Fourier methods for turbomachinery

Conference item : Presentation

Advanced turbomachinery development calls for efficient and accurate methods development. In a design cycle, large number flow solutions are sought to interact iteratively or concurrently with various options, opportunities and constraints from multiple disciplines. This basic requirement for fast prediction methods in a multi-disciplinary design environment remains unchanged, regardless of ever-increasing computer power. A general issue of interest in understanding and prediction of turbomachinery flows is: how do periodic unsteady disturbances affect time-averaged flow? Bear in mind that engine performance parameters are based on a time-averaged (’steady’) flow state. Multi-disciplinary, often competing factors are also compared, ranked and accounted for on a common time-averaged (’steady’) base state. In a fundamental sense, the situation is no different to how general turbulent (unsteady) disturbances affect time-average flows through nonlinearity-generated ‘Reynolds Stresses’. Then, how should we treat turbomachinery unsteady flows, similarly to (or differently from) how turbulence has been treated? It is against this overall background that the Fourier methods have been developed for efficient nonlinear flow solutions to unsteady turbomachinery flows since 1990. The main impetus is to develop efficient and adequately accurate computational methodologies and working methods for prediction and analysis of the unsteady flow effects on aerothermal performance (loading and efficiency) and aeroelasticity (blade vibration due to flutter and forced response) in turbomachinery. This lecture provides an updated and extended overview based on a review paper on the subject (He 2010 [1]). We will start with a brief look at some major historic milestones in turbomachinery flow computations, underlining the context and motivation for Fourier spectral methods. We will then look at various forms of Fourier method development and implementation. Although the main emphasis has been on the temporal Fourier harmonic models where major efforts and progress have been made, the spatial Fourier modelling development is also described. Some case examples are given to illustrate validity and effectiveness of the corresponding methods discussed.

Authors: He, LI

• Publication status: Published
• Publisher: von Karman Institute for Fluid Dynamics
• Publication date: 2025-07-02
• Event title: Turbomachinery Flow Simulation and Modeling
• Event series: von Karman Institute Lecture Series
• Event location: Rhode-Saint-Genèse, Brussels, Belgium
• Event website: https://www.vki.ac.be/index.php/events-ls/lecture-series-events-2025/turbomachinery-flow-simulation-modeling-2025
• Event start date: 2025-06-30
• Event end date: 2025-07-04
• Language: English
• Subtype: Presentation