdn =0

(18a) (18b)

120000-

100000

80000-

60000-

40000-

20000

Tinh toan dugc thuc hien cho khoang thdi gian 5 ngay (tir 26/12 tdi 31/12/1993) vdi budc thdi gian At=3,6s va m4t 100 phut tren may Laptop HP520 (Core 2 Duo l,83Ghz).

Hinh H.7 la trudng vector van tdc tren toan bg mang sdng vao thai diem trilu xudng. Hinh anh chi tiet ddng chay tai mot sd nai tren mang song dugc trinh bay tren cac hinh H.8 va H.9. Dien biln muc nude va luu lugng tai mot sd vi tri tren mang sdng dugc cho tren cac hinh H.IO va H.ll.

Nhin chung kit qua tinh kha phii hgp . . r^ u,„ ^uk ^k <:A lieu vdi sd lieu do cua Vien KHTL Miln Nam [4] trong ciing thai gian. Do ban che n?

do nen viec danh gia kit qua tinh van tdc dilm da khdng the thyc hien dugc.

140000 160000 180000 200000 220000

Hinh H 7 Ddng chay trong mgng sdng

[46

1 tun luurt uorig criuy mcirig SOng Sai Gdn-Ddns Nai bdng md hinh todn sd lyygj^dlliu

59000n

58000-

57000-

56000-

55000-

54000H

53000-i

52000-1

51000

50000

49000

- : * *

\ yt '^is\s'^

186000 187000 188000 189000 190000 191000 192000

aJ Luc trieu len

186000 187000 188000 189000 190000 191000 192000

h) Luc trieu xudng Hinh H.8 Ddng chay Iren sdng Nhd be

25000

20000

15000

190000 195000 200000 205000 210000 215000 220000

Hinh H. 9 Ddng chay tai cdc cira sdng liic tridu rut

[pSons Gians. Nguyen Thi Phmrns 147

E

E

N

E

N

2.0 i- ^{, L _}

-2.0

E

N" 0

I]

-1.0 l' -2.0-1 0 24 48 72

Sd gid tir lOg ngdy 28/12/1993

0 24 48 72 24 So gid tir 1 Og ngdy 28/12/1993 Hinh H 10 Mac nude tai mdt sd diem tren mang sdng

a) tai Bien hod tren s. Dong nai: b) tgl Cat lai tren s. Ddng nai;

c) tgl mid Den do tren s. Sdi gdn; d) tgl Vam Idng ir cira s. Sudi rap (Dudng lien - tinh todn , Symbol - do dac f4]j

600 a) 5000 b)

^ 300

CO

E 0

„

O -300 -600 8000 -i2 4000

CO

E 0 C -4000

• • • '. . . ••

•• •

• • . • • . • . . . • / . *

C) .-. A A

. • • •

• • • • •

• • • • •

/ V V

,w 2500

CO

E 0 O -2500 .

-5000 8000 -i2 4000

CO

E 0 O -4000 .

. \ .N

A

V

d)

A •

W

-8000 -8000

Q 24 48 72 Sdgid tir lOg ngdy 28/12/1993

0 24 48 72 Sd sid tir lOg ngdy 28/12/1993 Hinh If 11 Lint luang tai mot sd mat edt tren mgng song

a) tgl Fhu an tren s. Saigon: b) tgl ngd ba Den do Iren s. Saigon;

c) tgl Cdt Idl tren s. Ddng nai; dj tgi Fhirdc khanh tren s. Long tim (Dudng bin - tinh todn ; Symbol - do dgc f4])

5. K e t l u a n

K i t qua tinh toan thir nghiem ddng chay trong mang sdng rach Sai Gdn - Ddng Nai co do chinh xac kha tdt, ddng thdi toe dd tinh loan ciing kha cao. Dicu nay cho phep ket luan vice sir dung md hinh loan k i t hop 1 va 2 chilu trong linh loan ddng chay cua mang song rach cho cac img dung thuc t l la hoan loan hicn thuc. Kcl qua linh eiing cho ihay uu diem md hinh 2 c h i l u la thSy d u a c cSu true chi tilt cua ddng chay; md phong dugc sy tuang cua mo

linh toan dong chdy mgng song 148 Sdi Gdn-Ddng Nai bdng md hinh todn sd I vd 2 chieu tac sdng bien va cac ycai id lac dgng khac; ddng thai giai quyll duac cac khd khan phat sinh lien quan tdi dieu kien bien tai cua sdng khi diing md hinh thuan tuy 1 chieu.

Loi cam on

Bai bao da dugc hoan thanh vdi su bd trg kinh phi cua Hdi ddng Khoa hge Tu nhien.

Cac tac gia cung cam an GS. Nguyen An Nien da cho phcp sir dung cac sd lieu dja hinh sdng va sd lieu do dac trong bai bao.

Tai lieu tham khao

[I] Le Song Giang, Tran Thi Ngoc Trieu, "Md hinh hdn hop 1 vd 2 chieu cho ddng chdy lii "

TTCTKH llgl nghi Ca hge todn qudc idn thd VIII, Ha Noi, ngay 06 - 07/12/2007, Tap 3. Ca ' hoe thuy khi, trg 149 - 160

[2] Le Song Giang, Tran Thi Ngoc Trieu, "Md hinh ddng chay 2 chieu nude ndng dimg phirang phdp the tich hiru han tren ludi phi cdu triic " TTCT Hdi nghi Khoa hoc Ca hoc Thuy khi Todn

qudc ndm 2007, Hue. ngay 26 - 28/7/2007. trg 1 6 9 - 1 7 8 .

[3] Hervouct, J, M, "Hydrodynamique des ecoulcments d surface lihre: modelisation numerlque ';

avec la methode des elementsJinis. " Edition Press de rEcole Nationale des Fonts et Chaussees, = Paris, 312(2003). .

[4] Phu luc ket qua do dac thiiy van - chat lugng nude tren he thong song Sai gon - Dong nai. Vien ; Nghien ciru Klioa hoc Thiiy Igi Nam bo, (1994), " " ' i