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

Eigenvector analysis of Taylor-Culick flow stability based on collocation method

对于固体火箭发动机中产生的流动不稳定现象,需要利用简化模型进行分析,目前最符合实际的简化模型为Taylor-Culick流模型。采用稳定性理论对轴对称的Taylor-Culick模型进行数值计算时,由于对称轴处径向坐标为零而带来奇性,以往的数值计算方法难以处理。采用一种配置微分矩阵的方式来改进算法,避免柱坐标所带有的奇性对数值计算的影响。对固体火箭发动机Taylor-Culick流动模型进行了局部稳定性计算,得到了一致的结果。分析了特征向量随计算参数的变化,发现频率、雷诺数与特征向量的形态变化有直接关系,且特征向量的变化代表着特定情况下流动区域振荡发生的范围与形式,这些流动不稳定的局部特征从细节上反映了整体流动对应于不同流动参数的状态。

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.