1
Fluid Mechanics
2
3
Chapter 11 Gas diffusion
§ 11–1 Introduction
§ 11–2 Character of submerging turbulent
diffusion in infinite space
§ 11–3 kinetic analysis of diffusion in
circular section
§ 11–4 plane diffusion
§ 11–5 Temperature or thickness difference
of diffusion
§ 11–6 Introduction of other diffusion in project and
equipment
Exercise of Chapter 11
4
第十一章 气体射流
§ 11–1 引言
§ 11–2 无限空间淹没紊流射流的特征
§ 11–3 圆断面射流的运动分析
§ 11–4 平面射流
§ 11–5 温差或浓差射流
§ 11–6 工程设备中常见的其他射流简介
第十一章 习题
5
Flow by gas diffusing from orifice,pipe mouth or slot called
gas submerged diffusion flow.When orifice velocity is high,flow is
in turbulent state,called turbulent diffusion,Most diffusion applied
in engineering is turbulent diffusion of gas,
Diffusion describe flow velocity,temperature and thickness
after coming out,
Diffuse to infinite space,flow is not restricted by solid wall
called free diffusion.Contrarily,called restricted diffusion,
Chapter 11 Diffusion of gas
§ 11-1 Introduction
6
气体自孔口、管嘴或条缝向外喷射所形成的流动，称为气
体淹没射流。当出口速度较大，流动呈紊流状态，叫做紊流射
流。工程上所应用的射流，多为气体紊流射流。
射流讨论的是出流后的流速场、温度场和浓度场。
射流到无限大空间中，流动不受固体边壁的限制，为无限
空间射流，又称自由射流。反之，为有限空间射流，又称受限
射流。
第十一章 气体射流
§ 11-1 引言
7
§ 11-2 Characteristic of turbulent diffusion in infinite space
Take circular section diffusion as example talk about diffusion
motion,
Airflow diffused from circular section muzzle with radii
R,Velocity of outlet section is considered uniform distributing,all
are u0 and is turbulent flow,Take axis of diffusion Mx as axis x
Owing to diffusion is turbulent flow type,transverse pulse of
diffusion make exchange between mass and momentum among
diffusion and medium.Driving medium moving,mass flux,
transverse section area along x increasing,come into cone form
flow diffused to around,as in fig.11—1 CAMDF。
8
§ 11-2 无限空间淹没紊流射流的特征
现以无限空间中圆断面紊流射流为例，讨论射流运动。
气流自半径为 R 的圆断面喷嘴喷出。出口断面上的速度
认为均匀分布，皆为 u0 值，且流动为紊流。取射流轴线 Mx为
x 轴。
由于射流为紊流型，紊流的横向脉动造成射流与周围介质
之间不断发生质量、动量交换，带动周围介质流动，使射流的
质量流量、射流的横断面积沿 x 方向不断增加，形成了向周围
扩散的锥体状流动场，如图 11—1所示的锥体 CAMDF。
9
th e startin g seg m en tt h e m a i n b o d y s e g m e n t
the core
th e b o u n d a r y la y e r
x
s
0s0x
o?M
A
D
B
C
E
F
Fig,11—1 Diffusion structure
Structure and characteristic of turbulent diffusion
10
起始段 主体段
核心
边
界
层
x
s
0s0x
o?M
A
D
B
C
E
F
图 11—1 射流结构
紊流射流的结构及特性。
11
1,Initial and main segment of transition section
Diffusion velocity is uniform when just ejected, Flow along x,
diffusion bring around medium constantly,making boundary larger,and
main velocity of diffusion reduce gradually,part with velocity u0 （ as
in 11—6 AoD cone） called core of diffusion,other part with velocity
lower than u0 called boundary layer,Boundary layer disperse
constantly from outlet to around along diffusion line,driving around
medium into boundary layer,and expanding to diffusion center till
certain distance,boundary expending to axes of diffusion,core region
disappeared,only velocity in axes is u0, This section as in fig.11—1
BoE,called transition section,Take transition section as dividing line,
outlet section till transition section called initial segment of diffusion,
Since transition section called main segment of diffusion,
12
一、过流断面（又称转折断面）起始段及主体段
刚喷出的射流速度仍然是均匀的。沿 x 方向流动，射流不断
代入周围介质，不仅使边界扩张，而且使射流主体的速度逐渐降
低，速度为 u0 的部分（如图其 11—6 AoD 锥体）称为射流核心，
其余部分速度小于 u0 称为边界层。射流边界层从出口开始沿射程
不断地向外扩散，带动周围介质进入边界层，同时向射流中心扩
展，至某一距离处，边界层扩展到射流轴心线，核心区域消失，
只有轴心上速度为 u0 。射流这一断面为图 11—1上的 BoE,称为过
渡断面或转折断面。以过渡断面分界，出口断面至过渡断面称为
射流起始段。过渡断面以后称为射流主体段。
13
2,Coefficient of turbulent flow ? and geometrical character
Outer boundary layer of diffusion is a beeline,as in fig.11—1
AB and DE,AB, DE prolong to muzzle meeting at point M,this
point called culmination.Half of called pole angle ?,as
well as called diffusing angle ? 。
Bo is radii R of circular diffusion section （ or half breadth of
boundary layer in plane diffusion yb ）,It is positive ratio with
distance from culmination,Bo ＝ Kx 。
oM is x distance calculated from culmination,Observing
from figure,Bo/oM =tan ?,so
AMD?
1)( 1 1 t a n —??? ??? KxKx
where K—experiment constant;
?— form coefficient of muzzle,circular muzzle,?＝ 3.4；
?— coefficient turbulent flow,determined by experiment
14
二、紊流系数 ? 及几何特征
射流外边界层是一条直线，如图 11—1上的 AB及 DE 线。
AB, DE 延至喷嘴内交于 M 点，此点称为极点,的
一半称为极角 ?,又称扩散角 ? 。
Bo为圆断面射流截面的半径 R（或平面射流边界层的半
宽度 yb ）。它和从极点起点算的距离成正比，即 Bo ＝ Kx 。
oM 是从极点起算的 x 距离。由图看出,Bo/oM =tan ?,故
AMD?
1)( 1 1 t a n —??? ??? KxKx
式中 K—试验常数；
?— 喷口形状系数，圆形喷嘴,?＝ 3.4；
?— 紊流系数，由实验决定，是表示射流流动结构的
特征系数。
15
Coefficient of turbulent flow ? relate to turbulent flow intensity in outlet
section,More high as intensity,more high as value a,which make diffusion expending
angle a increase,Driving around medium more,velocity along diffusion line reducing
more fast,a relates to the uniform of velocity distributing in outlet section.Practical
value of turbulent flow coefficient and expending angle on different form muzzle.as in
table 11—1,
Coefficient of turbulent flow table11—1
Wind machine of axis flow
with metal gridding
well shrink plane muzzle
narrow gap in plane wall
portrait gap of wind way
with grind round outlet
kinds of muzzle
muzzle with shrink outlet
cylindrical pipe
Right-angle pipe with
leading wind plank
? ?2 kinds of muzzle ? ?2
071.0066.0
08.0076.0
20.012.0
0127 02250
0
??
00290 ?
0368 03440
0
??
155.0
118.0
108.0
24.0
0241
0132
0329
0478
0
0
0
0
?
?
?
?
From formula（ 11—1—1）,a is conformed,outer boundary line of diffusion
boundary layer,diffusion expending forward along certain expending angle a,this
is its geometrical character.Applying this character,variety rule of diffusion radii
can be obtained along diffusion way in circular section,
16
紊流系数 ? 与出口断面上紊流强度有关，紊流强度越大,a
值也大，使射流扩散角 a 增大，被带动的周围介质增多，射流速
度沿程下降加速。 a 还与射流出口断面上速度分布的均匀性有关。
各种不同形状喷嘴的紊流系数和扩散角的实测值列表 11—1。
紊 流 系 数 表 11—1
喷 嘴 种 类
带有收缩口的喷嘴
圆柱形管
带有导风板的轴流式通风
机带导流板的直角弯管
? ?2 喷 嘴 种 类 ? ?2
071.0066.0
08.0076.0
20.012.0
0127 02250
0
??
00290 ?
0368 03440
0
??
带金属网格的轴流风机
收缩极好的平面喷口
平面壁上锐缘狭缝
具有导叶且加工磨圆边口
的风道上纵向缝 155.0
118.0
108.0
24.0
0241
0132
0329
0478
0
0
0
0
?
?
?
?
由（ 11—1—1）式可知,a 值确定，射流边界层的外边界
线也就被确定，射流即按一定的扩散角 a 向前作扩散运动，这
就是它的几何特征。应用这一特征，对圆断面射流可求出射流
半径沿射程的变化规律。
17
2)( 1 1 4.3
)294.0(4.34.31
t a n/
1
0
000.0
0
0
—asrR
r
as
r
s
r
s
x
sx
r
R
??
???????? ?
?
3,Characteristic of motion
Many experiment showing, velocity distributing taking on
comparability in different section.This is characteristic of motion,
Expressing velocity distributing in different section with half-
empirical formula,
1, 5 2
1, 5 2
[ 1 ( ) ] 11 3
y
m a k e
R
[ 1 ] ( 11
m
m
y
R
?
?
?
?
?
?
??
?
??
（ — ）
— 3 a )
18
2)( 1 1 4.3
)294.0(4.34.31
t a n/
1
0
000.0
0
0
—asrR
r
as
r
s
r
s
x
sx
r
R
??
???????? ?
?
三、运动特征
大量实验研究表明，射流各截面上速度分布具有相似
性。这就是射流的运动特征。
用半经验公式表示射流各横截面上的无因次速度分布如下,
3 a )( 1 1 ]1[
R
y
311 ])(1[
25.1
25.1
—
令
）—（
?
?
?
?
?
?
??
?
??
m
m
R
y
19
Above formulas are suitable for main segment,then in formula,
y—distance from any point to axes in transverse section
R—diffusion radii of this section;
—velocity of point y;
—axes velocity in this section,
Above formulas are suitable for initial segment,only considering
flow velocity distributing in boundary layer,then in formulas
y—distance from any point to core boundary;
R—thickness of boundary layer in same section;
—velocity of point y in boundary layer of section;
—core velocity
?
m?
m?
?
0?
20
上式如用于主体段，则式中
y—横断面上任意点至轴心距离；
R—该截面上射流半径（半宽度）；
—y点上速度；
—该截面轴心速度。
上式如用于起始段，仅考虑边界层中流速分布，则式中
y—截面上任意点至核心边界的距离；
R—同截面上边界层厚度；
—截面上边界层中 y 点的速度；
—核心速度 。
?
m?
m?
?
0?
21
Therefore obtained variety spectrum of y/R from axes or core
boundary to outer boundary is 0 1.Variety spectrum of from
axes or core boundary to boundary of diffusion is1 0。
m??/
4,Characteristic of kinetics
Proved by experiment,static pressure at any point in diffusion
is equal to pressure of around air.Taking one diffusion segment
from11—2 and 1—1,2—2,analyzing force in it.Owing to static
pressure is equal in different section,then sum of outside force is o
in axis x,Due to momentum equation,momentum conservation in
different section,this is characteristic of kinetics of diffusion,
Take circular section as example apply momentum
conservation equation,
Momentum flex of outlet section is,
Integrating momentum flex in any transverse section,
02000 ????? rQ ?
2
00
2 2 2
00 0
2 2
m o m e n t u m c o n s e r v a t i o n f o r m u l a
2 ( 1 1 1 4 )
RR
R
y d y y d y
r y d y
? ? ? ? ? ? ?
? ? ? ? ? ?
?
?
??
?
：
— —
22
由此得出 y/R 从轴心或核心边界到射流外边界的变化范围为
0 1。 从轴心或核心边界到射流边界的变化范围为 1 0。 m??/
四、动力特征
实验证明，射流中任意点上的静压强均等于周围气体的压
强。现取 11—2中 1—1,2—2所截的一段射流脱离体，分析其
上受力情况。因各面上所受静压强均相等，则 x 轴外力之和为
零。据动量方程可知，各横截面上动量相等 —动量守恒，这就
是射流的动力学特征。
以圆断面射流为例应用动量守恒原理
出口截面上动量流量为,任意横截面上的动
量流量则需积分。
02000 ????? rQ ?
4)1( 1 1 2
22
0
22
0
2
0
0
2
0
——
列动量守恒式：
?
??
?
?
R
RR
y d yr
y d yy d y
? ? ????
? ? ?????
23
?M
0x s
x
y?
y?
x
r
R
y
y?
1
1 2
2
R
y y
dy
Fig,11—2 Proved of diffusion calculation
24
?M
0x s
x
y?
y?
x
r
R
y
y?
1
1 2
2
R
y y
dy
图 11—2 射流计算式的推证
25
§ 11-3 Kinetic analysis of diffusion in circular section
Studying variety rule of diffusion velocity in circular section
and throughput Q along diffusion way s （ or x ） due to
characteristic of turbulent diffusion,
?
1,Velocity of axes
m?
2 2 2
00
0
22
1
2 2 200
0
1.
a ppl y i ng 11 1 4
2
div i de obta i n
( ) 2 ( ) ( )
substi t uti ng 11 1 3 [ 1 ( )
R
m
mm
m
r y dy
R
r yy
d
R R R
y
R
? ? ? ? ? ?
? ? ?
? ?
??
?
?
?
?
?
?
?
（ — — ）
：
（ ）
（ — — ） ＝
52
1
1,5 2 2
2
0
] i nto t he n
[ ( 1 ) ]d B? ? ???
?
，
26
§ 11-3 圆断面射流的运动分析
现在根据紊流射流特征来研究圆断面射流的速度,流量
Q 沿射程 s （或 x ）的变化规律。
?
一、轴心速度
m?
2
1
0
225.1
25.1
1
0
22020
22
0
22
0
2
0
d])[ ( 1
])(1[3111
)()(2)(
2
4111
B
R
y
R
y
d
R
y
R
r
R
y d yr
m
mm
m
R
??
?
?
?
?
?
?
???
?
?
?
?
?
?
???
? ? ????
代入，则＝）——应用式（
）（
除两端，得：以
）——应用式（
27
According to above variety spectrum of and, value
table of B2 listed in table11—2。 R
y
m?
?
n
aB
aC
1 5.1 2 5.2 3
0985.0
3845.0
064.0
3065.0
0464.0
2585.0
0359.0
2256.0
0286.0
2015.0
v a lu e o f a n d aaBC table 11—2
11
00
2200
2
0
0
( ) ( )
t he n ( ) 2 2 0,04 64
3.28
nn
nn
mm
m
m
B d C d
r
B
R
r
R
??
? ? ?
??
?
?
?
?
??
? ? ?
?
??
（ ）
28
按前述 及 的变化范围,B2 的数值列于表 11—2。
R
y
m?
?
n
aB
aC
1 5.1 2 5.2 3
0985.0
3845.0
064.0
3065.0
0464.0
2585.0
0359.0
2256.0
0286.0
2015.0
值和 aa CB 表 11—2
R
r
B
R
r
dCdB
m
m
n
m
n
n
m
n
0
0
2
2020
1
0
1
0
28.3
0 4 6 4.022)(
)( )(
?
???
?? ??
?
?
?
?
?
?
?
??
?
?
）于是（
29
0
00
su b stitu tin g v a r ie ty r u l e o f d if f u sio n r a d ii
a l o n g d if f u sio n w a y 1 1 1 2 in t
0,9 6 5 0,4 8
( 1 1 2 1 )
0,2 9 4 0,1 4 7
m
o o b ta in
a s a s
rd
?
?
??
??
（ — — ）,
— —
2,Throughput Q of section
0
2
0
0 0 0 0 0 0
0 0 0 0
1
2
0
0 0 0
2
2 ( ) ( ) ( )
s u b s tit u tin g ; in to
2 ( ) ( ) ( ) ( )
s
R
R
r
m
m
m
m
y d y
Q y y
d
Q r r r
y y R
r R r
Q R y y
d
Q r R R
??
?
? ? ?
???
? ? ?
? ?
??
??
? ? ?
??
?
?
?
＝
30
1)2( 1 1
1 4 7.0
48.0
2 9 4.0
9 6 5.0
2111
00
0
——
）式代入，得——沿程变化规律（再将射流半径
?
?
?
?
d
as
r
as
R
m
?
?
二、断面流量 Q
取无因次流量,
)()()()(2;
)()()(2
2
1
0
2
000
0000
00
0
00
2
0
0
0
R
y
d
R
y
r
R
Q
Q
r
R
R
y
r
y
r
y
d
r
y
r
y d y
Q
Q
m
m
m
m
r
R
R
s
?
?
?
??
???
??
?
?
?
?
?
?
?
?
?
?
?
?
??
??
代换＝再用
31
Consulting table 11—1, B1=0.0985 ; substituting formula（ 11—
1—2），（ 11—2—1） into
）——（ 2211 )1 4 7.0(4.4)2 9 4.0(2.2
000
???? dasrasQQ
Substituting formula（ 11—1—2）,（ 11—2—2） into and obtaining
3)2( 1 1
1 4 7.0
0 9 5.0
2 9 4.0
19.0
00
0
1 ——
?
?
?
?
d
as
r
as?
?
3,Average velocity of section
Average velocity is, 20
00
0
0
1 )( RrQQAQQA ????
1?
32
查表 11—1, B1=0.0985 ; 再将（ 11—1—2），（ 11—2—1）式
代入
）——（ 2211 )1 4 7.0(4.4)2 9 4.0(2.2
000
???? dasrasQQ
三、断面平均流速
无因次断面平均流速为,20
00
0
0
1 )( RrQQAQQA ????
将（ 11—1—2），（ 11—2—2）式代入得
3)2( 1 1
1 4 7.0
0 9 5.0
2 9 4.0
19.0
00
0
1 ——
?
?
?
?
d
as
r
as?
?
1?
33
4,Average flow velocity v2 of mass
4)2( 1 1
1 4 7.0
23.0
2 9 4.0
4 5 4 5.0
00
0
0
2
200
——
?
?
?
??
?
d
as
r
asQ
Q
QQ
?
?
????
Average velocity denoting arithmetic average value in diffusion
section.Comparing formula (11-2-1) and (11-2-3) obtaining,
Showing average flow velocity of section is only 20％ of axes
velocity.Ventilation,air-condition engineering usually used high velocity
region around axes.So,is not reflect velocity in used region,Therefor
applying average velocity of mass, It is defined that take
multiply mass obtain virtual momentum,Deducing momentum
conservation equation of outlet section and any transverse section,
1?
m?? 2.01 ?
1?
2?
Comparing（ 11—2—1） and（ 11—2—4）,.So,
take denote flow velocity is more suitable than,But must
notice,,not only different in value,more important different in
definition,
m?? 47.02 ?
2? 1?
1? 2?
2?
34
四、质量平均流速 v2
断面平均流速 表示射流断面上的算术平均值。比较
（ 11—2—1）、（ 11—2—3）两式，可得 。说明断
面平均流速仅为轴心流速的 20％。通风、空调工程上通常使
用的是轴心附近较高的速度区。因此 不能恰当的反映被使
用区的速度。为此引入质量平均流速 。质量平均流速定义
为：用 乘以质量即得真实动量。列出口截面与任一横截面
的动量守恒式,
1?
m?? 2.01 ?
1?
2?
2?
4)2( 1 1
1 4 7.0
23.0
2 9 4.0
4 5 4 5.0
00
0
0
2
200
——
?
?
?
??
?
d
as
r
asQ
Q
QQ
?
?
????
比较（ 11—2—1）与（ 11—2—4）式,。因此用
代表使用区的流速要比 更合适。但必须注意,,不仅在
数值上不同，更重要的是在定义上根本不同，不可混淆。
m?? 47.02 ? 2?
1? 1? 2?
35
Variety rule of motion parameter of diffusion main segment in
circular section,this rule is also suitable for rectangle muzzle.But
translate rectangle into corresponding diameter of flow velocity
and substitute into calculating,
Solution,Consulting table 11-1 obtaining a＝ 0.12.Applying (11-2-1)
/sm 7.2610)6.0(
4
45.9
4
45.945.9
45.9147.24.4)147.0(4.4
m / s 25.210225.0225.0
225.0
147.0
6.0
1012.0
48.0
147.0
48.0
32
0
2
00
00
0
0
0
????????
?????
????
?
?
?
?
?
?
?
?
?
??
?
?
dQQ
d
as
Q
Q
d
as
m
m
Example 11—1 Transporting wind with axes flow wind machine,
its diameter d0=600 mm 。 Wind velocity of outlet 10 m/s,what
are axes velocity and throughput from outlet 10 m?
36
以上分析出圆断面射流主体段内运动参数变化规律，这些
规律亦适用于矩形喷嘴。但要将矩形换算成为流速当量直径代
入进行计算。
解 由表 11—1查得 a＝ 0.12。用（ 11—2—1）式
/sm 7.2610)6.0(
4
45.9
4
45.945.9
45.9147.24.4)147.0(4.4
m / s 25.210225.0225.0
225.0
147.0
6.0
1012.0
48.0
147.0
48.0
32
0
2
00
00
0
0
0
????????
?????
????
?
?
?
?
?
?
?
?
?
??
?
?
dQQ
d
as
Q
Q
d
as
m
m
例 11—1 用轴流风机水平送风，风机直径 d0=600 mm 。出口
风速 10 m/s,求距出口 10 m 处的轴心速度和风量。
37
§ 11-4 Plane diffusion
Gas diffusing from narrow gap,diffusion expending in plane of
upright gap,If the gap is quite long,this flow can be considered as
plane motion called plane diffusion,
Height of muzzle in plane diffusion expressed with 2b0（ b0
half height）,value a is back three item in table11-1; value j is
2.44,and then tan a＝ 2.44a。 And characteristics of
geometrical,kinetic,moving are similar to diffusion in section,So,
deducing kinetic parameter and rule are also similar to circular
section’s,Listing formula in table 11-3,
38
§ 11-4 平面射流
气体从狭长缝隙中外射运动时，射流只能在垂直条缝长度
的平面上扩散运动。如果条缝相当长，这种流动可视为平面运
动，故称为平面射流。
平面射流喷口高度以 2b0（ b0半高度）表示,a值见表 11-1
后三项； j值为 2.44，于是 tan a＝ 2.44a。而几何、运动、动力
特征则完全与圆断面射流相似。所以各运动参数规律的推导基
本与圆断面类似，这里不再推导，列公式于表 11-3中。
39
average velocity of
mass
Calculation of diffusion parameter Table 11—3
parameter sequence diffusion in circular section plane diffusion
expending angle
diffusion diameter
throughput
average velocity of
section
axes velocity
a
D
d
m?
Q
1?
2?
a4.3tan ??
)1 4 7.0(8.6
00
?? dadD s
1 4 7.0
48.0
0
0 ?
?
d
asm?
?
)147.0(4.4
00
?? dasQQ
1 4 7.0
0 9 5.0
0
0
1
?
?
d
as?
?
1 4 7.0
23.0
0
0
2
?
?
d
as?
?
?? 44.2ta n ?
)41.0(44.2
00
?? basbb
41.0
2.1
0
0 ?
?
b
as
m
?
?
41.02.1
00
?? basQQ
41.0
4 9 2.0
0
0
1
?
?
b
as?
?
41.0
8 3 3.0
0
0
2
?
?
b
as?
?
main
segment
name
segment
40
射流参数的计算 表 11—3
段名
主
体
段
参数名称 序号 圆断面射流 平面射流
扩散角
射流直径或半高度
流量
断面平均流速
质量平均流速
轴心速度
a
D
d
m?
Q
1?
2?
a4.3tan ??
)1 4 7.0(8.6
00
?? dadD s
1 4 7.0
48.0
0
0 ?
?
d
asm?
?
)147.0(4.4
00
?? dasQQ
1 4 7.0
0 9 5.0
0
0
1
?
?
d
as?
?
1 4 7.0
23.0
0
0
2
?
?
d
as?
?
?? 44.2ta n ?
)41.0(44.2
00
?? basbb
41.0
2.1
0
0 ?
?
b
as
m
?
?
41.02.1
00
?? basQQ
41.0
4 9 2.0
0
0
1
?
?
b
as?
?
41.0
8 3 3.0
0
0
2
?
?
b
as?
?
41
average
velocity of
section
average
velocity of
mass
core length
distance from muzzle
to pole point
convergent angle
throughput Q
1?
2?
ns
0x
?
2
000
)(32.176.01 rasrasQQ ???
2
00
2
00
0
1
)(56.118.61
)(32.176.01
r
as
r
as
r
as
r
as
??
??
?
?
?
2
00
0
2
)(32.176.01
1
r
as
r
as ????
?
arsn 0672.0?
arx 00 294.0?
a49.1tan ??
00
43.01 basQQ ??
0
0
0
1
44.21
43.01
b
as
b
as
?
?
?
?
?
0
0
2
43.01
1
b
as???
?
absn 003.1?
abx 00 41.0?
a97.0tan ??
initial
segment
42
起
始
段
流量
断面平均流速
质量平均流速
核心长度
喷嘴至极点距离
收敛角
Q
1?
2?
ns
0x
?
2
000
)(32.176.01 rasrasQQ ???
2
00
2
00
0
1
)(56.118.61
)(32.176.01
r
as
r
as
r
as
r
as
??
??
?
?
?
2
00
0
2
)(32.176.01
1
r
as
r
as ????
?
arsn 0672.0?
arx 00 294.0?
a49.1tan ??
00
43.01 basQQ ??
0
0
0
1
44.21
43.01
b
as
b
as
?
?
?
?
?
0
0
2
43.01
1
b
as???
?
absn 003.1?
abx 00 41.0?
a97.0tan ??
43
§ 11-5 Diffusion of temperature and thickness difference
In heating and ventilating engineering,usually applying cold wind for
dropping heating,applying sirocco for heating,here diffusion of temperature
difference is used,It is used diffusion of thickness difference to drop thickness of
nocuous gas and gas,So called diffusion of temperature and thickness difference
is the difference between temperature and thickness of diffusion and around gas,
Analyzing diffusion of temperature and thickness difference,mostly studying
distributing rule of temperature and thickness difference,Talking about curly
axes track produced by temperature and thickness difference,
In forming process of diffusion,producing transverse momentum
exchange,vortex appearing,making its mass exchange,heat exchange,thickness
exchange,In these exchange,heat expending faster than momentum expending,
so temperature boundary layer is thicker than velocity boundary layer.As 11-3a,
Real line is velocity boundary layer,broken line is inside and outside line of
temperature boundary layer,
44
§ 11-5 温差或浓差射流
在采暖通风空调工程中，常采用冷风降温，热风采暖，这
时就要用温差射流。将有害气体及灰尘浓度降低就要用浓差射
流。所谓温差、浓差射流就是射流本身的温度或浓度与周围气
体的温度、浓度有差异。
温差或浓差射流分析，主要是研究射流温差、浓差分布场
的规律。同时讨论由温差、浓差引起射流弯曲的轴心轨迹。
在射流的形成过程中，会产生横向动量交换，旋涡的出现，
使之质量交换，热量交换，浓度交换。在这些交换中，热量扩
散比动量扩散要快些，因此温度边界比速度边界层发展要快些
厚些，如图 11-3a所示。实线为速度边界层，虚线为温度边界
层的内外界线。
45
Thickness expending is similar to temperature’s,in practice,in
order to predigest,considering boundary besides temperature and
thickness are equal with outside and inside boundary of velocity,
(a)
0 1? 2? 3? 4?4? 3? 2? 1?
2.0
4.0
6.0
8.0
0.1
m?
?
mT
T??
(b)
Fig.11—3 boundary layer of temperature and velocity
Supposing to express around gas with subscript e
46
浓度扩散与温度相似，在实际应用中，为了简化起见，可以
认为，温度、浓度内外的边界与速度内外的边界相同。
(a)
0 1? 2? 3? 4?4? 3? 2? 1?
2.0
4.0
6.0
8.0
0.1
m?
?
mT
T??
(b)
图 11—3 温度边界层与速度边界层的对比
设以足标 e表示周围气体的符号。
47
eTTT ??? 00
emm TTT ???
For diffusion of temperature difference,
Temperature difference
in outlet section
Temperature difference of axes
eTTT ???
Any point temperature
difference of section
exxx ??? 00
emm xxx ???
exxx ???
Thickness of outlet section
Thickness
difference of axes
Any point thickness
difference of section
For diffusion of thickness difference,
48
eTTT ??? 00
emm TTT ???
对温差射流,
出口断面温差
轴心上温差
eTTT ???
截面上任一点温差
对浓差射流,
exxx ??? 00
emm xxx ???
exxx ???
出口断面浓度
轴心上浓差
断面上任意一点浓差
49
Distributing relation of temperature difference,thickness
difference and velocity obtained by experiments,
5.1
1 ?????????????? RyxxTT
mmm ?
? 11-4-1
In isotonic instance,taking enthalpy value of around gas as
initial calculating point,relatively enthalpy value in diffusion
sections keeping invariably,This is called heat power character,
Supposing relative enthalpy value of section per unit time is;relative enthalpy value of per unit time through any
transverse section is
00 TCQ ??
? ?Q TdQc?
一,Temperature difference in axes mT?
Owing to relative enthalpy value is equal,obtaining
? ???? R y d yTcTcQ 000 2 ????
After division by,and substituting formula 11-4-1
into,deducing just as section 2,parameters calculating formula listed
in table 11-4,
mm TcR ???? 2
50
试验得出，截面上温差分布，浓差分布与速度分布关系
如下,
5.1
1 ?????????????? RyxxTT
mmm ?
? 11-4-1
在等压的情况下，以周围气体的焓值作为起算点，射流各
横截面上的相对焓值不变。这一特点称为热力特征。
设喷嘴断面上单位时间的相对焓值为,射流任意
横截面上单位时间通过的相对焓值 。
00 TCQ ??
? ?Q TdQc?
一、轴心温差 mT?
根据相对焓值相等，得,? ???? R y d yTcTcQ
000 2 ????
两端除以,并将 11-4-1式代入，其推导与第二节
方法类似，各参数计算公式列于表 11-4中。
mm TcR ???? 2
51
Diffusion calculation of thickness difference table 11—4
segment name
main
segment
circular section
diffusion plane diffusion
parameter
name
axes
temperature
difference
average
temperature
difference in
mass
thickness
difference
in axes
symbol
mT?
2T?
mx?
1 4 7.0
35.0
0
0 ?
???
d
asT
T m
147.0
23.0
0
0
2
?
???
d
asT
T
1 4 7.0
35.0
0
0 ?
???
d
asx
x m
41.0
032.1
0
0 ?
???
b
asT
T m
41.0
8 3 3.0
0
0
2
?
???
b
asT
T
41.0
032.1
0
0 ?
???
b
asx
x m
52
浓差温差的射流计算 表 11—4
段名
主
体
段
参数名称
轴心温差
质量平均
温差
轴心浓差
符号 圆 断 面 射 流 平 面 射 流
mT?
2T?
mx?
1 4 7.0
35.0
0
0 ?
???
d
asT
T m
147.0
23.0
0
0
2
?
???
d
asT
T
1 4 7.0
35.0
0
0 ?
???
d
asx
x m
41.0
032.1
0
0 ?
???
b
asT
T m
41.0
8 3 3.0
0
0
2
?
???
b
asT
T
41.0
032.1
0
0 ?
???
b
asx
x m
53
continuous table
segment
name
main
segment
symbol
average
thickness
difference in
mass
track
equation
in axes
2x?
2T?
2x?
1 4 7.0
23.0
0
0
2
?
???
d
asx
x
2
00
0
2
)(32.176.01
1
r
as
r
asT
T
??
???
2
00
0
2
)(32.176.01
1
r
as
r
asx
x
??
???
41.0
8 3 3.0
0
0
2
?
???
b
asx
x
0
0
2
43.01
1
b
asT
T
?
???
0
0
2
43.01
1
b
asx
x
?
???
)35.0c o s51.0(
)c o sA r (t a n
0
2
000
??
??
?
??
a
ax
d
x
d
x
d
y
2/5
0
2
01
0
01
2
2/5
0
0
)205.0
2
(226.0
r
/
2
/
)205.0
2
(r226.0
2
??
?
?
??
?
b
xa
a
TT
b
y
TTa
b
xa
b
y
Initial
segment
parameter
name
average
thickness
difference in
mass
average
temperature
difference in
mass
circular section
diffusion plane diffusion
54
续表
段名
主
体
段
参数名称
质量平均
温差
符号 圆 断 面 射 流 平 面 射 流
2x?
2T?
2x?
1 4 7.0
23.0
0
0
2
?
???
d
asx
x
2
00
0
2
)(32.176.01
1
r
as
r
asT
T
??
???
2
00
0
2
)(32.176.01
1
r
as
r
asx
x
??
???
41.0
8 3 3.0
0
0
2
?
???
b
asx
x
0
0
2
43.01
1
b
asT
T
?
???
0
0
2
43.01
1
b
asx
x
?
???
质量平均
浓差
质量平均
浓差
起
始
段
轴线轨迹
方程 )35.0
c o s51.0(
)c o sA r (t a n
0
2
000
??
??
?
??
a
ax
d
x
d
x
d
y
2/5
0
2
01
0
01
2
2/5
0
0
)205.0
2
(226.0
r
/
2
/
)205.0
2
(r226.0
2
??
?
?
??
?
b
xa
a
TT
b
y
TTa
b
xa
b
y
55
2,diffusion inflecting
Temperature or thickness difference diffusion is owing to
density different from around density,gravity and buoyancy is not
balance,which making diffusion inflect downwards or upwards,as
show in fig.11-4,But whole diffusion is still symmetrical to axes
line,So finding out inflecting track of axes line,then obtaining
whole inflecting diffusion,
x x
y
y?
?tanx
y
d
?
A?
A
?A
ge??
gm??
Fig.11—4 inflection of diffusion axes
56
二、射流弯曲
温差射流或浓差射流由于密度与周围密度不同，所受的重
力与浮力不相平衡，使整个射流将发生向下或向上弯曲，见图
11-4。但整个射流仍可看作是对称于轴心线。因此了解轴心线
的弯曲轨迹后，便可得出整个弯曲的射流。
x x
y
y?
?tanx
y
d
?
A?
A
?A
ge??
gm??
图 11—4 射 流 轴 线 的 弯 曲
57
Applying approximate disposal method,taking flow of per unit
volume in axes as study object.Only considering gravity and
buoyancy,applying Newton law and experiment data,deducing half
empirical formula listed in table 11-4
here：, is Archimedes standard number
e
r Tv
TgdASx
2
0
00,
c o s
???
?Example 11-2 In working spot requiring average wind velocity is
3m/s,working face diameter D＝ 2.5m,giving wind temperature 5℃,
air temperature 30℃, requiring average temperature of mass fall to
25℃, applying ventilator with guide leaf,its turbulent coefficient a＝
0.12。 find（ 1） diameter and velocity of outlet;（ 2） distance from
outlet to working face,
Solution,
Temperature
difference
C1530150 ?????? T
C530252 ?????? T
15
5
147.0
23.0
0
0
2
?
??
?
???
d
asT
T
58
采用近似的处理方法：取轴心线上的单位体积流体作为研究
对象，只考虑受重力与浮力作用，应用牛顿定律和实验数据，导
出半经验公式列于表 11-4中。
该公式中：,成为阿基米德准数。
e
r Tv
TgdASx
2
0
00,
c o s
???
?
例 11-2 工作地点质量平均风速要求 3m/s，工作面直径 D＝ 2.5m，
送风温度为 15℃,车间空气温度 30℃,要求工作地点的质量平均
温度降到 25℃,采用带导叶的通风机，其紊流系数 a＝ 0.12。求
（ 1）风口的直径及速度；（ 2）风口到工作面的距离。
解 温差 C1530150 ?????? T
C530252 ?????? T
15
5
147.0
23.0
0
0
2
?
??
?
???
d
asT
T
59
69.051523.01 4 7.0
0
????das
finding, substituting into
69.08.6147.08.6
00
????
?
?
???
? ??
d
as
d
D
so
average wind velocity of mass in
working spot required 3m/s
for
therefore
m5 2 5.069.08.6 5.269.08.60 ????? Dd
0
0
0
2 3
15
5
1 4 7.0
23.0
v
d
asv
v ??
?
?
m /s90 ?v
60
求出,代入下式
69.051523.01 4 7.0
0
????das
69.08.6147.08.6
00
????
?
?
???
? ??
d
as
d
D
所以
工作地点质量平均风速要求 3m/s
因为
所以
m5 2 5.069.08.6 5.269.08.60 ????? Dd
0
0
0
2 3
15
5
1 4 7.0
23.0
v
d
asv
v ??
?
?
m /s90 ?v
61
（ 2） finding distance s from wind outlet to
working face by
。 m4.2 5 4 3.05 2 5.0 12.0 ; 69.01 4 7.0
0
???? ssdas
Thinking problems
11-3 what is average velocity in mass?Why citing this flow
velocity？
11-4 why diffusion temperature difference track inflecting？
How to find track equation？
2?
62
（ 2）风口到工作面距离 s 可用下式求出
。 m4.2 5 4 3.05 2 5.0 12.0 ; 69.01 4 7.0
0
???? ssdas
复习思考题
11—3 什么是质量平均流速？为什么要引入这一流速？
11—4 温差射流轨迹为什么弯曲？是怎样寻求轨迹方程的？
2?
63
§ 11-6 Other familiar diffusion in engineering equipment
1,adherence diffusion
Different from free diffusion,if put muzzle adhere to top
shed or wall,show as fig.11—6,then because of restrict of wall,it
can‘ t roll and absorb air in wall face,velocity attenuate slowly,
so velocity is high,resting pressure is low,then velocity is low
and resting pressure is high in the other side,which making
airflow moving adhere wall,called adherence diffusion,
b
s
02b
0b
Fig,11—6 adherence diffusion
64
§ 11-6 工程设备中常见的其他射流简介
一、贴附射流
与自由射流不同，如把喷口贴近顶棚或墙壁布置，如图
11—6所示，则由于壁面的限制，壁面处不能卷吸空气，速
度衰减慢，因而流速大，静压小，而另一侧则流速小，静压
大，使得气流贴附于壁面流动，并称之为贴附射流。
b
s
02b
0b
图 11—6 贴附射流
65
Due to adherence diffusion roll and absorb around fluid
only in one surface,so attenuate slowly,diffusion way is longer
than free diffusion with same muzzle,
Adherence diffusion can be regarded as half of integral
diffusion,Its law invariable,so can calculate as double
according to outlet section,outlet flow velocity invariable.In
calculating,substituting outlet diameter d0 in free diffusion with
d0,for plane diffusion,substituting half height of outlet b0 with
2b0。
2
66
由于贴附射流仅一面卷吸周围流体，故衰减较慢，射程
较同样喷口的自由射流为长。
贴附射流可视为完整射流得一半，其规律不变，因而可
按风口断面加倍，出口流速不变的完整射流进行计算。也就
是说，计算中只需将自由射流公式的送风口直径 d0代以 d0，
对于平面射流，则需将风口半高度 b0代以 2b0。
2
67
2,Diffusion in finite space
Usually in project,diffusion don’t diffuse to infinite space,
because of finite size of room,which restrict expending motion of
diffusion,here free diffusion law isn’t suitable,must restudy its
kinetic law.At present,there is no well results,most is empirical
formula or curve by experiment,now introducing,
As show in fig.11-7 is diffusion field structure in finite space,
From diffusion outlet to Ⅰ － Ⅰ section,because solid wall faces
don’t restrict diffusion expending,free diffusion rules are suitable,
calculation can also use free diffusion formula.Ⅰ － Ⅰ section called
first critical section,
68
二、有限空间射流
通常，工程中射流并不是射入无限大空间，因房间尺寸有
限，限制了射流的扩散运动，此时自由射流规律不再适用，须
重新研究其运动规律。目前，理论上还没有成熟的结果，大多
是由实验得到的经验公式或无因次曲线，现作简介。
图 11-7所示为有限空间射流流场结构。从射流出口至 Ⅰ －
Ⅰ 断面，因固体壁面尚未妨碍射流的扩展，射流的发展按照自
由射流的规律，计算亦可用自由射流公式。称 Ⅰ － Ⅰ 断面为第
一临界断面。
69
fig.11—7 diffusion field in finite space
70
图 11—7 有限空间射流流场
71
Starting from sectionⅠ － Ⅰ,diffusion expending is affected,
action of rolling and aborbing around liquid become weak,so
expending of diffusion section and increasing of throughput become
slowly,to sectionⅡ － Ⅱ,diffusion streamline begin to exceed
boundary layer and engender refluence,diffusion throughput begin to
reduce along diffusion way,so diffusion throughput get max value in
sectionⅡ － Ⅱ, Through experiment,average velocity and throughput
of refluence are also max,SectionⅡ － Ⅱ called second critical section,
From sectionⅡ － Ⅱ,main segment throughput,throughput of
refluence and average velocity of refluence are all becoming low in
turn,till section Ⅳ － Ⅳ,main segment throughput reduce to 0,
In this way,it may plot three segment of diffusion in finite space,
（ 1） free expending segment,from spout to first critical section
（ 2） finite expending segment,from first to second critical section
（ 3） contracted segment,from second critical section to last;
72
从 Ⅰ － Ⅰ 断面开始，射流的扩展受到影响，卷吸周围流
体的作用减弱，因而射流断面的扩大以及流量的增加比较缓
慢，达到 Ⅱ － Ⅱ 断面，射流流线开始越出边界层产生回流，
射流流量开始沿程减少，因而射流流量在 Ⅱ － Ⅱ 断面取得最
大值。由实验得知，该处的回流平均流速、回流流量亦为最
大。称 Ⅱ － Ⅱ 断面为第二临界断面。
从 Ⅱ － Ⅱ 断面以后，射流主体流量、回流流量、回流平
均流速都依次变小，直至 Ⅳ － Ⅳ 断面，射流主体流量减至为
零。
这样，有限空间射流可以划分为三段,
（ 1）自由扩张段，喷口至第一临界断面；
（ 2）有限扩张段，第一临界断面至第二临界断面；
（ 3）收缩段，第二临界断面以后。
73
Diffusion structure behaving when diameter and throughput
increasing to certain,then decreasing,making its boundary
become olive form,
Diffusion structure relates to fixed place of muzzle,If muzzle
fixed in the middle of height and width in room,diffusion structure
is symmetrical from up to down,left to right,main segment
showing olive form,around is refluence region.But in practice,
muzzle fixed close to top shed,if fixed height h and room H are
,diffusion appears adherence phenomenon,Hh 7.0?
74
而射流结构则表现为射流半径和流量在增大到一定程
度后反而减小，使其边界线呈橄榄形。
射流结构还与喷嘴的安装位置有关。如喷嘴安装在房间高
度、宽度的中央处，射流结构上下对称，左右对称，射流主体
呈橄榄形，四周为回流区。但实际送风时多将喷嘴靠近顶棚安
置，如安装高度 h与房高 H为 时，射流出现贴附现象,Hh 7.0?
75
Characteristic of diffusion in finite space is different free
diffusion is, there is refluence region reverse to diffusion region
outside the olive boundary,and working region is often in
refluence region in air-condition project,so there is restrict to
wind velocity in refluence region,The empirical formula of
average velocity in refluence region is, ?
come into half-olive form diffusion field,correspond to half of
integral diffusion in finite space,and that refluence focus on
bottom of main segment and ground,its kinetic law is same
with diffusion in finite space,considered half of diffusion in
finite space,
76
形成呈半个橄榄状的流场，相当于完整的有限空间射流的
一半，而回流区集中在射流主体下部与地面间，其运动规律与
有限空间射流相同，看作有限空间射流的一半。
有限空间射流不同于自由射流的重要特征是橄榄形边界
外部存在与射流方向相反的回流区，而空调工程中工作区通
常就设在回流区内，因此对回流区的风速有限定要求。回流
平均速度 的半经验公式为 ?
77
)()10(1 7 7.0 2377.10
00
xfexd F xx ?? ???
11-5-1
here,is outlet velocity and diameter of muzzle;F is cross
section area upright to diffusion room； is distance from
diffusion section to pole point;a为 is turbulent flow coefficient,
00,d?
F
axx ?
If basing on design,distance from L,requiring average velocity
of diffusion refluence is certain restricted value,then from
formula 11-5-1 1?
)(
00
1 LfdF ???? 11-5-3
69.0
00
?d Fm?? 11-5-2
In section － Ⅱ,refluence velocity is max,express with
from expriment obtain corresponding,substituting above
formula obtaining max refluence velocity,
2.0?x
m?
78
)()10(1 7 7.0 2377.10
00
xfexd F xx ?? ???
11-5-1
式中,为喷嘴出口速度、直径； F为垂直于射流的房
间横截面积； 为射流截面至极点的无因次距离； a为紊
流系数。
00,d?
F
axx ?
69.0
00
?d Fm?? 11-5-2
若根据设计要求，在距离 L处，要求射流回流平均流速为
某一限定值,则由式 11-5-1得
1?
)(
00
1 LfdF ???? 11-5-3
在 Ⅱ － Ⅱ 断面上，回流流速为最大，以 表示，由实验
得对应,代入上式得最大回流速度为 2.0?x m
?
79
Uniting formula 11-5-2 and 11-5-3,obtaining
m
Lf ?? 169.0)( ?
11-5-4
In project design and determined by designer,so is
known,solution is, in order to predigest calculation give table
11-5,through, consulting table 11-5,obtaining
then through obtaining 。
m? 1?
)(Lf
L
m? 1?
L
a
FLL ? L
above formulas are suitable for or in
adherence diffusion,when,it is integral finite space
diffusion,substituting with,then obtaining diffusion way
here.,
Hh 7.0? Hh 3.0?
HhH 7.03.0 ??
F5.0F
L
80
联立式 11-5-2和式 11-5-3可得
m
Lf ?? 169.0)( ?
11-5-4
工程设计中 与 由设计者限定，故 相当于已知，由
此可解出,为简化计算给出表 11-5。由, 查表 11-5得到
后可由 求出 。
m? 1? )(Lf
L m? 1? L
a
FLL ? L
以上所给出公式适用于 或 的贴附射流，当
时，射流为完整的有限空间射流，计算时应以 代
替,即可求得此时的射程 。
Hh 7.0? Hh 3.0?
HhH 7.03.0 ?? F5.0
F L
81
table 11-5 dimensionless distance
)m/s(
m?
)m/s/(1?
0.07 0.10 0.15 0.20 0.30 0.40
0.50
0.60
0.75
1.00
1.25
1.50
0.42
0.43
0.44
0.46
0.47
0.48
0.40
0.41
0.42
0.44
0.46
0.47
0.37
0.38
0.40
0.42
0.43
0.44
0.35
0.37
0.38
0.40
0.41
0.43
0.31
0.33
0.35
0.37
0.39
0.40
0.28
0.30
0.33
0.35
0.37
0.38
L
82
表 11-5 无因次距离
)m/s(
m?
)m/s/(1?
0.07 0.10 0.15 0.20 0.30 0.40
0.50
0.60
0.75
1.00
1.25
1.50
0.42
0.43
0.44
0.46
0.47
0.48
0.40
0.41
0.42
0.44
0.46
0.47
0.37
0.38
0.40
0.42
0.43
0.44
0.35
0.37
0.38
0.40
0.41
0.43
0.31
0.33
0.35
0.37
0.39
0.40
0.28
0.30
0.33
0.35
0.37
0.38
L
83
Example 11-4 In workshop length× width× height ＝
70m× 30m× 12m,giving wind along direct length,circular wind
outlet with diameter1m,it fixed on place 6m distance from wall height,
turbulent flow coefficient is 0.08,Max refluence velocity is 0.75m/s,
refluence velocity is 0.3m/s in workaround,what is giving wind
throughput and where is workaround? If wind outlet improving 3m,
how to change above calculation results?
Solution （ 1） height of wind outlet h＝ 0.6m,H＝ 12m then h/H
＝ 0.5,in spectrum（ 0.3～ 0.7） H,diffusion doesn’t adherence,in
formula substituting F with 0.5F,from formula 11-5-2 obtaining
m / s6.1469.01 12305.075.069.0 5.0
0
0 ??
?????? F
d
m??
s/m45.116.14144 320200 ????? ??? dQ
Through consulting table 11-5
obtaining, then
,3.0,75.0 1 ?? ?? m
35.0?L
84
例 11-4 车间空间长 × 宽 × 高＝ 70m× 30m× 12m，长度方向送
风，直径 1m的圆形风口设在墙高中央 6m处，紊流系数为 0.08。设
计限制最大回流速度为 0.75m/s，工作区处回流速度为 0.3m/s，求
风口送风量和工作区设置在何处？若风口提高 3m，以上计算结果
如何改变？
解 （ 1）风口高 h＝ 0.6m,H＝ 12m则 h/H＝ 0.5，在（ 0.3～ 0.7）
H范围内，射流不贴附，公式中 F用 0.5F代，由式 11-5-2得
m / s6.1469.01 12305.075.069.0 5.0
0
0 ??
?????? F
d
m??
s/m45.116.14144 320200 ????? ??? dQ
由 查表 11-5得,则,3.0,75.0
1 ?? ?? m
35.0?L
85
m7.5808.0 12305.035.05.0 ?????? a FLL
with non-adherence diffusion increasing times
（ 2）,then,comparing adherence diffusion
69.000
F
dm
?? ?
5.0
1
m9?h 7.075.0
12
9 ???
H
h
6 7, 0 3 m5 8, 7
5.0
1
/s1 6, 2 m1 1, 4 5
5.0
1
m / s65.206.14
5.0
1
3
0
0
???
???
???
L
Q
?
三,Diffusion in crosscurrent
86
m7.5808.0 12305.035.05.0 ?????? a FLL
与不贴附相比增大
（ 2） m9?h,则 7.075.0
12
9 ???
H
h,为贴附射流 69.0
0
0
F
dm
?? ?
5.0
1 倍，即
6 7, 0 3 m5 8, 7
5.0
1
/s1 6, 2 m1 1, 4 5
5.0
1
m / s65.206.14
5.0
1
3
0
0
???
???
???
L
Q
?
三、横流中的射流
87
In project,often meet diffusion as show in fig.11-8,its main airflow with
velocity,its size larger than size of diffusion muzzle,diffusion with original
velocity diffuse above main airflow at obliquity a,after coming into,
exchanging momentum with main airflow,due to mass of main airflow more
large,corresponding momentum is also large more,when diffusion diffuse into
main airflow certain depth,gradually turning around oppressed by main airflow,
at last assimilated by main airflow,
1?
2?
main a ir flow
trochoid of
diffusion
diffusio
n
y
y?
1V 1T
d
22TV
?
fig,11—8 flow of diffusing into upright airflow
88
射流轨迹线
射流
y
y?
1V 1T 主气流
d
22TV
?
图 11—8 射流射入垂直主气流时的流动
工程上常能遇到如图 11-8所示得射流情况，具有 流速得
主气流，其尺寸比射流喷嘴尺寸大得多，具有初速 的射流以
某 a倾角射入上述主气流中，射流进入主气流后，即与主气流
发生动量交换，由于主气流总的质量大得多，相应的总动量也
大得多，当射流射入主气流一定深度后，逐渐被主气流压迫而
转向，最后被主气流同化。
1?
2?
89
Kinetic rule and track of diffusion（ linking line of different
velocity point in different section） relate to diffusing angle a,
muzzle shape,velocity of spout and velocity of main
airflow,If temperature of diffusing air T2 different from
temperature of main airflow T1,then considering effect of
thickness difference by temperature difference,
2?
1?
Indicating by experiment,after diffusion diffusing into main
airflow,as diffusion track expanding forwards,axes velocity
decreasing constantly,and changing direct gradually,at last have the
same value and direct with main airflow velocity,
1
2
?
?
1?
90
射流的运动规律及运动轨迹（不同断面上最大速度点连
线）与喷射角度 a、喷嘴型式、射流喷口速度 及主气流速度
等因素有关。若射流气体温度 T2与主气流温度 T1不同，则还要
考虑由于温差造成的密度差的影响。
2? 1?
实验表明，射流射入主气流后，随着射流轨迹向前发展，
轴心速度不断降低，并逐渐转向，最后趋于与主流流速 同值
同向，并且速度比值 越小，则射流轴心速度下降得越快，也
就是说 越小，主气流, 同化, 射流的能力越强，所以欲使射
流射入更深，可提高 值，也就是提高射流的射入速度 。
1
2??
1
2??
1
2??
1?
2?
91
and more little as velocity ratio,more fast as axes velocity of
diffusion,is more little,the ability of main airflow,assimilate”
diffusion is more strong,so wish diffusion diffuse deeper should
improve, namely improving diffusing velocity,
1
2??
1
2??
2?
Effects of temperature difference of airflow incarnate effects
of thickness difference, Cold diffusion with uniform velocity
ratio,due to its high density,momentum is also great,so
penetrating depth of cold diffusion is larger than cold diffusion’s,12?
? 22??
Ivanov concluded diffusion track equation by experiment,this is
empirical formula,embodying effects of velocity ratio,temperature
ratio and diffusing angle,
92
气流温度差别的影响体现在气流密度差别的影响上。速
度比值 相同的冷射流由于其密度大，单位质量的动量 相
应也大，故冷射流穿透深度比热射流大。
1
2?? 2
2??
伊万诺夫由实验归纳得到下述射流轨迹方程，这是一个经验
公式，其中同时体现了速度比、温度比及射入角的共同影响。
实验表明，射流射入主气流后，随着射流轨迹向前发展，
轴心速度不断降低，并逐渐转向，最后趋于与主流流速 同值
同向，并且速度比值 越小，则射流轴心速度下降得越快，也
就是说 越小，主气流, 同化, 射流的能力越强，所以欲使射
流射入更深，可提高 值，也就是提高射流的射入速度 。
1
2??
1
2??
1
2??
1?
2?
93
Here,x is horizontal distance; y is vertical distance; d is diameter of
diffusion muzzle; a is diffusing angle,
using spectrum of formula,400~25,2,120~60
211
222
1
2 ??? ?? ??TTa ??
)90t a n (
33.1
2
22
2
11 ???
?
??
?
???
?
??
?
???
?
?
???
?? a
d
x
d
x
d
y
??
?? 11-5-5 。
As for velocity field of this diffusion,due to similar law
doesn’t exist,so can’t conclude empirical formula,can but
measure,
94
至于该射流的速度场，因不存在相似的规律，故总结不
出经验公式，只能具体测定。
)90t a n (
33.1
2
22
2
11 ???
?
??
?
???
?
??
?
???
?
?
???
?? a
d
x
d
x
d
y
??
?? 11-5-5
式中,x为水平距离； y为垂直距离； d为射流喷嘴直径； a为射
入角。
公式的使用范围为,
400~25,2,120~60 2
11
2
22
1
2 ???
??
??
T
Ta ??
。
95
Example 10-5 as fig.11-9 show,there is air diffusion with diameter
d＝ 100mm,its initial momentum is with horizontal
line form 60° upwards,It diffuing into vertical upwards main
airflow,main airflow momentum is, Temperature of
them is same,try to protract trochoid after diffusion diffusing into
main airflow,
N4000222 ???
N1 6 0211 ???
Solution,according to definition of a in fig.11-8,here a＝ 150°,
substituting a and known condition into formula into11-5-5,
obtaining
x
y?
y
o
fig,11—9 of example 11—5
96
例 10-5 如图 11-9所示，有一股直径为 d＝ 100mm的空气射流以
初始动量 与水平线成向下 60° 方向射入到一股垂直
向上的主气流中，主气流的动量为 。射流温度与主气
流温度相同，试绘制射流射入主气流后的轨迹线。
N4000222 ???
N1 6 0211 ???
解 按图 11-8所示的 a角定义，此处 a＝ 150°,把 a及所给已知
条件代入式 11-5-5，得
x
y?
y
o
图 11—9 例 11—5
97
table 11-6 corresponding table of value of x and y
x/m 0.2 0.4 0.6 0.8 1.0 1.2 1.4
y/m -0.334 -0.595 -0.71 -0.606 -0.209 0.553 1.754
Review and thinking problem
1.why strip and slot diffusion called plane diffusion?
2.why adherence diffusion can attain more far diffusing way?
732.10 1 5 2 3.0)90150t a n (4 0 0 0160
333.1
????????????????????????????? dxdxdxdy ??
Taking different value of,obtaining different value of
and y,results as in table 11-6,diffusion track in fig.11-9 d
x
dy
98
表 11-6 x,y 值 对 应 表
x/m 0.2 0.4 0.6 0.8 1.0 1.2 1.4
y/m -0.334 -0.595 -0.71 -0.606 -0.209 0.553 1.754
复习思考题
1.为何称条缝射流为平面射流？
2.为何贴附射流可以达到更远的射程？
732.10 1 5 2 3.0)90150t a n (4 0 0 0160
333.1
????????????????????????????? dxdxdxdy ??
取不同的 值，即可得到不同的 值及 y值，结果如表
11-6所示，射流轨迹见图 11-9。 d
x dy
99
Exercise of Chapter 11
11—1 Air shower region required diffusion radii is 1.2 m,average
velocity of mass,diameter of circular muzzle is 0.3
m,find（ 1） the distance s from spout to working zone ;
(2) throughput of muzzle。
m /s 32 ??
Solution （ 1） from11—1,obtaining coefficient of turbulent
flow a=0.08 。
（ 2） find s, from formula（ 11—1—2） obtaining,
00
0
3,4 ( 0,2 9 4 )
1, 2 0, 0 8
3,4 ( 0,2 9 4 )
0, 1 5 0, 1 5
th e r e f o r e 3, 8 6 m
R a s
rr
R
s
r
s
??
??
?
100
第十一章 习 题
11—1 已知空气淋浴地带要求射流半径为 1.2 m,质量平均流速
。圆形喷嘴直径为 0.3 m 。求（ 1）喷口至工作地带
的距离 s ; (2) 喷嘴流量。
m /s 32 ??
解 （ 1）由 11—1查得紊流系数 a=0.08 。
（ 2）求 s,由（ 11—1—2）式知,
m 86.3
)294.0
15.0
08.0
(4.3
15.0
2.1
)294.0(4.3
0
00
?
??
??
s
s
r
R
r
as
r
R
所以
101
0?
（ 4） find throughput Q0
applying average flow velocity of mass in main segment (11—2—4）
obtaining outlet velocity,
/sm 0 9 5.15.15)3.0(7 8 5.0
4
m / s 5.15
1 9 3.0
3
1 9 3.0
1 9 3.0
2 9 4.0
15.0
86.308.0
4 5 4 5.0
2 9 4.0
4 5 4 5.0
32
0
2
00
0
2
0
0
2
0
0
2
?????
?
???
?
?
?
?
?
?
?
?
?
?
?
?
?
?
dQ
r
as
0
0, 1 50 6 7 1 0, 6 7 1 1, 2 6,s o,
0, 0 8
f in d e d c r o s s c r o s s is in m a in s e g m e n t
nns, r /a s s? ? ? ? ?
（ 3） find core length sn
from formula（ 11—2—1），,s=sn,substituting into,obtaining 0m???
102
（ 4）求流量 Q0
应用主体段质量平均流速公式（ 11—2—4）求得出口速度,
0?
/sm 0 9 5.15.15)3.0(7 8 5.0
4
m / s 5.15
1 9 3.0
3
1 9 3.0
1 9 3.0
2 9 4.0
15.0
86.308.0
4 5 4 5.0
2 9 4.0
4 5 4 5.0
32
0
2
00
0
2
0
0
2
0
0
2
?????
?
???
?
?
?
?
?
?
?
?
?
?
?
?
?
?
dQ
r
as
（ 3）求核心长度 sn
由式（ 11—2—1），,s=sn,代入，解得
主体段内。
所求横截面在故,,26.1
0, 0 8
0, 1 50, 6 7 1 6 7 10
0 nn ss / ar.s ?????
0m???
103
11-2 Outside air diffusing into through orifice in outer wall
which distant from floor is 7.0m,Size of orifice,height is 0.35m，
length is12m。 Outside air temperature is － 10℃, inner air
temperature is 20℃, diffusion initial velocity is 2m/s,find the
temperature in floor,
calculation
Solution, taking a is 0.12
2035.0 0.72
0
??by
0022
0
( 2 ) 9, 8 0, 3 5 ( 1 0 2 0 ) 1 0 3 0, 0 8 8
2 ( 2 7 3 2 0 ) 1 1 7 0r e
g b TA
T?
? ? ? ? ?? ? ? ?
??
2 7 310
2 7 320
0 ??
??
T
T e
104
习题 11-2 室外空气以射流方式，由位于热车间外墙上离地板
7.0m处的孔口送入。孔口的尺寸，高 0.35m，长 12m。室外空
气的温度为－ 10℃,室内空气温度为 20℃,射流初速度为 2m/s，
求地板上的温度。
解, a取为 0.12
计算 20
35.0
0.7
2 0 ??b
y
0022
0
( 2 ) 9, 8 0, 3 5 ( 1 0 2 0 ) 1 0 3 0, 0 8 8
2 ( 2 7 3 2 0 ) 1 1 7 0r e
g b TA
T?
? ? ? ? ?? ? ? ?
??
2 7 310
2 7 320
0 ??
??
T
T e
105
00
2 0 2 9 3 / 2 6 3 220
2 0, 0 8 8
e
r
Ty
A b T ??
Obtaining
46;232
00
?? bxbx
Apply axes temperature difference formula
425.0
30
20
2010
20
425.0
93.5
032.1
41.04612.0
032.1
0
0
?
?
?
?
??
?
?
?
?
??
??
?
?
?
tt
TT
TT
T
T
e
e
m
C3.7 ???t
106
00
2 0 2 9 3 / 2 6 3 220
2 0, 0 8 8
e
r
Ty
A b T ??
计算求出
46;232
00
?? bxbx
用轴心温差公式
425.0
30
20
2010
20
425.0
93.5
032.1
41.04612.0
032.1
0
0
?
?
?
?
??
?
?
?
?
??
??
?
?
?
tt
TT
TT
T
T
e
e
m
C3.7 ???t
107
11-3 Data is same with example11—2,find diffusion descending
value in working face,fig.11-5）。
Solution, around air temperature Te＝ 273+30＝ 303k
y?
m43.2 m525.0 12.0 m / s9 15 000 ??????? sdakT ?
? ? m0 2 2 1.007.264.10 0 6.0
43.235.043.2
5 2 5.0
12.051.0
3 0 39
)15(8.935.051.0 23
2
23
0
2
0
0
??????
?
?
??
?
? ????
?
???
???
?
???
?
???? ss
d
a
T
Tgy
e?
m 43.2
y?
fig,11—5 diffusion descending
108
例 11-3 数据与例 11—2题相同，求射流在工作面的下降值
（图 11-5）。
解, 周围气体温度 Te＝ 273+30＝ 303k
y?
m43.2 m525.0 12.0 m / s9 15 000 ??????? sdakT ?
? ? m0 2 2 1.007.264.10 0 6.0
43.235.043.2
5 2 5.0
12.051.0
3 0 39
)15(8.935.051.0 23
2
23
0
2
0
0
??????
?
?
??
?
? ????
?
???
???
?
???
?
???? ss
d
a
T
Tgy
e?
m 43.2
y?
图 11—5射流的下降
109
110
Fluid Mechanics
2
3
Chapter 11 Gas diffusion
§ 11–1 Introduction
§ 11–2 Character of submerging turbulent
diffusion in infinite space
§ 11–3 kinetic analysis of diffusion in
circular section
§ 11–4 plane diffusion
§ 11–5 Temperature or thickness difference
of diffusion
§ 11–6 Introduction of other diffusion in project and
equipment
Exercise of Chapter 11
4
第十一章 气体射流
§ 11–1 引言
§ 11–2 无限空间淹没紊流射流的特征
§ 11–3 圆断面射流的运动分析
§ 11–4 平面射流
§ 11–5 温差或浓差射流
§ 11–6 工程设备中常见的其他射流简介
第十一章 习题
5
Flow by gas diffusing from orifice,pipe mouth or slot called
gas submerged diffusion flow.When orifice velocity is high,flow is
in turbulent state,called turbulent diffusion,Most diffusion applied
in engineering is turbulent diffusion of gas,
Diffusion describe flow velocity,temperature and thickness
after coming out,
Diffuse to infinite space,flow is not restricted by solid wall
called free diffusion.Contrarily,called restricted diffusion,
Chapter 11 Diffusion of gas
§ 11-1 Introduction
6
气体自孔口、管嘴或条缝向外喷射所形成的流动，称为气
体淹没射流。当出口速度较大，流动呈紊流状态，叫做紊流射
流。工程上所应用的射流，多为气体紊流射流。
射流讨论的是出流后的流速场、温度场和浓度场。
射流到无限大空间中，流动不受固体边壁的限制，为无限
空间射流，又称自由射流。反之，为有限空间射流，又称受限
射流。
第十一章 气体射流
§ 11-1 引言
7
§ 11-2 Characteristic of turbulent diffusion in infinite space
Take circular section diffusion as example talk about diffusion
motion,
Airflow diffused from circular section muzzle with radii
R,Velocity of outlet section is considered uniform distributing,all
are u0 and is turbulent flow,Take axis of diffusion Mx as axis x
Owing to diffusion is turbulent flow type,transverse pulse of
diffusion make exchange between mass and momentum among
diffusion and medium.Driving medium moving,mass flux,
transverse section area along x increasing,come into cone form
flow diffused to around,as in fig.11—1 CAMDF。
8
§ 11-2 无限空间淹没紊流射流的特征
现以无限空间中圆断面紊流射流为例，讨论射流运动。
气流自半径为 R 的圆断面喷嘴喷出。出口断面上的速度
认为均匀分布，皆为 u0 值，且流动为紊流。取射流轴线 Mx为
x 轴。
由于射流为紊流型，紊流的横向脉动造成射流与周围介质
之间不断发生质量、动量交换，带动周围介质流动，使射流的
质量流量、射流的横断面积沿 x 方向不断增加，形成了向周围
扩散的锥体状流动场，如图 11—1所示的锥体 CAMDF。
9
th e startin g seg m en tt h e m a i n b o d y s e g m e n t
the core
th e b o u n d a r y la y e r
x
s
0s0x
o?M
A
D
B
C
E
F
Fig,11—1 Diffusion structure
Structure and characteristic of turbulent diffusion
10
起始段 主体段
核心
边
界
层
x
s
0s0x
o?M
A
D
B
C
E
F
图 11—1 射流结构
紊流射流的结构及特性。
11
1,Initial and main segment of transition section
Diffusion velocity is uniform when just ejected, Flow along x,
diffusion bring around medium constantly,making boundary larger,and
main velocity of diffusion reduce gradually,part with velocity u0 （ as
in 11—6 AoD cone） called core of diffusion,other part with velocity
lower than u0 called boundary layer,Boundary layer disperse
constantly from outlet to around along diffusion line,driving around
medium into boundary layer,and expanding to diffusion center till
certain distance,boundary expending to axes of diffusion,core region
disappeared,only velocity in axes is u0, This section as in fig.11—1
BoE,called transition section,Take transition section as dividing line,
outlet section till transition section called initial segment of diffusion,
Since transition section called main segment of diffusion,
12
一、过流断面（又称转折断面）起始段及主体段
刚喷出的射流速度仍然是均匀的。沿 x 方向流动，射流不断
代入周围介质，不仅使边界扩张，而且使射流主体的速度逐渐降
低，速度为 u0 的部分（如图其 11—6 AoD 锥体）称为射流核心，
其余部分速度小于 u0 称为边界层。射流边界层从出口开始沿射程
不断地向外扩散，带动周围介质进入边界层，同时向射流中心扩
展，至某一距离处，边界层扩展到射流轴心线，核心区域消失，
只有轴心上速度为 u0 。射流这一断面为图 11—1上的 BoE,称为过
渡断面或转折断面。以过渡断面分界，出口断面至过渡断面称为
射流起始段。过渡断面以后称为射流主体段。
13
2,Coefficient of turbulent flow ? and geometrical character
Outer boundary layer of diffusion is a beeline,as in fig.11—1
AB and DE,AB, DE prolong to muzzle meeting at point M,this
point called culmination.Half of called pole angle ?,as
well as called diffusing angle ? 。
Bo is radii R of circular diffusion section （ or half breadth of
boundary layer in plane diffusion yb ）,It is positive ratio with
distance from culmination,Bo ＝ Kx 。
oM is x distance calculated from culmination,Observing
from figure,Bo/oM =tan ?,so
AMD?
1)( 1 1 t a n —??? ??? KxKx
where K—experiment constant;
?— form coefficient of muzzle,circular muzzle,?＝ 3.4；
?— coefficient turbulent flow,determined by experiment
14
二、紊流系数 ? 及几何特征
射流外边界层是一条直线，如图 11—1上的 AB及 DE 线。
AB, DE 延至喷嘴内交于 M 点，此点称为极点,的
一半称为极角 ?,又称扩散角 ? 。
Bo为圆断面射流截面的半径 R（或平面射流边界层的半
宽度 yb ）。它和从极点起点算的距离成正比，即 Bo ＝ Kx 。
oM 是从极点起算的 x 距离。由图看出,Bo/oM =tan ?,故
AMD?
1)( 1 1 t a n —??? ??? KxKx
式中 K—试验常数；
?— 喷口形状系数，圆形喷嘴,?＝ 3.4；
?— 紊流系数，由实验决定，是表示射流流动结构的
特征系数。
15
Coefficient of turbulent flow ? relate to turbulent flow intensity in outlet
section,More high as intensity,more high as value a,which make diffusion expending
angle a increase,Driving around medium more,velocity along diffusion line reducing
more fast,a relates to the uniform of velocity distributing in outlet section.Practical
value of turbulent flow coefficient and expending angle on different form muzzle.as in
table 11—1,
Coefficient of turbulent flow table11—1
Wind machine of axis flow
with metal gridding
well shrink plane muzzle
narrow gap in plane wall
portrait gap of wind way
with grind round outlet
kinds of muzzle
muzzle with shrink outlet
cylindrical pipe
Right-angle pipe with
leading wind plank
? ?2 kinds of muzzle ? ?2
071.0066.0
08.0076.0
20.012.0
0127 02250
0
??
00290 ?
0368 03440
0
??
155.0
118.0
108.0
24.0
0241
0132
0329
0478
0
0
0
0
?
?
?
?
From formula（ 11—1—1）,a is conformed,outer boundary line of diffusion
boundary layer,diffusion expending forward along certain expending angle a,this
is its geometrical character.Applying this character,variety rule of diffusion radii
can be obtained along diffusion way in circular section,
16
紊流系数 ? 与出口断面上紊流强度有关，紊流强度越大,a
值也大，使射流扩散角 a 增大，被带动的周围介质增多，射流速
度沿程下降加速。 a 还与射流出口断面上速度分布的均匀性有关。
各种不同形状喷嘴的紊流系数和扩散角的实测值列表 11—1。
紊 流 系 数 表 11—1
喷 嘴 种 类
带有收缩口的喷嘴
圆柱形管
带有导风板的轴流式通风
机带导流板的直角弯管
? ?2 喷 嘴 种 类 ? ?2
071.0066.0
08.0076.0
20.012.0
0127 02250
0
??
00290 ?
0368 03440
0
??
带金属网格的轴流风机
收缩极好的平面喷口
平面壁上锐缘狭缝
具有导叶且加工磨圆边口
的风道上纵向缝 155.0
118.0
108.0
24.0
0241
0132
0329
0478
0
0
0
0
?
?
?
?
由（ 11—1—1）式可知,a 值确定，射流边界层的外边界
线也就被确定，射流即按一定的扩散角 a 向前作扩散运动，这
就是它的几何特征。应用这一特征，对圆断面射流可求出射流
半径沿射程的变化规律。
17
2)( 1 1 4.3
)294.0(4.34.31
t a n/
1
0
000.0
0
0
—asrR
r
as
r
s
r
s
x
sx
r
R
??
???????? ?
?
3,Characteristic of motion
Many experiment showing, velocity distributing taking on
comparability in different section.This is characteristic of motion,
Expressing velocity distributing in different section with half-
empirical formula,
1, 5 2
1, 5 2
[ 1 ( ) ] 11 3
y
m a k e
R
[ 1 ] ( 11
m
m
y
R
?
?
?
?
?
?
??
?
??
（ — ）
— 3 a )
18
2)( 1 1 4.3
)294.0(4.34.31
t a n/
1
0
000.0
0
0
—asrR
r
as
r
s
r
s
x
sx
r
R
??
???????? ?
?
三、运动特征
大量实验研究表明，射流各截面上速度分布具有相似
性。这就是射流的运动特征。
用半经验公式表示射流各横截面上的无因次速度分布如下,
3 a )( 1 1 ]1[
R
y
311 ])(1[
25.1
25.1
—
令
）—（
?
?
?
?
?
?
??
?
??
m
m
R
y
19
Above formulas are suitable for main segment,then in formula,
y—distance from any point to axes in transverse section
R—diffusion radii of this section;
—velocity of point y;
—axes velocity in this section,
Above formulas are suitable for initial segment,only considering
flow velocity distributing in boundary layer,then in formulas
y—distance from any point to core boundary;
R—thickness of boundary layer in same section;
—velocity of point y in boundary layer of section;
—core velocity
?
m?
m?
?
0?
20
上式如用于主体段，则式中
y—横断面上任意点至轴心距离；
R—该截面上射流半径（半宽度）；
—y点上速度；
—该截面轴心速度。
上式如用于起始段，仅考虑边界层中流速分布，则式中
y—截面上任意点至核心边界的距离；
R—同截面上边界层厚度；
—截面上边界层中 y 点的速度；
—核心速度 。
?
m?
m?
?
0?
21
Therefore obtained variety spectrum of y/R from axes or core
boundary to outer boundary is 0 1.Variety spectrum of from
axes or core boundary to boundary of diffusion is1 0。
m??/
4,Characteristic of kinetics
Proved by experiment,static pressure at any point in diffusion
is equal to pressure of around air.Taking one diffusion segment
from11—2 and 1—1,2—2,analyzing force in it.Owing to static
pressure is equal in different section,then sum of outside force is o
in axis x,Due to momentum equation,momentum conservation in
different section,this is characteristic of kinetics of diffusion,
Take circular section as example apply momentum
conservation equation,
Momentum flex of outlet section is,
Integrating momentum flex in any transverse section,
02000 ????? rQ ?
2
00
2 2 2
00 0
2 2
m o m e n t u m c o n s e r v a t i o n f o r m u l a
2 ( 1 1 1 4 )
RR
R
y d y y d y
r y d y
? ? ? ? ? ? ?
? ? ? ? ? ?
?
?
??
?
：
— —
22
由此得出 y/R 从轴心或核心边界到射流外边界的变化范围为
0 1。 从轴心或核心边界到射流边界的变化范围为 1 0。 m??/
四、动力特征
实验证明，射流中任意点上的静压强均等于周围气体的压
强。现取 11—2中 1—1,2—2所截的一段射流脱离体，分析其
上受力情况。因各面上所受静压强均相等，则 x 轴外力之和为
零。据动量方程可知，各横截面上动量相等 —动量守恒，这就
是射流的动力学特征。
以圆断面射流为例应用动量守恒原理
出口截面上动量流量为,任意横截面上的动
量流量则需积分。
02000 ????? rQ ?
4)1( 1 1 2
22
0
22
0
2
0
0
2
0
——
列动量守恒式：
?
??
?
?
R
RR
y d yr
y d yy d y
? ? ????
? ? ?????
23
?M
0x s
x
y?
y?
x
r
R
y
y?
1
1 2
2
R
y y
dy
Fig,11—2 Proved of diffusion calculation
24
?M
0x s
x
y?
y?
x
r
R
y
y?
1
1 2
2
R
y y
dy
图 11—2 射流计算式的推证
25
§ 11-3 Kinetic analysis of diffusion in circular section
Studying variety rule of diffusion velocity in circular section
and throughput Q along diffusion way s （ or x ） due to
characteristic of turbulent diffusion,
?
1,Velocity of axes
m?
2 2 2
00
0
22
1
2 2 200
0
1.
a ppl y i ng 11 1 4
2
div i de obta i n
( ) 2 ( ) ( )
substi t uti ng 11 1 3 [ 1 ( )
R
m
mm
m
r y dy
R
r yy
d
R R R
y
R
? ? ? ? ? ?
? ? ?
? ?
??
?
?
?
?
?
?
?
（ — — ）
：
（ ）
（ — — ） ＝
52
1
1,5 2 2
2
0
] i nto t he n
[ ( 1 ) ]d B? ? ???
?
，
26
§ 11-3 圆断面射流的运动分析
现在根据紊流射流特征来研究圆断面射流的速度,流量
Q 沿射程 s （或 x ）的变化规律。
?
一、轴心速度
m?
2
1
0
225.1
25.1
1
0
22020
22
0
22
0
2
0
d])[ ( 1
])(1[3111
)()(2)(
2
4111
B
R
y
R
y
d
R
y
R
r
R
y d yr
m
mm
m
R
??
?
?
?
?
?
?
???
?
?
?
?
?
?
???
? ? ????
代入，则＝）——应用式（
）（
除两端，得：以
）——应用式（
27
According to above variety spectrum of and, value
table of B2 listed in table11—2。 R
y
m?
?
n
aB
aC
1 5.1 2 5.2 3
0985.0
3845.0
064.0
3065.0
0464.0
2585.0
0359.0
2256.0
0286.0
2015.0
v a lu e o f a n d aaBC table 11—2
11
00
2200
2
0
0
( ) ( )
t he n ( ) 2 2 0,04 64
3.28
nn
nn
mm
m
m
B d C d
r
B
R
r
R
??
? ? ?
??
?
?
?
?
??
? ? ?
?
??
（ ）
28
按前述 及 的变化范围,B2 的数值列于表 11—2。
R
y
m?
?
n
aB
aC
1 5.1 2 5.2 3
0985.0
3845.0
064.0
3065.0
0464.0
2585.0
0359.0
2256.0
0286.0
2015.0
值和 aa CB 表 11—2
R
r
B
R
r
dCdB
m
m
n
m
n
n
m
n
0
0
2
2020
1
0
1
0
28.3
0 4 6 4.022)(
)( )(
?
???
?? ??
?
?
?
?
?
?
?
??
?
?
）于是（
29
0
00
su b stitu tin g v a r ie ty r u l e o f d if f u sio n r a d ii
a l o n g d if f u sio n w a y 1 1 1 2 in t
0,9 6 5 0,4 8
( 1 1 2 1 )
0,2 9 4 0,1 4 7
m
o o b ta in
a s a s
rd
?
?
??
??
（ — — ）,
— —
2,Throughput Q of section
0
2
0
0 0 0 0 0 0
0 0 0 0
1
2
0
0 0 0
2
2 ( ) ( ) ( )
s u b s tit u tin g ; in to
2 ( ) ( ) ( ) ( )
s
R
R
r
m
m
m
m
y d y
Q y y
d
Q r r r
y y R
r R r
Q R y y
d
Q r R R
??
?
? ? ?
???
? ? ?
? ?
??
??
? ? ?
??
?
?
?
＝
30
1)2( 1 1
1 4 7.0
48.0
2 9 4.0
9 6 5.0
2111
00
0
——
）式代入，得——沿程变化规律（再将射流半径
?
?
?
?
d
as
r
as
R
m
?
?
二、断面流量 Q
取无因次流量,
)()()()(2;
)()()(2
2
1
0
2
000
0000
00
0
00
2
0
0
0
R
y
d
R
y
r
R
Q
Q
r
R
R
y
r
y
r
y
d
r
y
r
y d y
Q
Q
m
m
m
m
r
R
R
s
?
?
?
??
???
??
?
?
?
?
?
?
?
?
?
?
?
?
??
??
代换＝再用
31
Consulting table 11—1, B1=0.0985 ; substituting formula（ 11—
1—2），（ 11—2—1） into
）——（ 2211 )1 4 7.0(4.4)2 9 4.0(2.2
000
???? dasrasQQ
Substituting formula（ 11—1—2）,（ 11—2—2） into and obtaining
3)2( 1 1
1 4 7.0
0 9 5.0
2 9 4.0
19.0
00
0
1 ——
?
?
?
?
d
as
r
as?
?
3,Average velocity of section
Average velocity is, 20
00
0
0
1 )( RrQQAQQA ????
1?
32
查表 11—1, B1=0.0985 ; 再将（ 11—1—2），（ 11—2—1）式
代入
）——（ 2211 )1 4 7.0(4.4)2 9 4.0(2.2
000
???? dasrasQQ
三、断面平均流速
无因次断面平均流速为,20
00
0
0
1 )( RrQQAQQA ????
将（ 11—1—2），（ 11—2—2）式代入得
3)2( 1 1
1 4 7.0
0 9 5.0
2 9 4.0
19.0
00
0
1 ——
?
?
?
?
d
as
r
as?
?
1?
33
4,Average flow velocity v2 of mass
4)2( 1 1
1 4 7.0
23.0
2 9 4.0
4 5 4 5.0
00
0
0
2
200
——
?
?
?
??
?
d
as
r
asQ
Q
?
?
????
Average velocity denoting arithmetic average value in diffusion
section.Comparing formula (11-2-1) and (11-2-3) obtaining,
Showing average flow velocity of section is only 20％ of axes
velocity.Ventilation,air-condition engineering usually used high velocity
region around axes.So,is not reflect velocity in used region,Therefor
applying average velocity of mass, It is defined that take
multiply mass obtain virtual momentum,Deducing momentum
conservation equation of outlet section and any transverse section,
1?
m?? 2.01 ?
1?
2?
Comparing（ 11—2—1） and（ 11—2—4）,.So,
take denote flow velocity is more suitable than,But must
notice,,not only different in value,more important different in
definition,
m?? 47.02 ?
2? 1?
1? 2?
2?
34
四、质量平均流速 v2
断面平均流速 表示射流断面上的算术平均值。比较
（ 11—2—1）、（ 11—2—3）两式，可得 。说明断
面平均流速仅为轴心流速的 20％。通风、空调工程上通常使
用的是轴心附近较高的速度区。因此 不能恰当的反映被使
用区的速度。为此引入质量平均流速 。质量平均流速定义
为：用 乘以质量即得真实动量。列出口截面与任一横截面
的动量守恒式,
1?
m?? 2.01 ?
1?
2?
2?
4)2( 1 1
1 4 7.0
23.0
2 9 4.0
4 5 4 5.0
00
0
0
2
200
——
?
?
?
??
?
d
as
r
asQ
Q
?
?
????
比较（ 11—2—1）与（ 11—2—4）式,。因此用
代表使用区的流速要比 更合适。但必须注意,,不仅在
数值上不同，更重要的是在定义上根本不同，不可混淆。
m?? 47.02 ? 2?
1? 1? 2?
35
Variety rule of motion parameter of diffusion main segment in
circular section,this rule is also suitable for rectangle muzzle.But
translate rectangle into corresponding diameter of flow velocity
and substitute into calculating,
Solution,Consulting table 11-1 obtaining a＝ 0.12.Applying (11-2-1)
/sm 7.2610)6.0(
4
45.9
4
45.945.9
45.9147.24.4)147.0(4.4
m / s 25.210225.0225.0
225.0
147.0
6.0
1012.0
48.0
147.0
48.0
32
0
2
00
00
0
0
0
????????
?????
????
?
?
?
?
?
?
?
?
?
??
?
?
dQQ
d
as
Q
Q
d
as
m
m
Example 11—1 Transporting wind with axes flow wind machine,
its diameter d0=600 mm 。 Wind velocity of outlet 10 m/s,what
are axes velocity and throughput from outlet 10 m?
36
以上分析出圆断面射流主体段内运动参数变化规律，这些
规律亦适用于矩形喷嘴。但要将矩形换算成为流速当量直径代
入进行计算。
解 由表 11—1查得 a＝ 0.12。用（ 11—2—1）式
/sm 7.2610)6.0(
4
45.9
4
45.945.9
45.9147.24.4)147.0(4.4
m / s 25.210225.0225.0
225.0
147.0
6.0
1012.0
48.0
147.0
48.0
32
0
2
00
00
0
0
0
????????
?????
????
?
?
?
?
?
?
?
?
?
??
?
?
dQQ
d
as
Q
Q
d
as
m
m
例 11—1 用轴流风机水平送风，风机直径 d0=600 mm 。出口
风速 10 m/s,求距出口 10 m 处的轴心速度和风量。
37
§ 11-4 Plane diffusion
Gas diffusing from narrow gap,diffusion expending in plane of
upright gap,If the gap is quite long,this flow can be considered as
plane motion called plane diffusion,
Height of muzzle in plane diffusion expressed with 2b0（ b0
half height）,value a is back three item in table11-1; value j is
2.44,and then tan a＝ 2.44a。 And characteristics of
geometrical,kinetic,moving are similar to diffusion in section,So,
deducing kinetic parameter and rule are also similar to circular
section’s,Listing formula in table 11-3,
38
§ 11-4 平面射流
气体从狭长缝隙中外射运动时，射流只能在垂直条缝长度
的平面上扩散运动。如果条缝相当长，这种流动可视为平面运
动，故称为平面射流。
平面射流喷口高度以 2b0（ b0半高度）表示,a值见表 11-1
后三项； j值为 2.44，于是 tan a＝ 2.44a。而几何、运动、动力
特征则完全与圆断面射流相似。所以各运动参数规律的推导基
本与圆断面类似，这里不再推导，列公式于表 11-3中。
39
average velocity of
mass
Calculation of diffusion parameter Table 11—3
parameter sequence diffusion in circular section plane diffusion
expending angle
diffusion diameter
throughput
average velocity of
section
axes velocity
a
D
d
m?
Q
1?
2?
a4.3tan ??
)1 4 7.0(8.6
00
?? dadD s
1 4 7.0
48.0
0
0 ?
?
d
asm?
?
)147.0(4.4
00
?? dasQQ
1 4 7.0
0 9 5.0
0
0
1
?
?
d
as?
?
1 4 7.0
23.0
0
0
2
?
?
d
as?
?
?? 44.2ta n ?
)41.0(44.2
00
?? basbb
41.0
2.1
0
0 ?
?
b
as
m
?
?
41.02.1
00
?? basQQ
41.0
4 9 2.0
0
0
1
?
?
b
as?
?
41.0
8 3 3.0
0
0
2
?
?
b
as?
?
main
segment
name
segment
40
射流参数的计算 表 11—3
段名
主
体
段
参数名称 序号 圆断面射流 平面射流
扩散角
射流直径或半高度
流量
断面平均流速
质量平均流速
轴心速度
a
D
d
m?
Q
1?
2?
a4.3tan ??
)1 4 7.0(8.6
00
?? dadD s
1 4 7.0
48.0
0
0 ?
?
d
asm?
?
)147.0(4.4
00
?? dasQQ
1 4 7.0
0 9 5.0
0
0
1
?
?
d
as?
?
1 4 7.0
23.0
0
0
2
?
?
d
as?
?
?? 44.2ta n ?
)41.0(44.2
00
?? basbb
41.0
2.1
0
0 ?
?
b
as
m
?
?
41.02.1
00
?? basQQ
41.0
4 9 2.0
0
0
1
?
?
b
as?
?
41.0
8 3 3.0
0
0
2
?
?
b
as?
?
41
average
velocity of
section
average
velocity of
mass
core length
distance from muzzle
to pole point
convergent angle
throughput Q
1?
2?
ns
0x
?
2
000
)(32.176.01 rasrasQQ ???
2
00
2
00
0
1
)(56.118.61
)(32.176.01
r
as
r
as
r
as
r
as
??
??
?
?
?
2
00
0
2
)(32.176.01
1
r
as
r
as ????
?
arsn 0672.0?
arx 00 294.0?
a49.1tan ??
00
43.01 basQQ ??
0
0
0
1
44.21
43.01
b
as
b
as
?
?
?
?
?
0
0
2
43.01
1
b
as???
?
absn 003.1?
abx 00 41.0?
a97.0tan ??
initial
segment
42
起
始
段
流量
断面平均流速
质量平均流速
核心长度
喷嘴至极点距离
收敛角
Q
1?
2?
ns
0x
?
2
000
)(32.176.01 rasrasQQ ???
2
00
2
00
0
1
)(56.118.61
)(32.176.01
r
as
r
as
r
as
r
as
??
??
?
?
?
2
00
0
2
)(32.176.01
1
r
as
r
as ????
?
arsn 0672.0?
arx 00 294.0?
a49.1tan ??
00
43.01 basQQ ??
0
0
0
1
44.21
43.01
b
as
b
as
?
?
?
?
?
0
0
2
43.01
1
b
as???
?
absn 003.1?
abx 00 41.0?
a97.0tan ??
43
§ 11-5 Diffusion of temperature and thickness difference
In heating and ventilating engineering,usually applying cold wind for
dropping heating,applying sirocco for heating,here diffusion of temperature
difference is used,It is used diffusion of thickness difference to drop thickness of
nocuous gas and gas,So called diffusion of temperature and thickness difference
is the difference between temperature and thickness of diffusion and around gas,
Analyzing diffusion of temperature and thickness difference,mostly studying
distributing rule of temperature and thickness difference,Talking about curly
axes track produced by temperature and thickness difference,
In forming process of diffusion,producing transverse momentum
exchange,vortex appearing,making its mass exchange,heat exchange,thickness
exchange,In these exchange,heat expending faster than momentum expending,
so temperature boundary layer is thicker than velocity boundary layer.As 11-3a,
Real line is velocity boundary layer,broken line is inside and outside line of
temperature boundary layer,
44
§ 11-5 温差或浓差射流
在采暖通风空调工程中，常采用冷风降温，热风采暖，这
时就要用温差射流。将有害气体及灰尘浓度降低就要用浓差射
流。所谓温差、浓差射流就是射流本身的温度或浓度与周围气
体的温度、浓度有差异。
温差或浓差射流分析，主要是研究射流温差、浓差分布场
的规律。同时讨论由温差、浓差引起射流弯曲的轴心轨迹。
在射流的形成过程中，会产生横向动量交换，旋涡的出现，
使之质量交换，热量交换，浓度交换。在这些交换中，热量扩
散比动量扩散要快些，因此温度边界比速度边界层发展要快些
厚些，如图 11-3a所示。实线为速度边界层，虚线为温度边界
层的内外界线。
45
Thickness expending is similar to temperature’s,in practice,in
order to predigest,considering boundary besides temperature and
thickness are equal with outside and inside boundary of velocity,
(a)
0 1? 2? 3? 4?4? 3? 2? 1?
2.0
4.0
6.0
8.0
0.1
m?
?
mT
T??
(b)
Fig.11—3 boundary layer of temperature and velocity
Supposing to express around gas with subscript e
46
浓度扩散与温度相似，在实际应用中，为了简化起见，可以
认为，温度、浓度内外的边界与速度内外的边界相同。
(a)
0 1? 2? 3? 4?4? 3? 2? 1?
2.0
4.0
6.0
8.0
0.1
m?
?
mT
T??
(b)
图 11—3 温度边界层与速度边界层的对比
设以足标 e表示周围气体的符号。
47
eTTT ??? 00
emm TTT ???
For diffusion of temperature difference,
Temperature difference
in outlet section
Temperature difference of axes
eTTT ???
Any point temperature
difference of section
exxx ??? 00
emm xxx ???
exxx ???
Thickness of outlet section
Thickness
difference of axes
Any point thickness
difference of section
For diffusion of thickness difference,
48
eTTT ??? 00
emm TTT ???
对温差射流,
出口断面温差
轴心上温差
eTTT ???
截面上任一点温差
对浓差射流,
exxx ??? 00
emm xxx ???
exxx ???
出口断面浓度
轴心上浓差
断面上任意一点浓差
49
Distributing relation of temperature difference,thickness
difference and velocity obtained by experiments,
5.1
1 ?????????????? RyxxTT
mmm ?
? 11-4-1
In isotonic instance,taking enthalpy value of around gas as
initial calculating point,relatively enthalpy value in diffusion
sections keeping invariably,This is called heat power character,
Supposing relative enthalpy value of section per unit time is;relative enthalpy value of per unit time through any
transverse section is
00 TCQ ??
? ?Q TdQc?
一,Temperature difference in axes mT?
Owing to relative enthalpy value is equal,obtaining
? ???? R y d yTcTcQ 000 2 ????
After division by,and substituting formula 11-4-1
into,deducing just as section 2,parameters calculating formula listed
in table 11-4,
mm TcR ???? 2
50
试验得出，截面上温差分布，浓差分布与速度分布关系
如下,
5.1
1 ?????????????? RyxxTT
mmm ?
? 11-4-1
在等压的情况下，以周围气体的焓值作为起算点，射流各
横截面上的相对焓值不变。这一特点称为热力特征。
设喷嘴断面上单位时间的相对焓值为,射流任意
横截面上单位时间通过的相对焓值 。
00 TCQ ??
? ?Q TdQc?
一、轴心温差 mT?
根据相对焓值相等，得,? ???? R y d yTcTcQ
000 2 ????
两端除以,并将 11-4-1式代入，其推导与第二节
方法类似，各参数计算公式列于表 11-4中。
mm TcR ???? 2
51
Diffusion calculation of thickness difference table 11—4
segment name
main
segment
circular section
diffusion plane diffusion
parameter
name
axes
temperature
difference
average
temperature
difference in
mass
thickness
difference
in axes
symbol
mT?
2T?
mx?
1 4 7.0
35.0
0
0 ?
???
d
asT
T m
147.0
23.0
0
0
2
?
???
d
asT
T
1 4 7.0
35.0
0
0 ?
???
d
asx
x m
41.0
032.1
0
0 ?
???
b
asT
T m
41.0
8 3 3.0
0
0
2
?
???
b
asT
T
41.0
032.1
0
0 ?
???
b
asx
x m
52
浓差温差的射流计算 表 11—4
段名
主
体
段
参数名称
轴心温差
质量平均
温差
轴心浓差
符号 圆 断 面 射 流 平 面 射 流
mT?
2T?
mx?
1 4 7.0
35.0
0
0 ?
???
d
asT
T m
147.0
23.0
0
0
2
?
???
d
asT
T
1 4 7.0
35.0
0
0 ?
???
d
asx
x m
41.0
032.1
0
0 ?
???
b
asT
T m
41.0
8 3 3.0
0
0
2
?
???
b
asT
T
41.0
032.1
0
0 ?
???
b
asx
x m
53
continuous table
segment
name
main
segment
symbol
average
thickness
difference in
mass
track
equation
in axes
2x?
2T?
2x?
1 4 7.0
23.0
0
0
2
?
???
d
asx
x
2
00
0
2
)(32.176.01
1
r
as
r
asT
T
??
???
2
00
0
2
)(32.176.01
1
r
as
r
asx
x
??
???
41.0
8 3 3.0
0
0
2
?
???
b
asx
x
0
0
2
43.01
1
b
asT
T
?
???
0
0
2
43.01
1
b
asx
x
?
???
)35.0c o s51.0(
)c o sA r (t a n
0
2
000
??
??
?
??
a
ax
d
x
d
x
d
y
2/5
0
2
01
0
01
2
2/5
0
0
)205.0
2
(226.0
r
/
2
/
)205.0
2
(r226.0
2
??
?
?
??
?
b
xa
a
TT
b
y
TTa
b
xa
b
y
Initial
segment
parameter
name
average
thickness
difference in
mass
average
temperature
difference in
mass
circular section
diffusion plane diffusion
54
续表
段名
主
体
段
参数名称
质量平均
温差
符号 圆 断 面 射 流 平 面 射 流
2x?
2T?
2x?
1 4 7.0
23.0
0
0
2
?
???
d
asx
x
2
00
0
2
)(32.176.01
1
r
as
r
asT
T
??
???
2
00
0
2
)(32.176.01
1
r
as
r
asx
x
??
???
41.0
8 3 3.0
0
0
2
?
???
b
asx
x
0
0
2
43.01
1
b
asT
T
?
???
0
0
2
43.01
1
b
asx
x
?
???
质量平均
浓差
质量平均
浓差
起
始
段
轴线轨迹
方程 )35.0
c o s51.0(
)c o sA r (t a n
0
2
000
??
??
?
??
a
ax
d
x
d
x
d
y
2/5
0
2
01
0
01
2
2/5
0
0
)205.0
2
(226.0
r
/
2
/
)205.0
2
(r226.0
2
??
?
?
??
?
b
xa
a
TT
b
y
TTa
b
xa
b
y
55
2,diffusion inflecting
Temperature or thickness difference diffusion is owing to
density different from around density,gravity and buoyancy is not
balance,which making diffusion inflect downwards or upwards,as
show in fig.11-4,But whole diffusion is still symmetrical to axes
line,So finding out inflecting track of axes line,then obtaining
whole inflecting diffusion,
x x
y
y?
?tanx
y
d
?
A?
A
?A
ge??
gm??
Fig.11—4 inflection of diffusion axes
56
二、射流弯曲
温差射流或浓差射流由于密度与周围密度不同，所受的重
力与浮力不相平衡，使整个射流将发生向下或向上弯曲，见图
11-4。但整个射流仍可看作是对称于轴心线。因此了解轴心线
的弯曲轨迹后，便可得出整个弯曲的射流。
x x
y
y?
?tanx
y
d
?
A?
A
?A
ge??
gm??
图 11—4 射 流 轴 线 的 弯 曲
57
Applying approximate disposal method,taking flow of per unit
volume in axes as study object.Only considering gravity and
buoyancy,applying Newton law and experiment data,deducing half
empirical formula listed in table 11-4
here：, is Archimedes standard number
e
r Tv
TgdASx
2
0
00,
c o s
???
?Example 11-2 In working spot requiring average wind velocity is
3m/s,working face diameter D＝ 2.5m,giving wind temperature 5℃,
air temperature 30℃, requiring average temperature of mass fall to
25℃, applying ventilator with guide leaf,its turbulent coefficient a＝
0.12。 find（ 1） diameter and velocity of outlet;（ 2） distance from
outlet to working face,
Solution,
Temperature
difference
C1530150 ?????? T
C530252 ?????? T
15
5
147.0
23.0
0
0
2
?
??
?
???
d
asT
T
58
采用近似的处理方法：取轴心线上的单位体积流体作为研究
对象，只考虑受重力与浮力作用，应用牛顿定律和实验数据，导
出半经验公式列于表 11-4中。
该公式中：,成为阿基米德准数。
e
r Tv
TgdASx
2
0
00,
c o s
???
?
例 11-2 工作地点质量平均风速要求 3m/s，工作面直径 D＝ 2.5m，
送风温度为 15℃,车间空气温度 30℃,要求工作地点的质量平均
温度降到 25℃,采用带导叶的通风机，其紊流系数 a＝ 0.12。求
（ 1）风口的直径及速度；（ 2）风口到工作面的距离。
解 温差 C1530150 ?????? T
C530252 ?????? T
15
5
147.0
23.0
0
0
2
?
??
?
???
d
asT
T
59
69.051523.01 4 7.0
0
????das
finding, substituting into
69.08.6147.08.6
00
????
?
?
???
? ??
d
as
d
D
so
average wind velocity of mass in
working spot required 3m/s
for
therefore
m5 2 5.069.08.6 5.269.08.60 ????? Dd
0
0
0
2 3
15
5
1 4 7.0
23.0
v
d
asv
v ??
?
?
m /s90 ?v
60
求出,代入下式
69.051523.01 4 7.0
0
????das
69.08.6147.08.6
00
????
?
?
???
? ??
d
as
d
D
所以
工作地点质量平均风速要求 3m/s
因为
所以
m5 2 5.069.08.6 5.269.08.60 ????? Dd
0
0
0
2 3
15
5
1 4 7.0
23.0
v
d
asv
v ??
?
?
m /s90 ?v
61
（ 2） finding distance s from wind outlet to
working face by
。 m4.2 5 4 3.05 2 5.0 12.0 ; 69.01 4 7.0
0
???? ssdas
Thinking problems
11-3 what is average velocity in mass?Why citing this flow
velocity？
11-4 why diffusion temperature difference track inflecting？
How to find track equation？
2?
62
（ 2）风口到工作面距离 s 可用下式求出
。 m4.2 5 4 3.05 2 5.0 12.0 ; 69.01 4 7.0
0
???? ssdas
复习思考题
11—3 什么是质量平均流速？为什么要引入这一流速？
11—4 温差射流轨迹为什么弯曲？是怎样寻求轨迹方程的？
2?
63
§ 11-6 Other familiar diffusion in engineering equipment
1,adherence diffusion
Different from free diffusion,if put muzzle adhere to top
shed or wall,show as fig.11—6,then because of restrict of wall,it
can‘ t roll and absorb air in wall face,velocity attenuate slowly,
so velocity is high,resting pressure is low,then velocity is low
and resting pressure is high in the other side,which making
airflow moving adhere wall,called adherence diffusion,
b
s
02b
0b
Fig,11—6 adherence diffusion
64
§ 11-6 工程设备中常见的其他射流简介
一、贴附射流
与自由射流不同，如把喷口贴近顶棚或墙壁布置，如图
11—6所示，则由于壁面的限制，壁面处不能卷吸空气，速
度衰减慢，因而流速大，静压小，而另一侧则流速小，静压
大，使得气流贴附于壁面流动，并称之为贴附射流。
b
s
02b
0b
图 11—6 贴附射流
65
Due to adherence diffusion roll and absorb around fluid
only in one surface,so attenuate slowly,diffusion way is longer
than free diffusion with same muzzle,
Adherence diffusion can be regarded as half of integral
diffusion,Its law invariable,so can calculate as double
according to outlet section,outlet flow velocity invariable.In
calculating,substituting outlet diameter d0 in free diffusion with
d0,for plane diffusion,substituting half height of outlet b0 with
2b0。
2
66
由于贴附射流仅一面卷吸周围流体，故衰减较慢，射程
较同样喷口的自由射流为长。
贴附射流可视为完整射流得一半，其规律不变，因而可
按风口断面加倍，出口流速不变的完整射流进行计算。也就
是说，计算中只需将自由射流公式的送风口直径 d0代以 d0，
对于平面射流，则需将风口半高度 b0代以 2b0。
2
67
2,Diffusion in finite space
Usually in project,diffusion don’t diffuse to infinite space,
because of finite size of room,which restrict expending motion of
diffusion,here free diffusion law isn’t suitable,must restudy its
kinetic law.At present,there is no well results,most is empirical
formula or curve by experiment,now introducing,
As show in fig.11-7 is diffusion field structure in finite space,
From diffusion outlet to Ⅰ － Ⅰ section,because solid wall faces
don’t restrict diffusion expending,free diffusion rules are suitable,
calculation can also use free diffusion formula.Ⅰ － Ⅰ section called
first critical section,
68
二、有限空间射流
通常，工程中射流并不是射入无限大空间，因房间尺寸有
限，限制了射流的扩散运动，此时自由射流规律不再适用，须
重新研究其运动规律。目前，理论上还没有成熟的结果，大多
是由实验得到的经验公式或无因次曲线，现作简介。
图 11-7所示为有限空间射流流场结构。从射流出口至 Ⅰ －
Ⅰ 断面，因固体壁面尚未妨碍射流的扩展，射流的发展按照自
由射流的规律，计算亦可用自由射流公式。称 Ⅰ － Ⅰ 断面为第
一临界断面。
69
fig.11—7 diffusion field in finite space
70
图 11—7 有限空间射流流场
71
Starting from sectionⅠ － Ⅰ,diffusion expending is affected,
action of rolling and aborbing around liquid become weak,so
expending of diffusion section and increasing of throughput become
slowly,to sectionⅡ － Ⅱ,diffusion streamline begin to exceed
boundary layer and engender refluence,diffusion throughput begin to
reduce along diffusion way,so diffusion throughput get max value in
sectionⅡ － Ⅱ, Through experiment,average velocity and throughput
of refluence are also max,SectionⅡ － Ⅱ called second critical section,
From sectionⅡ － Ⅱ,main segment throughput,throughput of
refluence and average velocity of refluence are all becoming low in
turn,till section Ⅳ － Ⅳ,main segment throughput reduce to 0,
In this way,it may plot three segment of diffusion in finite space,
（ 1） free expending segment,from spout to first critical section
（ 2） finite expending segment,from first to second critical section
（ 3） contracted segment,from second critical section to last;
72
从 Ⅰ － Ⅰ 断面开始，射流的扩展受到影响，卷吸周围流
体的作用减弱，因而射流断面的扩大以及流量的增加比较缓
慢，达到 Ⅱ － Ⅱ 断面，射流流线开始越出边界层产生回流，
射流流量开始沿程减少，因而射流流量在 Ⅱ － Ⅱ 断面取得最
大值。由实验得知，该处的回流平均流速、回流流量亦为最
大。称 Ⅱ － Ⅱ 断面为第二临界断面。
从 Ⅱ － Ⅱ 断面以后，射流主体流量、回流流量、回流平
均流速都依次变小，直至 Ⅳ － Ⅳ 断面，射流主体流量减至为
零。
这样，有限空间射流可以划分为三段,
（ 1）自由扩张段，喷口至第一临界断面；
（ 2）有限扩张段，第一临界断面至第二临界断面；
（ 3）收缩段，第二临界断面以后。
73
Diffusion structure behaving when diameter and throughput
increasing to certain,then decreasing,making its boundary
become olive form,
Diffusion structure relates to fixed place of muzzle,If muzzle
fixed in the middle of height and width in room,diffusion structure
is symmetrical from up to down,left to right,main segment
showing olive form,around is refluence region.But in practice,
muzzle fixed close to top shed,if fixed height h and room H are
,diffusion appears adherence phenomenon,Hh 7.0?
74
而射流结构则表现为射流半径和流量在增大到一定程
度后反而减小，使其边界线呈橄榄形。
射流结构还与喷嘴的安装位置有关。如喷嘴安装在房间高
度、宽度的中央处，射流结构上下对称，左右对称，射流主体
呈橄榄形，四周为回流区。但实际送风时多将喷嘴靠近顶棚安
置，如安装高度 h与房高 H为 时，射流出现贴附现象,Hh 7.0?
75
Characteristic of diffusion in finite space is different free
diffusion is, there is refluence region reverse to diffusion region
outside the olive boundary,and working region is often in
refluence region in air-condition project,so there is restrict to
wind velocity in refluence region,The empirical formula of
average velocity in refluence region is, ?
come into half-olive form diffusion field,correspond to half of
integral diffusion in finite space,and that refluence focus on
bottom of main segment and ground,its kinetic law is same
with diffusion in finite space,considered half of diffusion in
finite space,
76
形成呈半个橄榄状的流场，相当于完整的有限空间射流的
一半，而回流区集中在射流主体下部与地面间，其运动规律与
有限空间射流相同，看作有限空间射流的一半。
有限空间射流不同于自由射流的重要特征是橄榄形边界
外部存在与射流方向相反的回流区，而空调工程中工作区通
常就设在回流区内，因此对回流区的风速有限定要求。回流
平均速度 的半经验公式为 ?
77
)()10(1 7 7.0 2377.10
00
xfexd F xx ?? ???
11-5-1
here,is outlet velocity and diameter of muzzle;F is cross
section area upright to diffusion room； is distance from
diffusion section to pole point;a为 is turbulent flow coefficient,
00,d?
F
axx ?
If basing on design,distance from L,requiring average velocity
of diffusion refluence is certain restricted value,then from
formula 11-5-1 1?
)(
00
1 LfdF ???? 11-5-3
69.0
00
?d Fm?? 11-5-2
In section － Ⅱ,refluence velocity is max,express with
from expriment obtain corresponding,substituting above
formula obtaining max refluence velocity,
2.0?x
m?
78
)()10(1 7 7.0 2377.10
00
xfexd F xx ?? ???
11-5-1
式中,为喷嘴出口速度、直径； F为垂直于射流的房
间横截面积； 为射流截面至极点的无因次距离； a为紊
流系数。
00,d?
F
axx ?
69.0
00
?d Fm?? 11-5-2
若根据设计要求，在距离 L处，要求射流回流平均流速为
某一限定值,则由式 11-5-1得
1?
)(
00
1 LfdF ???? 11-5-3
在 Ⅱ － Ⅱ 断面上，回流流速为最大，以 表示，由实验
得对应,代入上式得最大回流速度为 2.0?x m
?
79
Uniting formula 11-5-2 and 11-5-3,obtaining
m
Lf ?? 169.0)( ?
11-5-4
In project design and determined by designer,so is
known,solution is, in order to predigest calculation give table
11-5,through, consulting table 11-5,obtaining
then through obtaining 。
m? 1?
)(Lf
L
m? 1?
L
a
FLL ? L
above formulas are suitable for or in
adherence diffusion,when,it is integral finite space
diffusion,substituting with,then obtaining diffusion way
here.,
Hh 7.0? Hh 3.0?
HhH 7.03.0 ??
F5.0F
L
80
联立式 11-5-2和式 11-5-3可得
m
Lf ?? 169.0)( ?
11-5-4
工程设计中 与 由设计者限定，故 相当于已知，由
此可解出,为简化计算给出表 11-5。由, 查表 11-5得到
后可由 求出 。
m? 1? )(Lf
L m? 1? L
a
FLL ? L
以上所给出公式适用于 或 的贴附射流，当
时，射流为完整的有限空间射流，计算时应以 代
替,即可求得此时的射程 。
Hh 7.0? Hh 3.0?
HhH 7.03.0 ?? F5.0
F L
81
table 11-5 dimensionless distance
)m/s(
m?
)m/s/(1?
0.07 0.10 0.15 0.20 0.30 0.40
0.50
0.60
0.75
1.00
1.25
1.50
0.42
0.43
0.44
0.46
0.47
0.48
0.40
0.41
0.42
0.44
0.46
0.47
0.37
0.38
0.40
0.42
0.43
0.44
0.35
0.37
0.38
0.40
0.41
0.43
0.31
0.33
0.35
0.37
0.39
0.40
0.28
0.30
0.33
0.35
0.37
0.38
L
82
表 11-5 无因次距离
)m/s(
m?
)m/s/(1?
0.07 0.10 0.15 0.20 0.30 0.40
0.50
0.60
0.75
1.00
1.25
1.50
0.42
0.43
0.44
0.46
0.47
0.48
0.40
0.41
0.42
0.44
0.46
0.47
0.37
0.38
0.40
0.42
0.43
0.44
0.35
0.37
0.38
0.40
0.41
0.43
0.31
0.33
0.35
0.37
0.39
0.40
0.28
0.30
0.33
0.35
0.37
0.38
L
83
Example 11-4 In workshop length× width× height ＝
70m× 30m× 12m,giving wind along direct length,circular wind
outlet with diameter1m,it fixed on place 6m distance from wall height,
turbulent flow coefficient is 0.08,Max refluence velocity is 0.75m/s,
refluence velocity is 0.3m/s in workaround,what is giving wind
throughput and where is workaround? If wind outlet improving 3m,
how to change above calculation results?
Solution （ 1） height of wind outlet h＝ 0.6m,H＝ 12m then h/H
＝ 0.5,in spectrum（ 0.3～ 0.7） H,diffusion doesn’t adherence,in
formula substituting F with 0.5F,from formula 11-5-2 obtaining
m / s6.1469.01 12305.075.069.0 5.0
0
0 ??
?????? F
d
m??
s/m45.116.14144 320200 ????? ??? dQ
Through consulting table 11-5
obtaining, then
,3.0,75.0 1 ?? ?? m
35.0?L
84
例 11-4 车间空间长 × 宽 × 高＝ 70m× 30m× 12m，长度方向送
风，直径 1m的圆形风口设在墙高中央 6m处，紊流系数为 0.08。设
计限制最大回流速度为 0.75m/s，工作区处回流速度为 0.3m/s，求
风口送风量和工作区设置在何处？若风口提高 3m，以上计算结果
如何改变？
解 （ 1）风口高 h＝ 0.6m,H＝ 12m则 h/H＝ 0.5，在（ 0.3～ 0.7）
H范围内，射流不贴附，公式中 F用 0.5F代，由式 11-5-2得
m / s6.1469.01 12305.075.069.0 5.0
0
0 ??
?????? F
d
m??
s/m45.116.14144 320200 ????? ??? dQ
由 查表 11-5得,则,3.0,75.0
1 ?? ?? m
35.0?L
85
m7.5808.0 12305.035.05.0 ?????? a FLL
with non-adherence diffusion increasing times
（ 2）,then,comparing adherence diffusion
69.000
F
dm
?? ?
5.0
1
m9?h 7.075.0
12
9 ???
H
h
6 7, 0 3 m5 8, 7
5.0
1
/s1 6, 2 m1 1, 4 5
5.0
1
m / s65.206.14
5.0
1
3
0
0
???
???
???
L
Q
?
三,Diffusion in crosscurrent
86
m7.5808.0 12305.035.05.0 ?????? a FLL
与不贴附相比增大
（ 2） m9?h,则 7.075.0
12
9 ???
H
h,为贴附射流 69.0
0
0
F
dm
?? ?
5.0
1 倍，即
6 7, 0 3 m5 8, 7
5.0
1
/s1 6, 2 m1 1, 4 5
5.0
1
m / s65.206.14
5.0
1
3
0
0
???
???
???
L
Q
?
三、横流中的射流
87
In project,often meet diffusion as show in fig.11-8,its main airflow with
velocity,its size larger than size of diffusion muzzle,diffusion with original
velocity diffuse above main airflow at obliquity a,after coming into,
exchanging momentum with main airflow,due to mass of main airflow more
large,corresponding momentum is also large more,when diffusion diffuse into
main airflow certain depth,gradually turning around oppressed by main airflow,
at last assimilated by main airflow,
1?
2?
main a ir flow
trochoid of
diffusion
diffusio
n
y
y?
1V 1T
d
22TV
?
fig,11—8 flow of diffusing into upright airflow
88
射流轨迹线
射流
y
y?
1V 1T 主气流
d
22TV
?
图 11—8 射流射入垂直主气流时的流动
工程上常能遇到如图 11-8所示得射流情况，具有 流速得
主气流，其尺寸比射流喷嘴尺寸大得多，具有初速 的射流以
某 a倾角射入上述主气流中，射流进入主气流后，即与主气流
发生动量交换，由于主气流总的质量大得多，相应的总动量也
大得多，当射流射入主气流一定深度后，逐渐被主气流压迫而
转向，最后被主气流同化。
1?
2?
89
Kinetic rule and track of diffusion（ linking line of different
velocity point in different section） relate to diffusing angle a,
muzzle shape,velocity of spout and velocity of main
airflow,If temperature of diffusing air T2 different from
temperature of main airflow T1,then considering effect of
thickness difference by temperature difference,
2?
1?
Indicating by experiment,after diffusion diffusing into main
airflow,as diffusion track expanding forwards,axes velocity
decreasing constantly,and changing direct gradually,at last have the
same value and direct with main airflow velocity,
1
2
?
?
1?
90
射流的运动规律及运动轨迹（不同断面上最大速度点连
线）与喷射角度 a、喷嘴型式、射流喷口速度 及主气流速度
等因素有关。若射流气体温度 T2与主气流温度 T1不同，则还要
考虑由于温差造成的密度差的影响。
2? 1?
实验表明，射流射入主气流后，随着射流轨迹向前发展，
轴心速度不断降低，并逐渐转向，最后趋于与主流流速 同值
同向，并且速度比值 越小，则射流轴心速度下降得越快，也
就是说 越小，主气流, 同化, 射流的能力越强，所以欲使射
流射入更深，可提高 值，也就是提高射流的射入速度 。
1
2??
1
2??
1
2??
1?
2?
91
and more little as velocity ratio,more fast as axes velocity of
diffusion,is more little,the ability of main airflow,assimilate”
diffusion is more strong,so wish diffusion diffuse deeper should
improve, namely improving diffusing velocity,
1
2??
1
2??
2?
Effects of temperature difference of airflow incarnate effects
of thickness difference, Cold diffusion with uniform velocity
ratio,due to its high density,momentum is also great,so
penetrating depth of cold diffusion is larger than cold diffusion’s,12?
? 22??
Ivanov concluded diffusion track equation by experiment,this is
empirical formula,embodying effects of velocity ratio,temperature
ratio and diffusing angle,
92
气流温度差别的影响体现在气流密度差别的影响上。速
度比值 相同的冷射流由于其密度大，单位质量的动量 相
应也大，故冷射流穿透深度比热射流大。
1
2?? 2
2??
伊万诺夫由实验归纳得到下述射流轨迹方程，这是一个经验
公式，其中同时体现了速度比、温度比及射入角的共同影响。
实验表明，射流射入主气流后，随着射流轨迹向前发展，
轴心速度不断降低，并逐渐转向，最后趋于与主流流速 同值
同向，并且速度比值 越小，则射流轴心速度下降得越快，也
就是说 越小，主气流, 同化, 射流的能力越强，所以欲使射
流射入更深，可提高 值，也就是提高射流的射入速度 。
1
2??
1
2??
1
2??
1?
2?
93
Here,x is horizontal distance; y is vertical distance; d is diameter of
diffusion muzzle; a is diffusing angle,
using spectrum of formula,400~25,2,120~60
211
222
1
2 ??? ?? ??TTa ??
)90t a n (
33.1
2
22
2
11 ???
?
??
?
???
?
??
?
???
?
?
???
?? a
d
x
d
x
d
y
??
?? 11-5-5 。
As for velocity field of this diffusion,due to similar law
doesn’t exist,so can’t conclude empirical formula,can but
measure,
94
至于该射流的速度场，因不存在相似的规律，故总结不
出经验公式，只能具体测定。
)90t a n (
33.1
2
22
2
11 ???
?
??
?
???
?
??
?
???
?
?
???
?? a
d
x
d
x
d
y
??
?? 11-5-5
式中,x为水平距离； y为垂直距离； d为射流喷嘴直径； a为射
入角。
公式的使用范围为,
400~25,2,120~60 2
11
2
22
1
2 ???
??
??
T
Ta ??
。
95
Example 10-5 as fig.11-9 show,there is air diffusion with diameter
d＝ 100mm,its initial momentum is with horizontal
line form 60° upwards,It diffuing into vertical upwards main
airflow,main airflow momentum is, Temperature of
them is same,try to protract trochoid after diffusion diffusing into
main airflow,
N4000222 ???
N1 6 0211 ???
Solution,according to definition of a in fig.11-8,here a＝ 150°,
substituting a and known condition into formula into11-5-5,
obtaining
x
y?
y
o
fig,11—9 of example 11—5
96
例 10-5 如图 11-9所示，有一股直径为 d＝ 100mm的空气射流以
初始动量 与水平线成向下 60° 方向射入到一股垂直
向上的主气流中，主气流的动量为 。射流温度与主气
流温度相同，试绘制射流射入主气流后的轨迹线。
N4000222 ???
N1 6 0211 ???
解 按图 11-8所示的 a角定义，此处 a＝ 150°,把 a及所给已知
条件代入式 11-5-5，得
x
y?
y
o
图 11—9 例 11—5
97
table 11-6 corresponding table of value of x and y
x/m 0.2 0.4 0.6 0.8 1.0 1.2 1.4
y/m -0.334 -0.595 -0.71 -0.606 -0.209 0.553 1.754
Review and thinking problem
1.why strip and slot diffusion called plane diffusion?
2.why adherence diffusion can attain more far diffusing way?
732.10 1 5 2 3.0)90150t a n (4 0 0 0160
333.1
????????????????????????????? dxdxdxdy ??
Taking different value of,obtaining different value of
and y,results as in table 11-6,diffusion track in fig.11-9 d
x
dy
98
表 11-6 x,y 值 对 应 表
x/m 0.2 0.4 0.6 0.8 1.0 1.2 1.4
y/m -0.334 -0.595 -0.71 -0.606 -0.209 0.553 1.754
复习思考题
1.为何称条缝射流为平面射流？
2.为何贴附射流可以达到更远的射程？
732.10 1 5 2 3.0)90150t a n (4 0 0 0160
333.1
????????????????????????????? dxdxdxdy ??
取不同的 值，即可得到不同的 值及 y值，结果如表
11-6所示，射流轨迹见图 11-9。 d
x dy
99
Exercise of Chapter 11
11—1 Air shower region required diffusion radii is 1.2 m,average
velocity of mass,diameter of circular muzzle is 0.3
m,find（ 1） the distance s from spout to working zone ;
(2) throughput of muzzle。
m /s 32 ??
Solution （ 1） from11—1,obtaining coefficient of turbulent
flow a=0.08 。
（ 2） find s, from formula（ 11—1—2） obtaining,
00
0
3,4 ( 0,2 9 4 )
1, 2 0, 0 8
3,4 ( 0,2 9 4 )
0, 1 5 0, 1 5
th e r e f o r e 3, 8 6 m
R a s
rr
R
s
r
s
??
??
?
100
第十一章 习 题
11—1 已知空气淋浴地带要求射流半径为 1.2 m,质量平均流速
。圆形喷嘴直径为 0.3 m 。求（ 1）喷口至工作地带
的距离 s ; (2) 喷嘴流量。
m /s 32 ??
解 （ 1）由 11—1查得紊流系数 a=0.08 。
（ 2）求 s,由（ 11—1—2）式知,
m 86.3
)294.0
15.0
08.0
(4.3
15.0
2.1
)294.0(4.3
0
00
?
??
??
s
s
r
R
r
as
r
R
所以
101
0?
（ 4） find throughput Q0
applying average flow velocity of mass in main segment (11—2—4）
obtaining outlet velocity,
/sm 0 9 5.15.15)3.0(7 8 5.0
4
m / s 5.15
1 9 3.0
3
1 9 3.0
1 9 3.0
2 9 4.0
15.0
86.308.0
4 5 4 5.0
2 9 4.0
4 5 4 5.0
32
0
2
00
0
2
0
0
2
0
0
2
?????
?
???
?
?
?
?
?
?
?
?
?
?
?
?
?
?
dQ
r
as
0
0, 1 50 6 7 1 0, 6 7 1 1, 2 6,s o,
0, 0 8
f in d e d c r o s s c r o s s is in m a in s e g m e n t
nns, r /a s s? ? ? ? ?
（ 3） find core length sn
from formula（ 11—2—1），,s=sn,substituting into,obtaining 0m???
102
（ 4）求流量 Q0
应用主体段质量平均流速公式（ 11—2—4）求得出口速度,
0?
/sm 0 9 5.15.15)3.0(7 8 5.0
4
m / s 5.15
1 9 3.0
3
1 9 3.0
1 9 3.0
2 9 4.0
15.0
86.308.0
4 5 4 5.0
2 9 4.0
4 5 4 5.0
32
0
2
00
0
2
0
0
2
0
0
2
?????
?
???
?
?
?
?
?
?
?
?
?
?
?
?
?
?
dQ
r
as
（ 3）求核心长度 sn
由式（ 11—2—1），,s=sn,代入，解得
主体段内。
所求横截面在故,,26.1
0, 0 8
0, 1 50, 6 7 1 6 7 10
0 nn ss / ar.s ?????
0m???
103
11-2 Outside air diffusing into through orifice in outer wall
which distant from floor is 7.0m,Size of orifice,height is 0.35m，
length is12m。 Outside air temperature is － 10℃, inner air
temperature is 20℃, diffusion initial velocity is 2m/s,find the
temperature in floor,
calculation
Solution, taking a is 0.12
2035.0 0.72
0
??by
0022
0
( 2 ) 9, 8 0, 3 5 ( 1 0 2 0 ) 1 0 3 0, 0 8 8
2 ( 2 7 3 2 0 ) 1 1 7 0r e
g b TA
T?
? ? ? ? ?? ? ? ?
??
2 7 310
2 7 320
0 ??
??
T
T e
104
习题 11-2 室外空气以射流方式，由位于热车间外墙上离地板
7.0m处的孔口送入。孔口的尺寸，高 0.35m，长 12m。室外空
气的温度为－ 10℃,室内空气温度为 20℃,射流初速度为 2m/s，
求地板上的温度。
解, a取为 0.12
计算 20
35.0
0.7
2 0 ??b
y
0022
0
( 2 ) 9, 8 0, 3 5 ( 1 0 2 0 ) 1 0 3 0, 0 8 8
2 ( 2 7 3 2 0 ) 1 1 7 0r e
g b TA
T?
? ? ? ? ?? ? ? ?
??
2 7 310
2 7 320
0 ??
??
T
T e
105
00
2 0 2 9 3 / 2 6 3 220
2 0, 0 8 8
e
r
Ty
A b T ??
Obtaining
46;232
00
?? bxbx
Apply axes temperature difference formula
425.0
30
20
2010
20
425.0
93.5
032.1
41.04612.0
032.1
0
0
?
?
?
?
??
?
?
?
?
??
??
?
?
?
tt
TT
TT
T
T
e
e
m
C3.7 ???t
106
00
2 0 2 9 3 / 2 6 3 220
2 0, 0 8 8
e
r
Ty
A b T ??
计算求出
46;232
00
?? bxbx
用轴心温差公式
425.0
30
20
2010
20
425.0
93.5
032.1
41.04612.0
032.1
0
0
?
?
?
?
??
?
?
?
?
??
??
?
?
?
tt
TT
TT
T
T
e
e
m
C3.7 ???t
107
11-3 Data is same with example11—2,find diffusion descending
value in working face,fig.11-5）。
Solution, around air temperature Te＝ 273+30＝ 303k
y?
m43.2 m525.0 12.0 m / s9 15 000 ??????? sdakT ?
? ? m0 2 2 1.007.264.10 0 6.0
43.235.043.2
5 2 5.0
12.051.0
3 0 39
)15(8.935.051.0 23
2
23
0
2
0
0
??????
?
?
??
?
? ????
?
???
???
?
???
?
???? ss
d
a
T
Tgy
e?
m 43.2
y?
fig,11—5 diffusion descending
108
例 11-3 数据与例 11—2题相同，求射流在工作面的下降值
（图 11-5）。
解, 周围气体温度 Te＝ 273+30＝ 303k
y?
m43.2 m525.0 12.0 m / s9 15 000 ??????? sdakT ?
? ? m0 2 2 1.007.264.10 0 6.0
43.235.043.2
5 2 5.0
12.051.0
3 0 39
)15(8.935.051.0 23
2
23
0
2
0
0
??????
?
?
??
?
? ????
?
???
???
?
???
?
???? ss
d
a
T
Tgy
e?
m 43.2
y?
图 11—5射流的下降
109
110
