Study on the Separation Technology of HGS and Its Effect
155
2.2 In the Lower Part of Annulus
π
4
(d 2
w − d 2
po )
∂(ρ d
ml c d
ml T p )
∂t
= π d pi h d
po (T a − T pi ) − (Q m + Q hgs (1 − ε))
∂(ρ d
ml c d
ml T p )
∂z
+S d
cp
(A-10)
If make A 1 = π(d 2
w − d 2
po )(ρc) d
ml /4, B 1 = π d po h d
po , C 1 = π d w h d
w , D 1 = (ρcQ) d
ml
α
∗
=Q hgs ∗ (1−ε)/(Q hgs ∗ (1−ε) + Q m )
Then the above equation can be changed into
A 1
T n
i,2 − T
n−1
i,2
t
= B 1 (T
n
i,1 − T
n
i,2 ) + C 1 (T
n
i,3 − T
n
i,2 ) + D 1
T n
i,2 − T n
i−1,2
z
+ (S ca )
n
i
(A-11)
To make a 1 = A 1 //t, b 1 = B, c 1 = C, d 1 = D//z
(a 1 + b 1 + c 1 + d 1 )T
n
i,1 − b 1 T
n
i,3 + d 1 T
n
i−1,2 = a 1 T
n−1
i,2 + (S ca )
n
i
(A-12)
3. Continuity Equation and Momentum Conservation Equation
3.1 Continuity Equation
∂(Aρ m α ∗ + Aρ hgs (1 − α ∗ ))
∂t
+
∂(Aρ m α ∗ ν m + Aρ hgs (1 − α ∗ )ν hgs )
∂z
= q hgs (A-13)
According to the above formula, we can get
A i (ρ hgs α ∗ ) n
i − A i (ρ hgs α ∗ )
n−1
i
+ A i (ρ m (1 − α ∗ )) n
i − A i (ρ m (1 − α ∗ ))
n−1
i
t
=
A i (ρ hgs α ∗ ) n
i − A i−1 (ρ hgs α ∗ ) n
i−1 + A i (ρ m (1 − α ∗ )) n
i − A i−1 (ρ m (1 − α ∗ )) n
i−1
z
+ q hgs
(A-14)
To make A i−1 /A i = Φ,
A i (ρ hgs α ∗ ) n
i − A i (ρ hgs α ∗ ) n−1
i
+ A i (ρ m (1 − α ∗ )) n
i − A i (ρ m (1 − α ∗ )) n−1
i
z
t
=
A i (ρ hgs α ∗ ) n
i − A i−1 (ρ hgs α ∗ ) n
i−1 + A i (ρ m (1 − α ∗ )) n
i − A i−1 (ρ m (1 − α ∗ )) n
i−1
+ q hgs z
(A-15)
Momentum Conservation Equation
∂(A(1 − α ∗ )ρ m ν m + Aα ∗ ρ hgs ν hgs )
∂t
= −
∂(AP)
∂z
−
∂(Aα ∗ ρ hgs ν 2
hgs + A(1 − α ∗ )ρ m ν 2
m )
∂z
− f m ρ m
ν 2
m
2
s m
− f hgs ρ hgs
ν 2
hgs
2
s hgs − A((1 − α ∗ )ρ m g + α ∗ ρ hgs g) + Aq hgs ν hgs
(A-16)
According to the equation, the following equation can be obtained
A i ((1 − α ∗ )ρ m ν m ) n
i − A i ((1 − α ∗ )ρ m ν m ) n−1
i
+ A i (α ∗ ρ hgs ν hgs ) n
i − A i (α ∗ ρ hgs ν hgs ) n−1
i
t
= −
A i P n
i − A i−1 P n
i−1
z