Fourier methods for turbomachinery applications

Rapid increase in computing power has made a huge difference in scales and complexities of the problems in turbomachinery that we can tackle by use of computational fluid dynamics (CFD). It is recognised, however, that there is always a need for developing efficient methods for applications to blade designs. In a design cycle, a large number of flow solutions are sought to interact iteratively or concurrently with various options, opportunities and constraints from other disciplines. This basic requirement for fast prediction methods in a multi-disciplinary design environment remains unchanged, regardless of computer speed. And it must be recognised that the multi-disciplinary nature of blading design increasingly influences outcomes of advanced gas turbine and aeroengine developments. Recently there has been considerable progress in the Fourier harmonic modelling method development for turbomachinery applications. The main driver is to develop efficient and accurate computational methodologies and working methods for prediction and analysis of unsteady effects on aerothermal performance (loading and efficiency) and aeroelasticity (blade vibration due to flutter and forced response) in turbomachinery. In this article, the developments and applications of this type of methods in the past 20 years or so are reviewed. The basic modelling assumptions and various forms of implementations for the temporal Fourier modelling approach are presented and discussed. Computational examples for realistic turbomachinery configurations/flow conditions are given to illustrate the validity and effectiveness of the approach. Although the major development has been in the temporal Fourier harmonic modelling, some recent progress in use of the spatial Fourier modelling is also described with demonstration examples.