空气动力学chapter学习.pptx
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1、8.4 能量方程的各种特殊表达形式在7.5节中我们得到了定常、绝热、无粘流动的能量方程:其中V1、V2是一条三维流线上的任意两点的速度。对于我们现在研究的一维流动,能量方程为:(8.28)(8.29)However,keep in mind that all the subsequent results in this section hold in general along a streamline and are by no means limited to just one dimensional flows.然而,应当记住的是:这一节中所有的结论对于一般的沿流线的问题都适用,并不只是
2、局限于一维流动。第1页/共28页(8.30)(8.31)(8.32)以温度表示:以音速表示:第2页/共28页Definition of stagnation speed of sound:滞止声速的定义(8.33)(8.34)对于沿流线的任意两点,我们可将能量方程写成如下形式:第3页/共28页Definition of a*:a*的定义7.5节最后一段引入 T*的定义:Consider a point in a subsonic flow where the local static temperature is T.At this point,imagine that the fluid e
3、lement is speeded up to sonic velocity,adiabatically.The Temperature it would have at such sonic conditions is denoted as T*.Similarly,consider a point in a supersonic flow,where the local static temperature is T.At this point,imagine that the fluid element is slowed down to sonic velocity,adiabatic
4、ally.Again,the Temperature it would have at such sonic conditions is denoted as T*.用*号表示的变量被称为临界参数.称为临界声速.第4页/共28页In Equation(8.35),a and u are the speed of sound and velocity,respectively,at any point of flow,and a*is a characteristic value associated with that same point.(8.35)临界音速的计算公式:第5页/共28页对于
5、沿一条流线上的任意两点,有:(8.36)(8.37)Clearly,these defined quantities,a0 and a*,are both constants along a given in a steady,adiabatic,inviscid flow.If all the streamlines emanate from the same uniform freestream conditions,then a0 and a*are constants throughout the entire flow field.很明显,a0 和 a*为定义的量,沿定常、绝热、无粘
6、流动的给定流线为常数。如果所有流线都来自于均匀自由来流,则a0 和 a*在整个流场为常数。第6页/共28页(8.38)总温的计算公式回忆7.5节中总温T0的定义,由方程(8.30)可得:(8.39)Equation(8.38)provides a formula from which the defined total temperature T0 can be calculated from the given actual conditions of T and u at any given points in a general flow field.方程(8.38)给出了由流场中给定点
7、处的实际温度T和速度u计算总温T0的计算公式。第7页/共28页(8.40)Equation(8.40)is very important;it states that only M(and,of course,the value of )dictates the ratio of total temperature to static temperature.方程(8.40)非常重要;表明只有马赫数(及 的值)决定总温与静温的比。For a calorically perfect gas,the ratio of total temperature to static temperature,
8、is a function of Mach number only,as follows:(对于量热完全气体,总温和静温的比对于量热完全气体,总温和静温的比 是是马赫数的唯一函数,马赫数的唯一函数,证明如下:)第8页/共28页 总压、总密度的计算公式:回忆7.5节总压和总密度的定义,在定义中包含了将气流速度等熵地压缩为零速度。由(7.32)式,我们有:(8.41)(8.42)(8.43)方程(8.42)和(8.43)表明:总压静压比 、总密度静密度比 只由M 和 决定。因此,对于给定气体,即给定 ,、只依赖于马赫数。第9页/共28页 Equation(8.40),(8.42)and(8.43)
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