NL
CC
National Lab,of Coal Combustion,HUST
Wuhan 430074,P,R,CHINA
E-mail,pcbnlcc@hust.edu.cn
HYDRODYNAMICS AND
HEAT MASS TRANSFER IN
COMBUSTION
PROCEDURE
NL
CC
National Lab,of Coal Combustion,HUST
Wuhan 430074,P,R,CHINA
E-mail,pcbnlcc@hust.edu.cn
参考书
周力行, 湍流两相流动与燃烧的数值模拟,,
清华大学出版社,1991年。
周力行, 湍流气粒两相流动和燃烧的理论与数
值模拟,, 1994年。
范维澄，万跃鹏, 流动及燃烧的模型与计算,,
中国科技大学出版社,1992年。
盖得 ·希特斯洛尼, 多相流动和传热手册,,机
械工业出版社,1993年
NL
CC
National Lab,of Coal Combustion,HUST
Wuhan 430074,P,R,CHINA
E-mail,pcbnlcc@hust.edu.cn
参考书（续）
王应时，范维澄，周力行，徐旭常, 燃烧过程的数
值计算,,科学出版社,1986年。
岑可发，樊建人, 工程气固两相流动的理论及计
算,,浙江大学出版社,1990年。
NL
CC
National Lab,of Coal Combustion,HUST
Wuhan 430074,P,R,CHINA
E-mail,pcbnlcc@hust.edu.cn
Chapter 1 Introduction
§ I Basic Procedures
Combustion
Hydrodynamics Heat Transfer Mass Transfer Chemical Reaction
Physical Procedures Chemical Procedure
NL
CC
National Lab,of Coal Combustion,HUST
Wuhan 430074,P,R,CHINA
E-mail,pcbnlcc@hust.edu.cn
Aim,Individual Procedures
Total Procedure
Note,Total Procedure ≠∑individual Procedures
NL
CC
National Lab,of Coal Combustion,HUST
Wuhan 430074,P,R,CHINA
E-mail,pcbnlcc@hust.edu.cn
§ II,Basic Equations
1,Reynolds Transport Principle
1) Two treatment methods
a) Euler method-variation of defined space point
b) Lagrange method-variation of defined fluid
element
Relation (for a fluid element)
j
j
x
v
tdt
d
?
?
?
?
?
?
???
NL
CC
National Lab,of Coal Combustion,HUST
Wuhan 430074,P,R,CHINA
E-mail,pcbnlcc@hust.edu.cn
In general,consider a particular quantity,?,for control
volume V,
? ? ? ????
v i
Vtxt ??,
Variation rate of ? along rue of control volume
? ?
? ??
?
??
? ?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
??
??
??
?
V
j
j
V
j
j
VV
V V
Vv
xt
V
x
v
Dt
D
V
V D t
VD
V
Dt
D
V
Dt
D
V
Dt
D
Dt
D
??
?
??
?
?
?
?
??
?
????
NL
CC
National Lab,of Coal Combustion,HUST
Wuhan 430074,P,R,CHINA
E-mail,pcbnlcc@hust.edu.cn
i.e,
? ? Vv
xt
V
Dt
D
V j
j
V
????? ??
?
?
?
?
?
?
?
?
?
??
?
??
or
???
??
?
?
S n
dSv
tDt
D
?
This is called Reynolds Transport Principle,
It means the variation rate of the intergral of
? in the control volume moved along rue
equals the change with time plus the varation
introduced by convection in Euler coordinate
NL
CC
National Lab,of Coal Combustion,HUST
Wuhan 430074,P,R,CHINA
E-mail,pcbnlcc@hust.edu.cn
The generalized conversion law
0??? ?
V
VSDtD ??
Where S? is the source term of ?
2,Continue Equation
with ??r,S? = 0,
? ?
0
0
0
?
?
?
?
?
?
?
?
?
?
?
?
j
j
j
j
x
v
Dt
D
v
xt
Dt
D
r
r
r
r
or
NL
CC
National Lab,of Coal Combustion,HUST
Wuhan 430074,P,R,CHINA
E-mail,pcbnlcc@hust.edu.cn
3,Diffusion Equation
with ? = rs =Ysr,and ??? ??
V sS sV VwdSjVS ???
0???
?
?
???
?
?
?
?
? ??
V s
j
sj
V s
Vw
x
j
VY
Dt
D ??r
With Reynolds transport low and Fick Law
? ? ? ?
?
?
?
?
?
?
?
?
?
?
?
?
??
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
? ??
j
s
jj
sj
V
js
j
s
V
s
x
Y
D
xx
j
VvY
x
Y
t
VY
Dt
D
r
?rr?r
NL
CC
National Lab,of Coal Combustion,HUST
Wuhan 430074,P,R,CHINA
E-mail,pcbnlcc@hust.edu.cn
So mass conversion equation for s component
? ? ? ? s
j
s
j
js
j
s wx
YD
x
vY
x
Y
t
???
?
?
???
?
?
?
?
??
?
??
?
? rrr
∵
0?? sw
∴ The sum of mass conversion equations is equal to
zero,
NL
CC
National Lab,of Coal Combustion,HUST
Wuhan 430074,P,R,CHINA
E-mail,pcbnlcc@hust.edu.cn
4,Momentum Equation
with ? = rvi
VF
x
p
Dt
D
VF
x
p
VS
V
sis
j
ij
V
sis
j
ij
V
?r
?r??
? ?
? ??
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
With Reynolds transport principle and Newton’s
viscous low
? ? ? ?
ij
i
j
j
i
ij
V
ij
j
j
V
i
p
x
v
x
v
p
Vvv
x
v
t
Vv
Dt
D
??
?rr?r
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
? ??
NL
CC
National Lab,of Coal Combustion,HUST
Wuhan 430074,P,R,CHINA
E-mail,pcbnlcc@hust.edu.cn
So
??
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?? sis
i
j
j
i
ji
i F
x
v
x
v
xx
p
Dt
Dv
r?r
Volume force may be gravity force rgi,
elctricity force and magnetic force
NL
CC
National Lab,of Coal Combustion,HUST
Wuhan 430074,P,R,CHINA
E-mail,pcbnlcc@hust.edu.cn
5,Energy Equation
with ? ? re,e ? e + v2/2
By Reynolds transport principle and continue equation
? ? ? ?
? ? ??
? ?
?
?
?
?
?
?
?
?
?
?
?
??
?
?
?
?
?
?
?
?
?
?
?
?
?
?
Vv
j
j
V V
j
j
V
Dt
D
V
x
v
Dt
D
Vv
xt
V
Dt
D
?
e
r?rere
?rerer e ?
NL
CC
National Lab,of Coal Combustion,HUST
Wuhan 430074,P,R,CHINA
E-mail,pcbnlcc@hust.edu.cn
Heat transfer to control volume by conduction,
convection,radiation and diffusion
?? ??????
?
?
???
?
?
?
?
?
S
rjs
j
s
V
jj
Vqh
x
YD
x
T
x
?r? )
Work of volume force
? ? VVFFvVvFV V ssssssss ?rr?r? ? ? ? ? ????? ??????
Where vs is relative velocity of component s to
combined gas
vvV ss ??
NL
CC
National Lab,of Coal Combustion,HUST
Wuhan 430074,P,R,CHINA
E-mail,pcbnlcc@hust.edu.cn
Work of surface force
? ?? ? ?
?
???
S V iij
j
n VvpxdSvp ?
??
So,
? ?
jij
j
sissisi
j
rj
s
s
j
s
jjj
vp
x
FFv
x
q
h
x
Y
D
xx
T
x
v
e
Dt
D
?
?
???
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
??
?
rr
r?r
2
2
NL
CC
National Lab,of Coal Combustion,HUST
Wuhan 430074,P,R,CHINA
E-mail,pcbnlcc@hust.edu.cn
§ III Dimensionless Parameters
With dimension analysis
For fluid flow
a
u
Tc
u
r g yT h e r m a lE n e
e r g yM o m e n tu m E n
Ma
Lu
Lu
Lu
r g yV is c o u s E n e
r g yI n a tia lE n e
u
p
u
Lp
M o m e n tu m
e s s u r e
Eu
p
?
?
?
?
?
??
??
??
?
??
?
???
???
???
2/
/
/
Re
/Pr
2
2
22
??
r
rr
NL
CC
National Lab,of Coal Combustion,HUST
Wuhan 430074,P,R,CHINA
E-mail,pcbnlcc@hust.edu.cn
For conduction
? ? PrRe//
/2 ????
??
?
??
???
r??
r
p
p
c
Lu
LT
LTcu
H e a tC o n d u c tio n
H e a tC o n v e c t io nPe
For combustion
c
dss
II
c
f
p
ss
I
LT
Qw
a c ti o n Ti m e
im eD if fu s io n T
c o n d u c ti o n
r e a c ti o n
D
LTcu
Qw
a c ti o n Ti m e
F lo w T im e
c o n v e c ti o
r e a c ti o n
D
?
?
?
?
?
r
????
????
??
?
???
?
/Re
/Re
NL
CC
National Lab,of Coal Combustion,HUST
Wuhan 430074,P,R,CHINA
E-mail,pcbnlcc@hust.edu.cn
DI,DII - Damkohler numbers
DII ～ f(DI,Pe)
For two low Ma combustion systems,
when Re = const.
Pr = const.
DI = const.
They are similar.