第八章气体的流动(双语)精品PPT课件

a
(
p
)
s
v
2
(
p v
)
s
For adiabatic process For Ideal Gas (对于理想气体)
a kpv kRT
2. Mach number (马赫数) 定义：流体某一点的运动速度和该点当地声速之比, 以M
表示
Definition: The Mach number, M, is the ratio of the flow speed, c, to the velocity of sound in the same fluid at the same state. It is denoted as M.
1. Physical Problem （物理问题）
(1) Gas steady flow 气体的稳定流动
(2)The flow in short duct with variable cross-sectional area 变截面短管中的流动
(3)The process is isentropic, that is, reversible adiabatic process 可逆绝热的流动过程，即定熵流动
kpvk1dv v k dp 0
vdp kpdv
k dv dp
(C )
vp
Eq. (B)× kp
c2
kp
kpv
c2 cdc c2 dp
a 2 kpv
kp dc 1 dp
c
M2
kp
From Eq.(C)
dp dv
v
M 2 dc dv
(D)
cv
Substitute Eq.(D) into Eq.(A)
Chapter 8 Thermodynamics of High-Speed Gas Flow
(第8章 气体和蒸气的流动)
8.1 声速与马赫数 Velocity of Sound and Mach Number
8.2 一维定熵稳定流动 One dimensional Isentropic Steady Flow
Mc a
Varieties of flow (流动的种类) M<1 subsonic flow (亚声速流) M=1 sonic flow (声速流) M 1 transonic flow (临界流) M>1 supersonic flow (超声速流) M>>1 hypersonic
8.2一维定熵稳定流动） One dimensional Isentropic Steady Flow
df (M 2 1) dc
f
c
M 1 M 1
Supersonic region Subsonic region
If dc 0, then df 0 If dc 0, then df 0
Summary (小结) 喷管(Nozzle):流体流经管道,压力降低,速度升高的管道. 扩压管:流体流经管道,速度降低,压力升高的管道
8.1 声速与马赫数 Velocity of Sound and Mach Number
1. Velocity of Sound (or Sonic Velocity) (声 速)
It is the velocity at which infinitesimally small pressure wave travels through a medium.
(1)喷管内参数的变化情况:dc>0, dp<0 To accelerate the flow, a converging nozzle must
dv dc vc
then df 源自文库0
adopted;
If
dv dc
advoptced;
then
df 0
(A) ,c , ,c ,
must be must be
For incompressible fluid
dv 0 v
df dc
f ,c
fc
f ,c
(2). Energy Equation (能量方程)
p, v,T , m , c, f
Conservation Equation of Mass (质量守恒方程） Conservation Equation of Energy (能量守恒方程） Equation of State (状态方程)
For Ideal Gas (对理想气体）
For Real Gas (对实际气体) Process Equation (过程方程）
8.3 喷管出口流速和流量的计算 Outlet Velocity and Flow rate Calculation for Nozzles
8.4具有摩擦的绝热稳定流动 Adiabatic steady flow with friction
8.5 绝热节流 Adiabatic throttling
2. Mathematical Model (数学模型） For flow in duct with variable cross-sectional area, it is necessary to use differential equations to reveal the relationships between
Equation of Entropy(熵方程）
Given m , p f, c, v,T 设计计算 Given p, f m , c, v,T 校核计算
(1) ContinufitycEqumatiovn (连续性方程）
f dc c df m dv
df dv dc f vc
If
0
00
q
dh
1 2
dc 2
g
dz
ws
dc 2 dh 2
c22 c12 2(h1 h2 )
c2 2(h1 h2 ) c12
For reversible process (可逆过程)
dh wt vdp dc2 vdp 2
cdc vdp (B)
If c
then p ; 如果c 变大（ dc >0),则p必减少(dp<0);
If c
then p
(3) Process Equation
;如果 c 变小（ dc <0),则p必变小 (dp>0).
pv k C
k cp
For ideal gas(对理想气体)
cv
For real gas, k is an empirical constant.(对实际气体来
说,k是经验常数)