Mô hình tính Gió, áp suất, nhiệt độ, độ ẩm trong khí quyển

MUC LUC
Mddau
4
Chirang
I: Tong quan ve
tinh
hinh nghien
curu
mo hinh khi
tuong
7
1.1. Tinh
hinh
nghien
cihi a nude
ngoai 7
1.1.1.
Phucfng
trinh thuy
tinh
8
1.1.2.
Phuong
trinh phi thuy
tinh
10
1.2. Tinh hinh nghien
cihi
of Viet Nam 11
Chirang II: Xay dung mo hinh toan 12
2.1.

He toa
d6
trong khi
tucmg
12
2.2.
Cac
lire
tac dong trong khi
quye'n
13
2.2.1.
Cac
luc
khoi 13
2.2.2. Cac
lire
mat 15
2.2.3.
Phucfng
trinh chuyen dong
ciia
khi
quy^n
17
2.2.4.
Phuong
trinh lien tuc 18
2.2.5.
Cac phuong trinh chuyen dong roi trong khi quyen 19

2.2.6. Cac phucfng trinh van chuyen nhiet va am 23
Chuang
III: Thuat toan giai mo hinh 28
3.1.
He phucfng trinh
cdban
28
3.2. Qua trinh tinh toan cho mot bucfc
thdi
gian At 30
3.3.
Phan
ra he phucfng trinh va tinh van
toe
thing
dung
30
3.4. Thuat toan tinh
trucmg toe
do (u, v, w) va ap
lire
P 32
3.4.1.
Sai phan hoa he phuong
Ulnh
(3.13) de xac dinh
u^^^^
va
p^^^^ 32
3.4.2. Sai phan hoa he phucfng trinh (3.14) de tinh

v^^^
va
p^^^
36
3.4.3.
Sai phan hoa phucfng trinh
(3.14)'
tinh
w^^^
38
3.4.4. Xac dinh trucmg nhiet do, do am 39
3.5.
Xac dinh dieu kien ban dau va bien 44
3.5.1.
Dieu kien ban dau 44
3.5.2. Dieu kien bien 45
3.6.
M6t
so phuong phap noi suy cho dieu kien ban
d^u,
bien
trong
md
hinh 45
3.6.1.
N6i
suy ham mot bien 45
3.6.2. Noi suy tuyen tinh ham hai bien 46
3.6.3.
Phucfng phap binh phucfng toi

thi^u
47
3.6.4.
Ndi
suy cac yeu
to
khi
tuong theochieu
cao 47
3.6.5.
N6i
suy ham bien d6i c6 chu ky 48
3.7.
Xac dinh he so
K 49
3.8.
Xac dinh cac ye'u t6 khi tuong trong
Icfp
bien khi
quyin
satmatd^t
50
Chirang
IV:
X^y
dung chuang trmh tinh va
umg
dung mo
hinh thur
nghiem cho mot khu

vuc
cu the 55
4.1.
Chucfng trinh tinh 55
4.2.
Tinh toan
ki^m
dinh mo hinh 58
4.3.
LJig
dung mo hinh thu nghiem tinh cac yeu to khi tucfng khu
vuc d6ng
b^ng
BSc
Bo va viing
bi^n
ke
c^n
vao
miia
dong 65
4.3.1.
Di^u
kien tunhien khu vuc nghien cuu 65
4.3.2.
Cac du lieu
ddu
vao va ke't qua tinh 67
Ket
luan

va khuyen
nghj
77
Tai lieu tham khao 78
Phuluc
80
MdDAU
Hien nay, mang
lu6i
quan
tr^c
khi tucfng
a
nude ta thua
thot.
Viec
cung
c^p
cac
thdng
tin khi tucfng (gio, ap
susit,
nhiet do, do am) gap rat nhieu
kho
khan
cho boat dong san
xua't,
tinh cac thong so moi
trucfng
khac: tai trong

gio,
song
bi^n,
dong chay gio, Thong thucfng tinh toan cac thong so khi
tuong
dira
vao cac tram quan
trdc
khi tucfng
Ian
can roi noi suy theo cac ham
tuyen tinh hoac da
thiic
hoac trung binh c6 trong
lugng
hoac phuong phap
binh phucfng toi
thi^u
Chua dap
umg
yeu cau do chinh xac cao. Can xay
dung mo hinh toan
dCng lire
khi quyen, giai bai toan nay cho nghiem la cac
tilling
khi tucfng
m6i
c6
the'
dap

img
do chinh xac, mat
dO
th6ng tin du day,
phan bo 3 chieu trong khong gian.
Qua trinh van dong khi quyen la qua trinh het
sire phiic
tap,
gay
nen
boi
nhieu nhan to khac nhau. Tuy vay, no cung phai tuan theo cac qui
luat co
hoc:
bao toan
khdi
lugng,
bao toan dong lugng va nang lugng.
Nhcf
cac quy
luat nay ngucfi ta da xay dung
dugc
mo hinh toan hoc mo phong dugc cac qua
trinh van dong
ciia
khi quyen. Day la bai toan
Idn,
phirc
tap ma the gidi da va
dang giai

quye't
ngay cang hoan thien cho
tirng
khu vuc
v6i
qui mo khac nhau.
De'n
nay,
b nu6c
ta bai toan nay chua dugc nghien cuu nhieu va chua
xay
dung dugc mot bo chucfng trinh rieng tinh cac
tmong
khi tugng day
dii
ma
chi CO
mot so chucfng trinh nhap
tir nu6c
ngoai ve.
V6i ly
do tren,
chiing
toi xin dang ky lam de tai luan van tot nghiep ve
va'n de nay,
bucfc
dau giai bai toan khi tugng, xay dung mot bg chucfng trinh
tinh:
truong
gio, ap

suat,
khi quyen, nhiet do, do am khong khi c6 nghiem
bang so vcfi cac thong so ban dau va bien cho
tmac
cung mot so he so roi.
De dat dugc muc tieu tren, de tai can giai quyet cac nhiem vu sau:
- Thu thap cac thong tin
co
so ve
xay
dung mo hinh toan mo phong
cac qua trinh van dong khi quyen.
- Thu thap cac mo hinh khi tugng.
- Danh gia, phan tich cac mo hinh,
lua
chon mo hinh thich hgp
d^
giai.
- Xay dung thuat toan giai.
-
Vie't
chucfng trinh tinh
- Hieu
chinh
va
ki^m
nghiem mo hinh qua mot so so lieu thuc te'.
- Danh gia do tin cay mo hinh va kha nang
van
dung vao thuc te'

Pham vi noi dung cua de tai chu ye'u tap trung vao nghien
cihi
thuat
toan giai mo hinh, ky thuat lap chucfng tnnh tinh, bu6c
ddu
giai quyet va'n de
Icfp
bien sat
d^t,
kie'm
nghiem mo hinh
v6i
mot so so lieu gia dinh va thuc te'.
Pham vi vung nghien
cihi
la mot so vi du cu the tinh
tmdng
gio, ap, nhiet, am
cho mot
ph^n
dong bang Song Hong va vung bien ke can.
So lieu dung tinh thu nghiem mo hinh ve dia hinh dugc thu thap
tir
ban
do dia hinh ty
le
l/10^
c6 tham khao them ban do dia hinh
1/2.10^
va so lieu

khi tugng
tir
cac tram: Ha Noi, Hung Yen, Hai Duong, Hong Gai (Quang
Ninh),
Van Li (Nam Dinh), Hon Dau, Bach Long
VT
(Hai Phong) thuoc
Tdng
cue
Khi tugng Thuy van quan ly.
Bd
cue luan van gom phan mo dau, ke't luan, tai lieu tham khao, phu
luc va 4 chucfng, cau
true
nhu sau:
- Mo dau.
- Chuang I: T6ng quan ve tinh hinh nghien cuu mo hinh khi tugng.
- Chucfng II: Xay dung mo hinh toan.
- Chucfng III: Thuat toan giai mo hinh.
- Chuang IV: Xay dung chuang trinh tinh va ung dung mo hinh thu
nghiem cho mot khu vuc cu the.
- Ket luan va khuye'n nghi.
Luan
van
nay da dugc hoan thanh tai Phong Co hoc bien, Vien Co hoc,
Trung tarn Khoa hoc Tu nhien va Cong nghe Quoc gia
vdi sir giiip
do va
hudng dSn
tan tinh ciia PGS.TS. Tran Gia Lich. Hoc vien xin dugc bay to long

bie't an
sau
sac
nh^t t6i
thay giao
hudng
dSn.
Trong qua trinh thuc hien, hoc
vien con nhan dugc su quan tarn, tao moi dieu kien thuan
Igi
cua
lanh
dao
Phong, Vien Ca hoc, Trung tarn dao tao va boi
duSng
Co hoc va nhieu y kien
dong gop qui bau cua cac giao su, tie'n sT, cac thay -
c6
giao, cac nha nghien
cihi,
cac ban dong nghiep
d
nhieu ca quan, t6
chiic
khoa hoc khac. Nhan dip
nay, tac gia xin dugc bay to long bie't an chan thanh doi vori nhiing
sir
giup
dd
quy do.

CHlfONG
1
TONG QUAN
vt
TINH HINH NGHIEN
ClTU
MO HINH KHI TUONG
Nghien
cihi
mo hinh khi tugng da c6
\\x
lau,
phuong phap so tri giai he
phuang trinh dong luc hoc
\in
dau tien dugc Richardson de
xuaTt
vao nhung
nam 1920. Do khdi lugng tinh toan rat
lofn
cung
vdi
cac thong tin trang thai
ban
d^u
khong
diy
dii (mang
lucfi
quan trac khi tugng thua

theft,
chua c6 quan
trac cao khong), phuang phap nay luc
ba^y
gi5 chua c6 hieu qua. Co the noi
giai cac m6 hinh khi tugng gan lien vcfi
sir
phat
tri^n ciia
may tinh. Vai thap
ky gan day nhieu the' he may tinh sieu tdc ra
d6i,
bai toan khi tugng da va
dang dugc giai ngay cang hoan thien dap
img
yeu cau nghien cuu khi quyen
va du bao thdi tiet.
LI.
Tinh hinh nghien
ciiru
a
nude
ngoai
O My, cac nude Tay Au nghien cuu mo hinh khi tugng
ra't
phat trien.
Co nhieu mo hinh khi tugng da dugc xay dung mo phong kha day
dii
cac trang
thai khi

quye'n
vai cac quy mo khac nhau. Chang han mo hinh GME (Global
model European), da mo ta va du bao cac trucfng khi tugng: ap sua't, gio, nhiet
do,
do am, cho cac khu vuc tren pham vi toan cau
vdi
31
Idp
do cao va
ludi
khong gian khoang 60 x 60 km,
ihcfi
gian du bao 6,12 gid. Mo hinh HRM co
do phan giai cao
ciia
Cong hoa
lien
bang
Dire,
mo ta va du bao cac yeu to khi
tugng khu vuc trong 24, 48 gia dap ung vcfi cac yeu cau
ciia
cac bai toan
Ian
truyen 6 nhiem khong khi, tinh toan hai van, nong nghiep, Mo hinh GME
ket hgp vdi HRM, tinh GME
lam
bien cho HRM ket qua kha tdt. Hai mo hinh
tren da va dang thu nghiem de mo phong va du bao cac truang khi tugng tai
khoa Khi tugng Thuy van,

Tmdng
Dai hoc Khoa hoc Tu nhien - Dai hoc Qudc
gia Ha Noi.
Nhieu nha toan hoc thuoc vien Han lam khoa hoc Nga (Lien X6 cu) da
nghien cuu cac mo hinh khi tugng trong bai toan
Ian
truyen
6
nhiem
khi
quyen, dien hinh nhu G.I.
Martriic,
B.B. Peneko, A.E.
Aloian,
Rat
nhieu
cdng
trinh nghien
clJu m6
hinh tinh
trudng
khi tugng da dugc cong bd trong
cac tap chi khoa hoc.
Su
CO
mat cac phucfng trinh tham gia trong he phucfng trinh dong luc
khi
quy^n
trong [4, 5, 6, 7, 8, 9], chung toi c6
th^

phan ra 2
loai
mo hinh khi
tugng sau:
-
M6
hinh thuy
tmh
dai dien nhu cua Australia, Nga (qui mo
c5
trung binh).
-
M6
hinh phi thuy tmh (qui mo ca trung binh).
1.1.1.
Phuang tnnh thuy
Snh
[9]:
Phucfng trinh thuy tmh dugc dua vao he, he phuang trinh ca ban viet
trong tga
d6
D^
cac:
(
dw
d\x
ifdn 5u » 1 5p 5 , 5u 5 , 5u
\
d\x
—

+
u — -pf-—+ w fV = ^ + — kh — + — kh — +
T^
d\. d\
dy dz
pdx
5x 5x 5y 5y
p
5z
dv dv dv dv
^ ldpd,dvd,dvld
—
+
u—
+
v—
+
w—
+
fu = - + —
kh—
+ — kh — + Tyz
dt
d\
dy dz p
5y dx
dx.
dy dy p dz
1 dp
-—= -g

P dz
^ + —(ptO
+ — (pv)
+
—(pw)
=
0
dt dx dy dz
de
dQ
—
-hu
—
at dx
dy
dQ d
dQ
dQ d
, 56
+
—k»,
— +
-hu —
+
v^
+ w — = —kjh — + —k^i . .vt2
dz dx dx dy dy dz dz
dQ
dt
rad

dt dx dy dz dx
"^^^
dx dy
"^^^
dy dz
'^'-
dz
trong dd: u, v, w la thanh phan tdc do theo cac
true
x, y, z
p la ap
sua^t
khi quyen
p la mat do khong khi
9
la nhiet do the vi
(1.1)
8
kh
la he so roi theo chieu ngang
j
k^
la he s6
rdi
theo chieu thing
ddtig /
ky^kt2
la he sd khuyech tan nhiet theo chieu ngang va thing
diing
kqh,

kq^
la he sd khuye'ch tan am theo chieu ngang va thing
dimg
T„,
Ty2
la ten xa
thig
suat, rdi theo chieu ngang va thing
dutig.
f la thong sd luc coriolis
dQ
dt
la thanh phan nhiet b6 xung hay mat di
rad
Cac nghiem
cdn
tim: u, v, w, 0, q, p.
D^
giai he phuang trinh (1.1)
c^
cac
dilu
kien sau:
Dieu kien ban dau:
- Dua vao muc dia hinh so vdi mat bien va dac tinh be mat
(d6
nham,
albedo,
d6
am be mat, tinh cha't da't, ).

- Dua ap
su^t
be mat va
profil
cua gid, nhiet
(tir
bdng tham khong).
Gid phai dugc phan anh trudng do cao dia the vi bdi cac ban do 850, 700, 500
mb,
Nhd profil noi suy dugc cac gia tri ban dau, ap sua't noi suy qua phuang
trinh thuy
tinh.
Dieu kien bien:
- Tai z = 0 van tdc gid bang 0, nhiet do nude
bi^n
la hing sd, nhiet do
mat dat dugc tinh bang phuang trinh can bang nhiet, giai phuang trinh sau:
dT ,
d^T
dt
'
dx'
trong dd:
k^
la he sd truyen nhiet, T la nhiet do da't.
- Bien tren cao, d do cao 8500 -
19700
m thi coi p = 0, q = 0, p = 0
- Bien hong: —
=

— = — = 0
dn
dt\
dn
Thong thudng dau tien giai ludi
thd,
sau dd
la'y
ket qua ludi thd lam
dieu kien bien cho ludi tinh. Mo hinh LADM thay z =
CT
=
p/po
1.L2.
Mo hinh phi thuy
finh
[8]:
He phuang trinh viet trong tga do De cac:
d\x d\x dw
di\
I
dp
,
d
dii
— + u — + v —
+w—
= ^ + lv + —
v^
—-i-zlu

dt dx dy dz p dx dz dz
dy
dw dw dw \ dp , d dw
^
—
+
u—
+
v—-i-w—
=
^-lu-i-
— Vy — -i-Av
^
dx dy dz p dy dz dz
dw dw
dv^
dw
I
dp d dw
,
— + u — + v —
-hw—
= ^-g + — V7 —
+ Aw
dt dx dy dz p dz dz dz
^
dJ dJ dJ dT
fy
/\dp
d

dT ,^
—
+
u —
+
v—
+ w 'y -^ =
—V.—
+
AT + e
dt dx dy dz
y /PEJ
dt
5z * az
~^-f-
—
(pu)
+
—
(pw)
—
(pw)
=
0
at 5x ay
az
P = pRT
,
d d d d
A=

—p^
—-I-
— p
—
dx dx dy ' dy
trong dd: T la nhiet do khong khi.
Yn
la gradient
nhiel
do
Irong
moi trudng doan nhiet
8 la lugng nhiel bd xung
p,
V
la he sd rdi
iheo
chieu nim ngang va thing dung.
Cac ky hieu
kliac luang ly
nhu tren.
6
day giai he phuang tnnh trong
he
toa do cong:
t,
=
I;
X2
= x;

y,
= y; a =
(/
-
/o).H
/ (H -
z^)
H la
chi^u
cao
Idp
bien tmh,
7^,
la do cao
dja
hinh.
Cac dieu kien ban dau va bien
lucfng lu
nhu mo
hinh
thuy
tTnh.
Hai mo hinh tren la nhung md
hinh
khi tugng rat ca ban, mot sd md
hinh khac trong [4, 5, 6, 7] da
IIICMH
cac
Ihanh
phan khac cho

phii
hgp
hcfn
dieu kien md phong thuc te.
10
1.2. Tmh hinh nghien curu mo hinh a Viet Nam
O Viet Nam, nghien curu giai mo hinh khi tugng con ra't it. Du bao
nghiep vu khi tugng chu yeu bang phuang phap sindp. Cac phan mem giai md
hinh khi tugng chii yeu dugc nhap
iix
nude ngoai, nhu GME, HRM, LADM,
TCLAPS, KBR, HOMACH,
ciia
chau Au,
Diic,
Uc, My. Viec su dung cac
phdn
mem cua nude ngoai cd nhieu thuan
Igi,
nhung cung khong it khd khan:
chucfng trinh chay theo
mdt
qui each nhat dinh khd sua chua theo y mudn, mot
sd chuang trinh nhu HRM
dix
lieu dau vao
ti^
Cong hoa Lien bang
Diic
cung

c^p,
mdt sd chucfng trinh budc ludi tinh qua
Idn,
G^n
day, mot sd cong trinh nghien
ciiu
md hinh khi tugng tai hoi thao
md hinh du bao khi tugng cua khoa Khi tugng thuy van thuoc trudng Dai hoc
Khoa
hgc
Tu nhien - Dai hoc Qudc gia Ha Noi nam 2002 vdi cac tac gia:
- Ths. Nguyen Minh Tudng: Ap dung md hinh chinh ap
ciia
Krishnamurti vao du bao trudng dudng dong dan muc 700 mh va
irng
dung du
bao
quT
dao
ciia
bao.
- TS. Phan Van Tan: Ky thuat phan tich xoay va kha nang ung dung
trong du bao dudng di
ciia
bao bang md hinh chinh ap.
Md hinh tinh cac yeu td khi tugng bien [10].
11
CHlfONG II
XAY DUNG MO HINH TOAN
2.1.

He toa do trong khi tugng
Trong khi tugng ngudi ta thudng chgn he tga do oxyz nhu sau:
Gdc tga dd la
di^m
0 nao dd tren trai
da^t,
true
Ox hudng theo
vT
tuyen
tir
hudng Tay sang hudng Dong, true Oy hudng theo kinh tuyen
tir
hudng Nam
len
hudng Bic, con
true
oz hudng theo chieu thing
dutig
ti^
dudi
len
tren. Nhu
vay khi chie'u vec ta tdc do c len he tga do nay ta dugc cac thanh phan
ti'en
true Ox, Oy, Oz
l^n
lugt
la u, v, w. Khi nghien curu chuyen dong khi quyen
ngudi ta thudng chu y de'n cac thanh phan u, v, w cua van tdc c la ham

ciia
tga
do
X,
y, z va thdi gian t.
u = V (x, y, z, t), V
= V
(x, y, z, t), w = w (x, y, z, t).
Chung ta da bie't dao ham toan phan
ciia
dai lugng
f
nao dd dugc bieu
dien dudi dang:
df
af af af af
—
=
—
+
u—
+
v—
+
w—
(2.1)
dt
at
ax
ay az

af
. ,
Trong khi tugng: — dac trung cho bien doi dia phuang theo thdi gian,
at
(u — + v
) duac goi la bien
ddi
binh
luu,
\^—
duac goi la bien doi ddi
dx dy) ' ' dz ' '
luu
ciia
dai lugng
f.
De cho ggn ta cd the viet:
— = —
+ (c.V).c
dt
a
trong do: V
= i
—
-i-j
—
-hk
—
ax ay
at

i,
j,
k la cac vec ta dan vi
Vdi cac ap dung tren (2.1) viet cho u, v, w:
12
'
du
au au au au
=
H-U
H-V
H-W
dt
at
ax
ay
az
,
dv
av
dw dw dw
< =
H-U
+
V
+
W
dt
at
ax

ay
az
dw aw aw aw aw
=
H-U
+
V
+
W
^
dt
at
dx dy dz
(2.2.)
y
2.2.
Cac luc tac dong trong khi quyen
Khi
quy^n
cd
th^
xem nhu la mdt dang ciia moi trudng lien tuc, cac
luc tac dong len nd bao
gdm
hai loai ca ban: luc khdi va luc be mat.
2.2
J.
Cac luc khoi (cdn goi
Id
luc the tich)

Dd la luc tac dong len mdi yeu td khdi lugng (hay mdi yeu td the tich)
ma diem dat
ciia
nd khong phu thuoc vao vi tri ben trong hay ngay tren be mat
ciia
yeu td khao sat. Cac
lire
khdi trong khi quyen bao gdm: trong luc, luc
li
tam va luc coriolis. De thuan
Igi
ngudi ta thudng khao sat cac
lire
khdi dan vi
nghla
la luc khdi tac dung len mdt dan vi khdi lugng.
2.2.1.1.
Trong luc g
Trgng
lire
g la thanh phan phap tuye'n tong hgp
ciia
2 luc:
lire hiit
cua
trai da't hudng vao tam (ki hieu
la
F) va luc li tam
(F^)
hudng theo ban kinh

vec ta:
g=
Fn+Fln
(2.3)
trong dd
F„
la thanh phan phap tuyen
ciia
F va
Fj,,
la thanh phan phap
tuye'n
ciia Fj
(xem hinh 2.1), xet ve gia trj:
g =
F„
- F,„ (2.4)
Chinh g la gia tdc trgng trudng.
Tir
hinh 2.1 ta tim duac:
13
w
F„=k —cosy
a"
Fjn
=
Fj coscp
=
co'a
coscp'

coscp
trong dd: k = 6,67.
10"^
cW
g'^s"
la
hang sd
h^ip
dan, a la khoang
each txx diim
P de'n tam trai dat,
M la khdi lugng trai
da^t,
CO
= 7,29.
10'^
s"^
la tdc do quay cua
trai
d^t,
(p la
vT
dd dia ly,
cp'
la
vT
do
dia tam cdn
7 =
9-9',

vi
y
ra't nhd cd the
Hinh
2.1.
Tinh trong luc g
coi cos
Y
= 1 va
9
= 9; thay a bang ban hinh trai dat R dugc:
g = K
—;-
-
CO
R cos
9
R'
(2.5)
tir
(2.5) tha'y g phu thuoc vao
vT
do dia
ly
va do cao so vdi mat
nude
bien. Neu
tinh g d
vT
do 9 =

45*^
tren
nude
bien bang 980.2
cm/s".
Nhin chung
lire
ly tam
nhd han ra't nhieu so vdi
lire
hut
ciia
trai
da't,
gia
tii Idn
nhat dat dugc d xich dao
vao khoang 3,4
cm/s'.
Chieu g len cac
U'uc
tga do
g^
=
gy
= 0 cdn
g^
= -g.
2.2.1.2. Luc Coriolis
Khi mdt vat the chuyen dong tren be mat trai da't, nd phai chiu tac

dong
ciia
gia tdc tuang ddi (gia tdc coriolis) do
sir
quay cua trai dat quanh true
ciia
nd
gay
nen. Luc coriolis la luc quan tinh, nd
chi
tac dong len phan tu dang
chuyen dong trong tmdng hgp chuyen dong dugc xet trong he tga do gin chat
vdi trai da't quay.
Neu ki hieu k la
luc
coriolis tac dong len mot dan vi khdi lugng, co la
tdc do quay
ciia
trai dat quay
true
va c la van tdc vat the, ta cd:
k = -2 (cox c )
Chieu len cac
true:
k^
= 2
(co^v
-
co^w)
k^,

= 2
(co^w
-
w^u)
k^
= 2
(uco,.
- vco
J
(2.6.)
(2.7)
14
Trong he tga dd khi tugng ta cd:
co^^
= 0,
co^
=
COCOS9,
co^
=
cosin9
Khi dd:
k^
= 2vco
sin9
- 2. wco
eos9
ky
= -2uco sin 9
k^

= 2uco cos 9
Iq
ve gia tri nhd thua trgng luc tdi 10000
Mn,
do dd cd the bd qua. Do
vay vai trd quye't dinh cua luc coriolis ddi vdi chuyen dong khong khi chinh la
cac thanh
ph^n
k^
va
ky.
Trong thuc te' u, v
Idn
han rat nhieu so vdi w, cho nen
2wco
COS9
cd
th^
bd qua. Ne'u ky hieu
1
= 2co
sin9 ggila
thong sd luc coriolis,
nhu vay thanh
ph^n
k^, k^
dugc viet
lai:
k,
=

Iv,
ky =
-lu (2.8)
2.2.1.3.
Luc ly tam
Luc ly tam xua't hien khi chuyen dong cua khdng khi cd quy dao cong.
Neu ban kinh cong
ciia quT
dao la
r,
tdc do chuyen dong tai mot diem nao dd
la c thi luc ly tam la:
F,
=cj/
(2.9)
2.2.2. Cac luc be mat
Dd la nhiing luc dac trung cho
sir
tac dong tuang hd giua mot the tich
khdng khi khao sat vdi mdi trudng xung quanh. Ddi vdi khi quyen
lire
nay
gom cd:
lire
gradient khi ap va luc ma sat nhdt.
1-2.2.1.
Luc gradient khi dp G.
Luc gradient khi ap sinh ra do su phan bd khdng deu cua ap sua't. Luc
nay tac dong len mot don vi khdi lugng khdng khi dugc xac dinh.
G

= gradp (2.10)
P
trong dd p la mat do khdng khi, p la ap sua't khi quyen, dau - la luc G
ludng tir
nai ap sua't cao den thap. Chieu (2.10)
len
cac
true
tga do:
G^
=—— ,
O,
-—— ,
O,
=—— (2.11)
p
ax
p
ay
p
az
15
2.2.2.2. Luc ma sat nhdt
Luc ma sat dugc gay ra bdi
sire
cang nhdt (cac ung suat nhdt). Neu ky
hieu cac
siic
cang nhdt bang
a^.Gy,

a^
thi
lire
ma sat nhdt ddi vdi 1 dan vi khdi
lugng dugc
hiin
dien dudi dang:
f =
1
da^
do^
da
dx
+
ay
az
^
(2.12)
Luc ma sat chieu len cac
true
toa dd:
fx =
5a^
^
5ay.
da
^
(2.13)
trong dd
a^^,

Gyy,
c^^
'^ ^'^^
thanh phan phap tuyen, cdn
a^^, a^^, a,,^,
c^,
a^y,
Gy^
la cac thanh phan tiep tuyen
ciia
ten xa ung sua't
nhcit.
Trong thuy
dong
lire
hgc ngudi ta da chung minh dugc cac ding thuc sau [2,3]
/
2
^. ^ ,
au
^xx
= }idivC+2)a
—
3 dx
>7
=
—jiaivC+2|u—
3 ay
^zz
= |^divC+2|i—-

3
az
(2.14)
^XV
=
^VV
=
1-^
^au
av^
av
dx
^vz
=^vz
=M
dw dw
—
+ —
az
ay
\
J
^V7
=<^7X=^
(dw
dw^
— +
—
V
dx dz

16
trong do
ji
la he so
nhdt ciia
chat long
thav
(2.14) vao (2.13)
dugc:
L
=-v—(divc)
+ vAu
"
3
ax
fy
=-v^^(divc)
+vAv
1 a
-V
—
3 dy
1
8
L
= -
V—(dive)
+
vAw
'

3
5z
ti'ong
dd
V
=
—
la he sd nhdt dong hoc cdn
A
= —-
+
—- + —-
viet
p
'
ax^
ay^
az^
ggn lai qua phucfng trinh vec ta;
f =
-vgrad dive
+ vAc (2.15)
3
2.2.3.
Phuang trinh chuyen dong cua
khi
quyen
Neu coi khi quyen la chat long nhdt va dua vao dinh ly bien thien
dong lugng ta cd the bieu dien phuang trinh chuyen dong
ciia

mdt dan vi khdi
lugng khdng khi dudi dang vec ta long quat sau:
Ac
—
=
g + K + G
+
f (2.16)
dt
^
Ne'u chuyen dong la cong:
de
—
=:g
+ K
+
G+f+F,
(2.17)
dt
^ '
Xac dinh g theo
(2.5),
K theo
(2.6),
G theo
(2.10),
f
theo
(2.15)
va ap

dung cho
(2.17)
dugc:
de 1
V
—
=
g-2(coxe)—gradp-H
- grad
dive +
vAc (2.18)
dt p 3
chieu (2.18) len cac
true
tc)a do:
17
•
du
1
ap
\
V
^
/J-
\
A
—
=
i-
+

2(co2V
-
co^w^) + (dive) +
vAu
dt
p
ax
3
ax
dv 1
ap
- V
a
, . .
—
= ^-2co2U + (divc) +vAv
dt p
ay
3
ay
dw 1 ap - V
a
,,. .
.
—
= ^ + 2cOyU + (divc)
+ vAw-g
L
dt
p

az
3
az
Neu
ch^ft
long khdng nen dugc dive
=
0, ta cd:
(2.19)
du
dt
J_ap
p dx
2((0zV-c0yW) +vAu
dv
1 ap - .
— = ^-2co2U + vAv
dt p
ay
dw 1
ap
^
.
— =
-
+ 2cOyU +
vAw -g
dt
p az
(2.20)

De thuan tien ngudi ta thudng bieu dien (2.20) dudi dang thu ggn
chi
sd. Qui dinh sd hang nao lap lai 2
Ian
thi sd hang dd lay tdng tu
1
den 3. Vdi
each
vie't nay v bie'n ddi phu thuoc vao tga do thi (2.20) viet lai la:
at
+ u
au
axk
^ =
F:-
1 ap
+
p
dx,
dx
du^
dx^
(2.21)
trong dd i, k nhan cac gia tri
tir 1
den 3 neu i
;tk,
F,
la tdng cac
lire

khdi
ung vdi tga do
x^
Ddi vdi cha't
Idng
nen dugc:
au:
ail:
^.
1
ap
v
—^
+
U;.
—- =
Fi
^-t
at
dx^
pax,
3
^au,^
+
V
d^
dx^-
(2.22)
2.2.4. Phuang trinh lien tuc
Di thie't lap phuang trinh lien tuc,

tir
khdi khi dang chuyen dong ta
tach ra mdt
the'
tich gidi ban bdi mat S (hinh 2.2) neu ky hieu
m
la khdi lugng
khdng khi qua mat S
ti'ong
mdt dan vi thdi gian theo hudng phap tuyen ngoai
—•
n
ciia
mat S . Khi dd m dugc xac
djnh:
m=J/pc,,ds
18
trong dd p la mat dd khdng khi,
c„
la thanh
phdn
c chieu len phap
tuye'n. Mat khac khdi lugng M
ciia
khdng khi choang bdi the tich
i
d
ben trong mat S dugc xac dinh:
M=jl\pdz
Hinh

2.2
Cdn dao
ham =J[[J—di
chinh la bie'n thien cua khdi lugng M theo
at
T
at
thdi gian t. Theo dinh luat bao toan khdi lugng ta cd m
=
nghTa la khdi
lugng khdng khi chay qua mat S trong mdt dan vi thdi gian phai bang tdc do
thay ddi khdi lugng d ben trong the tich
x.
Tu dd ta cd:
Jlpc„d5 = -|llf dx
s
T
at
(2.23)
co:
Ap dung cong
thiic
Astrogratski chuyen
tich
phan 2 Idp sang 3 lap ta
Jjpc„ds
=
jjj
div
(pc)dT

Khi do (2.23)
ira
thanh :
JH
X
L
— + div(pc)
at
dT
= 0
(2.24)
do
T
la the tich chgn tuy y nen ham dudi da'u tich phan phai bang 0, vay:
(2-25)
^ +
div(pc)
=
0
at
hay (2.25) vie't dudi dang khac:
dp
dt
+pdive = 0
(2.26)
> iv.^-^^x
.
,
au av dw
,,

Neu p = cost
thi
(225) tra thanh —
+
—
+
— = 0
ax ay az
2.2.5,
Cac phuang trinh chuyen dong rdi trong
khi
quyen
2.2.5.1.
Cac
Ung
suat roi
Di danh gia chuye'n dong rdi
ciia
chat long trong dng thudng dugc
danh gia qua sd Reynols Re
19
Re = —
•
(2.27)
V
trong dd u la tdc dd dong, d la dudng kinh dng, v he sd nhdt dong hgc
ciia
cha't
long.
Ndu

ap dung (2.27) cho chuyen dong khi
quye'n,
ta cd
th^
thay v
cua khdng khi
r^t
nhd (d
20*^C
v =
1,53.10-^)
ma d
Idn
(be day
Idp
bien, tang
khi
quye'n
ddi luu, )
ling
vdi tdc do u khdng
Idn
lam thi Re cd gia tri rat
Idn.
Dieu dd chiing td ring
chuyin
dong khi quyen la
ludn ludn chuydn
dong rdi
vdi

mire
dd manh yeu khac nhau. Nghien cuu rdi ddi vdi mdi dac trung dugc
dua 2
ph^n:
thanh
phin
trung binh va thanh phan thang
giang.
D^
tach dugc
cac dai lugng dac trung trung binh ta su dung phep lay trung binh hda sau [2].
Trung binh hda theo thdi gian cua dai lugng vat li
cp
(x,y,z,t) dugc xac
dinh
theo-cdng thire
sau:
^ = Yt*T/2Vx,y,z,t)dt
(2.28)
- Trung binh theo khdng gian:
9
=
-|(p(x,y,z,t)di
(2.29)
,__
trong dd
i
la the tich khdng gian choang bdi khdng khi d thdi diem t.
- Nhieu dong
ciia

dai lugng cp dugc xac dinh:
cp*
= cp -
(p
(2.30)
Cac phep tinh ve trung binh tuan theo nhiing qui tac sau:
a.
(p^
= 0
(2.31)
b.
cpi
+(p^
=cp,
+(pn
(2.32)
cpjCp.
=(Pi(p.
+(Pi(p2
(2.33)
acp
a
-
acp
a(p,
acp acp
d. — = —
cp
, — = —
,

—
=
— (2.34)
dx dx dy dy dz dz
e.
cp
= cp ;
cpcp'=
0
; (pj
(p.
=(piCP2
(2.35)
20
Ddi
vdfi
mdi dac trung khi
quydn
dugc dac trung 2 thanh phan: trung
binh va thang giang, dua vao cac phep tinh trung binh (2.31) - (2.35) trung
binh hda cac phuang trinh
chuyen
dong cua khdng khi cua chat long khdng
nen dugc, ta dugc:
aui
-
aui
-
1
ap.

i
a
+ Uk
=
Fi \- (aki
-p
\x\
u'i)
(2.36)
at
dx^
paxj
paxj.
Phuang trinh (2.3 6) cd ca'u
triic
tuang tu (2.2 1)
chi
cd khac ngoai
oki
cdn
xua^t
hien them thanh
ph^n
T^J
= -
pu'^
u\
dugc tao thanh
tir
cac thang

giang cua cac thanh
phdn
tdc do. Dai lugng
T^^
tao nen mot tenxa hang 2 dugc
ggi la ten xa
ling su^t
rdi hay ten xa dug
su^t
Reynold. Di vie't cho ggn ngudi
ta thudng viet
Cy^
=
aki + Xki ^^ ^^S sua't
tdng hgp tao thanh
tir ling
suat
nhai
trong binh va
utig
sua't rdi.
Bay gid ta xet y nghTa vat ly
ciia
cac thanh phan
i^i.
Neu coi p
=
const thi:
x^x
=

-w'pu'
=
-w'(puy
Vi
pw
la hinh chie'u
ciia
vec ta dong lugng tren tuc x,
w'
la nhieu dong
ciia tdc do thing
diing.
Do dd w'pu' bieu thi di chuye'n rdi cua thanh
phSn
dong lugng theo chieu thang
diing
trong mot dan vi thdi gian. Vay
x^^
chinh la
ddng rdi thang dimg cua thanh phan dong lugng theo true x. Tuang tu ta cd
the giai thich y nghTa cua cac thanh phan
img
suat khac
x^,., x^^,
va di den
tdng quat
x^j
la ddng rdi hudng k
ciia
thanh phan dong lugng theo hudng i.

2.2.5.2. He so rdi, ly thuyet ban kinh nghiem
Di ddng kin phuang trinh (2.36) ta phai nghien
ciiu
tenxa ung suat
Xj,,.
ca sd
d^u
tien
ciia
ly thuyet rdi ban kinh nghiem dugc de cap tir cac cong trinh
ciia
Smit, Prant va
Kaiman
[2]. Ap dung ly thuyet ban kinh nghiem [2], tenxa
ung sua't rdi vie't cho cac true tga do cd dang:
p az p
•
az p az
(2.37)
21
XV
= k
xy
av
ax
dx
p
'OX
p
Trong dd

k^,
k^
dac trung cho
miic
do xao trdn rdi
ciia
cac thanh phan
ddng lugng
x^y
ra theo chieu thang dimg va dugc coi la bang nhau:
k„ =
k^
=
k^
=
k,
(2.38)
Tuang
tuk3„ =
k,y
= kyx = kyy = kQ
dugc coi la he sd rdi ngang, trong dd:
az
dx
(2.39)
1^
la doan dudng xao trdn theo chieu thang dung.
1^
la doan dudng xao trdn theo chieu nam ngang.
He sd rdi

Iq
cd
ciing
thir nguyen vdi vva
k^
+
v cd
th^
coi la he sd nhdt
tdng hgp.
Oig
sua't nhdt tdng hgp trong trudng hgp nay cd dang:
^zx =CJzx +X^x
=p(v
+ kj
—
az
(2.40)
d
day
cin
luu y rang he sd nhdt v dac trung cho ban
cha^t
vat ly mdi
tiirdng
cdn k dac
tiimg
cho ca'u
true
ddng hgc ddng rdi va do dd nd phu thuoc

vao van tdc ddng, khoang
each
tdi cac vat ran, cung nhu dd
Idi
1dm
ciia
thanh
ran va nhieu nhan td khac cd lien quan de'n tinh cha't vat li mdi trudng. Hon
nira gia tri k thudng
Idn
ga'p hang 100 hang 1000
Ian
v.
Vi
vay ngudi ta thudng
bd
V
so vdi k. Vi the' cho nen:
^^x
=
^^x
=
Pk
au
az
(2.41)
Nhu vay he phuang trinh chuyen ddng trung binh cd dang:
r

du

dt
1 ap
- .
—^ + lv +
k,
p dx
a
11
a
u
dv 1 ap
- .
— = ^-lu
+ k,
dt
dw
"dT
dx"
ay
a
V
a v
-f
az
au
az
pay
\_dp_
pdy
+

dx'
dw
f
+
az
dw
'
az
(2.42)
-g + ko
aw aw
ox
dy
r
+
az
aw
11
CJ
day ta bd qua nhieu ddng khi ap
(p*
= 0) va p = p vi nd nhd hcfn rat
nhi^u
so vdi nhieu ddng cua cac ye'u td khac.
2.2.6. Cac phuang trinh van chuyen nhiet va dm.
2.2.6.1.
Phuang trinh van chuyen nhiet
Ndu
khdng cd cac nhap nhiet
biie

xa va ngung ke't thi phuang trinh
bi^u
dien nguyen ly
thii nh^t
cua nhiet ddng
lire
hgc khi quyen [2] cd dang:
de^^
ae ae ae
ae^
—
= 0 hay
—+ u—
+
v—
+
w—
= 0
dt
at
ax ay az
trong dd 9 la nhiet do
the'
vi cua khdng
khi.
(2.43)
Ne'u ta coi khi quyen la mdi trudng nen dugc p
^
const, khi dd phucfng
trinh lien tuc:

ap^apu^apv^
apw^Q
at
ax ay az
Nhan 2 ve (2.43) vdi p va (2.44) vdi
9
sau dd cong lai dugc:
at ax
dy
dz
Dat
(j)
= p9 thay vao (2.45) va lay trung
binh
2 ve, ta duac:
ad) aud) avd) aw(t»
_L
+ +
1+
a dx
dy dz
aii'ct)'
av'f
d
-T-
— +
—
+ —
W
(j)

ax ay az
>
J
Tir (j)
= p9 lay trung
binh
2 ve
ducfc:
(t)
=
pe
+
p'G^
(2.44)
(2.45)
(2.46)
(2.47)
Mat khac:
^ = ^
+ (j)' nen:
f=(t)-^
= pe-0=(p +
p')(0
+
e')-^
=pe+pG'+p'e+p'e'-pe-p'e'
=pe'
+
p'e+p'e'-p'e'
tfch

cac phan nhieu
nho
han cac thanh phan khac nen co the bo qua. khi do:
23
(t)'=pe'+p'e
Phuong trinh (2.46) viet lai dudi dang
chi
sd:
(2.48)
aO
du^,^ _.du\
(|)'
dt
axfc
dx
(2.49)
r6i thay (|), (j)' xac djnh (2.47) va (2.48) va qua phep bien ddi dan gian ta thu
duoc:
r
ae - ae
^
at
dx
kj
-dp
;rUkp
ap'G'
+
0^
+ 9

+
at
dx
at
-au.p'
apuve' aukp'e'
-7-^
ae
=
-0
—— —^^ —^-
p
U
t
dx dx dx
dx
(2.50)
Mat khac neu la'y trung binh hda phuang trinh lien tuc (2.44) va nhan
2 ve vdi 9 la duac:
Qap^-apu^_-ap'u,
a
axk
dx
(2.51)
Su dung
(2.51)
vao (2.50) ta
dugc:
ae
a

+ Uk
_a0^
axky
apu'.e-
au,-
dx
axk
P'e'-p'u'k
ae
axk
(2.52)
P =
Phuang
ti-inh
(2.52) la phuang trinh van chuyen nhiet, tmdng hgp
0, p = p
thi
ta cd:
^ae
a
+
u,
ae^
dxy
dpu\
Q'
dx.
hay viet dudi dang thong thudng:
de
dpu'Q'

apv'0'
apw'e']
dx
dy
dz
(2.53)
(2.54)
. '
de
Neu p = const co: —
=
-
dt
^au'0'
dVQ'
aw'G'^
—
+
— +
dx
oy
cz
(2.55)
24
Ap dung ly thuyet ban thuc nghiem rdi ta cd:
ae
ae
a9 a9
a,
a9

a,
a9
a.
ae
,, ,^,
— + u —
+v—
+
w—
=
—kj^—4-
— k — +
—k,^
— (2.56)
at
dx dy dz dx dx dy dy dz dz
thdng thudng ngudi ta
l^y:
k^^
=
kty=
k^^
trong dd
k^h,
k^^
la he sd khuye'ch tan nhiet rdi theo chieu ngang va thang
dung.
2.2.6.2. Phuang trinh van chuyen dm
Ne'u q la do
im

rieng cua phan tu khdng khi khi
chuyen
ddng, gia thie't
qua
tiinh
chuyen ddng khdng khi khdng cd trao ddi am vdi ben ngoai, do dd ta
cd:
dq A L ^q ^q ^q ^q
A
—^
=
Ohay —^ + u-^ +
v—^
+
w—i
= 0
dt
at
ax ay az
(2.57)
Cung lam tuang tu nhu thanh lap phuang trinh van chuyen nhiet do the'
vi,
tir
phucfng
ti'inh
lien tuc (2.44) nhan 2
ve'
vdi q va (2.57) ham 2 ve vdi p rdi
cong lai, ta dugc:
a(pq)

^
au(pq)
^
av(pq)
^ aw(pq)^Q
at ax ay az
dat a = pq thay vao (2.57) va la'y trung binh 2
ve'
dugc:
(2.58)
aa aua a
va
awa
— + + +
dt dx
dy
dz
V
au'a'
av'a'
aw'a'^
+ +
dx dy dz
^
(2.59)
Neu thay a
=
pq+p'q'
va
a'=

pq'
+
qp'
vao (2.58) ta cd:
do
-
aq
—^
+
Uk^
at
dx
ky
apu'i^q'
aukp^q*
——
aq
+ +
p u
1;
^
\
dx
dx^
dx
(2.60)
trong trudng hgp khdng cd nhieu ddng mat do (p'
=
0) thi (2.60) trd thanh:
/'-\

i_i
-^
f_i
•^ '^tA
dq
dt
apu'q'
apv'q'
apw'q'
dx
dy
dz
(2.61)
Xet vdi chat long khdng nen dugc (p = const)
thi (2.61)
trd
ihanh:
25
—^ = uq+ — vq+ —
wq
dt
l^ax
ay
az
Ap dung ly thuye't ban thuc nghiem rdi ta cd:
(2.62)
aq aq aq aq
a.
aq
a,

aq
a,
aq
-=^
+ u-^ +
v-^
+
w-^
=
—k„^-^
+ —k,^—+
—k^^-^
(2.63)
a
dx dy dz dx
"^^
dx dy
^
dy dz
"^^
dz
trong dd:
kq^,
k^y,
k^^
la he sd
khuyech
tan
im
theo cac true tga do x,y,z

thudng thudng ngudi ta
la^y
k^^
=
k^y
=
kq^.
Cac he sd rdi
k^, k,, k^
cd mdi quan
he,
thdng thudng bang quan he tuye'n tinh
k^-
=
Oq-k^,
k^
=
a^k^,
trong dd
o^,
a^
la cac he sd cd bac dai lugng
x^^p
xi
dan vi.
2.2.6.3.
Dan gian hoa va khep kin he phuang trinh chuyen dong cua khi
quyen:
Trong
ti-udng

hgp tdng quat, cac phuang trinh chuyen ddng dua ra d
phan
trude
cd ca'u
triic
he't
siic
phue tap. Vi vay khi xay dung cac md hinh toan
hgc dac trung cho mot qua trinh cu the nao dd, trude he't ngudi ta phai tie'n
hanh dan gian hda cac phucfng trinh de nhan dugc cac phuang trinh dan gian
han ma van phu hgp vdi nhung dac diem
ciia
qua trinh dugc nghien cuu.
Trong khi tugng, ngudi ta thudng tie'n hanh dan gian hda cac phuang
trinh chuyen ddng cung nhu cac phuang trinh khac dua tren ly thuye't ddng
dang (tuang tu) va
thii
nguyen
[3]
cung vdi viec danh gia bac cua cac yeu td
khi tugng theo
each
phan tich thdng ke cac sd lieu quan trac thuc te', cac ket
qua nay cho tha'y:
-
Cac thanh phan nam ngang
ciia
van tdc chuyen ddng (u, v)
Idn
han

ra't nhieu so vdi thanh phan thang dung
w,
do cd cac thanh phan nam ngang
ciia lire
coriolis dugc bieu dien qua he thuc (2.8).
- Cd the bd qua cac thanh phan
ciia lye
ma sat nhdt so vdi luc ma sat
rdi,
nhu vay hai phuang
ti'inh
chuyen ddng ddi vdi thanh phan nam ngang la'y
d (2.42).
- Ddi vdi chuyen dong
ihang
dung thi thanh phan luc giadient khi ap
va trgng luc
giir
vai trd
chii
yeu. cac thanh phan khac cd the bd qua, phuong
26