BiGlobal stability analysis for flow in complex geometry based on immersed boundary method

Abstract

A numerical framework of global stability analysis based on the immersed boundary (IB) method is established for predicting the unsteadiness onset of flow system including complex geometry. The solid wall is considered as the boundary force term and the stability analysis is applied on the orthogonal Cartesian grid, which facilitate the application of spectral collocation method in the stability analysis. To convert the linearized N-S equation with source term to homogeneous, the boundary force can be viewed as an unknown quantity, and then the no-slip boundary condition is introduced into the governing equation to close the system. The method is first tested on two canonical cases, the flow past a stationary cylinder and an isolated airfoil. The relevant results are consistent with phenomena observed in the numerical calculations and experiments, verifying the effectiveness of the method. Applying the spectral collocation method contributes to the accuracy of stability analysis and reduces the grid nodes, making it more feasible to consider complex geometry. Then, to highlight the superiority of treating the flow system with complex geometry, such as including multi-objects, the method is applied to the stability analysis of the flow past a four-square-arranged cylinder cascade. The abundant instability perturbation modes induced by the interaction of multi-objects and the corresponding relationship with the whole system are captured, which is also verified by the unsteady calculation.