基于collocation方法的Taylor-Culick模型流动稳定性的特征向量分析

The flow instability in solid rocket motors needs to be analyzed using a simplified model. The most realistic simplified model at present is the Taylor-Culick flow model. When the Taylor-Culick model is numerically calculated using the stability theory, the radial coordinate is zero due to the symmetry axis, which results in singularity. Previous numerical methods are difficult to handle. In this paper, the method of configuring differential matrix is used to improve the algorithm, which avoids the influence of the singularity of cylindrical coordinates on numerical calculation. The local stability of the Taylor-Culick flow model for a solid rocket motor was calculated and consistent results have been obtained. By analyzing the variation of eigenvectors with the calculation parameters, it has been found that the frequency and the Reynolds number are directly related to the changes of the eigenvectors, which indicates the oscillation range and the form of the flow field under certain conditions. The local features reflect the details of the overall flow status corresponding to different parameters.