Analysis, optimization and uncertainty quantification of the aerodynamic behaviour of turbomachinery components is a fundamental part of the current industrial design process and requires the extensive use of compute-intensive CFD simulations. In this paper we investigate whether graph neural networks can be useful as surrogate models to accelerate the design process, for example in a multi-fidelity framework. Graph neural networks promise to provide good estimates of flow quantities while maintaining the geometric accuracy at a fraction of the computational effort of classical CFD. An application to industrially relevant turbomachinery flows is performed to gain a good understanding of the capabilities and limitations of such methods. We therefore apply a state-of-the-art graph neural network to a turbomachinery setup of industry-relevant mesh size. In particular, a multiscale graph neural network is used to overcome the problems of large information distances when applying message-passing based graph-net blocks to large meshes. The database used to train the network consists of a space-filling DoE of 100 CFD solutions with different geometries. The first use case encompasses the prediction of the flow quantities of the complete fluid domain with 2.5e6 mesh points. The second use case focuses on predicting a single scalar (e.g. pressure or temperature) on surface meshes with up to 30e3 mesh points. In both cases, the networks are employed to predict time-averaged and unsteady flow fields on unstructured meshes of variable point sizes for new geometries not present in the training set. The results demonstrate the proficiency of the approach in predicting time-averaged and unsteady flow quantities on surfaces as well as for full fluid domains for new geometries.