This is the first part of a series of two papers on unsteady CFD methods for the numerical simulation of aerodynamic noise generation and propagation. In this part, the stability, accuracy and efficiency of implicit Runge-Kutta schemes for the temporal integration of the compressible Navier-Stokes equations are investigated in the context of a CFD code for turbomachinery applications. Using two model academic problems, the properties of two Explicit first stage, Singly Diagonal Implicit Runge-Kutta (ESDIRK) schemes of second- and third-order accuracy are quantified and compared with more conventional second-order multi-step methods. Finally, to assess the ESDIRK schemes in the context of an industrially relevant configuration, the schemes are applied to predict the tonal noise generation and transmission in a modern high bypass ratio fan stage and comparisons with the corresponding experimental data are provided.

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