A critical challenge underpinning the adoption of Additive Manufacture (AM) as a technology is the postprocessing of manufactured components. For Selective Laser Sintering (SLS) this can involve the removal of powder from the interior of the component, often by vibrating the component to fluidise the powder to encourage drainage. In this paper we develop and validate a computational model of the flow of metal powder suitable for predicting powder removal from such AM components. The model is a continuum Eulerian multiphase model of the powder including models for the granular temperature; the effect of vibration can be included through appropriate wall boundaries for this granular temperature. We validate the individual sub-models appropriate for AM metal powders by comparison with in-house and literature experimental results, and then apply the full model to a more complex geometry typical of an AM Heat Exchanger. The model is shown to provide valuable and accurate results at a fraction of the computational cost of a particle-based model.