242 Chuygn ddng cua tui khi trong dudng dng nam ngang
CHUYEN
D O N GCUA TUI KHI TRONG DUTOfNG ONG
N A MNGANG
Ha Ngge Hien Vien Ca hpc
TOM TAT
Bdo cdo ndy trinh bdy mdt sd kit qud ly thuyit vd md phdng sd chuyin dpng tiii khi trong duong dng ndm ngang. Kit qud ly thuyit cho trudng hgp tui khi phdng chi ra rdng van tdc tiii khi phu thupe chd yiu vdo van tdc trung binh ciia chdt long, phdn bo van tdc chi cd dnh hudng thir yiu. Md hinh sd 2D phdt triin dua trin phuong phdp phdn tie biin cho phep xdc dinh hiiu img ciia siec cdng bi mat. Cudi ciing, mpt sd kit qud ban ddu cua md hinh sd 3D dugc gidi thieu.
MdoAu
Trong ddng chay hai pha khi ldng, ddng chay che do nut ldng - tui khi la che do thudng gap trong dudng dng van chuyen cung nhu khai thac dau khi. De tinh toan cac thdng sd ddng chay d che do nay, van tde va binh dang tui khi ddng vai trd quyet dinh trong cac md hinh tinh toan. Cac thi nghiem da chi ra rang trong ddng chay phat trien hoan toan, tui khi cd van tdc khdng ddi va chi phy thudc vao ddng chay d trudc nd. Viec nghien cim chuyen ddng cua tui khi trong ddng chay che do nut ldng - tui khi do dd cd the dua ve viec nghien cuu chuyen ddng cua tui khi don ddc trong cac che do chay khae nhau cua chat ldng. Nhin chung, van tdc cua tui khi cd the bieu dien dudi dang edng thuc Nicklin (Nicklin et al, 1962):
V,=C,J,+V, (1) trong dd: JL la van tdc trung binh cua chat ldng, VQ la van tdc cua tui khi trong chat ldng
dung yen. CQ la hang sd phy thudc vao tinh chat cua chat ldng cung nhu cac tham sd khae cua ddng chay. Trong bao eao nay chung ta chi gidi ban den che do chay quan tinh khi
{VB- JL)F>IVI » 1, d day D la dudng kinh cua dng, v^ la do nhdt ddng hgc cua chat ldng.
O che do chay nay Co phy thudc gian tiep vao do nhdt cua chat ldng thdng qua phan bo van tdc cho trudc d phia trudc tui khi (Collins et al., 1978; Bendiksen, 1985).
Trong trudng hgp dudng dng thang dung, cac nghien cuu ly thuyit cua Collins et al.
va Bendiksen chi ra rang Co la ham sd phuc tap cua sd Reynolds Re = JJ)/ Vi va sd Edtvds Eo = ApgD2/o, trong dd Ap=pi-pG la hieu sd giua mat do chat ldng va chat khi, g la gia tde trgng trudng va a la sue cang be mat giua chat ldng va chat kbi. CQ thay ddi tu 2,0 den 1,2 khi ma che do ddng chay chuyen tu phan tang sang chay rdi. Sue cang be mat cd anh hudng lam giam van tdc va thay ddi hinh dang cua tui khi (Bendiksen, 1985; Ha Ngoc, 2003).
Chuyen ddng cua tui khi trong dng nam ngang bay nghieng phuc tap ban nhilu trong trudng hgp thang dung. Vin dl tui khi tilp xuc vdi thanh dng va bai toan khdng ddi xung lam cho cac phan tich ly thuyet trd nen rat khd thyc bien. Cac nghien cuu thuc nghiem (Bendiksen, 1985; Cook & Behnia, 2001; Hernandez et al., 2004) ehi ra sy phu thudc cua van tde tui khi vao van toe trung binh chat ldng cd the ehia thanh 3 vung khae
Tuygn tap bap eao Hdi nghj KHCN "30 nam D^u khi Viet Nam: Cff hdi mdi, thach thde mdi 243
biet (Hinh 1). Trong mdi vung he so Co cd the coi nhu khdng ddi: van tdc tui khi phu thudc tuyen tinh vao van toe trung binh chat ldng. Dieu do cd the eho thay rang phan bd van tdc cua chat ldng anh hudng it den van tde tui khi.
vimg II
Va (m/s)
-a
0 ^ counter-current
0.6 -
0,4 -
[5>
.4 ^|L££f^ -0,2 ; 9.3-
, ^ "
1
co-current D
^ °
^°^
0,2 0
?iom chujdn tidp vung III
JL (m/s)
(a) (b) Hinh 1: (a) Ket qua thi nghiem cua Hernandez (b) Phan viing anh hirdng
Co che chuyen tiep gida cac vung van la van de gay tranh cai. Bendiksen cho rang dieu dd lien quan den sy dich chuyen mui cua tui kbi ve tam cua dudng dng khi van tdc trung binh chat ldng tang dan va cho rang diem chuyen tiep xay ra khi sd Froude Fr^ = JJ{gD)^'^ = 3,5. Trong khi dd Cook & Behnia [6] chi ra sy tuong quan mat thiet giua diem chuyen tiep vao ndng do bgt khi trong nut ldng phia sau tui khi va de nghi mdt cdng thue tinh van tdc tui khi nhu sau:
Vg = m a x \l.OJ,+V,
[\.2J, (2)
Cdng thuc nay cho phep tinh ra diem chuyen tiep tai VB = 5,0Fo. Cd the thay rang van tdc tui khi trong chat ldng dung yen VQ cd y nghia quan trgng trong viec xac dinh diem chuyen tiep.
Tuy nhien, ket qua nghien cuu ly thuyet va md phdng sd ve chuyen ddng cua tui khi trong trudng hgp dng nam ngang hay nghieng la rat ban che. Cac nghien cuu ly thuyet cua Benjamin (1967) va md phdng sd 2D cua Vanden Broeck (1984), Couet & Strumulo (1987) va 3D cua Cook & Behnia (2001) chi gidi ban trong trudng hgp chat long dung yen.
Bao cao nay gidi thieu mdt sd ket qua nghien cuu ly thuyet md rdng phuong phap Benjamin cho trudng hgp chat ldng chuyen ddng va ket qua md phdng sd 2D va 3D dya tren phuang phap phan tu bien phat trien bdi Ha Ngoc Hien (2003) [7].
L6I GIAI L Y
THUYET CHO VAN TOC CUA TUI KHI HAI CHIEU TRONG KENH PHANG NAM NGANG
Ndi chung, ve mat binh hgc, tui khi hai chieu khdng tdn tai trong thye te do anh hudng cua sue cang be mat. Tuy nhien, trong nhieu trudng hgp anh hudng ba chieu cua hinh dang tui khi ed the bd qua. Vi dy, trong trudng hgp tui khi chuyen ddng trong kenh
244 Chuyin dgng cua tui khi trong duoTig ong nam ngang
hep vdi Eo du ldn. Dieu dd cd the dugc chung minh qua so sanh cac ket qua thi nghiem va cac nghien cuu ly thuyet cua Collin (1965) va Couet & Strumolo (1987).
Trong phin nay phuong phap Benjamin [2] dugc md rdng dl nghien cuu anh hudng cua chuyin ddng cua chat ldng len chuyen ddng cua tui khi trong kenh nam ngang khi bo qua anh hudng cua sue cang bl mat. Trong trudng hgp nay, van tdc tui khi Vg va be day cua ldp phim mdng dudi tui khi d chi phy thudc vao trgng trudng, chieu cao kenh va phan bd van tdc cua chit ldng phia trudc tui khi (Ha Ngoc Hien, 2003). Ldi giai giai tich tdng quat nhan dugc cho 3 trudng hgp phan bd van tdc: ddng cd xoay khdng ddi, ddng cd phan bd van toe parabol va ddng cd phan bd van tdc rdi. Trong trudng hgp sd Froude nhd Fri«\, ldi giai giai tich dudi dang ehudi cd dang:
Ddng cd xoay khdng ddi
~ = \-Fr, + — Fr' + — Fr,' +..
D ^ 12 12 1
4sD 2
r 5 2 1
\ + Fr, +—Fr,
V ^ 12 ^ 12 Fr,+
(3)
Ddng cd phdn bd van tdc parabol
d = \-Fr, + — Fr,^ +-Fr' +..
D ^ 20 7 F„ 1
gD
1 + Fr, + - F r '
±Fr,^^...
35 '
(4)
• Ddng cd phdn bd van tdc rdi d
D = 1 + d,Fr^ + d^Fr^^ + d^Fr^^ +.
V. 1 , _ „ „ 2 . . . ^ 3 (5)
trong dd
= -+V,Fr,+V,Fr,+V,Fr:+....
gD 2
, _ 45n' (2ra -^ 3) -h SOn{n -l){2n- l)r + {n-1)' {32n^ +2n + S)/'^
20{2n + 3)(4ra -F 1)[(3 - r)n + y]
V =-d ' 2 '
n va ^la tham sd cua phan bd van tdc rdi (Bendiksen, 1985).
Cd the nhan thay rang cac ldi giai tren chi khae nhau d he sd cua sd hang thu 3 (he sd ttr FrL trd len). Nhu vay, phan bd van tdc chi can thiep vao ldi giai tu sd hang bae 2 trd len. So sanh van tdc cua tui khi trong cac trudng hgp phan bd van tdc khae nhau dugc trinh bay tren Hinh 2. Cd thi nhan thiy ring anh hudng cua phan bd van toe chit ldng len van tdc tui khi la rit nhd.
Tuygn tap bao cao Hdi nghj KHCN "30 nam Dau khi Viet Nam: Co hdi mdi, thach thde mdi" 245
0.8-
--- xoay khong doi
— phan bo parabol - - phan bo rol
0.2 0J25 J,/(gD)'
Hinh 2: Van toe tiii khi trong 3 trudng hop phan bo van toe chat long
ANH HirONG CUA SlTC CANG BE MAT: M O PHONG SO CHUYEN DONG CUA TUI KHI HAI CHIEU TRONG KENH
P H A N G N A MNGANG
De tinh den anh hudng cua sue cang be mat va do nghieng cua kenh, mdt phuong phap sd md phdng chuyen ddng cua tui khi hai chieu da dugc phat trien cho trudng hgp chi do quan tinh cua ddng chay khi anh hudng cua do nhdt cd the bd qua. Phuang phap nay giai he phuong trinh Ole hai chieu vdi mat bien ty do. Ldi giai cho phep nhan dugc ddng thdi hinh dang va van tdc cua tui khi. Phuong phap cd the dugc md ta tdm tat nhu sau:
Ddi vdi ddng chay phang khdng nhdt, xoay van tdc cd gia tri khdng ddi tren dudng ddng va ddng chay dugc md ta bdi phuong trinh Poisson cho ham ddng y/:
fM (6)
vol
Aif/ ••
f(\l/)^-(0
trong dd o) la xoay van tdc,/la ham sd dugc xac dinh bdi phan bd van tdc chat ldng phia trudc tui khi.
Phuang trinh xac dinh hinh dang tui khi nhan dugc tu phuong trinh Bernoulli va dieu kien ap suat Kelvin-Laplace tren mat phan each chat ldng -'tui khi:
duj . r ^t s-i 1 dH ^
sin[a + ^{5)J + - — - - = 2t^/
Eo ds ds (7)
trong dd: a - gdc nghieng cua kenh, 9 - gdc nghieng cua mat phan each, H do cong trung binh va M/ la van tdc tren mat phan each. Sd Eotvos Eo bieu thi anh hudng cua sue cajfig be mat.
Phuong trinh (6) va (7) dugc giai ddng thdi trong mdt vdng lap su dyng phuong phap phin tu bien kit hgp vdi phuong phap sai phan hdu ban (Ha Ngoc, 2003). Ldi giai sd trong trudng hgp chat ldng dung yen va trong trudng hgp bd qua anh hudng cua sue
246 Chuyin dgng cua tui khi trong dudng dng nam ngang
cang bl mat (fo-^oo) dugc so sanh vdi cac ldi giai ly thuyit va cac ldi giai sd khae cho kit qua phu hgp dugc trinh bay trong [7, 8].
Anh hudng cua sue cang be mat va van tde trung binh cua chit ldng len van tde va hinh dang tui khi dugc trinh bay tren Hinh 3 va 4. Trong trudng hgp tui kbi hai chieu he sd Co tang tu 0,5 din xip xi 1,0 khi Eo giam din tu Eo = 1000 din Eo = 10. Dieu do chung td ring anh hudng cua van tdc trung binh chat ldng tang khi sue cang be mat tang.
1.2
0.8
tf 0.6
0.4
0.2
0
••—loi giai giai tich - - Eo=1000
- Eo=IO
-Eo=vo cung Eo=100
0.05 0.1 0.15
JJ(gD)'
0.2 0.25 0.3
Hinh 3: He so Co phu thuoc vao sire cang be mat
Hinh 4: Hinh dang tui khi phu thuoc vao liru lucmg chat Idng
M O T SO KET QUA M O PHONG SO CHUYEN
D O N GCUA TUI KHI 3D TRONG DUonVG ONG
Md phdng sd chuyen ddng eua tui khi 3D trong dudng dng trong dudng ong nim ngang hay nam nghieng cd nhieu van de phuc tap can phai giai quyet. Vl mat binh hgc:
mat phan each ed cau tao phuc tap, dae biet la phan dinh cua tui khi noi cd dudng tilp xuc giua chat ldng va thanh dng, yeu ciu cac thuat toan xu ly bien ddng rat phuc tap. Vl mat md hinh toan: chua cd cac kit qua ly thuyit thich hgp ve dieu kien bien tren dudng tilp
Tuyen tap bao cao Hdi nghj KHCN "30 nam Diu khi Viet Nam: Co hgi mdi, thach thde mdi" 247
xue 3 pha khi - long - ran. Gan day Cook va Behnia (2001) da su dyng phuang phao so VOF de nghien cuu chuyen ddng cua tui khi trong dudng dng nam ngang va nghieng, trong dd anh hudng cua thanh dng len mat phan each dugc cho bdi gdc tiep xuc cho trudc ma thye chat cac gdc tiep xuc dd phy thudc vao tinh chat vat ly cua cac pha, hinh hgc va ddng lyc mat phan each (Kafka & Dussan, 1979). Ngoai ra, phuang phap VOF coi chuyin dgng eua tui khi nhu la lan truyen ndng do va vi the viee xu ly cac dieu kien tren mat phan each edn chua dugc thda dang. Ket qua cua Cook va Behnia cung ehi gidi ban trong trudng hgp chat long dung yen.
Trong phan nay chung tdi trinh bay md hinh sd 3D dya tren phuong phap phin tu bien md phdng chuyen ddng cua tui khi trong dudng dng nam ngang va nghieng trong chat ldng dung yen. Phuong phap nay cd the cho phep thda man cac dilu kien bien tren mat phan each mgt each chinh xac. Tuy nhien, cung gidng Cook va Behnia, anh hudng cua thanh dng len mat phan each dugc eho bdi gdc tiep xuc cho trudc (Ha Ngoc Hien &
Fabre, 2004b). Phuong phap cd the tdm tat nhu sau:
Chuyen ddng khdng xoay cua chat ldng ly tudng cd the duge md ta bdi phuong trinh Laplace cho the van tdc cp:
d'cp d^cp S V r.
dx- dy^ 5z' (8)
Mat phan each duge xac dinh bdi 2 gdc: gdc 0 - gdc nghieng cua mat phan each dge theo true ddi xung (Hinh 5) va gdc /? - gdc nghieng cua mat phan each tren mat phang {Zp, yp) di qua diem A cd dinh (Hinh 5, 6). Dieu kien bien tren mat phan each thu nhan dugc tu phuong trinh Bernoulli va dieu kien gian doan ap suat Kelvin-Laplace:
^x 2 5 / / , du, sm.\a + 0)-\ =
ic
2M ,Eo ds, sin(y9)sin(7 - a ) -
5.S,
2 OH _ Eo ds.. • 2uj
du, ds..
(9)
Hinh 5 : Xac djnh goc 6 tren mat phang doi xirng
Hinh 6 : Xac djnh goc P tren mat phang
(yp, Zp)
248 Chuygn ddng eua tiii khi trong du-dng ong nam ngang
He phuong trinh (8) - (9) dugc giai ddng thdi dl thu nhan rp, 0 va fi. Phuong trinh Laplace (8) dugc giai bing phuong phap phin tu bien cdn cac phuong trinh (9) dugc giai bing phuong phap sai phan huu ban. Van tdc eua tui khi dugc xac dinh tu dieu kien bien ap dat gdc t»ep xue 6Q tai dinh cua tui khi.
20
3"
CO
0.6 -
0 . 5 -
0.4-
0 . 3 -
0 . 2 -
0.1 -
n -
•
^^^y^
•
•
•
thi
•
nghiem -tinh toan
•
Zukoski
•
•
40 60 goc nghieng
80
Hinh 7: Su phu thuoc van toe tiii khi vao do nghieng dirdng ong
0.6
0.5
0.4
I 0.3
0.2
0.1 thi nghiem Zukoski
•tinh toan
I I I I I 1 1 1 1
1 10
I I I I I I I l | I I I I I I
100 Eo
1000 10000
Hinh 8: Sir phu thudc van toe tiii khi vao sire cang be mat
Tuyen tap bao cao Hgi nghj KHCN "30 nam Dau khi Viet Nam: Cff hgi mdi, thach thde mdi" 249
Hinh 9: Ludi tinh toan vdi gia thiet mat phan each nam ngang trong mat eat vudng goc vdi true ong
Chuong trinh may tinh bang ngdn ngu FORTRAN da dugc thilt lap dk thuc hien thuat toan ke tren. Mdt thuat toan chia ludi thich nghi don gian da dugc thilt lap dl xac dinh hinh dang tui khi (Ha Ngoc Hien & Fabre, 2004b). Cac phuang an chay thu nghiem da chi ra rang chuong trinh tinh toan khdng hdi tu trong trudng hgp anh hudng cua sue cang be mat la dang ke. Khi anh hudng cua sue cang be mat cd the bd qua {Eo > 1000), mat phan each cd the coi nhu nam ngang trong mat cat vudng gdc vdi true cua dng. Trong trudng hgp nay, chuang trinh hdi tu va cho ket qua phu hgp vdi thyc nghiem. Tren Hinh 7 trinh bay sy phu thudc cua van tde tui khi vao do nghieng dudng dng vdi Eo = 4000. Ket qua tinh toan phu hgp tdt vdi ket qua thi nghiem cua Zukoski. Sy phy thudc cua van tdc tui khi vao sue cang be mat trong dudng dng nam ngang dugc trinh bay tren Hinh 8. Cd the nhan thay rang sy sai khae giua tinh toan va thyc nghiem cang tang khi anh hudng cua sue cang be mat tang {Eo giam). Rd rang la gia thiet mat phan each nam ngang trong mat cat vudng gdc vdi tryc dng la khdng phu hgp khi anh hudng cua sue cang be mat ldn. Nhu vay, anh hudng cua sue cang be mat ddi hdi mdt thuat toan chia ludi tinh te ban. Mdt vi du chia ludi tinh toan trong chuong trinh tinh dugc trinh bay tren Hinh 9.
KET LUAN
Van tdc tui khi la mdt thdng sd quan trgng trong md hinh tinh toan cac dac trung thuy lyc cua ddng chay hai pha trong dudng dng. Cac thi nghiem chi ra rang trong dudng dng nam ngang van tdc tui khi it phy thudc vao phan bd van tdc chat ldng ma phy thudc chu yeu vao luu lugng chat ldng.
Bao cao da trinh bay mdt sd ket qua nghien cuu chuyen ddng cua tui khi trong trudng hgp 2D va 3D trong dudng dng nam ngang. Cac nghien cuu ly thuyet 2D da chi ra rang anh hudng cua phan bd la nhd. Ket qua md hinh sd 2D cho phep nghien cuu anh hudng cua sue cang be mat len van tdc va hinh dang cua tui khi. Ket qua ban dau cua md hinh 3D phu hgp vdi thyc nghiem. Tuy nhien, kha nang iing dung cdn ban chi. Phat triln md hinh 3D ddi hdi nhung thuat toan xu ly hinh hgc phuc tap hon va cac nghien cuu ly thuyet ve anh hudng cua thanh dng len do cong cua mat phan each.
250 Chuyin dgng cua tui khi trong dudng dng nam ngang
TAI LIEU T H A M K H A O
1. Bendiksen K.H., 1985. On the motion of long bubbles in vertical tubes. Int. J.
Multiphase Flow 11, p. 797 - 812.
2. Benjamin T.B., 1967. Gravity currents and related phenomena. J. Fluid Mech. 31, p.
209 - 248.
3. Collins R., De Moraes F.F., Davidson J.F., Harrison D., 1978. The motion of a large gas bubble rising through liquidfiowing in a tube. J. Fluid Mech. 89, p. 497 - 514.
4. Collins R., 1965. A simple model of the plane gas bubble in a finite liquid. J. Fluid.
Mech. 22, p. 763-771.
5. Couet B., Strumulo G.S., 1987. The effects of surface tension and tube inclination on a two-dimensional rising bubble. J. Fluids Mech. 184, p. 1 - 14.
6. Cook M., Behnia M., 2001. Bubble motion during inclined intermittent fiow.
International Joumal of Heat and Fluid Flow 22, p. 543 - 551.
7. Ha Ngoc Hien, 2003. Etude theorique et numerique du mouvement de poches de gaz en canal et en tube. These, INPT, France.
8. Ha Ngoc Hien, Fabre Jean, 2004a. Test-case number 29B: The velocity and shape of 2D long bubbles in inclined channels or in vertical tubes (PA, PN) - Part II: In a fiowing liquid. Multiphase Science and Technology,Vol. 16, Nos. 1 - 3, p. 189 - 204.
9. Ha Ngoc Hien, Fabre Jean, 2004b. Simulation numerique d'une poche isolee dans un canal ou dans tube. Rapport IMFT-Interface.
10. Hernandez Gomez A., Fabre J., Ha Ngoc H., 2004. Infiuence of velocity distribution on the motion of long bubbles in tube. 5"^ International Conference on Multiphase Flow, ICMF'04, Yokohama, Japan, May 30 - June 4, 2004.
1 I.Kafka F.Y., Dussan V.E., 1979. Interpretation of dynamic contact angles in capillaries. J. Fluid Mech. 95, p. 539 - 549.
12.Maneri C , Zuber N., 1974. An experimental study of plane bubbles rising at inclination. Int. J. Multiphase Flow 1, p. 623 - 645.
13. Nicklin J., Wilkes J.O., Davidson J.F., 1962. Two phase flow in vertical tubes. Trans.
Inst. Chem. Eng. 40, p. 61 - 68.
14.Vanden-Broeck J.M., 1984. Rising bubble in two-dimensional tube with surface tension. Phys. Fluids 27, p. 2604 - 2607.
15. Zukoski E.E., 1966. Influence of viscosity, surface tension, and inclination angle on motion of long bubbles in closed tubes. J. Fluid Mech. 25, p. 821 - 837.
