g ggg=

28
~1
i
|f = |fH + |f K
2|f g| i 2|f
g| r g| i 2|f
2 ^1 - |h | _ | | i
g| r 2 | + | | - |
=
| J f, f
r
r 2g r
r 2g| i
r
g| = _ g| r, g| i, g| z i
|f _ r| , g| i
| = r1 /r2, Kn = m/ ^r2 - r1h
J| _ |f, |f i
^2RT0h3/2
g
r
r| = , g =
, |f =
t av
m
^2RT0 h1/2
~ 1 r1
T| = T/T0
V| 1 =
^2RT0 h1/2
t
f, t| = t av ,
|f K
|fH
|fH = |fH + |fH f + |fH f 2 + K
|f K = |f K + |f K f + |f K f 2 + K
0
1
2
0
1
2
r
f = 2 Kn % 1
t|
T|
ui
|f
p|
t| H = t| H + t| H f + t| H f 2 + K
0
t av
-1
m = ^ 2 rd 2 t av /mh
1
2
u i, H = u i, H + u i, H f + u i, H f 2 + K
T| H = T| H + T| H f + T| H f 2 + K
0
1
0
t|
2
1
2
p| H = p| H + p| H f + p| H f 2 + K
0
1
2
r2
2|
# r| t| dr| = 1
1 - |2 r
2
1
1
J| _ |f1, |f2 i = 2
# #
R3
S2
J| _ |f, |f i
| X ^ e h dg 2
_ |f1l |f2l - |f1l |f2li Bd
f
f1 = f ^r, g 1, th f2 = f ^r, g 2, th
f1l = f ^r, gl1 , th f2l = f ^r, gl2 , th
B| = B| ^ V : e / V h V = g 2 - g 1l
gl1 = g 1 + ^V : eh e gl2 = g 2 - ^V : eh e
g 1, g 2 ! R 3
gl1 , gl2 ! R
3
X^ e he
V
B| = V : e /4 2r
dg 2 = dg 2,r dg 2,i dg 2,z :
dp| H
2t| H u 2i,H
=0
dr|
r|
u i,H mE
d ; | 2 | 1/2 c du i,H
c
=0
1 r TH
|
|
dr
dr
r|
u i, H 2
5 d c | 1/2 dT| H m
1/2 du i, H
|
k =0
c
+
c
2 rT H
1 rT
H a
4 dr|
dr|
dr|
r|
0
0
0
0
0
0
0
0
0
0
0
B| , V : e
c 1 T| 1H/2
0
29
c 2 T| 1H/2
(l)
(l)
v (l)
(j) + F ^ x (j), v (j), t h dt
0
u i,H
ui
0
N (l)
(l)
(l)
f ^x, v, th = T / / d ^x - x (l)
(j) - v (j) dt h d ^ v - v (j)
M
d : | 2 a du i u i kD
dr| r dr| - r| = 0
l=1 j=1
- F ^x , v , th dth, xdD
(l)
(j)
(l)
(j)
(l)
^v (l)
(j), v (k) h
P (s) ^v ((lj)), v ((lk))h dX (s) =
Tdt | (s)
BdX
mdC (l)
B| ^v 1 - v 2, eh
^v ((lj)), v ((lk)) h
^v ((lj)), v ((lk)) h
^vl((lj)), vl((lk)) h
vl((lj)) = v ((lj)) + ^^v ((lk)) - v ((lj))h, e (s)h e (s)
vl((lk)) = v ((lk)) - ^^v ((lk)) - v ((lj))h, e (s)h e (s)
N (l)
f ^x , v, th dC = T / d ^v - v h, x ddC
( l)
( l)
( j)
( l)
(l)
( l)
(l)
^v (l)
(j), v (k) h
j=1
N (l)
f ^x, v, th = T / / d ^x - x ((lj))h d ^v - v ((lj))h, xdD
M
l=1 j=1
P ^v ((lj)), v ((lk))h = / P (s) ^v ((lj)), v ((lk))h dX (s)
s
rr{ 2 T dt
( l)
( l)
= m
(l) v (k), v (j)
dC
r{
(l)
(j)
o 3
x d
(l)
(j)
o 3
v d
1 - P ^v ((lj)), v ((lk))h
x (l)
(j)
v (l)
(j)
(l)
x (l)
(j) + v (j) dt
30
a=
v
4 ^2 - vh Kn
du
u
x = n a dr|i - r| k
x| = xm/ ^n~r1h
r
u i ^r1h = a 1 r1 ~ 1 + ^1 - a 1h u i ^ r h r1
r
u i ^r2h = ^1 - a 2h u i ^ r h r2
1/2
r = ^^r 31 + r 32h / ^r1 + r2hh
0.4
a 1 a 2 r| 2 | ^1 - ^1 - |h |h
B=
^1 - | h^a 2 + a 1 | 3 h
r
| = r12
| ^a - ^1 - |h |h
ar| 2 |
u| i ^ r| h =- |
3
4 r +
^1 - | 2h r
r2 ^ 1 - | + | - | h
uθ/V1
u| i = u i ^ r| h = Ar| + Br| -1
a 1 | ^a 2 - ^1 - |h |h
A= |
^
r2 a 2 - a 2 | + a 1 | 3 - a 1 | 4 h
DSMC data σ = 0.7
DSMC data σ = 0.4
DSMC data σ = 0.1
Langmuir σ = 0.7
Langmuir σ = 0.4
Langmuir σ = 0.1
Maxwell σ = 0.7
Maxwell σ = 0.4
Maxwell σ = 0.1
0.5
0.3
0.2
0.1
3
3.5
4
r/λ
4.5
5
31
Kayma gerilmeleri
1
τ λ / (μ ω r )
0
a2 1
Langmuir
Maxwell
−0.05
du i /dr 1 0
rd6r1, r2@
r 2 ^1 - |h | - a 2 ^r 2 + R 22 ^1 - ^1 - |h |hh 1 0
−0.1
a2 2
−0.15
0
^1 - |h | 3
R 21 ^1 - |h |
=
R 21 + R 22 ^1 - ^1 - |h |h 1 - ^1 - 2|h |
0.2
0.4
σ
0.6
0.8
r 2 ^1 - |h |
r 2 + R 22 ^1 - ^1 - |h |h
rd6r1, r2@
1
a2 2
^1 - |h |
R 22 ^1 - |h |
=
2
2
R 2 + R 2 ^1 - ^1 - |h |h 2 - ^1 - |h |
du i /dr = 0
r d 6r1, r2@
r) =
a 2 R 22 ^- 1 + ^1 - |h |h
a 2 - ^1 - |h |
du i /dr 2 0
du i
dr =
a 1 | ^r 2 ^1 - |h | - a 2 ^r 2 + R 22 ^1 - ^1 - |h |hhh
20
r 2 R 2 ^1 - |h^a 2 + a 1 | 3h
2a 1 a 1 R 2 | ^1 - ^1 - |h |h
d2 ui
2 =dr
r 3 ^1 - |h^a 2 + a 1 | 3h
a 2 1 ^1 - |h |
^r 2 ^1 - | h | - a 2 ^r 2 + R 22 ^1 - ^1 - | h | hhh 2 0
a2 1
r2 ^ 1 - | h |
r + R 22 ^1 - ^1 - |h |h
2
r d 6r1, r2@
r )d6r1, r2@
^1 - |h | 3
^1 - |h |
1 a2 1
h
^
1 - 1 - 2| |
2 - ^1 - |h |
32
0.36
Langmuir σ = 0.5
Langmuir σ = 0.4
Langmuir σ = 0.3
Maxwell σ = 0.5
Maxwell σ = 0.4
Maxwell σ = 0.3
0.34
uθ/V1
0.32
0.3
0.28
0.26
0.24
3
3.5
4
r/λ
r
4.5
5