《空气动力学》（双语版）Chapter 7 Compressible Flow：Some Preliminary Aspects（2/2）

完全气体 内能和焓 热力学复习 热力学第一定律 熵及热力学第二定律 等熵关系式 第七章路线图 压缩性定义 无粘可压缩流动的控制方程 总条件的定义 有激波的超音速流动的定性了解

完全气体 内能和焓 热力学复习 热力学第一定律 熵及热力学第二定律 等熵关系式 压缩性定义 无粘可压缩流动的控制方程 总条件的定义 有激波的超音速流动的定性了解 第 七 章 路 线 图

7.3. DEFINITION OF COMPRESSIBILITY (压缩性定义 All real substances are compressible to some greater or lesser extend d. When you squeeze or press on them, their density will change. This is particularly true of gase (所有的真实物质都是可压缩的,当我们压挤 它们时,它们的密度会发生变化对于气体尤 其是这样

7.3. DEFINITION OF COMPRESSIBILITY (压缩性定义) All real substances are compressible to some greater or lesser extend. When you squeeze or press on them, their density will change. This is particularly true of gases. (所有的真实物质都是可压缩的,当我们压挤 它们时,它们的密度会发生变化,对于气体尤 其是这样.)

The amount by which a substance can be compressed is given by a specific property of the substance called the compressibilty, defined below 物质可被压缩的大小程度称为物质的压缩性 Consider a small element of fluid of volume v The pressure exerted on the sides of the element is p If the pressure s increased by an infinitesimal amount d, the volume will change by a negative amoumt d

The amount by which a substance can be compressed is given by a specific property of the substance called the compressibilty , defined below. 物质可被压缩的大小程度称为物质的压缩性. Consider a small element of fluid of volume . The pressure exerted on the sides of the element is p. If the pressure is increased by an infinitesimal amount dp, the volume will change by a negative amount . v dv

t+du FIGURE 73 Defnition of compressibility

By definition, the compressibility is given by (7.33) (7.36 Physically the compressibility is a fractional change in volume of he fluid element per unit change in pressure(从物理上讲,压缩 性就是每单位压强变化引起的流体微元单位体积内的体积 变化

By definition, the compressibility is given by: (7.33) as (7.36) Physically, the compressibility is a fractional change in volume of the fluid element per unit change in pressure.(从物理上讲,压缩 性就是每单位压强变化引起的流体微元单位体积内的体积 变化) dp dv v 1  = − dp d   1 =  1 v =

If the temperature of the fluid element is held constant, Tn is identified as the thermal compression等温缩 T (7.34) If the process takes place isentropically, then 等熵压缩性 v(op (7.35

If the temperature of the fluid element is held constant, then is identified as the isothermal compressibility (等温压缩性) (7.34) If the process takes place isentropically, then (等熵压缩性) (7.35)  T T p v v           = − 1  s s p v v           = − 1 

p=pt ap 7.37 If the fluid is a ous, where comprpsibin T is large then for a given pressure change dp from one point to another in the flow, Eq. 7. 37) states that decan be large.(如果流体为气体则值大对于一个给定压强 变化方程3指出也会大 Thus, p is not constant the flow of a gas is a compressible ow The exception is the -speed flow of a g. Where is the limit? If the mach number mev/a>0.3. the flow should be considered

If the fluid is a gas, where compressibility is large, then for a given pressure change from one point to another in the flow , Eq.(7.37) states that can be large. (如果流体为气体,则 值大,对于一个给定压强 变化 ,方程.(7.37)指出, 也会大.) Thus, is not constant; the flow of a gas is a compressible flow. The exception is the low-speed flow of a gas. Where is the limit? If the Mach number , the flow should be considered compressible. d =  dp d  M V / a  0.3  (7.37) dp  dp d

7.4 GOVERNING EQUATIONS FOR INVISCID COMPRESSIBLE FLOW(无粘、可压缩流控制方程) For inviscid, incompressible flow, the primary dependent variables are the pressure b and the veloci Hence, we need only o bas equator, namely the contin and the omentum e∥ 对于无粘 基本自变量是 E囗 压强力和速度 因此我们只需要 即罗方和量方

7.4 GOVERNING EQUATIONS FOR INVISCID, COMPRESSIBLE FLOW (无粘、可压缩流控制方程) For inviscid, incompressible flow, the primary dependent variables are the pressure p and the velocity . Hence, we need only two basic equations, namely the continuity and the momentum equations. 对于无粘、不可压缩流动，基本自变量是 压强 p和速度 。因此我们只需要两个基 本方程，即连续方程和动量方程

Indeed. the basic equations are combined to obtain Laplace's equation and Bernoullis equation, which are the primarily tools the applications discussed in Chaps. 3 to 6. Note that both p and Tare assumed to be constant through out such inviscid incompressible flows 连续方程与动量方程相结合可以得到 Laplace方 程和 Bernoulli方程,这是我们讨论第三章至第 六章内容用到的基本工具.对于无粘不可压缩 流动,我们假定密度和温度保持不变 Basically, incompressible flows obey purel echanical laws and do not need thermodynamic consideratons

Indeed, the basic equations are combined to obtain Laplace’s equation and Bernoulli’s equation, which are the primarily tools the applications discussed in Chaps. 3 to 6. Note that both and T are assumed to be constant through out such inviscid, incompressible flows. 连续方程与动量方程相结合可以得到Laplace 方 程和Bernoulli 方程，这是我们讨论第三章至第 六章内容用到的基本工具．对于无粘不可压缩 流动，我们假定密度和温度保持不变．  Basically, incompressible flows obey purely mechanical laws and do not need thermodynamic considerations

In contrast, for compressible flow, is variable and becomes an unknown. Hence we need an additional equation the energy equation-which in turn introduces internal energy e as an unknown 对于可压缩流,相反的是 是一个变量 并且是一个未知数.因此,我们需要一个附加 方程一能量方程一进而引入未知数肉能 Internal energy e is related to emperature then T also becomes an important variable Therefore, the 5 primary dependent variables are v,p, e, and T To solve for these me vorable s, we need ne governing

In contrast, for compressible flow, is variable and becomes an unknown. Hence we need an additional equation – the energy equation – which in turn introduces internal energy e as an unknown. 对于可压缩流，相反的是 是一个变量， 并且是一个未知数． 因此，我们需要一个附加 方程－能量方程－进而引入未知数内能e。 Internal energy e is related to temperature, then T also becomes an important variable. Therefore, the 5 primary dependent variables are: To solve for these five variables, we need five governing equations  p,V, , e, and T  