Renewable sources of energy are on the rise and will continue to increase the coming decades [1]. A common problem with the renewable energy sources is that they rely on effects which cannot be controlled, for instance the strength of the wind or the intensity of the sunlight. The ALPHEUS Horizon 2020 EU project has the aim to develop a low-head hydraulic pump-turbine which can work as a grid stabilising unit. This work presents numerical results of an initial hub-driven counter-rotating pump-turbine design within ALPHEUS. Computational fluid dynamics simulations are carried out in both prototype and model scale, for pump and turbine modes, and under steady-state and unsteady conditions. The results indicate that the initial design have a hydraulic efficiency of roughly 90 % in both modes and for a wide range of operating conditions. The unsteady simulations reveal a complex flow pattern downstream the two runners and frequency analysis show that the dominating pressure pulsations originates from the rotor dynamics. Given the promising high efficiency, this initial design makes an ideal platform to continue the work to optimise efficiency and transient operations further.