A Low Mach Preconditioned Harmonic Balance Solver for Cavity Flutter Computations

Abstract Labyrinth seal flutter is a critical phenomenon in turbomachinery, as it can lead to severe structural vibrations and potential component damage. Accurate prediction and mitigation of flutter are paramount to ensuring the reliability and performance of modern turbomachinery systems. This paper explores the numerical computation of a labyrinth seal flutter test case using a low Mach preconditioned harmonic balance (HB) solver and investigates how this approach can improve the accuracy and response time of flutter computations. HB solvers have gained prominence in turbomachinery computations for their ability to efficiently capture unsteady flow phenomena and significantly reduce computational time compared to time-domain analyses. In labyrinth seals, however, the flow is often characterized by low Mach numbers, and preconditioning for these conditions has been shown to significantly improve convergence and accuracy. The goal of this paper is to demonstrate how to implement low Mach preconditioning in a HB solver in the frequency domain. We employ iterative preconditioning to alleviate the stiffness associated with density-based solvers under low Mach conditions and analyze the effect of the preconditioning parameters on the convergence rate. Furthermore, we address inaccuracies linked to the classical Roe solver in low Mach scenarios by adapting it to the low Mach preconditioned governing equations. Through the combined utilization of iterative preconditioning and a preconditioned Roe solver, this study aims to improve convergence rates and the overall quality of flutter predictions. We demonstrate the method with an academic labyrinth seal test case originally presented by Corral et al. (“Higher Order Conceptual Model for Labyrinth Seal Flutter,” ASME J. Turbomach., 143(7), p. 071006). While previous investigations have primarily relied on linearized frequency domain solvers and reduce-order models, in this research a preconditioned HB solver is applied to this test case.