Domain reduction strategy for the stability analysis of complex aerodynamic flows

다국어 초록 (Multilingual Abstract)

Stability analysis in the framework of fluid dynamics is often expressed in terms of a complex eigenvalue problem (EVP). The solution of this EVP describes underlying flow features and their stability characteristics. The main shortcoming of this approach is the high computational cost necessary to solve the EVP, limiting the applicability of this analysis to simple two‐dimensional configurations. Many efforts have been focused on overcoming this limitation. Reducing the computational domain to encompass only those regions of physical interest may help alleviate the computational cost. However, the accuracy of the eigenmodes recovered from a reduced region needs to be carefully assessed. In this work, an in‐depth analysis of the domain reduction (DR) strategy is presented, and an error estimation tool is provided. The applicability and limitations of this methodology are studied on the open‐cavity problem. Next, the error estimation tool is exploited in the transonic buffet phenomenon on a NACA 0012 profile, giving valuable recommendations for the best use of this methodology. Finally, the DR strategy has been applied to investigate the asymmetries induced by jet cooling of turbine blades.
Solving large eigenvalue problems (EVPs) is the main bottleneck in the stability analysis of complex flows. Domain reduction (DR) tool is a widely used method for alleviating the computational demand of solving the EVP. In this work, we first derive explicit expressions that quantify the errors committed when DR technique is applied without computing the EVP in the original domain. DR has been successfully applied to analyze industrially relevant aerodynamic cases: the onset of the buffet phenomenon on a NACA profile, and the pressure bifurcation on the wake of supersonic‐jet‐cooled turbine blades.