Study On The Effect Of Heat Transfer On Flow Stability:The Establishment Of Linear Stability Analysis Tool For Compressible Viscous Flow And Its Application In The Pipe Flow With Heat Transfer

It is very important to study the stability of internal flow of aero-engine to improve the performance.And heat transfer has an important impact on the internal flow stability of the aero-engine.In this paper,a stability analysis tool for compressible viscous flow in cylindrical coordinates is established to explore the effect of heat transfer on flow stability.Based on the analysis of the linear stability of quasi-parallel flow in cylindrical coordinate system,this paper deduces the compressible Orr-Sommerfeld equation of cylindrical coordinate system,and solves it numerically based on Chebyshev spectral collocation method.A linear stability analysis tool for quasi-parallel flow in cylindrical coordinate system is established.In this paper,we then consider the influence of non-parallel characteristic on the linear stability of the flow.The linearized Navier-Stokes equation is derived for the first time in cylindrical coordinate system.The equation can take into account the effect of compressibility and viscosity when analyze the linear stability of the flow.The numerical solution of this equation under the axisymmetric assumption is carried out by using the Chebyshev spectral collocation method.A linear stability analysis tool for the axisymmetric flow is established.By checking the linear stability examples in the classical literature,the stability analysis tools of the quasi-parallel flow and the stability analysis tools of the axisymmetric flow are validated in this paper.In order to investigate the effect of heat transfer on the flow stability,the flow stability analysis was conducted to analyze the stability of the pipe flow with heat transfer.In this paper,the effects of different wall temperature and flow temperature on the flow stability,especially the disturbance growth factor,are analyzed.The analysis results of spatial mode show that the stability of the flow field is enhanced when the wall is cooling the flow.The analysis results of global mode show that the frequency of global mode is decreased when the wall is cooling the flow.