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 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

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. 　 For adiabatic process For Ideal Gas (对于理想气体)　 　 　　

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. Varieties of flow (流动的种类) 　M<1 　 subsonic flow (亚声速流) 　M=1　 sonic flow (声速流) 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 Physical Problem （物理问题） 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

Conservation Equation of Mass (质量守恒方程） 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 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） Equation of Entropy(熵方程）　 　　 　 　

(1) Continuity Equation (连续性方程） If then , c , must be adopted; (A)

For incompressible fluid , (2). Energy Equation (能量方程) ,

For reversible process (可逆过程) If then ; If then ; (3) Process Equation For ideal gas(对理想气体) For real gas, k is an empirical constant.(对实际气体来说,k是经验常数) (B) 如果   变大（　     >0),则p必减少(dp<0); 如果   变小（　     <0),则p必变小 (dp>0).

(C ) Eq. (B)× From Eq.(C)

(D) Substitute Eq.(D) into Eq.(A) Supersonic region Subsonic region

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 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 (1)喷管内参数的变化情况:dc>0, dp<0 To accelerate the flow, a converging nozzle must be used at subsonic velocities; 当来流速度是亚音速时,截面做成渐缩形 the highest velocity can be achieved by converging nozzle is sonic velocity. 渐缩喷管最多可使流速达到音速 a diverging nozzle must be used at supersonic velocities 当来流速度是超音速时,截面做成渐扩形 a converging-diverging nozzle must be used to accelerate fluid from subsonic to supersonic velocity. 当要求气流从亚音速变成超音速时,截面做成缩放形

2

(2)扩压管内参数的变化: dc<0, dp>0 当来流是亚音速时,截面做成渐扩形; 当来流是超音速时,截面做成渐缩形.

Isentropic steady flow through nozzles 渐缩喷管中流动的特点 3.喷管中的定熵稳定流动 Isentropic steady flow through nozzles 渐缩喷管中流动的特点 Characteristics of flow through converging nozzle If ,there will be no flow through the nozzle; As , also , and , , but ; continues , , as it reaches sonic flow . If , continues , , . p1 pb

(2)拉伐尔喷管中的流动特征 Characteristic of Flow through converging-diverging nozzle

8.3 喷管的计算 Calculation on the velocity through nozzle 1.滞止参数 Stagnation Properties Suppose that our steady flow control volume is a set of streamlines describing the flow up to the nose of a blunt object. 定义: 气体速度为零时的状态称为滞止状态,该状态的参 　数称为滞止参数.

Stagnation Enthalpy and Stagnation Temperature The streamlines are stationary in space, so there is no external work done on the fluid as it flows. If there is also no heat transferred to the flow (adiabatic), then the steady flow energy equation becomes   (1)滞止焓和滞止温度 Stagnation Enthalpy and Stagnation Temperature

the fluid would reach if it were brought to zero speed by Stagnation enthalpy represents the enthalpy of a fluid when it is brought to rest adiabatically.                . Stagnation temperature is the temperature that the fluid would reach if it were brought to zero speed by a steady, adiabatic process with no external work. Note that for any steady, adiabatic flow with no external work, the stagnation temperature is constant

(2)滞止压力和滞止比容 Stagnation Pressure and Stagnation Volume Note that for a reversible adiabatic process  

Calculation and Analysis on flow Velocity 2.气体流速的计算与分析 Calculation and Analysis on flow Velocity 　 (1).Caluclation Equation (计算式) 　　 For Isentropic flow(对于定熵流动) 　

(2).Analysis (分析) 当 　　 时 ,　 　,无流动现象发生； 当 　 　 减小时, 　 　变大。 当　 　 趋于0时 　

3.临界流速与临界压力 Critical velocity and critical pressure 临界截面:M=1的截面. 临界压力比:临界压力与滞止压力之比,以 表示,其中 　　 　 常用的值: 　双原子理想气体:　 　　 　 三原子理想气体:　 　　 　 过饱和水蒸气:　　 　　 　 干饱和水蒸气:　　 　

　临界流速的计算式: 　　                                                           　4.流量的计算与分析 　(1)渐缩喷管: 　　                                                                      　变化曲线如图示: 　由图可以看出,随着　       　 的减小,质量流量先是增大; 　当　       =        时,质量流量达到最大. 2)缩放喷管 　流体由渐缩管出来后,经渐 　扩管可继续进一步的膨胀,加速,出口压力可降至   以下 　　　　　　　　　　　　　　　　 　　　                   　　                 

5.喷管的设计与校核计算　 设计计算: 　 已知条件:气体的种类,气体的初态参数 , 背压 和气体的质量流量 . 原则: 喷管的外形和尺寸应符合气流定熵膨胀时所需的截面积变化,以保证气流充分膨胀,使出口压力 能降到 , 达到使气流的技术功充分转化为动能的目的　

　设计步骤: 　 A.选择外形; 　 根据背压的高低选择适当形状的喷管: 　 当 时,选择渐缩喷管; 当 时,选择缩放喷管

渐缩喷管:需计算出口截面积       　                        　　                          　                                                                 缩放喷管:需计算                                                                                     B. 出口流速的计算 对渐缩喷管: 对缩放喷管, 喉部流速:

C. 出口截面积计算 渐缩喷管:需计算出口截面积　 　                        　                          　                                                               　     缩放喷管:需计算 的确定依据经验,通常                       　故: 　　                         

已知条件:给定喷管的外形和尺寸,进口处的气体参数 和背压 . 求:不同条件下喷管的工作情况以及是否可达到背压. (2) 校核计算 　 已知条件:给定喷管的外形和尺寸,进口处的气体参数                      和背压       . 求:不同条件下喷管的工作情况以及是否可达到背压. 　                                     　　                                     

8.4 有摩擦阻力的绝热流动 　 1. 喷管的速度系数: 实际流速     与理论流速     的比值,以   表示,则有:　　        　 2.喷管效率: 实际出口动能      与理想出口动能      之比,以    表示,则有: 　　                     

     　有效能的损失: 　　                           

8.5 绝热节流 1. 绝热节流: 　流速为的气流,由于局部阻力使流体降压膨胀的现象称为节流, 　又因流速高,时间短,与外界换热少,可视作绝热,故称绝热节流. 2. 特点: 　节流是典型的不可逆过程,节流前后焓值不变; 理想气体绝热节流前后温度相等; 实际的气体绝热节流后温度可降低,可升高,也可不变. 3. 节流的应用: (1)　测定蒸汽的干度x; (2)　调节功率; (3)　制冷或使气体液化.