音速喷嘴一元流动模型详解及其激波计算

One Dimensional Flow Analysis for Sonic Nozzles with Computation of Shock

针对文丘里音速喷嘴,阐述了如临界背压比等概念,指出了ISO 9300中背压比定义存在容易造成歧义的缺陷。然后基于一元等熵流动理论,从数学上证明了:当文丘里喷嘴喉部压力与上游滞止压力之比达到临界压比时,喉部产生音速,通过喷嘴的质量流量达到最大值;推导了实际条件下喷嘴的流量公式,导出的流量公式相较于ISO 9300给出的相应公式,增加了喉部状态参数下的压缩性系数修正项1/√Z_(nt)。最后从气体动力学基本方程出发,讨论了在较大背压比范围内,喷嘴扩散段中产生激波的机理,给出了激波产生的位置、激波前、后的压力和马赫数的一元流动计算模型,并运用数值模拟方法对计算结果进行了验证,同时还与Craig A的实验数据作了对比。对最小出口压比对比的结果显示,一元流动模型与实验数据的最大误差≤17%。

A discussion of some concepts such as critical back pressure ratio in detail for venturi sonic nozzles was presented.A flaw of the definition of back pressure ratio in ISO 9300 was pointed out.Then it has been mathematically proved,according to the one-dimensional isentropic flow theory,that when the ratio of the throat pressure to the upstream stagnation pressure of venturi nozzles reaches the critical pressure ratio,the fluid flow reaches a sonic speed at the throat with a maximum mass flow rate through the nozzle.A formula for flow through the venturi nozzle under real conditions was mathematically derived based on the previous discussion.Compared with ISO 9300,the derived formula includes a correction of compressibility factor at throat condition 1/√Z_(nt).At last,a discussion of the mechanism of shock generation in the diffuser was also presented from the basic equations of gas dynamics with the aim to develop the one-dimensional flow computational models for the shockwave generation position,pressure,and Mach number before and after the shockwave.The computational results were verified by numerical simulation and compared with the experimental data of Craig A.The results show that the maximum error of the minimum exit pressure ratio between the computational results and the experimental data is less than 17%.