Accurate simulation of unsteady turbulent flow is critical for improved design of greener aircraft that are quieter and more fuel-efficient. We demonstrate application of PyFR, a Python based computational fluid dynamics solver, to petascale simulation of such flow problems. Rationale behind algorithmic choices, which offer increased levels of accuracy and enable sustained computation at up to 58% of peak DP-FLOP/s on unstructured grids, will be discussed in the context of modern hardware. A range of software innovations will also be detailed, including use of runtime code generation, which enables PyFR to efficiently target multiple platforms, including heterogeneous systems, via a single implementation. Finally, results will be presented from a fullscale simulation of flow over a low-pressure turbine blade cascade, along with weak/strong scaling statistics from the Piz Daint and Titan supercomputers, and performance data demonstrating sustained computation at up to 13.7 DP-PFLOP/s.