可压缩管流中真实气体效应的理论分析与数值模拟

Theoretical Analysis and Numerical Simulation of Real Gas Effect in Compressible Pipe Flow

关键词:  超临界流体  碳氢燃料  真实气体效应  可压缩流动  数值模拟

Key words:  Supercritical fluid  Hydrocarbon fuel  Real gas effect  Compressible flow  Numerical simulation

摘要:

为研究超燃冲压发动机内复杂碳氢燃料的可压缩流动特性及相关影响因素，在典型工况条件下讨论了可压缩流动中真实气体效应的影响。基于平衡热力学理论，从理论层面明确了气体动力学基础导数（Γ）对可压缩流动的关键影响。同时，考察了多种碳氢燃料在临界点附近的特性，发现随着碳氢燃料分子结构复杂度的增加，Γ极小值降低，甚至出现为负值的情况，且该区域主要集中在近临界点的饱和蒸汽线附近。基于立方型状态方程对超临界条件下的二维超声速膨胀管流进行了数值模拟，证实了超声速扩张管流中马赫数下降的现象主要由声速随密度的非线性变化主导。进一步的参数化研究表明，随着入口压力增加或温度降低，管道内的压强、温度变化路径在p-T相图上将靠近饱和蒸汽线，这将导致更为显著的非经典气体动力学现象。

Abstract:

To explore the characteristics of compressible flow and influential factors of complex hydrocarbon fuels in scramjet engines， the role of real gas effect in compressible flow is revealed under typical operating conditions. The crucial influence of fundamental derivative of gas dynamics（Γ） is illustrated theoretically based on the equilibrium thermodynamics， and the characteristics close to critical point of various hydrocarbon fuels are clarified by exploiting the fundamental derivative. It is found that the minimum value of Γ decreases and even becomes negative as the molecular structure of hydrocarbon fuels getting more complex， and the negative value region is mainly concentrated near the saturated steam line. Meanwhile， a serial of numerical simulations are conducted for two-dimensional supercritical pipe flow by leveraging the equation of state in cubic form. It is confirmed that the abnormal decrease of Mach number in supersonic expansion flow is mainly dominated by the nonlinear dependence of sound speed on the fluid density. Further parametric studies also exhibit that the thermal dynamic routes of pressure and temperature along the channel approach the saturated steam line in the p-T phase diagram with increased inlet pressure or decreased inlet temperature， which induces more remarkable non-classical aerodynamic phenomena.