Chapter 7 Compressible Flow: Some Preliminary Aspects 第七章可压缩流动:相关的预备知识 71引言 A.连续流动 B.低密度和自由分子流 Continuum Flow Low-density and free-molecule flows C粘性流动D.无粘流动 Viscous Flow Inviscid Flow E.不可压缩流动 Incompressible Flow F.可压缩流动 Compressible Flow G.亚音速流H跨音速流|超音速流J高超音速流 Subsonic Transonic Supersonic Hypersonic
Chapter 7 Compressible Flow: Some Preliminary Aspects 第七章 可压缩流动: 相关的预备知识 7.1 引言 空气动力学 A. 连续流动 B. 低密度和自由分子流 Continuum Flow Low-density and free-molecule flows C.粘性流动 D. 无粘流动 Viscous Flow Inviscid Flow E. 不可压缩流动 Incompressible Flow F. 可压缩流动 Compressible Flow G. 亚音速流 H.跨音速流 I.超音速流 J.高超音速流 Subsonic Transonic Supersonic Hypersonic
可压缩流动的基本特征: k The pivotal aspect of high-speed flow is that the density is a variable一一密度是变量 k Another pivotal aspect of high-speed compressible flow is energy.Ahgh- speed flow is a high energy flow.-一是一个高 能量的流动 k Energy transformation and temperature changes are important considerations.一一必须考虑能量转换与温度变化
可压缩流动的基本特征: ＊The pivotal aspect of high -speed flow is that the density is a variable－－密度是变量． ＊Another pivotal aspect of high-speed compressible flow is energy. A high-speed flow is a high energy flow.－－是一个高 能量的流动． ＊Energy transformation and temperature changes are important considerations.－－必须考虑能量转换与温度变化．
Perlect gas internal ener gy and enthalp Review ol First law of thermodynamics ther mody na mics Entropy and the second law of ther mody humics Definition of Isentropic relations compressibility Governing equati pressable now Definition ot total conditions Qualitative aspects of supersonic nc ith shock w FIGURE 7.1 Road map for Chap. 7
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. A BRIEF REVIEW OF THERMODYNAMICS (热力学简要复习) 7.2.1 Perfect gas(完全气体) 定义 a gas in which the intermolecular forces are neglected is defined as a perfect gas.(忽略分子间作用力的气体定义为 完全气体) 完全气体满足状态方程:( equation of state P=pRT (7.1) pv=Rt R为气体常数( specific gas constant)R=287J/(kgK)
７.2 A BRIEF REVIEW OF THERMODYNAMICS (热力学简要复习） 7.2.1 Perfect gas (完全气体) 定义： A gas in which the intermolecular forces are neglected is defined as a perfect gas. (忽略分子间作用力的气体定义为 完全气体） 完全气体满足状态方程：（equation of state) p = RT pv = RT (7.1) (7.2) R为气体常数（specific gas constant) R=287J/(kg·K)
7.2.2 Internal Energy and enthalpy(内能和焓) The energy of a given molecule is the sum of its translational, rotational, vibrational, and electronic energies.(一个给定分子 的能量是其平动动能、转动动能、振动动能和电子能的总和。) 对于由大量分子组成的给定体积的气体,所有分子所具有的能量的 总和称为气体的内能。 单位质量气体的内能称为气体的比内能。( The internal energy per unit mass of gas is defined as the specific internal energy. 用e表示
7.2.2 Internal Energy and Enthalpy (内能和焓） The energy of a given molecule is the sum of its translational, rotational, vibrational, and electronic energies. （一个给定分子 的能量是其平动动能、转动动能、振动动能和电子能的总和。） 对于由大量分子组成的给定体积的气体，所有分子所具有的能量的 总和称为气体的内能。 单位质量气体的内能称为气体的比内能。（The internal energy per unit mass of gas is defined as the specific internal energy.) 用e表示．
与比内能e相联系的另一个量为比焓h,定义为: h=e+ pv=e+ (73) 对于完全气体,e和h都只是温度的函数: (74a) h=h(t) (7.4b)
与比内能e相联系的另一个量为比焓h，定义为： p h = e + pv = e + (7.3) 对于完全气体，e和h都只是温度的函数： ( ) (7.4b) ( ) (7.4a) h h T e e T = =
de=c dt (7.5a) dh=c dt (7.5b) 定容比热 定压比热 Specific heats at constant Specific heat at constant ⅴ olume pressure
(7.5b) (7.5a) dh c dT de c dT p v = = cv －－定容比热 c p －－ 定压比热 Specific heats at constant volume Specific heat at constant pressure
7<1000K,气体为量热完全气体( calorically perfect gas), 为常数 已=C T (7.6a) h=c t (7.6b) 注意:e和h均为热状态变量( thermodynamic state variables) 它们只依赖与气体的状态而与过程无关.( they depend only on the state of the gas and are independent of any process)
T<1000Ｋ，气体为量热完全气体（calorically perfect gas ), cv 、 c p 为常数 (7.6b) (7.6a) h c T e c T p v = = 注意：e和h均为热状态变量（thermodynamic state variables ), 它们只依赖与气体的状态而与过程无关．（they depend only on the state of the gas and are independent of any process)
T (7.6a) h=c T (7.6b) (76b)-(76a) C R (7.7) 定义比热比 y R I R (78) R (7.10) y y
(7.6b) (7.6a) h c T e c T p v = = (7.6b)-(7.6a): c p − cv = R (7.7) 定义比热比 v p c c = 1 (7.8) p p v c R c c − = 1 1 p c R − = −1 = R c p −1 = R cv (7.９) (7.１０)