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Favre-Averaged Fourier-Based Methods for Gas Turbine Flows


 Steady Reynolds-Averaged Navier-Stokes (RANS) simulations are the workhorse of turbomachinery design. Recent trends in gas turbine design require full consideration of flow unsteadiness at the design stage to address issues of performance as well as integrity. Unsteady calculations using non-linear time marching methods are too computationally expensive to be used at the design stage. An alternative way is needed to reduce computational cost whilst retaining control on the accuracy of the simulations. To address this need, this paper presents a framework of Fourier-based methods for turbomachinery flows. The method is based on the non-linear harmonic (NLH) method. The method uses the favourable properties of Favre-averaging to obtain a simpler and more flexible formulation of the time-averaged system for NLH. This is ideal for implementing NLH in a CFD code where minimum modifications are desired. The approach allows the fidelity of the simulations to be tuned by switching on or off the coupling between the flow perturbations and the mean flow or the cross-coupling among the harmonics. This leads to a range of modelling fidelity for unsteady flows. For example, if the unsteady flow is linear, a linear harmonic method is sufficient for the design instead of using a harmonic balance simulation which has extra computational cost and slower convergence. The method has been tested on compressors and turbines which covers gas turbine flows in a range of flow regimes. Good agreement with data from non-linear time marching simulations are observed for all cases.