文档介绍：正激波基本控制方程的推导
音速
能量方程的特殊形式
什么情况下流动是可压缩的?
用于计算通过正激波气体特性变化的方程的详细推导; 物理特性变化趋势的讨论
用皮托管测量可压缩流的流动速度
第八章路线图
CALCULATION OF NORMAL SHOCK-WAVE PROPERTIES 正激波性质的计算
本节要点只有一个:
•计算通过正激波的流动特性变化
即
问题: 已知激波前区域1的条件,计算激波后区域2的条件。
:
()
()
()
()
()
Examining the five equations given above, we see that they involve five unknowns, namely, ρ2,u2,p2,h2,and T2. Hence, Eqs.() , (), (), (),and () are sufficient for determining the properties behind a normal shock wave in a calorically perfect gas. Let us proceed.
()式除以()式:
()
()
因为:
由公式(): 可得:
()
()
将(),()式代入()式:
整理为:
两边同除以u2-u1:
()
()
Equation () is called the Prandtl relation and is a useful intermediate relation for normal shock waves. 方程()被称为Prandtl 关系式,是一个很有用的正激波中间关系式.
()
()式还可写成:
由特征马赫数的定义: 可得:
()
应用()式:
()
()
Equation () is our first major result for a normal shock wave. Examine Eq. () closely; it states that the Mach number behind the wave, M2, is a function only of the Mach number ahead of the wave, M1.
方程()是我们得到的第一个主要正激波关系式,表明波后马赫数M2是波前马赫数M1的唯一函数.
Moreover, if M1=1, then M2=1. This is the case of an infinitely weak normal shock wave, defined as a Mach wave.
如果M1=1,则M2=1。这种情况对应无限弱的正激波,我们定义为马赫波。
Furthermore, if M1>1, then M2<1; ., the Mach number behind the normal shock wave is subsonic.
如果M1>1, 则 M2<1;也就是: 正激波后的流动是亚音速的。
As M1 increases above 1, the normal shock wave es stronger, and M2 ing progressively less than 1.
当 M1 由1逐渐增大时,正激波越来越强,激波后马赫数M2越来越小(在小于1的范围内)。
However, in the limit as M1→∞,M2 approaches a finite minimum value,M2→, which for air is .
然而,当M1趋于无穷大,M2趋于一有限的最小值M2→,。
下面我们来推导通过正激波的热力学特性,即、、的表达式:
()
()
()
()
()
()
()