As redox flow batteries are being commercialised and demonstrated in a range of energy storage applications, further cost reductions are needed to make these batteries economically viable. In reducing cost, one important aspect is to minimise concentration polarisation, which allows for an increase in the power density of the battery stack. To make significant advances in increasing the power density of flow batteries it is critical to overcome the conventional design approach and explore new design concepts that alleviate the constraints in existing flow battery systems. This study investigates flow-through electrodes with new geometries that increase the velocity from inlet to outlet within cells. This velocity increase can address mass transport limitations, improving the delivery of electrochemical species to reactive sites on the electrode/electrolyte interface under varying states of charge. Three dimensional hydraulic-electrochemical coupled models were used to simulate different stack geometries; a rectangular geometry, a trapezoidal geometry and a radial geometry. The trapezoidal and radial geometries can accelerate the electrolyte during each pass in the battery stack. A new geometric stack arrangement is also proposed, which can deliver a higher power output with radially displaced cells.